% 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_104__5185990_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:15:59.666

% Could-be-implicit typings (5)
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_se2071012361le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_Pr367596371le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc16571293le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    set_Ar1665529862le_alt : $tType).
thf(ty_n_t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    arrow_1857593510le_alt : $tType).

% Explicit typings (34)
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_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_Lattices_Osup__class_Osup_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    sup_su1032097242le_alt : set_Ar1665529862le_alt > set_Ar1665529862le_alt > set_Ar1665529862le_alt).
thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    sup_su1902543487le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Lattices_Osup__class_Osup_001t__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,
    sup_su255583029le_alt : set_se2071012361le_alt > set_se2071012361le_alt > set_se2071012361le_alt).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J, type,
    bot_bo1380086507_alt_o : arrow_1857593510le_alt > $o).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_Eo_J, type,
    bot_bo91657054_alt_o : produc16571293le_alt > $o).
thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_M_Eo_J, type,
    bot_bo2065212968_alt_o : set_Pr367596371le_alt > $o).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    bot_bo1127707250le_alt : set_Ar1665529862le_alt).
thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    bot_bo1596236775le_alt : set_Pr367596371le_alt).
thf(sy_c_Orderings_Obot__class_Obot_001t__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,
    bot_bo1518363805le_alt : set_se2071012361le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    top_to958727510le_alt : set_Ar1665529862le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    top_to224369155le_alt : set_Pr367596371le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__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,
    top_to469035705le_alt : set_se2071012361le_alt).
thf(sy_c_Product__Type_OPair_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1494124311le_alt : arrow_1857593510le_alt > arrow_1857593510le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_Eo, type,
    produc624247124_alt_o : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > produc16571293le_alt > $o).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc860300173le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt) > produc16571293le_alt > set_Pr367596371le_alt).
thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__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,
    produc1042938349le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt) > produc16571293le_alt > set_se2071012361le_alt).
thf(sy_c_Set_OBall_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    ball_P2077952115le_alt : set_Pr367596371le_alt > (produc16571293le_alt > $o) > $o).
thf(sy_c_Set_OBall_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    ball_s1517873193le_alt : set_se2071012361le_alt > (set_Pr367596371le_alt > $o) > $o).
thf(sy_c_Set_OCollect_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    collec1364151825le_alt : (arrow_1857593510le_alt > $o) > set_Ar1665529862le_alt).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    collec531981554le_alt : (produc16571293le_alt > $o) > set_Pr367596371le_alt).
thf(sy_c_Set_OCollect_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    collec1399441576le_alt : (set_Pr367596371le_alt > $o) > set_se2071012361le_alt).
thf(sy_c_Set_Oinsert_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    insert1093389942le_alt : arrow_1857593510le_alt > set_Ar1665529862le_alt > set_Ar1665529862le_alt).
thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    insert1454465485le_alt : produc16571293le_alt > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    insert15522179le_alt : set_Pr367596371le_alt > set_se2071012361le_alt > set_se2071012361le_alt).
thf(sy_c_member_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    member519365071le_alt : arrow_1857593510le_alt > set_Ar1665529862le_alt > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member2048039092le_alt : produc16571293le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member1334244458le_alt : set_Pr367596371le_alt > set_se2071012361le_alt > $o).
thf(sy_v_L, type,
    l : set_Pr367596371le_alt).
thf(sy_v_x, type,
    x : arrow_1857593510le_alt).
thf(sy_v_y, type,
    y : arrow_1857593510le_alt).

% Relevant facts (249)
thf(fact_0_Arrow__Order__Mirabelle__riepwfubkl_Oabove__def, axiom,
    ((arrow_1726226719_above = (^[L : set_Pr367596371le_alt]: (^[A : arrow_1857593510le_alt]: (^[B : arrow_1857593510le_alt]: (sup_su1902543487le_alt @ (sup_su1902543487le_alt @ (sup_su1902543487le_alt @ (collec531981554le_alt @ (produc624247124_alt_o @ (^[X : arrow_1857593510le_alt]: (^[Y : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L)) & ((((~ ((X = B)))) & ((~ ((Y = B))))))))))) @ (insert1454465485le_alt @ (produc1494124311le_alt @ A @ B) @ bot_bo1596236775le_alt)) @ (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[X : arrow_1857593510le_alt]: (((Uu = (produc1494124311le_alt @ X @ B))) & ((((member2048039092le_alt @ (produc1494124311le_alt @ X @ A) @ L)) & ((~ ((X = B))))))))))) @ (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[Y : arrow_1857593510le_alt]: (((Uu = (produc1494124311le_alt @ B @ Y))) & ((((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y) @ L)) & ((~ ((Y = B))))))))))))))))). % Arrow_Order_Mirabelle_riepwfubkl.above_def
thf(fact_1_below__def, axiom,
    ((arrow_887341619_below = (^[L : set_Pr367596371le_alt]: (^[A : arrow_1857593510le_alt]: (^[B : arrow_1857593510le_alt]: (sup_su1902543487le_alt @ (sup_su1902543487le_alt @ (sup_su1902543487le_alt @ (collec531981554le_alt @ (produc624247124_alt_o @ (^[X : arrow_1857593510le_alt]: (^[Y : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L)) & ((((~ ((X = A)))) & ((~ ((Y = A))))))))))) @ (insert1454465485le_alt @ (produc1494124311le_alt @ A @ B) @ bot_bo1596236775le_alt)) @ (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[X : arrow_1857593510le_alt]: (((Uu = (produc1494124311le_alt @ X @ A))) & ((((member2048039092le_alt @ (produc1494124311le_alt @ X @ B) @ L)) & ((~ ((X = A))))))))))) @ (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[Y : arrow_1857593510le_alt]: (((Uu = (produc1494124311le_alt @ A @ Y))) & ((((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y) @ L)) & ((~ ((Y = A))))))))))))))))). % below_def
thf(fact_2_ball__UNIV, axiom,
    ((![P : produc16571293le_alt > $o]: ((![X : produc16571293le_alt]: (((member2048039092le_alt @ X @ top_to224369155le_alt)) => ((P @ X)))) = (![X2 : produc16571293le_alt]: (P @ X2)))))). % ball_UNIV
thf(fact_3_ball__UNIV, axiom,
    ((![P : set_Pr367596371le_alt > $o]: ((![X : set_Pr367596371le_alt]: (((member1334244458le_alt @ X @ top_to469035705le_alt)) => ((P @ X)))) = (![X2 : set_Pr367596371le_alt]: (P @ X2)))))). % ball_UNIV
thf(fact_4_ball__UNIV, axiom,
    ((![P : arrow_1857593510le_alt > $o]: ((![X : arrow_1857593510le_alt]: (((member519365071le_alt @ X @ top_to958727510le_alt)) => ((P @ X)))) = (![X2 : arrow_1857593510le_alt]: (P @ X2)))))). % ball_UNIV
thf(fact_5_case__prodI, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: ((F @ A2 @ B2) => (produc624247124_alt_o @ F @ (produc1494124311le_alt @ A2 @ B2)))))). % case_prodI
thf(fact_6_case__prodI2, axiom,
    ((![P2 : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P2 = (produc1494124311le_alt @ A3 @ B3)) => (C @ A3 @ B3))) => (produc624247124_alt_o @ C @ P2))))). % case_prodI2
thf(fact_7_case__prod__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: ((produc624247124_alt_o @ F @ (produc1494124311le_alt @ A2 @ B2)) = (F @ A2 @ B2))))). % case_prod_conv
thf(fact_8_Collect__const, axiom,
    ((![P : $o]: ((P => ((collec1399441576le_alt @ (^[S : set_Pr367596371le_alt]: P)) = top_to469035705le_alt)) & ((~ (P)) => ((collec1399441576le_alt @ (^[S : set_Pr367596371le_alt]: P)) = bot_bo1518363805le_alt)))))). % Collect_const
thf(fact_9_Collect__const, axiom,
    ((![P : $o]: ((P => ((collec531981554le_alt @ (^[S : produc16571293le_alt]: P)) = top_to224369155le_alt)) & ((~ (P)) => ((collec531981554le_alt @ (^[S : produc16571293le_alt]: P)) = bot_bo1596236775le_alt)))))). % Collect_const
thf(fact_10_Collect__const, axiom,
    ((![P : $o]: ((P => ((collec1364151825le_alt @ (^[S : arrow_1857593510le_alt]: P)) = top_to958727510le_alt)) & ((~ (P)) => ((collec1364151825le_alt @ (^[S : arrow_1857593510le_alt]: P)) = bot_bo1127707250le_alt)))))). % Collect_const
thf(fact_11_singleton__conv, axiom,
    ((![A2 : arrow_1857593510le_alt]: ((collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: (X = A2))) = (insert1093389942le_alt @ A2 @ bot_bo1127707250le_alt))))). % singleton_conv
thf(fact_12_singleton__conv, axiom,
    ((![A2 : set_Pr367596371le_alt]: ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (X = A2))) = (insert15522179le_alt @ A2 @ bot_bo1518363805le_alt))))). % singleton_conv
thf(fact_13_singleton__conv, axiom,
    ((![A2 : produc16571293le_alt]: ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (X = A2))) = (insert1454465485le_alt @ A2 @ bot_bo1596236775le_alt))))). % singleton_conv
thf(fact_14_singleton__conv2, axiom,
    ((![A2 : arrow_1857593510le_alt]: ((collec1364151825le_alt @ ((^[Y2 : arrow_1857593510le_alt]: (^[Z : arrow_1857593510le_alt]: (Y2 = Z))) @ A2)) = (insert1093389942le_alt @ A2 @ bot_bo1127707250le_alt))))). % singleton_conv2
thf(fact_15_singleton__conv2, axiom,
    ((![A2 : set_Pr367596371le_alt]: ((collec1399441576le_alt @ ((^[Y2 : set_Pr367596371le_alt]: (^[Z : set_Pr367596371le_alt]: (Y2 = Z))) @ A2)) = (insert15522179le_alt @ A2 @ bot_bo1518363805le_alt))))). % singleton_conv2
thf(fact_16_singleton__conv2, axiom,
    ((![A2 : produc16571293le_alt]: ((collec531981554le_alt @ ((^[Y2 : produc16571293le_alt]: (^[Z : produc16571293le_alt]: (Y2 = Z))) @ A2)) = (insert1454465485le_alt @ A2 @ bot_bo1596236775le_alt))))). % singleton_conv2
thf(fact_17_mkbot__def, axiom,
    ((arrow_843587755_mkbot = (^[L : set_Pr367596371le_alt]: (^[B : arrow_1857593510le_alt]: (sup_su1902543487le_alt @ (collec531981554le_alt @ (produc624247124_alt_o @ (^[X : arrow_1857593510le_alt]: (^[Y : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L)) & ((((~ ((X = B)))) & ((~ ((Y = B))))))))))) @ (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[Y : arrow_1857593510le_alt]: (((Uu = (produc1494124311le_alt @ B @ Y))) & ((~ ((Y = B)))))))))))))). % mkbot_def
thf(fact_18_mktop__def, axiom,
    ((arrow_992294841_mktop = (^[L : set_Pr367596371le_alt]: (^[B : arrow_1857593510le_alt]: (sup_su1902543487le_alt @ (collec531981554le_alt @ (produc624247124_alt_o @ (^[X : arrow_1857593510le_alt]: (^[Y : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L)) & ((((~ ((X = B)))) & ((~ ((Y = B))))))))))) @ (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[X : arrow_1857593510le_alt]: (((Uu = (produc1494124311le_alt @ X @ B))) & ((~ ((X = B)))))))))))))). % mktop_def
thf(fact_19_Un__insert__left, axiom,
    ((![A2 : set_Pr367596371le_alt, B4 : set_se2071012361le_alt, C2 : set_se2071012361le_alt]: ((sup_su255583029le_alt @ (insert15522179le_alt @ A2 @ B4) @ C2) = (insert15522179le_alt @ A2 @ (sup_su255583029le_alt @ B4 @ C2)))))). % Un_insert_left
thf(fact_20_Un__insert__left, axiom,
    ((![A2 : produc16571293le_alt, B4 : set_Pr367596371le_alt, C2 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ (insert1454465485le_alt @ A2 @ B4) @ C2) = (insert1454465485le_alt @ A2 @ (sup_su1902543487le_alt @ B4 @ C2)))))). % Un_insert_left
thf(fact_21_old_Oprod_Oinject, axiom,
    ((![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, A4 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A2 @ B2) = (produc1494124311le_alt @ A4 @ B5)) = (((A2 = A4)) & ((B2 = B5))))))). % old.prod.inject
thf(fact_22_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_23_empty__Collect__eq, axiom,
    ((![P : produc16571293le_alt > $o]: ((bot_bo1596236775le_alt = (collec531981554le_alt @ P)) = (![X : produc16571293le_alt]: (~ ((P @ X)))))))). % empty_Collect_eq
thf(fact_24_empty__Collect__eq, axiom,
    ((![P : arrow_1857593510le_alt > $o]: ((bot_bo1127707250le_alt = (collec1364151825le_alt @ P)) = (![X : arrow_1857593510le_alt]: (~ ((P @ X)))))))). % empty_Collect_eq
thf(fact_25_empty__Collect__eq, axiom,
    ((![P : set_Pr367596371le_alt > $o]: ((bot_bo1518363805le_alt = (collec1399441576le_alt @ P)) = (![X : set_Pr367596371le_alt]: (~ ((P @ X)))))))). % empty_Collect_eq
thf(fact_26_Collect__empty__eq, axiom,
    ((![P : produc16571293le_alt > $o]: (((collec531981554le_alt @ P) = bot_bo1596236775le_alt) = (![X : produc16571293le_alt]: (~ ((P @ X)))))))). % Collect_empty_eq
thf(fact_27_Collect__empty__eq, axiom,
    ((![P : arrow_1857593510le_alt > $o]: (((collec1364151825le_alt @ P) = bot_bo1127707250le_alt) = (![X : arrow_1857593510le_alt]: (~ ((P @ X)))))))). % Collect_empty_eq
thf(fact_28_Collect__empty__eq, axiom,
    ((![P : set_Pr367596371le_alt > $o]: (((collec1399441576le_alt @ P) = bot_bo1518363805le_alt) = (![X : set_Pr367596371le_alt]: (~ ((P @ X)))))))). % Collect_empty_eq
thf(fact_29_all__not__in__conv, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((![X : produc16571293le_alt]: (~ ((member2048039092le_alt @ X @ A5)))) = (A5 = bot_bo1596236775le_alt))))). % all_not_in_conv
thf(fact_30_all__not__in__conv, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((![X : arrow_1857593510le_alt]: (~ ((member519365071le_alt @ X @ A5)))) = (A5 = bot_bo1127707250le_alt))))). % all_not_in_conv
thf(fact_31_all__not__in__conv, axiom,
    ((![A5 : set_se2071012361le_alt]: ((![X : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ X @ A5)))) = (A5 = bot_bo1518363805le_alt))))). % all_not_in_conv
thf(fact_32_empty__iff, axiom,
    ((![C : produc16571293le_alt]: (~ ((member2048039092le_alt @ C @ bot_bo1596236775le_alt)))))). % empty_iff
thf(fact_33_empty__iff, axiom,
    ((![C : arrow_1857593510le_alt]: (~ ((member519365071le_alt @ C @ bot_bo1127707250le_alt)))))). % empty_iff
thf(fact_34_empty__iff, axiom,
    ((![C : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ C @ bot_bo1518363805le_alt)))))). % empty_iff
thf(fact_35_insert__absorb2, axiom,
    ((![X3 : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((insert1454465485le_alt @ X3 @ (insert1454465485le_alt @ X3 @ A5)) = (insert1454465485le_alt @ X3 @ A5))))). % insert_absorb2
thf(fact_36_insert__absorb2, axiom,
    ((![X3 : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((insert15522179le_alt @ X3 @ (insert15522179le_alt @ X3 @ A5)) = (insert15522179le_alt @ X3 @ A5))))). % insert_absorb2
thf(fact_37_insert__iff, axiom,
    ((![A2 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((member1334244458le_alt @ A2 @ (insert15522179le_alt @ B2 @ A5)) = (((A2 = B2)) | ((member1334244458le_alt @ A2 @ A5))))))). % insert_iff
thf(fact_38_insert__iff, axiom,
    ((![A2 : produc16571293le_alt, B2 : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ A2 @ (insert1454465485le_alt @ B2 @ A5)) = (((A2 = B2)) | ((member2048039092le_alt @ A2 @ A5))))))). % insert_iff
thf(fact_39_insertCI, axiom,
    ((![A2 : set_Pr367596371le_alt, B4 : set_se2071012361le_alt, B2 : set_Pr367596371le_alt]: (((~ ((member1334244458le_alt @ A2 @ B4))) => (A2 = B2)) => (member1334244458le_alt @ A2 @ (insert15522179le_alt @ B2 @ B4)))))). % insertCI
thf(fact_40_insertCI, axiom,
    ((![A2 : produc16571293le_alt, B4 : set_Pr367596371le_alt, B2 : produc16571293le_alt]: (((~ ((member2048039092le_alt @ A2 @ B4))) => (A2 = B2)) => (member2048039092le_alt @ A2 @ (insert1454465485le_alt @ B2 @ B4)))))). % insertCI
thf(fact_41_UNIV__I, axiom,
    ((![X3 : arrow_1857593510le_alt]: (member519365071le_alt @ X3 @ top_to958727510le_alt)))). % UNIV_I
thf(fact_42_UNIV__I, axiom,
    ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_I
thf(fact_43_UNIV__I, axiom,
    ((![X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_I
thf(fact_44_Un__iff, axiom,
    ((![C : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B4 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ (sup_su255583029le_alt @ A5 @ B4)) = (((member1334244458le_alt @ C @ A5)) | ((member1334244458le_alt @ C @ B4))))))). % Un_iff
thf(fact_45_Un__iff, axiom,
    ((![C : produc16571293le_alt, A5 : set_Pr367596371le_alt, B4 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (sup_su1902543487le_alt @ A5 @ B4)) = (((member2048039092le_alt @ C @ A5)) | ((member2048039092le_alt @ C @ B4))))))). % Un_iff
thf(fact_46_UnCI, axiom,
    ((![C : set_Pr367596371le_alt, B4 : set_se2071012361le_alt, A5 : set_se2071012361le_alt]: (((~ ((member1334244458le_alt @ C @ B4))) => (member1334244458le_alt @ C @ A5)) => (member1334244458le_alt @ C @ (sup_su255583029le_alt @ A5 @ B4)))))). % UnCI
thf(fact_47_UnCI, axiom,
    ((![C : produc16571293le_alt, B4 : set_Pr367596371le_alt, A5 : set_Pr367596371le_alt]: (((~ ((member2048039092le_alt @ C @ B4))) => (member2048039092le_alt @ C @ A5)) => (member2048039092le_alt @ C @ (sup_su1902543487le_alt @ A5 @ B4)))))). % UnCI
thf(fact_48_mem__case__prodI2, axiom,
    ((![P2 : produc16571293le_alt, Z2 : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P2 = (produc1494124311le_alt @ A3 @ B3)) => (member1334244458le_alt @ Z2 @ (C @ A3 @ B3)))) => (member1334244458le_alt @ Z2 @ (produc1042938349le_alt @ C @ P2)))))). % mem_case_prodI2
thf(fact_49_mem__case__prodI2, axiom,
    ((![P2 : produc16571293le_alt, Z2 : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: ((P2 = (produc1494124311le_alt @ A3 @ B3)) => (member2048039092le_alt @ Z2 @ (C @ A3 @ B3)))) => (member2048039092le_alt @ Z2 @ (produc860300173le_alt @ C @ P2)))))). % mem_case_prodI2
thf(fact_50_mem__case__prodI, axiom,
    ((![Z2 : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: ((member1334244458le_alt @ Z2 @ (C @ A2 @ B2)) => (member1334244458le_alt @ Z2 @ (produc1042938349le_alt @ C @ (produc1494124311le_alt @ A2 @ B2))))))). % mem_case_prodI
thf(fact_51_mem__case__prodI, axiom,
    ((![Z2 : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ Z2 @ (C @ A2 @ B2)) => (member2048039092le_alt @ Z2 @ (produc860300173le_alt @ C @ (produc1494124311le_alt @ A2 @ B2))))))). % mem_case_prodI
thf(fact_52_split__part, axiom,
    ((![P : $o, Q : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((produc624247124_alt_o @ (^[A : arrow_1857593510le_alt]: (^[B : arrow_1857593510le_alt]: ((P) & ((Q @ A @ B)))))) = (^[Ab : produc16571293le_alt]: ((P) & ((produc624247124_alt_o @ Q @ Ab)))))))). % split_part
thf(fact_53_singletonI, axiom,
    ((![A2 : produc16571293le_alt]: (member2048039092le_alt @ A2 @ (insert1454465485le_alt @ A2 @ bot_bo1596236775le_alt))))). % singletonI
thf(fact_54_singletonI, axiom,
    ((![A2 : arrow_1857593510le_alt]: (member519365071le_alt @ A2 @ (insert1093389942le_alt @ A2 @ bot_bo1127707250le_alt))))). % singletonI
thf(fact_55_singletonI, axiom,
    ((![A2 : set_Pr367596371le_alt]: (member1334244458le_alt @ A2 @ (insert15522179le_alt @ A2 @ bot_bo1518363805le_alt))))). % singletonI
thf(fact_56_ball__empty, axiom,
    ((![P : produc16571293le_alt > $o, X4 : produc16571293le_alt]: ((member2048039092le_alt @ X4 @ bot_bo1596236775le_alt) => (P @ X4))))). % ball_empty
thf(fact_57_ball__empty, axiom,
    ((![P : arrow_1857593510le_alt > $o, X4 : arrow_1857593510le_alt]: ((member519365071le_alt @ X4 @ bot_bo1127707250le_alt) => (P @ X4))))). % ball_empty
thf(fact_58_ball__empty, axiom,
    ((![P : set_Pr367596371le_alt > $o, X4 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X4 @ bot_bo1518363805le_alt) => (P @ X4))))). % ball_empty
thf(fact_59_Un__empty, axiom,
    ((![A5 : set_Pr367596371le_alt, B4 : set_Pr367596371le_alt]: (((sup_su1902543487le_alt @ A5 @ B4) = bot_bo1596236775le_alt) = (((A5 = bot_bo1596236775le_alt)) & ((B4 = bot_bo1596236775le_alt))))))). % Un_empty
thf(fact_60_Un__empty, axiom,
    ((![A5 : set_Ar1665529862le_alt, B4 : set_Ar1665529862le_alt]: (((sup_su1032097242le_alt @ A5 @ B4) = bot_bo1127707250le_alt) = (((A5 = bot_bo1127707250le_alt)) & ((B4 = bot_bo1127707250le_alt))))))). % Un_empty
thf(fact_61_Un__empty, axiom,
    ((![A5 : set_se2071012361le_alt, B4 : set_se2071012361le_alt]: (((sup_su255583029le_alt @ A5 @ B4) = bot_bo1518363805le_alt) = (((A5 = bot_bo1518363805le_alt)) & ((B4 = bot_bo1518363805le_alt))))))). % Un_empty
thf(fact_62_Un__insert__right, axiom,
    ((![A5 : set_se2071012361le_alt, A2 : set_Pr367596371le_alt, B4 : set_se2071012361le_alt]: ((sup_su255583029le_alt @ A5 @ (insert15522179le_alt @ A2 @ B4)) = (insert15522179le_alt @ A2 @ (sup_su255583029le_alt @ A5 @ B4)))))). % Un_insert_right
thf(fact_63_Un__insert__right, axiom,
    ((![A5 : set_Pr367596371le_alt, A2 : produc16571293le_alt, B4 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ A5 @ (insert1454465485le_alt @ A2 @ B4)) = (insert1454465485le_alt @ A2 @ (sup_su1902543487le_alt @ A5 @ B4)))))). % Un_insert_right
thf(fact_64_Collect__const__case__prod, axiom,
    ((![P : $o]: ((P => ((collec531981554le_alt @ (produc624247124_alt_o @ (^[A : arrow_1857593510le_alt]: (^[B : arrow_1857593510le_alt]: P)))) = top_to224369155le_alt)) & ((~ (P)) => ((collec531981554le_alt @ (produc624247124_alt_o @ (^[A : arrow_1857593510le_alt]: (^[B : arrow_1857593510le_alt]: P)))) = bot_bo1596236775le_alt)))))). % Collect_const_case_prod
thf(fact_65_mem__case__prodE, axiom,
    ((![Z2 : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt, P2 : produc16571293le_alt]: ((member1334244458le_alt @ Z2 @ (produc1042938349le_alt @ C @ P2)) => (~ ((![X5 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P2 = (produc1494124311le_alt @ X5 @ Y3)) => (~ ((member1334244458le_alt @ Z2 @ (C @ X5 @ Y3)))))))))))). % mem_case_prodE
thf(fact_66_mem__case__prodE, axiom,
    ((![Z2 : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt, P2 : produc16571293le_alt]: ((member2048039092le_alt @ Z2 @ (produc860300173le_alt @ C @ P2)) => (~ ((![X5 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P2 = (produc1494124311le_alt @ X5 @ Y3)) => (~ ((member2048039092le_alt @ Z2 @ (C @ X5 @ Y3)))))))))))). % mem_case_prodE
thf(fact_67_old_Oprod_Oinducts, axiom,
    ((![P : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A3 @ B3))) => (P @ Prod))))). % old.prod.inducts
thf(fact_68_old_Oprod_Oexhaust, axiom,
    ((![Y4 : produc16571293le_alt]: (~ ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (~ ((Y4 = (produc1494124311le_alt @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_69_mem__Collect__eq, axiom,
    ((![A2 : set_Pr367596371le_alt, P : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A2 @ (collec1399441576le_alt @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_70_mem__Collect__eq, axiom,
    ((![A2 : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A2 @ (collec531981554le_alt @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_71_mem__Collect__eq, axiom,
    ((![A2 : arrow_1857593510le_alt, P : arrow_1857593510le_alt > $o]: ((member519365071le_alt @ A2 @ (collec1364151825le_alt @ P)) = (P @ A2))))). % mem_Collect_eq
thf(fact_72_Collect__mem__eq, axiom,
    ((![A5 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_73_Collect__mem__eq, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (member2048039092le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_74_Collect__mem__eq, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ A5))) = A5)))). % Collect_mem_eq
thf(fact_75_Collect__cong, axiom,
    ((![P : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((![X5 : set_Pr367596371le_alt]: ((P @ X5) = (Q @ X5))) => ((collec1399441576le_alt @ P) = (collec1399441576le_alt @ Q)))))). % Collect_cong
thf(fact_76_Collect__cong, axiom,
    ((![P : produc16571293le_alt > $o, Q : produc16571293le_alt > $o]: ((![X5 : produc16571293le_alt]: ((P @ X5) = (Q @ X5))) => ((collec531981554le_alt @ P) = (collec531981554le_alt @ Q)))))). % Collect_cong
thf(fact_77_Collect__cong, axiom,
    ((![P : arrow_1857593510le_alt > $o, Q : arrow_1857593510le_alt > $o]: ((![X5 : arrow_1857593510le_alt]: ((P @ X5) = (Q @ X5))) => ((collec1364151825le_alt @ P) = (collec1364151825le_alt @ Q)))))). % Collect_cong
thf(fact_78_Pair__inject, axiom,
    ((![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, A4 : arrow_1857593510le_alt, B5 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A2 @ B2) = (produc1494124311le_alt @ A4 @ B5)) => (~ (((A2 = A4) => (~ ((B2 = B5)))))))))). % Pair_inject
thf(fact_79_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P2 : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A3 @ B3))) => (P @ P2))))). % prod_cases
thf(fact_80_surj__pair, axiom,
    ((![P2 : produc16571293le_alt]: (?[X5 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P2 = (produc1494124311le_alt @ X5 @ Y3)))))). % surj_pair
thf(fact_81_ex__in__conv, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((?[X : produc16571293le_alt]: (member2048039092le_alt @ X @ A5)) = (~ ((A5 = bot_bo1596236775le_alt))))))). % ex_in_conv
thf(fact_82_ex__in__conv, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((?[X : arrow_1857593510le_alt]: (member519365071le_alt @ X @ A5)) = (~ ((A5 = bot_bo1127707250le_alt))))))). % ex_in_conv
thf(fact_83_ex__in__conv, axiom,
    ((![A5 : set_se2071012361le_alt]: ((?[X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ A5)) = (~ ((A5 = bot_bo1518363805le_alt))))))). % ex_in_conv
thf(fact_84_equals0I, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((![Y3 : produc16571293le_alt]: (~ ((member2048039092le_alt @ Y3 @ A5)))) => (A5 = bot_bo1596236775le_alt))))). % equals0I
thf(fact_85_equals0I, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((![Y3 : arrow_1857593510le_alt]: (~ ((member519365071le_alt @ Y3 @ A5)))) => (A5 = bot_bo1127707250le_alt))))). % equals0I
thf(fact_86_equals0I, axiom,
    ((![A5 : set_se2071012361le_alt]: ((![Y3 : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ Y3 @ A5)))) => (A5 = bot_bo1518363805le_alt))))). % equals0I
thf(fact_87_equals0D, axiom,
    ((![A5 : set_Pr367596371le_alt, A2 : produc16571293le_alt]: ((A5 = bot_bo1596236775le_alt) => (~ ((member2048039092le_alt @ A2 @ A5))))))). % equals0D
thf(fact_88_equals0D, axiom,
    ((![A5 : set_Ar1665529862le_alt, A2 : arrow_1857593510le_alt]: ((A5 = bot_bo1127707250le_alt) => (~ ((member519365071le_alt @ A2 @ A5))))))). % equals0D
thf(fact_89_equals0D, axiom,
    ((![A5 : set_se2071012361le_alt, A2 : set_Pr367596371le_alt]: ((A5 = bot_bo1518363805le_alt) => (~ ((member1334244458le_alt @ A2 @ A5))))))). % equals0D
thf(fact_90_emptyE, axiom,
    ((![A2 : produc16571293le_alt]: (~ ((member2048039092le_alt @ A2 @ bot_bo1596236775le_alt)))))). % emptyE
thf(fact_91_emptyE, axiom,
    ((![A2 : arrow_1857593510le_alt]: (~ ((member519365071le_alt @ A2 @ bot_bo1127707250le_alt)))))). % emptyE
thf(fact_92_emptyE, axiom,
    ((![A2 : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ A2 @ bot_bo1518363805le_alt)))))). % emptyE
thf(fact_93_mk__disjoint__insert, axiom,
    ((![A2 : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((member1334244458le_alt @ A2 @ A5) => (?[B6 : set_se2071012361le_alt]: ((A5 = (insert15522179le_alt @ A2 @ B6)) & (~ ((member1334244458le_alt @ A2 @ B6))))))))). % mk_disjoint_insert
thf(fact_94_mk__disjoint__insert, axiom,
    ((![A2 : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ A2 @ A5) => (?[B6 : set_Pr367596371le_alt]: ((A5 = (insert1454465485le_alt @ A2 @ B6)) & (~ ((member2048039092le_alt @ A2 @ B6))))))))). % mk_disjoint_insert
thf(fact_95_insert__commute, axiom,
    ((![X3 : produc16571293le_alt, Y4 : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((insert1454465485le_alt @ X3 @ (insert1454465485le_alt @ Y4 @ A5)) = (insert1454465485le_alt @ Y4 @ (insert1454465485le_alt @ X3 @ A5)))))). % insert_commute
thf(fact_96_insert__commute, axiom,
    ((![X3 : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((insert15522179le_alt @ X3 @ (insert15522179le_alt @ Y4 @ A5)) = (insert15522179le_alt @ Y4 @ (insert15522179le_alt @ X3 @ A5)))))). % insert_commute
thf(fact_97_insert__eq__iff, axiom,
    ((![A2 : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B2 : set_Pr367596371le_alt, B4 : set_se2071012361le_alt]: ((~ ((member1334244458le_alt @ A2 @ A5))) => ((~ ((member1334244458le_alt @ B2 @ B4))) => (((insert15522179le_alt @ A2 @ A5) = (insert15522179le_alt @ B2 @ B4)) = (((((A2 = B2)) => ((A5 = B4)))) & ((((~ ((A2 = B2)))) => ((?[C3 : set_se2071012361le_alt]: (((A5 = (insert15522179le_alt @ B2 @ C3))) & ((((~ ((member1334244458le_alt @ B2 @ C3)))) & ((((B4 = (insert15522179le_alt @ A2 @ C3))) & ((~ ((member1334244458le_alt @ A2 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_98_insert__eq__iff, axiom,
    ((![A2 : produc16571293le_alt, A5 : set_Pr367596371le_alt, B2 : produc16571293le_alt, B4 : set_Pr367596371le_alt]: ((~ ((member2048039092le_alt @ A2 @ A5))) => ((~ ((member2048039092le_alt @ B2 @ B4))) => (((insert1454465485le_alt @ A2 @ A5) = (insert1454465485le_alt @ B2 @ B4)) = (((((A2 = B2)) => ((A5 = B4)))) & ((((~ ((A2 = B2)))) => ((?[C3 : set_Pr367596371le_alt]: (((A5 = (insert1454465485le_alt @ B2 @ C3))) & ((((~ ((member2048039092le_alt @ B2 @ C3)))) & ((((B4 = (insert1454465485le_alt @ A2 @ C3))) & ((~ ((member2048039092le_alt @ A2 @ C3)))))))))))))))))))). % insert_eq_iff
thf(fact_99_insert__absorb, axiom,
    ((![A2 : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((member1334244458le_alt @ A2 @ A5) => ((insert15522179le_alt @ A2 @ A5) = A5))))). % insert_absorb
thf(fact_100_insert__absorb, axiom,
    ((![A2 : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ A2 @ A5) => ((insert1454465485le_alt @ A2 @ A5) = A5))))). % insert_absorb
thf(fact_101_insert__ident, axiom,
    ((![X3 : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B4 : set_se2071012361le_alt]: ((~ ((member1334244458le_alt @ X3 @ A5))) => ((~ ((member1334244458le_alt @ X3 @ B4))) => (((insert15522179le_alt @ X3 @ A5) = (insert15522179le_alt @ X3 @ B4)) = (A5 = B4))))))). % insert_ident
thf(fact_102_insert__ident, axiom,
    ((![X3 : produc16571293le_alt, A5 : set_Pr367596371le_alt, B4 : set_Pr367596371le_alt]: ((~ ((member2048039092le_alt @ X3 @ A5))) => ((~ ((member2048039092le_alt @ X3 @ B4))) => (((insert1454465485le_alt @ X3 @ A5) = (insert1454465485le_alt @ X3 @ B4)) = (A5 = B4))))))). % insert_ident
thf(fact_103_Set_Oset__insert, axiom,
    ((![X3 : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((member1334244458le_alt @ X3 @ A5) => (~ ((![B6 : set_se2071012361le_alt]: ((A5 = (insert15522179le_alt @ X3 @ B6)) => (member1334244458le_alt @ X3 @ B6))))))))). % Set.set_insert
thf(fact_104_Set_Oset__insert, axiom,
    ((![X3 : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ X3 @ A5) => (~ ((![B6 : set_Pr367596371le_alt]: ((A5 = (insert1454465485le_alt @ X3 @ B6)) => (member2048039092le_alt @ X3 @ B6))))))))). % Set.set_insert
thf(fact_105_insertI2, axiom,
    ((![A2 : set_Pr367596371le_alt, B4 : set_se2071012361le_alt, B2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ A2 @ B4) => (member1334244458le_alt @ A2 @ (insert15522179le_alt @ B2 @ B4)))))). % insertI2
thf(fact_106_insertI2, axiom,
    ((![A2 : produc16571293le_alt, B4 : set_Pr367596371le_alt, B2 : produc16571293le_alt]: ((member2048039092le_alt @ A2 @ B4) => (member2048039092le_alt @ A2 @ (insert1454465485le_alt @ B2 @ B4)))))). % insertI2
thf(fact_107_insertI1, axiom,
    ((![A2 : set_Pr367596371le_alt, B4 : set_se2071012361le_alt]: (member1334244458le_alt @ A2 @ (insert15522179le_alt @ A2 @ B4))))). % insertI1
thf(fact_108_insertI1, axiom,
    ((![A2 : produc16571293le_alt, B4 : set_Pr367596371le_alt]: (member2048039092le_alt @ A2 @ (insert1454465485le_alt @ A2 @ B4))))). % insertI1
thf(fact_109_insertE, axiom,
    ((![A2 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: ((member1334244458le_alt @ A2 @ (insert15522179le_alt @ B2 @ A5)) => ((~ ((A2 = B2))) => (member1334244458le_alt @ A2 @ A5)))))). % insertE
thf(fact_110_insertE, axiom,
    ((![A2 : produc16571293le_alt, B2 : produc16571293le_alt, A5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ A2 @ (insert1454465485le_alt @ B2 @ A5)) => ((~ ((A2 = B2))) => (member2048039092le_alt @ A2 @ A5)))))). % insertE
thf(fact_111_UNIV__witness, axiom,
    ((?[X5 : arrow_1857593510le_alt]: (member519365071le_alt @ X5 @ top_to958727510le_alt)))). % UNIV_witness
thf(fact_112_UNIV__witness, axiom,
    ((?[X5 : produc16571293le_alt]: (member2048039092le_alt @ X5 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_113_UNIV__witness, axiom,
    ((?[X5 : set_Pr367596371le_alt]: (member1334244458le_alt @ X5 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_114_UNIV__eq__I, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((![X5 : arrow_1857593510le_alt]: (member519365071le_alt @ X5 @ A5)) => (top_to958727510le_alt = A5))))). % UNIV_eq_I
thf(fact_115_UNIV__eq__I, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((![X5 : produc16571293le_alt]: (member2048039092le_alt @ X5 @ A5)) => (top_to224369155le_alt = A5))))). % UNIV_eq_I
thf(fact_116_UNIV__eq__I, axiom,
    ((![A5 : set_se2071012361le_alt]: ((![X5 : set_Pr367596371le_alt]: (member1334244458le_alt @ X5 @ A5)) => (top_to469035705le_alt = A5))))). % UNIV_eq_I
thf(fact_117_Ball__def, axiom,
    ((ball_s1517873193le_alt = (^[A6 : set_se2071012361le_alt]: (^[P3 : set_Pr367596371le_alt > $o]: (![X : set_Pr367596371le_alt]: (((member1334244458le_alt @ X @ A6)) => ((P3 @ X))))))))). % Ball_def
thf(fact_118_Ball__def, axiom,
    ((ball_P2077952115le_alt = (^[A6 : set_Pr367596371le_alt]: (^[P3 : produc16571293le_alt > $o]: (![X : produc16571293le_alt]: (((member2048039092le_alt @ X @ A6)) => ((P3 @ X))))))))). % Ball_def
thf(fact_119_Un__left__commute, axiom,
    ((![A5 : set_Pr367596371le_alt, B4 : set_Pr367596371le_alt, C2 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ A5 @ (sup_su1902543487le_alt @ B4 @ C2)) = (sup_su1902543487le_alt @ B4 @ (sup_su1902543487le_alt @ A5 @ C2)))))). % Un_left_commute
thf(fact_120_Un__left__absorb, axiom,
    ((![A5 : set_Pr367596371le_alt, B4 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ A5 @ (sup_su1902543487le_alt @ A5 @ B4)) = (sup_su1902543487le_alt @ A5 @ B4))))). % Un_left_absorb
thf(fact_121_Un__commute, axiom,
    ((sup_su1902543487le_alt = (^[A6 : set_Pr367596371le_alt]: (^[B7 : set_Pr367596371le_alt]: (sup_su1902543487le_alt @ B7 @ A6)))))). % Un_commute
thf(fact_122_Un__absorb, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ A5 @ A5) = A5)))). % Un_absorb
thf(fact_123_Un__assoc, axiom,
    ((![A5 : set_Pr367596371le_alt, B4 : set_Pr367596371le_alt, C2 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ (sup_su1902543487le_alt @ A5 @ B4) @ C2) = (sup_su1902543487le_alt @ A5 @ (sup_su1902543487le_alt @ B4 @ C2)))))). % Un_assoc
thf(fact_124_ball__Un, axiom,
    ((![A5 : set_Pr367596371le_alt, B4 : set_Pr367596371le_alt, P : produc16571293le_alt > $o]: ((![X : produc16571293le_alt]: (((member2048039092le_alt @ X @ (sup_su1902543487le_alt @ A5 @ B4))) => ((P @ X)))) = (((![X : produc16571293le_alt]: (((member2048039092le_alt @ X @ A5)) => ((P @ X))))) & ((![X : produc16571293le_alt]: (((member2048039092le_alt @ X @ B4)) => ((P @ X)))))))))). % ball_Un
thf(fact_125_bex__Un, axiom,
    ((![A5 : set_Pr367596371le_alt, B4 : set_Pr367596371le_alt, P : produc16571293le_alt > $o]: ((?[X : produc16571293le_alt]: (((member2048039092le_alt @ X @ (sup_su1902543487le_alt @ A5 @ B4))) & ((P @ X)))) = (((?[X : produc16571293le_alt]: (((member2048039092le_alt @ X @ A5)) & ((P @ X))))) | ((?[X : produc16571293le_alt]: (((member2048039092le_alt @ X @ B4)) & ((P @ X)))))))))). % bex_Un
thf(fact_126_UnI2, axiom,
    ((![C : set_Pr367596371le_alt, B4 : set_se2071012361le_alt, A5 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ B4) => (member1334244458le_alt @ C @ (sup_su255583029le_alt @ A5 @ B4)))))). % UnI2
thf(fact_127_UnI2, axiom,
    ((![C : produc16571293le_alt, B4 : set_Pr367596371le_alt, A5 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ B4) => (member2048039092le_alt @ C @ (sup_su1902543487le_alt @ A5 @ B4)))))). % UnI2
thf(fact_128_UnI1, axiom,
    ((![C : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B4 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ A5) => (member1334244458le_alt @ C @ (sup_su255583029le_alt @ A5 @ B4)))))). % UnI1
thf(fact_129_UnI1, axiom,
    ((![C : produc16571293le_alt, A5 : set_Pr367596371le_alt, B4 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ A5) => (member2048039092le_alt @ C @ (sup_su1902543487le_alt @ A5 @ B4)))))). % UnI1
thf(fact_130_UnE, axiom,
    ((![C : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B4 : set_se2071012361le_alt]: ((member1334244458le_alt @ C @ (sup_su255583029le_alt @ A5 @ B4)) => ((~ ((member1334244458le_alt @ C @ A5))) => (member1334244458le_alt @ C @ B4)))))). % UnE
thf(fact_131_UnE, axiom,
    ((![C : produc16571293le_alt, A5 : set_Pr367596371le_alt, B4 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (sup_su1902543487le_alt @ A5 @ B4)) => ((~ ((member2048039092le_alt @ C @ A5))) => (member2048039092le_alt @ C @ B4)))))). % UnE
thf(fact_132_in__mktop, axiom,
    ((![X3 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, Z2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y4) @ (arrow_992294841_mktop @ L2 @ Z2)) = (((~ ((X3 = Z2)))) & ((((((Y4 = Z2)) => ((~ ((X3 = Y4)))))) & ((((~ ((Y4 = Z2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y4) @ L2))))))))))). % in_mktop
thf(fact_133_in__mkbot, axiom,
    ((![X3 : arrow_1857593510le_alt, Y4 : arrow_1857593510le_alt, L2 : set_Pr367596371le_alt, Z2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y4) @ (arrow_843587755_mkbot @ L2 @ Z2)) = (((~ ((Y4 = Z2)))) & ((((((X3 = Z2)) => ((~ ((X3 = Y4)))))) & ((((~ ((X3 = Z2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y4) @ L2))))))))))). % in_mkbot
thf(fact_134_empty__def, axiom,
    ((bot_bo1596236775le_alt = (collec531981554le_alt @ (^[X : produc16571293le_alt]: $false))))). % empty_def
thf(fact_135_empty__def, axiom,
    ((bot_bo1127707250le_alt = (collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: $false))))). % empty_def
thf(fact_136_empty__def, axiom,
    ((bot_bo1518363805le_alt = (collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: $false))))). % empty_def
thf(fact_137_insert__Collect, axiom,
    ((![A2 : set_Pr367596371le_alt, P : set_Pr367596371le_alt > $o]: ((insert15522179le_alt @ A2 @ (collec1399441576le_alt @ P)) = (collec1399441576le_alt @ (^[U : set_Pr367596371le_alt]: (((~ ((U = A2)))) => ((P @ U))))))))). % insert_Collect
thf(fact_138_insert__Collect, axiom,
    ((![A2 : produc16571293le_alt, P : produc16571293le_alt > $o]: ((insert1454465485le_alt @ A2 @ (collec531981554le_alt @ P)) = (collec531981554le_alt @ (^[U : produc16571293le_alt]: (((~ ((U = A2)))) => ((P @ U))))))))). % insert_Collect
thf(fact_139_insert__Collect, axiom,
    ((![A2 : arrow_1857593510le_alt, P : arrow_1857593510le_alt > $o]: ((insert1093389942le_alt @ A2 @ (collec1364151825le_alt @ P)) = (collec1364151825le_alt @ (^[U : arrow_1857593510le_alt]: (((~ ((U = A2)))) => ((P @ U))))))))). % insert_Collect
thf(fact_140_insert__compr, axiom,
    ((insert15522179le_alt = (^[A : set_Pr367596371le_alt]: (^[B7 : set_se2071012361le_alt]: (collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (((X = A)) | ((member1334244458le_alt @ X @ B7)))))))))). % insert_compr
thf(fact_141_insert__compr, axiom,
    ((insert1454465485le_alt = (^[A : produc16571293le_alt]: (^[B7 : set_Pr367596371le_alt]: (collec531981554le_alt @ (^[X : produc16571293le_alt]: (((X = A)) | ((member2048039092le_alt @ X @ B7)))))))))). % insert_compr
thf(fact_142_insert__compr, axiom,
    ((insert1093389942le_alt = (^[A : arrow_1857593510le_alt]: (^[B7 : set_Ar1665529862le_alt]: (collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: (((X = A)) | ((member519365071le_alt @ X @ B7)))))))))). % insert_compr
thf(fact_143_UNIV__def, axiom,
    ((top_to958727510le_alt = (collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: $true))))). % UNIV_def
thf(fact_144_UNIV__def, axiom,
    ((top_to224369155le_alt = (collec531981554le_alt @ (^[X : produc16571293le_alt]: $true))))). % UNIV_def
thf(fact_145_UNIV__def, axiom,
    ((top_to469035705le_alt = (collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: $true))))). % UNIV_def
thf(fact_146_prod_Ocase__distrib, axiom,
    ((![H : $o > $o, F : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, Prod : produc16571293le_alt]: ((H @ (produc624247124_alt_o @ F @ Prod)) = (produc624247124_alt_o @ (^[X12 : arrow_1857593510le_alt]: (^[X23 : arrow_1857593510le_alt]: (H @ (F @ X12 @ X23)))) @ Prod))))). % prod.case_distrib
thf(fact_147_Collect__disj__eq, axiom,
    ((![P : set_Pr367596371le_alt > $o, Q : set_Pr367596371le_alt > $o]: ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (((P @ X)) | ((Q @ X))))) = (sup_su255583029le_alt @ (collec1399441576le_alt @ P) @ (collec1399441576le_alt @ Q)))))). % Collect_disj_eq
thf(fact_148_Collect__disj__eq, axiom,
    ((![P : arrow_1857593510le_alt > $o, Q : arrow_1857593510le_alt > $o]: ((collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: (((P @ X)) | ((Q @ X))))) = (sup_su1032097242le_alt @ (collec1364151825le_alt @ P) @ (collec1364151825le_alt @ Q)))))). % Collect_disj_eq
thf(fact_149_Collect__disj__eq, axiom,
    ((![P : produc16571293le_alt > $o, Q : produc16571293le_alt > $o]: ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (((P @ X)) | ((Q @ X))))) = (sup_su1902543487le_alt @ (collec531981554le_alt @ P) @ (collec531981554le_alt @ Q)))))). % Collect_disj_eq
thf(fact_150_Un__def, axiom,
    ((sup_su255583029le_alt = (^[A6 : set_se2071012361le_alt]: (^[B7 : set_se2071012361le_alt]: (collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (((member1334244458le_alt @ X @ A6)) | ((member1334244458le_alt @ X @ B7)))))))))). % Un_def
thf(fact_151_Un__def, axiom,
    ((sup_su1032097242le_alt = (^[A6 : set_Ar1665529862le_alt]: (^[B7 : set_Ar1665529862le_alt]: (collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: (((member519365071le_alt @ X @ A6)) | ((member519365071le_alt @ X @ B7)))))))))). % Un_def
thf(fact_152_Un__def, axiom,
    ((sup_su1902543487le_alt = (^[A6 : set_Pr367596371le_alt]: (^[B7 : set_Pr367596371le_alt]: (collec531981554le_alt @ (^[X : produc16571293le_alt]: (((member2048039092le_alt @ X @ A6)) | ((member2048039092le_alt @ X @ B7)))))))))). % Un_def
thf(fact_153_prod_Odisc__eq__case, axiom,
    ((![Prod : produc16571293le_alt]: (produc624247124_alt_o @ (^[Uu : arrow_1857593510le_alt]: (^[Uv : arrow_1857593510le_alt]: $true)) @ Prod)))). % prod.disc_eq_case
thf(fact_154_singleton__inject, axiom,
    ((![A2 : produc16571293le_alt, B2 : produc16571293le_alt]: (((insert1454465485le_alt @ A2 @ bot_bo1596236775le_alt) = (insert1454465485le_alt @ B2 @ bot_bo1596236775le_alt)) => (A2 = B2))))). % singleton_inject
thf(fact_155_singleton__inject, axiom,
    ((![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((insert1093389942le_alt @ A2 @ bot_bo1127707250le_alt) = (insert1093389942le_alt @ B2 @ bot_bo1127707250le_alt)) => (A2 = B2))))). % singleton_inject
thf(fact_156_singleton__inject, axiom,
    ((![A2 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt]: (((insert15522179le_alt @ A2 @ bot_bo1518363805le_alt) = (insert15522179le_alt @ B2 @ bot_bo1518363805le_alt)) => (A2 = B2))))). % singleton_inject
thf(fact_157_insert__not__empty, axiom,
    ((![A2 : produc16571293le_alt, A5 : set_Pr367596371le_alt]: (~ (((insert1454465485le_alt @ A2 @ A5) = bot_bo1596236775le_alt)))))). % insert_not_empty
thf(fact_158_insert__not__empty, axiom,
    ((![A2 : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt]: (~ (((insert1093389942le_alt @ A2 @ A5) = bot_bo1127707250le_alt)))))). % insert_not_empty
thf(fact_159_insert__not__empty, axiom,
    ((![A2 : set_Pr367596371le_alt, A5 : set_se2071012361le_alt]: (~ (((insert15522179le_alt @ A2 @ A5) = bot_bo1518363805le_alt)))))). % insert_not_empty
thf(fact_160_doubleton__eq__iff, axiom,
    ((![A2 : produc16571293le_alt, B2 : produc16571293le_alt, C : produc16571293le_alt, D : produc16571293le_alt]: (((insert1454465485le_alt @ A2 @ (insert1454465485le_alt @ B2 @ bot_bo1596236775le_alt)) = (insert1454465485le_alt @ C @ (insert1454465485le_alt @ D @ bot_bo1596236775le_alt))) = (((((A2 = C)) & ((B2 = D)))) | ((((A2 = D)) & ((B2 = C))))))))). % doubleton_eq_iff
thf(fact_161_doubleton__eq__iff, axiom,
    ((![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, C : arrow_1857593510le_alt, D : arrow_1857593510le_alt]: (((insert1093389942le_alt @ A2 @ (insert1093389942le_alt @ B2 @ bot_bo1127707250le_alt)) = (insert1093389942le_alt @ C @ (insert1093389942le_alt @ D @ bot_bo1127707250le_alt))) = (((((A2 = C)) & ((B2 = D)))) | ((((A2 = D)) & ((B2 = C))))))))). % doubleton_eq_iff
thf(fact_162_doubleton__eq__iff, axiom,
    ((![A2 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt, C : set_Pr367596371le_alt, D : set_Pr367596371le_alt]: (((insert15522179le_alt @ A2 @ (insert15522179le_alt @ B2 @ bot_bo1518363805le_alt)) = (insert15522179le_alt @ C @ (insert15522179le_alt @ D @ bot_bo1518363805le_alt))) = (((((A2 = C)) & ((B2 = D)))) | ((((A2 = D)) & ((B2 = C))))))))). % doubleton_eq_iff
thf(fact_163_singleton__iff, axiom,
    ((![B2 : produc16571293le_alt, A2 : produc16571293le_alt]: ((member2048039092le_alt @ B2 @ (insert1454465485le_alt @ A2 @ bot_bo1596236775le_alt)) = (B2 = A2))))). % singleton_iff
thf(fact_164_singleton__iff, axiom,
    ((![B2 : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt]: ((member519365071le_alt @ B2 @ (insert1093389942le_alt @ A2 @ bot_bo1127707250le_alt)) = (B2 = A2))))). % singleton_iff
thf(fact_165_singleton__iff, axiom,
    ((![B2 : set_Pr367596371le_alt, A2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ B2 @ (insert15522179le_alt @ A2 @ bot_bo1518363805le_alt)) = (B2 = A2))))). % singleton_iff
thf(fact_166_singletonD, axiom,
    ((![B2 : produc16571293le_alt, A2 : produc16571293le_alt]: ((member2048039092le_alt @ B2 @ (insert1454465485le_alt @ A2 @ bot_bo1596236775le_alt)) => (B2 = A2))))). % singletonD
thf(fact_167_singletonD, axiom,
    ((![B2 : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt]: ((member519365071le_alt @ B2 @ (insert1093389942le_alt @ A2 @ bot_bo1127707250le_alt)) => (B2 = A2))))). % singletonD
thf(fact_168_singletonD, axiom,
    ((![B2 : set_Pr367596371le_alt, A2 : set_Pr367596371le_alt]: ((member1334244458le_alt @ B2 @ (insert15522179le_alt @ A2 @ bot_bo1518363805le_alt)) => (B2 = A2))))). % singletonD
thf(fact_169_empty__not__UNIV, axiom,
    ((~ ((bot_bo1127707250le_alt = top_to958727510le_alt))))). % empty_not_UNIV
thf(fact_170_empty__not__UNIV, axiom,
    ((~ ((bot_bo1596236775le_alt = top_to224369155le_alt))))). % empty_not_UNIV
thf(fact_171_empty__not__UNIV, axiom,
    ((~ ((bot_bo1518363805le_alt = top_to469035705le_alt))))). % empty_not_UNIV
thf(fact_172_old_Oprod_Ocase, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X1 : arrow_1857593510le_alt, X22 : arrow_1857593510le_alt]: ((produc624247124_alt_o @ F @ (produc1494124311le_alt @ X1 @ X22)) = (F @ X1 @ X22))))). % old.prod.case
thf(fact_173_insert__UNIV, axiom,
    ((![X3 : arrow_1857593510le_alt]: ((insert1093389942le_alt @ X3 @ top_to958727510le_alt) = top_to958727510le_alt)))). % insert_UNIV
thf(fact_174_insert__UNIV, axiom,
    ((![X3 : produc16571293le_alt]: ((insert1454465485le_alt @ X3 @ top_to224369155le_alt) = top_to224369155le_alt)))). % insert_UNIV
thf(fact_175_insert__UNIV, axiom,
    ((![X3 : set_Pr367596371le_alt]: ((insert15522179le_alt @ X3 @ top_to469035705le_alt) = top_to469035705le_alt)))). % insert_UNIV
thf(fact_176_Un__empty__right, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ A5 @ bot_bo1596236775le_alt) = A5)))). % Un_empty_right
thf(fact_177_Un__empty__right, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((sup_su1032097242le_alt @ A5 @ bot_bo1127707250le_alt) = A5)))). % Un_empty_right
thf(fact_178_Un__empty__right, axiom,
    ((![A5 : set_se2071012361le_alt]: ((sup_su255583029le_alt @ A5 @ bot_bo1518363805le_alt) = A5)))). % Un_empty_right
thf(fact_179_Un__empty__left, axiom,
    ((![B4 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ bot_bo1596236775le_alt @ B4) = B4)))). % Un_empty_left
thf(fact_180_Un__empty__left, axiom,
    ((![B4 : set_Ar1665529862le_alt]: ((sup_su1032097242le_alt @ bot_bo1127707250le_alt @ B4) = B4)))). % Un_empty_left
thf(fact_181_Un__empty__left, axiom,
    ((![B4 : set_se2071012361le_alt]: ((sup_su255583029le_alt @ bot_bo1518363805le_alt @ B4) = B4)))). % Un_empty_left
thf(fact_182_Un__UNIV__right, axiom,
    ((![A5 : set_Ar1665529862le_alt]: ((sup_su1032097242le_alt @ A5 @ top_to958727510le_alt) = top_to958727510le_alt)))). % Un_UNIV_right
thf(fact_183_Un__UNIV__right, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ A5 @ top_to224369155le_alt) = top_to224369155le_alt)))). % Un_UNIV_right
thf(fact_184_Un__UNIV__right, axiom,
    ((![A5 : set_se2071012361le_alt]: ((sup_su255583029le_alt @ A5 @ top_to469035705le_alt) = top_to469035705le_alt)))). % Un_UNIV_right
thf(fact_185_Un__UNIV__left, axiom,
    ((![B4 : set_Ar1665529862le_alt]: ((sup_su1032097242le_alt @ top_to958727510le_alt @ B4) = top_to958727510le_alt)))). % Un_UNIV_left
thf(fact_186_Un__UNIV__left, axiom,
    ((![B4 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ top_to224369155le_alt @ B4) = top_to224369155le_alt)))). % Un_UNIV_left
thf(fact_187_Un__UNIV__left, axiom,
    ((![B4 : set_se2071012361le_alt]: ((sup_su255583029le_alt @ top_to469035705le_alt @ B4) = top_to469035705le_alt)))). % Un_UNIV_left
thf(fact_188_Collect__conv__if2, axiom,
    ((![P : produc16571293le_alt > $o, A2 : produc16571293le_alt]: (((P @ A2) => ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (((A2 = X)) & ((P @ X))))) = (insert1454465485le_alt @ A2 @ bot_bo1596236775le_alt))) & ((~ ((P @ A2))) => ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (((A2 = X)) & ((P @ X))))) = bot_bo1596236775le_alt)))))). % Collect_conv_if2
thf(fact_189_Collect__conv__if2, axiom,
    ((![P : arrow_1857593510le_alt > $o, A2 : arrow_1857593510le_alt]: (((P @ A2) => ((collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: (((A2 = X)) & ((P @ X))))) = (insert1093389942le_alt @ A2 @ bot_bo1127707250le_alt))) & ((~ ((P @ A2))) => ((collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: (((A2 = X)) & ((P @ X))))) = bot_bo1127707250le_alt)))))). % Collect_conv_if2
thf(fact_190_Collect__conv__if2, axiom,
    ((![P : set_Pr367596371le_alt > $o, A2 : set_Pr367596371le_alt]: (((P @ A2) => ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (((A2 = X)) & ((P @ X))))) = (insert15522179le_alt @ A2 @ bot_bo1518363805le_alt))) & ((~ ((P @ A2))) => ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (((A2 = X)) & ((P @ X))))) = bot_bo1518363805le_alt)))))). % Collect_conv_if2
thf(fact_191_Collect__conv__if, axiom,
    ((![P : produc16571293le_alt > $o, A2 : produc16571293le_alt]: (((P @ A2) => ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (((X = A2)) & ((P @ X))))) = (insert1454465485le_alt @ A2 @ bot_bo1596236775le_alt))) & ((~ ((P @ A2))) => ((collec531981554le_alt @ (^[X : produc16571293le_alt]: (((X = A2)) & ((P @ X))))) = bot_bo1596236775le_alt)))))). % Collect_conv_if
thf(fact_192_Collect__conv__if, axiom,
    ((![P : arrow_1857593510le_alt > $o, A2 : arrow_1857593510le_alt]: (((P @ A2) => ((collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: (((X = A2)) & ((P @ X))))) = (insert1093389942le_alt @ A2 @ bot_bo1127707250le_alt))) & ((~ ((P @ A2))) => ((collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: (((X = A2)) & ((P @ X))))) = bot_bo1127707250le_alt)))))). % Collect_conv_if
thf(fact_193_Collect__conv__if, axiom,
    ((![P : set_Pr367596371le_alt > $o, A2 : set_Pr367596371le_alt]: (((P @ A2) => ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (((X = A2)) & ((P @ X))))) = (insert15522179le_alt @ A2 @ bot_bo1518363805le_alt))) & ((~ ((P @ A2))) => ((collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (((X = A2)) & ((P @ X))))) = bot_bo1518363805le_alt)))))). % Collect_conv_if
thf(fact_194_cond__case__prod__eta, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, G : produc16571293le_alt > $o]: ((![X5 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((F @ X5 @ Y3) = (G @ (produc1494124311le_alt @ X5 @ Y3)))) => ((produc624247124_alt_o @ F) = G))))). % cond_case_prod_eta
thf(fact_195_case__prod__eta, axiom,
    ((![F : produc16571293le_alt > $o]: ((produc624247124_alt_o @ (^[X : arrow_1857593510le_alt]: (^[Y : arrow_1857593510le_alt]: (F @ (produc1494124311le_alt @ X @ Y))))) = F)))). % case_prod_eta
thf(fact_196_case__prodE2, axiom,
    ((![Q : $o > $o, P : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, Z2 : produc16571293le_alt]: ((Q @ (produc624247124_alt_o @ P @ Z2)) => (~ ((![X5 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((Z2 = (produc1494124311le_alt @ X5 @ Y3)) => (~ ((Q @ (P @ X5 @ Y3)))))))))))). % case_prodE2
thf(fact_197_insert__def, axiom,
    ((insert15522179le_alt = (^[A : set_Pr367596371le_alt]: (sup_su255583029le_alt @ (collec1399441576le_alt @ (^[X : set_Pr367596371le_alt]: (X = A)))))))). % insert_def
thf(fact_198_insert__def, axiom,
    ((insert1093389942le_alt = (^[A : arrow_1857593510le_alt]: (sup_su1032097242le_alt @ (collec1364151825le_alt @ (^[X : arrow_1857593510le_alt]: (X = A)))))))). % insert_def
thf(fact_199_insert__def, axiom,
    ((insert1454465485le_alt = (^[A : produc16571293le_alt]: (sup_su1902543487le_alt @ (collec531981554le_alt @ (^[X : produc16571293le_alt]: (X = A)))))))). % insert_def
thf(fact_200_case__prodE, axiom,
    ((![C : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, P2 : produc16571293le_alt]: ((produc624247124_alt_o @ C @ P2) => (~ ((![X5 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P2 = (produc1494124311le_alt @ X5 @ Y3)) => (~ ((C @ X5 @ Y3))))))))))). % case_prodE
thf(fact_201_case__prodD, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: ((produc624247124_alt_o @ F @ (produc1494124311le_alt @ A2 @ B2)) => (F @ A2 @ B2))))). % case_prodD
thf(fact_202_singleton__Un__iff, axiom,
    ((![X3 : produc16571293le_alt, A5 : set_Pr367596371le_alt, B4 : set_Pr367596371le_alt]: (((insert1454465485le_alt @ X3 @ bot_bo1596236775le_alt) = (sup_su1902543487le_alt @ A5 @ B4)) = (((((A5 = bot_bo1596236775le_alt)) & ((B4 = (insert1454465485le_alt @ X3 @ bot_bo1596236775le_alt))))) | ((((((A5 = (insert1454465485le_alt @ X3 @ bot_bo1596236775le_alt))) & ((B4 = bot_bo1596236775le_alt)))) | ((((A5 = (insert1454465485le_alt @ X3 @ bot_bo1596236775le_alt))) & ((B4 = (insert1454465485le_alt @ X3 @ bot_bo1596236775le_alt)))))))))))). % singleton_Un_iff
thf(fact_203_singleton__Un__iff, axiom,
    ((![X3 : arrow_1857593510le_alt, A5 : set_Ar1665529862le_alt, B4 : set_Ar1665529862le_alt]: (((insert1093389942le_alt @ X3 @ bot_bo1127707250le_alt) = (sup_su1032097242le_alt @ A5 @ B4)) = (((((A5 = bot_bo1127707250le_alt)) & ((B4 = (insert1093389942le_alt @ X3 @ bot_bo1127707250le_alt))))) | ((((((A5 = (insert1093389942le_alt @ X3 @ bot_bo1127707250le_alt))) & ((B4 = bot_bo1127707250le_alt)))) | ((((A5 = (insert1093389942le_alt @ X3 @ bot_bo1127707250le_alt))) & ((B4 = (insert1093389942le_alt @ X3 @ bot_bo1127707250le_alt)))))))))))). % singleton_Un_iff
thf(fact_204_singleton__Un__iff, axiom,
    ((![X3 : set_Pr367596371le_alt, A5 : set_se2071012361le_alt, B4 : set_se2071012361le_alt]: (((insert15522179le_alt @ X3 @ bot_bo1518363805le_alt) = (sup_su255583029le_alt @ A5 @ B4)) = (((((A5 = bot_bo1518363805le_alt)) & ((B4 = (insert15522179le_alt @ X3 @ bot_bo1518363805le_alt))))) | ((((((A5 = (insert15522179le_alt @ X3 @ bot_bo1518363805le_alt))) & ((B4 = bot_bo1518363805le_alt)))) | ((((A5 = (insert15522179le_alt @ X3 @ bot_bo1518363805le_alt))) & ((B4 = (insert15522179le_alt @ X3 @ bot_bo1518363805le_alt)))))))))))). % singleton_Un_iff
thf(fact_205_Un__singleton__iff, axiom,
    ((![A5 : set_Pr367596371le_alt, B4 : set_Pr367596371le_alt, X3 : produc16571293le_alt]: (((sup_su1902543487le_alt @ A5 @ B4) = (insert1454465485le_alt @ X3 @ bot_bo1596236775le_alt)) = (((((A5 = bot_bo1596236775le_alt)) & ((B4 = (insert1454465485le_alt @ X3 @ bot_bo1596236775le_alt))))) | ((((((A5 = (insert1454465485le_alt @ X3 @ bot_bo1596236775le_alt))) & ((B4 = bot_bo1596236775le_alt)))) | ((((A5 = (insert1454465485le_alt @ X3 @ bot_bo1596236775le_alt))) & ((B4 = (insert1454465485le_alt @ X3 @ bot_bo1596236775le_alt)))))))))))). % Un_singleton_iff
thf(fact_206_Un__singleton__iff, axiom,
    ((![A5 : set_Ar1665529862le_alt, B4 : set_Ar1665529862le_alt, X3 : arrow_1857593510le_alt]: (((sup_su1032097242le_alt @ A5 @ B4) = (insert1093389942le_alt @ X3 @ bot_bo1127707250le_alt)) = (((((A5 = bot_bo1127707250le_alt)) & ((B4 = (insert1093389942le_alt @ X3 @ bot_bo1127707250le_alt))))) | ((((((A5 = (insert1093389942le_alt @ X3 @ bot_bo1127707250le_alt))) & ((B4 = bot_bo1127707250le_alt)))) | ((((A5 = (insert1093389942le_alt @ X3 @ bot_bo1127707250le_alt))) & ((B4 = (insert1093389942le_alt @ X3 @ bot_bo1127707250le_alt)))))))))))). % Un_singleton_iff
thf(fact_207_Un__singleton__iff, axiom,
    ((![A5 : set_se2071012361le_alt, B4 : set_se2071012361le_alt, X3 : set_Pr367596371le_alt]: (((sup_su255583029le_alt @ A5 @ B4) = (insert15522179le_alt @ X3 @ bot_bo1518363805le_alt)) = (((((A5 = bot_bo1518363805le_alt)) & ((B4 = (insert15522179le_alt @ X3 @ bot_bo1518363805le_alt))))) | ((((((A5 = (insert15522179le_alt @ X3 @ bot_bo1518363805le_alt))) & ((B4 = bot_bo1518363805le_alt)))) | ((((A5 = (insert15522179le_alt @ X3 @ bot_bo1518363805le_alt))) & ((B4 = (insert15522179le_alt @ X3 @ bot_bo1518363805le_alt)))))))))))). % Un_singleton_iff
thf(fact_208_insert__is__Un, axiom,
    ((insert1454465485le_alt = (^[A : produc16571293le_alt]: (sup_su1902543487le_alt @ (insert1454465485le_alt @ A @ bot_bo1596236775le_alt)))))). % insert_is_Un
thf(fact_209_insert__is__Un, axiom,
    ((insert1093389942le_alt = (^[A : arrow_1857593510le_alt]: (sup_su1032097242le_alt @ (insert1093389942le_alt @ A @ bot_bo1127707250le_alt)))))). % insert_is_Un
thf(fact_210_insert__is__Un, axiom,
    ((insert15522179le_alt = (^[A : set_Pr367596371le_alt]: (sup_su255583029le_alt @ (insert15522179le_alt @ A @ bot_bo1518363805le_alt)))))). % insert_is_Un
thf(fact_211_sup__top__right, axiom,
    ((![X3 : set_Ar1665529862le_alt]: ((sup_su1032097242le_alt @ X3 @ top_to958727510le_alt) = top_to958727510le_alt)))). % sup_top_right
thf(fact_212_sup__top__right, axiom,
    ((![X3 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ X3 @ top_to224369155le_alt) = top_to224369155le_alt)))). % sup_top_right
thf(fact_213_sup__top__right, axiom,
    ((![X3 : set_se2071012361le_alt]: ((sup_su255583029le_alt @ X3 @ top_to469035705le_alt) = top_to469035705le_alt)))). % sup_top_right
thf(fact_214_sup__top__left, axiom,
    ((![X3 : set_Ar1665529862le_alt]: ((sup_su1032097242le_alt @ top_to958727510le_alt @ X3) = top_to958727510le_alt)))). % sup_top_left
thf(fact_215_sup__top__left, axiom,
    ((![X3 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ top_to224369155le_alt @ X3) = top_to224369155le_alt)))). % sup_top_left
thf(fact_216_sup__top__left, axiom,
    ((![X3 : set_se2071012361le_alt]: ((sup_su255583029le_alt @ top_to469035705le_alt @ X3) = top_to469035705le_alt)))). % sup_top_left
thf(fact_217_sup__bot_Oright__neutral, axiom,
    ((![A2 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ A2 @ bot_bo1596236775le_alt) = A2)))). % sup_bot.right_neutral
thf(fact_218_sup__bot_Oright__neutral, axiom,
    ((![A2 : set_Ar1665529862le_alt]: ((sup_su1032097242le_alt @ A2 @ bot_bo1127707250le_alt) = A2)))). % sup_bot.right_neutral
thf(fact_219_sup__bot_Oright__neutral, axiom,
    ((![A2 : set_se2071012361le_alt]: ((sup_su255583029le_alt @ A2 @ bot_bo1518363805le_alt) = A2)))). % sup_bot.right_neutral
thf(fact_220_sup__bot_Oneutr__eq__iff, axiom,
    ((![A2 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt]: ((bot_bo1596236775le_alt = (sup_su1902543487le_alt @ A2 @ B2)) = (((A2 = bot_bo1596236775le_alt)) & ((B2 = bot_bo1596236775le_alt))))))). % sup_bot.neutr_eq_iff
thf(fact_221_sup__bot_Oneutr__eq__iff, axiom,
    ((![A2 : set_Ar1665529862le_alt, B2 : set_Ar1665529862le_alt]: ((bot_bo1127707250le_alt = (sup_su1032097242le_alt @ A2 @ B2)) = (((A2 = bot_bo1127707250le_alt)) & ((B2 = bot_bo1127707250le_alt))))))). % sup_bot.neutr_eq_iff
thf(fact_222_sup__bot_Oneutr__eq__iff, axiom,
    ((![A2 : set_se2071012361le_alt, B2 : set_se2071012361le_alt]: ((bot_bo1518363805le_alt = (sup_su255583029le_alt @ A2 @ B2)) = (((A2 = bot_bo1518363805le_alt)) & ((B2 = bot_bo1518363805le_alt))))))). % sup_bot.neutr_eq_iff
thf(fact_223_sup__bot_Oleft__neutral, axiom,
    ((![A2 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ bot_bo1596236775le_alt @ A2) = A2)))). % sup_bot.left_neutral
thf(fact_224_sup__bot_Oleft__neutral, axiom,
    ((![A2 : set_Ar1665529862le_alt]: ((sup_su1032097242le_alt @ bot_bo1127707250le_alt @ A2) = A2)))). % sup_bot.left_neutral
thf(fact_225_sup__bot_Oleft__neutral, axiom,
    ((![A2 : set_se2071012361le_alt]: ((sup_su255583029le_alt @ bot_bo1518363805le_alt @ A2) = A2)))). % sup_bot.left_neutral
thf(fact_226_sup__bot_Oeq__neutr__iff, axiom,
    ((![A2 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt]: (((sup_su1902543487le_alt @ A2 @ B2) = bot_bo1596236775le_alt) = (((A2 = bot_bo1596236775le_alt)) & ((B2 = bot_bo1596236775le_alt))))))). % sup_bot.eq_neutr_iff
thf(fact_227_sup__bot_Oeq__neutr__iff, axiom,
    ((![A2 : set_Ar1665529862le_alt, B2 : set_Ar1665529862le_alt]: (((sup_su1032097242le_alt @ A2 @ B2) = bot_bo1127707250le_alt) = (((A2 = bot_bo1127707250le_alt)) & ((B2 = bot_bo1127707250le_alt))))))). % sup_bot.eq_neutr_iff
thf(fact_228_sup__bot_Oeq__neutr__iff, axiom,
    ((![A2 : set_se2071012361le_alt, B2 : set_se2071012361le_alt]: (((sup_su255583029le_alt @ A2 @ B2) = bot_bo1518363805le_alt) = (((A2 = bot_bo1518363805le_alt)) & ((B2 = bot_bo1518363805le_alt))))))). % sup_bot.eq_neutr_iff
thf(fact_229_sup__eq__bot__iff, axiom,
    ((![X3 : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt]: (((sup_su1902543487le_alt @ X3 @ Y4) = bot_bo1596236775le_alt) = (((X3 = bot_bo1596236775le_alt)) & ((Y4 = bot_bo1596236775le_alt))))))). % sup_eq_bot_iff
thf(fact_230_sup__eq__bot__iff, axiom,
    ((![X3 : set_Ar1665529862le_alt, Y4 : set_Ar1665529862le_alt]: (((sup_su1032097242le_alt @ X3 @ Y4) = bot_bo1127707250le_alt) = (((X3 = bot_bo1127707250le_alt)) & ((Y4 = bot_bo1127707250le_alt))))))). % sup_eq_bot_iff
thf(fact_231_sup__eq__bot__iff, axiom,
    ((![X3 : set_se2071012361le_alt, Y4 : set_se2071012361le_alt]: (((sup_su255583029le_alt @ X3 @ Y4) = bot_bo1518363805le_alt) = (((X3 = bot_bo1518363805le_alt)) & ((Y4 = bot_bo1518363805le_alt))))))). % sup_eq_bot_iff
thf(fact_232_bot__eq__sup__iff, axiom,
    ((![X3 : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt]: ((bot_bo1596236775le_alt = (sup_su1902543487le_alt @ X3 @ Y4)) = (((X3 = bot_bo1596236775le_alt)) & ((Y4 = bot_bo1596236775le_alt))))))). % bot_eq_sup_iff
thf(fact_233_bot__eq__sup__iff, axiom,
    ((![X3 : set_Ar1665529862le_alt, Y4 : set_Ar1665529862le_alt]: ((bot_bo1127707250le_alt = (sup_su1032097242le_alt @ X3 @ Y4)) = (((X3 = bot_bo1127707250le_alt)) & ((Y4 = bot_bo1127707250le_alt))))))). % bot_eq_sup_iff
thf(fact_234_bot__eq__sup__iff, axiom,
    ((![X3 : set_se2071012361le_alt, Y4 : set_se2071012361le_alt]: ((bot_bo1518363805le_alt = (sup_su255583029le_alt @ X3 @ Y4)) = (((X3 = bot_bo1518363805le_alt)) & ((Y4 = bot_bo1518363805le_alt))))))). % bot_eq_sup_iff
thf(fact_235_sup__bot__right, axiom,
    ((![X3 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ X3 @ bot_bo1596236775le_alt) = X3)))). % sup_bot_right
thf(fact_236_sup__bot__right, axiom,
    ((![X3 : set_Ar1665529862le_alt]: ((sup_su1032097242le_alt @ X3 @ bot_bo1127707250le_alt) = X3)))). % sup_bot_right
thf(fact_237_sup__bot__right, axiom,
    ((![X3 : set_se2071012361le_alt]: ((sup_su255583029le_alt @ X3 @ bot_bo1518363805le_alt) = X3)))). % sup_bot_right
thf(fact_238_sup__bot__left, axiom,
    ((![X3 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ bot_bo1596236775le_alt @ X3) = X3)))). % sup_bot_left
thf(fact_239_sup__bot__left, axiom,
    ((![X3 : set_Ar1665529862le_alt]: ((sup_su1032097242le_alt @ bot_bo1127707250le_alt @ X3) = X3)))). % sup_bot_left
thf(fact_240_sup__bot__left, axiom,
    ((![X3 : set_se2071012361le_alt]: ((sup_su255583029le_alt @ bot_bo1518363805le_alt @ X3) = X3)))). % sup_bot_left
thf(fact_241_sup_Oidem, axiom,
    ((![A2 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ A2 @ A2) = A2)))). % sup.idem
thf(fact_242_sup__idem, axiom,
    ((![X3 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ X3 @ X3) = X3)))). % sup_idem
thf(fact_243_sup_Oleft__idem, axiom,
    ((![A2 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ A2 @ (sup_su1902543487le_alt @ A2 @ B2)) = (sup_su1902543487le_alt @ A2 @ B2))))). % sup.left_idem
thf(fact_244_sup__left__idem, axiom,
    ((![X3 : set_Pr367596371le_alt, Y4 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ X3 @ (sup_su1902543487le_alt @ X3 @ Y4)) = (sup_su1902543487le_alt @ X3 @ Y4))))). % sup_left_idem
thf(fact_245_sup_Oright__idem, axiom,
    ((![A2 : set_Pr367596371le_alt, B2 : set_Pr367596371le_alt]: ((sup_su1902543487le_alt @ (sup_su1902543487le_alt @ A2 @ B2) @ B2) = (sup_su1902543487le_alt @ A2 @ B2))))). % sup.right_idem
thf(fact_246_bot__set__def, axiom,
    ((bot_bo1596236775le_alt = (collec531981554le_alt @ bot_bo91657054_alt_o)))). % bot_set_def
thf(fact_247_bot__set__def, axiom,
    ((bot_bo1127707250le_alt = (collec1364151825le_alt @ bot_bo1380086507_alt_o)))). % bot_set_def
thf(fact_248_bot__set__def, axiom,
    ((bot_bo1518363805le_alt = (collec1399441576le_alt @ bot_bo2065212968_alt_o)))). % bot_set_def

% Conjectures (3)
thf(conj_0, hypothesis,
    ((~ ((x = y))))).
thf(conj_1, hypothesis,
    ((member1334244458le_alt @ l @ (collec1399441576le_alt @ (^[L : set_Pr367596371le_alt]: (((![X : arrow_1857593510le_alt]: (![Y : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L)) => ((![Z3 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ Y @ Z3) @ L)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Z3) @ L))))))))) & ((((![A : arrow_1857593510le_alt]: (~ ((member2048039092le_alt @ (produc1494124311le_alt @ A @ A) @ L))))) & ((![X : arrow_1857593510le_alt]: (((member519365071le_alt @ X @ top_to958727510le_alt)) => ((![Y : arrow_1857593510le_alt]: (((member519365071le_alt @ Y @ top_to958727510le_alt)) => ((((~ ((X = Y)))) => ((((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L)) | ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ L)))))))))))))))))))).
thf(conj_2, conjecture,
    ((member1334244458le_alt @ (sup_su1902543487le_alt @ (sup_su1902543487le_alt @ (sup_su1902543487le_alt @ (collec531981554le_alt @ (produc624247124_alt_o @ (^[X : arrow_1857593510le_alt]: (^[Y : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ l)) & ((((~ ((X = x)))) & ((~ ((Y = x))))))))))) @ (insert1454465485le_alt @ (produc1494124311le_alt @ x @ y) @ bot_bo1596236775le_alt)) @ (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[X : arrow_1857593510le_alt]: (((Uu = (produc1494124311le_alt @ X @ x))) & ((((member2048039092le_alt @ (produc1494124311le_alt @ X @ y) @ l)) & ((~ ((X = x))))))))))) @ (collec531981554le_alt @ (^[Uu : produc16571293le_alt]: (?[Y : arrow_1857593510le_alt]: (((Uu = (produc1494124311le_alt @ x @ Y))) & ((((member2048039092le_alt @ (produc1494124311le_alt @ y @ Y) @ l)) & ((~ ((Y = x))))))))))) @ (collec1399441576le_alt @ (^[L : set_Pr367596371le_alt]: (((![X : arrow_1857593510le_alt]: (![Y : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L)) => ((![Z3 : arrow_1857593510le_alt]: (((member2048039092le_alt @ (produc1494124311le_alt @ Y @ Z3) @ L)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Z3) @ L))))))))) & ((((![A : arrow_1857593510le_alt]: (~ ((member2048039092le_alt @ (produc1494124311le_alt @ A @ A) @ L))))) & ((![X : arrow_1857593510le_alt]: (((member519365071le_alt @ X @ top_to958727510le_alt)) => ((![Y : arrow_1857593510le_alt]: (((member519365071le_alt @ Y @ top_to958727510le_alt)) => ((((~ ((X = Y)))) => ((((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L)) | ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ L)))))))))))))))))))).
