% 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_147__5187326_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:16:16.661

% Could-be-implicit typings (6)
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__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 (38)
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_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    ord_le1885758387le_alt : set_Pr367596371le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_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,
    ord_le1836905577le_alt : set_se2071012361le_alt > set_se2071012361le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_M_Eo_J, type,
    top_to1074038850_alt_o : produc16571293le_alt > $o).
thf(sy_c_Orderings_Otop__class_Otop_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,
    top_to1900088076_alt_o : set_Pr367596371le_alt > $o).
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_Oapfst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1245692284le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Oapsnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1710313402le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_alt > produc16571293le_alt).
thf(sy_c_Product__Type_Ocurry_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001_Eo, type,
    produc392997491_alt_o : (produc16571293le_alt > $o) > arrow_1857593510le_alt > arrow_1857593510le_alt > $o).
thf(sy_c_Product__Type_Omap__prod_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1074667658le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc16571293le_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_Product__Type_Oprod_Ofst_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc2071652395le_alt : produc16571293le_alt > arrow_1857593510le_alt).
thf(sy_c_Product__Type_Oprod_Osnd_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1272650601le_alt : produc16571293le_alt > arrow_1857593510le_alt).
thf(sy_c_Product__Type_Oprod_Oswap_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc1794822519le_alt : produc16571293le_alt > produc16571293le_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_Oimage_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    image_1873259469le_alt : (produc16571293le_alt > produc16571293le_alt) > set_Pr367596371le_alt > set_Pr367596371le_alt).
thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    image_715032109le_alt : (produc16571293le_alt > set_Pr367596371le_alt) > set_Pr367596371le_alt > set_se2071012361le_alt).
thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    image_2105633431le_alt : (set_Pr367596371le_alt > produc16571293le_alt) > set_se2071012361le_alt > set_Pr367596371le_alt).
thf(sy_c_Set_Oimage_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    image_71834871le_alt : (set_Pr367596371le_alt > set_Pr367596371le_alt) > set_se2071012361le_alt > set_se2071012361le_alt).
thf(sy_c_member_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member684274596le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt > $o).
thf(sy_c_member_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_R____, type,
    r : set_Pr367596371le_alt).
thf(sy_v_a, type,
    a : arrow_1857593510le_alt).
thf(sy_v_b, type,
    b : arrow_1857593510le_alt).

% Relevant facts (82)
thf(fact_0__092_060open_062R_A_092_060in_062_ALin_092_060close_062, axiom,
    ((member1334244458le_alt @ r @ arrow_1848678355le_Lin))). % \<open>R \<in> Lin\<close>
thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062R_O_AR_A_092_060in_062_ALin_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![R : set_Pr367596371le_alt]: (~ ((member1334244458le_alt @ R @ arrow_1848678355le_Lin)))))))). % \<open>\<And>thesis. (\<And>R. R \<in> Lin \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_2_assms, axiom,
    ((~ ((a = b))))). % assms
thf(fact_3_Lin__irrefl, axiom,
    ((![L : set_Pr367596371le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ L) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ L)))))))). % Lin_irrefl
thf(fact_4_linear__alt, axiom,
    ((?[L2 : set_Pr367596371le_alt]: (member1334244458le_alt @ L2 @ arrow_1848678355le_Lin)))). % linear_alt
thf(fact_5_notin__Lin__iff, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((~ ((X = Y))) => ((~ ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))) = (member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ L))))))). % notin_Lin_iff
thf(fact_6_prod_Oinject, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X1 @ X2) = (produc1494124311le_alt @ Y1 @ Y2)) = (((X1 = Y1)) & ((X2 = Y2))))))). % prod.inject
thf(fact_7_old_Oprod_Oinject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A2 @ B2)) = (((A = A2)) & ((B = B2))))))). % old.prod.inject
thf(fact_8_in__above, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_1726226719_above @ L @ A @ B)) = (((~ ((X = Y)))) & ((((((X = B)) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ Y) @ L)))) & ((((~ ((X = B)))) => ((((((Y = B)) => ((((X = A)) | ((member2048039092le_alt @ (produc1494124311le_alt @ X @ A) @ L)))))) & ((((~ ((Y = B)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))))))))). % in_above
thf(fact_9_in__below, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, L : set_Pr367596371le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((~ ((A = B))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_887341619_below @ L @ A @ B)) = (((~ ((X = Y)))) & ((((((Y = A)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ B) @ L)))) & ((((~ ((Y = A)))) => ((((((X = A)) => ((((Y = B)) | ((member2048039092le_alt @ (produc1494124311le_alt @ B @ Y) @ L)))))) & ((((~ ((X = A)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))))))))). % in_below
thf(fact_10_above__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_1726226719_above @ L @ X @ Y) @ arrow_1848678355le_Lin)))))). % above_Lin
thf(fact_11_below__Lin, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt]: ((~ ((X = Y))) => ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_887341619_below @ L @ X @ Y) @ arrow_1848678355le_Lin)))))). % below_Lin
thf(fact_12_mkbot__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_843587755_mkbot @ L @ X) @ arrow_1848678355le_Lin))))). % mkbot_Lin
thf(fact_13_mktop__Lin, axiom,
    ((![L : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member1334244458le_alt @ L @ arrow_1848678355le_Lin) => (member1334244458le_alt @ (arrow_992294841_mktop @ L @ X) @ arrow_1848678355le_Lin))))). % mktop_Lin
thf(fact_14_in__mkbot, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_843587755_mkbot @ L @ Z)) = (((~ ((Y = Z)))) & ((((((X = Z)) => ((~ ((X = Y)))))) & ((((~ ((X = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))). % in_mkbot
thf(fact_15_in__mktop, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, L : set_Pr367596371le_alt, Z : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (arrow_992294841_mktop @ L @ Z)) = (((~ ((X = Z)))) & ((((((Y = Z)) => ((~ ((X = Y)))))) & ((((~ ((Y = Z)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ L))))))))))). % in_mktop
thf(fact_16_surj__pair, axiom,
    ((![P : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_17_prod__cases, axiom,
    ((![P2 : produc16571293le_alt > $o, P : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ P))))). % prod_cases
thf(fact_18_old_Oprod_Oinducts, axiom,
    ((![P2 : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (P2 @ (produc1494124311le_alt @ A3 @ B3))) => (P2 @ Prod))))). % old.prod.inducts
thf(fact_19_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A3 @ B3)))))))))). % old.prod.exhaust
thf(fact_20_Pair__inject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A2 @ B2)) => (~ (((A = A2) => (~ ((B = B2)))))))))). % Pair_inject
thf(fact_21_ssubst__Pair__rhs, axiom,
    ((![R2 : arrow_1857593510le_alt, S : arrow_1857593510le_alt, R3 : set_Pr367596371le_alt, S2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ R2 @ S) @ R3) => ((S2 = S) => (member2048039092le_alt @ (produc1494124311le_alt @ R2 @ S2) @ R3)))))). % ssubst_Pair_rhs
thf(fact_22_curryI, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((F @ (produc1494124311le_alt @ A @ B)) => (produc392997491_alt_o @ F @ A @ B))))). % curryI
thf(fact_23_swap__simp, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1794822519le_alt @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ Y @ X))))). % swap_simp
thf(fact_24_apsnd__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1710313402le_alt @ F @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ X @ (F @ Y)))))). % apsnd_conv
thf(fact_25_curryD, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F @ A @ B) => (F @ (produc1494124311le_alt @ A @ B)))))). % curryD
thf(fact_26_curryE, axiom,
    ((![F : produc16571293le_alt > $o, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc392997491_alt_o @ F @ A @ B) => (F @ (produc1494124311le_alt @ A @ B)))))). % curryE
thf(fact_27_pair__in__swap__image, axiom,
    ((![Y : arrow_1857593510le_alt, X : arrow_1857593510le_alt, A4 : set_Pr367596371le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ X) @ (image_1873259469le_alt @ produc1794822519le_alt @ A4)) = (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ A4))))). % pair_in_swap_image
thf(fact_28_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P2 : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_29_mem__Collect__eq, axiom,
    ((![A : set_Pr367596371le_alt, P2 : set_Pr367596371le_alt > $o]: ((member1334244458le_alt @ A @ (collec1399441576le_alt @ P2)) = (P2 @ A))))). % mem_Collect_eq
thf(fact_30_Collect__mem__eq, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_31_Collect__mem__eq, axiom,
    ((![A4 : set_se2071012361le_alt]: ((collec1399441576le_alt @ (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_32_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => ((![Y4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y4 @ arrow_1951607831e_Prof)) => ((![A5 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (X4 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (Y4 @ I))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F2 @ X4)) = (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F2 @ Y4))))))))))))))))). % IIA_def
thf(fact_33_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => ((![A5 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (X4 @ I)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F2 @ X4))))))))))))). % unanimity_def
thf(fact_34_mem__case__prodE, axiom,
    ((![Z : produc16571293le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_Pr367596371le_alt, P : produc16571293le_alt]: ((member2048039092le_alt @ Z @ (produc860300173le_alt @ C @ P)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member2048039092le_alt @ Z @ (C @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_35_mem__case__prodE, axiom,
    ((![Z : set_Pr367596371le_alt, C : arrow_1857593510le_alt > arrow_1857593510le_alt > set_se2071012361le_alt, P : produc16571293le_alt]: ((member1334244458le_alt @ Z @ (produc1042938349le_alt @ C @ P)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((P = (produc1494124311le_alt @ X3 @ Y3)) => (~ ((member1334244458le_alt @ Z @ (C @ X3 @ Y3)))))))))))). % mem_case_prodE
thf(fact_36_image__eqI, axiom,
    ((![B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt, X : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((B = (F @ X)) => ((member2048039092le_alt @ X @ A4) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ A4))))))). % image_eqI
thf(fact_37_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt, X : produc16571293le_alt, A4 : set_Pr367596371le_alt]: ((B = (F @ X)) => ((member2048039092le_alt @ X @ A4) => (member1334244458le_alt @ B @ (image_715032109le_alt @ F @ A4))))))). % image_eqI
thf(fact_38_image__eqI, axiom,
    ((![B : produc16571293le_alt, F : set_Pr367596371le_alt > produc16571293le_alt, X : set_Pr367596371le_alt, A4 : set_se2071012361le_alt]: ((B = (F @ X)) => ((member1334244458le_alt @ X @ A4) => (member2048039092le_alt @ B @ (image_2105633431le_alt @ F @ A4))))))). % image_eqI
thf(fact_39_image__eqI, axiom,
    ((![B : set_Pr367596371le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt, X : set_Pr367596371le_alt, A4 : set_se2071012361le_alt]: ((B = (F @ X)) => ((member1334244458le_alt @ X @ A4) => (member1334244458le_alt @ B @ (image_71834871le_alt @ F @ A4))))))). % image_eqI
thf(fact_40_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F2 : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I : arrow_1429744205e_indi]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => (((F2 @ X4) = (X4 @ I)))))))))). % dictator_def
thf(fact_41_imageI, axiom,
    ((![X : produc16571293le_alt, A4 : set_Pr367596371le_alt, F : produc16571293le_alt > produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (image_1873259469le_alt @ F @ A4)))))). % imageI
thf(fact_42_imageI, axiom,
    ((![X : produc16571293le_alt, A4 : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (image_715032109le_alt @ F @ A4)))))). % imageI
thf(fact_43_imageI, axiom,
    ((![X : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > produc16571293le_alt]: ((member1334244458le_alt @ X @ A4) => (member2048039092le_alt @ (F @ X) @ (image_2105633431le_alt @ F @ A4)))))). % imageI
thf(fact_44_imageI, axiom,
    ((![X : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => (member1334244458le_alt @ (F @ X) @ (image_71834871le_alt @ F @ A4)))))). % imageI
thf(fact_45_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_46_UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % UNIV_I
thf(fact_47_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_48_UNIV__witness, axiom,
    ((?[X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ top_to469035705le_alt)))). % UNIV_witness
thf(fact_49_UNIV__eq__I, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A4)) => (top_to224369155le_alt = A4))))). % UNIV_eq_I
thf(fact_50_UNIV__eq__I, axiom,
    ((![A4 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: (member1334244458le_alt @ X3 @ A4)) => (top_to469035705le_alt = A4))))). % UNIV_eq_I
thf(fact_51_rev__image__eqI, axiom,
    ((![X : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : produc16571293le_alt, F : produc16571293le_alt > produc16571293le_alt]: ((member2048039092le_alt @ X @ A4) => ((B = (F @ X)) => (member2048039092le_alt @ B @ (image_1873259469le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_52_rev__image__eqI, axiom,
    ((![X : produc16571293le_alt, A4 : set_Pr367596371le_alt, B : set_Pr367596371le_alt, F : produc16571293le_alt > set_Pr367596371le_alt]: ((member2048039092le_alt @ X @ A4) => ((B = (F @ X)) => (member1334244458le_alt @ B @ (image_715032109le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_53_rev__image__eqI, axiom,
    ((![X : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : produc16571293le_alt, F : set_Pr367596371le_alt > produc16571293le_alt]: ((member1334244458le_alt @ X @ A4) => ((B = (F @ X)) => (member2048039092le_alt @ B @ (image_2105633431le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_54_rev__image__eqI, axiom,
    ((![X : set_Pr367596371le_alt, A4 : set_se2071012361le_alt, B : set_Pr367596371le_alt, F : set_Pr367596371le_alt > set_Pr367596371le_alt]: ((member1334244458le_alt @ X @ A4) => ((B = (F @ X)) => (member1334244458le_alt @ B @ (image_71834871le_alt @ F @ A4))))))). % rev_image_eqI
thf(fact_55_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_56_iso__tuple__UNIV__I, axiom,
    ((![X : set_Pr367596371le_alt]: (member1334244458le_alt @ X @ top_to469035705le_alt)))). % iso_tuple_UNIV_I
thf(fact_57_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_58_top__empty__eq, axiom,
    ((top_to1900088076_alt_o = (^[X4 : set_Pr367596371le_alt]: (member1334244458le_alt @ X4 @ top_to469035705le_alt))))). % top_empty_eq
thf(fact_59_map__prod__simp, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt, A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((produc1074667658le_alt @ F @ G @ (produc1494124311le_alt @ A @ B)) = (produc1494124311le_alt @ (F @ A) @ (G @ B)))))). % map_prod_simp
thf(fact_60_map__prod__imageI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R3 : set_Pr367596371le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R3) => (member2048039092le_alt @ (produc1494124311le_alt @ (F @ A) @ (G @ B)) @ (image_1873259469le_alt @ (produc1074667658le_alt @ F @ G) @ R3)))))). % map_prod_imageI
thf(fact_61_prod__fun__imageE, axiom,
    ((![C : produc16571293le_alt, F : arrow_1857593510le_alt > arrow_1857593510le_alt, G : arrow_1857593510le_alt > arrow_1857593510le_alt, R3 : set_Pr367596371le_alt]: ((member2048039092le_alt @ C @ (image_1873259469le_alt @ (produc1074667658le_alt @ F @ G) @ R3)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((C = (produc1494124311le_alt @ (F @ X3) @ (G @ Y3))) => (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R3))))))))))). % prod_fun_imageE
thf(fact_62_prod_Ocollapse, axiom,
    ((![Prod : produc16571293le_alt]: ((produc1494124311le_alt @ (produc2071652395le_alt @ Prod) @ (produc1272650601le_alt @ Prod)) = Prod)))). % prod.collapse
thf(fact_63_Product__Type_OCollect__case__prodD, axiom,
    ((![X : produc16571293le_alt, A4 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: ((member2048039092le_alt @ X @ (collec531981554le_alt @ (produc624247124_alt_o @ A4))) => (A4 @ (produc2071652395le_alt @ X) @ (produc1272650601le_alt @ X)))))). % Product_Type.Collect_case_prodD
thf(fact_64_prod_Oswap__def, axiom,
    ((produc1794822519le_alt = (^[P3 : produc16571293le_alt]: (produc1494124311le_alt @ (produc1272650601le_alt @ P3) @ (produc2071652395le_alt @ P3)))))). % prod.swap_def
thf(fact_65_snd__eqD, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, A : arrow_1857593510le_alt]: (((produc1272650601le_alt @ (produc1494124311le_alt @ X @ Y)) = A) => (Y = A))))). % snd_eqD
thf(fact_66_snd__conv, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt]: ((produc1272650601le_alt @ (produc1494124311le_alt @ X1 @ X2)) = X2)))). % snd_conv
thf(fact_67_fst__eqD, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, A : arrow_1857593510le_alt]: (((produc2071652395le_alt @ (produc1494124311le_alt @ X @ Y)) = A) => (X = A))))). % fst_eqD
thf(fact_68_fst__conv, axiom,
    ((![X1 : arrow_1857593510le_alt, X2 : arrow_1857593510le_alt]: ((produc2071652395le_alt @ (produc1494124311le_alt @ X1 @ X2)) = X1)))). % fst_conv
thf(fact_69_prod_Oexhaust__sel, axiom,
    ((![Prod : produc16571293le_alt]: (Prod = (produc1494124311le_alt @ (produc2071652395le_alt @ Prod) @ (produc1272650601le_alt @ Prod)))))). % prod.exhaust_sel
thf(fact_70_surjective__pairing, axiom,
    ((![T : produc16571293le_alt]: (T = (produc1494124311le_alt @ (produc2071652395le_alt @ T) @ (produc1272650601le_alt @ T)))))). % surjective_pairing
thf(fact_71_exI__realizer, axiom,
    ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, Y : arrow_1857593510le_alt, X : arrow_1857593510le_alt]: ((P2 @ Y @ X) => (P2 @ (produc1272650601le_alt @ (produc1494124311le_alt @ X @ Y)) @ (produc2071652395le_alt @ (produc1494124311le_alt @ X @ Y))))))). % exI_realizer
thf(fact_72_conjI__realizer, axiom,
    ((![P2 : arrow_1857593510le_alt > $o, P : arrow_1857593510le_alt, Q : arrow_1857593510le_alt > $o, Q2 : arrow_1857593510le_alt]: ((P2 @ P) => ((Q @ Q2) => ((P2 @ (produc2071652395le_alt @ (produc1494124311le_alt @ P @ Q2))) & (Q @ (produc1272650601le_alt @ (produc1494124311le_alt @ P @ Q2))))))))). % conjI_realizer
thf(fact_73_BNF__Greatest__Fixpoint_Osubst__Pair, axiom,
    ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, A : produc16571293le_alt]: ((P2 @ X @ Y) => ((A = (produc1494124311le_alt @ X @ Y)) => (P2 @ (produc2071652395le_alt @ A) @ (produc1272650601le_alt @ A))))))). % BNF_Greatest_Fixpoint.subst_Pair
thf(fact_74_apfst__conv, axiom,
    ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: ((produc1245692284le_alt @ F @ (produc1494124311le_alt @ X @ Y)) = (produc1494124311le_alt @ (F @ X) @ Y))))). % apfst_conv
thf(fact_75_eq__snd__iff, axiom,
    ((![B : arrow_1857593510le_alt, P : produc16571293le_alt]: ((B = (produc1272650601le_alt @ P)) = (?[A5 : arrow_1857593510le_alt]: (P = (produc1494124311le_alt @ A5 @ B))))))). % eq_snd_iff
thf(fact_76_sndI, axiom,
    ((![X : produc16571293le_alt, Y : arrow_1857593510le_alt, Z : arrow_1857593510le_alt]: ((X = (produc1494124311le_alt @ Y @ Z)) => ((produc1272650601le_alt @ X) = Z))))). % sndI
thf(fact_77_fstI, axiom,
    ((![X : produc16571293le_alt, Y : arrow_1857593510le_alt, Z : arrow_1857593510le_alt]: ((X = (produc1494124311le_alt @ Y @ Z)) => ((produc2071652395le_alt @ X) = Y))))). % fstI
thf(fact_78_eq__fst__iff, axiom,
    ((![A : arrow_1857593510le_alt, P : produc16571293le_alt]: ((A = (produc2071652395le_alt @ P)) = (?[B4 : arrow_1857593510le_alt]: (P = (produc1494124311le_alt @ A @ B4))))))). % eq_fst_iff
thf(fact_79_subsetI, axiom,
    ((![A4 : set_Pr367596371le_alt, B5 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: ((member2048039092le_alt @ X3 @ A4) => (member2048039092le_alt @ X3 @ B5))) => (ord_le1885758387le_alt @ A4 @ B5))))). % subsetI
thf(fact_80_subsetI, axiom,
    ((![A4 : set_se2071012361le_alt, B5 : set_se2071012361le_alt]: ((![X3 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X3 @ A4) => (member1334244458le_alt @ X3 @ B5))) => (ord_le1836905577le_alt @ A4 @ B5))))). % subsetI
thf(fact_81_subrelI, axiom,
    ((![R2 : set_Pr367596371le_alt, S : set_Pr367596371le_alt]: ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R2) => (member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ S))) => (ord_le1885758387le_alt @ R2 @ S))))). % subrelI

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[X5 : set_Pr367596371le_alt]: ((member1334244458le_alt @ X5 @ arrow_1848678355le_Lin) & (member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ X5))))).
