% 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_142__5187184_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:16:13.493

% Could-be-implicit typings (21)
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_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    set_Ar1612966069e_indi : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Ar1666424426le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J_J, type,
    set_Ar528567456e_indi : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Ar1380421567le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    set_Ar1007576579e_indi : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    set_Ar1665529862le_alt : $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).

% Explicit typings (94)
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_Omkbot, type,
    arrow_843587755_mkbot : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
thf(sy_c_Arrow__Order__Mirabelle__riepwfubkl_Omktop, type,
    arrow_992294841_mktop : set_Pr367596371le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt).
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_OPiE_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,
    piE_Ar1900467852le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt) > set_Ar1108837783le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_Ar974971248le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar3481041le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_Ar236171216le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_Ar182050865le_alt).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    piE_Ar1187035700le_alt : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1665529862le_alt) > set_Ar1380421567le_alt).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    piE_Ar415527999e_indi : set_Ar1665529862le_alt > (arrow_1857593510le_alt > set_Ar1007576579e_indi) > set_Ar528567456e_indi).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    piE_Ar1084018769le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1665529862le_alt) > set_Ar1666424426le_alt).
thf(sy_c_FuncSet_OPiE_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    piE_Ar738911586e_indi : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_Ar1007576579e_indi) > set_Ar1612966069e_indi).
thf(sy_c_FuncSet_OPiE_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,
    piE_Ar1580347400le_alt : set_Ar1007576579e_indi > (arrow_1429744205e_indi > set_se2071012361le_alt) > set_Ar809243995le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_Pr1024471460le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Ar809243995le_alt) > set_Pr1911398973le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_Pr2084141144le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr665675179le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_Pr757114552le_alt : set_Pr367596371le_alt > (produc16571293le_alt > set_se2071012361le_alt) > set_Pr720748555le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_se1100287834le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Ar809243995le_alt) > set_se1538189555le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_se232226le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se791007093le_alt).
thf(sy_c_FuncSet_OPiE_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,
    piE_se1902809474le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > set_se2071012361le_alt) > set_se370278869le_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_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).
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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__Oalt, type,
    member519365071le_alt : arrow_1857593510le_alt > set_Ar1665529862le_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_L, type,
    l : set_Pr367596371le_alt).

% Relevant facts (249)
thf(fact_0_linear__alt, axiom,
    ((?[L : set_Pr367596371le_alt]: (member1334244458le_alt @ L @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_1_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_2_above__Lin, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt]: ((~ ((X2 = Y))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L2 @ X2 @ Y) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_3_below__Lin, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt]: ((~ ((X2 = Y))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L2 @ X2 @ Y) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_4_mkbot__Lin, axiom,
    ((![L2 : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L2 @ X2) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_5_mktop__Lin, axiom,
    ((![L2 : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L2 @ X2) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_6_converse__in__Lin, axiom,
    ((![L2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ (conver1781819635le_alt @ L2) @ arrow_1848678355le_Lin) = (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin))))). % converse_in_Lin
thf(fact_7_Prof__def, axiom,
    ((arrow_1951607831e_Prof = (pi_Arr1981691447le_alt @ top_to1799531699e_indi @ (^[Uu : arrow_1429744205e_indi]: arrow_1848678355le_Lin))))). % Prof_def
thf(fact_8_Lin__irrefl, axiom,
    ((![L2 : set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ L2) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ L2)))))))). % Lin_irrefl
thf(fact_9_notin__Lin__iff, axiom,
    ((![L2 : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((~ ((X2 = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L2))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X2) @ L2))))))). % notin_Lin_iff
thf(fact_10_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)) => ((![Y2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y2 @ arrow_1951607831e_Prof)) => ((![A2 : arrow_1857593510le_alt]: (![B2 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (X @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (Y2 @ I))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (F @ X)) = (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (F @ Y2))))))))))))))))). % IIA_def
thf(fact_11_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)) => ((![A2 : arrow_1857593510le_alt]: (![B2 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (X @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (F @ X))))))))))))). % unanimity_def
thf(fact_12_Lin__def, axiom,
    ((arrow_1848678355le_Lin = (collec1399441576le_alt @ (order_257197092le_alt @ top_to958727510le_alt))))). % Lin_def
thf(fact_13_in__mkbot, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ (arrow_843587755_mkbot @ L2 @ Z)) = (((~ ((Y = Z)))) & ((((((X2 = Z)) => ((~ ((X2 = Y)))))) & ((((~ ((X2 = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L2))))))))))). % in_mkbot
thf(fact_14_in__mktop, axiom,
    ((![X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ (arrow_992294841_mktop @ L2 @ Z)) = (((~ ((X2 = Z)))) & ((((((Y = Z)) => ((~ ((X2 = Y)))))) & ((((~ ((Y = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L2))))))))))). % in_mktop
thf(fact_15_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ (arrow_887341619_below @ L2 @ A @ B)) = (((~ ((X2 = Y)))) & ((((((Y = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ B) @ L2)))) & ((((~ ((Y = A)))) => ((((((X2 = A)) => ((((Y = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y) @ L2)))))) & ((((~ ((X2 = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L2))))))))))))))))). % in_below
thf(fact_16_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, X2 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ (arrow_1726226719_above @ L2 @ A @ B)) = (((~ ((X2 = Y)))) & ((((((X2 = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y) @ L2)))) & ((((~ ((X2 = B)))) => ((((((Y = B)) => ((((X2 = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ A) @ L2)))))) & ((((~ ((Y = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X2 @ Y) @ L2))))))))))))))))). % in_above
thf(fact_17_Pi__UNIV, axiom,
    ((![A3 : set_Ar1007576579e_indi]: ((pi_Arr1981691447le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi]: top_to469035705le_alt)) = top_to685525675le_alt)))). % Pi_UNIV
thf(fact_18_Pi__UNIV, axiom,
    ((![A3 : set_Ar809243995le_alt]: ((pi_Arr479247969le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: top_to469035705le_alt)) = top_to803745505le_alt)))). % Pi_UNIV
thf(fact_19_converse__iff, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (conver1781819635le_alt @ R)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ R))))). % converse_iff
thf(fact_20_Pi__I, axiom,
    ((![A3 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_21_Pi__I, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B3 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_22_Pi__I, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_23_Pi__I, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B3 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_24_Pi__I, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B3 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_25_Pi__I, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_26_Pi__I, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member684274596le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_27_Pi__I, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member684274596le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_28_Pi__I, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_29_Pi__I, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (member684274596le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A3 @ B3)))))). % Pi_I
thf(fact_30_converse__inject, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: (((conver1781819635le_alt @ R) = (conver1781819635le_alt @ S)) = (R = S))))). % converse_inject
thf(fact_31_converse__converse, axiom,
    ((![R : set_Pr367596371le_alt]: ((conver1781819635le_alt @ (conver1781819635le_alt @ R)) = R)))). % converse_converse
thf(fact_32_UNIV__I, axiom,
    ((![X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ top_to469035705le_alt)))). % UNIV_I
thf(fact_33_UNIV__I, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ top_to685525675le_alt)))). % UNIV_I
thf(fact_34_UNIV__I, axiom,
    ((![X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ top_to224369155le_alt)))). % UNIV_I
thf(fact_35_UNIV__I, axiom,
    ((![X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X2 @ top_to803745505le_alt)))). % UNIV_I
thf(fact_36_UNIV__I, axiom,
    ((![X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ top_to1799531699e_indi)))). % UNIV_I
thf(fact_37_UNIV__I, axiom,
    ((![X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ top_to958727510le_alt)))). % UNIV_I
thf(fact_38_iso__tuple__UNIV__I, axiom,
    ((![X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_39_iso__tuple__UNIV__I, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ top_to685525675le_alt)))). % iso_tuple_UNIV_I
thf(fact_40_iso__tuple__UNIV__I, axiom,
    ((![X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_41_iso__tuple__UNIV__I, axiom,
    ((![X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X2 @ top_to803745505le_alt)))). % iso_tuple_UNIV_I
thf(fact_42_iso__tuple__UNIV__I, axiom,
    ((![X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ top_to1799531699e_indi)))). % iso_tuple_UNIV_I
thf(fact_43_iso__tuple__UNIV__I, axiom,
    ((![X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ top_to958727510le_alt)))). % iso_tuple_UNIV_I
thf(fact_44_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X22 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y22 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X22) = (produc1494124311le_alt @ Y1 @ Y22)) = (((X1 = Y1)) & ((X22 = Y22))))))). % prod.inject
thf(fact_45_old_Oprod_Oinject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A4 @ B4)) = (((A = A4)) & ((B = B4))))))). % old.prod.inject
thf(fact_46_converse__UNIV, axiom,
    (((conver1781819635le_alt @ top_to224369155le_alt) = top_to224369155le_alt))). % converse_UNIV
thf(fact_47_top__empty__eq2, axiom,
    ((top_to701951606_alt_o = (^[X : arrow_1857593510le_alt]: (^[Y2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ top_to224369155le_alt)))))). % top_empty_eq2
thf(fact_48_top__empty__eq, axiom,
    ((top_to1900088076_alt_o = (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt))))). % top_empty_eq
thf(fact_49_top__empty__eq, axiom,
    ((top_to1344581618_alt_o = (^[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt))))). % top_empty_eq
thf(fact_50_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_51_top__empty__eq, axiom,
    ((top_to1892800228_alt_o = (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ top_to803745505le_alt))))). % top_empty_eq
thf(fact_52_top__empty__eq, axiom,
    ((top_to1473733010indi_o = (^[X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi))))). % top_empty_eq
thf(fact_53_top__empty__eq, axiom,
    ((top_to516240647_alt_o = (^[X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt))))). % top_empty_eq
thf(fact_54_top__set__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ top_to1900088076_alt_o)))). % top_set_def
thf(fact_55_top__set__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ top_to1473733010indi_o)))). % top_set_def
thf(fact_56_top__set__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ top_to516240647_alt_o)))). % top_set_def
thf(fact_57_old_Oprod_Oinducts, axiom,
    ((![P : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A5 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A5 @ B5))) => (P @ Prod))))). % old.prod.inducts
thf(fact_58_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A5 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A5 @ B5)))))))))). % old.prod.exhaust
thf(fact_59_Pair__inject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A4 : arrow_1857593510le_alt, B4 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A4 @ B4)) => (~ (((A = A4) => (~ ((B = B4)))))))))). % Pair_inject
thf(fact_60_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P2 : produc16571293le_alt]: ((![A5 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A5 @ B5))) => (P @ P2))))). % prod_cases
thf(fact_61_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_62_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_63_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_64_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_65_Collect__mem__eq, axiom,
    ((![A3 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_66_Collect__mem__eq, axiom,
    ((![A3 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_67_Collect__mem__eq, axiom,
    ((![A3 : set_Ar182050865le_alt]: ((collec1382217680le_alt @ (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_68_Collect__mem__eq, axiom,
    ((![A3 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ A3))) = A3)))). % Collect_mem_eq
thf(fact_69_Collect__cong, axiom,
    ((![P : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((![X3 : set_Pr367596371le_alt]: ((P @ X3) = (Q @ X3))) => ((collec1399441576le_alt @ P) = (collec1399441576le_alt @ Q)))))). % Collect_cong
thf(fact_70_surj__pair, axiom,
    ((![P2 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P2 = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_71_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_72_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ top_to685525675le_alt)))). % UNIV_witness
thf(fact_73_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_74_UNIV__witness, axiom,
    ((?[X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X3 @ top_to803745505le_alt)))). % UNIV_witness
thf(fact_75_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ top_to1799531699e_indi)))). % UNIV_witness
thf(fact_76_UNIV__witness, axiom,
    ((?[X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ top_to958727510le_alt)))). % UNIV_witness
thf(fact_77_UNIV__eq__I, axiom,
    ((![A3 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ A3)) => (top_to469035705le_alt = A3))))). % UNIV_eq_I
thf(fact_78_UNIV__eq__I, axiom,
    ((![A3 : set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ A3)) => (top_to685525675le_alt = A3))))). % UNIV_eq_I
thf(fact_79_UNIV__eq__I, axiom,
    ((![A3 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A3)) => (top_to224369155le_alt = A3))))). % UNIV_eq_I
thf(fact_80_UNIV__eq__I, axiom,
    ((![A3 : set_Ar182050865le_alt]: ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X3 @ A3)) => (top_to803745505le_alt = A3))))). % UNIV_eq_I
thf(fact_81_UNIV__eq__I, axiom,
    ((![A3 : set_Ar1007576579e_indi]: ((![X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ A3)) => (top_to1799531699e_indi = A3))))). % UNIV_eq_I
thf(fact_82_UNIV__eq__I, axiom,
    ((![A3 : set_Ar1665529862le_alt]: ((![X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ A3)) => (top_to958727510le_alt = A3))))). % UNIV_eq_I
thf(fact_83_Pi__cong, axiom,
    ((![A3 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, G : arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi]: ((member1966420836e_indi @ W @ A3) => ((F2 @ W) = (G @ W)))) => ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ B3)) = (member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ A3 @ B3))))))). % Pi_cong
thf(fact_84_Pi__cong, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ W @ A3) => ((F2 @ W) = (G @ W)))) => ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ B3)) = (member183760530le_alt @ G @ (pi_Arr479247969le_alt @ A3 @ B3))))))). % Pi_cong
thf(fact_85_Pi__mem, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar1007576579e_indi, B3 : arrow_1429744205e_indi > set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ B3)) => ((member1966420836e_indi @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_86_Pi__mem, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A3 : set_Pr367596371le_alt, B3 : produc16571293le_alt > set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A3 @ B3)) => ((member2048039092le_alt @ X2 @ A3) => (member2048039092le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_87_Pi__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A3 @ B3)) => ((member1334244458le_alt @ X2 @ A3) => (member2048039092le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_88_Pi__mem, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A3 : set_Pr367596371le_alt, B3 : produc16571293le_alt > set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A3 @ B3)) => ((member2048039092le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_89_Pi__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ B3)) => ((member1334244458le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_90_Pi__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A3 : set_Ar809243995le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A3 @ B3)) => ((member684274596le_alt @ X2 @ A3) => (member2048039092le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_91_Pi__mem, axiom,
    ((![F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Pr367596371le_alt, B3 : produc16571293le_alt > set_Ar809243995le_alt, X2 : produc16571293le_alt]: ((member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A3 @ B3)) => ((member2048039092le_alt @ X2 @ A3) => (member684274596le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_92_Pi__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_Ar809243995le_alt, X2 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A3 @ B3)) => ((member1334244458le_alt @ X2 @ A3) => (member684274596le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_93_Pi__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ B3)) => ((member684274596le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_94_Pi__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A3 @ B3)) => ((member684274596le_alt @ X2 @ A3) => (member684274596le_alt @ (F2 @ X2) @ (B3 @ X2))))))). % Pi_mem
thf(fact_95_Pi__iff, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, I2 : set_Ar1007576579e_indi, X4 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ I2 @ X4)) = (![X : arrow_1429744205e_indi]: (((member1966420836e_indi @ X @ I2)) => ((member1334244458le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_96_Pi__iff, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I2 : set_Ar809243995le_alt, X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ I2 @ X4)) = (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ I2)) => ((member1334244458le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_97_Pi__I_H, axiom,
    ((![A3 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_98_Pi__I_H, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B3 : produc16571293le_alt > set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_99_Pi__I_H, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B3 : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_100_Pi__I_H, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B3 : produc16571293le_alt > set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_101_Pi__I_H, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B3 : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_102_Pi__I_H, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_103_Pi__I_H, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : produc16571293le_alt > set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member684274596le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_104_Pi__I_H, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member684274596le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_105_Pi__I_H, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_106_Pi__I_H, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (member684274596le_alt @ (F2 @ X3) @ (B3 @ X3)))) => (member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A3 @ B3)))))). % Pi_I'
thf(fact_107_PiE, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar1007576579e_indi, B3 : arrow_1429744205e_indi > set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ B3)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member1966420836e_indi @ X2 @ A3)))))))). % PiE
thf(fact_108_PiE, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A3 : set_Pr367596371le_alt, B3 : produc16571293le_alt > set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A3 @ B3)) => ((~ ((member2048039092le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A3)))))))). % PiE
thf(fact_109_PiE, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A3 : set_Pr367596371le_alt, B3 : produc16571293le_alt > set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A3 @ B3)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A3)))))))). % PiE
thf(fact_110_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A3 @ B3)) => ((~ ((member2048039092le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A3)))))))). % PiE
thf(fact_111_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ B3)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A3)))))))). % PiE
thf(fact_112_PiE, axiom,
    ((![F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Pr367596371le_alt, B3 : produc16571293le_alt > set_Ar809243995le_alt, X2 : produc16571293le_alt]: ((member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A3 @ B3)) => ((~ ((member684274596le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member2048039092le_alt @ X2 @ A3)))))))). % PiE
thf(fact_113_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A3 : set_Ar809243995le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A3 @ B3)) => ((~ ((member2048039092le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A3)))))))). % PiE
thf(fact_114_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt > set_Ar809243995le_alt, X2 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A3 @ B3)) => ((~ ((member684274596le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member1334244458le_alt @ X2 @ A3)))))))). % PiE
thf(fact_115_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ B3)) => ((~ ((member1334244458le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A3)))))))). % PiE
thf(fact_116_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A3 @ B3)) => ((~ ((member684274596le_alt @ (F2 @ X2) @ (B3 @ X2)))) => (~ ((member684274596le_alt @ X2 @ A3)))))))). % PiE
thf(fact_117_pred__equals__eq2, axiom,
    ((![R2 : set_Pr367596371le_alt, S2 : set_Pr367596371le_alt]: (((^[X : arrow_1857593510le_alt]: (^[Y2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ R2))) = (^[X : arrow_1857593510le_alt]: (^[Y2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ S2)))) = (R2 = S2))))). % pred_equals_eq2
thf(fact_118_UNIV__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: $true))))). % UNIV_def
thf(fact_119_UNIV__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ (^[X : arrow_1429744205e_indi]: $true))))). % UNIV_def
thf(fact_120_UNIV__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: $true))))). % UNIV_def
thf(fact_121_funcset__mem, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar1007576579e_indi, B3 : set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi]: B3))) => ((member1966420836e_indi @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_122_funcset__mem, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A3 : set_Pr367596371le_alt, B3 : set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A3 @ (^[Uu : produc16571293le_alt]: B3))) => ((member2048039092le_alt @ X2 @ A3) => (member2048039092le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_123_funcset__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A3 : set_se2071012361le_alt, B3 : set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: B3))) => ((member1334244458le_alt @ X2 @ A3) => (member2048039092le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_124_funcset__mem, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A3 : set_Pr367596371le_alt, B3 : set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A3 @ (^[Uu : produc16571293le_alt]: B3))) => ((member2048039092le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_125_funcset__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: B3))) => ((member1334244458le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_126_funcset__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A3 : set_Ar809243995le_alt, B3 : set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B3))) => ((member684274596le_alt @ X2 @ A3) => (member2048039092le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_127_funcset__mem, axiom,
    ((![F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Pr367596371le_alt, B3 : set_Ar809243995le_alt, X2 : produc16571293le_alt]: ((member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A3 @ (^[Uu : produc16571293le_alt]: B3))) => ((member2048039092le_alt @ X2 @ A3) => (member684274596le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_128_funcset__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_Ar809243995le_alt, X2 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: B3))) => ((member1334244458le_alt @ X2 @ A3) => (member684274596le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_129_funcset__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, B3 : set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B3))) => ((member684274596le_alt @ X2 @ A3) => (member1334244458le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_130_funcset__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, B3 : set_Ar809243995le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B3))) => ((member684274596le_alt @ X2 @ A3) => (member684274596le_alt @ (F2 @ X2) @ B3)))))). % funcset_mem
thf(fact_131_funcsetI, axiom,
    ((![A3 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ B3))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi]: B3))))))). % funcsetI
thf(fact_132_funcsetI, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B3 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ B3))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A3 @ (^[Uu : produc16571293le_alt]: B3))))))). % funcsetI
thf(fact_133_funcsetI, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B3 : set_Pr367596371le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ B3))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: B3))))))). % funcsetI
thf(fact_134_funcsetI, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B3 : set_se2071012361le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ B3))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A3 @ (^[Uu : produc16571293le_alt]: B3))))))). % funcsetI
thf(fact_135_funcsetI, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B3 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ B3))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: B3))))))). % funcsetI
thf(fact_136_funcsetI, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B3 : set_Pr367596371le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (member2048039092le_alt @ (F2 @ X3) @ B3))) => (member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B3))))))). % funcsetI
thf(fact_137_funcsetI, axiom,
    ((![A3 : set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : set_Ar809243995le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (member684274596le_alt @ (F2 @ X3) @ B3))) => (member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A3 @ (^[Uu : produc16571293le_alt]: B3))))))). % funcsetI
thf(fact_138_funcsetI, axiom,
    ((![A3 : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : set_Ar809243995le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (member684274596le_alt @ (F2 @ X3) @ B3))) => (member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A3 @ (^[Uu : set_Pr367596371le_alt]: B3))))))). % funcsetI
thf(fact_139_funcsetI, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B3 : set_se2071012361le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (member1334244458le_alt @ (F2 @ X3) @ B3))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B3))))))). % funcsetI
thf(fact_140_funcsetI, axiom,
    ((![A3 : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B3 : set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (member684274596le_alt @ (F2 @ X3) @ B3))) => (member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B3))))))). % funcsetI
thf(fact_141_dictatorI, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : arrow_1429744205e_indi]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))) => ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ arrow_1951607831e_Prof) => (![A5 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: ((~ ((A5 = B5))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B5) @ (X3 @ I3)) => (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B5) @ (F3 @ X3))))))) => (arrow_960434986ctator @ F3 @ I3)))))). % dictatorI
thf(fact_142_converse_Oinducts, axiom,
    ((![X1 : arrow_1857593510le_alt, X22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt, P : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((member2048039092le_alt @ (produc1494124311le_alt @ X1 @ X22) @ (conver1781819635le_alt @ R)) => ((![A5 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B5) @ R) => (P @ B5 @ A5))) => (P @ X1 @ X22)))))). % converse.inducts
thf(fact_143_converse_Ointros, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R) => (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (conver1781819635le_alt @ R)))))). % converse.intros
thf(fact_144_converse_Osimps, axiom,
    ((![A1 : arrow_1857593510le_alt, A22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A1 @ A22) @ (conver1781819635le_alt @ R)) = (?[A2 : arrow_1857593510le_alt]: (?[B2 : arrow_1857593510le_alt]: (((A1 = B2)) & ((((A22 = A2)) & ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ R))))))))))). % converse.simps
thf(fact_145_converse_Ocases, axiom,
    ((![A1 : arrow_1857593510le_alt, A22 : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A1 @ A22) @ (conver1781819635le_alt @ R)) => (member2048039092le_alt @ (produc1494124311le_alt @ A22 @ A1) @ R))))). % converse.cases
thf(fact_146_converseE, axiom,
    ((![Yx : produc16571293le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ Yx @ (conver1781819635le_alt @ R)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((Yx = (produc1494124311le_alt @ Y3 @ X3)) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R))))))))))). % converseE
thf(fact_147_converseD, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (conver1781819635le_alt @ R)) => (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ R))))). % converseD
thf(fact_148_Pi__empty, axiom,
    ((![B3 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((pi_Arr1981691447le_alt @ bot_bo1390904983e_indi @ B3) = top_to685525675le_alt)))). % Pi_empty
thf(fact_149_Pi__empty, axiom,
    ((![B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((pi_Arr479247969le_alt @ bot_bo365569479le_alt @ B3) = top_to803745505le_alt)))). % Pi_empty
thf(fact_150_PiE__UNIV, axiom,
    (((piE_Ar738911586e_indi @ top_to1799531699e_indi @ (^[I : arrow_1429744205e_indi]: top_to1799531699e_indi)) = top_to498310661e_indi))). % PiE_UNIV
thf(fact_151_PiE__UNIV, axiom,
    (((piE_Ar1084018769le_alt @ top_to1799531699e_indi @ (^[I : arrow_1429744205e_indi]: top_to958727510le_alt)) = top_to1139905818le_alt))). % PiE_UNIV
thf(fact_152_PiE__UNIV, axiom,
    (((piE_Ar415527999e_indi @ top_to958727510le_alt @ (^[I : arrow_1857593510le_alt]: top_to1799531699e_indi)) = top_to2048848e_indi))). % PiE_UNIV
thf(fact_153_PiE__UNIV, axiom,
    (((piE_Ar1187035700le_alt @ top_to958727510le_alt @ (^[I : arrow_1857593510le_alt]: top_to958727510le_alt)) = top_to290516239le_alt))). % PiE_UNIV
thf(fact_154_ssubst__Pair__rhs, axiom,
    ((![R : arrow_1857593510le_alt, S : arrow_1857593510le_alt, R2 : set_Pr367596371le_alt, S3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R @ S) @ R2) => ((S3 = S) => (member2048039092le_alt @ (produc1494124311le_alt @ R @ S3) @ R2)))))). % ssubst_Pair_rhs
thf(fact_155_curryI, axiom,
    ((![F2 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F2 @ (produc1494124311le_alt @ A @ B)) => (produc392997491_alt_o @ F2 @ A @ B))))). % curryI
thf(fact_156_empty__Collect__eq, axiom,
    ((![P : set_Pr367596371le_alt > $o]: ((bot_bo1518363805le_alt = (collec1399441576le_alt @ P)) = (![X : set_Pr367596371le_alt]: (~ ((P @ X)))))))). % empty_Collect_eq
thf(fact_157_Collect__empty__eq, axiom,
    ((![P : set_Pr367596371le_alt > $o]: (((collec1399441576le_alt @ P) = bot_bo1518363805le_alt) = (![X : set_Pr367596371le_alt]: (~ ((P @ X)))))))). % Collect_empty_eq
thf(fact_158_all__not__in__conv, axiom,
    ((![A3 : set_se2071012361le_alt]: ((![X : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ X @ A3)))) = (A3 = bot_bo1518363805le_alt))))). % all_not_in_conv
thf(fact_159_all__not__in__conv, axiom,
    ((![A3 : set_Ar809243995le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (~ ((member684274596le_alt @ X @ A3)))) = (A3 = bot_bo365569479le_alt))))). % all_not_in_conv
thf(fact_160_all__not__in__conv, axiom,
    ((![A3 : set_Pr367596371le_alt]: ((![X : produc16571293le_alt]: (~ ((member2048039092le_alt @ X @ A3)))) = (A3 = bot_bo1596236775le_alt))))). % all_not_in_conv
thf(fact_161_all__not__in__conv, axiom,
    ((![A3 : set_Ar182050865le_alt]: ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member183760530le_alt @ X @ A3)))) = (A3 = bot_bo13098693le_alt))))). % all_not_in_conv
thf(fact_162_empty__iff, axiom,
    ((![C : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ C @ bot_bo1518363805le_alt)))))). % empty_iff
thf(fact_163_empty__iff, axiom,
    ((![C : arrow_1429744205e_indi > set_Pr367596371le_alt]: (~ ((member684274596le_alt @ C @ bot_bo365569479le_alt)))))). % empty_iff
thf(fact_164_empty__iff, axiom,
    ((![C : produc16571293le_alt]: (~ ((member2048039092le_alt @ C @ bot_bo1596236775le_alt)))))). % empty_iff
thf(fact_165_empty__iff, axiom,
    ((![C : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member183760530le_alt @ C @ bot_bo13098693le_alt)))))). % empty_iff
thf(fact_166_converse__empty, axiom,
    (((conver1781819635le_alt @ bot_bo1596236775le_alt) = bot_bo1596236775le_alt))). % converse_empty
thf(fact_167_Collect__const, axiom,
    ((![P : $o]: ((P => ((collec1399441576le_alt @ (^[S4 : set_Pr367596371le_alt]: P)) = top_to469035705le_alt)) & ((~ (P)) => ((collec1399441576le_alt @ (^[S4 : set_Pr367596371le_alt]: P)) = bot_bo1518363805le_alt)))))). % Collect_const
thf(fact_168_Collect__const, axiom,
    ((![P : $o]: ((P => ((collec1169676194e_indi @ (^[S4 : arrow_1429744205e_indi]: P)) = top_to1799531699e_indi)) & ((~ (P)) => ((collec1169676194e_indi @ (^[S4 : arrow_1429744205e_indi]: P)) = bot_bo1390904983e_indi)))))). % Collect_const
thf(fact_169_Collect__const, axiom,
    ((![P : $o]: ((P => ((collec1364151825le_alt @ (^[S4 : arrow_1857593510le_alt]: P)) = top_to958727510le_alt)) & ((~ (P)) => ((collec1364151825le_alt @ (^[S4 : arrow_1857593510le_alt]: P)) = bot_bo1127707250le_alt)))))). % Collect_const
thf(fact_170_Pi__eq__empty, axiom,
    ((![A3 : set_Ar1007576579e_indi, B3 : arrow_1429744205e_indi > set_se2071012361le_alt]: (((pi_Arr1981691447le_alt @ A3 @ B3) = bot_bo365569479le_alt) = (?[X : arrow_1429744205e_indi]: (((member1966420836e_indi @ X @ A3)) & (((B3 @ X) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_171_Pi__eq__empty, axiom,
    ((![A3 : set_Ar809243995le_alt, B3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: (((pi_Arr479247969le_alt @ A3 @ B3) = bot_bo13098693le_alt) = (?[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ A3)) & (((B3 @ X) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_172_extensionalityI, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar1007576579e_indi, G : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ F2 @ (extens1528283402le_alt @ A3)) => ((member684274596le_alt @ G @ (extens1528283402le_alt @ A3)) => ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A3) => ((F2 @ X3) = (G @ X3)))) => (F2 = G))))))). % extensionalityI
thf(fact_173_extensionalityI, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (extens951643470le_alt @ A3)) => ((member183760530le_alt @ G @ (extens951643470le_alt @ A3)) => ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => ((F2 @ X3) = (G @ X3)))) => (F2 = G))))))). % extensionalityI
thf(fact_174_PiE__mem, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, S2 : set_Ar1007576579e_indi, T : arrow_1429744205e_indi > set_se2071012361le_alt, X2 : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (piE_Ar1580347400le_alt @ S2 @ T)) => ((member1966420836e_indi @ X2 @ S2) => (member1334244458le_alt @ (F2 @ X2) @ (T @ X2))))))). % PiE_mem
thf(fact_175_PiE__mem, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, S2 : set_Pr367596371le_alt, T : produc16571293le_alt > set_Pr367596371le_alt, X2 : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (piE_Pr2084141144le_alt @ S2 @ T)) => ((member2048039092le_alt @ X2 @ S2) => (member2048039092le_alt @ (F2 @ X2) @ (T @ X2))))))). % PiE_mem
thf(fact_176_PiE__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, S2 : set_se2071012361le_alt, T : set_Pr367596371le_alt > set_Pr367596371le_alt, X2 : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (piE_se232226le_alt @ S2 @ T)) => ((member1334244458le_alt @ X2 @ S2) => (member2048039092le_alt @ (F2 @ X2) @ (T @ X2))))))). % PiE_mem
thf(fact_177_PiE__mem, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, S2 : set_Pr367596371le_alt, T : produc16571293le_alt > set_se2071012361le_alt, X2 : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (piE_Pr757114552le_alt @ S2 @ T)) => ((member2048039092le_alt @ X2 @ S2) => (member1334244458le_alt @ (F2 @ X2) @ (T @ X2))))))). % PiE_mem
thf(fact_178_PiE__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, S2 : set_se2071012361le_alt, T : set_Pr367596371le_alt > set_se2071012361le_alt, X2 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (piE_se1902809474le_alt @ S2 @ T)) => ((member1334244458le_alt @ X2 @ S2) => (member1334244458le_alt @ (F2 @ X2) @ (T @ X2))))))). % PiE_mem
thf(fact_179_PiE__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, S2 : set_Ar809243995le_alt, T : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F2 @ (piE_Ar974971248le_alt @ S2 @ T)) => ((member684274596le_alt @ X2 @ S2) => (member2048039092le_alt @ (F2 @ X2) @ (T @ X2))))))). % PiE_mem
thf(fact_180_PiE__mem, axiom,
    ((![F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, S2 : set_Pr367596371le_alt, T : produc16571293le_alt > set_Ar809243995le_alt, X2 : produc16571293le_alt]: ((member167063198le_alt @ F2 @ (piE_Pr1024471460le_alt @ S2 @ T)) => ((member2048039092le_alt @ X2 @ S2) => (member684274596le_alt @ (F2 @ X2) @ (T @ X2))))))). % PiE_mem
thf(fact_181_PiE__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, S2 : set_se2071012361le_alt, T : set_Pr367596371le_alt > set_Ar809243995le_alt, X2 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F2 @ (piE_se1100287834le_alt @ S2 @ T)) => ((member1334244458le_alt @ X2 @ S2) => (member684274596le_alt @ (F2 @ X2) @ (T @ X2))))))). % PiE_mem
thf(fact_182_PiE__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, S2 : set_Ar809243995le_alt, T : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (piE_Ar236171216le_alt @ S2 @ T)) => ((member684274596le_alt @ X2 @ S2) => (member1334244458le_alt @ (F2 @ X2) @ (T @ X2))))))). % PiE_mem
thf(fact_183_PiE__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, S2 : set_Ar809243995le_alt, T : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F2 @ (piE_Ar1900467852le_alt @ S2 @ T)) => ((member684274596le_alt @ X2 @ S2) => (member684274596le_alt @ (F2 @ X2) @ (T @ X2))))))). % PiE_mem
thf(fact_184_PiE__iff, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, I2 : set_Ar1007576579e_indi, X4 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F2 @ (piE_Ar1580347400le_alt @ I2 @ X4)) = (((![X : arrow_1429744205e_indi]: (((member1966420836e_indi @ X @ I2)) => ((member1334244458le_alt @ (F2 @ X) @ (X4 @ X)))))) & ((member684274596le_alt @ F2 @ (extens1528283402le_alt @ I2)))))))). % PiE_iff
thf(fact_185_PiE__iff, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I2 : set_Ar809243995le_alt, X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F2 @ (piE_Ar236171216le_alt @ I2 @ X4)) = (((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ I2)) => ((member1334244458le_alt @ (F2 @ X) @ (X4 @ X)))))) & ((member183760530le_alt @ F2 @ (extens951643470le_alt @ I2)))))))). % PiE_iff
thf(fact_186_PiE__ext, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt, K : set_Ar1007576579e_indi, S : arrow_1429744205e_indi > set_se2071012361le_alt, Y : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ (piE_Ar1580347400le_alt @ K @ S)) => ((member684274596le_alt @ Y @ (piE_Ar1580347400le_alt @ K @ S)) => ((![I4 : arrow_1429744205e_indi]: ((member1966420836e_indi @ I4 @ K) => ((X2 @ I4) = (Y @ I4)))) => (X2 = Y))))))). % PiE_ext
thf(fact_187_PiE__ext, axiom,
    ((![X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, K : set_Ar809243995le_alt, S : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, Y : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ X2 @ (piE_Ar236171216le_alt @ K @ S)) => ((member183760530le_alt @ Y @ (piE_Ar236171216le_alt @ K @ S)) => ((![I4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ I4 @ K) => ((X2 @ I4) = (Y @ I4)))) => (X2 = Y))))))). % PiE_ext
thf(fact_188_ex__in__conv, axiom,
    ((![A3 : set_se2071012361le_alt]: ((?[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ A3)) = (~ ((A3 = bot_bo1518363805le_alt))))))). % ex_in_conv
thf(fact_189_ex__in__conv, axiom,
    ((![A3 : set_Ar809243995le_alt]: ((?[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ A3)) = (~ ((A3 = bot_bo365569479le_alt))))))). % ex_in_conv
thf(fact_190_ex__in__conv, axiom,
    ((![A3 : set_Pr367596371le_alt]: ((?[X : produc16571293le_alt]: (member2048039092le_alt @ X @ A3)) = (~ ((A3 = bot_bo1596236775le_alt))))))). % ex_in_conv
thf(fact_191_ex__in__conv, axiom,
    ((![A3 : set_Ar182050865le_alt]: ((?[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ A3)) = (~ ((A3 = bot_bo13098693le_alt))))))). % ex_in_conv
thf(fact_192_empty__def, axiom,
    ((bot_bo1518363805le_alt = (collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: $false))))). % empty_def
thf(fact_193_equals0I, axiom,
    ((![A3 : set_se2071012361le_alt]: ((![Y3 : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ Y3 @ A3)))) => (A3 = bot_bo1518363805le_alt))))). % equals0I
thf(fact_194_equals0I, axiom,
    ((![A3 : set_Ar809243995le_alt]: ((![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (~ ((member684274596le_alt @ Y3 @ A3)))) => (A3 = bot_bo365569479le_alt))))). % equals0I
thf(fact_195_equals0I, axiom,
    ((![A3 : set_Pr367596371le_alt]: ((![Y3 : produc16571293le_alt]: (~ ((member2048039092le_alt @ Y3 @ A3)))) => (A3 = bot_bo1596236775le_alt))))). % equals0I
thf(fact_196_equals0I, axiom,
    ((![A3 : set_Ar182050865le_alt]: ((![Y3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member183760530le_alt @ Y3 @ A3)))) => (A3 = bot_bo13098693le_alt))))). % equals0I
thf(fact_197_equals0D, axiom,
    ((![A3 : set_se2071012361le_alt, A : set_Pr367596371le_alt]: ((A3 = bot_bo1518363805le_alt) => (~ ((member1334244458le_alt @ A @ A3))))))). % equals0D
thf(fact_198_equals0D, axiom,
    ((![A3 : set_Ar809243995le_alt, A : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((A3 = bot_bo365569479le_alt) => (~ ((member684274596le_alt @ A @ A3))))))). % equals0D
thf(fact_199_equals0D, axiom,
    ((![A3 : set_Pr367596371le_alt, A : produc16571293le_alt]: ((A3 = bot_bo1596236775le_alt) => (~ ((member2048039092le_alt @ A @ A3))))))). % equals0D
thf(fact_200_equals0D, axiom,
    ((![A3 : set_Ar182050865le_alt, A : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((A3 = bot_bo13098693le_alt) => (~ ((member183760530le_alt @ A @ A3))))))). % equals0D
thf(fact_201_emptyE, axiom,
    ((![A : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ A @ bot_bo1518363805le_alt)))))). % emptyE
thf(fact_202_emptyE, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt]: (~ ((member684274596le_alt @ A @ bot_bo365569479le_alt)))))). % emptyE
thf(fact_203_emptyE, axiom,
    ((![A : produc16571293le_alt]: (~ ((member2048039092le_alt @ A @ bot_bo1596236775le_alt)))))). % emptyE
thf(fact_204_emptyE, axiom,
    ((![A : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member183760530le_alt @ A @ bot_bo13098693le_alt)))))). % emptyE
thf(fact_205_empty__not__UNIV, axiom,
    ((~ ((bot_bo1390904983e_indi = top_to1799531699e_indi))))). % empty_not_UNIV
thf(fact_206_empty__not__UNIV, axiom,
    ((~ ((bot_bo1127707250le_alt = top_to958727510le_alt))))). % empty_not_UNIV
thf(fact_207_funcset__to__empty__iff, axiom,
    ((![A3 : set_Ar1007576579e_indi]: (((A3 = bot_bo1390904983e_indi) => ((pi_Arr1981691447le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi]: bot_bo1518363805le_alt)) = top_to685525675le_alt)) & ((~ ((A3 = bot_bo1390904983e_indi))) => ((pi_Arr1981691447le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi]: bot_bo1518363805le_alt)) = bot_bo365569479le_alt)))))). % funcset_to_empty_iff
thf(fact_208_funcset__to__empty__iff, axiom,
    ((![A3 : set_Ar809243995le_alt]: (((A3 = bot_bo365569479le_alt) => ((pi_Arr479247969le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: bot_bo1518363805le_alt)) = top_to803745505le_alt)) & ((~ ((A3 = bot_bo365569479le_alt))) => ((pi_Arr479247969le_alt @ A3 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: bot_bo1518363805le_alt)) = bot_bo13098693le_alt)))))). % funcset_to_empty_iff
thf(fact_209_curryD, axiom,
    ((![F2 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F2 @ A @ B) => (F2 @ (produc1494124311le_alt @ A @ B)))))). % curryD
thf(fact_210_curryE, axiom,
    ((![F2 : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F2 @ A @ B) => (F2 @ (produc1494124311le_alt @ A @ B)))))). % curryE
thf(fact_211_PiE__UNIV__domain, axiom,
    ((![T : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((piE_Ar236171216le_alt @ top_to685525675le_alt @ T) = (pi_Arr479247969le_alt @ top_to685525675le_alt @ T))))). % PiE_UNIV_domain
thf(fact_212_PiE__UNIV__domain, axiom,
    ((![T : arrow_1429744205e_indi > set_se2071012361le_alt]: ((piE_Ar1580347400le_alt @ top_to1799531699e_indi @ T) = (pi_Arr1981691447le_alt @ top_to1799531699e_indi @ T))))). % PiE_UNIV_domain
thf(fact_213_extensional__funcset__def, axiom,
    ((![S2 : set_Ar1007576579e_indi, T : set_se2071012361le_alt]: ((piE_Ar1580347400le_alt @ S2 @ (^[I : arrow_1429744205e_indi]: T)) = (inf_in82880073le_alt @ (pi_Arr1981691447le_alt @ S2 @ (^[Uu : arrow_1429744205e_indi]: T)) @ (extens1528283402le_alt @ S2)))))). % extensional_funcset_def
thf(fact_214_extensional__funcset__def, axiom,
    ((![S2 : set_Ar809243995le_alt, T : set_se2071012361le_alt]: ((piE_Ar236171216le_alt @ S2 @ (^[I : arrow_1429744205e_indi > set_Pr367596371le_alt]: T)) = (inf_in2014612675le_alt @ (pi_Arr479247969le_alt @ S2 @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: T)) @ (extens951643470le_alt @ S2)))))). % extensional_funcset_def
thf(fact_215_IntI, axiom,
    ((![C : set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ A3) => ((member1334244458le_alt @ C @ B3) => (member1334244458le_alt @ C @ (inf_in322684315le_alt @ A3 @ B3))))))). % IntI
thf(fact_216_IntI, axiom,
    ((![C : arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, B3 : set_Ar809243995le_alt]: ((member684274596le_alt @ C @ A3) => ((member684274596le_alt @ C @ B3) => (member684274596le_alt @ C @ (inf_in82880073le_alt @ A3 @ B3))))))). % IntI
thf(fact_217_IntI, axiom,
    ((![C : produc16571293le_alt, A3 : set_Pr367596371le_alt, B3 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ A3) => ((member2048039092le_alt @ C @ B3) => (member2048039092le_alt @ C @ (inf_in607321317le_alt @ A3 @ B3))))))). % IntI
thf(fact_218_IntI, axiom,
    ((![C : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_Ar182050865le_alt, B3 : set_Ar182050865le_alt]: ((member183760530le_alt @ C @ A3) => ((member183760530le_alt @ C @ B3) => (member183760530le_alt @ C @ (inf_in2014612675le_alt @ A3 @ B3))))))). % IntI
thf(fact_219_Int__iff, axiom,
    ((![C : set_Pr367596371le_alt, A3 : set_se2071012361le_alt, B3 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ (inf_in322684315le_alt @ A3 @ B3)) = (((member1334244458le_alt @ C @ A3)) & ((member1334244458le_alt @ C @ B3))))))). % Int_iff
thf(fact_220_Int__iff, axiom,
    ((![C : arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, B3 : set_Ar809243995le_alt]: ((member684274596le_alt @ C @ (inf_in82880073le_alt @ A3 @ B3)) = (((member684274596le_alt @ C @ A3)) & ((member684274596le_alt @ C @ B3))))))). % Int_iff
thf(fact_221_Int__iff, axiom,
    ((![C : produc16571293le_alt, A3 : set_Pr367596371le_alt, B3 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (inf_in607321317le_alt @ A3 @ B3)) = (((member2048039092le_alt @ C @ A3)) & ((member2048039092le_alt @ C @ B3))))))). % Int_iff
thf(fact_222_Int__iff, axiom,
    ((![C : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_Ar182050865le_alt, B3 : set_Ar182050865le_alt]: ((member183760530le_alt @ C @ (inf_in2014612675le_alt @ A3 @ B3)) = (((member183760530le_alt @ C @ A3)) & ((member183760530le_alt @ C @ B3))))))). % Int_iff
thf(fact_223_Int__UNIV, axiom,
    ((![A3 : set_Ar1007576579e_indi, B3 : set_Ar1007576579e_indi]: (((inf_in1270134677e_indi @ A3 @ B3) = top_to1799531699e_indi) = (((A3 = top_to1799531699e_indi)) & ((B3 = top_to1799531699e_indi))))))). % Int_UNIV
thf(fact_224_Int__UNIV, axiom,
    ((![A3 : set_Ar1665529862le_alt, B3 : set_Ar1665529862le_alt]: (((inf_in840442356le_alt @ A3 @ B3) = top_to958727510le_alt) = (((A3 = top_to958727510le_alt)) & ((B3 = top_to958727510le_alt))))))). % Int_UNIV
thf(fact_225_bot__empty__eq2, axiom,
    ((bot_bo1596608602_alt_o = (^[X : arrow_1857593510le_alt]: (^[Y2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ bot_bo1596236775le_alt)))))). % bot_empty_eq2
thf(fact_226_bot__empty__eq, axiom,
    ((bot_bo2065212968_alt_o = (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ bot_bo1518363805le_alt))))). % bot_empty_eq
thf(fact_227_bot__empty__eq, axiom,
    ((bot_bo955514838_alt_o = (^[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ bot_bo365569479le_alt))))). % bot_empty_eq
thf(fact_228_bot__empty__eq, axiom,
    ((bot_bo91657054_alt_o = (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ bot_bo1596236775le_alt))))). % bot_empty_eq
thf(fact_229_bot__empty__eq, axiom,
    ((bot_bo49069056_alt_o = (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ bot_bo13098693le_alt))))). % bot_empty_eq
thf(fact_230_Collect__conj__eq, axiom,
    ((![P : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (((P @ X)) & ((Q @ X))))) = (inf_in322684315le_alt @ (collec1399441576le_alt @ P) @ (collec1399441576le_alt @ Q)))))). % Collect_conj_eq
thf(fact_231_disjoint__iff, axiom,
    ((![A3 : set_se2071012361le_alt, B3 : set_se2071012361le_alt]: (((inf_in322684315le_alt @ A3 @ B3) = bot_bo1518363805le_alt) = (![X : set_Pr367596371le_alt]: (((member1334244458le_alt @ X @ A3)) => ((~ ((member1334244458le_alt @ X @ B3)))))))))). % disjoint_iff
thf(fact_232_disjoint__iff, axiom,
    ((![A3 : set_Ar809243995le_alt, B3 : set_Ar809243995le_alt]: (((inf_in82880073le_alt @ A3 @ B3) = bot_bo365569479le_alt) = (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ A3)) => ((~ ((member684274596le_alt @ X @ B3)))))))))). % disjoint_iff
thf(fact_233_disjoint__iff, axiom,
    ((![A3 : set_Pr367596371le_alt, B3 : set_Pr367596371le_alt]: (((inf_in607321317le_alt @ A3 @ B3) = bot_bo1596236775le_alt) = (![X : produc16571293le_alt]: (((member2048039092le_alt @ X @ A3)) => ((~ ((member2048039092le_alt @ X @ B3)))))))))). % disjoint_iff
thf(fact_234_disjoint__iff, axiom,
    ((![A3 : set_Ar182050865le_alt, B3 : set_Ar182050865le_alt]: (((inf_in2014612675le_alt @ A3 @ B3) = bot_bo13098693le_alt) = (![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ A3)) => ((~ ((member183760530le_alt @ X @ B3)))))))))). % disjoint_iff
thf(fact_235_bot__set__def, axiom,
    ((bot_bo1518363805le_alt = (collec1399441576le_alt @ bot_bo2065212968_alt_o)))). % bot_set_def
thf(fact_236_Int__Collect, axiom,
    ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A3 : set_Ar809243995le_alt, P : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ X2 @ (inf_in82880073le_alt @ A3 @ (collec1559089382le_alt @ P))) = (((member684274596le_alt @ X2 @ A3)) & ((P @ X2))))))). % Int_Collect
thf(fact_237_Int__Collect, axiom,
    ((![X2 : produc16571293le_alt, A3 : set_Pr367596371le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ X2 @ (inf_in607321317le_alt @ A3 @ (collec531981554le_alt @ P))) = (((member2048039092le_alt @ X2 @ A3)) & ((P @ X2))))))). % Int_Collect
thf(fact_238_Int__Collect, axiom,
    ((![X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A3 : set_Ar182050865le_alt, P : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member183760530le_alt @ X2 @ (inf_in2014612675le_alt @ A3 @ (collec1382217680le_alt @ P))) = (((member183760530le_alt @ X2 @ A3)) & ((P @ X2))))))). % Int_Collect
thf(fact_239_Int__Collect, axiom,
    ((![X2 : set_Pr367596371le_alt, A3 : set_se2071012361le_alt, P : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ X2 @ (inf_in322684315le_alt @ A3 @ (collec1399441576le_alt @ P))) = (((member1334244458le_alt @ X2 @ A3)) & ((P @ X2))))))). % Int_Collect
thf(fact_240_Int__emptyI, axiom,
    ((![A3 : set_se2071012361le_alt, B3 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A3) => (~ ((member1334244458le_alt @ X3 @ B3))))) => ((inf_in322684315le_alt @ A3 @ B3) = bot_bo1518363805le_alt))))). % Int_emptyI
thf(fact_241_Int__emptyI, axiom,
    ((![A3 : set_Ar809243995le_alt, B3 : set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X3 @ A3) => (~ ((member684274596le_alt @ X3 @ B3))))) => ((inf_in82880073le_alt @ A3 @ B3) = bot_bo365569479le_alt))))). % Int_emptyI
thf(fact_242_Int__emptyI, axiom,
    ((![A3 : set_Pr367596371le_alt, B3 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A3) => (~ ((member2048039092le_alt @ X3 @ B3))))) => ((inf_in607321317le_alt @ A3 @ B3) = bot_bo1596236775le_alt))))). % Int_emptyI
thf(fact_243_Int__emptyI, axiom,
    ((![A3 : set_Ar182050865le_alt, B3 : set_Ar182050865le_alt]: ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ X3 @ A3) => (~ ((member183760530le_alt @ X3 @ B3))))) => ((inf_in2014612675le_alt @ A3 @ B3) = bot_bo13098693le_alt))))). % Int_emptyI
thf(fact_244_Int__def, axiom,
    ((inf_in82880073le_alt = (^[A6 : set_Ar809243995le_alt]: (^[B6 : set_Ar809243995le_alt]: (collec1559089382le_alt @ (^[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ A6)) & ((member684274596le_alt @ X @ B6)))))))))). % Int_def
thf(fact_245_Int__def, axiom,
    ((inf_in607321317le_alt = (^[A6 : set_Pr367596371le_alt]: (^[B6 : set_Pr367596371le_alt]: (collec531981554le_alt @ (^[X : produc16571293le_alt]: (((member2048039092le_alt @ X @ A6)) & ((member2048039092le_alt @ X @ B6)))))))))). % Int_def
thf(fact_246_Int__def, axiom,
    ((inf_in2014612675le_alt = (^[A6 : set_Ar182050865le_alt]: (^[B6 : set_Ar182050865le_alt]: (collec1382217680le_alt @ (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ A6)) & ((member183760530le_alt @ X @ B6)))))))))). % Int_def
thf(fact_247_Int__def, axiom,
    ((inf_in322684315le_alt = (^[A6 : set_se2071012361le_alt]: (^[B6 : set_se2071012361le_alt]: (collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (((member1334244458le_alt @ X @ A6)) & ((member1334244458le_alt @ X @ B6)))))))))). % Int_def
thf(fact_248_Pi__Int, axiom,
    ((![I2 : set_Ar809243995le_alt, E : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((inf_in2014612675le_alt @ (pi_Arr479247969le_alt @ I2 @ E) @ (pi_Arr479247969le_alt @ I2 @ F3)) = (pi_Arr479247969le_alt @ I2 @ (^[I : arrow_1429744205e_indi > set_Pr367596371le_alt]: (inf_in322684315le_alt @ (E @ I) @ (F3 @ I)))))))). % Pi_Int

% Conjectures (2)
thf(conj_0, hypothesis,
    ((member1334244458le_alt @ l @ arrow_1848678355le_Lin))).
thf(conj_1, conjecture,
    ((member684274596le_alt @ (^[P3 : arrow_1429744205e_indi]: l) @ arrow_1951607831e_Prof))).
