% 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_285__5189360_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:17:18.012

% Could-be-implicit typings (14)
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_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Nat__Onat_J_J, type,
    list_A532482797lt_nat : $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__Set__Oset_It__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J, type,
    set_li397942028le_alt : $tType).
thf(ty_n_t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    list_A2130511660le_alt : $tType).
thf(ty_n_t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    set_Ar1007576579e_indi : $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).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (46)
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_Ounanimity, type,
    arrow_52334694nimity : ((arrow_1429744205e_indi > set_Pr367596371le_alt) > set_Pr367596371le_alt) > $o).
thf(sy_c_Finite__Set_Ocard_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    finite927127589e_indi : set_Ar1007576579e_indi > nat).
thf(sy_c_Fun_Oinj__on_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat, type,
    inj_on528257168di_nat : (arrow_1429744205e_indi > nat) > set_Ar1007576579e_indi > $o).
thf(sy_c_Fun_Oinj__on_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_001t__List__Olist_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    inj_on689828947le_alt : (list_A2130511660le_alt > list_A2130511660le_alt) > set_li397942028le_alt > $o).
thf(sy_c_Hilbert__Choice_Oinv__into_001t__Arrow____Order____Mirabelle____riepwfubkl__Oindi_001t__Nat__Onat, type,
    hilber1586975467di_nat : set_Ar1007576579e_indi > (arrow_1429744205e_indi > nat) > nat > arrow_1429744205e_indi).
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_Olexord_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    lexord1313992857le_alt : set_Pr367596371le_alt > set_Pr269449961le_alt).
thf(sy_c_List_Olist_OCons_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Nat__Onat_J, type,
    cons_A403191837lt_nat : (arrow_1857593510le_alt > nat) > list_A532482797lt_nat > list_A532482797lt_nat).
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_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Nat__Onat_J, type,
    nil_Ar1460642925lt_nat : list_A532482797lt_nat).
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_Omeasures_001t__Arrow____Order____Mirabelle____riepwfubkl__Oalt, type,
    measur1683305894le_alt : list_A532482797lt_nat > set_Pr367596371le_alt).
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_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    ord_le1187139159e_indi : set_Ar1007576579e_indi > set_Ar1007576579e_indi > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_I_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_Mt__Set__Oset_It__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J_J_J_M_Eo_J, type,
    top_to1344581618_alt_o : (arrow_1429744205e_indi > set_Pr367596371le_alt) > $o).
thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_M_Eo_J, type,
    top_to1473733010indi_o : arrow_1429744205e_indi > $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_001t__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,
    top_to685525675le_alt : set_Ar809243995le_alt).
thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Arrow____Order____Mirabelle____riepwfubkl__Oindi_J, type,
    top_to1799531699e_indi : set_Ar1007576579e_indi).
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_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_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__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    collec1169676194e_indi : (arrow_1429744205e_indi > $o) > set_Ar1007576579e_indi).
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_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__Arrow____Order____Mirabelle____riepwfubkl__Oindi, type,
    member1966420836e_indi : arrow_1429744205e_indi > set_Ar1007576579e_indi > $o).
thf(sy_c_member_001t__Product____Type__Oprod_It__Arrow____Order____Mirabelle____riepwfubkl__Oalt_Mt__Arrow____Order____Mirabelle____riepwfubkl__Oalt_J, type,
    member2048039092le_alt : produc16571293le_alt > set_Pr367596371le_alt > $o).
thf(sy_c_member_001t__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____, type,
    p : arrow_1429744205e_indi > set_Pr367596371le_alt).
thf(sy_v_c____, type,
    c : arrow_1857593510le_alt).
thf(sy_v_d____, type,
    d : arrow_1857593510le_alt).
thf(sy_v_h____, type,
    h : arrow_1429744205e_indi > nat).
thf(sy_v_n____, type,
    n : nat).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (135)
thf(fact_0_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_1__092_060open_062c_A_092_060noteq_062_Ad_092_060close_062, axiom,
    ((~ ((c = d))))). % \<open>c \<noteq> d\<close>
thf(fact_2__092_060open_062c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_092_060close_062, axiom,
    ((member2048039092le_alt @ (produc1494124311le_alt @ c @ d) @ (p @ (hilber1586975467di_nat @ top_to1799531699e_indi @ h @ n))))). % \<open>c <\<^bsub>P (inv h n)\<^esub> d\<close>
thf(fact_3_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_4_distinct__singleton, axiom,
    ((![X : arrow_1857593510le_alt]: (distin2037765919le_alt @ (cons_A1864255580le_alt @ X @ nil_Ar277507244le_alt))))). % distinct_singleton
thf(fact_5_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_6_distinct_Osimps_I1_J, axiom,
    ((distin2037765919le_alt @ nil_Ar277507244le_alt))). % distinct.simps(1)
thf(fact_7_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_8_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_9_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_10_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_11_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_12_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_13_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_14_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_15_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_16__092_060open_062P_A_092_060in_062_AProf_092_060close_062, axiom,
    ((member684274596le_alt @ p @ arrow_1951607831e_Prof))). % \<open>P \<in> Prof\<close>
thf(fact_17_injh, axiom,
    ((inj_on528257168di_nat @ h @ top_to1799531699e_indi))). % injh
thf(fact_18_not__Cons__self2, axiom,
    ((![X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: (~ (((cons_A1864255580le_alt @ X @ Xs) = Xs)))))). % not_Cons_self2
thf(fact_19_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]: ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, X_1 : list_A2130511660le_alt]: (P @ F @ nil_Ar277507244le_alt @ X_1)) => ((![F : arrow_1857593510le_alt > arrow_1857593510le_alt, A2 : arrow_1857593510le_alt, As : list_A2130511660le_alt, Bs : list_A2130511660le_alt]: ((P @ F @ As @ (cons_A1864255580le_alt @ (F @ A2) @ Bs)) => (P @ F @ (cons_A1864255580le_alt @ A2 @ As) @ Bs))) => (P @ A0 @ A1 @ A22)))))). % map_tailrec_rev.induct
thf(fact_20_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_21_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]: ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (P @ P2 @ nil_Ar277507244le_alt)) => ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt]: (P @ P2 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt))) => ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: ((P @ P2 @ (cons_A1864255580le_alt @ Y3 @ Xs2)) => (P @ P2 @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y3 @ Xs2))))) => (P @ A0 @ A1))))))). % successively.induct
thf(fact_22_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_23_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]: ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (P @ P2 @ nil_Ar277507244le_alt)) => ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Ys3 : list_A2130511660le_alt]: ((P @ P2 @ Ys3) => (P @ P2 @ (cons_A1864255580le_alt @ X3 @ Ys3)))) => (P @ A0 @ A1)))))). % sorted_wrt.induct
thf(fact_24_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_25_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_26_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_27_UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % UNIV_I
thf(fact_28_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % UNIV_I
thf(fact_29_UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % UNIV_I
thf(fact_30_iso__tuple__UNIV__I, axiom,
    ((![X : produc16571293le_alt]: (member2048039092le_alt @ X @ top_to224369155le_alt)))). % iso_tuple_UNIV_I
thf(fact_31_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X @ top_to685525675le_alt)))). % iso_tuple_UNIV_I
thf(fact_32_iso__tuple__UNIV__I, axiom,
    ((![X : arrow_1429744205e_indi]: (member1966420836e_indi @ X @ top_to1799531699e_indi)))). % iso_tuple_UNIV_I
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_inv__equality, axiom,
    ((![G : nat > arrow_1429744205e_indi, F2 : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi]: ((G @ (F2 @ X3)) = X3)) => ((![Y3 : nat]: ((F2 @ (G @ Y3)) = Y3)) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F2) = G)))))). % inv_equality
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_n_I1_J, axiom,
    ((ord_less_nat @ n @ (finite927127589e_indi @ top_to1799531699e_indi)))). % n(1)
thf(fact_39_inv__into__f__f, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, A4 : set_Ar1007576579e_indi, X : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ A4) => ((member1966420836e_indi @ X @ A4) => ((hilber1586975467di_nat @ A4 @ F2 @ (F2 @ X)) = X)))))). % inv_into_f_f
thf(fact_40_distinct__insert, axiom,
    ((![X : arrow_1857593510le_alt, Xs : list_A2130511660le_alt]: ((distin2037765919le_alt @ (insert1859930562le_alt @ X @ Xs)) = (distin2037765919le_alt @ Xs))))). % distinct_insert
thf(fact_41_top__set__def, axiom,
    ((top_to1799531699e_indi = (collec1169676194e_indi @ top_to1473733010indi_o)))). % top_set_def
thf(fact_42_mem__Collect__eq, axiom,
    ((![A : produc16571293le_alt, P : produc16571293le_alt > $o]: ((member2048039092le_alt @ A @ (collec531981554le_alt @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_43_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_44_Collect__mem__eq, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((collec531981554le_alt @ (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_45_Collect__mem__eq, axiom,
    ((![A4 : set_Ar809243995le_alt]: ((collec1559089382le_alt @ (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X4 @ A4))) = A4)))). % Collect_mem_eq
thf(fact_46_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_47_order_Ostrict__implies__not__eq, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_48_not__less__iff__gr__or__eq, axiom,
    ((![X : nat, Y : nat]: ((~ ((ord_less_nat @ X @ Y))) = (((ord_less_nat @ Y @ X)) | ((X = Y))))))). % not_less_iff_gr_or_eq
thf(fact_49_dual__order_Ostrict__trans, axiom,
    ((![B : nat, A : nat, C2 : nat]: ((ord_less_nat @ B @ A) => ((ord_less_nat @ C2 @ B) => (ord_less_nat @ C2 @ A)))))). % dual_order.strict_trans
thf(fact_50_linorder__less__wlog, axiom,
    ((![P : nat > nat > $o, A : nat, B : nat]: ((![A2 : nat, B2 : nat]: ((ord_less_nat @ A2 @ B2) => (P @ A2 @ B2))) => ((![A2 : nat]: (P @ A2 @ A2)) => ((![A2 : nat, B2 : nat]: ((P @ B2 @ A2) => (P @ A2 @ B2))) => (P @ A @ B))))))). % linorder_less_wlog
thf(fact_51_exists__least__iff, axiom,
    (((^[P3 : nat > $o]: (?[X5 : nat]: (P3 @ X5))) = (^[P4 : nat > $o]: (?[N : nat]: (((P4 @ N)) & ((![M : nat]: (((ord_less_nat @ M @ N)) => ((~ ((P4 @ M))))))))))))). % exists_least_iff
thf(fact_52_less__imp__not__less, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((ord_less_nat @ Y @ X))))))). % less_imp_not_less
thf(fact_53_order_Ostrict__trans, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ B @ C2) => (ord_less_nat @ A @ C2)))))). % order.strict_trans
thf(fact_54_dual__order_Oirrefl, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ A)))))). % dual_order.irrefl
thf(fact_55_linorder__cases, axiom,
    ((![X : nat, Y : nat]: ((~ ((ord_less_nat @ X @ Y))) => ((~ ((X = Y))) => (ord_less_nat @ Y @ X)))))). % linorder_cases
thf(fact_56_less__imp__triv, axiom,
    ((![X : nat, Y : nat, P : $o]: ((ord_less_nat @ X @ Y) => ((ord_less_nat @ Y @ X) => P))))). % less_imp_triv
thf(fact_57_less__imp__not__eq2, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((Y = X))))))). % less_imp_not_eq2
thf(fact_58_antisym__conv3, axiom,
    ((![Y : nat, X : nat]: ((~ ((ord_less_nat @ Y @ X))) => ((~ ((ord_less_nat @ X @ Y))) = (X = Y)))))). % antisym_conv3
thf(fact_59_less__induct, axiom,
    ((![P : nat > $o, A : nat]: ((![X3 : nat]: ((![Y4 : nat]: ((ord_less_nat @ Y4 @ X3) => (P @ Y4))) => (P @ X3))) => (P @ A))))). % less_induct
thf(fact_60_less__not__sym, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((ord_less_nat @ Y @ X))))))). % less_not_sym
thf(fact_61_less__imp__not__eq, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((X = Y))))))). % less_imp_not_eq
thf(fact_62_dual__order_Oasym, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ B @ A) => (~ ((ord_less_nat @ A @ B))))))). % dual_order.asym
thf(fact_63_ord__less__eq__trans, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_nat @ A @ B) => ((B = C2) => (ord_less_nat @ A @ C2)))))). % ord_less_eq_trans
thf(fact_64_ord__eq__less__trans, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((A = B) => ((ord_less_nat @ B @ C2) => (ord_less_nat @ A @ C2)))))). % ord_eq_less_trans
thf(fact_65_less__irrefl, axiom,
    ((![X : nat]: (~ ((ord_less_nat @ X @ X)))))). % less_irrefl
thf(fact_66_less__linear, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) | ((X = Y) | (ord_less_nat @ Y @ X)))))). % less_linear
thf(fact_67_less__trans, axiom,
    ((![X : nat, Y : nat, Z : nat]: ((ord_less_nat @ X @ Y) => ((ord_less_nat @ Y @ Z) => (ord_less_nat @ X @ Z)))))). % less_trans
thf(fact_68_less__asym_H, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((ord_less_nat @ B @ A))))))). % less_asym'
thf(fact_69_less__asym, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((ord_less_nat @ Y @ X))))))). % less_asym
thf(fact_70_less__imp__neq, axiom,
    ((![X : nat, Y : nat]: ((ord_less_nat @ X @ Y) => (~ ((X = Y))))))). % less_imp_neq
thf(fact_71_order_Oasym, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((ord_less_nat @ B @ A))))))). % order.asym
thf(fact_72_neq__iff, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) = (((ord_less_nat @ X @ Y)) | ((ord_less_nat @ Y @ X))))))). % neq_iff
thf(fact_73_neqE, axiom,
    ((![X : nat, Y : nat]: ((~ ((X = Y))) => ((~ ((ord_less_nat @ X @ Y))) => (ord_less_nat @ Y @ X)))))). % neqE
thf(fact_74_gt__ex, axiom,
    ((![X : nat]: (?[X_1 : nat]: (ord_less_nat @ X @ X_1))))). % gt_ex
thf(fact_75_order__less__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C2 : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ (F2 @ B) @ C2) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F2 @ X3) @ (F2 @ Y3)))) => (ord_less_nat @ (F2 @ A) @ C2))))))). % order_less_subst2
thf(fact_76_order__less__subst1, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C2 : nat]: ((ord_less_nat @ A @ (F2 @ B)) => ((ord_less_nat @ B @ C2) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F2 @ X3) @ (F2 @ Y3)))) => (ord_less_nat @ A @ (F2 @ C2)))))))). % order_less_subst1
thf(fact_77_ord__less__eq__subst, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C2 : nat]: ((ord_less_nat @ A @ B) => (((F2 @ B) = C2) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F2 @ X3) @ (F2 @ Y3)))) => (ord_less_nat @ (F2 @ A) @ C2))))))). % ord_less_eq_subst
thf(fact_78_ord__eq__less__subst, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C2 : nat]: ((A = (F2 @ B)) => ((ord_less_nat @ B @ C2) => ((![X3 : nat, Y3 : nat]: ((ord_less_nat @ X3 @ Y3) => (ord_less_nat @ (F2 @ X3) @ (F2 @ Y3)))) => (ord_less_nat @ A @ (F2 @ C2)))))))). % ord_eq_less_subst
thf(fact_79_top_Onot__eq__extremum, axiom,
    ((![A : set_Ar1007576579e_indi]: ((~ ((A = top_to1799531699e_indi))) = (ord_le1187139159e_indi @ A @ top_to1799531699e_indi))))). % top.not_eq_extremum
thf(fact_80_top_Oextremum__strict, axiom,
    ((![A : set_Ar1007576579e_indi]: (~ ((ord_le1187139159e_indi @ top_to1799531699e_indi @ A)))))). % top.extremum_strict
thf(fact_81_inv__into__f__eq, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, A4 : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y : nat]: ((inj_on528257168di_nat @ F2 @ A4) => ((member1966420836e_indi @ X @ A4) => (((F2 @ X) = Y) => ((hilber1586975467di_nat @ A4 @ F2 @ Y) = X))))))). % inv_into_f_eq
thf(fact_82_inj__imp__inv__eq, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, G : nat > arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ top_to1799531699e_indi) => ((![X3 : nat]: ((F2 @ (G @ X3)) = X3)) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F2) = G)))))). % inj_imp_inv_eq
thf(fact_83_inv__f__eq, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, X : arrow_1429744205e_indi, Y : nat]: ((inj_on528257168di_nat @ F2 @ top_to1799531699e_indi) => (((F2 @ X) = Y) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F2 @ Y) = X)))))). % inv_f_eq
thf(fact_84_inv__f__f, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, X : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ top_to1799531699e_indi) => ((hilber1586975467di_nat @ top_to1799531699e_indi @ F2 @ (F2 @ X)) = X))))). % inv_f_f
thf(fact_85_sorted__wrt_Ocases, axiom,
    ((![X : produc1094320767le_alt]: ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (~ ((X = (produc2047839287le_alt @ P2 @ nil_Ar277507244le_alt))))) => (~ ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Ys3 : list_A2130511660le_alt]: (~ ((X = (produc2047839287le_alt @ P2 @ (cons_A1864255580le_alt @ X3 @ Ys3)))))))))))). % sorted_wrt.cases
thf(fact_86_successively_Ocases, axiom,
    ((![X : produc1094320767le_alt]: ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o]: (~ ((X = (produc2047839287le_alt @ P2 @ nil_Ar277507244le_alt))))) => ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt]: (~ ((X = (produc2047839287le_alt @ P2 @ (cons_A1864255580le_alt @ X3 @ nil_Ar277507244le_alt)))))) => (~ ((![P2 : arrow_1857593510le_alt > arrow_1857593510le_alt > $o, X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt, Xs2 : list_A2130511660le_alt]: (~ ((X = (produc2047839287le_alt @ P2 @ (cons_A1864255580le_alt @ X3 @ (cons_A1864255580le_alt @ Y3 @ Xs2)))))))))))))). % successively.cases
thf(fact_87_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_88_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_89_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_90_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_91_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_92_prod__cases, axiom,
    ((![P : produc16571293le_alt > $o, P5 : produc16571293le_alt]: ((![A2 : arrow_1857593510le_alt, B2 : arrow_1857593510le_alt]: (P @ (produc1494124311le_alt @ A2 @ B2))) => (P @ P5))))). % prod_cases
thf(fact_93_surj__pair, axiom,
    ((![P5 : produc16571293le_alt]: (?[X3 : arrow_1857593510le_alt, Y3 : arrow_1857593510le_alt]: (P5 = (produc1494124311le_alt @ X3 @ Y3)))))). % surj_pair
thf(fact_94_UNIV__witness, axiom,
    ((?[X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ top_to224369155le_alt)))). % UNIV_witness
thf(fact_95_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ top_to685525675le_alt)))). % UNIV_witness
thf(fact_96_UNIV__witness, axiom,
    ((?[X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ top_to1799531699e_indi)))). % UNIV_witness
thf(fact_97_UNIV__eq__I, axiom,
    ((![A4 : set_Pr367596371le_alt]: ((![X3 : produc16571293le_alt]: (member2048039092le_alt @ X3 @ A4)) => (top_to224369155le_alt = A4))))). % UNIV_eq_I
thf(fact_98_UNIV__eq__I, axiom,
    ((![A4 : set_Ar809243995le_alt]: ((![X3 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X3 @ A4)) => (top_to685525675le_alt = A4))))). % UNIV_eq_I
thf(fact_99_UNIV__eq__I, axiom,
    ((![A4 : set_Ar1007576579e_indi]: ((![X3 : arrow_1429744205e_indi]: (member1966420836e_indi @ X3 @ A4)) => (top_to1799531699e_indi = A4))))). % UNIV_eq_I
thf(fact_100_unanimity__def, axiom,
    ((arrow_52334694nimity = (^[F3 : (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) @ (F3 @ X4))))))))))))). % unanimity_def
thf(fact_101_IIA__def, axiom,
    ((arrow_1821794627le_IIA = (^[F3 : (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)) => ((![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) @ (Y2 @ I))))) => (((member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F3 @ X4)) = (member2048039092le_alt @ (produc1494124311le_alt @ A5 @ B4) @ (F3 @ Y2))))))))))))))))). % IIA_def
thf(fact_102_injD, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, X : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ top_to1799531699e_indi) => (((F2 @ X) = (F2 @ Y)) => (X = Y)))))). % injD
thf(fact_103_injI, axiom,
    ((![F2 : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi, Y3 : arrow_1429744205e_indi]: (((F2 @ X3) = (F2 @ Y3)) => (X3 = Y3))) => (inj_on528257168di_nat @ F2 @ top_to1799531699e_indi))))). % injI
thf(fact_104_u, axiom,
    ((arrow_52334694nimity @ f))). % u
thf(fact_105_assms_I3_J, axiom,
    ((arrow_1821794627le_IIA @ f))). % assms(3)
thf(fact_106_inj__on__Cons1, axiom,
    ((![X : arrow_1857593510le_alt, A4 : set_li397942028le_alt]: (inj_on689828947le_alt @ (cons_A1864255580le_alt @ X) @ A4)))). % inj_on_Cons1
thf(fact_107_inj__onD, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, A4 : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ A4) => (((F2 @ X) = (F2 @ Y)) => ((member1966420836e_indi @ X @ A4) => ((member1966420836e_indi @ Y @ A4) => (X = Y)))))))). % inj_onD
thf(fact_108_inj__onI, axiom,
    ((![A4 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi, Y3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A4) => ((member1966420836e_indi @ Y3 @ A4) => (((F2 @ X3) = (F2 @ Y3)) => (X3 = Y3))))) => (inj_on528257168di_nat @ F2 @ A4))))). % inj_onI
thf(fact_109_inj__on__def, axiom,
    ((inj_on528257168di_nat = (^[F4 : arrow_1429744205e_indi > nat]: (^[A6 : set_Ar1007576579e_indi]: (![X4 : arrow_1429744205e_indi]: (((member1966420836e_indi @ X4 @ A6)) => ((![Y2 : arrow_1429744205e_indi]: (((member1966420836e_indi @ Y2 @ A6)) => (((((F4 @ X4) = (F4 @ Y2))) => ((X4 = Y2)))))))))))))). % inj_on_def
thf(fact_110_inj__on__cong, axiom,
    ((![A4 : set_Ar1007576579e_indi, F2 : arrow_1429744205e_indi > nat, G : arrow_1429744205e_indi > nat]: ((![A2 : arrow_1429744205e_indi]: ((member1966420836e_indi @ A2 @ A4) => ((F2 @ A2) = (G @ A2)))) => ((inj_on528257168di_nat @ F2 @ A4) = (inj_on528257168di_nat @ G @ A4)))))). % inj_on_cong
thf(fact_111_inj__on__eq__iff, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, A4 : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ A4) => ((member1966420836e_indi @ X @ A4) => ((member1966420836e_indi @ Y @ A4) => (((F2 @ X) = (F2 @ Y)) = (X = Y)))))))). % inj_on_eq_iff
thf(fact_112_inj__on__contraD, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, A4 : set_Ar1007576579e_indi, X : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ A4) => ((~ ((X = Y))) => ((member1966420836e_indi @ X @ A4) => ((member1966420836e_indi @ Y @ A4) => (~ (((F2 @ X) = (F2 @ Y))))))))))). % inj_on_contraD
thf(fact_113_inj__on__inverseI, axiom,
    ((![A4 : set_Ar1007576579e_indi, G : nat > arrow_1429744205e_indi, F2 : arrow_1429744205e_indi > nat]: ((![X3 : arrow_1429744205e_indi]: ((member1966420836e_indi @ X3 @ A4) => ((G @ (F2 @ X3)) = X3))) => (inj_on528257168di_nat @ F2 @ A4))))). % inj_on_inverseI
thf(fact_114_inj__def, axiom,
    ((![F2 : arrow_1429744205e_indi > nat]: ((inj_on528257168di_nat @ F2 @ top_to1799531699e_indi) = (![X4 : arrow_1429744205e_indi]: (![Y2 : arrow_1429744205e_indi]: ((((F2 @ X4) = (F2 @ Y2))) => ((X4 = Y2))))))))). % inj_def
thf(fact_115_inj__eq, axiom,
    ((![F2 : arrow_1429744205e_indi > nat, X : arrow_1429744205e_indi, Y : arrow_1429744205e_indi]: ((inj_on528257168di_nat @ F2 @ top_to1799531699e_indi) => (((F2 @ X) = (F2 @ Y)) = (X = Y)))))). % inj_eq
thf(fact_116_top__empty__eq, axiom,
    ((top_to1074038850_alt_o = (^[X4 : produc16571293le_alt]: (member2048039092le_alt @ X4 @ top_to224369155le_alt))))). % top_empty_eq
thf(fact_117_top__empty__eq, axiom,
    ((top_to1344581618_alt_o = (^[X4 : arrow_1429744205e_indi > set_Pr367596371le_alt]: (member684274596le_alt @ X4 @ top_to685525675le_alt))))). % top_empty_eq
thf(fact_118_top__empty__eq, axiom,
    ((top_to1473733010indi_o = (^[X4 : arrow_1429744205e_indi]: (member1966420836e_indi @ X4 @ top_to1799531699e_indi))))). % top_empty_eq
thf(fact_119_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_120_pairwise__neutrality, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, A3 : arrow_1857593510le_alt, B3 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P6 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A3 = B3))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P6 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (P6 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (f @ P6))))))))))). % pairwise_neutrality
thf(fact_121__C4_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, C2 : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P6 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((B = C2))) => ((~ ((A = C2))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P6 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C2) @ (P6 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ C2) @ (f @ P6)))))))))))). % "4"
thf(fact_122__C3_C, axiom,
    ((![A : arrow_1857593510le_alt, B : arrow_1857593510le_alt, P : arrow_1429744205e_indi > set_Pr367596371le_alt, P6 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P6 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (P6 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ B @ A) @ (f @ P6)))))))))). % "3"
thf(fact_123__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, P6 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A3 = B3))) => ((~ ((A = B3))) => ((~ ((B = A3))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P6 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (P6 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (f @ P6))))))))))))). % "2"
thf(fact_124__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, P6 : arrow_1429744205e_indi > set_Pr367596371le_alt]: ((~ ((A = B))) => ((~ ((A3 = B3))) => ((~ ((A = B3))) => ((~ ((B = A3))) => ((member684274596le_alt @ P @ arrow_1951607831e_Prof) => ((member684274596le_alt @ P6 @ arrow_1951607831e_Prof) => ((![I2 : arrow_1429744205e_indi]: ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (P @ I2)) = (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (P6 @ I2)))) => ((member2048039092le_alt @ (produc1494124311le_alt @ A @ B) @ (f @ P)) => (member2048039092le_alt @ (produc1494124311le_alt @ A3 @ B3) @ (f @ P6))))))))))))). % "1"
thf(fact_125_in__measures_I2_J, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, F2 : arrow_1857593510le_alt > nat, Fs : list_A532482797lt_nat]: ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (measur1683305894le_alt @ (cons_A403191837lt_nat @ F2 @ Fs))) = (((ord_less_nat @ (F2 @ X) @ (F2 @ Y))) | (((((F2 @ X) = (F2 @ Y))) & ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (measur1683305894le_alt @ Fs)))))))))). % in_measures(2)
thf(fact_126_subseqs_Osimps_I1_J, axiom,
    (((subseq1380156923le_alt @ nil_Ar277507244le_alt) = (cons_l157309922le_alt @ nil_Ar277507244le_alt @ nil_li2110134322le_alt)))). % subseqs.simps(1)
thf(fact_127_in__measures_I1_J, axiom,
    ((![X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt]: (~ ((member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (measur1683305894le_alt @ nil_Ar1460642925lt_nat))))))). % in_measures(1)
thf(fact_128_measures__less, axiom,
    ((![F2 : arrow_1857593510le_alt > nat, X : arrow_1857593510le_alt, Y : arrow_1857593510le_alt, Fs : list_A532482797lt_nat]: ((ord_less_nat @ (F2 @ X) @ (F2 @ Y)) => (member2048039092le_alt @ (produc1494124311le_alt @ X @ Y) @ (measur1683305894le_alt @ (cons_A403191837lt_nat @ F2 @ Fs))))))). % measures_less
thf(fact_129_dictator__def, axiom,
    ((arrow_960434986ctator = (^[F3 : (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)) => (((F3 @ X4) = (X4 @ I)))))))))). % dictator_def
thf(fact_130_lexord__Nil__left, axiom,
    ((![Y : list_A2130511660le_alt, R : set_Pr367596371le_alt]: ((member681312074le_alt @ (produc961395117le_alt @ nil_Ar277507244le_alt @ Y) @ (lexord1313992857le_alt @ R)) = (?[A5 : arrow_1857593510le_alt]: (?[X4 : list_A2130511660le_alt]: (Y = (cons_A1864255580le_alt @ A5 @ X4)))))))). % lexord_Nil_left
thf(fact_131_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_132_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_133_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_134_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

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