% 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_197__5187950_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:16:32.587

% Could-be-implicit typings (11)
thf(ty_n_t__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    produc1535544729le_alt : $tType).
thf(ty_n_t__Set__Oset_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_J, type,
    set_Ar809243995le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc1094320767le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    set_Pr269449961le_alt : $tType).
thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc518943027le_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__List__Olist_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    list_l1515872562le_alt : $tType).
thf(ty_n_t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    list_A2130511660le_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 (40)
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_OProf, type,
    arrow_1951607831e_Prof : set_Ar809243995le_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_List_Oappend_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    append714424641le_alt : list_A2130511660le_alt > list_A2130511660le_alt > list_A2130511660le_alt).
thf(sy_c_List_Odistinct_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    distin2037765919le_alt : list_A2130511660le_alt > $o).
thf(sy_c_List_Oinsert_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    insert1859930562le_alt : arrow_1857593510le_alt > list_A2130511660le_alt > list_A2130511660le_alt).
thf(sy_c_List_Olenlex_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    lenlex1434338225le_alt : set_Pr367596371le_alt > set_Pr269449961le_alt).
thf(sy_c_List_Olexord_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    lexord1313992857le_alt : set_Pr367596371le_alt > set_Pr269449961le_alt).
thf(sy_c_List_Olist_OCons_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    cons_A1864255580le_alt : arrow_1857593510le_alt > list_A2130511660le_alt > list_A2130511660le_alt).
thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    cons_l157309922le_alt : list_A2130511660le_alt > list_l1515872562le_alt > list_l1515872562le_alt).
thf(sy_c_List_Olist_ONil_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    nil_Ar277507244le_alt : list_A2130511660le_alt).
thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    nil_li2110134322le_alt : list_l1515872562le_alt).
thf(sy_c_List_Olist__ex1_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    list_e746053615le_alt : (arrow_1857593510le_alt > $o) > list_A2130511660le_alt > $o).
thf(sy_c_List_Olistrel1_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    listre1329599109le_alt : set_Pr367596371le_alt > set_Pr269449961le_alt).
thf(sy_c_List_Olistrel_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    listre1681044285le_alt : set_Pr367596371le_alt > set_Pr269449961le_alt).
thf(sy_c_List_Omap__tailrec__rev_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    map_ta1047575097le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > list_A2130511660le_alt > list_A2130511660le_alt > list_A2130511660le_alt).
thf(sy_c_List_Omap__tailrec__rev__rel_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    map_ta2067538602le_alt : produc1535544729le_alt > produc1535544729le_alt > $o).
thf(sy_c_List_Oord_Olexordp__eq_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    lexord115420914le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > list_A2130511660le_alt > list_A2130511660le_alt > $o).
thf(sy_c_List_Oproduct__lists_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    produc608939669le_alt : list_l1515872562le_alt > list_l1515872562le_alt).
thf(sy_c_List_Osubseqs_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    subseq1380156923le_alt : list_A2130511660le_alt > list_l1515872562le_alt).
thf(sy_c_List_Ounion_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    union_420169888le_alt : list_A2130511660le_alt > list_A2130511660le_alt > list_A2130511660le_alt).
thf(sy_c_Product__Type_OPair_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_M_Eo_J_J_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc2047839287le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > list_A2130511660le_alt > produc1094320767le_alt).
thf(sy_c_Product__Type_OPair_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__Product____Type__Oprod_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    produc189241481le_alt : (arrow_1857593510le_alt > arrow_1857593510le_alt) > produc518943027le_alt > produc1535544729le_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_OPair_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    produc961395117le_alt : list_A2130511660le_alt > list_A2130511660le_alt > produc518943027le_alt).
thf(sy_c_Set_OCollect_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    collec1559089382le_alt : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > $o) > set_Ar809243995le_alt).
thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    collec531981554le_alt : (produc16571293le_alt > $o) > set_Pr367596371le_alt).
thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__Product____Type__Oprod_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    accp_P272680738le_alt : (produc1535544729le_alt > produc1535544729le_alt > $o) > produc1535544729le_alt > $o).
thf(sy_c_member_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J, type,
    member684274596le_alt : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Ar809243995le_alt > $o).
thf(sy_c_member_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__Product____Type__Oprod_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_Mt__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    member681312074le_alt : produc518943027le_alt > set_Pr269449961le_alt > $o).
thf(sy_v_F, type,
    f : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt).
thf(sy_v_P_H____, type,
    p : arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_v_P____, type,
    p2 : arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_v_a____, type,
    a : arrow_1857593510le_alt).
thf(sy_v_b____, type,
    b : arrow_1857593510le_alt).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (118)
thf(fact_0__092_060open_062a_A_092_060noteq_062_Ab_092_060close_062, axiom,
    ((~ ((a = b))))). % \<open>a \<noteq> b\<close>
thf(fact_1_third__alt, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt]: ((~ ((A = B))) => (?[C : arrow_1857593510le_alt]: (distin2037765919le_alt @ (cons_A1864255580le_alt @ A @ (cons_A1864255580le_alt @ B @ (cons_A1864255580le_alt @ C @ nil_Ar277507244le_alt))))))))). % third_alt
thf(fact_2__092_060open_062P_H_A_092_060in_062_AProf_092_060close_062, axiom,
    ((member684274596le_alt @ p @ arrow_1951607831e_Prof))). % \<open>P' \<in> Prof\<close>
thf(fact_3__092_060open_062P_A_092_060in_062_AProf_092_060close_062, axiom,
    ((member684274596le_alt @ p2 @ arrow_1951607831e_Prof))). % \<open>P \<in> Prof\<close>
thf(fact_4_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_5_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_6_alt3, axiom,
    ((?[A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt, C : arrow_1857593510le_alt]: (distin2037765919le_alt @ (cons_A1864255580le_alt @ A2 @ (cons_A1864255580le_alt @ B2 @ (cons_A1864255580le_alt @ C @ nil_Ar277507244le_alt))))))). % alt3
thf(fact_7_distinct__singleton, axiom,
    ((![X : arrow_1857593510le_alt]: (distin2037765919le_alt @ (cons_A1864255580le_alt @ X @ nil_Ar277507244le_alt))))). % distinct_singleton
thf(fact_8_iff, axiom,
    ((![I : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ a @ b) @ (p2 @ I)) = (member2048039092le_alt @ (produc1494124311le_alt @ b @ a) @ (p @ I)))))). % iff
thf(fact_9_list_Oinject, axiom,
    ((![X21 : arrow_1857593510le_alt, X22 : list_A2130511660le_alt, Y21 : arrow_1857593510le_alt, Y22 : list_A2130511660le_alt]: (((cons_A1864255580le_alt @ X21 @ X22) = (cons_A1864255580le_alt @ Y21 @ Y22)) = (((X21 = Y21)) & ((X22 = Y22))))))). % list.inject
thf(fact_10_distinct_Osimps_I1_J, axiom,
    ((distin2037765919le_alt @ nil_Ar277507244le_alt))). % distinct.simps(1)
thf(fact_11_distinct__length__2__or__more, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: ((distin2037765919le_alt @ (cons_A1864255580le_alt @ A @ (cons_A1864255580le_alt @ B @ Xs))) = (((~ ((A = B)))) & ((((distin2037765919le_alt @ (cons_A1864255580le_alt @ A @ Xs))) & ((distin2037765919le_alt @ (cons_A1864255580le_alt @ B @ Xs)))))))))). % distinct_length_2_or_more
thf(fact_12_list_Odistinct_I1_J, axiom,
    ((![X21 : arrow_1857593510le_alt, X22 : list_A2130511660le_alt]: (~ ((nil_Ar277507244le_alt = (cons_A1864255580le_alt @ X21 @ X22))))))). % list.distinct(1)
thf(fact_13_list_OdiscI, axiom,
    ((![List : list_A2130511660le_alt, X21 : arrow_1857593510le_alt, X22 : list_A2130511660le_alt]: ((List = (cons_A1864255580le_alt @ X21 @ X22)) => (~ ((List = nil_Ar277507244le_alt))))))). % list.discI
thf(fact_14_list_Oexhaust, axiom,
    ((![Y : list_A2130511660le_alt]: ((~ ((Y = nil_Ar277507244le_alt))) => (~ ((![X212 : arrow_1857593510le_alt, X222 : list_A2130511660le_alt]: (~ ((Y = (cons_A1864255580le_alt @ X212 @ X222))))))))))). % list.exhaust
thf(fact_15_list_Oinducts, axiom,
    ((![P : list_A2130511660le_alt > $o, List : list_A2130511660le_alt]: ((P @ nil_Ar277507244le_alt) => ((![X1 : arrow_1857593510le_alt, X2 : list_A2130511660le_alt]: ((P @ X2) => (P @ (cons_A1864255580le_alt @ X1 @ X2)))) => (P @ List)))))). % list.inducts
thf(fact_16_neq__Nil__conv, axiom,
    ((![Xs : list_A2130511660le_alt]: ((~ ((Xs = nil_Ar277507244le_alt))) = (?[Y2 : arrow_1857593510le_alt]: (?[Ys : list_A2130511660le_alt]: (Xs = (cons_A1864255580le_alt @ Y2 @ Ys)))))))). % neq_Nil_conv
thf(fact_17_list__induct2_H, axiom,
    ((![P : list_A2130511660le_alt > list_A2130511660le_alt > $o, Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((P @ nil_Ar277507244le_alt @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (P @ (cons_A1864255580le_alt @ X3 @ Xs2) @ nil_Ar277507244le_alt)) => ((![Y3 : arrow_1857593510le_alt, Ys3 : list_A2130511660le_alt]: (P @ nil_Ar277507244le_alt @ (cons_A1864255580le_alt @ Y3 @ Ys3))) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Y3 : arrow_1857593510le_alt, Ys3 : list_A2130511660le_alt]: ((P @ Xs2 @ Ys3) => (P @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y3 @ Ys3)))) => (P @ Xs @ Ys2)))))))). % list_induct2'
thf(fact_18_splice_Oinduct, axiom,
    ((![P : list_A2130511660le_alt > list_A2130511660le_alt > $o, A0 : list_A2130511660le_alt, A1 : list_A2130511660le_alt]: ((![X_1 : list_A2130511660le_alt]: (P @ nil_Ar277507244le_alt @ X_1)) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Ys3 : list_A2130511660le_alt]: ((P @ Ys3 @ Xs2) => (P @ (cons_A1864255580le_alt @ X3 @ Xs2) @ Ys3))) => (P @ A0 @ A1)))))). % splice.induct
thf(fact_19__C1_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A3 = B3))) => ((~ ((A = B3))) => ((~ ((B = A3))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) => (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (f @ P2))))))))))))). % "1"
thf(fact_20__C2_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A3 = B3))) => ((~ ((A = B3))) => ((~ ((B = A3))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P2 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (P2 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (f @ P2))))))))))))). % "2"
thf(fact_21_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => ((![Y2 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ Y2 @ arrow_1951607831e_Prof)) => ((![A4 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I3 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X4 @ I3)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (Y2 @ I3))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ X4)) = (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ Y2))))))))))))))))). % IIA_def
thf(fact_22_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => ((![A4 : arrow_1857593510le_alt]: (![B4 : arrow_1857593510le_alt]: (((![I3 : arrow_1429744205e_indi]: (member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (X4 @ I3)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A4 @ B4) @ (F @ X4))))))))))))). % unanimity_def
thf(fact_23_not__Cons__self2, axiom,
    ((![X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: (~ (((cons_A1864255580le_alt @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_24_map__tailrec__rev_Oinduct, axiom,
    ((![P : (arrow_1857593510le_alt > arrow_1857593510le_alt) > list_A2130511660le_alt > list_A2130511660le_alt > $o, A0 : arrow_1857593510le_alt > arrow_1857593510le_alt, A1 : list_A2130511660le_alt, A22 : list_A2130511660le_alt]: ((![F2 : arrow_1857593510le_alt > arrow_1857593510le_alt, X_1 : list_A2130511660le_alt]: (P @ F2 @ nil_Ar277507244le_alt @ X_1)) => ((![F2 : arrow_1857593510le_alt > arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, As : list_A2130511660le_alt, Bs : list_A2130511660le_alt]: ((P @ F2 @ As @ (cons_A1864255580le_alt @ (F2 @ A2) @ Bs)) => (P @ F2 @ (cons_A1864255580le_alt @ A2 @ As) @ Bs))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_25_list__nonempty__induct, axiom,
    ((![Xs : list_A2130511660le_alt, P : list_A2130511660le_alt > $o]: ((~ ((Xs = nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt]: (P @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((~ ((Xs2 = nil_Ar277507244le_alt))) => ((P @ Xs2) => (P @ (cons_A1864255580le_alt @ X3 @ Xs2))))) => (P @ Xs))))))). % list_nonempty_induct
thf(fact_26_successively_Oinduct, axiom,
    ((![P : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > list_A2130511660le_alt > $o, A0 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A1 : list_A2130511660le_alt]: ((![P3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (P @ P3 @ nil_Ar277507244le_alt)) => ((![P3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt]: (P @ P3 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![P3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((P @ P3 @ (cons_A1864255580le_alt @ Y3 @ Xs2)) => (P @ P3 @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y3 @ Xs2))))) => (P @ A0 @ A1))))))). % successively.induct
thf(fact_27_remdups__adj_Oinduct, axiom,
    ((![P : list_A2130511660le_alt > $o, A0 : list_A2130511660le_alt]: ((P @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt]: (P @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (((X3 = Y3) => (P @ (cons_A1864255580le_alt @ X3 @ Xs2))) => (((~ ((X3 = Y3))) => (P @ (cons_A1864255580le_alt @ Y3 @ Xs2))) => (P @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y3 @ Xs2)))))) => (P @ A0))))))). % remdups_adj.induct
thf(fact_28_sorted__wrt_Oinduct, axiom,
    ((![P : (arrow_1857593510le_alt > arrow_1857593510le_alt > $o) > list_A2130511660le_alt > $o, A0 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A1 : list_A2130511660le_alt]: ((![P3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (P @ P3 @ nil_Ar277507244le_alt)) => ((![P3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Ys3 : list_A2130511660le_alt]: ((P @ P3 @ Ys3) => (P @ P3 @ (cons_A1864255580le_alt @ X3 @ Ys3)))) => (P @ A0 @ A1)))))). % sorted_wrt.induct
thf(fact_29_remdups__adj_Ocases, axiom,
    ((![X : list_A2130511660le_alt]: ((~ ((X = nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt]: (~ ((X = (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))))) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (~ ((X = (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y3 @ Xs2))))))))))))). % remdups_adj.cases
thf(fact_30_transpose_Ocases, axiom,
    ((![X : list_l1515872562le_alt]: ((~ ((X = nil_li2110134322le_alt))) => ((![Xss : list_l1515872562le_alt]: (~ ((X = (cons_l157309922le_alt @ nil_Ar277507244le_alt @ Xss))))) => (~ ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Xss : list_l1515872562le_alt]: (~ ((X = (cons_l157309922le_alt @ (cons_A1864255580le_alt @ X3 @ Xs2) @ Xss)))))))))))). % transpose.cases
thf(fact_31_shuffles_Oinduct, axiom,
    ((![P : list_A2130511660le_alt > list_A2130511660le_alt > $o, A0 : list_A2130511660le_alt, A1 : list_A2130511660le_alt]: ((![X_1 : list_A2130511660le_alt]: (P @ nil_Ar277507244le_alt @ X_1)) => ((![Xs2 : list_A2130511660le_alt]: (P @ Xs2 @ nil_Ar277507244le_alt)) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Y3 : arrow_1857593510le_alt, Ys3 : list_A2130511660le_alt]: ((P @ Xs2 @ (cons_A1864255580le_alt @ Y3 @ Ys3)) => ((P @ (cons_A1864255580le_alt @ X3 @ Xs2) @ Ys3) => (P @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y3 @ Ys3))))) => (P @ A0 @ A1))))))). % shuffles.induct
thf(fact_32_induct__list012, axiom,
    ((![P : list_A2130511660le_alt > $o, Xs : list_A2130511660le_alt]: ((P @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt]: (P @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Zs : list_A2130511660le_alt]: ((P @ Zs) => ((P @ (cons_A1864255580le_alt @ Y3 @ Zs)) => (P @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y3 @ Zs)))))) => (P @ Xs))))))). % induct_list012
thf(fact_33_prod_Oinject, axiom,
    ((![X12 : arrow_1857593510le_alt, X23 : arrow_1857593510le_alt, Y1 : arrow_1857593510le_alt, Y23 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ X12 @ X23) = (produc1494124311le_alt @ Y1 @ Y23)) = (((X12 = Y1)) & ((X23 = Y23))))))). % prod.inject
thf(fact_34_old_Oprod_Oinject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A3 @ B3)) = (((A = A3)) & ((B = B3))))))). % old.prod.inject
thf(fact_35_distinct__union, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((distin2037765919le_alt @ (union_420169888le_alt @ Xs @ Ys2)) = (distin2037765919le_alt @ Ys2))))). % distinct_union
thf(fact_36_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F : (arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt]: (^[I3 : arrow_1429744205e_indi]: (![X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (((member684274596le_alt @ X4 @ arrow_1951607831e_Prof)) => (((F @ X4) = (X4 @ I3)))))))))). % dictator_def
thf(fact_37_insert__Nil, axiom,
    ((![X : arrow_1857593510le_alt]: ((insert1859930562le_alt @ X @ nil_Ar277507244le_alt) = (cons_A1864255580le_alt @ X @ nil_Ar277507244le_alt))))). % insert_Nil
thf(fact_38_list__ex1__simps_I1_J, axiom,
    ((![P : arrow_1857593510le_alt > $o]: (~ ((list_e746053615le_alt @ P @ nil_Ar277507244le_alt)))))). % list_ex1_simps(1)
thf(fact_39_mem__Collect__eq, axiom,
    ((![A : arrow_1429744205e_indi > set_Pr367596371le_alt, P : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o]: ((member684274596le_alt @ A @ (collec1559089382le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_40_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_41_Collect__mem__eq, axiom,
    ((![A5 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_42_Collect__mem__eq, axiom,
    ((![A5 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ A5))) = A5)))). % Collect_mem_eq
thf(fact_43_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_44_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_45_map__tailrec__rev_Oelims, axiom,
    ((![X : arrow_1857593510le_alt > arrow_1857593510le_alt, Xa : list_A2130511660le_alt, Xb : list_A2130511660le_alt, Y : list_A2130511660le_alt]: (((map_ta1047575097le_alt @ X @ Xa @ Xb) = Y) => (((Xa = nil_Ar277507244le_alt) => (~ ((Y = Xb)))) => (~ ((![A2 : arrow_1857593510le_alt, As : list_A2130511660le_alt]: ((Xa = (cons_A1864255580le_alt @ A2 @ As)) => (~ ((Y = (map_ta1047575097le_alt @ X @ As @ (cons_A1864255580le_alt @ (X @ A2) @ Xb)))))))))))))). % map_tailrec_rev.elims
thf(fact_46_distinct__insert, axiom,
    ((![X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: ((distin2037765919le_alt @ (insert1859930562le_alt @ X @ Xs)) = (distin2037765919le_alt @ Xs))))). % distinct_insert
thf(fact_47_sorted__wrt_Ocases, axiom,
    ((![X : produc1094320767le_alt]: ((![P3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (~ ((X = (produc2047839287le_alt @ P3 @ nil_Ar277507244le_alt))))) => (~ ((![P3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Ys3 : list_A2130511660le_alt]: (~ ((X = (produc2047839287le_alt @ P3 @ (cons_A1864255580le_alt @ X3 @ Ys3)))))))))))). % sorted_wrt.cases
thf(fact_48_successively_Ocases, axiom,
    ((![X : produc1094320767le_alt]: ((![P3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (~ ((X = (produc2047839287le_alt @ P3 @ nil_Ar277507244le_alt))))) => ((![P3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt]: (~ ((X = (produc2047839287le_alt @ P3 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt)))))) => (~ ((![P3 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (~ ((X = (produc2047839287le_alt @ P3 @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y3 @ Xs2)))))))))))))). % successively.cases
thf(fact_49_map__tailrec__rev_Osimps_I2_J, axiom,
    ((![F3 : arrow_1857593510le_alt > arrow_1857593510le_alt, A : arrow_1857593510le_alt, As2 : list_A2130511660le_alt, Bs2 : list_A2130511660le_alt]: ((map_ta1047575097le_alt @ F3 @ (cons_A1864255580le_alt @ A @ As2) @ Bs2) = (map_ta1047575097le_alt @ F3 @ As2 @ (cons_A1864255580le_alt @ (F3 @ A) @ Bs2)))))). % map_tailrec_rev.simps(2)
thf(fact_50_splice_Ocases, axiom,
    ((![X : produc518943027le_alt]: ((![Ys3 : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ nil_Ar277507244le_alt @ Ys3))))) => (~ ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Ys3 : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ (cons_A1864255580le_alt @ X3 @ Xs2) @ Ys3))))))))))). % splice.cases
thf(fact_51_shuffles_Ocases, axiom,
    ((![X : produc518943027le_alt]: ((![Ys3 : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ nil_Ar277507244le_alt @ Ys3))))) => ((![Xs2 : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ Xs2 @ nil_Ar277507244le_alt))))) => (~ ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Y3 : arrow_1857593510le_alt, Ys3 : list_A2130511660le_alt]: (~ ((X = (produc961395117le_alt @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y3 @ Ys3))))))))))))). % shuffles.cases
thf(fact_52_old_Oprod_Oinducts, axiom,
    ((![P : produc16571293le_alt > $o, Prod : produc16571293le_alt]: ((![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A2 @ B2))) => (P @ Prod))))). % old.prod.inducts
thf(fact_53_old_Oprod_Oexhaust, axiom,
    ((![Y : produc16571293le_alt]: (~ ((![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (~ ((Y = (produc1494124311le_alt @ A2 @ B2)))))))))). % old.prod.exhaust
thf(fact_54_Pair__inject, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt]: (((produc1494124311le_alt @ A @ B) = (produc1494124311le_alt @ A3 @ B3)) => (~ (((A = A3) => (~ ((B = B3)))))))))). % Pair_inject
thf(fact_55_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P4 : produc16571293le_alt]: ((![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A2 @ B2))) => (P @ P4))))). % prod_cases
thf(fact_56_surj__pair, axiom,
    ((![P4 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P4 = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_57_product__lists_Osimps_I1_J, axiom,
    (((produc608939669le_alt @ nil_li2110134322le_alt) = (cons_l157309922le_alt @ nil_Ar277507244le_alt @ nil_li2110134322le_alt)))). % product_lists.simps(1)
thf(fact_58_subseqs_Osimps_I1_J, axiom,
    (((subseq1380156923le_alt @ nil_Ar277507244le_alt) = (cons_l157309922le_alt @ nil_Ar277507244le_alt @ nil_li2110134322le_alt)))). % subseqs.simps(1)
thf(fact_59_ord_Olexordp__eq__simps_I3_J, axiom,
    ((![Less : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: (~ ((lexord115420914le_alt @ Less @ (cons_A1864255580le_alt @ X @ Xs) @ nil_Ar277507244le_alt)))))). % ord.lexordp_eq_simps(3)
thf(fact_60_ord_Olexordp__eq__simps_I4_J, axiom,
    ((![Less : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt, Y : arrow_1857593510le_alt, Ys2 : list_A2130511660le_alt]: ((lexord115420914le_alt @ Less @ (cons_A1864255580le_alt @ X @ Xs) @ (cons_A1864255580le_alt @ Y @ Ys2)) = (((Less @ X @ Y)) | ((((~ ((Less @ Y @ X)))) & ((lexord115420914le_alt @ Less @ Xs @ Ys2))))))))). % ord.lexordp_eq_simps(4)
thf(fact_61_ord_Olexordp__eq__simps_I1_J, axiom,
    ((![Less : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, Ys2 : list_A2130511660le_alt]: (lexord115420914le_alt @ Less @ nil_Ar277507244le_alt @ Ys2)))). % ord.lexordp_eq_simps(1)
thf(fact_62_ord_Olexordp__eq__simps_I2_J, axiom,
    ((![Less : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, Xs : list_A2130511660le_alt]: ((lexord115420914le_alt @ Less @ Xs @ nil_Ar277507244le_alt) = (Xs = nil_Ar277507244le_alt))))). % ord.lexordp_eq_simps(2)
thf(fact_63_ord_Olexordp__eq_OCons__eq, axiom,
    ((![Less : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((~ ((Less @ X @ Y))) => ((~ ((Less @ Y @ X))) => ((lexord115420914le_alt @ Less @ Xs @ Ys2) => (lexord115420914le_alt @ Less @ (cons_A1864255580le_alt @ X @ Xs) @ (cons_A1864255580le_alt @ Y @ Ys2)))))))). % ord.lexordp_eq.Cons_eq
thf(fact_64_ord_Olexordp__eq_OCons, axiom,
    ((![Less : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((Less @ X @ Y) => (lexord115420914le_alt @ Less @ (cons_A1864255580le_alt @ X @ Xs) @ (cons_A1864255580le_alt @ Y @ Ys2)))))). % ord.lexordp_eq.Cons
thf(fact_65_ord_Olexordp__eq_ONil, axiom,
    ((![Less : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, Ys2 : list_A2130511660le_alt]: (lexord115420914le_alt @ Less @ nil_Ar277507244le_alt @ Ys2)))). % ord.lexordp_eq.Nil
thf(fact_66_ord_Olexordp__eq_Oinducts, axiom,
    ((![Less : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X12 : list_A2130511660le_alt, X23 : list_A2130511660le_alt, P : list_A2130511660le_alt > list_A2130511660le_alt > $o]: ((lexord115420914le_alt @ Less @ X12 @ X23) => ((![X_1 : list_A2130511660le_alt]: (P @ nil_Ar277507244le_alt @ X_1)) => ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Ys3 : list_A2130511660le_alt]: ((Less @ X3 @ Y3) => (P @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y3 @ Ys3)))) => ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Ys3 : list_A2130511660le_alt]: ((~ ((Less @ X3 @ Y3))) => ((~ ((Less @ Y3 @ X3))) => ((lexord115420914le_alt @ Less @ Xs2 @ Ys3) => ((P @ Xs2 @ Ys3) => (P @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y3 @ Ys3))))))) => (P @ X12 @ X23)))))))). % ord.lexordp_eq.inducts
thf(fact_67_ord_Olexordp__eq_Osimps, axiom,
    ((lexord115420914le_alt = (^[Less2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (^[A12 : list_A2130511660le_alt]: (^[A23 : list_A2130511660le_alt]: (((?[Ys : list_A2130511660le_alt]: (((A12 = nil_Ar277507244le_alt)) & ((A23 = Ys))))) | ((((?[X4 : arrow_1857593510le_alt]: (?[Y2 : arrow_1857593510le_alt]: (?[Xs3 : list_A2130511660le_alt]: (?[Ys : list_A2130511660le_alt]: (((A12 = (cons_A1864255580le_alt @ X4 @ Xs3))) & ((((A23 = (cons_A1864255580le_alt @ Y2 @ Ys))) & ((Less2 @ X4 @ Y2)))))))))) | ((?[X4 : arrow_1857593510le_alt]: (?[Y2 : arrow_1857593510le_alt]: (?[Xs3 : list_A2130511660le_alt]: (?[Ys : list_A2130511660le_alt]: (((A12 = (cons_A1864255580le_alt @ X4 @ Xs3))) & ((((A23 = (cons_A1864255580le_alt @ Y2 @ Ys))) & ((((~ ((Less2 @ X4 @ Y2)))) & ((((~ ((Less2 @ Y2 @ X4)))) & ((lexord115420914le_alt @ Less2 @ Xs3 @ Ys))))))))))))))))))))))). % ord.lexordp_eq.simps
thf(fact_68_ord_Olexordp__eq_Ocases, axiom,
    ((![Less : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, A1 : list_A2130511660le_alt, A22 : list_A2130511660le_alt]: ((lexord115420914le_alt @ Less @ A1 @ A22) => ((~ ((A1 = nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt]: ((?[Xs2 : list_A2130511660le_alt]: (A1 = (cons_A1864255580le_alt @ X3 @ Xs2))) => (![Y3 : arrow_1857593510le_alt]: ((?[Ys3 : list_A2130511660le_alt]: (A22 = (cons_A1864255580le_alt @ Y3 @ Ys3))) => (~ ((Less @ X3 @ Y3))))))) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((A1 = (cons_A1864255580le_alt @ X3 @ Xs2)) => (![Ys3 : list_A2130511660le_alt]: ((A22 = (cons_A1864255580le_alt @ Y3 @ Ys3)) => ((~ ((Less @ X3 @ Y3))) => ((~ ((Less @ Y3 @ X3))) => (~ ((lexord115420914le_alt @ Less @ Xs2 @ Ys3))))))))))))))))). % ord.lexordp_eq.cases
thf(fact_69_lexord__Nil__left, axiom,
    ((![Y : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ nil_Ar277507244le_alt @ Y) @ (lexord1313992857le_alt @ R)) = (?[A4 : arrow_1857593510le_alt]: (?[X4 : list_A2130511660le_alt]: (Y = (cons_A1864255580le_alt @ A4 @ X4)))))))). % lexord_Nil_left
thf(fact_70_lexord__cons__cons, axiom,
    ((![A : arrow_1857593510le_alt, X : list_A2130511660le_alt, B : arrow_1857593510le_alt, Y : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ A @ X) @ (cons_A1864255580le_alt @ B @ Y)) @ (lexord1313992857le_alt @ R)) = (((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R)) | ((((A = B)) & ((member681312074le_alt @ (produc961395117le_alt @ X @ Y) @ (lexord1313992857le_alt @ R)))))))))). % lexord_cons_cons
thf(fact_71_map__tailrec__rev_Opelims, axiom,
    ((![X : arrow_1857593510le_alt > arrow_1857593510le_alt, Xa : list_A2130511660le_alt, Xb : list_A2130511660le_alt, Y : list_A2130511660le_alt]: (((map_ta1047575097le_alt @ X @ Xa @ Xb) = Y) => ((accp_P272680738le_alt @ map_ta2067538602le_alt @ (produc189241481le_alt @ X @ (produc961395117le_alt @ Xa @ Xb))) => (((Xa = nil_Ar277507244le_alt) => ((Y = Xb) => (~ ((accp_P272680738le_alt @ map_ta2067538602le_alt @ (produc189241481le_alt @ X @ (produc961395117le_alt @ nil_Ar277507244le_alt @ Xb))))))) => (~ ((![A2 : arrow_1857593510le_alt, As : list_A2130511660le_alt]: ((Xa = (cons_A1864255580le_alt @ A2 @ As)) => ((Y = (map_ta1047575097le_alt @ X @ As @ (cons_A1864255580le_alt @ (X @ A2) @ Xb))) => (~ ((accp_P272680738le_alt @ map_ta2067538602le_alt @ (produc189241481le_alt @ X @ (produc961395117le_alt @ (cons_A1864255580le_alt @ A2 @ As) @ Xb)))))))))))))))). % map_tailrec_rev.pelims
thf(fact_72_listrel_Oinducts, axiom,
    ((![X12 : list_A2130511660le_alt, X23 : list_A2130511660le_alt, R : set_Pr367596371le_alt, P : list_A2130511660le_alt > list_A2130511660le_alt > $o]: ((member681312074le_alt @ (produc961395117le_alt @ X12 @ X23) @ (listre1681044285le_alt @ R)) => ((P @ nil_Ar277507244le_alt @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt, Ys3 : list_A2130511660le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R) => ((member681312074le_alt @ (produc961395117le_alt @ Xs2 @ Ys3) @ (listre1681044285le_alt @ R)) => ((P @ Xs2 @ Ys3) => (P @ (cons_A1864255580le_alt @ X3 @ Xs2) @ (cons_A1864255580le_alt @ Y3 @ Ys3)))))) => (P @ X12 @ X23))))))). % listrel.inducts
thf(fact_73_listrel_ONil, axiom,
    ((![R : set_Pr367596371le_alt]: (member681312074le_alt @ (produc961395117le_alt @ nil_Ar277507244le_alt @ nil_Ar277507244le_alt) @ (listre1681044285le_alt @ R))))). % listrel.Nil
thf(fact_74_listrel__Nil1, axiom,
    ((![Xs : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ nil_Ar277507244le_alt @ Xs) @ (listre1681044285le_alt @ R)) => (Xs = nil_Ar277507244le_alt))))). % listrel_Nil1
thf(fact_75_listrel__Nil2, axiom,
    ((![Xs : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ Xs @ nil_Ar277507244le_alt) @ (listre1681044285le_alt @ R)) => (Xs = nil_Ar277507244le_alt))))). % listrel_Nil2
thf(fact_76_lexord__irreflexive, axiom,
    ((![R : set_Pr367596371le_alt, Xs : list_A2130511660le_alt]: ((![X3 : arrow_1857593510le_alt]: (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ X3) @ R)))) => (~ ((member681312074le_alt @ (produc961395117le_alt @ Xs @ Xs) @ (lexord1313992857le_alt @ R)))))))). % lexord_irreflexive
thf(fact_77_lexord__linear, axiom,
    ((![R : set_Pr367596371le_alt, X : list_A2130511660le_alt, Y : list_A2130511660le_alt]: ((![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ B2) @ R) | ((A2 = B2) | (member2048039092le_alt @ (produc1494124311le_alt @ B2 @ A2) @ R)))) => ((member681312074le_alt @ (produc961395117le_alt @ X @ Y) @ (lexord1313992857le_alt @ R)) | ((X = Y) | (member681312074le_alt @ (produc961395117le_alt @ Y @ X) @ (lexord1313992857le_alt @ R)))))))). % lexord_linear
thf(fact_78_lexord__Nil__right, axiom,
    ((![X : list_A2130511660le_alt, R : set_Pr367596371le_alt]: (~ ((member681312074le_alt @ (produc961395117le_alt @ X @ nil_Ar277507244le_alt) @ (lexord1313992857le_alt @ R))))))). % lexord_Nil_right
thf(fact_79_listrel__Cons2, axiom,
    ((![Xs : list_A2130511660le_alt, Y : arrow_1857593510le_alt, Ys2 : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ Xs @ (cons_A1864255580le_alt @ Y @ Ys2)) @ (listre1681044285le_alt @ R)) => (~ ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((Xs = (cons_A1864255580le_alt @ X3 @ Xs2)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y) @ R) => (~ ((member681312074le_alt @ (produc961395117le_alt @ Xs2 @ Ys2) @ (listre1681044285le_alt @ R))))))))))))). % listrel_Cons2
thf(fact_80_listrel__Cons1, axiom,
    ((![Y : arrow_1857593510le_alt, Ys2 : list_A2130511660le_alt, Xs : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ Y @ Ys2) @ Xs) @ (listre1681044285le_alt @ R)) => (~ ((![Y3 : arrow_1857593510le_alt, Ys3 : list_A2130511660le_alt]: ((Xs = (cons_A1864255580le_alt @ Y3 @ Ys3)) => ((member2048039092le_alt @ (produc1494124311le_alt @ Y @ Y3) @ R) => (~ ((member681312074le_alt @ (produc961395117le_alt @ Ys2 @ Ys3) @ (listre1681044285le_alt @ R))))))))))))). % listrel_Cons1
thf(fact_81_listrel_OCons, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt, Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R) => ((member681312074le_alt @ (produc961395117le_alt @ Xs @ Ys2) @ (listre1681044285le_alt @ R)) => (member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ X @ Xs) @ (cons_A1864255580le_alt @ Y @ Ys2)) @ (listre1681044285le_alt @ R))))))). % listrel.Cons
thf(fact_82_listrel_Ocases, axiom,
    ((![A1 : list_A2130511660le_alt, A22 : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ A1 @ A22) @ (listre1681044285le_alt @ R)) => (((A1 = nil_Ar277507244le_alt) => (~ ((A22 = nil_Ar277507244le_alt)))) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((A1 = (cons_A1864255580le_alt @ X3 @ Xs2)) => (![Ys3 : list_A2130511660le_alt]: ((A22 = (cons_A1864255580le_alt @ Y3 @ Ys3)) => ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R) => (~ ((member681312074le_alt @ (produc961395117le_alt @ Xs2 @ Ys3) @ (listre1681044285le_alt @ R)))))))))))))))). % listrel.cases
thf(fact_83_listrel_Osimps, axiom,
    ((![A1 : list_A2130511660le_alt, A22 : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ A1 @ A22) @ (listre1681044285le_alt @ R)) = (((((A1 = nil_Ar277507244le_alt)) & ((A22 = nil_Ar277507244le_alt)))) | ((?[X4 : arrow_1857593510le_alt]: (?[Y2 : arrow_1857593510le_alt]: (?[Xs3 : list_A2130511660le_alt]: (?[Ys : list_A2130511660le_alt]: (((A1 = (cons_A1864255580le_alt @ X4 @ Xs3))) & ((((A22 = (cons_A1864255580le_alt @ Y2 @ Ys))) & ((((member2048039092le_alt @ (produc1494124311le_alt @ X4 @ Y2) @ R)) & ((member681312074le_alt @ (produc961395117le_alt @ Xs3 @ Ys) @ (listre1681044285le_alt @ R)))))))))))))))))). % listrel.simps
thf(fact_84_Cons__listrel1__Cons, axiom,
    ((![X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt, Y : arrow_1857593510le_alt, Ys2 : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ X @ Xs) @ (cons_A1864255580le_alt @ Y @ Ys2)) @ (listre1329599109le_alt @ R)) = (((((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R)) & ((Xs = Ys2)))) | ((((X = Y)) & ((member681312074le_alt @ (produc961395117le_alt @ Xs @ Ys2) @ (listre1329599109le_alt @ R)))))))))). % Cons_listrel1_Cons
thf(fact_85_lexord__append__left__rightI, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, R : set_Pr367596371le_alt, U : list_A2130511660le_alt, X : list_A2130511660le_alt, Y : list_A2130511660le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ R) => (member681312074le_alt @ (produc961395117le_alt @ (append714424641le_alt @ U @ (cons_A1864255580le_alt @ A @ X)) @ (append714424641le_alt @ U @ (cons_A1864255580le_alt @ B @ Y))) @ (lexord1313992857le_alt @ R)))))). % lexord_append_left_rightI
thf(fact_86_Nil__lenlex__iff1, axiom,
    ((![Ns : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ nil_Ar277507244le_alt @ Ns) @ (lenlex1434338225le_alt @ R)) = (~ ((Ns = nil_Ar277507244le_alt))))))). % Nil_lenlex_iff1
thf(fact_87_append__Nil2, axiom,
    ((![Xs : list_A2130511660le_alt]: ((append714424641le_alt @ Xs @ nil_Ar277507244le_alt) = Xs)))). % append_Nil2
thf(fact_88_append__self__conv, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: (((append714424641le_alt @ Xs @ Ys2) = Xs) = (Ys2 = nil_Ar277507244le_alt))))). % append_self_conv
thf(fact_89_self__append__conv, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((Xs = (append714424641le_alt @ Xs @ Ys2)) = (Ys2 = nil_Ar277507244le_alt))))). % self_append_conv
thf(fact_90_append__self__conv2, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: (((append714424641le_alt @ Xs @ Ys2) = Ys2) = (Xs = nil_Ar277507244le_alt))))). % append_self_conv2
thf(fact_91_self__append__conv2, axiom,
    ((![Ys2 : list_A2130511660le_alt, Xs : list_A2130511660le_alt]: ((Ys2 = (append714424641le_alt @ Xs @ Ys2)) = (Xs = nil_Ar277507244le_alt))))). % self_append_conv2
thf(fact_92_Nil__is__append__conv, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((nil_Ar277507244le_alt = (append714424641le_alt @ Xs @ Ys2)) = (((Xs = nil_Ar277507244le_alt)) & ((Ys2 = nil_Ar277507244le_alt))))))). % Nil_is_append_conv
thf(fact_93_append__is__Nil__conv, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: (((append714424641le_alt @ Xs @ Ys2) = nil_Ar277507244le_alt) = (((Xs = nil_Ar277507244le_alt)) & ((Ys2 = nil_Ar277507244le_alt))))))). % append_is_Nil_conv
thf(fact_94_append_Oright__neutral, axiom,
    ((![A : list_A2130511660le_alt]: ((append714424641le_alt @ A @ nil_Ar277507244le_alt) = A)))). % append.right_neutral
thf(fact_95_append1__eq__conv, axiom,
    ((![Xs : list_A2130511660le_alt, X : arrow_1857593510le_alt, Ys2 : list_A2130511660le_alt, Y : arrow_1857593510le_alt]: (((append714424641le_alt @ Xs @ (cons_A1864255580le_alt @ X @ nil_Ar277507244le_alt)) = (append714424641le_alt @ Ys2 @ (cons_A1864255580le_alt @ Y @ nil_Ar277507244le_alt))) = (((Xs = Ys2)) & ((X = Y))))))). % append1_eq_conv
thf(fact_96_eq__Nil__appendI, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((Xs = Ys2) => (Xs = (append714424641le_alt @ nil_Ar277507244le_alt @ Ys2)))))). % eq_Nil_appendI
thf(fact_97_append__Nil, axiom,
    ((![Ys2 : list_A2130511660le_alt]: ((append714424641le_alt @ nil_Ar277507244le_alt @ Ys2) = Ys2)))). % append_Nil
thf(fact_98_append_Oleft__neutral, axiom,
    ((![A : list_A2130511660le_alt]: ((append714424641le_alt @ nil_Ar277507244le_alt @ A) = A)))). % append.left_neutral
thf(fact_99_Cons__eq__appendI, axiom,
    ((![X : arrow_1857593510le_alt, Xs1 : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt, Xs : list_A2130511660le_alt, Zs2 : list_A2130511660le_alt]: (((cons_A1864255580le_alt @ X @ Xs1) = Ys2) => ((Xs = (append714424641le_alt @ Xs1 @ Zs2)) => ((cons_A1864255580le_alt @ X @ Xs) = (append714424641le_alt @ Ys2 @ Zs2))))))). % Cons_eq_appendI
thf(fact_100_append__Cons, axiom,
    ((![X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((append714424641le_alt @ (cons_A1864255580le_alt @ X @ Xs) @ Ys2) = (cons_A1864255580le_alt @ X @ (append714424641le_alt @ Xs @ Ys2)))))). % append_Cons
thf(fact_101_listrel1E, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ Xs @ Ys2) @ (listre1329599109le_alt @ R)) => (~ ((![X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ Y3) @ R) => (![Us : list_A2130511660le_alt, Vs : list_A2130511660le_alt]: ((Xs = (append714424641le_alt @ Us @ (cons_A1864255580le_alt @ X3 @ Vs))) => (~ ((Ys2 = (append714424641le_alt @ Us @ (cons_A1864255580le_alt @ Y3 @ Vs))))))))))))))). % listrel1E
thf(fact_102_listrel1I, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt, Xs : list_A2130511660le_alt, Us2 : list_A2130511660le_alt, Vs2 : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R) => ((Xs = (append714424641le_alt @ Us2 @ (cons_A1864255580le_alt @ X @ Vs2))) => ((Ys2 = (append714424641le_alt @ Us2 @ (cons_A1864255580le_alt @ Y @ Vs2))) => (member681312074le_alt @ (produc961395117le_alt @ Xs @ Ys2) @ (listre1329599109le_alt @ R)))))))). % listrel1I
thf(fact_103_snoc__listrel1__snoc__iff, axiom,
    ((![Xs : list_A2130511660le_alt, X : arrow_1857593510le_alt, Ys2 : list_A2130511660le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ (append714424641le_alt @ Xs @ (cons_A1864255580le_alt @ X @ nil_Ar277507244le_alt)) @ (append714424641le_alt @ Ys2 @ (cons_A1864255580le_alt @ Y @ nil_Ar277507244le_alt))) @ (listre1329599109le_alt @ R)) = (((((member681312074le_alt @ (produc961395117le_alt @ Xs @ Ys2) @ (listre1329599109le_alt @ R))) & ((X = Y)))) | ((((Xs = Ys2)) & ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R))))))))). % snoc_listrel1_snoc_iff
thf(fact_104_rev__nonempty__induct, axiom,
    ((![Xs : list_A2130511660le_alt, P : list_A2130511660le_alt > $o]: ((~ ((Xs = nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt]: (P @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((~ ((Xs2 = nil_Ar277507244le_alt))) => ((P @ Xs2) => (P @ (append714424641le_alt @ Xs2 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt)))))) => (P @ Xs))))))). % rev_nonempty_induct
thf(fact_105_append__eq__Cons__conv, axiom,
    ((![Ys2 : list_A2130511660le_alt, Zs2 : list_A2130511660le_alt, X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: (((append714424641le_alt @ Ys2 @ Zs2) = (cons_A1864255580le_alt @ X @ Xs)) = (((((Ys2 = nil_Ar277507244le_alt)) & ((Zs2 = (cons_A1864255580le_alt @ X @ Xs))))) | ((?[Ys4 : list_A2130511660le_alt]: (((Ys2 = (cons_A1864255580le_alt @ X @ Ys4))) & (((append714424641le_alt @ Ys4 @ Zs2) = Xs)))))))))). % append_eq_Cons_conv
thf(fact_106_Cons__eq__append__conv, axiom,
    ((![X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt, Zs2 : list_A2130511660le_alt]: (((cons_A1864255580le_alt @ X @ Xs) = (append714424641le_alt @ Ys2 @ Zs2)) = (((((Ys2 = nil_Ar277507244le_alt)) & (((cons_A1864255580le_alt @ X @ Xs) = Zs2)))) | ((?[Ys4 : list_A2130511660le_alt]: ((((cons_A1864255580le_alt @ X @ Ys4) = Ys2)) & ((Xs = (append714424641le_alt @ Ys4 @ Zs2))))))))))). % Cons_eq_append_conv
thf(fact_107_rev__exhaust, axiom,
    ((![Xs : list_A2130511660le_alt]: ((~ ((Xs = nil_Ar277507244le_alt))) => (~ ((![Ys3 : list_A2130511660le_alt, Y3 : arrow_1857593510le_alt]: (~ ((Xs = (append714424641le_alt @ Ys3 @ (cons_A1864255580le_alt @ Y3 @ nil_Ar277507244le_alt)))))))))))). % rev_exhaust
thf(fact_108_rev__induct, axiom,
    ((![P : list_A2130511660le_alt > $o, Xs : list_A2130511660le_alt]: ((P @ nil_Ar277507244le_alt) => ((![X3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((P @ Xs2) => (P @ (append714424641le_alt @ Xs2 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))))) => (P @ Xs)))))). % rev_induct
thf(fact_109_listrel1I2, axiom,
    ((![Xs : list_A2130511660le_alt, Ys2 : list_A2130511660le_alt, R : set_Pr367596371le_alt, X : arrow_1857593510le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ Xs @ Ys2) @ (listre1329599109le_alt @ R)) => (member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ X @ Xs) @ (cons_A1864255580le_alt @ X @ Ys2)) @ (listre1329599109le_alt @ R)))))). % listrel1I2
thf(fact_110_not__listrel1__Nil, axiom,
    ((![Xs : list_A2130511660le_alt, R : set_Pr367596371le_alt]: (~ ((member681312074le_alt @ (produc961395117le_alt @ Xs @ nil_Ar277507244le_alt) @ (listre1329599109le_alt @ R))))))). % not_listrel1_Nil
thf(fact_111_not__Nil__listrel1, axiom,
    ((![Xs : list_A2130511660le_alt, R : set_Pr367596371le_alt]: (~ ((member681312074le_alt @ (produc961395117le_alt @ nil_Ar277507244le_alt @ Xs) @ (listre1329599109le_alt @ R))))))). % not_Nil_listrel1
thf(fact_112_not__distinct__decomp, axiom,
    ((![Ws : list_A2130511660le_alt]: ((~ ((distin2037765919le_alt @ Ws))) => (?[Xs2 : list_A2130511660le_alt, Ys3 : list_A2130511660le_alt, Zs : list_A2130511660le_alt, Y3 : arrow_1857593510le_alt]: (Ws = (append714424641le_alt @ Xs2 @ (append714424641le_alt @ (cons_A1864255580le_alt @ Y3 @ nil_Ar277507244le_alt) @ (append714424641le_alt @ Ys3 @ (append714424641le_alt @ (cons_A1864255580le_alt @ Y3 @ nil_Ar277507244le_alt) @ Zs)))))))))). % not_distinct_decomp
thf(fact_113_lenlex__irreflexive, axiom,
    ((![R : set_Pr367596371le_alt, Xs : list_A2130511660le_alt]: ((![X3 : arrow_1857593510le_alt]: (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X3 @ X3) @ R)))) => (~ ((member681312074le_alt @ (produc961395117le_alt @ Xs @ Xs) @ (lenlex1434338225le_alt @ R)))))))). % lenlex_irreflexive
thf(fact_114_Nil__lenlex__iff2, axiom,
    ((![Ns : list_A2130511660le_alt, R : set_Pr367596371le_alt]: (~ ((member681312074le_alt @ (produc961395117le_alt @ Ns @ nil_Ar277507244le_alt) @ (lenlex1434338225le_alt @ R))))))). % Nil_lenlex_iff2
thf(fact_115_lexord__append__leftD, axiom,
    ((![X : list_A2130511660le_alt, U : list_A2130511660le_alt, V : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ (append714424641le_alt @ X @ U) @ (append714424641le_alt @ X @ V)) @ (lexord1313992857le_alt @ R)) => ((![A2 : arrow_1857593510le_alt]: (~ ((member2048039092le_alt @ (produc1494124311le_alt @ A2 @ A2) @ R)))) => (member681312074le_alt @ (produc961395117le_alt @ U @ V) @ (lexord1313992857le_alt @ R))))))). % lexord_append_leftD
thf(fact_116_lexord__append__rightI, axiom,
    ((![Y : list_A2130511660le_alt, X : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((?[B5 : arrow_1857593510le_alt, Z2 : list_A2130511660le_alt]: (Y = (cons_A1864255580le_alt @ B5 @ Z2))) => (member681312074le_alt @ (produc961395117le_alt @ X @ (append714424641le_alt @ X @ Y)) @ (lexord1313992857le_alt @ R)))))). % lexord_append_rightI
thf(fact_117_listrel1I1, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, R : set_Pr367596371le_alt, Xs : list_A2130511660le_alt]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ R) => (member681312074le_alt @ (produc961395117le_alt @ (cons_A1864255580le_alt @ X @ Xs) @ (cons_A1864255580le_alt @ Y @ Xs)) @ (listre1329599109le_alt @ R)))))). % listrel1I1

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![C2 : arrow_1857593510le_alt]: ((distin2037765919le_alt @ (cons_A1864255580le_alt @ a @ (cons_A1864255580le_alt @ b @ (cons_A1864255580le_alt @ C2 @ nil_Ar277507244le_alt)))) => thesis)))).
thf(conj_1, conjecture,
    (thesis)).
