% 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_154__5187408_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:16:17.776

% Could-be-implicit typings (26)
thf(ty_n_t__Set__Oset_I_062_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_M_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_J, type,
    set_Ar2014526681le_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_M_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_J, type,
    set_Ar1840689629le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_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_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_Ar517773211le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_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_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_Ar883249453le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_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_Mt__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Ar350387917le_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_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 (99)
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_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_OPi_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    pi_Arr1706749621le_alt : set_Ar182050865le_alt > (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt) > set_Ar2014526681le_alt).
thf(sy_c_FuncSet_OPi_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_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_Arr9039763le_alt : set_Ar182050865le_alt > (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar809243995le_alt) > set_Ar517773211le_alt).
thf(sy_c_FuncSet_OPi_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    pi_Arr1460089257le_alt : set_Ar182050865le_alt > (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar350387917le_alt).
thf(sy_c_FuncSet_OPi_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    pi_Arr2098764809le_alt : set_Ar182050865le_alt > (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_se2071012361le_alt) > set_Ar883249453le_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_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    pi_Arr582931725le_alt : set_Ar809243995le_alt > ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar182050865le_alt) > set_Ar1840689629le_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).
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% Relevant facts (249)
thf(fact_0_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_1_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_2_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_3_assms_I1_J, axiom,
    ((member183760530le_alt @ f @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))))). % assms(1)
thf(fact_4_linear__alt, axiom,
    ((?[L : set_Pr367596371le_alt]: (member1334244458le_alt @ L @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_5_const__Lin__Prof, axiom,
    ((![L2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member684274596le_alt @ (^[P : arrow_1429744205e_indi]: L2) @ arrow_1951607831e_Prof))))). % const_Lin_Prof
thf(fact_6_Pi__I, axiom,
    ((![A : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X2 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X2 @ A) => (member1334244458le_alt @ (F2 @ X2) @ (B @ X2)))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A @ B)))))). % Pi_I
thf(fact_7_Pi__I, axiom,
    ((![A : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B : produc16571293le_alt > set_Pr367596371le_alt]: ((![X2 : produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A) => (member2048039092le_alt @ (F2 @ X2) @ (B @ X2)))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A @ B)))))). % Pi_I
thf(fact_8_Pi__I, axiom,
    ((![A : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A) => (member2048039092le_alt @ (F2 @ X2) @ (B @ X2)))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A @ B)))))). % Pi_I
thf(fact_9_Pi__I, axiom,
    ((![A : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B : produc16571293le_alt > set_se2071012361le_alt]: ((![X2 : produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A) => (member1334244458le_alt @ (F2 @ X2) @ (B @ X2)))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A @ B)))))). % Pi_I
thf(fact_10_Pi__I, axiom,
    ((![A : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A) => (member1334244458le_alt @ (F2 @ X2) @ (B @ X2)))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A @ B)))))). % Pi_I
thf(fact_11_Pi__I, axiom,
    ((![A : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A) => (member2048039092le_alt @ (F2 @ X2) @ (B @ X2)))) => (member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A @ B)))))). % Pi_I
thf(fact_12_Pi__I, axiom,
    ((![A : set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B : produc16571293le_alt > set_Ar809243995le_alt]: ((![X2 : produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A) => (member684274596le_alt @ (F2 @ X2) @ (B @ X2)))) => (member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A @ B)))))). % Pi_I
thf(fact_13_Pi__I, axiom,
    ((![A : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A) => (member684274596le_alt @ (F2 @ X2) @ (B @ X2)))) => (member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A @ B)))))). % Pi_I
thf(fact_14_Pi__I, axiom,
    ((![A : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A) => (member1334244458le_alt @ (F2 @ X2) @ (B @ X2)))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A @ B)))))). % Pi_I
thf(fact_15_Pi__I, axiom,
    ((![A : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A) => (member684274596le_alt @ (F2 @ X2) @ (B @ X2)))) => (member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A @ B)))))). % Pi_I
thf(fact_16_dictatorI, axiom,
    ((![F3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I2 : arrow_1429744205e_indi]: ((member183760530le_alt @ F3 @ (pi_Arr479247969le_alt @ arrow_1951607831e_Prof @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: arrow_1848678355le_Lin))) => ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ arrow_1951607831e_Prof) => (![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: ((~ ((A2 = B2))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (X2 @ I2)) => (member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ (F3 @ X2))))))) => (arrow_960434986ctator @ F3 @ I2)))))). % dictatorI
thf(fact_17_funcsetI, axiom,
    ((![A : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B : set_se2071012361le_alt]: ((![X2 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X2 @ A) => (member1334244458le_alt @ (F2 @ X2) @ B))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A @ (^[Uu : arrow_1429744205e_indi]: B))))))). % funcsetI
thf(fact_18_funcsetI, axiom,
    ((![A : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B : set_Pr367596371le_alt]: ((![X2 : produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A) => (member2048039092le_alt @ (F2 @ X2) @ B))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A @ (^[Uu : produc16571293le_alt]: B))))))). % funcsetI
thf(fact_19_funcsetI, axiom,
    ((![A : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B : set_Pr367596371le_alt]: ((![X2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A) => (member2048039092le_alt @ (F2 @ X2) @ B))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A @ (^[Uu : set_Pr367596371le_alt]: B))))))). % funcsetI
thf(fact_20_funcsetI, axiom,
    ((![A : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B : set_se2071012361le_alt]: ((![X2 : produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A) => (member1334244458le_alt @ (F2 @ X2) @ B))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A @ (^[Uu : produc16571293le_alt]: B))))))). % funcsetI
thf(fact_21_funcsetI, axiom,
    ((![A : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B : set_se2071012361le_alt]: ((![X2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A) => (member1334244458le_alt @ (F2 @ X2) @ B))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A @ (^[Uu : set_Pr367596371le_alt]: B))))))). % funcsetI
thf(fact_22_funcsetI, axiom,
    ((![A : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B : set_Pr367596371le_alt]: ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A) => (member2048039092le_alt @ (F2 @ X2) @ B))) => (member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B))))))). % funcsetI
thf(fact_23_funcsetI, axiom,
    ((![A : set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B : set_Ar809243995le_alt]: ((![X2 : produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A) => (member684274596le_alt @ (F2 @ X2) @ B))) => (member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A @ (^[Uu : produc16571293le_alt]: B))))))). % funcsetI
thf(fact_24_funcsetI, axiom,
    ((![A : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B : set_Ar809243995le_alt]: ((![X2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A) => (member684274596le_alt @ (F2 @ X2) @ B))) => (member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A @ (^[Uu : set_Pr367596371le_alt]: B))))))). % funcsetI
thf(fact_25_funcsetI, axiom,
    ((![A : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B : set_se2071012361le_alt]: ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A) => (member1334244458le_alt @ (F2 @ X2) @ B))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B))))))). % funcsetI
thf(fact_26_funcsetI, axiom,
    ((![A : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B : set_Ar809243995le_alt]: ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A) => (member684274596le_alt @ (F2 @ X2) @ B))) => (member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B))))))). % funcsetI
thf(fact_27_funcset__id, axiom,
    ((![A : set_Ar182050865le_alt]: (member902395426le_alt @ (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: X) @ (pi_Arr1706749621le_alt @ A @ (^[Uu : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: A)))))). % funcset_id
thf(fact_28_funcset__mem, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A : set_Ar1007576579e_indi, B : set_se2071012361le_alt, X3 : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A @ (^[Uu : arrow_1429744205e_indi]: B))) => ((member1966420836e_indi @ X3 @ A) => (member1334244458le_alt @ (F2 @ X3) @ B)))))). % funcset_mem
thf(fact_29_funcset__mem, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A : set_Pr367596371le_alt, B : set_Pr367596371le_alt, X3 : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A @ (^[Uu : produc16571293le_alt]: B))) => ((member2048039092le_alt @ X3 @ A) => (member2048039092le_alt @ (F2 @ X3) @ B)))))). % funcset_mem
thf(fact_30_funcset__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A : set_se2071012361le_alt, B : set_Pr367596371le_alt, X3 : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A @ (^[Uu : set_Pr367596371le_alt]: B))) => ((member1334244458le_alt @ X3 @ A) => (member2048039092le_alt @ (F2 @ X3) @ B)))))). % funcset_mem
thf(fact_31_funcset__mem, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A : set_Pr367596371le_alt, B : set_se2071012361le_alt, X3 : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A @ (^[Uu : produc16571293le_alt]: B))) => ((member2048039092le_alt @ X3 @ A) => (member1334244458le_alt @ (F2 @ X3) @ B)))))). % funcset_mem
thf(fact_32_funcset__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A : set_se2071012361le_alt, B : set_se2071012361le_alt, X3 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A @ (^[Uu : set_Pr367596371le_alt]: B))) => ((member1334244458le_alt @ X3 @ A) => (member1334244458le_alt @ (F2 @ X3) @ B)))))). % funcset_mem
thf(fact_33_funcset__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A : set_Ar809243995le_alt, B : set_Pr367596371le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B))) => ((member684274596le_alt @ X3 @ A) => (member2048039092le_alt @ (F2 @ X3) @ B)))))). % funcset_mem
thf(fact_34_funcset__mem, axiom,
    ((![F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A : set_Pr367596371le_alt, B : set_Ar809243995le_alt, X3 : produc16571293le_alt]: ((member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A @ (^[Uu : produc16571293le_alt]: B))) => ((member2048039092le_alt @ X3 @ A) => (member684274596le_alt @ (F2 @ X3) @ B)))))). % funcset_mem
thf(fact_35_funcset__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A : set_se2071012361le_alt, B : set_Ar809243995le_alt, X3 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A @ (^[Uu : set_Pr367596371le_alt]: B))) => ((member1334244458le_alt @ X3 @ A) => (member684274596le_alt @ (F2 @ X3) @ B)))))). % funcset_mem
thf(fact_36_funcset__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A : set_Ar809243995le_alt, B : set_se2071012361le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B))) => ((member684274596le_alt @ X3 @ A) => (member1334244458le_alt @ (F2 @ X3) @ B)))))). % funcset_mem
thf(fact_37_funcset__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A : set_Ar809243995le_alt, B : set_Ar809243995le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: B))) => ((member684274596le_alt @ X3 @ A) => (member684274596le_alt @ (F2 @ X3) @ B)))))). % funcset_mem
thf(fact_38_above__Lin, axiom,
    ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt]: ((~ ((X3 = Y))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L2 @ X3 @ Y) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_39_below__Lin, axiom,
    ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt]: ((~ ((X3 = Y))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L2 @ X3 @ Y) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_40_mkbot__Lin, axiom,
    ((![L2 : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L2 @ X3) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_41_mktop__Lin, axiom,
    ((![L2 : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L2 @ X3) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_42_PiE, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A : set_Ar1007576579e_indi, B : arrow_1429744205e_indi > set_se2071012361le_alt, X3 : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A @ B)) => ((~ ((member1334244458le_alt @ (F2 @ X3) @ (B @ X3)))) => (~ ((member1966420836e_indi @ X3 @ A)))))))). % PiE
thf(fact_43_PiE, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A : set_Pr367596371le_alt, B : produc16571293le_alt > set_Pr367596371le_alt, X3 : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A @ B)) => ((~ ((member2048039092le_alt @ (F2 @ X3) @ (B @ X3)))) => (~ ((member2048039092le_alt @ X3 @ A)))))))). % PiE
thf(fact_44_PiE, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A : set_Pr367596371le_alt, B : produc16571293le_alt > set_se2071012361le_alt, X3 : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A @ B)) => ((~ ((member1334244458le_alt @ (F2 @ X3) @ (B @ X3)))) => (~ ((member2048039092le_alt @ X3 @ A)))))))). % PiE
thf(fact_45_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A : set_se2071012361le_alt, B : set_Pr367596371le_alt > set_Pr367596371le_alt, X3 : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A @ B)) => ((~ ((member2048039092le_alt @ (F2 @ X3) @ (B @ X3)))) => (~ ((member1334244458le_alt @ X3 @ A)))))))). % PiE
thf(fact_46_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A : set_se2071012361le_alt, B : set_Pr367596371le_alt > set_se2071012361le_alt, X3 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A @ B)) => ((~ ((member1334244458le_alt @ (F2 @ X3) @ (B @ X3)))) => (~ ((member1334244458le_alt @ X3 @ A)))))))). % PiE
thf(fact_47_PiE, axiom,
    ((![F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A : set_Pr367596371le_alt, B : produc16571293le_alt > set_Ar809243995le_alt, X3 : produc16571293le_alt]: ((member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A @ B)) => ((~ ((member684274596le_alt @ (F2 @ X3) @ (B @ X3)))) => (~ ((member2048039092le_alt @ X3 @ A)))))))). % PiE
thf(fact_48_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A : set_Ar809243995le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A @ B)) => ((~ ((member2048039092le_alt @ (F2 @ X3) @ (B @ X3)))) => (~ ((member684274596le_alt @ X3 @ A)))))))). % PiE
thf(fact_49_PiE, axiom,
    ((![F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A : set_se2071012361le_alt, B : set_Pr367596371le_alt > set_Ar809243995le_alt, X3 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A @ B)) => ((~ ((member684274596le_alt @ (F2 @ X3) @ (B @ X3)))) => (~ ((member1334244458le_alt @ X3 @ A)))))))). % PiE
thf(fact_50_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A : set_Ar809243995le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A @ B)) => ((~ ((member1334244458le_alt @ (F2 @ X3) @ (B @ X3)))) => (~ ((member684274596le_alt @ X3 @ A)))))))). % PiE
thf(fact_51_PiE, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A : set_Ar809243995le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A @ B)) => ((~ ((member684274596le_alt @ (F2 @ X3) @ (B @ X3)))) => (~ ((member684274596le_alt @ X3 @ A)))))))). % PiE
thf(fact_52_Pi__I_H, axiom,
    ((![A : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![X2 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X2 @ A) => (member1334244458le_alt @ (F2 @ X2) @ (B @ X2)))) => (member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A @ B)))))). % Pi_I'
thf(fact_53_Pi__I_H, axiom,
    ((![A : set_Pr367596371le_alt, F2 : produc16571293le_alt > produc16571293le_alt, B : produc16571293le_alt > set_Pr367596371le_alt]: ((![X2 : produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A) => (member2048039092le_alt @ (F2 @ X2) @ (B @ X2)))) => (member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A @ B)))))). % Pi_I'
thf(fact_54_Pi__I_H, axiom,
    ((![A : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > produc16571293le_alt, B : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((![X2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A) => (member2048039092le_alt @ (F2 @ X2) @ (B @ X2)))) => (member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A @ B)))))). % Pi_I'
thf(fact_55_Pi__I_H, axiom,
    ((![A : set_Pr367596371le_alt, F2 : produc16571293le_alt > set_Pr367596371le_alt, B : produc16571293le_alt > set_se2071012361le_alt]: ((![X2 : produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A) => (member1334244458le_alt @ (F2 @ X2) @ (B @ X2)))) => (member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A @ B)))))). % Pi_I'
thf(fact_56_Pi__I_H, axiom,
    ((![A : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, B : set_Pr367596371le_alt > set_se2071012361le_alt]: ((![X2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A) => (member1334244458le_alt @ (F2 @ X2) @ (B @ X2)))) => (member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A @ B)))))). % Pi_I'
thf(fact_57_Pi__I_H, axiom,
    ((![A : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A) => (member2048039092le_alt @ (F2 @ X2) @ (B @ X2)))) => (member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A @ B)))))). % Pi_I'
thf(fact_58_Pi__I_H, axiom,
    ((![A : set_Pr367596371le_alt, F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B : produc16571293le_alt > set_Ar809243995le_alt]: ((![X2 : produc16571293le_alt]: ((member2048039092le_alt @ X2 @ A) => (member684274596le_alt @ (F2 @ X2) @ (B @ X2)))) => (member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A @ B)))))). % Pi_I'
thf(fact_59_Pi__I_H, axiom,
    ((![A : set_se2071012361le_alt, F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, B : set_Pr367596371le_alt > set_Ar809243995le_alt]: ((![X2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ A) => (member684274596le_alt @ (F2 @ X2) @ (B @ X2)))) => (member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A @ B)))))). % Pi_I'
thf(fact_60_Pi__I_H, axiom,
    ((![A : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A) => (member1334244458le_alt @ (F2 @ X2) @ (B @ X2)))) => (member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A @ B)))))). % Pi_I'
thf(fact_61_Pi__I_H, axiom,
    ((![A : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ X2 @ A) => (member684274596le_alt @ (F2 @ X2) @ (B @ X2)))) => (member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A @ B)))))). % Pi_I'
thf(fact_62_in__mktop, axiom,
    ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ (arrow_992294841_mktop @ L2 @ Z)) = (((~ ((X3 = Z)))) & ((((((Y = Z)) => ((~ ((X3 = Y)))))) & ((((~ ((Y = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ L2))))))))))). % in_mktop
thf(fact_63_in__mkbot, axiom,
    ((![X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ (arrow_843587755_mkbot @ L2 @ Z)) = (((~ ((Y = Z)))) & ((((((X3 = Z)) => ((~ ((X3 = Y)))))) & ((((~ ((X3 = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ L2))))))))))). % in_mkbot
thf(fact_64_in__below, axiom,
    ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A3 = B3))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ (arrow_887341619_below @ L2 @ A3 @ B3)) = (((~ ((X3 = Y)))) & ((((((Y = A3)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ B3) @ L2)))) & ((((~ ((Y = A3)))) => ((((((X3 = A3)) => ((((Y = B3)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B3 @ Y) @ L2)))))) & ((((~ ((X3 = A3)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ L2))))))))))))))))). % in_below
thf(fact_65_in__above, axiom,
    ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A3 = B3))) => ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ (arrow_1726226719_above @ L2 @ A3 @ B3)) = (((~ ((X3 = Y)))) & ((((((X3 = B3)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ Y) @ L2)))) & ((((~ ((X3 = B3)))) => ((((((Y = B3)) => ((((X3 = A3)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ A3) @ L2)))))) & ((((~ ((Y = B3)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ L2))))))))))))))))). % in_above
thf(fact_66_notin__Lin__iff, axiom,
    ((![L2 : set_Pr367596371le_alt, X3 : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((~ ((X3 = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ L2))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X3) @ L2))))))). % notin_Lin_iff
thf(fact_67_complete__Lin, axiom,
    ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((~ ((A3 = B3))) => (?[X2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X2 @ arrow_1848678355le_Lin) & (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ X2))))))). % complete_Lin
thf(fact_68_Lin__irrefl, axiom,
    ((![L2 : set_Pr367596371le_alt, A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((member1334244458le_alt @ L2 @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ L2) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B3 @ A3) @ L2)))))))). % Lin_irrefl
thf(fact_69_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)) => ((![A4 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ X))))))))))))). % unanimity_def
thf(fact_70_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)) => ((![A4 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (Y2 @ I))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ X)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ Y2))))))))))))))))). % IIA_def
thf(fact_71_Pi__cong, axiom,
    ((![A : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, G : arrow_1429744205e_indi > set_Pr367596371le_alt, B : arrow_1429744205e_indi > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi]: ((member1966420836e_indi @ W @ A) => ((F2 @ W) = (G @ W)))) => ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A @ B)) = (member684274596le_alt @ G @ (pi_Arr1981691447le_alt @ A @ B))))))). % Pi_cong
thf(fact_72_Pi__cong, axiom,
    ((![A : set_Ar182050865le_alt, F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, G : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, B : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((![W : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ W @ A) => ((F2 @ W) = (G @ W)))) => ((member2001237014le_alt @ F2 @ (pi_Arr1460089257le_alt @ A @ B)) = (member2001237014le_alt @ G @ (pi_Arr1460089257le_alt @ A @ B))))))). % Pi_cong
thf(fact_73_Pi__cong, axiom,
    ((![A : set_Ar182050865le_alt, F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt, B : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![W : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ W @ A) => ((F2 @ W) = (G @ W)))) => ((member966567542le_alt @ F2 @ (pi_Arr2098764809le_alt @ A @ B)) = (member966567542le_alt @ G @ (pi_Arr2098764809le_alt @ A @ B))))))). % Pi_cong
thf(fact_74_Pi__cong, axiom,
    ((![A : set_Ar182050865le_alt, F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, G : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, B : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((![W : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ W @ A) => ((F2 @ W) = (G @ W)))) => ((member1567880444le_alt @ F2 @ (pi_Arr9039763le_alt @ A @ B)) = (member1567880444le_alt @ G @ (pi_Arr9039763le_alt @ A @ B))))))). % Pi_cong
thf(fact_75_Pi__cong, axiom,
    ((![A : set_Ar182050865le_alt, F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt]: ((![W : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member183760530le_alt @ W @ A) => ((F2 @ W) = (G @ W)))) => ((member902395426le_alt @ F2 @ (pi_Arr1706749621le_alt @ A @ B)) = (member902395426le_alt @ G @ (pi_Arr1706749621le_alt @ A @ B))))))). % Pi_cong
thf(fact_76_Pi__cong, axiom,
    ((![A : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((![W : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ W @ A) => ((F2 @ W) = (G @ W)))) => ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A @ B)) = (member183760530le_alt @ G @ (pi_Arr479247969le_alt @ A @ B))))))). % Pi_cong
thf(fact_77_Pi__cong, axiom,
    ((![A : set_Ar809243995le_alt, F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, G : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar182050865le_alt]: ((![W : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member684274596le_alt @ W @ A) => ((F2 @ W) = (G @ W)))) => ((member65769534le_alt @ F2 @ (pi_Arr582931725le_alt @ A @ B)) = (member65769534le_alt @ G @ (pi_Arr582931725le_alt @ A @ B))))))). % Pi_cong
thf(fact_78_Pi__mem, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, A : set_Ar1007576579e_indi, B : arrow_1429744205e_indi > set_se2071012361le_alt, X3 : arrow_1429744205e_indi]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ A @ B)) => ((member1966420836e_indi @ X3 @ A) => (member1334244458le_alt @ (F2 @ X3) @ (B @ X3))))))). % Pi_mem
thf(fact_79_Pi__mem, axiom,
    ((![F2 : produc16571293le_alt > produc16571293le_alt, A : set_Pr367596371le_alt, B : produc16571293le_alt > set_Pr367596371le_alt, X3 : produc16571293le_alt]: ((member1154116596le_alt @ F2 @ (pi_Pro1847889543le_alt @ A @ B)) => ((member2048039092le_alt @ X3 @ A) => (member2048039092le_alt @ (F2 @ X3) @ (B @ X3))))))). % Pi_mem
thf(fact_80_Pi__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > produc16571293le_alt, A : set_se2071012361le_alt, B : set_Pr367596371le_alt > set_Pr367596371le_alt, X3 : set_Pr367596371le_alt]: ((member594528958le_alt @ F2 @ (pi_set365323601le_alt @ A @ B)) => ((member1334244458le_alt @ X3 @ A) => (member2048039092le_alt @ (F2 @ X3) @ (B @ X3))))))). % Pi_mem
thf(fact_81_Pi__mem, axiom,
    ((![F2 : produc16571293le_alt > set_Pr367596371le_alt, A : set_Pr367596371le_alt, B : produc16571293le_alt > set_se2071012361le_alt, X3 : produc16571293le_alt]: ((member1038100052le_alt @ F2 @ (pi_Pro1122205927le_alt @ A @ B)) => ((member2048039092le_alt @ X3 @ A) => (member1334244458le_alt @ (F2 @ X3) @ (B @ X3))))))). % Pi_mem
thf(fact_82_Pi__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > set_Pr367596371le_alt, A : set_se2071012361le_alt, B : set_Pr367596371le_alt > set_se2071012361le_alt, X3 : set_Pr367596371le_alt]: ((member1775590686le_alt @ F2 @ (pi_set1240805297le_alt @ A @ B)) => ((member1334244458le_alt @ X3 @ A) => (member1334244458le_alt @ (F2 @ X3) @ (B @ X3))))))). % Pi_mem
thf(fact_83_Pi__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > produc16571293le_alt, A : set_Ar809243995le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member361641010le_alt @ F2 @ (pi_Arr1114944513le_alt @ A @ B)) => ((member684274596le_alt @ X3 @ A) => (member2048039092le_alt @ (F2 @ X3) @ (B @ X3))))))). % Pi_mem
thf(fact_84_Pi__mem, axiom,
    ((![F2 : produc16571293le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A : set_Pr367596371le_alt, B : produc16571293le_alt > set_Ar809243995le_alt, X3 : produc16571293le_alt]: ((member167063198le_alt @ F2 @ (pi_Pro1164444725le_alt @ A @ B)) => ((member2048039092le_alt @ X3 @ A) => (member684274596le_alt @ (F2 @ X3) @ (B @ X3))))))). % Pi_mem
thf(fact_85_Pi__mem, axiom,
    ((![F2 : set_Pr367596371le_alt > arrow_1429744205e_indi > set_Pr367596371le_alt, A : set_se2071012361le_alt, B : set_Pr367596371le_alt > set_Ar809243995le_alt, X3 : set_Pr367596371le_alt]: ((member1117110356le_alt @ F2 @ (pi_set1343364587le_alt @ A @ B)) => ((member1334244458le_alt @ X3 @ A) => (member684274596le_alt @ (F2 @ X3) @ (B @ X3))))))). % Pi_mem
thf(fact_86_Pi__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, A : set_Ar809243995le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ A @ B)) => ((member684274596le_alt @ X3 @ A) => (member1334244458le_alt @ (F2 @ X3) @ (B @ X3))))))). % Pi_mem
thf(fact_87_Pi__mem, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, A : set_Ar809243995le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt, X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((member896258016le_alt @ F2 @ (pi_Arr1849985851le_alt @ A @ B)) => ((member684274596le_alt @ X3 @ A) => (member684274596le_alt @ (F2 @ X3) @ (B @ X3))))))). % Pi_mem
thf(fact_88_Pi__iff, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : set_Ar809243995le_alt, X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member183760530le_alt @ F2 @ (pi_Arr479247969le_alt @ I3 @ X4)) = (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ I3)) => ((member1334244458le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_89_Pi__iff, axiom,
    ((![F2 : arrow_1429744205e_indi > set_Pr367596371le_alt, I3 : set_Ar1007576579e_indi, X4 : arrow_1429744205e_indi > set_se2071012361le_alt]: ((member684274596le_alt @ F2 @ (pi_Arr1981691447le_alt @ I3 @ X4)) = (![X : arrow_1429744205e_indi]: (((member1966420836e_indi @ X @ I3)) => ((member1334244458le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_90_Pi__iff, axiom,
    ((![F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : set_Ar809243995le_alt, X4 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar182050865le_alt]: ((member65769534le_alt @ F2 @ (pi_Arr582931725le_alt @ I3 @ X4)) = (![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ I3)) => ((member183760530le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_91_Pi__iff, axiom,
    ((![F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, I3 : set_Ar182050865le_alt, X4 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((member2001237014le_alt @ F2 @ (pi_Arr1460089257le_alt @ I3 @ X4)) = (![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ I3)) => ((member2048039092le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_92_Pi__iff, axiom,
    ((![F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : set_Ar182050865le_alt, X4 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((member966567542le_alt @ F2 @ (pi_Arr2098764809le_alt @ I3 @ X4)) = (![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ I3)) => ((member1334244458le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_93_Pi__iff, axiom,
    ((![F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, I3 : set_Ar182050865le_alt, X4 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((member1567880444le_alt @ F2 @ (pi_Arr9039763le_alt @ I3 @ X4)) = (![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ I3)) => ((member684274596le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_94_Pi__iff, axiom,
    ((![F2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, I3 : set_Ar182050865le_alt, X4 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt]: ((member902395426le_alt @ F2 @ (pi_Arr1706749621le_alt @ I3 @ X4)) = (![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ I3)) => ((member183760530le_alt @ (F2 @ X) @ (X4 @ X))))))))). % Pi_iff
thf(fact_95_old_Oprod_Oinject, axiom,
    ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, A5 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A3 @ B3) = (produc1494124311le_alt @ A5 @ B5)) = (((A3 = A5)) & ((B3 = B5))))))). % old.prod.inject
thf(fact_96_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_97_pred__equals__eq2, axiom,
    ((![R : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: (((^[X : arrow_1857593510le_alt]: (^[Y2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ R))) = (^[X : arrow_1857593510le_alt]: (^[Y2 : arrow_1857593510le_alt]: (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y2) @ S)))) = (R = S))))). % pred_equals_eq2
thf(fact_98_Prof__def, axiom,
    ((arrow_1951607831e_Prof = (pi_Arr1981691447le_alt @ top_to1799531699e_indi @ (^[Uu : arrow_1429744205e_indi]: arrow_1848678355le_Lin))))). % Prof_def
thf(fact_99_ssubst__Pair__rhs, axiom,
    ((![R2 : arrow_1857593510le_alt, S2 : arrow_1857593510le_alt, R : set_Pr367596371le_alt, S3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R2 @ S2) @ R) => ((S3 = S2) => (member2048039092le_alt @ (produc1494124311le_alt @ R2 @ S3) @ R)))))). % ssubst_Pair_rhs
thf(fact_100_old_Oprod_Oinducts, axiom,
    ((![P2 : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A2 @ B2))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_101_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A2 @ B2)))))))))). % old.prod.exhaust
thf(fact_102_Pi__UNIV, axiom,
    ((![A : set_Ar809243995le_alt]: ((pi_Arr479247969le_alt @ A @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: top_to469035705le_alt)) = top_to803745505le_alt)))). % Pi_UNIV
thf(fact_103_Pi__UNIV, axiom,
    ((![A : set_Ar1007576579e_indi]: ((pi_Arr1981691447le_alt @ A @ (^[Uu : arrow_1429744205e_indi]: top_to469035705le_alt)) = top_to685525675le_alt)))). % Pi_UNIV
thf(fact_104_Pi__UNIV, axiom,
    ((![A : set_Ar809243995le_alt]: ((pi_Arr582931725le_alt @ A @ (^[Uu : arrow_1429744205e_indi > set_Pr367596371le_alt]: top_to803745505le_alt)) = top_to1138460813le_alt)))). % Pi_UNIV
thf(fact_105_Pi__UNIV, axiom,
    ((![A : set_Ar182050865le_alt]: ((pi_Arr1460089257le_alt @ A @ (^[Uu : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: top_to224369155le_alt)) = top_to1430252573le_alt)))). % Pi_UNIV
thf(fact_106_Pi__UNIV, axiom,
    ((![A : set_Ar182050865le_alt]: ((pi_Arr2098764809le_alt @ A @ (^[Uu : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: top_to469035705le_alt)) = top_to1646624381le_alt)))). % Pi_UNIV
thf(fact_107_Pi__UNIV, axiom,
    ((![A : set_Ar182050865le_alt]: ((pi_Arr9039763le_alt @ A @ (^[Uu : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: top_to685525675le_alt)) = top_to1963028043le_alt)))). % Pi_UNIV
thf(fact_108_Pi__UNIV, axiom,
    ((![A : set_Ar182050865le_alt]: ((pi_Arr1706749621le_alt @ A @ (^[Uu : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: top_to803745505le_alt)) = top_to1977016873le_alt)))). % Pi_UNIV
thf(fact_109_surj__pair, axiom,
    ((![P3 : produc16571293le_alt]: (?[X2 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P3 = (produc1494124311le_alt @ X2 @ Y3)))))). % surj_pair
thf(fact_110_prod__cases, axiom,
    ((![P2 : produc16571293le_alt > $o, P3 : produc16571293le_alt]: ((![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A2 @ B2))) => (P2 @ P3))))). % prod_cases
thf(fact_111_Pair__inject, axiom,
    ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, A5 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A3 @ B3) = (produc1494124311le_alt @ A5 @ B5)) => (~ (((A3 = A5) => (~ ((B3 = B5)))))))))). % Pair_inject
thf(fact_112_mem__Collect__eq, axiom,
    ((![A3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member183760530le_alt @ A3 @ (collec1382217680le_alt @ P2)) = (P2 @ A3))))). % mem_Collect_eq
thf(fact_113_mem__Collect__eq, axiom,
    ((![A3 : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ A3 @ (collec1559089382le_alt @ P2)) = (P2 @ A3))))). % mem_Collect_eq
thf(fact_114_mem__Collect__eq, axiom,
    ((![A3 : produc16571293le_alt, P2 : produc16571293le_alt > $o]: ((member2048039092le_alt @ A3 @ (collec531981554le_alt @ P2)) = (P2 @ A3))))). % mem_Collect_eq
thf(fact_115_mem__Collect__eq, axiom,
    ((![A3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member65769534le_alt @ A3 @ (collec1633828476le_alt @ P2)) = (P2 @ A3))))). % mem_Collect_eq
thf(fact_116_mem__Collect__eq, axiom,
    ((![A3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt, P2 : (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt) > $o]: ((member2001237014le_alt @ A3 @ (collec1890909272le_alt @ P2)) = (P2 @ A3))))). % mem_Collect_eq
thf(fact_117_mem__Collect__eq, axiom,
    ((![A3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt, P2 : (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member966567542le_alt @ A3 @ (collec1765222072le_alt @ P2)) = (P2 @ A3))))). % mem_Collect_eq
thf(fact_118_mem__Collect__eq, axiom,
    ((![A3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member1567880444le_alt @ A3 @ (collec988455738le_alt @ P2)) = (P2 @ A3))))). % mem_Collect_eq
thf(fact_119_mem__Collect__eq, axiom,
    ((![A3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt, P2 : (((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o]: ((member902395426le_alt @ A3 @ (collec1942128996le_alt @ P2)) = (P2 @ A3))))). % mem_Collect_eq
thf(fact_120_mem__Collect__eq, axiom,
    ((![A3 : set_Pr367596371le_alt, P2 : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A3 @ (collec1399441576le_alt @ P2)) = (P2 @ A3))))). % mem_Collect_eq
thf(fact_121_Collect__mem__eq, axiom,
    ((![A : set_Ar182050865le_alt]: ((collec1382217680le_alt @ (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ A))) = A)))). % Collect_mem_eq
thf(fact_122_Collect__mem__eq, axiom,
    ((![A : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ A))) = A)))). % Collect_mem_eq
thf(fact_123_Collect__mem__eq, axiom,
    ((![A : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ A))) = A)))). % Collect_mem_eq
thf(fact_124_Collect__mem__eq, axiom,
    ((![A : set_Ar1840689629le_alt]: ((collec1633828476le_alt @ (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member65769534le_alt @ X @ A))) = A)))). % Collect_mem_eq
thf(fact_125_Collect__mem__eq, axiom,
    ((![A : set_Ar350387917le_alt]: ((collec1890909272le_alt @ (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X @ A))) = A)))). % Collect_mem_eq
thf(fact_126_Collect__mem__eq, axiom,
    ((![A : set_Ar883249453le_alt]: ((collec1765222072le_alt @ (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X @ A))) = A)))). % Collect_mem_eq
thf(fact_127_Collect__mem__eq, axiom,
    ((![A : set_Ar517773211le_alt]: ((collec988455738le_alt @ (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: (member1567880444le_alt @ X @ A))) = A)))). % Collect_mem_eq
thf(fact_128_Collect__mem__eq, axiom,
    ((![A : set_Ar2014526681le_alt]: ((collec1942128996le_alt @ (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member902395426le_alt @ X @ A))) = A)))). % Collect_mem_eq
thf(fact_129_Collect__mem__eq, axiom,
    ((![A : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ A))) = A)))). % Collect_mem_eq
thf(fact_130_Collect__cong, axiom,
    ((![P2 : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((![X2 : set_Pr367596371le_alt]: ((P2 @ X2) = (Q @ X2))) => ((collec1399441576le_alt @ P2) = (collec1399441576le_alt @ Q)))))). % Collect_cong
thf(fact_131_UNIV__I, axiom,
    ((![X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ top_to1799531699e_indi)))). % UNIV_I
thf(fact_132_UNIV__I, axiom,
    ((![X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ top_to958727510le_alt)))). % UNIV_I
thf(fact_133_UNIV__I, axiom,
    ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_I
thf(fact_134_UNIV__I, axiom,
    ((![X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_I
thf(fact_135_UNIV__I, axiom,
    ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ top_to685525675le_alt)))). % UNIV_I
thf(fact_136_UNIV__I, axiom,
    ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X3 @ top_to803745505le_alt)))). % UNIV_I
thf(fact_137_UNIV__I, axiom,
    ((![X3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X3 @ top_to1430252573le_alt)))). % UNIV_I
thf(fact_138_UNIV__I, axiom,
    ((![X3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X3 @ top_to1646624381le_alt)))). % UNIV_I
thf(fact_139_UNIV__I, axiom,
    ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member65769534le_alt @ X3 @ top_to1138460813le_alt)))). % UNIV_I
thf(fact_140_UNIV__I, axiom,
    ((![X3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: (member1567880444le_alt @ X3 @ top_to1963028043le_alt)))). % UNIV_I
thf(fact_141_iso__tuple__UNIV__I, axiom,
    ((![X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ top_to1799531699e_indi)))). % iso_tuple_UNIV_I
thf(fact_142_iso__tuple__UNIV__I, axiom,
    ((![X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ top_to958727510le_alt)))). % iso_tuple_UNIV_I
thf(fact_143_iso__tuple__UNIV__I, axiom,
    ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_144_iso__tuple__UNIV__I, axiom,
    ((![X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_145_iso__tuple__UNIV__I, axiom,
    ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ top_to685525675le_alt)))). % iso_tuple_UNIV_I
thf(fact_146_iso__tuple__UNIV__I, axiom,
    ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X3 @ top_to803745505le_alt)))). % iso_tuple_UNIV_I
thf(fact_147_iso__tuple__UNIV__I, axiom,
    ((![X3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X3 @ top_to1430252573le_alt)))). % iso_tuple_UNIV_I
thf(fact_148_iso__tuple__UNIV__I, axiom,
    ((![X3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X3 @ top_to1646624381le_alt)))). % iso_tuple_UNIV_I
thf(fact_149_iso__tuple__UNIV__I, axiom,
    ((![X3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member65769534le_alt @ X3 @ top_to1138460813le_alt)))). % iso_tuple_UNIV_I
thf(fact_150_iso__tuple__UNIV__I, axiom,
    ((![X3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: (member1567880444le_alt @ X3 @ top_to1963028043le_alt)))). % iso_tuple_UNIV_I
thf(fact_151_UNIV__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: $true))))). % UNIV_def
thf(fact_152_UNIV__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ (^[X : arrow_1429744205e_indi]: $true))))). % UNIV_def
thf(fact_153_UNIV__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: $true))))). % UNIV_def
thf(fact_154_UNIV__eq__I, axiom,
    ((![A : set_Ar1007576579e_indi]: ((![X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ A)) => (top_to1799531699e_indi = A))))). % UNIV_eq_I
thf(fact_155_UNIV__eq__I, axiom,
    ((![A : set_Ar1665529862le_alt]: ((![X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ A)) => (top_to958727510le_alt = A))))). % UNIV_eq_I
thf(fact_156_UNIV__eq__I, axiom,
    ((![A : set_Pr367596371le_alt]: ((![X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ A)) => (top_to224369155le_alt = A))))). % UNIV_eq_I
thf(fact_157_UNIV__eq__I, axiom,
    ((![A : set_se2071012361le_alt]: ((![X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ A)) => (top_to469035705le_alt = A))))). % UNIV_eq_I
thf(fact_158_UNIV__eq__I, axiom,
    ((![A : set_Ar809243995le_alt]: ((![X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ A)) => (top_to685525675le_alt = A))))). % UNIV_eq_I
thf(fact_159_UNIV__eq__I, axiom,
    ((![A : set_Ar182050865le_alt]: ((![X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X2 @ A)) => (top_to803745505le_alt = A))))). % UNIV_eq_I
thf(fact_160_UNIV__eq__I, axiom,
    ((![A : set_Ar350387917le_alt]: ((![X2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X2 @ A)) => (top_to1430252573le_alt = A))))). % UNIV_eq_I
thf(fact_161_UNIV__eq__I, axiom,
    ((![A : set_Ar883249453le_alt]: ((![X2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X2 @ A)) => (top_to1646624381le_alt = A))))). % UNIV_eq_I
thf(fact_162_UNIV__eq__I, axiom,
    ((![A : set_Ar1840689629le_alt]: ((![X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member65769534le_alt @ X2 @ A)) => (top_to1138460813le_alt = A))))). % UNIV_eq_I
thf(fact_163_UNIV__eq__I, axiom,
    ((![A : set_Ar517773211le_alt]: ((![X2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: (member1567880444le_alt @ X2 @ A)) => (top_to1963028043le_alt = A))))). % UNIV_eq_I
thf(fact_164_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_165_top__set__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ top_to1900088076_alt_o)))). % top_set_def
thf(fact_166_top__set__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ top_to1473733010indi_o)))). % top_set_def
thf(fact_167_top__set__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ top_to516240647_alt_o)))). % top_set_def
thf(fact_168_top__empty__eq, axiom,
    ((top_to1473733010indi_o = (^[X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi))))). % top_empty_eq
thf(fact_169_top__empty__eq, axiom,
    ((top_to516240647_alt_o = (^[X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ top_to958727510le_alt))))). % top_empty_eq
thf(fact_170_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_171_top__empty__eq, axiom,
    ((top_to1900088076_alt_o = (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt))))). % top_empty_eq
thf(fact_172_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_173_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_174_top__empty__eq, axiom,
    ((top_to369610496_alt_o = (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X @ top_to1430252573le_alt))))). % top_empty_eq
thf(fact_175_top__empty__eq, axiom,
    ((top_to491816096_alt_o = (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X @ top_to1646624381le_alt))))). % top_empty_eq
thf(fact_176_top__empty__eq, axiom,
    ((top_to1742467640_alt_o = (^[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member65769534le_alt @ X @ top_to1138460813le_alt))))). % top_empty_eq
thf(fact_177_top__empty__eq, axiom,
    ((top_to753170938_alt_o = (^[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: (member1567880444le_alt @ X @ top_to1963028043le_alt))))). % top_empty_eq
thf(fact_178_UNIV__witness, axiom,
    ((?[X2 : arrow_1429744205e_indi]: (member1966420836e_indi @ X2 @ top_to1799531699e_indi)))). % UNIV_witness
thf(fact_179_UNIV__witness, axiom,
    ((?[X2 : arrow_1857593510le_alt]: (member519365071le_alt @ X2 @ top_to958727510le_alt)))). % UNIV_witness
thf(fact_180_UNIV__witness, axiom,
    ((?[X2 : produc16571293le_alt]: (member2048039092le_alt @ X2 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_181_UNIV__witness, axiom,
    ((?[X2 : set_Pr367596371le_alt]: (member1334244458le_alt @ X2 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_182_UNIV__witness, axiom,
    ((?[X2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X2 @ top_to685525675le_alt)))). % UNIV_witness
thf(fact_183_UNIV__witness, axiom,
    ((?[X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X2 @ top_to803745505le_alt)))). % UNIV_witness
thf(fact_184_UNIV__witness, axiom,
    ((?[X2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X2 @ top_to1430252573le_alt)))). % UNIV_witness
thf(fact_185_UNIV__witness, axiom,
    ((?[X2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X2 @ top_to1646624381le_alt)))). % UNIV_witness
thf(fact_186_UNIV__witness, axiom,
    ((?[X2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member65769534le_alt @ X2 @ top_to1138460813le_alt)))). % UNIV_witness
thf(fact_187_UNIV__witness, axiom,
    ((?[X2 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: (member1567880444le_alt @ X2 @ top_to1963028043le_alt)))). % UNIV_witness
thf(fact_188_Lin__def, axiom,
    ((arrow_1848678355le_Lin = (collec1399441576le_alt @ (order_257197092le_alt @ top_to958727510le_alt))))). % Lin_def
thf(fact_189_Pi__empty, axiom,
    ((![B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((pi_Arr479247969le_alt @ bot_bo365569479le_alt @ B) = top_to803745505le_alt)))). % Pi_empty
thf(fact_190_Pi__empty, axiom,
    ((![B : arrow_1429744205e_indi > set_se2071012361le_alt]: ((pi_Arr1981691447le_alt @ bot_bo1390904983e_indi @ B) = top_to685525675le_alt)))). % Pi_empty
thf(fact_191_Pi__empty, axiom,
    ((![B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar182050865le_alt]: ((pi_Arr582931725le_alt @ bot_bo365569479le_alt @ B) = top_to1138460813le_alt)))). % Pi_empty
thf(fact_192_Pi__empty, axiom,
    ((![B : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: ((pi_Arr1460089257le_alt @ bot_bo13098693le_alt @ B) = top_to1430252573le_alt)))). % Pi_empty
thf(fact_193_Pi__empty, axiom,
    ((![B : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_se2071012361le_alt]: ((pi_Arr2098764809le_alt @ bot_bo13098693le_alt @ B) = top_to1646624381le_alt)))). % Pi_empty
thf(fact_194_Pi__empty, axiom,
    ((![B : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar809243995le_alt]: ((pi_Arr9039763le_alt @ bot_bo13098693le_alt @ B) = top_to1963028043le_alt)))). % Pi_empty
thf(fact_195_Pi__empty, axiom,
    ((![B : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt]: ((pi_Arr1706749621le_alt @ bot_bo13098693le_alt @ B) = top_to1977016873le_alt)))). % Pi_empty
thf(fact_196_PiE__UNIV, axiom,
    (((piE_Ar738911586e_indi @ top_to1799531699e_indi @ (^[I : arrow_1429744205e_indi]: top_to1799531699e_indi)) = top_to498310661e_indi))). % PiE_UNIV
thf(fact_197_PiE__UNIV, axiom,
    (((piE_Ar1084018769le_alt @ top_to1799531699e_indi @ (^[I : arrow_1429744205e_indi]: top_to958727510le_alt)) = top_to1139905818le_alt))). % PiE_UNIV
thf(fact_198_PiE__UNIV, axiom,
    (((piE_Ar415527999e_indi @ top_to958727510le_alt @ (^[I : arrow_1857593510le_alt]: top_to1799531699e_indi)) = top_to2048848e_indi))). % PiE_UNIV
thf(fact_199_PiE__UNIV, axiom,
    (((piE_Ar1187035700le_alt @ top_to958727510le_alt @ (^[I : arrow_1857593510le_alt]: top_to958727510le_alt)) = top_to290516239le_alt))). % PiE_UNIV
thf(fact_200_curryI, axiom,
    ((![F2 : produc16571293le_alt > $o, A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((F2 @ (produc1494124311le_alt @ A3 @ B3)) => (produc392997491_alt_o @ F2 @ A3 @ B3))))). % curryI
thf(fact_201_empty__Collect__eq, axiom,
    ((![P2 : set_Pr367596371le_alt > $o]: ((bot_bo1518363805le_alt = (collec1399441576le_alt @ P2)) = (![X : set_Pr367596371le_alt]: (~ ((P2 @ X)))))))). % empty_Collect_eq
thf(fact_202_Collect__empty__eq, axiom,
    ((![P2 : set_Pr367596371le_alt > $o]: (((collec1399441576le_alt @ P2) = bot_bo1518363805le_alt) = (![X : set_Pr367596371le_alt]: (~ ((P2 @ X)))))))). % Collect_empty_eq
thf(fact_203_all__not__in__conv, axiom,
    ((![A : set_Ar182050865le_alt]: ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member183760530le_alt @ X @ A)))) = (A = bot_bo13098693le_alt))))). % all_not_in_conv
thf(fact_204_all__not__in__conv, axiom,
    ((![A : set_se2071012361le_alt]: ((![X : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ X @ A)))) = (A = bot_bo1518363805le_alt))))). % all_not_in_conv
thf(fact_205_all__not__in__conv, axiom,
    ((![A : set_Ar809243995le_alt]: ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (~ ((member684274596le_alt @ X @ A)))) = (A = bot_bo365569479le_alt))))). % all_not_in_conv
thf(fact_206_all__not__in__conv, axiom,
    ((![A : set_Pr367596371le_alt]: ((![X : produc16571293le_alt]: (~ ((member2048039092le_alt @ X @ A)))) = (A = bot_bo1596236775le_alt))))). % all_not_in_conv
thf(fact_207_all__not__in__conv, axiom,
    ((![A : set_Ar1840689629le_alt]: ((![X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member65769534le_alt @ X @ A)))) = (A = bot_bo309358193le_alt))))). % all_not_in_conv
thf(fact_208_all__not__in__conv, axiom,
    ((![A : set_Ar350387917le_alt]: ((![X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (~ ((member2001237014le_alt @ X @ A)))) = (A = bot_bo709157177le_alt))))). % all_not_in_conv
thf(fact_209_all__not__in__conv, axiom,
    ((![A : set_Ar883249453le_alt]: ((![X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member966567542le_alt @ X @ A)))) = (A = bot_bo1793590169le_alt))))). % all_not_in_conv
thf(fact_210_all__not__in__conv, axiom,
    ((![A : set_Ar517773211le_alt]: ((![X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: (~ ((member1567880444le_alt @ X @ A)))) = (A = bot_bo1133925423le_alt))))). % all_not_in_conv
thf(fact_211_all__not__in__conv, axiom,
    ((![A : set_Ar2014526681le_alt]: ((![X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member902395426le_alt @ X @ A)))) = (A = bot_bo1697362245le_alt))))). % all_not_in_conv
thf(fact_212_empty__iff, axiom,
    ((![C : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member183760530le_alt @ C @ bot_bo13098693le_alt)))))). % empty_iff
thf(fact_213_empty__iff, axiom,
    ((![C : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ C @ bot_bo1518363805le_alt)))))). % empty_iff
thf(fact_214_empty__iff, axiom,
    ((![C : arrow_1429744205e_indi > set_Pr367596371le_alt]: (~ ((member684274596le_alt @ C @ bot_bo365569479le_alt)))))). % empty_iff
thf(fact_215_empty__iff, axiom,
    ((![C : produc16571293le_alt]: (~ ((member2048039092le_alt @ C @ bot_bo1596236775le_alt)))))). % empty_iff
thf(fact_216_empty__iff, axiom,
    ((![C : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member65769534le_alt @ C @ bot_bo309358193le_alt)))))). % empty_iff
thf(fact_217_empty__iff, axiom,
    ((![C : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (~ ((member2001237014le_alt @ C @ bot_bo709157177le_alt)))))). % empty_iff
thf(fact_218_empty__iff, axiom,
    ((![C : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member966567542le_alt @ C @ bot_bo1793590169le_alt)))))). % empty_iff
thf(fact_219_empty__iff, axiom,
    ((![C : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: (~ ((member1567880444le_alt @ C @ bot_bo1133925423le_alt)))))). % empty_iff
thf(fact_220_empty__iff, axiom,
    ((![C : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member902395426le_alt @ C @ bot_bo1697362245le_alt)))))). % empty_iff
thf(fact_221_Collect__const, axiom,
    ((![P2 : $o]: ((P2 => ((collec1399441576le_alt @ (^[S4 : set_Pr367596371le_alt]: P2)) = top_to469035705le_alt)) & ((~ (P2)) => ((collec1399441576le_alt @ (^[S4 : set_Pr367596371le_alt]: P2)) = bot_bo1518363805le_alt)))))). % Collect_const
thf(fact_222_Collect__const, axiom,
    ((![P2 : $o]: ((P2 => ((collec1169676194e_indi @ (^[S4 : arrow_1429744205e_indi]: P2)) = top_to1799531699e_indi)) & ((~ (P2)) => ((collec1169676194e_indi @ (^[S4 : arrow_1429744205e_indi]: P2)) = bot_bo1390904983e_indi)))))). % Collect_const
thf(fact_223_Collect__const, axiom,
    ((![P2 : $o]: ((P2 => ((collec1364151825le_alt @ (^[S4 : arrow_1857593510le_alt]: P2)) = top_to958727510le_alt)) & ((~ (P2)) => ((collec1364151825le_alt @ (^[S4 : arrow_1857593510le_alt]: P2)) = bot_bo1127707250le_alt)))))). % Collect_const
thf(fact_224_Pi__eq__empty, axiom,
    ((![A : set_Ar809243995le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_se2071012361le_alt]: (((pi_Arr479247969le_alt @ A @ B) = bot_bo13098693le_alt) = (?[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ A)) & (((B @ X) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_225_Pi__eq__empty, axiom,
    ((![A : set_Ar1007576579e_indi, B : arrow_1429744205e_indi > set_se2071012361le_alt]: (((pi_Arr1981691447le_alt @ A @ B) = bot_bo365569479le_alt) = (?[X : arrow_1429744205e_indi]: (((member1966420836e_indi @ X @ A)) & (((B @ X) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_226_Pi__eq__empty, axiom,
    ((![A : set_Ar809243995le_alt, B : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar182050865le_alt]: (((pi_Arr582931725le_alt @ A @ B) = bot_bo309358193le_alt) = (?[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X @ A)) & (((B @ X) = bot_bo13098693le_alt)))))))). % Pi_eq_empty
thf(fact_227_Pi__eq__empty, axiom,
    ((![A : set_Ar182050865le_alt, B : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((pi_Arr1460089257le_alt @ A @ B) = bot_bo709157177le_alt) = (?[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ A)) & (((B @ X) = bot_bo1596236775le_alt)))))))). % Pi_eq_empty
thf(fact_228_Pi__eq__empty, axiom,
    ((![A : set_Ar182050865le_alt, B : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_se2071012361le_alt]: (((pi_Arr2098764809le_alt @ A @ B) = bot_bo1793590169le_alt) = (?[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ A)) & (((B @ X) = bot_bo1518363805le_alt)))))))). % Pi_eq_empty
thf(fact_229_Pi__eq__empty, axiom,
    ((![A : set_Ar182050865le_alt, B : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar809243995le_alt]: (((pi_Arr9039763le_alt @ A @ B) = bot_bo1133925423le_alt) = (?[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ A)) & (((B @ X) = bot_bo365569479le_alt)))))))). % Pi_eq_empty
thf(fact_230_Pi__eq__empty, axiom,
    ((![A : set_Ar182050865le_alt, B : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Ar182050865le_alt]: (((pi_Arr1706749621le_alt @ A @ B) = bot_bo1697362245le_alt) = (?[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (((member183760530le_alt @ X @ A)) & (((B @ X) = bot_bo13098693le_alt)))))))). % Pi_eq_empty
thf(fact_231_ex__in__conv, axiom,
    ((![A : set_Ar182050865le_alt]: ((?[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member183760530le_alt @ X @ A)) = (~ ((A = bot_bo13098693le_alt))))))). % ex_in_conv
thf(fact_232_ex__in__conv, axiom,
    ((![A : set_se2071012361le_alt]: ((?[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ A)) = (~ ((A = bot_bo1518363805le_alt))))))). % ex_in_conv
thf(fact_233_ex__in__conv, axiom,
    ((![A : set_Ar809243995le_alt]: ((?[X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ A)) = (~ ((A = bot_bo365569479le_alt))))))). % ex_in_conv
thf(fact_234_ex__in__conv, axiom,
    ((![A : set_Pr367596371le_alt]: ((?[X : produc16571293le_alt]: (member2048039092le_alt @ X @ A)) = (~ ((A = bot_bo1596236775le_alt))))))). % ex_in_conv
thf(fact_235_ex__in__conv, axiom,
    ((![A : set_Ar1840689629le_alt]: ((?[X : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member65769534le_alt @ X @ A)) = (~ ((A = bot_bo309358193le_alt))))))). % ex_in_conv
thf(fact_236_ex__in__conv, axiom,
    ((![A : set_Ar350387917le_alt]: ((?[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (member2001237014le_alt @ X @ A)) = (~ ((A = bot_bo709157177le_alt))))))). % ex_in_conv
thf(fact_237_ex__in__conv, axiom,
    ((![A : set_Ar883249453le_alt]: ((?[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member966567542le_alt @ X @ A)) = (~ ((A = bot_bo1793590169le_alt))))))). % ex_in_conv
thf(fact_238_ex__in__conv, axiom,
    ((![A : set_Ar517773211le_alt]: ((?[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: (member1567880444le_alt @ X @ A)) = (~ ((A = bot_bo1133925423le_alt))))))). % ex_in_conv
thf(fact_239_ex__in__conv, axiom,
    ((![A : set_Ar2014526681le_alt]: ((?[X : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (member902395426le_alt @ X @ A)) = (~ ((A = bot_bo1697362245le_alt))))))). % ex_in_conv
thf(fact_240_equals0I, axiom,
    ((![A : set_Ar182050865le_alt]: ((![Y3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member183760530le_alt @ Y3 @ A)))) => (A = bot_bo13098693le_alt))))). % equals0I
thf(fact_241_equals0I, axiom,
    ((![A : set_se2071012361le_alt]: ((![Y3 : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ Y3 @ A)))) => (A = bot_bo1518363805le_alt))))). % equals0I
thf(fact_242_equals0I, axiom,
    ((![A : set_Ar809243995le_alt]: ((![Y3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (~ ((member684274596le_alt @ Y3 @ A)))) => (A = bot_bo365569479le_alt))))). % equals0I
thf(fact_243_equals0I, axiom,
    ((![A : set_Pr367596371le_alt]: ((![Y3 : produc16571293le_alt]: (~ ((member2048039092le_alt @ Y3 @ A)))) => (A = bot_bo1596236775le_alt))))). % equals0I
thf(fact_244_equals0I, axiom,
    ((![A : set_Ar1840689629le_alt]: ((![Y3 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member65769534le_alt @ Y3 @ A)))) => (A = bot_bo309358193le_alt))))). % equals0I
thf(fact_245_equals0I, axiom,
    ((![A : set_Ar350387917le_alt]: ((![Y3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > produc16571293le_alt]: (~ ((member2001237014le_alt @ Y3 @ A)))) => (A = bot_bo709157177le_alt))))). % equals0I
thf(fact_246_equals0I, axiom,
    ((![A : set_Ar883249453le_alt]: ((![Y3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member966567542le_alt @ Y3 @ A)))) => (A = bot_bo1793590169le_alt))))). % equals0I
thf(fact_247_equals0I, axiom,
    ((![A : set_Ar517773211le_alt]: ((![Y3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > arrow_1429744205e_indi > set_Pr367596371le_alt]: (~ ((member1567880444le_alt @ Y3 @ A)))) => (A = bot_bo1133925423le_alt))))). % equals0I
thf(fact_248_equals0I, axiom,
    ((![A : set_Ar2014526681le_alt]: ((![Y3 : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (~ ((member902395426le_alt @ Y3 @ A)))) => (A = bot_bo1697362245le_alt))))). % equals0I

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[I4 : arrow_1429744205e_indi]: (arrow_960434986ctator @ f @ I4)))).
