% TIMEFORMAT='%3R'; { time (exec 2>&1; /home/martin/bin/satallax -E /home/martin/.isabelle/contrib/e-2.5-1/x86_64-linux/eprover -p tstp -t 5 /home/martin/judgement-day/tptp-thf/tptp/Arrow_Order/prob_270__5189158_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:17:10.939

% Could-be-implicit typings (18)
thf(ty_n_t__Set__Oset_I_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
    set_Ar1108837783le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
    set_se1538189555le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Ar182050865le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J_J, type,
    set_Pr1911398973le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Ar3481041le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_se370278869le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se791007093le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Pr720748555le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr665675179le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Ar809243995le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se2071012361le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr367596371le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc16571293le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    set_Ar1007576579e_indi : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    arrow_1429744205e_indi : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    arrow_1857593510le_alt : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_t__Int__Oint, type,
    int : $tType).

% Explicit typings (51)
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OIIA, type,
    arrow_1821794627le_IIA : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OLin, type,
    arrow_1848678355le_Lin : set_se2071012361le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_OProf, type,
    arrow_1951607831e_Prof : set_Ar809243995le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Oabove, type,
    arrow_1726226719_above : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Obelow, type,
    arrow_887341619_below : set_Pr367596371le_alt > arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Odictator, type,
    arrow_960434986ctator : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > $o).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Ounanimity, type,
    arrow_52334694nimity : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    pi_Arr1849985851le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt) > set_Ar1108837783le_alt).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_Arr1114944513le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar3481041le_alt).
thf(sy_c_FuncSet_OPi_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr479247969le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_Ar182050865le_alt).
thf(sy_c_FuncSet_OPi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr1981691447le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_se2071012361le_alt) > set_Ar809243995le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    pi_Pro1164444725le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar809243995le_alt) > set_Pr1911398973le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_Pro1847889543le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr665675179le_alt).
thf(sy_c_FuncSet_OPi_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Pro1122205927le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_se2071012361le_alt) > set_Pr720748555le_alt).
thf(sy_c_FuncSet_OPi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    pi_set1343364587le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Ar809243995le_alt) > set_se1538189555le_alt).
thf(sy_c_FuncSet_OPi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_set365323601le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se791007093le_alt).
thf(sy_c_FuncSet_OPi_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_set1240805297le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_se2071012361le_alt) > set_se370278869le_alt).
thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint, type,
    uminus_uminus_int : int > int).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint, type,
    zero_zero_int : int).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_If_001t__Nat__Onat, type,
    if_nat : $o > nat > nat > nat).
thf(sy_c_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    if_set550155277le_alt : $o > set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Int_Onat, type,
    nat2 : int > nat).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint, type,
    semiri2019852685at_int : nat > int).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat, type,
    semiri1382578993at_nat : nat > nat).
thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint, type,
    ord_less_int : int > int > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1494124311le_alt : arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_alt).
thf(sy_c_Set_OCollect_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    collec1382217680le_alt : (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o) > set_Ar182050865le_alt).
thf(sy_c_Set_OCollect_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    collec1559089382le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > $o) > set_Ar809243995le_alt).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    collec531981554le_alt : (produc16571293le_alt > $o) > set_Pr367596371le_alt).
thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    collec1399441576le_alt : (set_Pr367596371le_alt > $o) > set_se2071012361le_alt).
thf(sy_c_member_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    member896258016le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar1108837783le_alt > $o).
thf(sy_c_member_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member361641010le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt) > set_Ar3481041le_alt > $o).
thf(sy_c_member_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member183760530le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt > $o).
thf(sy_c_member_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member684274596le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt > $o).
thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    member167063198le_alt : (produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr1911398973le_alt > $o).
thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1154116596le_alt : (produc16571293le_alt > produc16571293le_alt) > set_Pr665675179le_alt > $o).
thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member1038100052le_alt : (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr720748555le_alt > $o).
thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    member1117110356le_alt : (set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se1538189555le_alt > $o).
thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member594528958le_alt : (set_Pr367596371le_alt > produc16571293le_alt) > set_se791007093le_alt > $o).
thf(sy_c_member_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member1775590686le_alt : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se370278869le_alt > $o).
thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    member1966420836e_indi : arrow_1429744205e_indi > set_Ar1007576579e_indi > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member2048039092le_alt : produc16571293le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1334244458le_alt : set_Pr367596371le_alt > set_se2071012361le_alt > $o).
thf(sy_v_F, type,
    f : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_v_Lab____, type,
    lab : set_Pr367596371le_alt).
thf(sy_v_Lba____, type,
    lba : set_Pr367596371le_alt).
thf(sy_v_a____, type,
    a : arrow_1857593510le_alt).
thf(sy_v_b____, type,
    b : arrow_1857593510le_alt).
thf(sy_v_h____, type,
    h : arrow_1429744205e_indi > nat).

% Relevant facts (202)
thf(fact_0_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_1__092_060open_062Lba_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ lba @ arrow_1848678355le_Lin))). % \<open>Lba \<in> Lin\<close>
thf(fact_2_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_3__092_060open_062Lab_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ lab @ arrow_1848678355le_Lin))). % \<open>Lab \<in> Lin\<close>
thf(fact_4__092_060open_062a_A_092_060noteq_062_Ab_092_060close_062, axiom,
    ((~ ((a = b))))). % \<open>a \<noteq> b\<close>
thf(fact_5__092_060open_062F_A_I_092_060lambda_062i_O_ALba_J_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ (f @ (^[I : arrow_1429744205e_indi]: lba)) @ arrow_1848678355le_Lin))). % \<open>F (\<lambda>i. Lba) \<in> Lin\<close>
thf(fact_6__092_060open_062_Ia_M_Ab_J_A_092_060notin_062_ALba_092_060close_062, axiom,
    ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ lba))))). % \<open>(a, b) \<notin> Lba\<close>
thf(fact_7__092_060open_062b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_092_060close_062, axiom,
    ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ lba))). % \<open>b <\<^bsub>Lba\<^esub> a\<close>
thf(fact_8__092_060open_062a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_092_060close_062, axiom,
    ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ lab))). % \<open>a <\<^bsub>Lab\<^esub> b\<close>
thf(fact_9__092_060open_062_Ib_M_Aa_J_A_092_060notin_062_ALab_092_060close_062, axiom,
    ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ lab))))). % \<open>(b, a) \<notin> Lab\<close>
thf(fact_10__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062Lab_O_A_092_060lbrakk_062a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_059_ALab_A_092_060in_062_ALin_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Lab : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ Lab) => (~ ((member1334244458le_alt @ Lab @ arrow_1848678355le_Lin))))))))). % \<open>\<And>thesis. (\<And>Lab. \<lbrakk>a <\<^bsub>Lab\<^esub> b; Lab \<in> Lin\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_11__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062Lba_O_A_092_060lbrakk_062b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_059_ALba_A_092_060in_062_ALin_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Lba : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ Lba) => (~ ((member1334244458le_alt @ Lba @ arrow_1848678355le_Lin))))))))). % \<open>\<And>thesis. (\<And>Lba. \<lbrakk>b <\<^bsub>Lba\<^esub> a; Lba \<in> Lin\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_12__C0_C, axiom,
    ((![N : nat]: (member1334244458le_alt @ (f @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ N) @ lab @ lba))) @ arrow_1848678355le_Lin)))). % "0"
thf(fact_13_PiProf, axiom,
    ((![N : nat]: (member684274596le_alt @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ N) @ lab @ lba)) @ arrow_1951607831e_Prof)))). % PiProf
thf(fact_14__C1_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))))). % "1"
thf(fact_15__C2_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((~ ((A = B2))) => ((~ ((B = A2))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))))). % "2"
thf(fact_16__C3_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (f @ P2)))))))))). % "3"
thf(fact_17__C4_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, C : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((B = C))) => ((~ ((A = C))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C) @ (f @ P2)))))))))))). % "4"
thf(fact_18_pairwise__neutrality, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A2 = B2))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (f @ P2))))))))))). % pairwise_neutrality
thf(fact_19_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_20_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_21_bot__nat__0_Onot__eq__extremum, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ A))))). % bot_nat_0.not_eq_extremum
thf(fact_22_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_23_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X2) = (produc1494124311le_alt @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_24_old_Oprod_Oinject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_25_assms_I1_J, axiom,
    ((member183760530le_alt @ f @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))))). % assms(1)
thf(fact_26_const__Lin__Prof, axiom,
    ((![L : set_Pr367596371le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member684274596le_alt @ (^[P3 : arrow_1429744205e_indi]: L) @ arrow_1951607831e_Prof))))). % const_Lin_Prof
thf(fact_27_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ arrow_1951607831e_Prof)) => ((![Y : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y @ arrow_1951607831e_Prof)) => ((![A3 : arrow_1857593510le_alt]: (![B3 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (Y @ I))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F @ X)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F @ Y))))))))))))))))). % IIA_def
thf(fact_28_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ arrow_1951607831e_Prof)) => ((![A3 : arrow_1857593510le_alt]: (![B3 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (X @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (F @ X))))))))))))). % unanimity_def
thf(fact_29_linear__alt, axiom,
    ((?[L2 : set_Pr367596371le_alt]: (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_30_zero__reorient, axiom,
    ((![X3 : nat]: ((zero_zero_nat = X3) = (X3 = zero_zero_nat))))). % zero_reorient
thf(fact_31_zero__reorient, axiom,
    ((![X3 : int]: ((zero_zero_int = X3) = (X3 = zero_zero_int))))). % zero_reorient
thf(fact_32_old_Oprod_Oinducts, axiom,
    ((![P : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A4 @ B4))) => (P @ Prod))))). % old.prod.inducts
thf(fact_33_old_Oprod_Oexhaust, axiom,
    ((![Y3 : produc16571293le_alt]: (~ ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (~ ((Y3 = (produc1494124311le_alt @ A4 @ B4)))))))))). % old.prod.exhaust
thf(fact_34_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_35_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt, P : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A @ (collec1399441576le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_36_mem__Collect__eq, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, P : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ A @ (collec1559089382le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_37_mem__Collect__eq, axiom,
    ((![A : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member183760530le_alt @ A @ (collec1382217680le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_38_Collect__mem__eq, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_39_Collect__mem__eq, axiom,
    ((![A5 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_40_Collect__mem__eq, axiom,
    ((![A5 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_41_Collect__mem__eq, axiom,
    ((![A5 : set_Ar182050865le_alt]: ((collec1382217680le_alt @ (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_42_Pair__inject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_43_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P4 : produc16571293le_alt]: ((![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A4 @ B4))) => (P @ P4))))). % prod_cases
thf(fact_44_surj__pair, axiom,
    ((![P4 : produc16571293le_alt]: (?[X4 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt]: (P4 = (produc1494124311le_alt @ X4 @ Y4)))))). % surj_pair
thf(fact_45_linorder__neqE__nat, axiom,
    ((![X3 : nat, Y3 : nat]: ((~ ((X3 = Y3))) => ((~ ((ord_less_nat @ X3 @ Y3))) => (ord_less_nat @ Y3 @ X3)))))). % linorder_neqE_nat
thf(fact_46_infinite__descent, axiom,
    ((![P : nat > $o, N : nat]: ((![N2 : nat]: ((~ ((P @ N2))) => (?[M : nat]: ((ord_less_nat @ M @ N2) & (~ ((P @ M))))))) => (P @ N))))). % infinite_descent
thf(fact_47_nat__less__induct, axiom,
    ((![P : nat > $o, N : nat]: ((![N2 : nat]: ((![M : nat]: ((ord_less_nat @ M @ N2) => (P @ M))) => (P @ N2))) => (P @ N))))). % nat_less_induct
thf(fact_48_less__irrefl__nat, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_irrefl_nat
thf(fact_49_less__not__refl3, axiom,
    ((![S : nat, T : nat]: ((ord_less_nat @ S @ T) => (~ ((S = T))))))). % less_not_refl3
thf(fact_50_less__not__refl2, axiom,
    ((![N : nat, M2 : nat]: ((ord_less_nat @ N @ M2) => (~ ((M2 = N))))))). % less_not_refl2
thf(fact_51_less__not__refl, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ N)))))). % less_not_refl
thf(fact_52_nat__neq__iff, axiom,
    ((![M2 : nat, N : nat]: ((~ ((M2 = N))) = (((ord_less_nat @ M2 @ N)) | ((ord_less_nat @ N @ M2))))))). % nat_neq_iff
thf(fact_53_zero__less__iff__neq__zero, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (~ ((N = zero_zero_nat))))))). % zero_less_iff_neq_zero
thf(fact_54_gr__implies__not__zero, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_55_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_56_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_57_bot__nat__0_Oextremum__strict, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ zero_zero_nat)))))). % bot_nat_0.extremum_strict
thf(fact_58_infinite__descent0, axiom,
    ((![P : nat > $o, N : nat]: ((P @ zero_zero_nat) => ((![N2 : nat]: ((ord_less_nat @ zero_zero_nat @ N2) => ((~ ((P @ N2))) => (?[M : nat]: ((ord_less_nat @ M @ N2) & (~ ((P @ M)))))))) => (P @ N)))))). % infinite_descent0
thf(fact_59_gr__implies__not0, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not0
thf(fact_60_less__zeroE, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_zeroE
thf(fact_61_not__less0, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less0
thf(fact_62_not__gr0, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr0
thf(fact_63_gr0I, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr0I
thf(fact_64_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X3 = Y3))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y3 @ X3) @ L))))))). % notin_Lin_iff
thf(fact_65_complete__Lin, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((~ ((A = B))) => (?[X4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X4 @ arrow_1848678355le_Lin) & (member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ X4))))))). % complete_Lin
thf(fact_66_Lin__irrefl, axiom,
    ((![L : set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ L) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ L)))))))). % Lin_irrefl
thf(fact_67_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ (arrow_887341619_below @ L @ A @ B)) = (((~ ((X3 = Y3)))) & ((((((Y3 = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ B) @ L)))) & ((((~ ((Y3 = A)))) => ((((((X3 = A)) => ((((Y3 = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y3) @ L)))))) & ((((~ ((X3 = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ L))))))))))))))))). % in_below
thf(fact_68_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ (arrow_1726226719_above @ L @ A @ B)) = (((~ ((X3 = Y3)))) & ((((((X3 = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y3) @ L)))) & ((((~ ((X3 = B)))) => ((((((Y3 = B)) => ((((X3 = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ A) @ L)))))) & ((((~ ((Y3 = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ L))))))))))))))))). % in_above
thf(fact_69_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_nat @ zero_zero_nat @ zero_zero_nat))))). % less_numeral_extra(3)
thf(fact_70_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_int @ zero_zero_int @ zero_zero_int))))). % less_numeral_extra(3)
thf(fact_71_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I : arrow_1429744205e_indi]: (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ arrow_1951607831e_Prof)) => (((F @ X) = (X @ I)))))))))). % dictator_def
thf(fact_72_pred__equals__eq2, axiom,
    ((![R : set_Pr367596371le_alt, S2 : set_Pr367596371le_alt]: (((^[X : arrow_1857593510le_alt]: (^[Y : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R))) = (^[X : arrow_1857593510le_alt]: (^[Y : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ S2)))) = (R = S2))))). % pred_equals_eq2
thf(fact_73_of__nat__0__less__iff, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ (semiri1382578993at_nat @ N)) = (ord_less_nat @ zero_zero_nat @ N))))). % of_nat_0_less_iff
thf(fact_74_of__nat__0__less__iff, axiom,
    ((![N : nat]: ((ord_less_int @ zero_zero_int @ (semiri2019852685at_int @ N)) = (ord_less_nat @ zero_zero_nat @ N))))). % of_nat_0_less_iff
thf(fact_75_of__nat__eq__iff, axiom,
    ((![M2 : nat, N : nat]: (((semiri2019852685at_int @ M2) = (semiri2019852685at_int @ N)) = (M2 = N))))). % of_nat_eq_iff
thf(fact_76_of__nat__0, axiom,
    (((semiri1382578993at_nat @ zero_zero_nat) = zero_zero_nat))). % of_nat_0
thf(fact_77_of__nat__0, axiom,
    (((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int))). % of_nat_0
thf(fact_78_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_nat = (semiri1382578993at_nat @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_79_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_int = (semiri2019852685at_int @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_80_of__nat__eq__0__iff, axiom,
    ((![M2 : nat]: (((semiri1382578993at_nat @ M2) = zero_zero_nat) = (M2 = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_81_of__nat__eq__0__iff, axiom,
    ((![M2 : nat]: (((semiri2019852685at_int @ M2) = zero_zero_int) = (M2 = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_82_of__nat__less__iff, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ (semiri1382578993at_nat @ M2) @ (semiri1382578993at_nat @ N)) = (ord_less_nat @ M2 @ N))))). % of_nat_less_iff
thf(fact_83_of__nat__less__iff, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_int @ (semiri2019852685at_int @ M2) @ (semiri2019852685at_int @ N)) = (ord_less_nat @ M2 @ N))))). % of_nat_less_iff
thf(fact_84_of__nat__less__0__iff, axiom,
    ((![M2 : nat]: (~ ((ord_less_nat @ (semiri1382578993at_nat @ M2) @ zero_zero_nat)))))). % of_nat_less_0_iff
thf(fact_85_of__nat__less__0__iff, axiom,
    ((![M2 : nat]: (~ ((ord_less_int @ (semiri2019852685at_int @ M2) @ zero_zero_int)))))). % of_nat_less_0_iff
thf(fact_86_less__imp__of__nat__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (ord_less_nat @ (semiri1382578993at_nat @ M2) @ (semiri1382578993at_nat @ N)))))). % less_imp_of_nat_less
thf(fact_87_less__imp__of__nat__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (ord_less_int @ (semiri2019852685at_int @ M2) @ (semiri2019852685at_int @ N)))))). % less_imp_of_nat_less
thf(fact_88_of__nat__less__imp__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ (semiri1382578993at_nat @ M2) @ (semiri1382578993at_nat @ N)) => (ord_less_nat @ M2 @ N))))). % of_nat_less_imp_less
thf(fact_89_of__nat__less__imp__less, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_int @ (semiri2019852685at_int @ M2) @ (semiri2019852685at_int @ N)) => (ord_less_nat @ M2 @ N))))). % of_nat_less_imp_less
thf(fact_90_dictatorI, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : arrow_1429744205e_indi]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))) => ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X4 @ arrow_1951607831e_Prof) => (![A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: ((~ ((A4 = B4))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X4 @ I3)) => (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F2 @ X4))))))) => (arrow_960434986ctator @ F2 @ I3)))))). % dictatorI
thf(fact_91_above__Lin, axiom,
    ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X3 = Y3))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L @ X3 @ Y3) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_92_below__Lin, axiom,
    ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X3 = Y3))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L @ X3 @ Y3) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_93_Pi__I, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X4 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X4 @ A5) => (member1334244458le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_94_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X4 : produc16571293le_alt]: ((member2048039092le_alt @ X4 @ A5) => (member2048039092le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_95_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X4 : produc16571293le_alt]: ((member2048039092le_alt @ X4 @ A5) => (member1334244458le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_96_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X4 @ A5) => (member2048039092le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_97_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X4 @ A5) => (member1334244458le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_98_Pi__I, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X4 : produc16571293le_alt]: ((member2048039092le_alt @ X4 @ A5) => (member684274596le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_99_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X4 @ A5) => (member2048039092le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_100_Pi__I, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X4 @ A5) => (member684274596le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_101_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X4 @ A5) => (member1334244458le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_102_Pi__I, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X4 @ A5) => (member684274596le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ B5)))))). % Pi_I
thf(fact_103_pos__int__cases, axiom,
    ((![K : int]: ((ord_less_int @ zero_zero_int @ K) => (~ ((![N2 : nat]: ((K = (semiri2019852685at_int @ N2)) => (~ ((ord_less_nat @ zero_zero_nat @ N2))))))))))). % pos_int_cases
thf(fact_104_zero__less__imp__eq__int, axiom,
    ((![K : int]: ((ord_less_int @ zero_zero_int @ K) => (?[N2 : nat]: ((ord_less_nat @ zero_zero_nat @ N2) & (K = (semiri2019852685at_int @ N2)))))))). % zero_less_imp_eq_int
thf(fact_105_funcset__mem, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : set_se2071012361le_alt, X3 : arrow_1429744205e_indi]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))) => ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ B5)))))). % funcset_mem
thf(fact_106_funcset__mem, axiom,
    ((![F3 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt, X3 : produc16571293le_alt]: ((member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ B5)))))). % funcset_mem
thf(fact_107_funcset__mem, axiom,
    ((![F3 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : set_se2071012361le_alt, X3 : produc16571293le_alt]: ((member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ B5)))))). % funcset_mem
thf(fact_108_funcset__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt, X3 : set_Pr367596371le_alt]: ((member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ B5)))))). % funcset_mem
thf(fact_109_funcset__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_se2071012361le_alt, X3 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ B5)))))). % funcset_mem
thf(fact_110_funcset__mem, axiom,
    ((![F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : set_Ar809243995le_alt, X3 : produc16571293le_alt]: ((member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))) => ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ B5)))))). % funcset_mem
thf(fact_111_funcset__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : set_Pr367596371le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ B5)))))). % funcset_mem
thf(fact_112_funcset__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Ar809243995le_alt, X3 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))) => ((member1334244458le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ B5)))))). % funcset_mem
thf(fact_113_funcset__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : set_se2071012361le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ B5)))))). % funcset_mem
thf(fact_114_funcset__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : set_Ar809243995le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))) => ((member684274596le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ B5)))))). % funcset_mem
thf(fact_115_int__int__eq, axiom,
    ((![M2 : nat, N : nat]: (((semiri2019852685at_int @ M2) = (semiri2019852685at_int @ N)) = (M2 = N))))). % int_int_eq
thf(fact_116_less__int__code_I1_J, axiom,
    ((~ ((ord_less_int @ zero_zero_int @ zero_zero_int))))). % less_int_code(1)
thf(fact_117_PiE, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X3 : arrow_1429744205e_indi]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (~ ((member1966420836e_indi @ X3 @ A5)))))))). % PiE
thf(fact_118_PiE, axiom,
    ((![F3 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X3 : produc16571293le_alt]: ((member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (~ ((member2048039092le_alt @ X3 @ A5)))))))). % PiE
thf(fact_119_PiE, axiom,
    ((![F3 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X3 : set_Pr367596371le_alt]: ((member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (~ ((member1334244458le_alt @ X3 @ A5)))))))). % PiE
thf(fact_120_PiE, axiom,
    ((![F3 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X3 : produc16571293le_alt]: ((member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (~ ((member2048039092le_alt @ X3 @ A5)))))))). % PiE
thf(fact_121_PiE, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X3 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (~ ((member1334244458le_alt @ X3 @ A5)))))))). % PiE
thf(fact_122_PiE, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ B5)) => ((~ ((member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (~ ((member684274596le_alt @ X3 @ A5)))))))). % PiE
thf(fact_123_PiE, axiom,
    ((![F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X3 : produc16571293le_alt]: ((member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (~ ((member2048039092le_alt @ X3 @ A5)))))))). % PiE
thf(fact_124_PiE, axiom,
    ((![F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt, X3 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (~ ((member1334244458le_alt @ X3 @ A5)))))))). % PiE
thf(fact_125_PiE, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)) => ((~ ((member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (~ ((member684274596le_alt @ X3 @ A5)))))))). % PiE
thf(fact_126_PiE, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ B5)) => ((~ ((member684274596le_alt @ (F3 @ X3) @ (B5 @ X3)))) => (~ ((member684274596le_alt @ X3 @ A5)))))))). % PiE
thf(fact_127_Pi__I_H, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X4 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X4 @ A5) => (member1334244458le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_128_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > produc16571293le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X4 : produc16571293le_alt]: ((member2048039092le_alt @ X4 @ A5) => (member2048039092le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_129_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt]: ((![X4 : produc16571293le_alt]: ((member2048039092le_alt @ X4 @ A5) => (member1334244458le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_130_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X4 @ A5) => (member2048039092le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_131_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X4 @ A5) => (member1334244458le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_132_Pi__I_H, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X4 : produc16571293le_alt]: ((member2048039092le_alt @ X4 @ A5) => (member684274596le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_133_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X4 @ A5) => (member2048039092le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_134_Pi__I_H, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X4 @ A5) => (member684274596le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_135_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X4 @ A5) => (member1334244458le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_136_Pi__I_H, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X4 @ A5) => (member684274596le_alt @ (F3 @ X4) @ (B5 @ X4)))) => (member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ B5)))))). % Pi_I'
thf(fact_137_Pi__iff, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, I4 : set_Ar1007576579e_indi, X5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ I4 @ X5)) = (![X : arrow_1429744205e_indi]: (((member1966420836e_indi @ X @ I4)) => ((member1334244458le_alt @ (F3 @ X) @ (X5 @ X))))))))). % Pi_iff
thf(fact_138_Pi__iff, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I4 : set_Ar809243995le_alt, X5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ I4 @ X5)) = (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ I4)) => ((member1334244458le_alt @ (F3 @ X) @ (X5 @ X))))))))). % Pi_iff
thf(fact_139_Pi__mem, axiom,
    ((![F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar1007576579e_indi, B5 : arrow_1429744205e_indi > set_se2071012361le_alt, X3 : arrow_1429744205e_indi]: ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)) => ((member1966420836e_indi @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_140_Pi__mem, axiom,
    ((![F3 : produc16571293le_alt > produc16571293le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Pr367596371le_alt, X3 : produc16571293le_alt]: ((member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_141_Pi__mem, axiom,
    ((![F3 : produc16571293le_alt > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_se2071012361le_alt, X3 : produc16571293le_alt]: ((member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_142_Pi__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > produc16571293le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Pr367596371le_alt, X3 : set_Pr367596371le_alt]: ((member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_143_Pi__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_se2071012361le_alt, X3 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_144_Pi__mem, axiom,
    ((![F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Pr367596371le_alt, B5 : produc16571293le_alt > set_Ar809243995le_alt, X3 : produc16571293le_alt]: ((member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ B5)) => ((member2048039092le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_145_Pi__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ B5)) => ((member684274596le_alt @ X3 @ A5) => (member2048039092le_alt @ (F3 @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_146_Pi__mem, axiom,
    ((![F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B5 : set_Pr367596371le_alt > set_Ar809243995le_alt, X3 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ B5)) => ((member1334244458le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_147_Pi__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)) => ((member684274596le_alt @ X3 @ A5) => (member1334244458le_alt @ (F3 @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_148_Pi__mem, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A5 : set_Ar809243995le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ B5)) => ((member684274596le_alt @ X3 @ A5) => (member684274596le_alt @ (F3 @ X3) @ (B5 @ X3))))))). % Pi_mem
thf(fact_149_Pi__cong, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, G : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi]: ((member1966420836e_indi @ W @ A5) => ((F3 @ W) = (G @ W)))) => ((member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ B5)) = (member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ A5 @ B5))))))). % Pi_cong
thf(fact_150_Pi__cong, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ W @ A5) => ((F3 @ W) = (G @ W)))) => ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ B5)) = (member183760530le_alt @ G @ (pi_Arr479247969le_alt @ A5 @ B5))))))). % Pi_cong
thf(fact_151_funcsetI, axiom,
    ((![A5 : set_Ar1007576579e_indi, F3 : arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X4 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X4 @ A5) => (member1334244458le_alt @ (F3 @ X4) @ B5))) => (member684274596le_alt @ F3 @ (pi_Arr1981691447le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi]: B5))))))). % funcsetI
thf(fact_152_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X4 : produc16571293le_alt]: ((member2048039092le_alt @ X4 @ A5) => (member2048039092le_alt @ (F3 @ X4) @ B5))) => (member1154116596le_alt @ F3 @ (pi_Pro1847889543le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_153_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X4 : produc16571293le_alt]: ((member2048039092le_alt @ X4 @ A5) => (member1334244458le_alt @ (F3 @ X4) @ B5))) => (member1038100052le_alt @ F3 @ (pi_Pro1122205927le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_154_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X4 @ A5) => (member2048039092le_alt @ (F3 @ X4) @ B5))) => (member594528958le_alt @ F3 @ (pi_set365323601le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_155_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X4 @ A5) => (member1334244458le_alt @ (F3 @ X4) @ B5))) => (member1775590686le_alt @ F3 @ (pi_set1240805297le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_156_funcsetI, axiom,
    ((![A5 : set_Pr367596371le_alt, F3 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X4 : produc16571293le_alt]: ((member2048039092le_alt @ X4 @ A5) => (member684274596le_alt @ (F3 @ X4) @ B5))) => (member167063198le_alt @ F3 @ (pi_Pro1164444725le_alt @ A5 @ (^[Uu : produc16571293le_alt]: B5))))))). % funcsetI
thf(fact_157_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B5 : set_Pr367596371le_alt]: ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X4 @ A5) => (member2048039092le_alt @ (F3 @ X4) @ B5))) => (member361641010le_alt @ F3 @ (pi_Arr1114944513le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_158_funcsetI, axiom,
    ((![A5 : set_se2071012361le_alt, F3 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X4 @ A5) => (member684274596le_alt @ (F3 @ X4) @ B5))) => (member1117110356le_alt @ F3 @ (pi_set1343364587le_alt @ A5 @ (^[Uu : set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_159_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B5 : set_se2071012361le_alt]: ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X4 @ A5) => (member1334244458le_alt @ (F3 @ X4) @ B5))) => (member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_160_funcsetI, axiom,
    ((![A5 : set_Ar809243995le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B5 : set_Ar809243995le_alt]: ((![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X4 @ A5) => (member684274596le_alt @ (F3 @ X4) @ B5))) => (member896258016le_alt @ F3 @ (pi_Arr1849985851le_alt @ A5 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B5))))))). % funcsetI
thf(fact_161_nat__less__as__int, axiom,
    ((ord_less_nat = (^[A3 : nat]: (^[B3 : nat]: (ord_less_int @ (semiri2019852685at_int @ A3) @ (semiri2019852685at_int @ B3))))))). % nat_less_as_int
thf(fact_162_nat__int__comparison_I2_J, axiom,
    ((ord_less_nat = (^[A3 : nat]: (^[B3 : nat]: (ord_less_int @ (semiri2019852685at_int @ A3) @ (semiri2019852685at_int @ B3))))))). % nat_int_comparison(2)
thf(fact_163_int__ops_I1_J, axiom,
    (((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int))). % int_ops(1)
thf(fact_164_verit__comp__simplify1_I1_J, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_165_verit__comp__simplify1_I1_J, axiom,
    ((![A : int]: (~ ((ord_less_int @ A @ A)))))). % verit_comp_simplify1(1)
thf(fact_166_nat__int__comparison_I1_J, axiom,
    (((^[Y5 : nat]: (^[Z : nat]: (Y5 = Z))) = (^[A3 : nat]: (^[B3 : nat]: ((semiri2019852685at_int @ A3) = (semiri2019852685at_int @ B3))))))). % nat_int_comparison(1)
thf(fact_167_int__if, axiom,
    ((![P : $o, A : nat, B : nat]: ((P => ((semiri2019852685at_int @ (if_nat @ P @ A @ B)) = (semiri2019852685at_int @ A))) & ((~ (P)) => ((semiri2019852685at_int @ (if_nat @ P @ A @ B)) = (semiri2019852685at_int @ B))))))). % int_if
thf(fact_168_neg__int__cases, axiom,
    ((![K : int]: ((ord_less_int @ K @ zero_zero_int) => (~ ((![N2 : nat]: ((K = (uminus_uminus_int @ (semiri2019852685at_int @ N2))) => (~ ((ord_less_nat @ zero_zero_nat @ N2))))))))))). % neg_int_cases
thf(fact_169_zero__less__nat__eq, axiom,
    ((![Z2 : int]: ((ord_less_nat @ zero_zero_nat @ (nat2 @ Z2)) = (ord_less_int @ zero_zero_int @ Z2))))). % zero_less_nat_eq
thf(fact_170_verit__minus__simplify_I4_J, axiom,
    ((![B : int]: ((uminus_uminus_int @ (uminus_uminus_int @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_171_neg__equal__iff__equal, axiom,
    ((![A : int, B : int]: (((uminus_uminus_int @ A) = (uminus_uminus_int @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_172_add_Oinverse__inverse, axiom,
    ((![A : int]: ((uminus_uminus_int @ (uminus_uminus_int @ A)) = A)))). % add.inverse_inverse
thf(fact_173_neg__equal__zero, axiom,
    ((![A : int]: (((uminus_uminus_int @ A) = A) = (A = zero_zero_int))))). % neg_equal_zero
thf(fact_174_equal__neg__zero, axiom,
    ((![A : int]: ((A = (uminus_uminus_int @ A)) = (A = zero_zero_int))))). % equal_neg_zero
thf(fact_175_neg__equal__0__iff__equal, axiom,
    ((![A : int]: (((uminus_uminus_int @ A) = zero_zero_int) = (A = zero_zero_int))))). % neg_equal_0_iff_equal
thf(fact_176_neg__0__equal__iff__equal, axiom,
    ((![A : int]: ((zero_zero_int = (uminus_uminus_int @ A)) = (zero_zero_int = A))))). % neg_0_equal_iff_equal
thf(fact_177_add_Oinverse__neutral, axiom,
    (((uminus_uminus_int @ zero_zero_int) = zero_zero_int))). % add.inverse_neutral
thf(fact_178_neg__less__iff__less, axiom,
    ((![B : int, A : int]: ((ord_less_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A)) = (ord_less_int @ A @ B))))). % neg_less_iff_less
thf(fact_179_nat__int, axiom,
    ((![N : nat]: ((nat2 @ (semiri2019852685at_int @ N)) = N)))). % nat_int
thf(fact_180_neg__less__0__iff__less, axiom,
    ((![A : int]: ((ord_less_int @ (uminus_uminus_int @ A) @ zero_zero_int) = (ord_less_int @ zero_zero_int @ A))))). % neg_less_0_iff_less
thf(fact_181_neg__0__less__iff__less, axiom,
    ((![A : int]: ((ord_less_int @ zero_zero_int @ (uminus_uminus_int @ A)) = (ord_less_int @ A @ zero_zero_int))))). % neg_0_less_iff_less
thf(fact_182_neg__less__pos, axiom,
    ((![A : int]: ((ord_less_int @ (uminus_uminus_int @ A) @ A) = (ord_less_int @ zero_zero_int @ A))))). % neg_less_pos
thf(fact_183_less__neg__neg, axiom,
    ((![A : int]: ((ord_less_int @ A @ (uminus_uminus_int @ A)) = (ord_less_int @ A @ zero_zero_int))))). % less_neg_neg
thf(fact_184_negative__eq__positive, axiom,
    ((![N : nat, M2 : nat]: (((uminus_uminus_int @ (semiri2019852685at_int @ N)) = (semiri2019852685at_int @ M2)) = (((N = zero_zero_nat)) & ((M2 = zero_zero_nat))))))). % negative_eq_positive
thf(fact_185_zless__nat__conj, axiom,
    ((![W2 : int, Z2 : int]: ((ord_less_nat @ (nat2 @ W2) @ (nat2 @ Z2)) = (((ord_less_int @ zero_zero_int @ Z2)) & ((ord_less_int @ W2 @ Z2))))))). % zless_nat_conj
thf(fact_186_nat__zminus__int, axiom,
    ((![N : nat]: ((nat2 @ (uminus_uminus_int @ (semiri2019852685at_int @ N))) = zero_zero_nat)))). % nat_zminus_int
thf(fact_187_verit__negate__coefficient_I2_J, axiom,
    ((![A : int, B : int]: ((ord_less_int @ A @ B) => (ord_less_int @ (uminus_uminus_int @ B) @ (uminus_uminus_int @ A)))))). % verit_negate_coefficient(2)
thf(fact_188_nat__zero__as__int, axiom,
    ((zero_zero_nat = (nat2 @ zero_zero_int)))). % nat_zero_as_int
thf(fact_189_verit__negate__coefficient_I3_J, axiom,
    ((![A : int, B : int]: ((A = B) => ((uminus_uminus_int @ A) = (uminus_uminus_int @ B)))))). % verit_negate_coefficient(3)
thf(fact_190_not__int__zless__negative, axiom,
    ((![N : nat, M2 : nat]: (~ ((ord_less_int @ (semiri2019852685at_int @ N) @ (uminus_uminus_int @ (semiri2019852685at_int @ M2)))))))). % not_int_zless_negative
thf(fact_191_minus__equation__iff, axiom,
    ((![A : int, B : int]: (((uminus_uminus_int @ A) = B) = ((uminus_uminus_int @ B) = A))))). % minus_equation_iff
thf(fact_192_equation__minus__iff, axiom,
    ((![A : int, B : int]: ((A = (uminus_uminus_int @ B)) = (B = (uminus_uminus_int @ A)))))). % equation_minus_iff
thf(fact_193_uminus__int__code_I1_J, axiom,
    (((uminus_uminus_int @ zero_zero_int) = zero_zero_int))). % uminus_int_code(1)
thf(fact_194_minus__less__iff, axiom,
    ((![A : int, B : int]: ((ord_less_int @ (uminus_uminus_int @ A) @ B) = (ord_less_int @ (uminus_uminus_int @ B) @ A))))). % minus_less_iff
thf(fact_195_less__minus__iff, axiom,
    ((![A : int, B : int]: ((ord_less_int @ A @ (uminus_uminus_int @ B)) = (ord_less_int @ B @ (uminus_uminus_int @ A)))))). % less_minus_iff
thf(fact_196_int__cases2, axiom,
    ((![Z2 : int]: ((![N2 : nat]: (~ ((Z2 = (semiri2019852685at_int @ N2))))) => (~ ((![N2 : nat]: (~ ((Z2 = (uminus_uminus_int @ (semiri2019852685at_int @ N2)))))))))))). % int_cases2
thf(fact_197_nat__mono__iff, axiom,
    ((![Z2 : int, W2 : int]: ((ord_less_int @ zero_zero_int @ Z2) => ((ord_less_nat @ (nat2 @ W2) @ (nat2 @ Z2)) = (ord_less_int @ W2 @ Z2)))))). % nat_mono_iff
thf(fact_198_zless__nat__eq__int__zless, axiom,
    ((![M2 : nat, Z2 : int]: ((ord_less_nat @ M2 @ (nat2 @ Z2)) = (ord_less_int @ (semiri2019852685at_int @ M2) @ Z2))))). % zless_nat_eq_int_zless
thf(fact_199_int__cases4, axiom,
    ((![M2 : int]: ((![N2 : nat]: (~ ((M2 = (semiri2019852685at_int @ N2))))) => (~ ((![N2 : nat]: ((ord_less_nat @ zero_zero_nat @ N2) => (~ ((M2 = (uminus_uminus_int @ (semiri2019852685at_int @ N2))))))))))))). % int_cases4
thf(fact_200_split__nat, axiom,
    ((![P : nat > $o, I3 : int]: ((P @ (nat2 @ I3)) = (((![N3 : nat]: (((I3 = (semiri2019852685at_int @ N3))) => ((P @ N3))))) & ((((ord_less_int @ I3 @ zero_zero_int)) => ((P @ zero_zero_nat))))))))). % split_nat
thf(fact_201_int__cases3, axiom,
    ((![K : int]: ((~ ((K = zero_zero_int))) => ((![N2 : nat]: ((K = (semiri2019852685at_int @ N2)) => (~ ((ord_less_nat @ zero_zero_nat @ N2))))) => (~ ((![N2 : nat]: ((K = (uminus_uminus_int @ (semiri2019852685at_int @ N2))) => (~ ((ord_less_nat @ zero_zero_nat @ N2)))))))))))). % int_cases3

% Helper facts (5)
thf(help_If_2_1_If_001t__Nat__Onat_T, axiom,
    ((![X3 : nat, Y3 : nat]: ((if_nat @ $false @ X3 @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__Nat__Onat_T, axiom,
    ((![X3 : nat, Y3 : nat]: ((if_nat @ $true @ X3 @ Y3) = X3)))).
thf(help_If_3_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_T, axiom,
    ((![P : $o]: ((P = $true) | (P = $false))))).
thf(help_If_2_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_T, axiom,
    ((![X3 : set_Pr367596371le_alt, Y3 : set_Pr367596371le_alt]: ((if_set550155277le_alt @ $false @ X3 @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_T, axiom,
    ((![X3 : set_Pr367596371le_alt, Y3 : set_Pr367596371le_alt]: ((if_set550155277le_alt @ $true @ X3 @ Y3) = X3)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (f @ (^[I : arrow_1429744205e_indi]: (if_set550155277le_alt @ (ord_less_nat @ (h @ I) @ zero_zero_nat) @ lab @ lba)))))))).
