DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP158^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Feb 25 08:56:01 AM UTC 2026

% Result   : Theorem 22.73s 4.68s
% Output   : Refutation 22.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   72 (  18 unt;   0 typ;   3 def)
%            Number of atoms       :  424 ( 103 equ;   0 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives : 1017 (  59   ~;  53   |;   4   &; 823   @)
%                                         (   3 <=>;  43  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Number of types       :   38 (  37 usr)
%            Number of type conns  :   77 (  77   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  250 ( 246 usr;  18 con; 0-6 aty)
%                                         (  32  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  137 (  42   ^;  89   !;   6   ?; 137   :)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    nat: $tType ).

thf(type_def_6,type,
    list_nat: $tType ).

thf(type_def_8,type,
    list_P512754263e_form: $tType ).

thf(type_def_9,type,
    list_list_nat: $tType ).

thf(type_def_10,type,
    list_l461858535e_form: $tType ).

thf(type_def_11,type,
    prover1687215943e_form: $tType ).

thf(type_def_12,type,
    set_nat: $tType ).

thf(type_def_13,type,
    set_Pr1986765409at_nat: $tType ).

thf(type_def_14,type,
    set_Pr1560408065st_nat: $tType ).

thf(type_def_15,type,
    set_Pr1189404964e_form: $tType ).

thf(type_def_16,type,
    set_Pr31825690e_form: $tType ).

thf(type_def_17,type,
    list_P796095576elle_U: $tType ).

thf(type_def_18,type,
    list_n2139828004le_U_o: $tType ).

thf(type_def_19,type,
    set_Pr619177522elle_U: $tType ).

thf(type_def_20,type,
    list_s1200803384elle_U: $tType ).

thf(type_def_21,type,
    set_list_nat: $tType ).

thf(type_def_22,type,
    set_li5074317e_form: $tType ).

thf(type_def_23,type,
    set_Pr554570749e_form: $tType ).

thf(type_def_24,type,
    set_Pr816919384e_form: $tType ).

thf(type_def_25,type,
    set_Pr1174364408e_form: $tType ).

thf(type_def_26,type,
    set_Pr957084504rm_nat: $tType ).

thf(type_def_27,type,
    set_Pr1057005944st_nat: $tType ).

thf(type_def_28,type,
    set_Pr1072215906le_U_o: $tType ).

thf(type_def_29,type,
    set_Pr2099245410le_U_o: $tType ).

thf(type_def_30,type,
    produc890077173st_nat: $tType ).

thf(type_def_31,type,
    produc957084248e_form: $tType ).

thf(type_def_32,type,
    produc1699244961st_nat: $tType ).

thf(type_def_33,type,
    produc1494932632e_form: $tType ).

thf(type_def_34,type,
    produc1473535256st_nat: $tType ).

thf(type_def_35,type,
    produc791938916e_form: $tType ).

thf(type_def_36,type,
    produc622718850le_U_o: $tType ).

thf(type_def_37,type,
    product_prod_nat_nat: $tType ).

thf(type_def_38,type,
    produc1296622072e_form: $tType ).

thf(type_def_39,type,
    produc117678584rm_nat: $tType ).

thf(type_def_40,type,
    produc825256814e_form: $tType ).

thf(type_def_41,type,
    produc227817602le_U_o: $tType ).

thf(type_def_42,type,
    prover_Mirabelle_U: $tType ).

thf(func_def_0,type,
    set_Pr2099245410le_U_o: $tType ).

thf(func_def_1,type,
    produc622718850le_U_o: $tType ).

thf(func_def_2,type,
    produc957084248e_form: $tType ).

thf(func_def_3,type,
    set_Pr1072215906le_U_o: $tType ).

thf(func_def_4,type,
    produc227817602le_U_o: $tType ).

thf(func_def_5,type,
    set_Pr31825690e_form: $tType ).

thf(func_def_6,type,
    produc791938916e_form: $tType ).

thf(func_def_7,type,
    set_Pr1057005944st_nat: $tType ).

thf(func_def_8,type,
    set_Pr1174364408e_form: $tType ).

thf(func_def_9,type,
    set_Pr1189404964e_form: $tType ).

thf(func_def_10,type,
    produc1473535256st_nat: $tType ).

thf(func_def_11,type,
    produc1494932632e_form: $tType ).

thf(func_def_12,type,
    produc825256814e_form: $tType ).

thf(func_def_13,type,
    list_n2139828004le_U_o: $tType ).

thf(func_def_14,type,
    produc890077173st_nat: $tType ).

thf(func_def_15,type,
    set_Pr1560408065st_nat: $tType ).

thf(func_def_16,type,
    set_Pr957084504rm_nat: $tType ).

thf(func_def_17,type,
    set_Pr816919384e_form: $tType ).

thf(func_def_18,type,
    produc1699244961st_nat: $tType ).

thf(func_def_19,type,
    produc117678584rm_nat: $tType ).

thf(func_def_20,type,
    produc1296622072e_form: $tType ).

thf(func_def_21,type,
    list_l461858535e_form: $tType ).

thf(func_def_22,type,
    set_li5074317e_form: $tType ).

thf(func_def_23,type,
    list_s1200803384elle_U: $tType ).

thf(func_def_24,type,
    set_Pr1986765409at_nat: $tType ).

thf(func_def_25,type,
    list_P512754263e_form: $tType ).

thf(func_def_26,type,
    set_Pr554570749e_form: $tType ).

thf(func_def_27,type,
    list_P796095576elle_U: $tType ).

thf(func_def_28,type,
    set_Pr619177522elle_U: $tType ).

thf(func_def_29,type,
    product_prod_nat_nat: $tType ).

thf(func_def_30,type,
    list_list_nat: $tType ).

thf(func_def_31,type,
    set_list_nat: $tType ).

thf(func_def_32,type,
    prover1687215943e_form: $tType ).

thf(func_def_33,type,
    prover_Mirabelle_U: $tType ).

thf(func_def_34,type,
    list_nat: $tType ).

thf(func_def_35,type,
    set_nat: $tType ).

thf(func_def_36,type,
    nat: $tType ).

thf(func_def_37,type,
    zero_zero_nat: nat ).

thf(func_def_38,type,
    if_list_nat: $o > list_nat > list_nat > list_nat ).

thf(func_def_39,type,
    if_lis1812881937e_form: $o > list_P512754263e_form > list_P512754263e_form > list_P512754263e_form ).

thf(func_def_40,type,
    append_list_nat: list_list_nat > list_list_nat > list_list_nat ).

thf(func_def_41,type,
    append1797078012e_form: list_l461858535e_form > list_l461858535e_form > list_l461858535e_form ).

thf(func_def_42,type,
    append_nat: list_nat > list_nat > list_nat ).

thf(func_def_43,type,
    append1038020460e_form: list_P512754263e_form > list_P512754263e_form > list_P512754263e_form ).

thf(func_def_44,type,
    bind_nat_nat: list_nat > ( nat > list_nat ) > list_nat ).

thf(func_def_45,type,
    bind_n1193922848e_form: list_nat > ( nat > list_P512754263e_form ) > list_P512754263e_form ).

thf(func_def_46,type,
    bind_P1359331232rm_nat: list_P512754263e_form > ( prover1687215943e_form > list_nat ) > list_nat ).

thf(func_def_47,type,
    bind_P1054726576e_form: list_P512754263e_form > ( prover1687215943e_form > list_P512754263e_form ) > list_P512754263e_form ).

thf(func_def_48,type,
    butlast_nat: list_nat > list_nat ).

thf(func_def_49,type,
    butlas664258165e_form: list_P512754263e_form > list_P512754263e_form ).

thf(func_def_50,type,
    can_select_nat: ( nat > $o ) > set_nat > $o ).

thf(func_def_51,type,
    concat_nat: list_list_nat > list_nat ).

thf(func_def_52,type,
    concat1664984646e_form: list_l461858535e_form > list_P512754263e_form ).

thf(func_def_53,type,
    insert_nat: nat > list_nat > list_nat ).

thf(func_def_54,type,
    insert697320747e_form: prover1687215943e_form > list_P512754263e_form > list_P512754263e_form ).

thf(func_def_55,type,
    last_nat: list_nat > nat ).

thf(func_def_56,type,
    last_P1811260776e_form: list_P512754263e_form > prover1687215943e_form ).

thf(func_def_57,type,
    lenlex_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).

thf(func_def_58,type,
    lenlex1927129340e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).

thf(func_def_59,type,
    lex_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).

thf(func_def_60,type,
    lex_Pr233218909e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).

thf(func_def_61,type,
    lexord_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).

thf(func_def_62,type,
    lexord1848469012e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).

thf(func_def_63,type,
    cons_n50929118le_U_o: ( nat > list_P796095576elle_U > $o ) > list_n2139828004le_U_o > list_n2139828004le_U_o ).

thf(func_def_64,type,
    cons_list_nat: list_nat > list_list_nat > list_list_nat ).

thf(func_def_65,type,
    cons_l1379921697e_form: list_P512754263e_form > list_l461858535e_form > list_l461858535e_form ).

thf(func_def_66,type,
    cons_nat: nat > list_nat > list_nat ).

thf(func_def_67,type,
    cons_P1475164433e_form: prover1687215943e_form > list_P512754263e_form > list_P512754263e_form ).

thf(func_def_68,type,
    cons_s32021736elle_U: set_Pr619177522elle_U > list_s1200803384elle_U > list_s1200803384elle_U ).

thf(func_def_69,type,
    nil_na1584420238le_U_o: list_n2139828004le_U_o ).

thf(func_def_70,type,
    nil_list_nat: list_list_nat ).

thf(func_def_71,type,
    nil_li1393862353e_form: list_l461858535e_form ).

thf(func_def_72,type,
    nil_nat: list_nat ).

thf(func_def_73,type,
    nil_Pr1384483009e_form: list_P512754263e_form ).

thf(func_def_74,type,
    nil_se944326968elle_U: list_s1200803384elle_U ).

thf(func_def_75,type,
    set_list_nat2: list_list_nat > set_list_nat ).

thf(func_def_76,type,
    set_li1219651714e_form: list_l461858535e_form > set_li5074317e_form ).

thf(func_def_77,type,
    set_nat2: list_nat > set_nat ).

thf(func_def_78,type,
    set_Pr1105237746e_form: list_P512754263e_form > set_Pr554570749e_form ).

thf(func_def_79,type,
    list_ex1_nat: ( nat > $o ) > list_nat > $o ).

thf(func_def_80,type,
    list_e2123636798e_form: ( prover1687215943e_form > $o ) > list_P512754263e_form > $o ).

thf(func_def_81,type,
    listrel1_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).

thf(func_def_82,type,
    listre502458152e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).

thf(func_def_83,type,
    listrel_nat_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).

thf(func_def_84,type,
    listre318297994e_form: set_Pr816919384e_form > set_Pr1174364408e_form ).

thf(func_def_85,type,
    listre483706378rm_nat: set_Pr957084504rm_nat > set_Pr1057005944st_nat ).

thf(func_def_86,type,
    listre1908795590e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).

thf(func_def_87,type,
    listre290852044le_U_o: set_Pr1072215906le_U_o > set_Pr2099245410le_U_o ).

thf(func_def_88,type,
    maps_nat_nat: ( nat > list_nat ) > list_nat > list_nat ).

thf(func_def_89,type,
    maps_n1383976154e_form: ( nat > list_P512754263e_form ) > list_nat > list_P512754263e_form ).

thf(func_def_90,type,
    maps_P1549384538rm_nat: ( prover1687215943e_form > list_nat ) > list_P512754263e_form > list_nat ).

thf(func_def_91,type,
    maps_P2058952566e_form: ( prover1687215943e_form > list_P512754263e_form ) > list_P512754263e_form > list_P512754263e_form ).

thf(func_def_92,type,
    product_lists_nat: list_list_nat > list_list_nat ).

thf(func_def_93,type,
    produc168439576e_form: list_l461858535e_form > list_l461858535e_form ).

thf(func_def_94,type,
    rotate1_nat: list_nat > list_nat ).

thf(func_def_95,type,
    rotate650061876e_form: list_P512754263e_form > list_P512754263e_form ).

thf(func_def_96,type,
    subseqs_nat: list_nat > list_list_nat ).

thf(func_def_97,type,
    subseq1471997234e_form: list_P512754263e_form > list_l461858535e_form ).

thf(func_def_98,type,
    produc939441135st_nat: ( nat > nat > $o ) > list_nat > produc890077173st_nat ).

thf(func_def_99,type,
    produc54611594e_form: ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > produc957084248e_form ).

thf(func_def_100,type,
    produc1625736153st_nat: list_nat > list_nat > produc1699244961st_nat ).

thf(func_def_101,type,
    produc1617574096e_form: list_nat > list_P512754263e_form > produc1494932632e_form ).

thf(func_def_102,type,
    produc1897654224st_nat: list_P512754263e_form > list_nat > produc1473535256st_nat ).

thf(func_def_103,type,
    produc891809686e_form: list_P512754263e_form > list_P512754263e_form > produc791938916e_form ).

thf(func_def_104,type,
    produc1377086578le_U_o: list_s1200803384elle_U > list_n2139828004le_U_o > produc622718850le_U_o ).

thf(func_def_105,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_106,type,
    produc876465968e_form: nat > prover1687215943e_form > produc1296622072e_form ).

thf(func_def_107,type,
    produc1041874352rm_nat: prover1687215943e_form > nat > produc117678584rm_nat ).

thf(func_def_108,type,
    produc1018812320e_form: prover1687215943e_form > prover1687215943e_form > produc825256814e_form ).

thf(func_def_109,type,
    produc1069574002le_U_o: set_Pr619177522elle_U > ( nat > list_P796095576elle_U > $o ) > produc227817602le_U_o ).

thf(func_def_110,type,
    prover1282070756_SEval: produc227817602le_U_o > ( nat > prover_Mirabelle_U ) > list_P512754263e_form > $o ).

thf(func_def_111,type,
    prover1539709396Svalid: list_P512754263e_form > $o ).

thf(func_def_112,type,
    prover1577896257_finst: prover1687215943e_form > nat > prover1687215943e_form ).

thf(func_def_113,type,
    prover886976490en_nat: list_list_nat > list_nat ).

thf(func_def_114,type,
    prover542312166e_form: list_l461858535e_form > list_P512754263e_form ).

thf(func_def_115,type,
    prover571163162e_FAll: prover1687215943e_form > prover1687215943e_form ).

thf(func_def_116,type,
    prover_Mirabelle_fv: prover1687215943e_form > list_nat ).

thf(func_def_117,type,
    prover1847600056is_env: produc227817602le_U_o > ( nat > prover_Mirabelle_U ) > $o ).

thf(func_def_118,type,
    prover1021675886maxvar: list_nat > nat ).

thf(func_def_119,type,
    prover2096325705preSuc: list_nat > list_nat ).

thf(func_def_120,type,
    prover_Mirabelle_sfv: list_P512754263e_form > list_nat ).

thf(func_def_121,type,
    irrefl_nat: set_Pr1986765409at_nat > $o ).

thf(func_def_122,type,
    irrefl2121388754e_form: set_Pr1189404964e_form > $o ).

thf(func_def_123,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(func_def_124,type,
    the_elem_nat: set_nat > nat ).

thf(func_def_125,type,
    the_el969789074e_form: set_Pr554570749e_form > prover1687215943e_form ).

thf(func_def_126,type,
    member_list_nat: list_nat > set_list_nat > $o ).

thf(func_def_127,type,
    member1828782574e_form: list_P512754263e_form > set_li5074317e_form > $o ).

thf(func_def_128,type,
    member_nat: nat > set_nat > $o ).

thf(func_def_129,type,
    member1926390090st_nat: produc1699244961st_nat > set_Pr1560408065st_nat > $o ).

thf(func_def_130,type,
    member1471151041e_form: produc1494932632e_form > set_Pr1174364408e_form > $o ).

thf(func_def_131,type,
    member1449753665st_nat: produc1473535256st_nat > set_Pr1057005944st_nat > $o ).

thf(func_def_132,type,
    member650892795e_form: produc791938916e_form > set_Pr31825690e_form > $o ).

thf(func_def_133,type,
    member493452075le_U_o: produc622718850le_U_o > set_Pr2099245410le_U_o > $o ).

thf(func_def_134,type,
    member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).

thf(func_def_135,type,
    member18158113e_form: produc1296622072e_form > set_Pr816919384e_form > $o ).

thf(func_def_136,type,
    member986698273rm_nat: produc117678584rm_nat > set_Pr957084504rm_nat > $o ).

thf(func_def_137,type,
    member189065477e_form: produc825256814e_form > set_Pr1189404964e_form > $o ).

thf(func_def_138,type,
    member1933006123le_U_o: produc227817602le_U_o > set_Pr1072215906le_U_o > $o ).

thf(func_def_139,type,
    member1793840734e_form: prover1687215943e_form > set_Pr554570749e_form > $o ).

thf(func_def_140,type,
    a: set_Pr619177522elle_U ).

thf(func_def_141,type,
    b: nat > list_P796095576elle_U > $o ).

thf(func_def_142,type,
    f: prover1687215943e_form ).

thf(func_def_143,type,
    s: list_P512754263e_form ).

thf(func_def_144,type,
    u: nat ).

thf(func_def_160,type,
    sK0: produc227817602le_U_o > nat > list_P796095576elle_U > $o ).

thf(func_def_161,type,
    sK1: produc227817602le_U_o > set_Pr619177522elle_U ).

thf(func_def_162,type,
    sK2: list_nat > ( nat > $o ) > nat ).

thf(func_def_163,type,
    sK3: list_nat > ( nat > $o ) > list_nat ).

thf(func_def_164,type,
    sK4: list_nat > ( nat > $o ) > list_nat ).

thf(func_def_165,type,
    sK5: ( ( prover1687215943e_form > prover1687215943e_form ) > list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_166,type,
    sK6: ( ( prover1687215943e_form > prover1687215943e_form ) > list_P512754263e_form > list_P512754263e_form > $o ) > prover1687215943e_form > prover1687215943e_form ).

thf(func_def_167,type,
    sK7: ( ( prover1687215943e_form > prover1687215943e_form ) > list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_168,type,
    sK8: ( ( prover1687215943e_form > prover1687215943e_form ) > list_P512754263e_form > list_P512754263e_form > $o ) > prover1687215943e_form > prover1687215943e_form ).

thf(func_def_169,type,
    sK9: ( ( prover1687215943e_form > prover1687215943e_form ) > list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_170,type,
    sK10: ( ( prover1687215943e_form > prover1687215943e_form ) > list_P512754263e_form > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_171,type,
    sK11: ( list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_172,type,
    sK12: ( list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_173,type,
    sK13: ( list_P512754263e_form > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_174,type,
    sK14: ( list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_175,type,
    sK15: list_nat > ( nat > $o ) > list_nat ).

thf(func_def_176,type,
    sK16: list_nat > ( nat > $o ) > nat ).

thf(func_def_177,type,
    sK17: list_nat > ( nat > $o ) > list_nat ).

thf(func_def_178,type,
    sK18: ( ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o ) > prover1687215943e_form > prover1687215943e_form > $o ).

thf(func_def_179,type,
    sK19: ( ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_180,type,
    sK20: ( ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_181,type,
    sK21: ( ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_182,type,
    sK22: ( ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_183,type,
    sK23: ( ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o ) > prover1687215943e_form > prover1687215943e_form > $o ).

thf(func_def_184,type,
    sK24: ( ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o ) > prover1687215943e_form > prover1687215943e_form > $o ).

thf(func_def_185,type,
    sK25: list_nat > ( nat > $o ) > list_nat ).

thf(func_def_186,type,
    sK26: list_nat > ( nat > $o ) > nat ).

thf(func_def_187,type,
    sK27: list_nat > ( nat > $o ) > list_nat ).

thf(func_def_188,type,
    sK28: ( ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_189,type,
    sK29: ( ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o ) > prover1687215943e_form > prover1687215943e_form > $o ).

thf(func_def_190,type,
    sK30: ( ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_191,type,
    sK31: ( ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o ) > prover1687215943e_form > prover1687215943e_form > $o ).

thf(func_def_192,type,
    sK32: ( produc227817602le_U_o > $o ) > nat > list_P796095576elle_U > $o ).

thf(func_def_193,type,
    sK33: ( produc227817602le_U_o > $o ) > set_Pr619177522elle_U ).

thf(func_def_194,type,
    sK34: nat > prover_Mirabelle_U ).

thf(func_def_195,type,
    sK35: ( ( prover1687215943e_form > nat ) > list_P512754263e_form > list_nat > $o ) > prover1687215943e_form > nat ).

thf(func_def_196,type,
    sK36: ( ( prover1687215943e_form > nat ) > list_P512754263e_form > list_nat > $o ) > list_nat ).

thf(func_def_197,type,
    sK37: ( ( prover1687215943e_form > nat ) > list_P512754263e_form > list_nat > $o ) > list_P512754263e_form ).

thf(func_def_198,type,
    sK38: ( ( prover1687215943e_form > nat ) > list_P512754263e_form > list_nat > $o ) > prover1687215943e_form > nat ).

thf(func_def_199,type,
    sK39: ( ( prover1687215943e_form > nat ) > list_P512754263e_form > list_nat > $o ) > prover1687215943e_form ).

thf(func_def_200,type,
    sK40: ( ( prover1687215943e_form > nat ) > list_P512754263e_form > list_nat > $o ) > list_nat ).

thf(func_def_201,type,
    sK41: list_P512754263e_form > list_P512754263e_form ).

thf(func_def_202,type,
    sK42: list_P512754263e_form > prover1687215943e_form ).

thf(func_def_203,type,
    sK43: list_nat > nat > list_nat ).

thf(func_def_204,type,
    sK44: list_nat > nat > list_nat ).

thf(func_def_205,type,
    sK45: ( list_nat > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_206,type,
    sK46: ( list_nat > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_207,type,
    sK47: ( list_nat > list_P512754263e_form > $o ) > list_nat ).

thf(func_def_208,type,
    sK48: ( list_nat > list_P512754263e_form > $o ) > nat ).

thf(func_def_209,type,
    sK49: ( list_nat > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_210,type,
    sK50: ( list_nat > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_211,type,
    sK51: ( list_nat > list_P512754263e_form > $o ) > nat ).

thf(func_def_212,type,
    sK52: ( list_nat > list_P512754263e_form > $o ) > list_nat ).

thf(func_def_213,type,
    sK53: set_Pr1072215906le_U_o > ( nat > list_P796095576elle_U > $o ) > list_s1200803384elle_U > list_n2139828004le_U_o > list_s1200803384elle_U ).

thf(func_def_214,type,
    sK54: set_Pr1072215906le_U_o > ( nat > list_P796095576elle_U > $o ) > list_s1200803384elle_U > list_n2139828004le_U_o > set_Pr619177522elle_U ).

thf(func_def_215,type,
    sK55: list_nat > nat > list_nat ).

thf(func_def_216,type,
    sK56: list_nat > nat > list_nat ).

thf(func_def_217,type,
    sK57: ( nat > prover_Mirabelle_U ) > list_P512754263e_form > ( nat > prover_Mirabelle_U ) > nat ).

thf(func_def_218,type,
    sK58: ( list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_219,type,
    sK59: ( list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_220,type,
    sK60: ( list_P512754263e_form > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_221,type,
    sK61: ( list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_222,type,
    sK62: ( list_P512754263e_form > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_223,type,
    sK63: ( list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_224,type,
    sK64: ( list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_225,type,
    sK65: ( list_P512754263e_form > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_226,type,
    sK66: ( list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_227,type,
    sK67: ( list_P512754263e_form > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_228,type,
    sK68: ( list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_229,type,
    sK69: ( list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_230,type,
    sK70: ( list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_231,type,
    sK71: set_Pr1072215906le_U_o > list_s1200803384elle_U > list_n2139828004le_U_o > list_s1200803384elle_U ).

thf(func_def_232,type,
    sK72: set_Pr1072215906le_U_o > list_s1200803384elle_U > list_n2139828004le_U_o > nat > list_P796095576elle_U > $o ).

thf(func_def_233,type,
    sK73: set_Pr1072215906le_U_o > list_s1200803384elle_U > list_n2139828004le_U_o > set_Pr619177522elle_U ).

thf(func_def_234,type,
    sK74: set_Pr1072215906le_U_o > list_s1200803384elle_U > list_n2139828004le_U_o > list_n2139828004le_U_o ).

thf(func_def_235,type,
    sK75: list_nat > ( nat > $o ) > list_nat ).

thf(func_def_236,type,
    sK76: list_nat > ( nat > $o ) > nat ).

thf(func_def_237,type,
    sK77: list_nat > ( nat > $o ) > list_nat ).

thf(func_def_238,type,
    sK78: ( list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_239,type,
    sK79: ( list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_240,type,
    sK80: ( list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_241,type,
    sK81: ( list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_242,type,
    sK82: ( list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_243,type,
    sK83: ( list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_244,type,
    sK84: ( list_P512754263e_form > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_245,type,
    sK85: ( list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_246,type,
    sK86: ( list_P512754263e_form > list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_247,type,
    sK87: ( list_P512754263e_form > list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_248,type,
    sK88: list_nat > ( nat > $o ) > list_nat ).

thf(func_def_249,type,
    sK89: list_nat > ( nat > $o ) > nat ).

thf(func_def_250,type,
    sK90: list_nat > ( nat > $o ) > list_nat ).

thf(func_def_251,type,
    sK91: list_P512754263e_form > prover1687215943e_form ).

thf(func_def_252,type,
    sK92: list_P512754263e_form > prover1687215943e_form ).

thf(func_def_253,type,
    sK93: list_P512754263e_form > list_P512754263e_form ).

thf(func_def_254,type,
    sK94: list_P512754263e_form > prover1687215943e_form ).

thf(func_def_255,type,
    sK95: nat > list_nat > list_nat ).

thf(func_def_256,type,
    sK96: nat > list_nat > list_nat ).

thf(func_def_257,type,
    sK97: ( nat > $o ) > list_nat > nat ).

thf(func_def_258,type,
    sK98: ( nat > $o ) > list_nat > list_nat ).

thf(func_def_259,type,
    sK99: ( nat > $o ) > list_nat > list_nat ).

thf(func_def_260,type,
    sK100: set_Pr1072215906le_U_o > ( list_s1200803384elle_U > list_n2139828004le_U_o > $o ) > list_s1200803384elle_U ).

thf(func_def_261,type,
    sK101: set_Pr1072215906le_U_o > ( list_s1200803384elle_U > list_n2139828004le_U_o > $o ) > set_Pr619177522elle_U ).

thf(func_def_262,type,
    sK102: set_Pr1072215906le_U_o > ( list_s1200803384elle_U > list_n2139828004le_U_o > $o ) > nat > list_P796095576elle_U > $o ).

thf(func_def_263,type,
    sK103: set_Pr1072215906le_U_o > ( list_s1200803384elle_U > list_n2139828004le_U_o > $o ) > list_n2139828004le_U_o ).

thf(func_def_264,type,
    sK104: produc227817602le_U_o > set_Pr619177522elle_U ).

thf(func_def_265,type,
    sK105: produc227817602le_U_o > nat > list_P796095576elle_U > $o ).

thf(func_def_266,type,
    sK106: ( produc227817602le_U_o > $o ) > nat > list_P796095576elle_U > $o ).

thf(func_def_267,type,
    sK107: ( produc227817602le_U_o > $o ) > set_Pr619177522elle_U ).

thf(func_def_268,type,
    sK108: ( list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_269,type,
    sK109: ( list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_270,type,
    sK110: list_n2139828004le_U_o > set_Pr1072215906le_U_o > set_Pr619177522elle_U > list_s1200803384elle_U > nat > list_P796095576elle_U > $o ).

thf(func_def_271,type,
    sK111: list_n2139828004le_U_o > set_Pr1072215906le_U_o > set_Pr619177522elle_U > list_s1200803384elle_U > list_n2139828004le_U_o ).

thf(func_def_272,type,
    sK112: list_P512754263e_form > list_P512754263e_form ).

thf(func_def_273,type,
    sK113: list_P512754263e_form > prover1687215943e_form ).

thf(func_def_274,type,
    sK114: ( list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_275,type,
    sK115: ( list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_276,type,
    sK116: ( list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_277,type,
    sK117: ( list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_278,type,
    sK118: ( list_P512754263e_form > $o ) > list_P512754263e_form ).

thf(func_def_279,type,
    sK119: ( list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_280,type,
    sK120: ( list_P512754263e_form > $o ) > prover1687215943e_form ).

thf(func_def_281,type,
    sK121: ( list_P512754263e_form > list_nat > $o ) > list_nat ).

thf(func_def_282,type,
    sK122: ( list_P512754263e_form > list_nat > $o ) > nat ).

thf(func_def_283,type,
    sK123: ( list_P512754263e_form > list_nat > $o ) > list_nat ).

thf(func_def_284,type,
    sK124: ( list_P512754263e_form > list_nat > $o ) > nat ).

thf(func_def_285,type,
    sK125: ( list_P512754263e_form > list_nat > $o ) > prover1687215943e_form ).

thf(func_def_286,type,
    sK126: ( list_P512754263e_form > list_nat > $o ) > list_P512754263e_form ).

thf(func_def_287,type,
    sK127: ( list_P512754263e_form > list_nat > $o ) > prover1687215943e_form ).

thf(func_def_288,type,
    sK128: ( list_P512754263e_form > list_nat > $o ) > list_P512754263e_form ).

thf(func_def_289,type,
    sK129: list_nat > nat > list_nat ).

thf(func_def_290,type,
    sK130: list_nat > nat > nat ).

thf(func_def_291,type,
    sK131: list_nat > nat > list_nat ).

thf(func_def_293,type,
    ph133: 
      !>[X0: $tType] : X0 ).

thf(func_def_295,type,
    sK134: nat > prover_Mirabelle_U ).

thf(func_def_296,type,
    sK135: produc227817602le_U_o ).

thf(f3302,plain,
    $false,
    inference(avatar_sat_refutation,[status(thm)],[f1765,f1770,f3070,f3301]) ).

thf(f3301,plain,
    ( ~ spl132_1
    | ~ spl132_3 ),
    inference(avatar_contradiction_clause,[status(thm)],[f3300]) ).

thf(f3300,plain,
    ( $false
    | ~ spl132_1
    | ~ spl132_3 ),
    inference(subsumption_resolution,[status(thm)],[f3284,f1769]) ).

thf(f1769,plain,
    ( ( ( prover1847600056is_env @ sK135 @ sK134 )
      = $true )
    | ~ spl132_3 ),
    inference(avatar_component_clause,[status(thm)],[f1767]) ).

thf(f1767,definition,
    ( spl132_3
  <=> ( ( prover1847600056is_env @ sK135 @ sK134 )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl132_3])],[avatar_definition]) ).

thf(f3284,plain,
    ( ( ( prover1847600056is_env @ sK135 @ sK134 )
     != $true )
    | ~ spl132_1 ),
    inference(trivial_inequality_removal,[status(thm)],[f3209]) ).

thf(f3209,plain,
    ( ( $false = $true )
    | ( ( prover1847600056is_env @ sK135 @ sK134 )
     != $true )
    | ~ spl132_1 ),
    inference(superposition,[status(thm)],[f2688,f1761]) ).

thf(f1761,plain,
    ( ( $false
      = ( prover1282070756_SEval @ sK135 @ sK134 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) )
    | ~ spl132_1 ),
    inference(avatar_component_clause,[status(thm)],[f1759]) ).

thf(f1759,definition,
    ( spl132_1
  <=> ( $false
      = ( prover1282070756_SEval @ sK135 @ sK134 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) ),
    introduced(definition,[new_symbols(naming,[spl132_1])],[avatar_definition]) ).

thf(f2688,plain,
    ! [X0: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
      ( ( ( prover1282070756_SEval @ X0 @ X1 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) )
        = $true )
      | ( ( prover1847600056is_env @ X0 @ X1 )
       != $true ) ),
    inference(superposition,[status(thm)],[f1148,f1153]) ).

thf(f1153,plain,
    ! [X0: produc227817602le_U_o] :
      ( ( produc1069574002le_U_o @ ( sK104 @ X0 ) @ ( sK105 @ X0 ) )
      = X0 ),
    inference(cnf_transformation,[status(thm)],[f1042]) ).

thf(f1042,plain,
    ! [X0: produc227817602le_U_o] :
      ( ( produc1069574002le_U_o @ ( sK104 @ X0 ) @ ( sK105 @ X0 ) )
      = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK104,sK105])],[f892,f1041]) ).

thf(f1041,plain,
    ! [X0: produc227817602le_U_o] :
      ( ? [X1: set_Pr619177522elle_U,X2: nat > list_P796095576elle_U > $o] :
          ( ( produc1069574002le_U_o @ X1 @ X2 )
          = X0 )
     => ( ( produc1069574002le_U_o @ ( sK104 @ X0 ) @ ( sK105 @ X0 ) )
        = X0 ) ),
    introduced(definition,[],[choice_axiom]) ).

thf(f892,plain,
    ! [X0: produc227817602le_U_o] :
    ? [X1: set_Pr619177522elle_U,X2: nat > list_P796095576elle_U > $o] :
      ( ( produc1069574002le_U_o @ X1 @ X2 )
      = X0 ),
    inference(ennf_transformation,[status(thm)],[f846]) ).

thf(f846,plain,
    ! [X0: produc227817602le_U_o] :
      ~ ! [X1: set_Pr619177522elle_U,X2: nat > list_P796095576elle_U > $o] :
          ( ( produc1069574002le_U_o @ X1 @ X2 )
         != X0 ),
    inference(rectify,[status(thm)],[f197]) ).

thf(f197,axiom,
    ! [X13: produc227817602le_U_o] :
      ~ ! [X37: set_Pr619177522elle_U,X70: nat > list_P796095576elle_U > $o] :
          ( ( produc1069574002le_U_o @ X37 @ X70 )
         != X13 ),
    file('/export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2THF_19870.p',fact_196_old_Oprod_Oexhaust) ).

thf(f1148,plain,
    ! [X2: nat > prover_Mirabelle_U,X0: nat > list_P796095576elle_U > $o,X1: set_Pr619177522elle_U] :
      ( ( ( prover1282070756_SEval @ ( produc1069574002le_U_o @ X1 @ X0 ) @ X2 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) )
        = $true )
      | ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ X1 @ X0 ) @ X2 )
       != $true ) ),
    inference(cnf_transformation,[status(thm)],[f910]) ).

thf(f910,plain,
    ! [X0: nat > list_P796095576elle_U > $o,X1: set_Pr619177522elle_U,X2: nat > prover_Mirabelle_U] :
      ( ( ( prover1282070756_SEval @ ( produc1069574002le_U_o @ X1 @ X0 ) @ X2 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) )
        = $true )
      | ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ X1 @ X0 ) @ X2 )
       != $true ) ),
    inference(ennf_transformation,[status(thm)],[f448]) ).

thf(f448,plain,
    ! [X0: nat > list_P796095576elle_U > $o,X1: set_Pr619177522elle_U,X2: nat > prover_Mirabelle_U] :
      ( ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ X1 @ X0 ) @ X2 )
        = $true )
     => ( ( prover1282070756_SEval @ ( produc1069574002le_U_o @ X1 @ X0 ) @ X2 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) )
        = $true ) ),
    inference(fool_elimination,[status(thm)],[f447]) ).

thf(f447,plain,
    ! [X0: nat > list_P796095576elle_U > $o,X1: set_Pr619177522elle_U,X2: nat > prover_Mirabelle_U] :
      ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ X1 @ X0 ) @ X2 )
     => ( prover1282070756_SEval @ ( produc1069574002le_U_o @ X1 @ X0 ) @ X2 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ),
    inference(rectify,[status(thm)],[f359]) ).

thf(f359,axiom,
    ! [X86: nat > list_P796095576elle_U > $o,X95: set_Pr619177522elle_U,X96: nat > prover_Mirabelle_U] :
      ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ X95 @ X86 ) @ X96 )
     => ( prover1282070756_SEval @ ( produc1069574002le_U_o @ X95 @ X86 ) @ X96 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2THF_19870.p',conj_1) ).

thf(f3070,plain,
    ~ spl132_2,
    inference(avatar_contradiction_clause,[status(thm)],[f3069]) ).

thf(f3069,plain,
    ( $false
    | ~ spl132_2 ),
    inference(trivial_inequality_removal,[status(thm)],[f3005]) ).

thf(f3005,plain,
    ( ( $false = $true )
    | ~ spl132_2 ),
    inference(superposition,[status(thm)],[f2633,f1096]) ).

thf(f1096,plain,
    ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ sK34 )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f981]) ).

thf(f981,plain,
    ( ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ sK34 )
      = $true )
    & ( ( prover1282070756_SEval @ ( produc1069574002le_U_o @ a @ b ) @ sK34 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) )
     != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f933,f980]) ).

thf(f980,plain,
    ( ? [X0: nat > prover_Mirabelle_U] :
        ( ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ X0 )
          = $true )
        & ( ( prover1282070756_SEval @ ( produc1069574002le_U_o @ a @ b ) @ X0 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) )
         != $true ) )
   => ( ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ sK34 )
        = $true )
      & ( ( prover1282070756_SEval @ ( produc1069574002le_U_o @ a @ b ) @ sK34 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) )
       != $true ) ) ),
    introduced(definition,[],[choice_axiom]) ).

thf(f933,plain,
    ? [X0: nat > prover_Mirabelle_U] :
      ( ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ X0 )
        = $true )
      & ( ( prover1282070756_SEval @ ( produc1069574002le_U_o @ a @ b ) @ X0 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) )
       != $true ) ),
    inference(ennf_transformation,[status(thm)],[f841]) ).

thf(f841,plain,
    ~ ! [X0: nat > prover_Mirabelle_U] :
        ( ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ X0 )
         != $true )
        | ( ( prover1282070756_SEval @ ( produc1069574002le_U_o @ a @ b ) @ X0 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) )
          = $true ) ),
    inference(flattening,[status(thm)],[f827]) ).

thf(f827,plain,
    ~ ! [X0: nat > prover_Mirabelle_U] :
        ( ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ X0 )
         != $true )
        | ( ( prover1282070756_SEval @ ( produc1069574002le_U_o @ a @ b ) @ X0 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) )
          = $true ) ),
    inference(fool_elimination,[status(thm)],[f826]) ).

thf(f826,plain,
    ~ ! [X0: nat > prover_Mirabelle_U] :
        ( ~ ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ X0 )
        | ( prover1282070756_SEval @ ( produc1069574002le_U_o @ a @ b ) @ X0 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ),
    inference(rectify,[status(thm)],[f361]) ).

thf(f361,negated_conjecture,
    ~ ! [X97: nat > prover_Mirabelle_U] :
        ( ~ ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ X97 )
        | ( prover1282070756_SEval @ ( produc1069574002le_U_o @ a @ b ) @ X97 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ),
    inference(negated_conjecture,[status(cth)],[f360]) ).

thf(f360,conjecture,
    ! [X97: nat > prover_Mirabelle_U] :
      ( ~ ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ X97 )
      | ( prover1282070756_SEval @ ( produc1069574002le_U_o @ a @ b ) @ X97 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2THF_19870.p',conj_2) ).

thf(f2633,plain,
    ( ( $false
      = ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ sK34 ) )
    | ~ spl132_2 ),
    inference(trivial_inequality_removal,[status(thm)],[f2374]) ).

thf(f2374,plain,
    ( ( $true != $true )
    | ( $false
      = ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ sK34 ) )
    | ~ spl132_2 ),
    inference(superposition,[status(thm)],[f1095,f1764]) ).

thf(f1764,plain,
    ( ! [X2: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
        ( ( ( prover1282070756_SEval @ X2 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) )
          = $true )
        | ( $false
          = ( prover1847600056is_env @ X2 @ X1 ) ) )
    | ~ spl132_2 ),
    inference(avatar_component_clause,[status(thm)],[f1763]) ).

thf(f1763,definition,
    ( spl132_2
  <=> ! [X2: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
        ( ( $false
          = ( prover1847600056is_env @ X2 @ X1 ) )
        | ( ( prover1282070756_SEval @ X2 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) )
          = $true ) ) ),
    introduced(definition,[new_symbols(naming,[spl132_2])],[avatar_definition]) ).

thf(f1095,plain,
    ( ( prover1282070756_SEval @ ( produc1069574002le_U_o @ a @ b ) @ sK34 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) )
   != $true ),
    inference(cnf_transformation,[status(thm)],[f981]) ).

thf(f1770,plain,
    ( spl132_2
    | spl132_3 ),
    inference(avatar_split_clause,[status(thm)],[f1683,f1767,f1763]) ).

thf(f1683,plain,
    ! [X2: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
      ( ( ( prover1847600056is_env @ sK135 @ sK134 )
        = $true )
      | ( ( prover1282070756_SEval @ X2 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) )
        = $true )
      | ( $false
        = ( prover1847600056is_env @ X2 @ X1 ) ) ),
    inference(binary_proxy_clausification,[status(thm)],[f1682]) ).

thf(f1682,plain,
    ! [X2: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
      ( ( ( prover1847600056is_env @ sK135 @ sK134 )
        = $true )
      | ( ( ( prover1847600056is_env @ X2 @ X1 )
         => ( prover1282070756_SEval @ X2 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) )
        = $true ) ),
    inference(binary_proxy_clausification,[status(thm)],[f1680]) ).

thf(f1680,plain,
    ! [X2: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
      ( ( $false
        = ( ( prover1847600056is_env @ sK135 @ sK134 )
         => ( prover1282070756_SEval @ sK135 @ sK134 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) )
      | ( ( ( prover1847600056is_env @ X2 @ X1 )
         => ( prover1282070756_SEval @ X2 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[status(thm)],[f1679]) ).

thf(f1679,plain,
    ! [X2: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
      ( ( $false
        = ( ^ [Y0: produc227817602le_U_o] :
              ( ( prover1847600056is_env @ Y0 @ sK134 )
             => ( prover1282070756_SEval @ Y0 @ sK134 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) )
          @ sK135 ) )
      | ( ( ( prover1847600056is_env @ X2 @ X1 )
         => ( prover1282070756_SEval @ X2 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) )
        = $true ) ),
    inference(sigma_clausification,[status(thm)],[f1678]) ).

thf(f1678,plain,
    ! [X2: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
      ( ( $false
        = ( !! @ produc227817602le_U_o
          @ ^ [Y0: produc227817602le_U_o] :
              ( ( prover1847600056is_env @ Y0 @ sK134 )
             => ( prover1282070756_SEval @ Y0 @ sK134 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) ) )
      | ( ( ( prover1847600056is_env @ X2 @ X1 )
         => ( prover1282070756_SEval @ X2 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[status(thm)],[f1677]) ).

thf(f1677,plain,
    ! [X2: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
      ( ( ( ( prover1847600056is_env @ X2 @ X1 )
         => ( prover1282070756_SEval @ X2 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) )
        = $true )
      | ( $false
        = ( ^ [Y0: nat > prover_Mirabelle_U] :
              ( !! @ produc227817602le_U_o
              @ ^ [Y1: produc227817602le_U_o] :
                  ( ( prover1847600056is_env @ Y1 @ Y0 )
                 => ( prover1282070756_SEval @ Y1 @ Y0 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) )
          @ sK134 ) ) ),
    inference(sigma_clausification,[status(thm)],[f1676]) ).

thf(f1676,plain,
    ! [X2: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
      ( ( ( !! @ ( nat > prover_Mirabelle_U )
          @ ^ [Y0: nat > prover_Mirabelle_U] :
              ( !! @ produc227817602le_U_o
              @ ^ [Y1: produc227817602le_U_o] :
                  ( ( prover1847600056is_env @ Y1 @ Y0 )
                 => ( prover1282070756_SEval @ Y1 @ Y0 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) ) )
       != $true )
      | ( ( ( prover1847600056is_env @ X2 @ X1 )
         => ( prover1282070756_SEval @ X2 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[status(thm)],[f1675]) ).

thf(f1675,plain,
    ! [X2: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
      ( ( ( !! @ ( nat > prover_Mirabelle_U )
          @ ^ [Y0: nat > prover_Mirabelle_U] :
              ( !! @ produc227817602le_U_o
              @ ^ [Y1: produc227817602le_U_o] :
                  ( ( prover1847600056is_env @ Y1 @ Y0 )
                 => ( prover1282070756_SEval @ Y1 @ Y0 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) ) )
       != $true )
      | ( ( ^ [Y0: produc227817602le_U_o] :
              ( ( prover1847600056is_env @ Y0 @ X1 )
             => ( prover1282070756_SEval @ Y0 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) )
          @ X2 )
        = $true ) ),
    inference(pi_clausification,[status(thm)],[f1674]) ).

thf(f1674,plain,
    ! [X1: nat > prover_Mirabelle_U] :
      ( ( $true
        = ( !! @ produc227817602le_U_o
          @ ^ [Y0: produc227817602le_U_o] :
              ( ( prover1847600056is_env @ Y0 @ X1 )
             => ( prover1282070756_SEval @ Y0 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) ) )
      | ( ( !! @ ( nat > prover_Mirabelle_U )
          @ ^ [Y0: nat > prover_Mirabelle_U] :
              ( !! @ produc227817602le_U_o
              @ ^ [Y1: produc227817602le_U_o] :
                  ( ( prover1847600056is_env @ Y1 @ Y0 )
                 => ( prover1282070756_SEval @ Y1 @ Y0 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) ) )
       != $true ) ),
    inference(beta_eta_normalization,[status(thm)],[f1673]) ).

thf(f1673,plain,
    ! [X1: nat > prover_Mirabelle_U] :
      ( ( ( !! @ ( nat > prover_Mirabelle_U )
          @ ^ [Y0: nat > prover_Mirabelle_U] :
              ( !! @ produc227817602le_U_o
              @ ^ [Y1: produc227817602le_U_o] :
                  ( ( prover1847600056is_env @ Y1 @ Y0 )
                 => ( prover1282070756_SEval @ Y1 @ Y0 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) ) )
       != $true )
      | ( ( ^ [Y0: nat > prover_Mirabelle_U] :
              ( !! @ produc227817602le_U_o
              @ ^ [Y1: produc227817602le_U_o] :
                  ( ( prover1847600056is_env @ Y1 @ Y0 )
                 => ( prover1282070756_SEval @ Y1 @ Y0 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) )
          @ X1 )
        = $true ) ),
    inference(pi_clausification,[status(thm)],[f1672]) ).

thf(f1672,plain,
    ( ( ( !! @ ( nat > prover_Mirabelle_U )
        @ ^ [Y0: nat > prover_Mirabelle_U] :
            ( !! @ produc227817602le_U_o
            @ ^ [Y1: produc227817602le_U_o] :
                ( ( prover1847600056is_env @ Y1 @ Y0 )
               => ( prover1282070756_SEval @ Y1 @ Y0 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) ) )
      = $true )
    | ( ( !! @ ( nat > prover_Mirabelle_U )
        @ ^ [Y0: nat > prover_Mirabelle_U] :
            ( !! @ produc227817602le_U_o
            @ ^ [Y1: produc227817602le_U_o] :
                ( ( prover1847600056is_env @ Y1 @ Y0 )
               => ( prover1282070756_SEval @ Y1 @ Y0 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) ) )
     != $true ) ),
    inference(trivial_inequality_removal,[status(thm)],[f1500]) ).

thf(f1500,plain,
    ( ( ( !! @ ( nat > prover_Mirabelle_U )
        @ ^ [Y0: nat > prover_Mirabelle_U] :
            ( !! @ produc227817602le_U_o
            @ ^ [Y1: produc227817602le_U_o] :
                ( ( prover1847600056is_env @ Y1 @ Y0 )
               => ( prover1282070756_SEval @ Y1 @ Y0 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) ) )
     != $true )
    | ( ( !! @ ( nat > prover_Mirabelle_U )
        @ ^ [Y0: nat > prover_Mirabelle_U] :
            ( !! @ produc227817602le_U_o
            @ ^ [Y1: produc227817602le_U_o] :
                ( ( prover1847600056is_env @ Y1 @ Y0 )
               => ( prover1282070756_SEval @ Y1 @ Y0 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) ) )
      = $true )
    | ( $true != $true ) ),
    inference(superposition,[status(thm)],[f1164,f1199]) ).

thf(f1199,plain,
    ! [X2: list_P512754263e_form,X0: prover1687215943e_form,X1: nat] :
      ( ( ( member_nat @ X1 @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) ) ) )
        = $true )
      | ( $true
       != ( !! @ ( nat > prover_Mirabelle_U )
          @ ^ [Y0: nat > prover_Mirabelle_U] :
              ( !! @ produc227817602le_U_o
              @ ^ [Y1: produc227817602le_U_o] :
                  ( ( prover1847600056is_env @ Y1 @ Y0 )
                 => ( prover1282070756_SEval @ Y1 @ Y0 @ ( append1038020460e_form @ X2 @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ X0 @ X1 ) @ nil_Pr1384483009e_form ) ) ) ) ) ) )
      | ( ( !! @ ( nat > prover_Mirabelle_U )
          @ ^ [Y0: nat > prover_Mirabelle_U] :
              ( !! @ produc227817602le_U_o
              @ ^ [Y1: produc227817602le_U_o] :
                  ( ( prover1847600056is_env @ Y1 @ Y0 )
                 => ( prover1282070756_SEval @ Y1 @ Y0 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) ) ) ) )
        = $true ) ),
    inference(beta_eta_normalization,[status(thm)],[f1190]) ).

thf(f1190,plain,
    ! [X2: list_P512754263e_form,X0: prover1687215943e_form,X1: nat] :
      ( ( ( member_nat @ X1 @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) ) ) )
        = $true )
      | ( ( ^ [Y0: list_P512754263e_form] :
              ( !! @ ( nat > prover_Mirabelle_U )
              @ ^ [Y1: nat > prover_Mirabelle_U] :
                  ( !! @ produc227817602le_U_o
                  @ ^ [Y2: produc227817602le_U_o] :
                      ( ( prover1847600056is_env @ Y2 @ Y1 )
                     => ( prover1282070756_SEval @ Y2 @ Y1 @ Y0 ) ) ) )
          @ ( append1038020460e_form @ X2 @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ X0 @ X1 ) @ nil_Pr1384483009e_form ) ) )
       != $true )
      | ( ( ^ [Y0: list_P512754263e_form] :
              ( !! @ ( nat > prover_Mirabelle_U )
              @ ^ [Y1: nat > prover_Mirabelle_U] :
                  ( !! @ produc227817602le_U_o
                  @ ^ [Y2: produc227817602le_U_o] :
                      ( ( prover1847600056is_env @ Y2 @ Y1 )
                     => ( prover1282070756_SEval @ Y2 @ Y1 @ Y0 ) ) ) )
          @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) )
        = $true ) ),
    inference(definition_unfolding,[status(thm)],[f1159,f1069,f1069]) ).

thf(f1069,plain,
    ( prover1539709396Svalid
    = ( ^ [Y0: list_P512754263e_form] :
          ( !! @ ( nat > prover_Mirabelle_U )
          @ ^ [Y1: nat > prover_Mirabelle_U] :
              ( !! @ produc227817602le_U_o
              @ ^ [Y2: produc227817602le_U_o] :
                  ( ( prover1847600056is_env @ Y2 @ Y1 )
                 => ( prover1282070756_SEval @ Y2 @ Y1 @ Y0 ) ) ) ) ) ),
    inference(cnf_transformation,[status(thm)],[f711]) ).

thf(f711,plain,
    ( prover1539709396Svalid
    = ( ^ [Y0: list_P512754263e_form] :
          ( !! @ ( nat > prover_Mirabelle_U )
          @ ^ [Y1: nat > prover_Mirabelle_U] :
              ( !! @ produc227817602le_U_o
              @ ^ [Y2: produc227817602le_U_o] :
                  ( ( prover1847600056is_env @ Y2 @ Y1 )
                 => ( prover1282070756_SEval @ Y2 @ Y1 @ Y0 ) ) ) ) ) ),
    inference(fool_elimination,[status(thm)],[f710]) ).

thf(f710,plain,
    ( ( ^ [X0: list_P512754263e_form] :
        ! [X1: produc227817602le_U_o,X2: nat > prover_Mirabelle_U] :
          ( ( prover1847600056is_env @ X1 @ X2 )
         => ( prover1282070756_SEval @ X1 @ X2 @ X0 ) ) )
    = prover1539709396Svalid ),
    inference(rectify,[status(thm)],[f24]) ).

thf(f24,axiom,
    ( ( ^ [X15: list_P512754263e_form] :
        ! [X16: produc227817602le_U_o,X17: nat > prover_Mirabelle_U] :
          ( ( prover1847600056is_env @ X16 @ X17 )
         => ( prover1282070756_SEval @ X16 @ X17 @ X15 ) ) )
    = prover1539709396Svalid ),
    file('/export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2THF_19870.p',fact_23_Svalid__def) ).

thf(f1159,plain,
    ! [X2: list_P512754263e_form,X0: prover1687215943e_form,X1: nat] :
      ( ( ( prover1539709396Svalid @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) )
        = $true )
      | ( ( member_nat @ X1 @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) ) ) )
        = $true )
      | ( ( prover1539709396Svalid @ ( append1038020460e_form @ X2 @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ X0 @ X1 ) @ nil_Pr1384483009e_form ) ) )
       != $true ) ),
    inference(cnf_transformation,[status(thm)],[f880]) ).

thf(f880,plain,
    ! [X0: prover1687215943e_form,X1: nat,X2: list_P512754263e_form] :
      ( ( ( prover1539709396Svalid @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) )
        = $true )
      | ( ( member_nat @ X1 @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) ) ) )
        = $true )
      | ( ( prover1539709396Svalid @ ( append1038020460e_form @ X2 @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ X0 @ X1 ) @ nil_Pr1384483009e_form ) ) )
       != $true ) ),
    inference(flattening,[status(thm)],[f879]) ).

thf(f879,plain,
    ! [X0: prover1687215943e_form,X1: nat,X2: list_P512754263e_form] :
      ( ( ( prover1539709396Svalid @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) )
        = $true )
      | ( ( prover1539709396Svalid @ ( append1038020460e_form @ X2 @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ X0 @ X1 ) @ nil_Pr1384483009e_form ) ) )
       != $true )
      | ( ( member_nat @ X1 @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) ) ) )
        = $true ) ),
    inference(ennf_transformation,[status(thm)],[f865]) ).

thf(f865,plain,
    ! [X0: prover1687215943e_form,X1: nat,X2: list_P512754263e_form] :
      ( ( ( member_nat @ X1 @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) ) ) )
       != $true )
     => ( ( ( prover1539709396Svalid @ ( append1038020460e_form @ X2 @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ X0 @ X1 ) @ nil_Pr1384483009e_form ) ) )
          = $true )
       => ( ( prover1539709396Svalid @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) )
          = $true ) ) ),
    inference(flattening,[status(thm)],[f761]) ).

thf(f761,plain,
    ! [X0: prover1687215943e_form,X1: nat,X2: list_P512754263e_form] :
      ( ( ( member_nat @ X1 @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) ) ) )
       != $true )
     => ( ( ( prover1539709396Svalid @ ( append1038020460e_form @ X2 @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ X0 @ X1 ) @ nil_Pr1384483009e_form ) ) )
          = $true )
       => ( ( prover1539709396Svalid @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) )
          = $true ) ) ),
    inference(fool_elimination,[status(thm)],[f760]) ).

thf(f760,plain,
    ! [X0: prover1687215943e_form,X1: nat,X2: list_P512754263e_form] :
      ( ~ ( member_nat @ X1 @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) ) ) )
     => ( ( prover1539709396Svalid @ ( append1038020460e_form @ X2 @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ X0 @ X1 ) @ nil_Pr1384483009e_form ) ) )
       => ( prover1539709396Svalid @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X0 ) @ X2 ) ) ) ),
    inference(rectify,[status(thm)],[f5]) ).

thf(f5,axiom,
    ! [X11: prover1687215943e_form,X10: nat,X4: list_P512754263e_form] :
      ( ~ ( member_nat @ X10 @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X11 ) @ X4 ) ) ) )
     => ( ( prover1539709396Svalid @ ( append1038020460e_form @ X4 @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ X11 @ X10 ) @ nil_Pr1384483009e_form ) ) )
       => ( prover1539709396Svalid @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ X11 ) @ X4 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2THF_19870.p',fact_4_sound__FAll) ).

thf(f1164,plain,
    ( ( member_nat @ u @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) )
   != $true ),
    inference(cnf_transformation,[status(thm)],[f840]) ).

thf(f840,plain,
    ( ( member_nat @ u @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) )
   != $true ),
    inference(flattening,[status(thm)],[f492]) ).

thf(f492,plain,
    ( ( member_nat @ u @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) )
   != $true ),
    inference(fool_elimination,[status(thm)],[f491]) ).

thf(f491,plain,
    ~ ( member_nat @ u @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) ),
    inference(rectify,[status(thm)],[f358]) ).

thf(f358,axiom,
    ~ ( member_nat @ u @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2THF_19870.p',conj_0) ).

thf(f1765,plain,
    ( spl132_1
    | spl132_2 ),
    inference(avatar_split_clause,[status(thm)],[f1684,f1763,f1759]) ).

thf(f1684,plain,
    ! [X2: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
      ( ( $false
        = ( prover1847600056is_env @ X2 @ X1 ) )
      | ( $false
        = ( prover1282070756_SEval @ sK135 @ sK134 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) )
      | ( ( prover1282070756_SEval @ X2 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) )
        = $true ) ),
    inference(binary_proxy_clausification,[status(thm)],[f1681]) ).

thf(f1681,plain,
    ! [X2: produc227817602le_U_o,X1: nat > prover_Mirabelle_U] :
      ( ( ( ( prover1847600056is_env @ X2 @ X1 )
         => ( prover1282070756_SEval @ X2 @ X1 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) )
        = $true )
      | ( $false
        = ( prover1282070756_SEval @ sK135 @ sK134 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) ),
    inference(binary_proxy_clausification,[status(thm)],[f1680]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : ITP158^1 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12  % Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32  % Computer : n013.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Tue Feb 24 08:27:53 EST 2026
% 0.12/0.32  % CPUTime  : 
% 0.12/0.32  Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.42  ---- Original DTF file ---
% 0.16/0.42  thf(spec,logic,$$dhol).
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  % File     : ITP158^1 : TPTP v9.2.1. Released v7.5.0.
% 0.16/0.42  % Domain   : Interactive Theorem Proving
% 0.16/0.42  % Problem  : Sledgehammer Prover problem prob_480__3258466_1
% 0.16/0.42  % Version  : Especial.
% 0.16/0.42  % English  :
% 0.16/0.42  
% 0.16/0.42  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.16/0.42  %          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.16/0.42  % Source   : [Des21]
% 0.16/0.42  % Names    : Prover/prob_480__3258466_1 [Des21]
% 0.16/0.42  
% 0.16/0.42  % Status   : Theorem
% 0.16/0.42  % Rating   : 0.78 v9.1.0, 0.75 v9.0.0, 0.70 v8.2.0, 0.62 v8.1.0, 0.73 v7.5.0
% 0.16/0.42  % Syntax   : Number of formulae    :  505 ( 173 unt; 145 typ;   0 def)
% 0.16/0.42  %            Number of atoms       :  933 ( 580 equ;   0 cnn)
% 0.16/0.42  %            Maximal formula atoms :    7 (   2 avg)
% 0.16/0.42  %            Number of connectives : 4078 ( 227   ~;  32   |; 133   &;3240   @)
% 0.16/0.42  %                                         (   0 <=>; 446  =>;   0  <=;   0 <~>)
% 0.16/0.42  %            Maximal formula depth :   19 (   8 avg)
% 0.16/0.42  %            Number of types       :   38 (  37 usr)
% 0.16/0.42  %            Number of type conns  :  389 ( 389   >;   0   *;   0   +;   0  <<)
% 0.16/0.42  %            Number of symbols     :  111 ( 108 usr;  13 con; 0-3 aty)
% 0.16/0.42  %            Number of variables   : 1360 (   8   ^;1213   !; 139   ?;1360   :)
% 0.16/0.42  % SPC      : TH0_THM_EQU_NAR
% 0.16/0.42  
% 0.16/0.42  % Comments : This file was generated by Sledgehammer 2021-02-23 15:35:33.970
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  % Could-be-implicit typings (37)
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_J_Mt__List__Olist_I_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J_J_J,type,
% 0.16/0.42      set_Pr2099245410le_U_o: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_J_Mt__List__Olist_I_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J_J,type,
% 0.16/0.42      produc622718850le_U_o: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_I_062_It__Prover____Mirabelle____icshcajtjh__Oform_M_062_It__Prover____Mirabelle____icshcajtjh__Oform_M_Eo_J_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.16/0.42      produc957084248e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_M_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J_J,type,
% 0.16/0.42      set_Pr1072215906le_U_o: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_M_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J,type,
% 0.16/0.42      produc227817602le_U_o: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J_J,type,
% 0.16/0.42      set_Pr31825690e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.16/0.42      produc791938916e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
% 0.16/0.42      set_Pr1057005944st_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J_J,type,
% 0.16/0.42      set_Pr1174364408e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Prover____Mirabelle____icshcajtjh__Oform_Mt__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.16/0.42      set_Pr1189404964e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 0.16/0.42      produc1473535256st_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.16/0.42      produc1494932632e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Prover____Mirabelle____icshcajtjh__Oform_Mt__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      produc825256814e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__List__Olist_I_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J,type,
% 0.16/0.42      list_n2139828004le_U_o: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 0.16/0.42      produc890077173st_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
% 0.16/0.42      set_Pr1560408065st_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Prover____Mirabelle____icshcajtjh__Oform_Mt__Nat__Onat_J_J,type,
% 0.16/0.42      set_Pr957084504rm_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.16/0.42      set_Pr816919384e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 0.16/0.42      produc1699244961st_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Prover____Mirabelle____icshcajtjh__Oform_Mt__Nat__Onat_J,type,
% 0.16/0.42      produc117678584rm_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      produc1296622072e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__List__Olist_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.16/0.42      list_l461858535e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.16/0.42      set_li5074317e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__List__Olist_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_J,type,
% 0.16/0.42      list_s1200803384elle_U: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.16/0.42      set_Pr1986765409at_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      list_P512754263e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      set_Pr554570749e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J,type,
% 0.16/0.42      list_P796095576elle_U: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J,type,
% 0.16/0.42      set_Pr619177522elle_U: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      product_prod_nat_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.16/0.42      list_list_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.16/0.42      set_list_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      prover1687215943e_form: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Prover____Mirabelle____icshcajtjh__OU,type,
% 0.16/0.42      prover_Mirabelle_U: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.16/0.42      list_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.16/0.42      set_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Nat__Onat,type,
% 0.16/0.42      nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  % Explicit typings (108)
% 0.16/0.42  thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.16/0.42      zero_zero_nat: nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_If_001t__List__Olist_It__Nat__Onat_J,type,
% 0.16/0.42      if_list_nat: $o > list_nat > list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_If_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      if_lis1812881937e_form: $o > list_P512754263e_form > list_P512754263e_form > list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oappend_001t__List__Olist_It__Nat__Onat_J,type,
% 0.16/0.42      append_list_nat: list_list_nat > list_list_nat > list_list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oappend_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      append1797078012e_form: list_l461858535e_form > list_l461858535e_form > list_l461858535e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 0.16/0.42      append_nat: list_nat > list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oappend_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      append1038020460e_form: list_P512754263e_form > list_P512754263e_form > list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Obind_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      bind_nat_nat: list_nat > ( nat > list_nat ) > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Obind_001t__Nat__Onat_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      bind_n1193922848e_form: list_nat > ( nat > list_P512754263e_form ) > list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Obind_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Nat__Onat,type,
% 0.16/0.42      bind_P1359331232rm_nat: list_P512754263e_form > ( prover1687215943e_form > list_nat ) > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Obind_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      bind_P1054726576e_form: list_P512754263e_form > ( prover1687215943e_form > list_P512754263e_form ) > list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
% 0.16/0.42      butlast_nat: list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Obutlast_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      butlas664258165e_form: list_P512754263e_form > list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Ocan__select_001t__Nat__Onat,type,
% 0.16/0.42      can_select_nat: ( nat > $o ) > set_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oconcat_001t__Nat__Onat,type,
% 0.16/0.42      concat_nat: list_list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oconcat_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      concat1664984646e_form: list_l461858535e_form > list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oinsert_001t__Nat__Onat,type,
% 0.16/0.42      insert_nat: nat > list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oinsert_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      insert697320747e_form: prover1687215943e_form > list_P512754263e_form > list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 0.16/0.42      last_nat: list_nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olast_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      last_P1811260776e_form: list_P512754263e_form > prover1687215943e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olenlex_001t__Nat__Onat,type,
% 0.16/0.42      lenlex_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olenlex_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      lenlex1927129340e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olex_001t__Nat__Onat,type,
% 0.16/0.42      lex_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olex_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      lex_Pr233218909e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olexord_001t__Nat__Onat,type,
% 0.16/0.42      lexord_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olexord_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      lexord1848469012e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_OCons_001_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J,type,
% 0.16/0.42      cons_n50929118le_U_o: ( nat > list_P796095576elle_U > $o ) > list_n2139828004le_U_o > list_n2139828004le_U_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Nat__Onat_J,type,
% 0.16/0.42      cons_list_nat: list_nat > list_list_nat > list_list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      cons_l1379921697e_form: list_P512754263e_form > list_l461858535e_form > list_l461858535e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.16/0.42      cons_nat: nat > list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_OCons_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      cons_P1475164433e_form: prover1687215943e_form > list_P512754263e_form > list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J,type,
% 0.16/0.42      cons_s32021736elle_U: set_Pr619177522elle_U > list_s1200803384elle_U > list_s1200803384elle_U ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_ONil_001_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J,type,
% 0.16/0.42      nil_na1584420238le_U_o: list_n2139828004le_U_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Nat__Onat_J,type,
% 0.16/0.42      nil_list_nat: list_list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      nil_li1393862353e_form: list_l461858535e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 0.16/0.42      nil_nat: list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_ONil_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      nil_Pr1384483009e_form: list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_ONil_001t__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J,type,
% 0.16/0.42      nil_se944326968elle_U: list_s1200803384elle_U ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 0.16/0.42      set_list_nat2: list_list_nat > set_list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      set_li1219651714e_form: list_l461858535e_form > set_li5074317e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 0.16/0.42      set_nat2: list_nat > set_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist_Oset_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      set_Pr1105237746e_form: list_P512754263e_form > set_Pr554570749e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist__ex1_001t__Nat__Onat,type,
% 0.16/0.42      list_ex1_nat: ( nat > $o ) > list_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olist__ex1_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      list_e2123636798e_form: ( prover1687215943e_form > $o ) > list_P512754263e_form > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olistrel1_001t__Nat__Onat,type,
% 0.16/0.42      listrel1_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olistrel1_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      listre502458152e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olistrel_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      listrel_nat_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olistrel_001t__Nat__Onat_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      listre318297994e_form: set_Pr816919384e_form > set_Pr1174364408e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olistrel_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Nat__Onat,type,
% 0.16/0.42      listre483706378rm_nat: set_Pr957084504rm_nat > set_Pr1057005944st_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olistrel_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      listre1908795590e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Olistrel_001t__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_001_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J,type,
% 0.16/0.42      listre290852044le_U_o: set_Pr1072215906le_U_o > set_Pr2099245410le_U_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Omaps_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      maps_nat_nat: ( nat > list_nat ) > list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Omaps_001t__Nat__Onat_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      maps_n1383976154e_form: ( nat > list_P512754263e_form ) > list_nat > list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Omaps_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Nat__Onat,type,
% 0.16/0.42      maps_P1549384538rm_nat: ( prover1687215943e_form > list_nat ) > list_P512754263e_form > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Omaps_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      maps_P2058952566e_form: ( prover1687215943e_form > list_P512754263e_form ) > list_P512754263e_form > list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct__lists_001t__Nat__Onat,type,
% 0.16/0.42      product_lists_nat: list_list_nat > list_list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Oproduct__lists_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      produc168439576e_form: list_l461858535e_form > list_l461858535e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 0.16/0.42      rotate1_nat: list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Orotate1_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      rotate650061876e_form: list_P512754263e_form > list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Osubseqs_001t__Nat__Onat,type,
% 0.16/0.42      subseqs_nat: list_nat > list_list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_List_Osubseqs_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      subseq1471997234e_form: list_P512754263e_form > list_l461858535e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001t__List__Olist_It__Nat__Onat_J,type,
% 0.16/0.42      produc939441135st_nat: ( nat > nat > $o ) > list_nat > produc890077173st_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001_062_It__Prover____Mirabelle____icshcajtjh__Oform_M_062_It__Prover____Mirabelle____icshcajtjh__Oform_M_Eo_J_J_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      produc54611594e_form: ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > produc957084248e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
% 0.16/0.42      produc1625736153st_nat: list_nat > list_nat > produc1699244961st_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      produc1617574096e_form: list_nat > list_P512754263e_form > produc1494932632e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_001t__List__Olist_It__Nat__Onat_J,type,
% 0.16/0.42      produc1897654224st_nat: list_P512754263e_form > list_nat > produc1473535256st_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      produc891809686e_form: list_P512754263e_form > list_P512754263e_form > produc791938916e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_J_001t__List__Olist_I_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J,type,
% 0.16/0.42      produc1377086578le_U_o: list_s1200803384elle_U > list_n2139828004le_U_o > produc622718850le_U_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      produc876465968e_form: nat > prover1687215943e_form > produc1296622072e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Nat__Onat,type,
% 0.16/0.42      produc1041874352rm_nat: prover1687215943e_form > nat > produc117678584rm_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      produc1018812320e_form: prover1687215943e_form > prover1687215943e_form > produc825256814e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_001_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J,type,
% 0.16/0.42      produc1069574002le_U_o: set_Pr619177522elle_U > ( nat > list_P796095576elle_U > $o ) > produc227817602le_U_o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Prover__Mirabelle__icshcajtjh_OSEval,type,
% 0.16/0.42      prover1282070756_SEval: produc227817602le_U_o > ( nat > prover_Mirabelle_U ) > list_P512754263e_form > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Prover__Mirabelle__icshcajtjh_OSvalid,type,
% 0.16/0.42      prover1539709396Svalid: list_P512754263e_form > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Prover__Mirabelle__icshcajtjh_Ofinst,type,
% 0.16/0.42      prover1577896257_finst: prover1687215943e_form > nat > prover1687215943e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Prover__Mirabelle__icshcajtjh_Oflatten_001t__Nat__Onat,type,
% 0.16/0.42      prover886976490en_nat: list_list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Prover__Mirabelle__icshcajtjh_Oflatten_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      prover542312166e_form: list_l461858535e_form > list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Prover__Mirabelle__icshcajtjh_Oform_OFAll,type,
% 0.16/0.42      prover571163162e_FAll: prover1687215943e_form > prover1687215943e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Prover__Mirabelle__icshcajtjh_Ofv,type,
% 0.16/0.42      prover_Mirabelle_fv: prover1687215943e_form > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Prover__Mirabelle__icshcajtjh_Ois__env,type,
% 0.16/0.42      prover1847600056is_env: produc227817602le_U_o > ( nat > prover_Mirabelle_U ) > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Prover__Mirabelle__icshcajtjh_Omaxvar,type,
% 0.16/0.42      prover1021675886maxvar: list_nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Prover__Mirabelle__icshcajtjh_OpreSuc,type,
% 0.16/0.42      prover2096325705preSuc: list_nat > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Prover__Mirabelle__icshcajtjh_Osfv,type,
% 0.16/0.42      prover_Mirabelle_sfv: list_P512754263e_form > list_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Relation_Oirrefl_001t__Nat__Onat,type,
% 0.16/0.42      irrefl_nat: set_Pr1986765409at_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Relation_Oirrefl_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      irrefl2121388754e_form: set_Pr1189404964e_form > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.16/0.42      collect_nat: ( nat > $o ) > set_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Othe__elem_001t__Nat__Onat,type,
% 0.16/0.42      the_elem_nat: set_nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Othe__elem_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      the_el969789074e_form: set_Pr554570749e_form > prover1687215943e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 0.16/0.42      member_list_nat: list_nat > set_list_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      member1828782574e_form: list_P512754263e_form > set_li5074317e_form > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Nat__Onat,type,
% 0.16/0.42      member_nat: nat > set_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 0.16/0.42      member1926390090st_nat: produc1699244961st_nat > set_Pr1560408065st_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.16/0.42      member1471151041e_form: produc1494932632e_form > set_Pr1174364408e_form > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 0.16/0.42      member1449753665st_nat: produc1473535256st_nat > set_Pr1057005944st_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.16/0.42      member650892795e_form: produc791938916e_form > set_Pr31825690e_form > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_J_Mt__List__Olist_I_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J_J,type,
% 0.16/0.42      member493452075le_U_o: produc622718850le_U_o > set_Pr2099245410le_U_o > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      member18158113e_form: produc1296622072e_form > set_Pr816919384e_form > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__Prover____Mirabelle____icshcajtjh__Oform_Mt__Nat__Onat_J,type,
% 0.16/0.42      member986698273rm_nat: produc117678584rm_nat > set_Pr957084504rm_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__Prover____Mirabelle____icshcajtjh__Oform_Mt__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.16/0.42      member189065477e_form: produc825256814e_form > set_Pr1189404964e_form > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_M_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J,type,
% 0.16/0.42      member1933006123le_U_o: produc227817602le_U_o > set_Pr1072215906le_U_o > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.16/0.42      member1793840734e_form: prover1687215943e_form > set_Pr554570749e_form > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_v_a,type,
% 0.16/0.42      a: set_Pr619177522elle_U ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_v_b,type,
% 0.16/0.42      b: nat > list_P796095576elle_U > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_v_f,type,
% 0.16/0.42      f: prover1687215943e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_v_s,type,
% 0.16/0.42      s: list_P512754263e_form ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_v_u,type,
% 0.16/0.42      u: nat ).
% 0.16/0.42  
% 0.16/0.42  % Relevant facts (352)
% 0.16/0.42  thf(fact_0_form_Oinject_I5_J,axiom,
% 0.16/0.42      ! [X5: prover1687215943e_form,Y5: prover1687215943e_form] :
% 0.16/0.42        ( ( ( prover571163162e_FAll @ X5 )
% 0.16/0.42          = ( prover571163162e_FAll @ Y5 ) )
% 0.16/0.42        = ( X5 = Y5 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % form.inject(5)
% 0.16/0.42  thf(fact_1_SEval_Osimps_I1_J,axiom,
% 0.16/0.42      ! [M: produc227817602le_U_o,E: nat > prover_Mirabelle_U] :
% 0.16/0.42        ~ ( prover1282070756_SEval @ M @ E @ nil_Pr1384483009e_form ) ).
% 0.16/0.42  
% 0.16/0.42  % SEval.simps(1)
% 0.16/0.42  thf(fact_2_SEval__cong,axiom,
% 0.16/0.42      ! [S: list_P512754263e_form,E1: nat > prover_Mirabelle_U,E2: nat > prover_Mirabelle_U,M: produc227817602le_U_o] :
% 0.16/0.42        ( ! [X: nat] :
% 0.16/0.42            ( ( member_nat @ X @ ( set_nat2 @ ( prover_Mirabelle_sfv @ S ) ) )
% 0.16/0.42           => ( ( E1 @ X )
% 0.16/0.42              = ( E2 @ X ) ) )
% 0.16/0.42       => ( ( prover1282070756_SEval @ M @ E1 @ S )
% 0.16/0.42          = ( prover1282070756_SEval @ M @ E2 @ S ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % SEval_cong
% 0.16/0.42  thf(fact_3_SEval__append,axiom,
% 0.16/0.42      ! [M: produc227817602le_U_o,E: nat > prover_Mirabelle_U,Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.42        ( ( prover1282070756_SEval @ M @ E @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.16/0.42        = ( ( prover1282070756_SEval @ M @ E @ Xs )
% 0.16/0.42          | ( prover1282070756_SEval @ M @ E @ Ys ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % SEval_append
% 0.16/0.42  thf(fact_4_sound__FAll,axiom,
% 0.16/0.42      ! [U: nat,F: prover1687215943e_form,S: list_P512754263e_form] :
% 0.16/0.42        ( ~ ( member_nat @ U @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ F ) @ S ) ) ) )
% 0.16/0.42       => ( ( prover1539709396Svalid @ ( append1038020460e_form @ S @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ F @ U ) @ nil_Pr1384483009e_form ) ) )
% 0.16/0.42         => ( prover1539709396Svalid @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ F ) @ S ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % sound_FAll
% 0.16/0.42  thf(fact_5_append1__eq__conv,axiom,
% 0.16/0.42      ! [Xs: list_nat,X2: nat,Ys: list_nat,Y: nat] :
% 0.16/0.42        ( ( ( append_nat @ Xs @ ( cons_nat @ X2 @ nil_nat ) )
% 0.16/0.42          = ( append_nat @ Ys @ ( cons_nat @ Y @ nil_nat ) ) )
% 0.16/0.42        = ( ( Xs = Ys )
% 0.16/0.42          & ( X2 = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append1_eq_conv
% 0.16/0.42  thf(fact_6_append1__eq__conv,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form,Ys: list_P512754263e_form,Y: prover1687215943e_form] :
% 0.16/0.42        ( ( ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) )
% 0.16/0.42          = ( append1038020460e_form @ Ys @ ( cons_P1475164433e_form @ Y @ nil_Pr1384483009e_form ) ) )
% 0.16/0.42        = ( ( Xs = Ys )
% 0.16/0.42          & ( X2 = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append1_eq_conv
% 0.16/0.42  thf(fact_7_append__Nil2,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( append1038020460e_form @ Xs @ nil_Pr1384483009e_form )
% 0.16/0.42        = Xs ) ).
% 0.16/0.42  
% 0.16/0.42  % append_Nil2
% 0.16/0.42  thf(fact_8_append__Nil2,axiom,
% 0.16/0.42      ! [Xs: list_nat] :
% 0.16/0.42        ( ( append_nat @ Xs @ nil_nat )
% 0.16/0.42        = Xs ) ).
% 0.16/0.42  
% 0.16/0.42  % append_Nil2
% 0.16/0.42  thf(fact_9_append__self__conv,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.42        ( ( ( append1038020460e_form @ Xs @ Ys )
% 0.16/0.42          = Xs )
% 0.16/0.42        = ( Ys = nil_Pr1384483009e_form ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_self_conv
% 0.16/0.42  thf(fact_10_append__self__conv,axiom,
% 0.16/0.42      ! [Xs: list_nat,Ys: list_nat] :
% 0.16/0.42        ( ( ( append_nat @ Xs @ Ys )
% 0.16/0.42          = Xs )
% 0.16/0.42        = ( Ys = nil_nat ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_self_conv
% 0.16/0.42  thf(fact_11_self__append__conv,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.42        ( ( Xs
% 0.16/0.42          = ( append1038020460e_form @ Xs @ Ys ) )
% 0.16/0.42        = ( Ys = nil_Pr1384483009e_form ) ) ).
% 0.16/0.42  
% 0.16/0.42  % self_append_conv
% 0.16/0.42  thf(fact_12_self__append__conv,axiom,
% 0.16/0.42      ! [Xs: list_nat,Ys: list_nat] :
% 0.16/0.42        ( ( Xs
% 0.16/0.42          = ( append_nat @ Xs @ Ys ) )
% 0.16/0.42        = ( Ys = nil_nat ) ) ).
% 0.16/0.42  
% 0.16/0.42  % self_append_conv
% 0.16/0.42  thf(fact_13_append__self__conv2,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.42        ( ( ( append1038020460e_form @ Xs @ Ys )
% 0.16/0.42          = Ys )
% 0.16/0.42        = ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_self_conv2
% 0.16/0.42  thf(fact_14_append__self__conv2,axiom,
% 0.16/0.42      ! [Xs: list_nat,Ys: list_nat] :
% 0.16/0.42        ( ( ( append_nat @ Xs @ Ys )
% 0.16/0.42          = Ys )
% 0.16/0.42        = ( Xs = nil_nat ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_self_conv2
% 0.16/0.42  thf(fact_15_self__append__conv2,axiom,
% 0.16/0.42      ! [Ys: list_P512754263e_form,Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( Ys
% 0.16/0.42          = ( append1038020460e_form @ Xs @ Ys ) )
% 0.16/0.42        = ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.16/0.42  
% 0.16/0.42  % self_append_conv2
% 0.16/0.42  thf(fact_16_self__append__conv2,axiom,
% 0.16/0.42      ! [Ys: list_nat,Xs: list_nat] :
% 0.16/0.42        ( ( Ys
% 0.16/0.42          = ( append_nat @ Xs @ Ys ) )
% 0.16/0.42        = ( Xs = nil_nat ) ) ).
% 0.16/0.42  
% 0.16/0.42  % self_append_conv2
% 0.16/0.42  thf(fact_17_Nil__is__append__conv,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.42        ( ( nil_Pr1384483009e_form
% 0.16/0.42          = ( append1038020460e_form @ Xs @ Ys ) )
% 0.16/0.42        = ( ( Xs = nil_Pr1384483009e_form )
% 0.16/0.42          & ( Ys = nil_Pr1384483009e_form ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % Nil_is_append_conv
% 0.16/0.42  thf(fact_18_Nil__is__append__conv,axiom,
% 0.16/0.42      ! [Xs: list_nat,Ys: list_nat] :
% 0.16/0.42        ( ( nil_nat
% 0.16/0.42          = ( append_nat @ Xs @ Ys ) )
% 0.16/0.42        = ( ( Xs = nil_nat )
% 0.16/0.42          & ( Ys = nil_nat ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % Nil_is_append_conv
% 0.16/0.42  thf(fact_19_append__is__Nil__conv,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.42        ( ( ( append1038020460e_form @ Xs @ Ys )
% 0.16/0.42          = nil_Pr1384483009e_form )
% 0.16/0.42        = ( ( Xs = nil_Pr1384483009e_form )
% 0.16/0.42          & ( Ys = nil_Pr1384483009e_form ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_is_Nil_conv
% 0.16/0.42  thf(fact_20_append__is__Nil__conv,axiom,
% 0.16/0.42      ! [Xs: list_nat,Ys: list_nat] :
% 0.16/0.42        ( ( ( append_nat @ Xs @ Ys )
% 0.16/0.42          = nil_nat )
% 0.16/0.42        = ( ( Xs = nil_nat )
% 0.16/0.42          & ( Ys = nil_nat ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_is_Nil_conv
% 0.16/0.42  thf(fact_21_append_Oright__neutral,axiom,
% 0.16/0.42      ! [A: list_P512754263e_form] :
% 0.16/0.42        ( ( append1038020460e_form @ A @ nil_Pr1384483009e_form )
% 0.16/0.42        = A ) ).
% 0.16/0.42  
% 0.16/0.42  % append.right_neutral
% 0.16/0.42  thf(fact_22_append_Oright__neutral,axiom,
% 0.16/0.42      ! [A: list_nat] :
% 0.16/0.42        ( ( append_nat @ A @ nil_nat )
% 0.16/0.42        = A ) ).
% 0.16/0.42  
% 0.16/0.42  % append.right_neutral
% 0.16/0.42  thf(fact_23_Svalid__def,axiom,
% 0.16/0.42      ( prover1539709396Svalid
% 0.16/0.42      = ( ^ [S2: list_P512754263e_form] :
% 0.16/0.42          ! [MI: produc227817602le_U_o,E3: nat > prover_Mirabelle_U] :
% 0.16/0.42            ( ( prover1847600056is_env @ MI @ E3 )
% 0.16/0.42           => ( prover1282070756_SEval @ MI @ E3 @ S2 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % Svalid_def
% 0.16/0.42  thf(fact_24_split__list,axiom,
% 0.16/0.42      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.42       => ? [Ys2: list_P512754263e_form,Zs: list_P512754263e_form] :
% 0.16/0.42            ( Xs
% 0.16/0.42            = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X2 @ Zs ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list
% 0.16/0.42  thf(fact_25_split__list,axiom,
% 0.16/0.42      ! [X2: nat,Xs: list_nat] :
% 0.16/0.42        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.16/0.42       => ? [Ys2: list_nat,Zs: list_nat] :
% 0.16/0.42            ( Xs
% 0.16/0.42            = ( append_nat @ Ys2 @ ( cons_nat @ X2 @ Zs ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list
% 0.16/0.42  thf(fact_26_list_Oinject,axiom,
% 0.16/0.42      ! [X21: prover1687215943e_form,X22: list_P512754263e_form,Y21: prover1687215943e_form,Y22: list_P512754263e_form] :
% 0.16/0.42        ( ( ( cons_P1475164433e_form @ X21 @ X22 )
% 0.16/0.42          = ( cons_P1475164433e_form @ Y21 @ Y22 ) )
% 0.16/0.42        = ( ( X21 = Y21 )
% 0.16/0.42          & ( X22 = Y22 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.inject
% 0.16/0.42  thf(fact_27_list_Oinject,axiom,
% 0.16/0.42      ! [X21: nat,X22: list_nat,Y21: nat,Y22: list_nat] :
% 0.16/0.42        ( ( ( cons_nat @ X21 @ X22 )
% 0.16/0.42          = ( cons_nat @ Y21 @ Y22 ) )
% 0.16/0.42        = ( ( X21 = Y21 )
% 0.16/0.42          & ( X22 = Y22 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.inject
% 0.16/0.42  thf(fact_28_same__append__eq,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.16/0.42        ( ( ( append1038020460e_form @ Xs @ Ys )
% 0.16/0.42          = ( append1038020460e_form @ Xs @ Zs2 ) )
% 0.16/0.42        = ( Ys = Zs2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % same_append_eq
% 0.16/0.42  thf(fact_29_same__append__eq,axiom,
% 0.16/0.42      ! [Xs: list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.16/0.42        ( ( ( append_nat @ Xs @ Ys )
% 0.16/0.42          = ( append_nat @ Xs @ Zs2 ) )
% 0.16/0.42        = ( Ys = Zs2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % same_append_eq
% 0.16/0.42  thf(fact_30_append__same__eq,axiom,
% 0.16/0.42      ! [Ys: list_P512754263e_form,Xs: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.16/0.42        ( ( ( append1038020460e_form @ Ys @ Xs )
% 0.16/0.42          = ( append1038020460e_form @ Zs2 @ Xs ) )
% 0.16/0.42        = ( Ys = Zs2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_same_eq
% 0.16/0.42  thf(fact_31_append__same__eq,axiom,
% 0.16/0.42      ! [Ys: list_nat,Xs: list_nat,Zs2: list_nat] :
% 0.16/0.42        ( ( ( append_nat @ Ys @ Xs )
% 0.16/0.42          = ( append_nat @ Zs2 @ Xs ) )
% 0.16/0.42        = ( Ys = Zs2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_same_eq
% 0.16/0.42  thf(fact_32_append__assoc,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.16/0.42        ( ( append1038020460e_form @ ( append1038020460e_form @ Xs @ Ys ) @ Zs2 )
% 0.16/0.42        = ( append1038020460e_form @ Xs @ ( append1038020460e_form @ Ys @ Zs2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_assoc
% 0.16/0.42  thf(fact_33_append__assoc,axiom,
% 0.16/0.42      ! [Xs: list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.16/0.42        ( ( append_nat @ ( append_nat @ Xs @ Ys ) @ Zs2 )
% 0.16/0.42        = ( append_nat @ Xs @ ( append_nat @ Ys @ Zs2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_assoc
% 0.16/0.42  thf(fact_34_append_Oassoc,axiom,
% 0.16/0.42      ! [A: list_P512754263e_form,B: list_P512754263e_form,C: list_P512754263e_form] :
% 0.16/0.42        ( ( append1038020460e_form @ ( append1038020460e_form @ A @ B ) @ C )
% 0.16/0.42        = ( append1038020460e_form @ A @ ( append1038020460e_form @ B @ C ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append.assoc
% 0.16/0.42  thf(fact_35_append_Oassoc,axiom,
% 0.16/0.42      ! [A: list_nat,B: list_nat,C: list_nat] :
% 0.16/0.42        ( ( append_nat @ ( append_nat @ A @ B ) @ C )
% 0.16/0.42        = ( append_nat @ A @ ( append_nat @ B @ C ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append.assoc
% 0.16/0.42  thf(fact_36_not__Cons__self2,axiom,
% 0.16/0.42      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( cons_P1475164433e_form @ X2 @ Xs )
% 0.16/0.42       != Xs ) ).
% 0.16/0.42  
% 0.16/0.42  % not_Cons_self2
% 0.16/0.42  thf(fact_37_not__Cons__self2,axiom,
% 0.16/0.42      ! [X2: nat,Xs: list_nat] :
% 0.16/0.42        ( ( cons_nat @ X2 @ Xs )
% 0.16/0.42       != Xs ) ).
% 0.16/0.42  
% 0.16/0.42  % not_Cons_self2
% 0.16/0.42  thf(fact_38_sfv__nil,axiom,
% 0.16/0.42      ( ( prover_Mirabelle_sfv @ nil_Pr1384483009e_form )
% 0.16/0.42      = nil_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % sfv_nil
% 0.16/0.42  thf(fact_39_append__eq__append__conv2,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form,Ts: list_P512754263e_form] :
% 0.16/0.42        ( ( ( append1038020460e_form @ Xs @ Ys )
% 0.16/0.42          = ( append1038020460e_form @ Zs2 @ Ts ) )
% 0.16/0.42        = ( ? [Us: list_P512754263e_form] :
% 0.16/0.42              ( ( ( Xs
% 0.16/0.42                  = ( append1038020460e_form @ Zs2 @ Us ) )
% 0.16/0.42                & ( ( append1038020460e_form @ Us @ Ys )
% 0.16/0.42                  = Ts ) )
% 0.16/0.42              | ( ( ( append1038020460e_form @ Xs @ Us )
% 0.16/0.42                  = Zs2 )
% 0.16/0.42                & ( Ys
% 0.16/0.42                  = ( append1038020460e_form @ Us @ Ts ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_eq_append_conv2
% 0.16/0.42  thf(fact_40_append__eq__append__conv2,axiom,
% 0.16/0.42      ! [Xs: list_nat,Ys: list_nat,Zs2: list_nat,Ts: list_nat] :
% 0.16/0.42        ( ( ( append_nat @ Xs @ Ys )
% 0.16/0.42          = ( append_nat @ Zs2 @ Ts ) )
% 0.16/0.42        = ( ? [Us: list_nat] :
% 0.16/0.42              ( ( ( Xs
% 0.16/0.42                  = ( append_nat @ Zs2 @ Us ) )
% 0.16/0.42                & ( ( append_nat @ Us @ Ys )
% 0.16/0.42                  = Ts ) )
% 0.16/0.42              | ( ( ( append_nat @ Xs @ Us )
% 0.16/0.42                  = Zs2 )
% 0.16/0.42                & ( Ys
% 0.16/0.42                  = ( append_nat @ Us @ Ts ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_eq_append_conv2
% 0.16/0.42  thf(fact_41_append__eq__appendI,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,Xs1: list_P512754263e_form,Zs2: list_P512754263e_form,Ys: list_P512754263e_form,Us2: list_P512754263e_form] :
% 0.16/0.42        ( ( ( append1038020460e_form @ Xs @ Xs1 )
% 0.16/0.42          = Zs2 )
% 0.16/0.42       => ( ( Ys
% 0.16/0.42            = ( append1038020460e_form @ Xs1 @ Us2 ) )
% 0.16/0.42         => ( ( append1038020460e_form @ Xs @ Ys )
% 0.16/0.42            = ( append1038020460e_form @ Zs2 @ Us2 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_eq_appendI
% 0.16/0.42  thf(fact_42_append__eq__appendI,axiom,
% 0.16/0.42      ! [Xs: list_nat,Xs1: list_nat,Zs2: list_nat,Ys: list_nat,Us2: list_nat] :
% 0.16/0.42        ( ( ( append_nat @ Xs @ Xs1 )
% 0.16/0.42          = Zs2 )
% 0.16/0.42       => ( ( Ys
% 0.16/0.42            = ( append_nat @ Xs1 @ Us2 ) )
% 0.16/0.42         => ( ( append_nat @ Xs @ Ys )
% 0.16/0.42            = ( append_nat @ Zs2 @ Us2 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_eq_appendI
% 0.16/0.42  thf(fact_43_strict__sorted_Oinduct,axiom,
% 0.16/0.42      ! [P: list_nat > $o,A0: list_nat] :
% 0.16/0.42        ( ( P @ nil_nat )
% 0.16/0.42       => ( ! [X: nat,Ys2: list_nat] :
% 0.16/0.42              ( ( P @ Ys2 )
% 0.16/0.42             => ( P @ ( cons_nat @ X @ Ys2 ) ) )
% 0.16/0.42         => ( P @ A0 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % strict_sorted.induct
% 0.16/0.42  thf(fact_44_strict__sorted_Ocases,axiom,
% 0.16/0.42      ! [X2: list_nat] :
% 0.16/0.42        ( ( X2 != nil_nat )
% 0.16/0.42       => ~ ! [X: nat,Ys2: list_nat] :
% 0.16/0.42              ( X2
% 0.16/0.42             != ( cons_nat @ X @ Ys2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % strict_sorted.cases
% 0.16/0.42  thf(fact_45_map__tailrec__rev_Oinduct,axiom,
% 0.16/0.42      ! [P: ( prover1687215943e_form > prover1687215943e_form ) > list_P512754263e_form > list_P512754263e_form > $o,A0: prover1687215943e_form > prover1687215943e_form,A1: list_P512754263e_form,A2: list_P512754263e_form] :
% 0.16/0.42        ( ! [F2: prover1687215943e_form > prover1687215943e_form,X_1: list_P512754263e_form] : ( P @ F2 @ nil_Pr1384483009e_form @ X_1 )
% 0.16/0.42       => ( ! [F2: prover1687215943e_form > prover1687215943e_form,A3: prover1687215943e_form,As: list_P512754263e_form,Bs: list_P512754263e_form] :
% 0.16/0.42              ( ( P @ F2 @ As @ ( cons_P1475164433e_form @ ( F2 @ A3 ) @ Bs ) )
% 0.16/0.42             => ( P @ F2 @ ( cons_P1475164433e_form @ A3 @ As ) @ Bs ) )
% 0.16/0.42         => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_tailrec_rev.induct
% 0.16/0.42  thf(fact_46_map__tailrec__rev_Oinduct,axiom,
% 0.16/0.42      ! [P: ( nat > prover1687215943e_form ) > list_nat > list_P512754263e_form > $o,A0: nat > prover1687215943e_form,A1: list_nat,A2: list_P512754263e_form] :
% 0.16/0.42        ( ! [F2: nat > prover1687215943e_form,X_1: list_P512754263e_form] : ( P @ F2 @ nil_nat @ X_1 )
% 0.16/0.42       => ( ! [F2: nat > prover1687215943e_form,A3: nat,As: list_nat,Bs: list_P512754263e_form] :
% 0.16/0.42              ( ( P @ F2 @ As @ ( cons_P1475164433e_form @ ( F2 @ A3 ) @ Bs ) )
% 0.16/0.42             => ( P @ F2 @ ( cons_nat @ A3 @ As ) @ Bs ) )
% 0.16/0.42         => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_tailrec_rev.induct
% 0.16/0.42  thf(fact_47_map__tailrec__rev_Oinduct,axiom,
% 0.16/0.42      ! [P: ( prover1687215943e_form > nat ) > list_P512754263e_form > list_nat > $o,A0: prover1687215943e_form > nat,A1: list_P512754263e_form,A2: list_nat] :
% 0.16/0.42        ( ! [F2: prover1687215943e_form > nat,X_1: list_nat] : ( P @ F2 @ nil_Pr1384483009e_form @ X_1 )
% 0.16/0.42       => ( ! [F2: prover1687215943e_form > nat,A3: prover1687215943e_form,As: list_P512754263e_form,Bs: list_nat] :
% 0.16/0.42              ( ( P @ F2 @ As @ ( cons_nat @ ( F2 @ A3 ) @ Bs ) )
% 0.16/0.42             => ( P @ F2 @ ( cons_P1475164433e_form @ A3 @ As ) @ Bs ) )
% 0.16/0.42         => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_tailrec_rev.induct
% 0.16/0.42  thf(fact_48_map__tailrec__rev_Oinduct,axiom,
% 0.16/0.42      ! [P: ( nat > nat ) > list_nat > list_nat > $o,A0: nat > nat,A1: list_nat,A2: list_nat] :
% 0.16/0.42        ( ! [F2: nat > nat,X_1: list_nat] : ( P @ F2 @ nil_nat @ X_1 )
% 0.16/0.42       => ( ! [F2: nat > nat,A3: nat,As: list_nat,Bs: list_nat] :
% 0.16/0.42              ( ( P @ F2 @ As @ ( cons_nat @ ( F2 @ A3 ) @ Bs ) )
% 0.16/0.42             => ( P @ F2 @ ( cons_nat @ A3 @ As ) @ Bs ) )
% 0.16/0.42         => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_tailrec_rev.induct
% 0.16/0.42  thf(fact_49_list__nonempty__induct,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,P: list_P512754263e_form > $o] :
% 0.16/0.42        ( ( Xs != nil_Pr1384483009e_form )
% 0.16/0.42       => ( ! [X: prover1687215943e_form] : ( P @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) )
% 0.16/0.42         => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.16/0.42                ( ( Xs2 != nil_Pr1384483009e_form )
% 0.16/0.42               => ( ( P @ Xs2 )
% 0.16/0.42                 => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) ) ) )
% 0.16/0.42           => ( P @ Xs ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list_nonempty_induct
% 0.16/0.42  thf(fact_50_list__nonempty__induct,axiom,
% 0.16/0.42      ! [Xs: list_nat,P: list_nat > $o] :
% 0.16/0.42        ( ( Xs != nil_nat )
% 0.16/0.42       => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 0.16/0.42         => ( ! [X: nat,Xs2: list_nat] :
% 0.16/0.42                ( ( Xs2 != nil_nat )
% 0.16/0.42               => ( ( P @ Xs2 )
% 0.16/0.42                 => ( P @ ( cons_nat @ X @ Xs2 ) ) ) )
% 0.16/0.42           => ( P @ Xs ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list_nonempty_induct
% 0.16/0.42  thf(fact_51_successively_Oinduct,axiom,
% 0.16/0.42      ! [P: ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o,A0: prover1687215943e_form > prover1687215943e_form > $o,A1: list_P512754263e_form] :
% 0.16/0.42        ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o] : ( P @ P2 @ nil_Pr1384483009e_form )
% 0.16/0.42       => ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o,X: prover1687215943e_form] : ( P @ P2 @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) )
% 0.16/0.42         => ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o,X: prover1687215943e_form,Y2: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.16/0.42                ( ( P @ P2 @ ( cons_P1475164433e_form @ Y2 @ Xs2 ) )
% 0.16/0.42               => ( P @ P2 @ ( cons_P1475164433e_form @ X @ ( cons_P1475164433e_form @ Y2 @ Xs2 ) ) ) )
% 0.16/0.42           => ( P @ A0 @ A1 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % successively.induct
% 0.16/0.42  thf(fact_52_successively_Oinduct,axiom,
% 0.16/0.42      ! [P: ( nat > nat > $o ) > list_nat > $o,A0: nat > nat > $o,A1: list_nat] :
% 0.16/0.42        ( ! [P2: nat > nat > $o] : ( P @ P2 @ nil_nat )
% 0.16/0.42       => ( ! [P2: nat > nat > $o,X: nat] : ( P @ P2 @ ( cons_nat @ X @ nil_nat ) )
% 0.16/0.42         => ( ! [P2: nat > nat > $o,X: nat,Y2: nat,Xs2: list_nat] :
% 0.16/0.42                ( ( P @ P2 @ ( cons_nat @ Y2 @ Xs2 ) )
% 0.16/0.42               => ( P @ P2 @ ( cons_nat @ X @ ( cons_nat @ Y2 @ Xs2 ) ) ) )
% 0.16/0.42           => ( P @ A0 @ A1 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % successively.induct
% 0.16/0.42  thf(fact_53_remdups__adj_Oinduct,axiom,
% 0.16/0.42      ! [P: list_P512754263e_form > $o,A0: list_P512754263e_form] :
% 0.16/0.42        ( ( P @ nil_Pr1384483009e_form )
% 0.16/0.42       => ( ! [X: prover1687215943e_form] : ( P @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) )
% 0.16/0.42         => ( ! [X: prover1687215943e_form,Y2: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.16/0.42                ( ( ( X = Y2 )
% 0.16/0.42                 => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) ) )
% 0.16/0.42               => ( ( ( X != Y2 )
% 0.16/0.42                   => ( P @ ( cons_P1475164433e_form @ Y2 @ Xs2 ) ) )
% 0.16/0.42                 => ( P @ ( cons_P1475164433e_form @ X @ ( cons_P1475164433e_form @ Y2 @ Xs2 ) ) ) ) )
% 0.16/0.42           => ( P @ A0 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % remdups_adj.induct
% 0.16/0.42  thf(fact_54_remdups__adj_Oinduct,axiom,
% 0.16/0.42      ! [P: list_nat > $o,A0: list_nat] :
% 0.16/0.42        ( ( P @ nil_nat )
% 0.16/0.42       => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 0.16/0.42         => ( ! [X: nat,Y2: nat,Xs2: list_nat] :
% 0.16/0.42                ( ( ( X = Y2 )
% 0.16/0.42                 => ( P @ ( cons_nat @ X @ Xs2 ) ) )
% 0.16/0.42               => ( ( ( X != Y2 )
% 0.16/0.42                   => ( P @ ( cons_nat @ Y2 @ Xs2 ) ) )
% 0.16/0.42                 => ( P @ ( cons_nat @ X @ ( cons_nat @ Y2 @ Xs2 ) ) ) ) )
% 0.16/0.42           => ( P @ A0 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % remdups_adj.induct
% 0.16/0.42  thf(fact_55_sorted__wrt_Oinduct,axiom,
% 0.16/0.42      ! [P: ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o,A0: prover1687215943e_form > prover1687215943e_form > $o,A1: list_P512754263e_form] :
% 0.16/0.42        ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o] : ( P @ P2 @ nil_Pr1384483009e_form )
% 0.16/0.42       => ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o,X: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.16/0.42              ( ( P @ P2 @ Ys2 )
% 0.16/0.42             => ( P @ P2 @ ( cons_P1475164433e_form @ X @ Ys2 ) ) )
% 0.16/0.42         => ( P @ A0 @ A1 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % sorted_wrt.induct
% 0.16/0.42  thf(fact_56_sorted__wrt_Oinduct,axiom,
% 0.16/0.42      ! [P: ( nat > nat > $o ) > list_nat > $o,A0: nat > nat > $o,A1: list_nat] :
% 0.16/0.42        ( ! [P2: nat > nat > $o] : ( P @ P2 @ nil_nat )
% 0.16/0.42       => ( ! [P2: nat > nat > $o,X: nat,Ys2: list_nat] :
% 0.16/0.42              ( ( P @ P2 @ Ys2 )
% 0.16/0.42             => ( P @ P2 @ ( cons_nat @ X @ Ys2 ) ) )
% 0.16/0.42         => ( P @ A0 @ A1 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % sorted_wrt.induct
% 0.16/0.42  thf(fact_57_remdups__adj_Ocases,axiom,
% 0.16/0.42      ! [X2: list_P512754263e_form] :
% 0.16/0.42        ( ( X2 != nil_Pr1384483009e_form )
% 0.16/0.42       => ( ! [X: prover1687215943e_form] :
% 0.16/0.42              ( X2
% 0.16/0.42             != ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) )
% 0.16/0.42         => ~ ! [X: prover1687215943e_form,Y2: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.16/0.42                ( X2
% 0.16/0.42               != ( cons_P1475164433e_form @ X @ ( cons_P1475164433e_form @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % remdups_adj.cases
% 0.16/0.42  thf(fact_58_remdups__adj_Ocases,axiom,
% 0.16/0.42      ! [X2: list_nat] :
% 0.16/0.42        ( ( X2 != nil_nat )
% 0.16/0.42       => ( ! [X: nat] :
% 0.16/0.42              ( X2
% 0.16/0.42             != ( cons_nat @ X @ nil_nat ) )
% 0.16/0.42         => ~ ! [X: nat,Y2: nat,Xs2: list_nat] :
% 0.16/0.42                ( X2
% 0.16/0.42               != ( cons_nat @ X @ ( cons_nat @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % remdups_adj.cases
% 0.16/0.42  thf(fact_59_transpose_Ocases,axiom,
% 0.16/0.42      ! [X2: list_l461858535e_form] :
% 0.16/0.42        ( ( X2 != nil_li1393862353e_form )
% 0.16/0.42       => ( ! [Xss: list_l461858535e_form] :
% 0.16/0.42              ( X2
% 0.16/0.42             != ( cons_l1379921697e_form @ nil_Pr1384483009e_form @ Xss ) )
% 0.16/0.42         => ~ ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Xss: list_l461858535e_form] :
% 0.16/0.42                ( X2
% 0.16/0.42               != ( cons_l1379921697e_form @ ( cons_P1475164433e_form @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % transpose.cases
% 0.16/0.42  thf(fact_60_transpose_Ocases,axiom,
% 0.16/0.42      ! [X2: list_list_nat] :
% 0.16/0.42        ( ( X2 != nil_list_nat )
% 0.16/0.42       => ( ! [Xss: list_list_nat] :
% 0.16/0.42              ( X2
% 0.16/0.42             != ( cons_list_nat @ nil_nat @ Xss ) )
% 0.16/0.42         => ~ ! [X: nat,Xs2: list_nat,Xss: list_list_nat] :
% 0.16/0.42                ( X2
% 0.16/0.42               != ( cons_list_nat @ ( cons_nat @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % transpose.cases
% 0.16/0.42  thf(fact_61_shuffles_Oinduct,axiom,
% 0.16/0.42      ! [P: list_P512754263e_form > list_P512754263e_form > $o,A0: list_P512754263e_form,A1: list_P512754263e_form] :
% 0.16/0.42        ( ! [X_1: list_P512754263e_form] : ( P @ nil_Pr1384483009e_form @ X_1 )
% 0.16/0.42       => ( ! [Xs2: list_P512754263e_form] : ( P @ Xs2 @ nil_Pr1384483009e_form )
% 0.16/0.42         => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Y2: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.16/0.42                ( ( P @ Xs2 @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.16/0.42               => ( ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ Ys2 )
% 0.16/0.42                 => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) ) ) )
% 0.16/0.42           => ( P @ A0 @ A1 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % shuffles.induct
% 0.16/0.42  thf(fact_62_shuffles_Oinduct,axiom,
% 0.16/0.42      ! [P: list_nat > list_nat > $o,A0: list_nat,A1: list_nat] :
% 0.16/0.42        ( ! [X_1: list_nat] : ( P @ nil_nat @ X_1 )
% 0.16/0.42       => ( ! [Xs2: list_nat] : ( P @ Xs2 @ nil_nat )
% 0.16/0.42         => ( ! [X: nat,Xs2: list_nat,Y2: nat,Ys2: list_nat] :
% 0.16/0.42                ( ( P @ Xs2 @ ( cons_nat @ Y2 @ Ys2 ) )
% 0.16/0.42               => ( ( P @ ( cons_nat @ X @ Xs2 ) @ Ys2 )
% 0.16/0.42                 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y2 @ Ys2 ) ) ) )
% 0.16/0.42           => ( P @ A0 @ A1 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % shuffles.induct
% 0.16/0.42  thf(fact_63_min__list_Oinduct,axiom,
% 0.16/0.42      ! [P: list_nat > $o,A0: list_nat] :
% 0.16/0.42        ( ! [X: nat,Xs2: list_nat] :
% 0.16/0.42            ( ! [X212: nat,X222: list_nat] :
% 0.16/0.42                ( ( Xs2
% 0.16/0.42                  = ( cons_nat @ X212 @ X222 ) )
% 0.16/0.42               => ( P @ Xs2 ) )
% 0.16/0.42           => ( P @ ( cons_nat @ X @ Xs2 ) ) )
% 0.16/0.42       => ( ( P @ nil_nat )
% 0.16/0.42         => ( P @ A0 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % min_list.induct
% 0.16/0.42  thf(fact_64_min__list_Ocases,axiom,
% 0.16/0.42      ! [X2: list_nat] :
% 0.16/0.42        ( ! [X: nat,Xs2: list_nat] :
% 0.16/0.42            ( X2
% 0.16/0.42           != ( cons_nat @ X @ Xs2 ) )
% 0.16/0.42       => ( X2 = nil_nat ) ) ).
% 0.16/0.42  
% 0.16/0.42  % min_list.cases
% 0.16/0.42  thf(fact_65_induct__list012,axiom,
% 0.16/0.42      ! [P: list_P512754263e_form > $o,Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( P @ nil_Pr1384483009e_form )
% 0.16/0.42       => ( ! [X: prover1687215943e_form] : ( P @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) )
% 0.16/0.42         => ( ! [X: prover1687215943e_form,Y2: prover1687215943e_form,Zs: list_P512754263e_form] :
% 0.16/0.42                ( ( P @ Zs )
% 0.16/0.42               => ( ( P @ ( cons_P1475164433e_form @ Y2 @ Zs ) )
% 0.16/0.42                 => ( P @ ( cons_P1475164433e_form @ X @ ( cons_P1475164433e_form @ Y2 @ Zs ) ) ) ) )
% 0.16/0.42           => ( P @ Xs ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % induct_list012
% 0.16/0.42  thf(fact_66_induct__list012,axiom,
% 0.16/0.42      ! [P: list_nat > $o,Xs: list_nat] :
% 0.16/0.42        ( ( P @ nil_nat )
% 0.16/0.42       => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 0.16/0.42         => ( ! [X: nat,Y2: nat,Zs: list_nat] :
% 0.16/0.42                ( ( P @ Zs )
% 0.16/0.42               => ( ( P @ ( cons_nat @ Y2 @ Zs ) )
% 0.16/0.42                 => ( P @ ( cons_nat @ X @ ( cons_nat @ Y2 @ Zs ) ) ) ) )
% 0.16/0.42           => ( P @ Xs ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % induct_list012
% 0.16/0.42  thf(fact_67_splice_Oinduct,axiom,
% 0.16/0.42      ! [P: list_P512754263e_form > list_P512754263e_form > $o,A0: list_P512754263e_form,A1: list_P512754263e_form] :
% 0.16/0.42        ( ! [X_1: list_P512754263e_form] : ( P @ nil_Pr1384483009e_form @ X_1 )
% 0.16/0.42       => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Ys2: list_P512754263e_form] :
% 0.16/0.42              ( ( P @ Ys2 @ Xs2 )
% 0.16/0.42             => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ Ys2 ) )
% 0.16/0.42         => ( P @ A0 @ A1 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % splice.induct
% 0.16/0.42  thf(fact_68_splice_Oinduct,axiom,
% 0.16/0.42      ! [P: list_nat > list_nat > $o,A0: list_nat,A1: list_nat] :
% 0.16/0.42        ( ! [X_1: list_nat] : ( P @ nil_nat @ X_1 )
% 0.16/0.42       => ( ! [X: nat,Xs2: list_nat,Ys2: list_nat] :
% 0.16/0.42              ( ( P @ Ys2 @ Xs2 )
% 0.16/0.42             => ( P @ ( cons_nat @ X @ Xs2 ) @ Ys2 ) )
% 0.16/0.42         => ( P @ A0 @ A1 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % splice.induct
% 0.16/0.42  thf(fact_69_list__induct2_H,axiom,
% 0.16/0.42      ! [P: list_P512754263e_form > list_P512754263e_form > $o,Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.42        ( ( P @ nil_Pr1384483009e_form @ nil_Pr1384483009e_form )
% 0.16/0.42       => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] : ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ nil_Pr1384483009e_form )
% 0.16/0.42         => ( ! [Y2: prover1687215943e_form,Ys2: list_P512754263e_form] : ( P @ nil_Pr1384483009e_form @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.16/0.42           => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Y2: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.16/0.42                  ( ( P @ Xs2 @ Ys2 )
% 0.16/0.42                 => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) ) )
% 0.16/0.42             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list_induct2'
% 0.16/0.42  thf(fact_70_list__induct2_H,axiom,
% 0.16/0.42      ! [P: list_P512754263e_form > list_nat > $o,Xs: list_P512754263e_form,Ys: list_nat] :
% 0.16/0.42        ( ( P @ nil_Pr1384483009e_form @ nil_nat )
% 0.16/0.42       => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] : ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ nil_nat )
% 0.16/0.42         => ( ! [Y2: nat,Ys2: list_nat] : ( P @ nil_Pr1384483009e_form @ ( cons_nat @ Y2 @ Ys2 ) )
% 0.16/0.42           => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Y2: nat,Ys2: list_nat] :
% 0.16/0.42                  ( ( P @ Xs2 @ Ys2 )
% 0.16/0.42                 => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ ( cons_nat @ Y2 @ Ys2 ) ) )
% 0.16/0.42             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list_induct2'
% 0.16/0.42  thf(fact_71_list__induct2_H,axiom,
% 0.16/0.42      ! [P: list_nat > list_P512754263e_form > $o,Xs: list_nat,Ys: list_P512754263e_form] :
% 0.16/0.42        ( ( P @ nil_nat @ nil_Pr1384483009e_form )
% 0.16/0.42       => ( ! [X: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X @ Xs2 ) @ nil_Pr1384483009e_form )
% 0.16/0.42         => ( ! [Y2: prover1687215943e_form,Ys2: list_P512754263e_form] : ( P @ nil_nat @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.16/0.42           => ( ! [X: nat,Xs2: list_nat,Y2: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.16/0.42                  ( ( P @ Xs2 @ Ys2 )
% 0.16/0.42                 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) ) )
% 0.16/0.42             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list_induct2'
% 0.16/0.42  thf(fact_72_list__induct2_H,axiom,
% 0.16/0.42      ! [P: list_nat > list_nat > $o,Xs: list_nat,Ys: list_nat] :
% 0.16/0.42        ( ( P @ nil_nat @ nil_nat )
% 0.16/0.42       => ( ! [X: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X @ Xs2 ) @ nil_nat )
% 0.16/0.42         => ( ! [Y2: nat,Ys2: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y2 @ Ys2 ) )
% 0.16/0.42           => ( ! [X: nat,Xs2: list_nat,Y2: nat,Ys2: list_nat] :
% 0.16/0.42                  ( ( P @ Xs2 @ Ys2 )
% 0.16/0.42                 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y2 @ Ys2 ) ) )
% 0.16/0.42             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list_induct2'
% 0.16/0.42  thf(fact_73_neq__Nil__conv,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( Xs != nil_Pr1384483009e_form )
% 0.16/0.42        = ( ? [Y3: prover1687215943e_form,Ys3: list_P512754263e_form] :
% 0.16/0.42              ( Xs
% 0.16/0.42              = ( cons_P1475164433e_form @ Y3 @ Ys3 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % neq_Nil_conv
% 0.16/0.42  thf(fact_74_neq__Nil__conv,axiom,
% 0.16/0.42      ! [Xs: list_nat] :
% 0.16/0.42        ( ( Xs != nil_nat )
% 0.16/0.42        = ( ? [Y3: nat,Ys3: list_nat] :
% 0.16/0.42              ( Xs
% 0.16/0.42              = ( cons_nat @ Y3 @ Ys3 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % neq_Nil_conv
% 0.16/0.42  thf(fact_75_list_Oinducts,axiom,
% 0.16/0.42      ! [P: list_P512754263e_form > $o,List: list_P512754263e_form] :
% 0.16/0.42        ( ( P @ nil_Pr1384483009e_form )
% 0.16/0.42       => ( ! [X1: prover1687215943e_form,X23: list_P512754263e_form] :
% 0.16/0.42              ( ( P @ X23 )
% 0.16/0.42             => ( P @ ( cons_P1475164433e_form @ X1 @ X23 ) ) )
% 0.16/0.42         => ( P @ List ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.inducts
% 0.16/0.42  thf(fact_76_list_Oinducts,axiom,
% 0.16/0.42      ! [P: list_nat > $o,List: list_nat] :
% 0.16/0.42        ( ( P @ nil_nat )
% 0.16/0.42       => ( ! [X1: nat,X23: list_nat] :
% 0.16/0.42              ( ( P @ X23 )
% 0.16/0.42             => ( P @ ( cons_nat @ X1 @ X23 ) ) )
% 0.16/0.42         => ( P @ List ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.inducts
% 0.16/0.42  thf(fact_77_list_Oexhaust,axiom,
% 0.16/0.42      ! [Y: list_P512754263e_form] :
% 0.16/0.42        ( ( Y != nil_Pr1384483009e_form )
% 0.16/0.42       => ~ ! [X213: prover1687215943e_form,X223: list_P512754263e_form] :
% 0.16/0.42              ( Y
% 0.16/0.42             != ( cons_P1475164433e_form @ X213 @ X223 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.exhaust
% 0.16/0.42  thf(fact_78_list_Oexhaust,axiom,
% 0.16/0.42      ! [Y: list_nat] :
% 0.16/0.42        ( ( Y != nil_nat )
% 0.16/0.42       => ~ ! [X213: nat,X223: list_nat] :
% 0.16/0.42              ( Y
% 0.16/0.42             != ( cons_nat @ X213 @ X223 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.exhaust
% 0.16/0.42  thf(fact_79_mem__Collect__eq,axiom,
% 0.16/0.42      ! [A: nat,P: nat > $o] :
% 0.16/0.42        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.16/0.42        = ( P @ A ) ) ).
% 0.16/0.42  
% 0.16/0.42  % mem_Collect_eq
% 0.16/0.42  thf(fact_80_Collect__mem__eq,axiom,
% 0.16/0.42      ! [A4: set_nat] :
% 0.16/0.42        ( ( collect_nat
% 0.16/0.42          @ ^ [X3: nat] : ( member_nat @ X3 @ A4 ) )
% 0.16/0.42        = A4 ) ).
% 0.16/0.42  
% 0.16/0.42  % Collect_mem_eq
% 0.16/0.42  thf(fact_81_list_OdiscI,axiom,
% 0.16/0.42      ! [List: list_P512754263e_form,X21: prover1687215943e_form,X22: list_P512754263e_form] :
% 0.16/0.42        ( ( List
% 0.16/0.42          = ( cons_P1475164433e_form @ X21 @ X22 ) )
% 0.16/0.42       => ( List != nil_Pr1384483009e_form ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.discI
% 0.16/0.42  thf(fact_82_list_OdiscI,axiom,
% 0.16/0.42      ! [List: list_nat,X21: nat,X22: list_nat] :
% 0.16/0.42        ( ( List
% 0.16/0.42          = ( cons_nat @ X21 @ X22 ) )
% 0.16/0.42       => ( List != nil_nat ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.discI
% 0.16/0.42  thf(fact_83_list_Odistinct_I1_J,axiom,
% 0.16/0.42      ! [X21: prover1687215943e_form,X22: list_P512754263e_form] :
% 0.16/0.42        ( nil_Pr1384483009e_form
% 0.16/0.42       != ( cons_P1475164433e_form @ X21 @ X22 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.distinct(1)
% 0.16/0.42  thf(fact_84_list_Odistinct_I1_J,axiom,
% 0.16/0.42      ! [X21: nat,X22: list_nat] :
% 0.16/0.42        ( nil_nat
% 0.16/0.42       != ( cons_nat @ X21 @ X22 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.distinct(1)
% 0.16/0.42  thf(fact_85_list_Oset__cases,axiom,
% 0.16/0.42      ! [E: prover1687215943e_form,A: list_P512754263e_form] :
% 0.16/0.42        ( ( member1793840734e_form @ E @ ( set_Pr1105237746e_form @ A ) )
% 0.16/0.42       => ( ! [Z2: list_P512754263e_form] :
% 0.16/0.42              ( A
% 0.16/0.42             != ( cons_P1475164433e_form @ E @ Z2 ) )
% 0.16/0.42         => ~ ! [Z1: prover1687215943e_form,Z2: list_P512754263e_form] :
% 0.16/0.42                ( ( A
% 0.16/0.42                  = ( cons_P1475164433e_form @ Z1 @ Z2 ) )
% 0.16/0.42               => ~ ( member1793840734e_form @ E @ ( set_Pr1105237746e_form @ Z2 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.set_cases
% 0.16/0.42  thf(fact_86_list_Oset__cases,axiom,
% 0.16/0.42      ! [E: nat,A: list_nat] :
% 0.16/0.42        ( ( member_nat @ E @ ( set_nat2 @ A ) )
% 0.16/0.42       => ( ! [Z2: list_nat] :
% 0.16/0.42              ( A
% 0.16/0.42             != ( cons_nat @ E @ Z2 ) )
% 0.16/0.42         => ~ ! [Z1: nat,Z2: list_nat] :
% 0.16/0.42                ( ( A
% 0.16/0.42                  = ( cons_nat @ Z1 @ Z2 ) )
% 0.16/0.42               => ~ ( member_nat @ E @ ( set_nat2 @ Z2 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.set_cases
% 0.16/0.42  thf(fact_87_set__ConsD,axiom,
% 0.16/0.42      ! [Y: prover1687215943e_form,X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( member1793840734e_form @ Y @ ( set_Pr1105237746e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) ) )
% 0.16/0.42       => ( ( Y = X2 )
% 0.16/0.42          | ( member1793840734e_form @ Y @ ( set_Pr1105237746e_form @ Xs ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % set_ConsD
% 0.16/0.42  thf(fact_88_set__ConsD,axiom,
% 0.16/0.42      ! [Y: nat,X2: nat,Xs: list_nat] :
% 0.16/0.42        ( ( member_nat @ Y @ ( set_nat2 @ ( cons_nat @ X2 @ Xs ) ) )
% 0.16/0.42       => ( ( Y = X2 )
% 0.16/0.42          | ( member_nat @ Y @ ( set_nat2 @ Xs ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % set_ConsD
% 0.16/0.42  thf(fact_89_list_Oset__intros_I1_J,axiom,
% 0.16/0.42      ! [X21: prover1687215943e_form,X22: list_P512754263e_form] : ( member1793840734e_form @ X21 @ ( set_Pr1105237746e_form @ ( cons_P1475164433e_form @ X21 @ X22 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.set_intros(1)
% 0.16/0.42  thf(fact_90_list_Oset__intros_I1_J,axiom,
% 0.16/0.42      ! [X21: nat,X22: list_nat] : ( member_nat @ X21 @ ( set_nat2 @ ( cons_nat @ X21 @ X22 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.set_intros(1)
% 0.16/0.42  thf(fact_91_list_Oset__intros_I2_J,axiom,
% 0.16/0.42      ! [Y: prover1687215943e_form,X22: list_P512754263e_form,X21: prover1687215943e_form] :
% 0.16/0.42        ( ( member1793840734e_form @ Y @ ( set_Pr1105237746e_form @ X22 ) )
% 0.16/0.42       => ( member1793840734e_form @ Y @ ( set_Pr1105237746e_form @ ( cons_P1475164433e_form @ X21 @ X22 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.set_intros(2)
% 0.16/0.42  thf(fact_92_list_Oset__intros_I2_J,axiom,
% 0.16/0.42      ! [Y: nat,X22: list_nat,X21: nat] :
% 0.16/0.42        ( ( member_nat @ Y @ ( set_nat2 @ X22 ) )
% 0.16/0.42       => ( member_nat @ Y @ ( set_nat2 @ ( cons_nat @ X21 @ X22 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % list.set_intros(2)
% 0.16/0.42  thf(fact_93_append__Cons,axiom,
% 0.16/0.42      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.42        ( ( append1038020460e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ Ys )
% 0.16/0.42        = ( cons_P1475164433e_form @ X2 @ ( append1038020460e_form @ Xs @ Ys ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_Cons
% 0.16/0.42  thf(fact_94_append__Cons,axiom,
% 0.16/0.42      ! [X2: nat,Xs: list_nat,Ys: list_nat] :
% 0.16/0.42        ( ( append_nat @ ( cons_nat @ X2 @ Xs ) @ Ys )
% 0.16/0.42        = ( cons_nat @ X2 @ ( append_nat @ Xs @ Ys ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_Cons
% 0.16/0.42  thf(fact_95_Cons__eq__appendI,axiom,
% 0.16/0.42      ! [X2: prover1687215943e_form,Xs1: list_P512754263e_form,Ys: list_P512754263e_form,Xs: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.16/0.42        ( ( ( cons_P1475164433e_form @ X2 @ Xs1 )
% 0.16/0.42          = Ys )
% 0.16/0.42       => ( ( Xs
% 0.16/0.42            = ( append1038020460e_form @ Xs1 @ Zs2 ) )
% 0.16/0.42         => ( ( cons_P1475164433e_form @ X2 @ Xs )
% 0.16/0.42            = ( append1038020460e_form @ Ys @ Zs2 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % Cons_eq_appendI
% 0.16/0.42  thf(fact_96_Cons__eq__appendI,axiom,
% 0.16/0.42      ! [X2: nat,Xs1: list_nat,Ys: list_nat,Xs: list_nat,Zs2: list_nat] :
% 0.16/0.42        ( ( ( cons_nat @ X2 @ Xs1 )
% 0.16/0.42          = Ys )
% 0.16/0.42       => ( ( Xs
% 0.16/0.42            = ( append_nat @ Xs1 @ Zs2 ) )
% 0.16/0.42         => ( ( cons_nat @ X2 @ Xs )
% 0.16/0.42            = ( append_nat @ Ys @ Zs2 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % Cons_eq_appendI
% 0.16/0.42  thf(fact_97_append_Oleft__neutral,axiom,
% 0.16/0.42      ! [A: list_P512754263e_form] :
% 0.16/0.42        ( ( append1038020460e_form @ nil_Pr1384483009e_form @ A )
% 0.16/0.42        = A ) ).
% 0.16/0.42  
% 0.16/0.42  % append.left_neutral
% 0.16/0.42  thf(fact_98_append_Oleft__neutral,axiom,
% 0.16/0.42      ! [A: list_nat] :
% 0.16/0.42        ( ( append_nat @ nil_nat @ A )
% 0.16/0.42        = A ) ).
% 0.16/0.42  
% 0.16/0.42  % append.left_neutral
% 0.16/0.42  thf(fact_99_append__Nil,axiom,
% 0.16/0.42      ! [Ys: list_P512754263e_form] :
% 0.16/0.42        ( ( append1038020460e_form @ nil_Pr1384483009e_form @ Ys )
% 0.16/0.42        = Ys ) ).
% 0.16/0.42  
% 0.16/0.42  % append_Nil
% 0.16/0.42  thf(fact_100_append__Nil,axiom,
% 0.16/0.42      ! [Ys: list_nat] :
% 0.16/0.42        ( ( append_nat @ nil_nat @ Ys )
% 0.16/0.42        = Ys ) ).
% 0.16/0.42  
% 0.16/0.42  % append_Nil
% 0.16/0.42  thf(fact_101_eq__Nil__appendI,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.42        ( ( Xs = Ys )
% 0.16/0.42       => ( Xs
% 0.16/0.42          = ( append1038020460e_form @ nil_Pr1384483009e_form @ Ys ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % eq_Nil_appendI
% 0.16/0.42  thf(fact_102_eq__Nil__appendI,axiom,
% 0.16/0.42      ! [Xs: list_nat,Ys: list_nat] :
% 0.16/0.42        ( ( Xs = Ys )
% 0.16/0.42       => ( Xs
% 0.16/0.42          = ( append_nat @ nil_nat @ Ys ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % eq_Nil_appendI
% 0.16/0.42  thf(fact_103_rev__nonempty__induct,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,P: list_P512754263e_form > $o] :
% 0.16/0.42        ( ( Xs != nil_Pr1384483009e_form )
% 0.16/0.42       => ( ! [X: prover1687215943e_form] : ( P @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) )
% 0.16/0.42         => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.16/0.42                ( ( Xs2 != nil_Pr1384483009e_form )
% 0.16/0.42               => ( ( P @ Xs2 )
% 0.16/0.42                 => ( P @ ( append1038020460e_form @ Xs2 @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) ) ) ) )
% 0.16/0.42           => ( P @ Xs ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % rev_nonempty_induct
% 0.16/0.42  thf(fact_104_rev__nonempty__induct,axiom,
% 0.16/0.42      ! [Xs: list_nat,P: list_nat > $o] :
% 0.16/0.42        ( ( Xs != nil_nat )
% 0.16/0.42       => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 0.16/0.42         => ( ! [X: nat,Xs2: list_nat] :
% 0.16/0.42                ( ( Xs2 != nil_nat )
% 0.16/0.42               => ( ( P @ Xs2 )
% 0.16/0.42                 => ( P @ ( append_nat @ Xs2 @ ( cons_nat @ X @ nil_nat ) ) ) ) )
% 0.16/0.42           => ( P @ Xs ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % rev_nonempty_induct
% 0.16/0.42  thf(fact_105_append__eq__Cons__conv,axiom,
% 0.16/0.42      ! [Ys: list_P512754263e_form,Zs2: list_P512754263e_form,X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( ( append1038020460e_form @ Ys @ Zs2 )
% 0.16/0.42          = ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.16/0.42        = ( ( ( Ys = nil_Pr1384483009e_form )
% 0.16/0.42            & ( Zs2
% 0.16/0.42              = ( cons_P1475164433e_form @ X2 @ Xs ) ) )
% 0.16/0.42          | ? [Ys4: list_P512754263e_form] :
% 0.16/0.42              ( ( Ys
% 0.16/0.42                = ( cons_P1475164433e_form @ X2 @ Ys4 ) )
% 0.16/0.42              & ( ( append1038020460e_form @ Ys4 @ Zs2 )
% 0.16/0.42                = Xs ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_eq_Cons_conv
% 0.16/0.42  thf(fact_106_append__eq__Cons__conv,axiom,
% 0.16/0.42      ! [Ys: list_nat,Zs2: list_nat,X2: nat,Xs: list_nat] :
% 0.16/0.42        ( ( ( append_nat @ Ys @ Zs2 )
% 0.16/0.42          = ( cons_nat @ X2 @ Xs ) )
% 0.16/0.42        = ( ( ( Ys = nil_nat )
% 0.16/0.42            & ( Zs2
% 0.16/0.42              = ( cons_nat @ X2 @ Xs ) ) )
% 0.16/0.42          | ? [Ys4: list_nat] :
% 0.16/0.42              ( ( Ys
% 0.16/0.42                = ( cons_nat @ X2 @ Ys4 ) )
% 0.16/0.42              & ( ( append_nat @ Ys4 @ Zs2 )
% 0.16/0.42                = Xs ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_eq_Cons_conv
% 0.16/0.42  thf(fact_107_Cons__eq__append__conv,axiom,
% 0.16/0.42      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.16/0.42        ( ( ( cons_P1475164433e_form @ X2 @ Xs )
% 0.16/0.42          = ( append1038020460e_form @ Ys @ Zs2 ) )
% 0.16/0.42        = ( ( ( Ys = nil_Pr1384483009e_form )
% 0.16/0.42            & ( ( cons_P1475164433e_form @ X2 @ Xs )
% 0.16/0.42              = Zs2 ) )
% 0.16/0.42          | ? [Ys4: list_P512754263e_form] :
% 0.16/0.42              ( ( ( cons_P1475164433e_form @ X2 @ Ys4 )
% 0.16/0.42                = Ys )
% 0.16/0.42              & ( Xs
% 0.16/0.42                = ( append1038020460e_form @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % Cons_eq_append_conv
% 0.16/0.42  thf(fact_108_Cons__eq__append__conv,axiom,
% 0.16/0.42      ! [X2: nat,Xs: list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.16/0.42        ( ( ( cons_nat @ X2 @ Xs )
% 0.16/0.42          = ( append_nat @ Ys @ Zs2 ) )
% 0.16/0.42        = ( ( ( Ys = nil_nat )
% 0.16/0.42            & ( ( cons_nat @ X2 @ Xs )
% 0.16/0.42              = Zs2 ) )
% 0.16/0.42          | ? [Ys4: list_nat] :
% 0.16/0.42              ( ( ( cons_nat @ X2 @ Ys4 )
% 0.16/0.42                = Ys )
% 0.16/0.42              & ( Xs
% 0.16/0.42                = ( append_nat @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % Cons_eq_append_conv
% 0.16/0.42  thf(fact_109_rev__exhaust,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( Xs != nil_Pr1384483009e_form )
% 0.16/0.42       => ~ ! [Ys2: list_P512754263e_form,Y2: prover1687215943e_form] :
% 0.16/0.42              ( Xs
% 0.16/0.42             != ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ Y2 @ nil_Pr1384483009e_form ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % rev_exhaust
% 0.16/0.42  thf(fact_110_rev__exhaust,axiom,
% 0.16/0.42      ! [Xs: list_nat] :
% 0.16/0.42        ( ( Xs != nil_nat )
% 0.16/0.42       => ~ ! [Ys2: list_nat,Y2: nat] :
% 0.16/0.42              ( Xs
% 0.16/0.42             != ( append_nat @ Ys2 @ ( cons_nat @ Y2 @ nil_nat ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % rev_exhaust
% 0.16/0.42  thf(fact_111_rev__induct,axiom,
% 0.16/0.42      ! [P: list_P512754263e_form > $o,Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( P @ nil_Pr1384483009e_form )
% 0.16/0.42       => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.16/0.42              ( ( P @ Xs2 )
% 0.16/0.42             => ( P @ ( append1038020460e_form @ Xs2 @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) ) ) )
% 0.16/0.42         => ( P @ Xs ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % rev_induct
% 0.16/0.42  thf(fact_112_rev__induct,axiom,
% 0.16/0.42      ! [P: list_nat > $o,Xs: list_nat] :
% 0.16/0.42        ( ( P @ nil_nat )
% 0.16/0.42       => ( ! [X: nat,Xs2: list_nat] :
% 0.16/0.42              ( ( P @ Xs2 )
% 0.16/0.42             => ( P @ ( append_nat @ Xs2 @ ( cons_nat @ X @ nil_nat ) ) ) )
% 0.16/0.42         => ( P @ Xs ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % rev_induct
% 0.16/0.42  thf(fact_113_split__list__first__prop__iff,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.16/0.42        ( ( ? [X3: prover1687215943e_form] :
% 0.16/0.42              ( ( member1793840734e_form @ X3 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.42              & ( P @ X3 ) ) )
% 0.16/0.42        = ( ? [Ys3: list_P512754263e_form,X3: prover1687215943e_form] :
% 0.16/0.42              ( ? [Zs3: list_P512754263e_form] :
% 0.16/0.42                  ( Xs
% 0.16/0.42                  = ( append1038020460e_form @ Ys3 @ ( cons_P1475164433e_form @ X3 @ Zs3 ) ) )
% 0.16/0.42              & ( P @ X3 )
% 0.16/0.42              & ! [Y3: prover1687215943e_form] :
% 0.16/0.42                  ( ( member1793840734e_form @ Y3 @ ( set_Pr1105237746e_form @ Ys3 ) )
% 0.16/0.42                 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list_first_prop_iff
% 0.16/0.42  thf(fact_114_split__list__first__prop__iff,axiom,
% 0.16/0.42      ! [Xs: list_nat,P: nat > $o] :
% 0.16/0.42        ( ( ? [X3: nat] :
% 0.16/0.42              ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.16/0.42              & ( P @ X3 ) ) )
% 0.16/0.42        = ( ? [Ys3: list_nat,X3: nat] :
% 0.16/0.42              ( ? [Zs3: list_nat] :
% 0.16/0.42                  ( Xs
% 0.16/0.42                  = ( append_nat @ Ys3 @ ( cons_nat @ X3 @ Zs3 ) ) )
% 0.16/0.42              & ( P @ X3 )
% 0.16/0.42              & ! [Y3: nat] :
% 0.16/0.42                  ( ( member_nat @ Y3 @ ( set_nat2 @ Ys3 ) )
% 0.16/0.42                 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list_first_prop_iff
% 0.16/0.42  thf(fact_115_split__list__last__prop__iff,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.16/0.42        ( ( ? [X3: prover1687215943e_form] :
% 0.16/0.42              ( ( member1793840734e_form @ X3 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.42              & ( P @ X3 ) ) )
% 0.16/0.42        = ( ? [Ys3: list_P512754263e_form,X3: prover1687215943e_form,Zs3: list_P512754263e_form] :
% 0.16/0.42              ( ( Xs
% 0.16/0.42                = ( append1038020460e_form @ Ys3 @ ( cons_P1475164433e_form @ X3 @ Zs3 ) ) )
% 0.16/0.42              & ( P @ X3 )
% 0.16/0.42              & ! [Y3: prover1687215943e_form] :
% 0.16/0.42                  ( ( member1793840734e_form @ Y3 @ ( set_Pr1105237746e_form @ Zs3 ) )
% 0.16/0.42                 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list_last_prop_iff
% 0.16/0.42  thf(fact_116_split__list__last__prop__iff,axiom,
% 0.16/0.42      ! [Xs: list_nat,P: nat > $o] :
% 0.16/0.42        ( ( ? [X3: nat] :
% 0.16/0.42              ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.16/0.42              & ( P @ X3 ) ) )
% 0.16/0.42        = ( ? [Ys3: list_nat,X3: nat,Zs3: list_nat] :
% 0.16/0.42              ( ( Xs
% 0.16/0.42                = ( append_nat @ Ys3 @ ( cons_nat @ X3 @ Zs3 ) ) )
% 0.16/0.42              & ( P @ X3 )
% 0.16/0.42              & ! [Y3: nat] :
% 0.16/0.42                  ( ( member_nat @ Y3 @ ( set_nat2 @ Zs3 ) )
% 0.16/0.42                 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list_last_prop_iff
% 0.16/0.42  thf(fact_117_in__set__conv__decomp__first,axiom,
% 0.16/0.42      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.42        = ( ? [Ys3: list_P512754263e_form,Zs3: list_P512754263e_form] :
% 0.16/0.42              ( ( Xs
% 0.16/0.42                = ( append1038020460e_form @ Ys3 @ ( cons_P1475164433e_form @ X2 @ Zs3 ) ) )
% 0.16/0.42              & ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Ys3 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % in_set_conv_decomp_first
% 0.16/0.42  thf(fact_118_in__set__conv__decomp__first,axiom,
% 0.16/0.42      ! [X2: nat,Xs: list_nat] :
% 0.16/0.42        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.16/0.42        = ( ? [Ys3: list_nat,Zs3: list_nat] :
% 0.16/0.42              ( ( Xs
% 0.16/0.42                = ( append_nat @ Ys3 @ ( cons_nat @ X2 @ Zs3 ) ) )
% 0.16/0.42              & ~ ( member_nat @ X2 @ ( set_nat2 @ Ys3 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % in_set_conv_decomp_first
% 0.16/0.42  thf(fact_119_in__set__conv__decomp__last,axiom,
% 0.16/0.42      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.42        = ( ? [Ys3: list_P512754263e_form,Zs3: list_P512754263e_form] :
% 0.16/0.42              ( ( Xs
% 0.16/0.42                = ( append1038020460e_form @ Ys3 @ ( cons_P1475164433e_form @ X2 @ Zs3 ) ) )
% 0.16/0.42              & ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Zs3 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % in_set_conv_decomp_last
% 0.16/0.42  thf(fact_120_in__set__conv__decomp__last,axiom,
% 0.16/0.42      ! [X2: nat,Xs: list_nat] :
% 0.16/0.42        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.16/0.42        = ( ? [Ys3: list_nat,Zs3: list_nat] :
% 0.16/0.42              ( ( Xs
% 0.16/0.42                = ( append_nat @ Ys3 @ ( cons_nat @ X2 @ Zs3 ) ) )
% 0.16/0.42              & ~ ( member_nat @ X2 @ ( set_nat2 @ Zs3 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % in_set_conv_decomp_last
% 0.16/0.42  thf(fact_121_split__list__first__propE,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.16/0.42        ( ? [X4: prover1687215943e_form] :
% 0.16/0.42            ( ( member1793840734e_form @ X4 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.42            & ( P @ X4 ) )
% 0.16/0.42       => ~ ! [Ys2: list_P512754263e_form,X: prover1687215943e_form] :
% 0.16/0.42              ( ? [Zs: list_P512754263e_form] :
% 0.16/0.42                  ( Xs
% 0.16/0.42                  = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X @ Zs ) ) )
% 0.16/0.42             => ( ( P @ X )
% 0.16/0.42               => ~ ! [Xa: prover1687215943e_form] :
% 0.16/0.42                      ( ( member1793840734e_form @ Xa @ ( set_Pr1105237746e_form @ Ys2 ) )
% 0.16/0.42                     => ~ ( P @ Xa ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list_first_propE
% 0.16/0.42  thf(fact_122_split__list__first__propE,axiom,
% 0.16/0.42      ! [Xs: list_nat,P: nat > $o] :
% 0.16/0.42        ( ? [X4: nat] :
% 0.16/0.42            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.16/0.42            & ( P @ X4 ) )
% 0.16/0.42       => ~ ! [Ys2: list_nat,X: nat] :
% 0.16/0.42              ( ? [Zs: list_nat] :
% 0.16/0.42                  ( Xs
% 0.16/0.42                  = ( append_nat @ Ys2 @ ( cons_nat @ X @ Zs ) ) )
% 0.16/0.42             => ( ( P @ X )
% 0.16/0.42               => ~ ! [Xa: nat] :
% 0.16/0.42                      ( ( member_nat @ Xa @ ( set_nat2 @ Ys2 ) )
% 0.16/0.42                     => ~ ( P @ Xa ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list_first_propE
% 0.16/0.42  thf(fact_123_split__list__last__propE,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.16/0.42        ( ? [X4: prover1687215943e_form] :
% 0.16/0.42            ( ( member1793840734e_form @ X4 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.42            & ( P @ X4 ) )
% 0.16/0.42       => ~ ! [Ys2: list_P512754263e_form,X: prover1687215943e_form,Zs: list_P512754263e_form] :
% 0.16/0.42              ( ( Xs
% 0.16/0.42                = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X @ Zs ) ) )
% 0.16/0.42             => ( ( P @ X )
% 0.16/0.42               => ~ ! [Xa: prover1687215943e_form] :
% 0.16/0.42                      ( ( member1793840734e_form @ Xa @ ( set_Pr1105237746e_form @ Zs ) )
% 0.16/0.42                     => ~ ( P @ Xa ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list_last_propE
% 0.16/0.42  thf(fact_124_split__list__last__propE,axiom,
% 0.16/0.42      ! [Xs: list_nat,P: nat > $o] :
% 0.16/0.42        ( ? [X4: nat] :
% 0.16/0.42            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.16/0.42            & ( P @ X4 ) )
% 0.16/0.42       => ~ ! [Ys2: list_nat,X: nat,Zs: list_nat] :
% 0.16/0.42              ( ( Xs
% 0.16/0.42                = ( append_nat @ Ys2 @ ( cons_nat @ X @ Zs ) ) )
% 0.16/0.42             => ( ( P @ X )
% 0.16/0.42               => ~ ! [Xa: nat] :
% 0.16/0.42                      ( ( member_nat @ Xa @ ( set_nat2 @ Zs ) )
% 0.16/0.42                     => ~ ( P @ Xa ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list_last_propE
% 0.16/0.42  thf(fact_125_split__list__first__prop,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.16/0.42        ( ? [X4: prover1687215943e_form] :
% 0.16/0.42            ( ( member1793840734e_form @ X4 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.42            & ( P @ X4 ) )
% 0.16/0.42       => ? [Ys2: list_P512754263e_form,X: prover1687215943e_form] :
% 0.16/0.42            ( ? [Zs: list_P512754263e_form] :
% 0.16/0.42                ( Xs
% 0.16/0.42                = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X @ Zs ) ) )
% 0.16/0.42            & ( P @ X )
% 0.16/0.42            & ! [Xa: prover1687215943e_form] :
% 0.16/0.42                ( ( member1793840734e_form @ Xa @ ( set_Pr1105237746e_form @ Ys2 ) )
% 0.16/0.42               => ~ ( P @ Xa ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list_first_prop
% 0.16/0.42  thf(fact_126_split__list__first__prop,axiom,
% 0.16/0.42      ! [Xs: list_nat,P: nat > $o] :
% 0.16/0.42        ( ? [X4: nat] :
% 0.16/0.42            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.16/0.42            & ( P @ X4 ) )
% 0.16/0.42       => ? [Ys2: list_nat,X: nat] :
% 0.16/0.42            ( ? [Zs: list_nat] :
% 0.16/0.42                ( Xs
% 0.16/0.42                = ( append_nat @ Ys2 @ ( cons_nat @ X @ Zs ) ) )
% 0.16/0.42            & ( P @ X )
% 0.16/0.42            & ! [Xa: nat] :
% 0.16/0.42                ( ( member_nat @ Xa @ ( set_nat2 @ Ys2 ) )
% 0.16/0.42               => ~ ( P @ Xa ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list_first_prop
% 0.16/0.42  thf(fact_127_split__list__last__prop,axiom,
% 0.16/0.42      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.16/0.42        ( ? [X4: prover1687215943e_form] :
% 0.16/0.42            ( ( member1793840734e_form @ X4 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.42            & ( P @ X4 ) )
% 0.16/0.42       => ? [Ys2: list_P512754263e_form,X: prover1687215943e_form,Zs: list_P512754263e_form] :
% 0.16/0.42            ( ( Xs
% 0.16/0.42              = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X @ Zs ) ) )
% 0.16/0.42            & ( P @ X )
% 0.16/0.42            & ! [Xa: prover1687215943e_form] :
% 0.16/0.42                ( ( member1793840734e_form @ Xa @ ( set_Pr1105237746e_form @ Zs ) )
% 0.16/0.42               => ~ ( P @ Xa ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list_last_prop
% 0.16/0.42  thf(fact_128_split__list__last__prop,axiom,
% 0.16/0.42      ! [Xs: list_nat,P: nat > $o] :
% 0.16/0.42        ( ? [X4: nat] :
% 0.16/0.42            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.16/0.42            & ( P @ X4 ) )
% 0.16/0.42       => ? [Ys2: list_nat,X: nat,Zs: list_nat] :
% 0.16/0.42            ( ( Xs
% 0.16/0.42              = ( append_nat @ Ys2 @ ( cons_nat @ X @ Zs ) ) )
% 0.16/0.42            & ( P @ X )
% 0.16/0.42            & ! [Xa: nat] :
% 0.16/0.42                ( ( member_nat @ Xa @ ( set_nat2 @ Zs ) )
% 0.16/0.42               => ~ ( P @ Xa ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % split_list_last_prop
% 0.16/0.42  thf(fact_129_in__set__conv__decomp,axiom,
% 0.16/0.42      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.42        ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.42        = ( ? [Ys3: list_P512754263e_form,Zs3: list_P512754263e_form] :
% 0.16/0.42              ( Xs
% 0.16/0.42              = ( append1038020460e_form @ Ys3 @ ( cons_P1475164433e_form @ X2 @ Zs3 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % in_set_conv_decomp
% 0.16/0.42  thf(fact_130_in__set__conv__decomp,axiom,
% 0.16/0.42      ! [X2: nat,Xs: list_nat] :
% 0.16/0.42        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.16/0.42        = ( ? [Ys3: list_nat,Zs3: list_nat] :
% 0.16/0.42              ( Xs
% 0.16/0.42              = ( append_nat @ Ys3 @ ( cons_nat @ X2 @ Zs3 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % in_set_conv_decomp
% 0.16/0.42  thf(fact_131_append__Cons__eq__iff,axiom,
% 0.16/0.42      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form,Xs3: list_P512754263e_form,Ys5: list_P512754263e_form] :
% 0.16/0.42        ( ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.42       => ( ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Ys ) )
% 0.16/0.42         => ( ( ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ Ys ) )
% 0.16/0.42              = ( append1038020460e_form @ Xs3 @ ( cons_P1475164433e_form @ X2 @ Ys5 ) ) )
% 0.16/0.42            = ( ( Xs = Xs3 )
% 0.16/0.42              & ( Ys = Ys5 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % append_Cons_eq_iff
% 0.16/0.42  thf(fact_132_append__Cons__eq__iff,axiom,
% 0.16/0.42      ! [X2: nat,Xs: list_nat,Ys: list_nat,Xs3: list_nat,Ys5: list_nat] :
% 0.16/0.43        ( ~ ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.16/0.43       => ( ~ ( member_nat @ X2 @ ( set_nat2 @ Ys ) )
% 0.16/0.43         => ( ( ( append_nat @ Xs @ ( cons_nat @ X2 @ Ys ) )
% 0.16/0.43              = ( append_nat @ Xs3 @ ( cons_nat @ X2 @ Ys5 ) ) )
% 0.16/0.43            = ( ( Xs = Xs3 )
% 0.16/0.43              & ( Ys = Ys5 ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % append_Cons_eq_iff
% 0.16/0.43  thf(fact_133_split__list__propE,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.16/0.43        ( ? [X4: prover1687215943e_form] :
% 0.16/0.43            ( ( member1793840734e_form @ X4 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.43            & ( P @ X4 ) )
% 0.16/0.43       => ~ ! [Ys2: list_P512754263e_form,X: prover1687215943e_form] :
% 0.16/0.43              ( ? [Zs: list_P512754263e_form] :
% 0.16/0.43                  ( Xs
% 0.16/0.43                  = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X @ Zs ) ) )
% 0.16/0.43             => ~ ( P @ X ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % split_list_propE
% 0.16/0.43  thf(fact_134_split__list__propE,axiom,
% 0.16/0.43      ! [Xs: list_nat,P: nat > $o] :
% 0.16/0.43        ( ? [X4: nat] :
% 0.16/0.43            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.16/0.43            & ( P @ X4 ) )
% 0.16/0.43       => ~ ! [Ys2: list_nat,X: nat] :
% 0.16/0.43              ( ? [Zs: list_nat] :
% 0.16/0.43                  ( Xs
% 0.16/0.43                  = ( append_nat @ Ys2 @ ( cons_nat @ X @ Zs ) ) )
% 0.16/0.43             => ~ ( P @ X ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % split_list_propE
% 0.16/0.43  thf(fact_135_split__list__first,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.43       => ? [Ys2: list_P512754263e_form,Zs: list_P512754263e_form] :
% 0.16/0.43            ( ( Xs
% 0.16/0.43              = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X2 @ Zs ) ) )
% 0.16/0.43            & ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Ys2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % split_list_first
% 0.16/0.43  thf(fact_136_split__list__first,axiom,
% 0.16/0.43      ! [X2: nat,Xs: list_nat] :
% 0.16/0.43        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.16/0.43       => ? [Ys2: list_nat,Zs: list_nat] :
% 0.16/0.43            ( ( Xs
% 0.16/0.43              = ( append_nat @ Ys2 @ ( cons_nat @ X2 @ Zs ) ) )
% 0.16/0.43            & ~ ( member_nat @ X2 @ ( set_nat2 @ Ys2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % split_list_first
% 0.16/0.43  thf(fact_137_split__list__prop,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.16/0.43        ( ? [X4: prover1687215943e_form] :
% 0.16/0.43            ( ( member1793840734e_form @ X4 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.43            & ( P @ X4 ) )
% 0.16/0.43       => ? [Ys2: list_P512754263e_form,X: prover1687215943e_form] :
% 0.16/0.43            ( ? [Zs: list_P512754263e_form] :
% 0.16/0.43                ( Xs
% 0.16/0.43                = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X @ Zs ) ) )
% 0.16/0.43            & ( P @ X ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % split_list_prop
% 0.16/0.43  thf(fact_138_split__list__prop,axiom,
% 0.16/0.43      ! [Xs: list_nat,P: nat > $o] :
% 0.16/0.43        ( ? [X4: nat] :
% 0.16/0.43            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.16/0.43            & ( P @ X4 ) )
% 0.16/0.43       => ? [Ys2: list_nat,X: nat] :
% 0.16/0.43            ( ? [Zs: list_nat] :
% 0.16/0.43                ( Xs
% 0.16/0.43                = ( append_nat @ Ys2 @ ( cons_nat @ X @ Zs ) ) )
% 0.16/0.43            & ( P @ X ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % split_list_prop
% 0.16/0.43  thf(fact_139_split__list__last,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.43       => ? [Ys2: list_P512754263e_form,Zs: list_P512754263e_form] :
% 0.16/0.43            ( ( Xs
% 0.16/0.43              = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X2 @ Zs ) ) )
% 0.16/0.43            & ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Zs ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % split_list_last
% 0.16/0.43  thf(fact_140_split__list__last,axiom,
% 0.16/0.43      ! [X2: nat,Xs: list_nat] :
% 0.16/0.43        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.16/0.43       => ? [Ys2: list_nat,Zs: list_nat] :
% 0.16/0.43            ( ( Xs
% 0.16/0.43              = ( append_nat @ Ys2 @ ( cons_nat @ X2 @ Zs ) ) )
% 0.16/0.43            & ~ ( member_nat @ X2 @ ( set_nat2 @ Zs ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % split_list_last
% 0.16/0.43  thf(fact_141_old_Oprod_Oinject,axiom,
% 0.16/0.43      ! [A: set_Pr619177522elle_U,B: nat > list_P796095576elle_U > $o,A5: set_Pr619177522elle_U,B2: nat > list_P796095576elle_U > $o] :
% 0.16/0.43        ( ( ( produc1069574002le_U_o @ A @ B )
% 0.16/0.43          = ( produc1069574002le_U_o @ A5 @ B2 ) )
% 0.16/0.43        = ( ( A = A5 )
% 0.16/0.43          & ( B = B2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % old.prod.inject
% 0.16/0.43  thf(fact_142_prod_Oinject,axiom,
% 0.16/0.43      ! [X12: set_Pr619177522elle_U,X24: nat > list_P796095576elle_U > $o,Y1: set_Pr619177522elle_U,Y23: nat > list_P796095576elle_U > $o] :
% 0.16/0.43        ( ( ( produc1069574002le_U_o @ X12 @ X24 )
% 0.16/0.43          = ( produc1069574002le_U_o @ Y1 @ Y23 ) )
% 0.16/0.43        = ( ( X12 = Y1 )
% 0.16/0.43          & ( X24 = Y23 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % prod.inject
% 0.16/0.43  thf(fact_143_the__elem__set,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form] :
% 0.16/0.43        ( ( the_el969789074e_form @ ( set_Pr1105237746e_form @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) ) )
% 0.16/0.43        = X2 ) ).
% 0.16/0.43  
% 0.16/0.43  % the_elem_set
% 0.16/0.43  thf(fact_144_the__elem__set,axiom,
% 0.16/0.43      ! [X2: nat] :
% 0.16/0.43        ( ( the_elem_nat @ ( set_nat2 @ ( cons_nat @ X2 @ nil_nat ) ) )
% 0.16/0.43        = X2 ) ).
% 0.16/0.43  
% 0.16/0.43  % the_elem_set
% 0.16/0.43  thf(fact_145_bind__simps_I2_J,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,F: prover1687215943e_form > list_P512754263e_form] :
% 0.16/0.43        ( ( bind_P1054726576e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ F )
% 0.16/0.43        = ( append1038020460e_form @ ( F @ X2 ) @ ( bind_P1054726576e_form @ Xs @ F ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % bind_simps(2)
% 0.16/0.43  thf(fact_146_bind__simps_I2_J,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,F: prover1687215943e_form > list_nat] :
% 0.16/0.43        ( ( bind_P1359331232rm_nat @ ( cons_P1475164433e_form @ X2 @ Xs ) @ F )
% 0.16/0.43        = ( append_nat @ ( F @ X2 ) @ ( bind_P1359331232rm_nat @ Xs @ F ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % bind_simps(2)
% 0.16/0.43  thf(fact_147_bind__simps_I2_J,axiom,
% 0.16/0.43      ! [X2: nat,Xs: list_nat,F: nat > list_P512754263e_form] :
% 0.16/0.43        ( ( bind_n1193922848e_form @ ( cons_nat @ X2 @ Xs ) @ F )
% 0.16/0.43        = ( append1038020460e_form @ ( F @ X2 ) @ ( bind_n1193922848e_form @ Xs @ F ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % bind_simps(2)
% 0.16/0.43  thf(fact_148_bind__simps_I2_J,axiom,
% 0.16/0.43      ! [X2: nat,Xs: list_nat,F: nat > list_nat] :
% 0.16/0.43        ( ( bind_nat_nat @ ( cons_nat @ X2 @ Xs ) @ F )
% 0.16/0.43        = ( append_nat @ ( F @ X2 ) @ ( bind_nat_nat @ Xs @ F ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % bind_simps(2)
% 0.16/0.43  thf(fact_149_maps__simps_I1_J,axiom,
% 0.16/0.43      ! [F: prover1687215943e_form > list_P512754263e_form,X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( maps_P2058952566e_form @ F @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.16/0.43        = ( append1038020460e_form @ ( F @ X2 ) @ ( maps_P2058952566e_form @ F @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % maps_simps(1)
% 0.16/0.43  thf(fact_150_maps__simps_I1_J,axiom,
% 0.16/0.43      ! [F: prover1687215943e_form > list_nat,X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( maps_P1549384538rm_nat @ F @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.16/0.43        = ( append_nat @ ( F @ X2 ) @ ( maps_P1549384538rm_nat @ F @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % maps_simps(1)
% 0.16/0.43  thf(fact_151_maps__simps_I1_J,axiom,
% 0.16/0.43      ! [F: nat > list_P512754263e_form,X2: nat,Xs: list_nat] :
% 0.16/0.43        ( ( maps_n1383976154e_form @ F @ ( cons_nat @ X2 @ Xs ) )
% 0.16/0.43        = ( append1038020460e_form @ ( F @ X2 ) @ ( maps_n1383976154e_form @ F @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % maps_simps(1)
% 0.16/0.43  thf(fact_152_maps__simps_I1_J,axiom,
% 0.16/0.43      ! [F: nat > list_nat,X2: nat,Xs: list_nat] :
% 0.16/0.43        ( ( maps_nat_nat @ F @ ( cons_nat @ X2 @ Xs ) )
% 0.16/0.43        = ( append_nat @ ( F @ X2 ) @ ( maps_nat_nat @ F @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % maps_simps(1)
% 0.16/0.43  thf(fact_153_not__in__set__insert,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.43       => ( ( insert697320747e_form @ X2 @ Xs )
% 0.16/0.43          = ( cons_P1475164433e_form @ X2 @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % not_in_set_insert
% 0.16/0.43  thf(fact_154_not__in__set__insert,axiom,
% 0.16/0.43      ! [X2: nat,Xs: list_nat] :
% 0.16/0.43        ( ~ ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.16/0.43       => ( ( insert_nat @ X2 @ Xs )
% 0.16/0.43          = ( cons_nat @ X2 @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % not_in_set_insert
% 0.16/0.43  thf(fact_155_insert__Nil,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form] :
% 0.16/0.43        ( ( insert697320747e_form @ X2 @ nil_Pr1384483009e_form )
% 0.16/0.43        = ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) ) ).
% 0.16/0.43  
% 0.16/0.43  % insert_Nil
% 0.16/0.43  thf(fact_156_insert__Nil,axiom,
% 0.16/0.43      ! [X2: nat] :
% 0.16/0.43        ( ( insert_nat @ X2 @ nil_nat )
% 0.16/0.43        = ( cons_nat @ X2 @ nil_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % insert_Nil
% 0.16/0.43  thf(fact_157_sfv__cons,axiom,
% 0.16/0.43      ! [A: prover1687215943e_form,List: list_P512754263e_form] :
% 0.16/0.43        ( ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ A @ List ) )
% 0.16/0.43        = ( append_nat @ ( prover_Mirabelle_fv @ A ) @ ( prover_Mirabelle_sfv @ List ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % sfv_cons
% 0.16/0.43  thf(fact_158_rotate1_Osimps_I2_J,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( rotate650061876e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.16/0.43        = ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % rotate1.simps(2)
% 0.16/0.43  thf(fact_159_rotate1_Osimps_I2_J,axiom,
% 0.16/0.43      ! [X2: nat,Xs: list_nat] :
% 0.16/0.43        ( ( rotate1_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.16/0.43        = ( append_nat @ Xs @ ( cons_nat @ X2 @ nil_nat ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % rotate1.simps(2)
% 0.16/0.43  thf(fact_160_butlast__snoc,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form] :
% 0.16/0.43        ( ( butlas664258165e_form @ ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) ) )
% 0.16/0.43        = Xs ) ).
% 0.16/0.43  
% 0.16/0.43  % butlast_snoc
% 0.16/0.43  thf(fact_161_butlast__snoc,axiom,
% 0.16/0.43      ! [Xs: list_nat,X2: nat] :
% 0.16/0.43        ( ( butlast_nat @ ( append_nat @ Xs @ ( cons_nat @ X2 @ nil_nat ) ) )
% 0.16/0.43        = Xs ) ).
% 0.16/0.43  
% 0.16/0.43  % butlast_snoc
% 0.16/0.43  thf(fact_162_rotate1__is__Nil__conv,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( ( rotate650061876e_form @ Xs )
% 0.16/0.43          = nil_Pr1384483009e_form )
% 0.16/0.43        = ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.16/0.43  
% 0.16/0.43  % rotate1_is_Nil_conv
% 0.16/0.43  thf(fact_163_rotate1__is__Nil__conv,axiom,
% 0.16/0.43      ! [Xs: list_nat] :
% 0.16/0.43        ( ( ( rotate1_nat @ Xs )
% 0.16/0.43          = nil_nat )
% 0.16/0.43        = ( Xs = nil_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % rotate1_is_Nil_conv
% 0.16/0.43  thf(fact_164_set__rotate1,axiom,
% 0.16/0.43      ! [Xs: list_nat] :
% 0.16/0.43        ( ( set_nat2 @ ( rotate1_nat @ Xs ) )
% 0.16/0.43        = ( set_nat2 @ Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % set_rotate1
% 0.16/0.43  thf(fact_165_in__set__insert,axiom,
% 0.16/0.43      ! [X2: nat,Xs: list_nat] :
% 0.16/0.43        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.16/0.43       => ( ( insert_nat @ X2 @ Xs )
% 0.16/0.43          = Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % in_set_insert
% 0.16/0.43  thf(fact_166_bind__simps_I1_J,axiom,
% 0.16/0.43      ! [F: prover1687215943e_form > list_P512754263e_form] :
% 0.16/0.43        ( ( bind_P1054726576e_form @ nil_Pr1384483009e_form @ F )
% 0.16/0.43        = nil_Pr1384483009e_form ) ).
% 0.16/0.43  
% 0.16/0.43  % bind_simps(1)
% 0.16/0.43  thf(fact_167_bind__simps_I1_J,axiom,
% 0.16/0.43      ! [F: prover1687215943e_form > list_nat] :
% 0.16/0.43        ( ( bind_P1359331232rm_nat @ nil_Pr1384483009e_form @ F )
% 0.16/0.43        = nil_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % bind_simps(1)
% 0.16/0.43  thf(fact_168_bind__simps_I1_J,axiom,
% 0.16/0.43      ! [F: nat > list_P512754263e_form] :
% 0.16/0.43        ( ( bind_n1193922848e_form @ nil_nat @ F )
% 0.16/0.43        = nil_Pr1384483009e_form ) ).
% 0.16/0.43  
% 0.16/0.43  % bind_simps(1)
% 0.16/0.43  thf(fact_169_bind__simps_I1_J,axiom,
% 0.16/0.43      ! [F: nat > list_nat] :
% 0.16/0.43        ( ( bind_nat_nat @ nil_nat @ F )
% 0.16/0.43        = nil_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % bind_simps(1)
% 0.16/0.43  thf(fact_170_butlast_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( butlas664258165e_form @ nil_Pr1384483009e_form )
% 0.16/0.43      = nil_Pr1384483009e_form ) ).
% 0.16/0.43  
% 0.16/0.43  % butlast.simps(1)
% 0.16/0.43  thf(fact_171_butlast_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( butlast_nat @ nil_nat )
% 0.16/0.43      = nil_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % butlast.simps(1)
% 0.16/0.43  thf(fact_172_in__set__butlastD,axiom,
% 0.16/0.43      ! [X2: nat,Xs: list_nat] :
% 0.16/0.43        ( ( member_nat @ X2 @ ( set_nat2 @ ( butlast_nat @ Xs ) ) )
% 0.16/0.43       => ( member_nat @ X2 @ ( set_nat2 @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % in_set_butlastD
% 0.16/0.43  thf(fact_173_rotate1_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( rotate650061876e_form @ nil_Pr1384483009e_form )
% 0.16/0.43      = nil_Pr1384483009e_form ) ).
% 0.16/0.43  
% 0.16/0.43  % rotate1.simps(1)
% 0.16/0.43  thf(fact_174_rotate1_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( rotate1_nat @ nil_nat )
% 0.16/0.43      = nil_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % rotate1.simps(1)
% 0.16/0.43  thf(fact_175_sorted__wrt_Ocases,axiom,
% 0.16/0.43      ! [X2: produc957084248e_form] :
% 0.16/0.43        ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o] :
% 0.16/0.43            ( X2
% 0.16/0.43           != ( produc54611594e_form @ P2 @ nil_Pr1384483009e_form ) )
% 0.16/0.43       => ~ ! [P2: prover1687215943e_form > prover1687215943e_form > $o,X: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.16/0.43              ( X2
% 0.16/0.43             != ( produc54611594e_form @ P2 @ ( cons_P1475164433e_form @ X @ Ys2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % sorted_wrt.cases
% 0.16/0.43  thf(fact_176_sorted__wrt_Ocases,axiom,
% 0.16/0.43      ! [X2: produc890077173st_nat] :
% 0.16/0.43        ( ! [P2: nat > nat > $o] :
% 0.16/0.43            ( X2
% 0.16/0.43           != ( produc939441135st_nat @ P2 @ nil_nat ) )
% 0.16/0.43       => ~ ! [P2: nat > nat > $o,X: nat,Ys2: list_nat] :
% 0.16/0.43              ( X2
% 0.16/0.43             != ( produc939441135st_nat @ P2 @ ( cons_nat @ X @ Ys2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % sorted_wrt.cases
% 0.16/0.43  thf(fact_177_successively_Ocases,axiom,
% 0.16/0.43      ! [X2: produc957084248e_form] :
% 0.16/0.43        ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o] :
% 0.16/0.43            ( X2
% 0.16/0.43           != ( produc54611594e_form @ P2 @ nil_Pr1384483009e_form ) )
% 0.16/0.43       => ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o,X: prover1687215943e_form] :
% 0.16/0.43              ( X2
% 0.16/0.43             != ( produc54611594e_form @ P2 @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) ) )
% 0.16/0.43         => ~ ! [P2: prover1687215943e_form > prover1687215943e_form > $o,X: prover1687215943e_form,Y2: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.16/0.43                ( X2
% 0.16/0.43               != ( produc54611594e_form @ P2 @ ( cons_P1475164433e_form @ X @ ( cons_P1475164433e_form @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % successively.cases
% 0.16/0.43  thf(fact_178_successively_Ocases,axiom,
% 0.16/0.43      ! [X2: produc890077173st_nat] :
% 0.16/0.43        ( ! [P2: nat > nat > $o] :
% 0.16/0.43            ( X2
% 0.16/0.43           != ( produc939441135st_nat @ P2 @ nil_nat ) )
% 0.16/0.43       => ( ! [P2: nat > nat > $o,X: nat] :
% 0.16/0.43              ( X2
% 0.16/0.43             != ( produc939441135st_nat @ P2 @ ( cons_nat @ X @ nil_nat ) ) )
% 0.16/0.43         => ~ ! [P2: nat > nat > $o,X: nat,Y2: nat,Xs2: list_nat] :
% 0.16/0.43                ( X2
% 0.16/0.43               != ( produc939441135st_nat @ P2 @ ( cons_nat @ X @ ( cons_nat @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % successively.cases
% 0.16/0.43  thf(fact_179_splice_Ocases,axiom,
% 0.16/0.43      ! [X2: produc791938916e_form] :
% 0.16/0.43        ( ! [Ys2: list_P512754263e_form] :
% 0.16/0.43            ( X2
% 0.16/0.43           != ( produc891809686e_form @ nil_Pr1384483009e_form @ Ys2 ) )
% 0.16/0.43       => ~ ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Ys2: list_P512754263e_form] :
% 0.16/0.43              ( X2
% 0.16/0.43             != ( produc891809686e_form @ ( cons_P1475164433e_form @ X @ Xs2 ) @ Ys2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % splice.cases
% 0.16/0.43  thf(fact_180_splice_Ocases,axiom,
% 0.16/0.43      ! [X2: produc1699244961st_nat] :
% 0.16/0.43        ( ! [Ys2: list_nat] :
% 0.16/0.43            ( X2
% 0.16/0.43           != ( produc1625736153st_nat @ nil_nat @ Ys2 ) )
% 0.16/0.43       => ~ ! [X: nat,Xs2: list_nat,Ys2: list_nat] :
% 0.16/0.43              ( X2
% 0.16/0.43             != ( produc1625736153st_nat @ ( cons_nat @ X @ Xs2 ) @ Ys2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % splice.cases
% 0.16/0.43  thf(fact_181_shuffles_Ocases,axiom,
% 0.16/0.43      ! [X2: produc791938916e_form] :
% 0.16/0.43        ( ! [Ys2: list_P512754263e_form] :
% 0.16/0.43            ( X2
% 0.16/0.43           != ( produc891809686e_form @ nil_Pr1384483009e_form @ Ys2 ) )
% 0.16/0.43       => ( ! [Xs2: list_P512754263e_form] :
% 0.16/0.43              ( X2
% 0.16/0.43             != ( produc891809686e_form @ Xs2 @ nil_Pr1384483009e_form ) )
% 0.16/0.43         => ~ ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Y2: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.16/0.43                ( X2
% 0.16/0.43               != ( produc891809686e_form @ ( cons_P1475164433e_form @ X @ Xs2 ) @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % shuffles.cases
% 0.16/0.43  thf(fact_182_shuffles_Ocases,axiom,
% 0.16/0.43      ! [X2: produc1699244961st_nat] :
% 0.16/0.43        ( ! [Ys2: list_nat] :
% 0.16/0.43            ( X2
% 0.16/0.43           != ( produc1625736153st_nat @ nil_nat @ Ys2 ) )
% 0.16/0.43       => ( ! [Xs2: list_nat] :
% 0.16/0.43              ( X2
% 0.16/0.43             != ( produc1625736153st_nat @ Xs2 @ nil_nat ) )
% 0.16/0.43         => ~ ! [X: nat,Xs2: list_nat,Y2: nat,Ys2: list_nat] :
% 0.16/0.43                ( X2
% 0.16/0.43               != ( produc1625736153st_nat @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y2 @ Ys2 ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % shuffles.cases
% 0.16/0.43  thf(fact_183_butlast_Osimps_I2_J,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form] :
% 0.16/0.43        ( ( ( Xs = nil_Pr1384483009e_form )
% 0.16/0.43         => ( ( butlas664258165e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.16/0.43            = nil_Pr1384483009e_form ) )
% 0.16/0.43        & ( ( Xs != nil_Pr1384483009e_form )
% 0.16/0.43         => ( ( butlas664258165e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.16/0.43            = ( cons_P1475164433e_form @ X2 @ ( butlas664258165e_form @ Xs ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % butlast.simps(2)
% 0.16/0.43  thf(fact_184_butlast_Osimps_I2_J,axiom,
% 0.16/0.43      ! [Xs: list_nat,X2: nat] :
% 0.16/0.43        ( ( ( Xs = nil_nat )
% 0.16/0.43         => ( ( butlast_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.16/0.43            = nil_nat ) )
% 0.16/0.43        & ( ( Xs != nil_nat )
% 0.16/0.43         => ( ( butlast_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.16/0.43            = ( cons_nat @ X2 @ ( butlast_nat @ Xs ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % butlast.simps(2)
% 0.16/0.43  thf(fact_185_butlast__append,axiom,
% 0.16/0.43      ! [Ys: list_P512754263e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( ( Ys = nil_Pr1384483009e_form )
% 0.16/0.43         => ( ( butlas664258165e_form @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.16/0.43            = ( butlas664258165e_form @ Xs ) ) )
% 0.16/0.43        & ( ( Ys != nil_Pr1384483009e_form )
% 0.16/0.43         => ( ( butlas664258165e_form @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.16/0.43            = ( append1038020460e_form @ Xs @ ( butlas664258165e_form @ Ys ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % butlast_append
% 0.16/0.43  thf(fact_186_butlast__append,axiom,
% 0.16/0.43      ! [Ys: list_nat,Xs: list_nat] :
% 0.16/0.43        ( ( ( Ys = nil_nat )
% 0.16/0.43         => ( ( butlast_nat @ ( append_nat @ Xs @ Ys ) )
% 0.16/0.43            = ( butlast_nat @ Xs ) ) )
% 0.16/0.43        & ( ( Ys != nil_nat )
% 0.16/0.43         => ( ( butlast_nat @ ( append_nat @ Xs @ Ys ) )
% 0.16/0.43            = ( append_nat @ Xs @ ( butlast_nat @ Ys ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % butlast_append
% 0.16/0.43  thf(fact_187_in__set__butlast__appendI,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.43        ( ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ ( butlas664258165e_form @ Xs ) ) )
% 0.16/0.43          | ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ ( butlas664258165e_form @ Ys ) ) ) )
% 0.16/0.43       => ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ ( butlas664258165e_form @ ( append1038020460e_form @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % in_set_butlast_appendI
% 0.16/0.43  thf(fact_188_in__set__butlast__appendI,axiom,
% 0.16/0.43      ! [X2: nat,Xs: list_nat,Ys: list_nat] :
% 0.16/0.43        ( ( ( member_nat @ X2 @ ( set_nat2 @ ( butlast_nat @ Xs ) ) )
% 0.16/0.43          | ( member_nat @ X2 @ ( set_nat2 @ ( butlast_nat @ Ys ) ) ) )
% 0.16/0.43       => ( member_nat @ X2 @ ( set_nat2 @ ( butlast_nat @ ( append_nat @ Xs @ Ys ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % in_set_butlast_appendI
% 0.16/0.43  thf(fact_189_maps__simps_I2_J,axiom,
% 0.16/0.43      ! [F: prover1687215943e_form > list_P512754263e_form] :
% 0.16/0.43        ( ( maps_P2058952566e_form @ F @ nil_Pr1384483009e_form )
% 0.16/0.43        = nil_Pr1384483009e_form ) ).
% 0.16/0.43  
% 0.16/0.43  % maps_simps(2)
% 0.16/0.43  thf(fact_190_maps__simps_I2_J,axiom,
% 0.16/0.43      ! [F: prover1687215943e_form > list_nat] :
% 0.16/0.43        ( ( maps_P1549384538rm_nat @ F @ nil_Pr1384483009e_form )
% 0.16/0.43        = nil_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % maps_simps(2)
% 0.16/0.43  thf(fact_191_maps__simps_I2_J,axiom,
% 0.16/0.43      ! [F: nat > list_P512754263e_form] :
% 0.16/0.43        ( ( maps_n1383976154e_form @ F @ nil_nat )
% 0.16/0.43        = nil_Pr1384483009e_form ) ).
% 0.16/0.43  
% 0.16/0.43  % maps_simps(2)
% 0.16/0.43  thf(fact_192_maps__simps_I2_J,axiom,
% 0.16/0.43      ! [F: nat > list_nat] :
% 0.16/0.43        ( ( maps_nat_nat @ F @ nil_nat )
% 0.16/0.43        = nil_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % maps_simps(2)
% 0.16/0.43  thf(fact_193_surj__pair,axiom,
% 0.16/0.43      ! [P3: produc227817602le_U_o] :
% 0.16/0.43      ? [X: set_Pr619177522elle_U,Y2: nat > list_P796095576elle_U > $o] :
% 0.16/0.43        ( P3
% 0.16/0.43        = ( produc1069574002le_U_o @ X @ Y2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % surj_pair
% 0.16/0.43  thf(fact_194_prod__cases,axiom,
% 0.16/0.43      ! [P: produc227817602le_U_o > $o,P3: produc227817602le_U_o] :
% 0.16/0.43        ( ! [A3: set_Pr619177522elle_U,B3: nat > list_P796095576elle_U > $o] : ( P @ ( produc1069574002le_U_o @ A3 @ B3 ) )
% 0.16/0.43       => ( P @ P3 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % prod_cases
% 0.16/0.43  thf(fact_195_Pair__inject,axiom,
% 0.16/0.43      ! [A: set_Pr619177522elle_U,B: nat > list_P796095576elle_U > $o,A5: set_Pr619177522elle_U,B2: nat > list_P796095576elle_U > $o] :
% 0.16/0.43        ( ( ( produc1069574002le_U_o @ A @ B )
% 0.16/0.43          = ( produc1069574002le_U_o @ A5 @ B2 ) )
% 0.16/0.43       => ~ ( ( A = A5 )
% 0.16/0.43           => ( B != B2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Pair_inject
% 0.16/0.43  thf(fact_196_old_Oprod_Oexhaust,axiom,
% 0.16/0.43      ! [Y: produc227817602le_U_o] :
% 0.16/0.43        ~ ! [A3: set_Pr619177522elle_U,B3: nat > list_P796095576elle_U > $o] :
% 0.16/0.43            ( Y
% 0.16/0.43           != ( produc1069574002le_U_o @ A3 @ B3 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % old.prod.exhaust
% 0.16/0.43  thf(fact_197_old_Oprod_Oinducts,axiom,
% 0.16/0.43      ! [P: produc227817602le_U_o > $o,Prod: produc227817602le_U_o] :
% 0.16/0.43        ( ! [A3: set_Pr619177522elle_U,B3: nat > list_P796095576elle_U > $o] : ( P @ ( produc1069574002le_U_o @ A3 @ B3 ) )
% 0.16/0.43       => ( P @ Prod ) ) ).
% 0.16/0.43  
% 0.16/0.43  % old.prod.inducts
% 0.16/0.43  thf(fact_198_List_Oinsert__def,axiom,
% 0.16/0.43      ( insert697320747e_form
% 0.16/0.43      = ( ^ [X3: prover1687215943e_form,Xs4: list_P512754263e_form] : ( if_lis1812881937e_form @ ( member1793840734e_form @ X3 @ ( set_Pr1105237746e_form @ Xs4 ) ) @ Xs4 @ ( cons_P1475164433e_form @ X3 @ Xs4 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % List.insert_def
% 0.16/0.43  thf(fact_199_List_Oinsert__def,axiom,
% 0.16/0.43      ( insert_nat
% 0.16/0.43      = ( ^ [X3: nat,Xs4: list_nat] : ( if_list_nat @ ( member_nat @ X3 @ ( set_nat2 @ Xs4 ) ) @ Xs4 @ ( cons_nat @ X3 @ Xs4 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % List.insert_def
% 0.16/0.43  thf(fact_200_flatten_Osimps_I2_J,axiom,
% 0.16/0.43      ! [A: list_P512754263e_form,List: list_l461858535e_form] :
% 0.16/0.43        ( ( prover542312166e_form @ ( cons_l1379921697e_form @ A @ List ) )
% 0.16/0.43        = ( append1038020460e_form @ A @ ( prover542312166e_form @ List ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % flatten.simps(2)
% 0.16/0.43  thf(fact_201_flatten_Osimps_I2_J,axiom,
% 0.16/0.43      ! [A: list_nat,List: list_list_nat] :
% 0.16/0.43        ( ( prover886976490en_nat @ ( cons_list_nat @ A @ List ) )
% 0.16/0.43        = ( append_nat @ A @ ( prover886976490en_nat @ List ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % flatten.simps(2)
% 0.16/0.43  thf(fact_202_flatten_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( prover542312166e_form @ nil_li1393862353e_form )
% 0.16/0.43      = nil_Pr1384483009e_form ) ).
% 0.16/0.43  
% 0.16/0.43  % flatten.simps(1)
% 0.16/0.43  thf(fact_203_flatten_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( prover886976490en_nat @ nil_list_nat )
% 0.16/0.43      = nil_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % flatten.simps(1)
% 0.16/0.43  thf(fact_204_product__lists_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( produc168439576e_form @ nil_li1393862353e_form )
% 0.16/0.43      = ( cons_l1379921697e_form @ nil_Pr1384483009e_form @ nil_li1393862353e_form ) ) ).
% 0.16/0.43  
% 0.16/0.43  % product_lists.simps(1)
% 0.16/0.43  thf(fact_205_product__lists_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( product_lists_nat @ nil_list_nat )
% 0.16/0.43      = ( cons_list_nat @ nil_nat @ nil_list_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % product_lists.simps(1)
% 0.16/0.43  thf(fact_206_append__butlast__last__id,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( Xs != nil_Pr1384483009e_form )
% 0.16/0.43       => ( ( append1038020460e_form @ ( butlas664258165e_form @ Xs ) @ ( cons_P1475164433e_form @ ( last_P1811260776e_form @ Xs ) @ nil_Pr1384483009e_form ) )
% 0.16/0.43          = Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % append_butlast_last_id
% 0.16/0.43  thf(fact_207_append__butlast__last__id,axiom,
% 0.16/0.43      ! [Xs: list_nat] :
% 0.16/0.43        ( ( Xs != nil_nat )
% 0.16/0.43       => ( ( append_nat @ ( butlast_nat @ Xs ) @ ( cons_nat @ ( last_nat @ Xs ) @ nil_nat ) )
% 0.16/0.43          = Xs ) ) ).
% 0.16/0.43  
% 0.16/0.43  % append_butlast_last_id
% 0.16/0.43  thf(fact_208_fv_Osimps_I5_J,axiom,
% 0.16/0.43      ! [F: prover1687215943e_form] :
% 0.16/0.43        ( ( prover_Mirabelle_fv @ ( prover571163162e_FAll @ F ) )
% 0.16/0.43        = ( prover2096325705preSuc @ ( prover_Mirabelle_fv @ F ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % fv.simps(5)
% 0.16/0.43  thf(fact_209_last__appendR,axiom,
% 0.16/0.43      ! [Ys: list_P512754263e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( Ys != nil_Pr1384483009e_form )
% 0.16/0.43       => ( ( last_P1811260776e_form @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.16/0.43          = ( last_P1811260776e_form @ Ys ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last_appendR
% 0.16/0.43  thf(fact_210_last__appendR,axiom,
% 0.16/0.43      ! [Ys: list_nat,Xs: list_nat] :
% 0.16/0.43        ( ( Ys != nil_nat )
% 0.16/0.43       => ( ( last_nat @ ( append_nat @ Xs @ Ys ) )
% 0.16/0.43          = ( last_nat @ Ys ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last_appendR
% 0.16/0.43  thf(fact_211_last__appendL,axiom,
% 0.16/0.43      ! [Ys: list_P512754263e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( Ys = nil_Pr1384483009e_form )
% 0.16/0.43       => ( ( last_P1811260776e_form @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.16/0.43          = ( last_P1811260776e_form @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last_appendL
% 0.16/0.43  thf(fact_212_last__appendL,axiom,
% 0.16/0.43      ! [Ys: list_nat,Xs: list_nat] :
% 0.16/0.43        ( ( Ys = nil_nat )
% 0.16/0.43       => ( ( last_nat @ ( append_nat @ Xs @ Ys ) )
% 0.16/0.43          = ( last_nat @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last_appendL
% 0.16/0.43  thf(fact_213_last__snoc,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form] :
% 0.16/0.43        ( ( last_P1811260776e_form @ ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) ) )
% 0.16/0.43        = X2 ) ).
% 0.16/0.43  
% 0.16/0.43  % last_snoc
% 0.16/0.43  thf(fact_214_last__snoc,axiom,
% 0.16/0.43      ! [Xs: list_nat,X2: nat] :
% 0.16/0.43        ( ( last_nat @ ( append_nat @ Xs @ ( cons_nat @ X2 @ nil_nat ) ) )
% 0.16/0.43        = X2 ) ).
% 0.16/0.43  
% 0.16/0.43  % last_snoc
% 0.16/0.43  thf(fact_215_last__ConsR,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form] :
% 0.16/0.43        ( ( Xs != nil_Pr1384483009e_form )
% 0.16/0.43       => ( ( last_P1811260776e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.16/0.43          = ( last_P1811260776e_form @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last_ConsR
% 0.16/0.43  thf(fact_216_last__ConsR,axiom,
% 0.16/0.43      ! [Xs: list_nat,X2: nat] :
% 0.16/0.43        ( ( Xs != nil_nat )
% 0.16/0.43       => ( ( last_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.16/0.43          = ( last_nat @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last_ConsR
% 0.16/0.43  thf(fact_217_last__ConsL,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form] :
% 0.16/0.43        ( ( Xs = nil_Pr1384483009e_form )
% 0.16/0.43       => ( ( last_P1811260776e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.16/0.43          = X2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last_ConsL
% 0.16/0.43  thf(fact_218_last__ConsL,axiom,
% 0.16/0.43      ! [Xs: list_nat,X2: nat] :
% 0.16/0.43        ( ( Xs = nil_nat )
% 0.16/0.43       => ( ( last_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.16/0.43          = X2 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last_ConsL
% 0.16/0.43  thf(fact_219_last_Osimps,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form] :
% 0.16/0.43        ( ( ( Xs = nil_Pr1384483009e_form )
% 0.16/0.43         => ( ( last_P1811260776e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.16/0.43            = X2 ) )
% 0.16/0.43        & ( ( Xs != nil_Pr1384483009e_form )
% 0.16/0.43         => ( ( last_P1811260776e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.16/0.43            = ( last_P1811260776e_form @ Xs ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last.simps
% 0.16/0.43  thf(fact_220_last_Osimps,axiom,
% 0.16/0.43      ! [Xs: list_nat,X2: nat] :
% 0.16/0.43        ( ( ( Xs = nil_nat )
% 0.16/0.43         => ( ( last_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.16/0.43            = X2 ) )
% 0.16/0.43        & ( ( Xs != nil_nat )
% 0.16/0.43         => ( ( last_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.16/0.43            = ( last_nat @ Xs ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last.simps
% 0.16/0.43  thf(fact_221_last__in__set,axiom,
% 0.16/0.43      ! [As2: list_P512754263e_form] :
% 0.16/0.43        ( ( As2 != nil_Pr1384483009e_form )
% 0.16/0.43       => ( member1793840734e_form @ ( last_P1811260776e_form @ As2 ) @ ( set_Pr1105237746e_form @ As2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last_in_set
% 0.16/0.43  thf(fact_222_last__in__set,axiom,
% 0.16/0.43      ! [As2: list_nat] :
% 0.16/0.43        ( ( As2 != nil_nat )
% 0.16/0.43       => ( member_nat @ ( last_nat @ As2 ) @ ( set_nat2 @ As2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last_in_set
% 0.16/0.43  thf(fact_223_longest__common__suffix,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.43      ? [Ss: list_P512754263e_form,Xs5: list_P512754263e_form,Ys6: list_P512754263e_form] :
% 0.16/0.43        ( ( Xs
% 0.16/0.43          = ( append1038020460e_form @ Xs5 @ Ss ) )
% 0.16/0.43        & ( Ys
% 0.16/0.43          = ( append1038020460e_form @ Ys6 @ Ss ) )
% 0.16/0.43        & ( ( Xs5 = nil_Pr1384483009e_form )
% 0.16/0.43          | ( Ys6 = nil_Pr1384483009e_form )
% 0.16/0.43          | ( ( last_P1811260776e_form @ Xs5 )
% 0.16/0.43           != ( last_P1811260776e_form @ Ys6 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % longest_common_suffix
% 0.16/0.43  thf(fact_224_longest__common__suffix,axiom,
% 0.16/0.43      ! [Xs: list_nat,Ys: list_nat] :
% 0.16/0.43      ? [Ss: list_nat,Xs5: list_nat,Ys6: list_nat] :
% 0.16/0.43        ( ( Xs
% 0.16/0.43          = ( append_nat @ Xs5 @ Ss ) )
% 0.16/0.43        & ( Ys
% 0.16/0.43          = ( append_nat @ Ys6 @ Ss ) )
% 0.16/0.43        & ( ( Xs5 = nil_nat )
% 0.16/0.43          | ( Ys6 = nil_nat )
% 0.16/0.43          | ( ( last_nat @ Xs5 )
% 0.16/0.43           != ( last_nat @ Ys6 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % longest_common_suffix
% 0.16/0.43  thf(fact_225_last__append,axiom,
% 0.16/0.43      ! [Ys: list_P512754263e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( ( Ys = nil_Pr1384483009e_form )
% 0.16/0.43         => ( ( last_P1811260776e_form @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.16/0.43            = ( last_P1811260776e_form @ Xs ) ) )
% 0.16/0.43        & ( ( Ys != nil_Pr1384483009e_form )
% 0.16/0.43         => ( ( last_P1811260776e_form @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.16/0.43            = ( last_P1811260776e_form @ Ys ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last_append
% 0.16/0.43  thf(fact_226_last__append,axiom,
% 0.16/0.43      ! [Ys: list_nat,Xs: list_nat] :
% 0.16/0.43        ( ( ( Ys = nil_nat )
% 0.16/0.43         => ( ( last_nat @ ( append_nat @ Xs @ Ys ) )
% 0.16/0.43            = ( last_nat @ Xs ) ) )
% 0.16/0.43        & ( ( Ys != nil_nat )
% 0.16/0.43         => ( ( last_nat @ ( append_nat @ Xs @ Ys ) )
% 0.16/0.43            = ( last_nat @ Ys ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % last_append
% 0.16/0.43  thf(fact_227_preSuc_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( prover2096325705preSuc @ nil_nat )
% 0.16/0.43      = nil_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % preSuc.simps(1)
% 0.16/0.43  thf(fact_228_snoc__eq__iff__butlast,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form,Ys: list_P512754263e_form] :
% 0.16/0.43        ( ( ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) )
% 0.16/0.43          = Ys )
% 0.16/0.43        = ( ( Ys != nil_Pr1384483009e_form )
% 0.16/0.43          & ( ( butlas664258165e_form @ Ys )
% 0.16/0.43            = Xs )
% 0.16/0.43          & ( ( last_P1811260776e_form @ Ys )
% 0.16/0.43            = X2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % snoc_eq_iff_butlast
% 0.16/0.43  thf(fact_229_snoc__eq__iff__butlast,axiom,
% 0.16/0.43      ! [Xs: list_nat,X2: nat,Ys: list_nat] :
% 0.16/0.43        ( ( ( append_nat @ Xs @ ( cons_nat @ X2 @ nil_nat ) )
% 0.16/0.43          = Ys )
% 0.16/0.43        = ( ( Ys != nil_nat )
% 0.16/0.43          & ( ( butlast_nat @ Ys )
% 0.16/0.43            = Xs )
% 0.16/0.43          & ( ( last_nat @ Ys )
% 0.16/0.43            = X2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % snoc_eq_iff_butlast
% 0.16/0.43  thf(fact_230_snoc__listrel1__snoc__iff,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form,Ys: list_P512754263e_form,Y: prover1687215943e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) ) @ ( append1038020460e_form @ Ys @ ( cons_P1475164433e_form @ Y @ nil_Pr1384483009e_form ) ) ) @ ( listre502458152e_form @ R ) )
% 0.16/0.43        = ( ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre502458152e_form @ R ) )
% 0.16/0.43            & ( X2 = Y ) )
% 0.16/0.43          | ( ( Xs = Ys )
% 0.16/0.43            & ( member189065477e_form @ ( produc1018812320e_form @ X2 @ Y ) @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % snoc_listrel1_snoc_iff
% 0.16/0.43  thf(fact_231_snoc__listrel1__snoc__iff,axiom,
% 0.16/0.43      ! [Xs: list_nat,X2: nat,Ys: list_nat,Y: nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ ( cons_nat @ X2 @ nil_nat ) ) @ ( append_nat @ Ys @ ( cons_nat @ Y @ nil_nat ) ) ) @ ( listrel1_nat @ R ) )
% 0.16/0.43        = ( ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) )
% 0.16/0.43            & ( X2 = Y ) )
% 0.16/0.43          | ( ( Xs = Ys )
% 0.16/0.43            & ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % snoc_listrel1_snoc_iff
% 0.16/0.43  thf(fact_232_subseqs_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( subseq1471997234e_form @ nil_Pr1384483009e_form )
% 0.16/0.43      = ( cons_l1379921697e_form @ nil_Pr1384483009e_form @ nil_li1393862353e_form ) ) ).
% 0.16/0.43  
% 0.16/0.43  % subseqs.simps(1)
% 0.16/0.43  thf(fact_233_subseqs_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( subseqs_nat @ nil_nat )
% 0.16/0.43      = ( cons_list_nat @ nil_nat @ nil_list_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % subseqs.simps(1)
% 0.16/0.43  thf(fact_234_concat__eq__append__conv,axiom,
% 0.16/0.43      ! [Xss2: list_l461858535e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.16/0.43        ( ( ( concat1664984646e_form @ Xss2 )
% 0.16/0.43          = ( append1038020460e_form @ Ys @ Zs2 ) )
% 0.16/0.43        = ( ( ( Xss2 = nil_li1393862353e_form )
% 0.16/0.43           => ( ( Ys = nil_Pr1384483009e_form )
% 0.16/0.43              & ( Zs2 = nil_Pr1384483009e_form ) ) )
% 0.16/0.43          & ( ( Xss2 != nil_li1393862353e_form )
% 0.16/0.43           => ? [Xss1: list_l461858535e_form,Xs4: list_P512754263e_form,Xs6: list_P512754263e_form,Xss22: list_l461858535e_form] :
% 0.16/0.43                ( ( Xss2
% 0.16/0.43                  = ( append1797078012e_form @ Xss1 @ ( cons_l1379921697e_form @ ( append1038020460e_form @ Xs4 @ Xs6 ) @ Xss22 ) ) )
% 0.16/0.43                & ( Ys
% 0.16/0.43                  = ( append1038020460e_form @ ( concat1664984646e_form @ Xss1 ) @ Xs4 ) )
% 0.16/0.43                & ( Zs2
% 0.16/0.43                  = ( append1038020460e_form @ Xs6 @ ( concat1664984646e_form @ Xss22 ) ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % concat_eq_append_conv
% 0.16/0.43  thf(fact_235_concat__eq__append__conv,axiom,
% 0.16/0.43      ! [Xss2: list_list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.16/0.43        ( ( ( concat_nat @ Xss2 )
% 0.16/0.43          = ( append_nat @ Ys @ Zs2 ) )
% 0.16/0.43        = ( ( ( Xss2 = nil_list_nat )
% 0.16/0.43           => ( ( Ys = nil_nat )
% 0.16/0.43              & ( Zs2 = nil_nat ) ) )
% 0.16/0.43          & ( ( Xss2 != nil_list_nat )
% 0.16/0.43           => ? [Xss1: list_list_nat,Xs4: list_nat,Xs6: list_nat,Xss22: list_list_nat] :
% 0.16/0.43                ( ( Xss2
% 0.16/0.43                  = ( append_list_nat @ Xss1 @ ( cons_list_nat @ ( append_nat @ Xs4 @ Xs6 ) @ Xss22 ) ) )
% 0.16/0.43                & ( Ys
% 0.16/0.43                  = ( append_nat @ ( concat_nat @ Xss1 ) @ Xs4 ) )
% 0.16/0.43                & ( Zs2
% 0.16/0.43                  = ( append_nat @ Xs6 @ ( concat_nat @ Xss22 ) ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % concat_eq_append_conv
% 0.16/0.43  thf(fact_236_lexord__same__pref__iff,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ Ys ) @ ( append1038020460e_form @ Xs @ Zs2 ) ) @ ( lexord1848469012e_form @ R ) )
% 0.16/0.43        = ( ? [X3: prover1687215943e_form] :
% 0.16/0.43              ( ( member1793840734e_form @ X3 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.16/0.43              & ( member189065477e_form @ ( produc1018812320e_form @ X3 @ X3 ) @ R ) )
% 0.16/0.43          | ( member650892795e_form @ ( produc891809686e_form @ Ys @ Zs2 ) @ ( lexord1848469012e_form @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_same_pref_iff
% 0.16/0.43  thf(fact_237_lexord__same__pref__iff,axiom,
% 0.16/0.43      ! [Xs: list_nat,Ys: list_nat,Zs2: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Ys ) @ ( append_nat @ Xs @ Zs2 ) ) @ ( lexord_nat @ R ) )
% 0.16/0.43        = ( ? [X3: nat] :
% 0.16/0.43              ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.16/0.43              & ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ R ) )
% 0.16/0.43          | ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Zs2 ) @ ( lexord_nat @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_same_pref_iff
% 0.16/0.43  thf(fact_238_concat__eq__Nil__conv,axiom,
% 0.16/0.43      ! [Xss2: list_l461858535e_form] :
% 0.16/0.43        ( ( ( concat1664984646e_form @ Xss2 )
% 0.16/0.43          = nil_Pr1384483009e_form )
% 0.16/0.43        = ( ! [X3: list_P512754263e_form] :
% 0.16/0.43              ( ( member1828782574e_form @ X3 @ ( set_li1219651714e_form @ Xss2 ) )
% 0.16/0.43             => ( X3 = nil_Pr1384483009e_form ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % concat_eq_Nil_conv
% 0.16/0.43  thf(fact_239_concat__eq__Nil__conv,axiom,
% 0.16/0.43      ! [Xss2: list_list_nat] :
% 0.16/0.43        ( ( ( concat_nat @ Xss2 )
% 0.16/0.43          = nil_nat )
% 0.16/0.43        = ( ! [X3: list_nat] :
% 0.16/0.43              ( ( member_list_nat @ X3 @ ( set_list_nat2 @ Xss2 ) )
% 0.16/0.43             => ( X3 = nil_nat ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % concat_eq_Nil_conv
% 0.16/0.43  thf(fact_240_Nil__eq__concat__conv,axiom,
% 0.16/0.43      ! [Xss2: list_l461858535e_form] :
% 0.16/0.43        ( ( nil_Pr1384483009e_form
% 0.16/0.43          = ( concat1664984646e_form @ Xss2 ) )
% 0.16/0.43        = ( ! [X3: list_P512754263e_form] :
% 0.16/0.43              ( ( member1828782574e_form @ X3 @ ( set_li1219651714e_form @ Xss2 ) )
% 0.16/0.43             => ( X3 = nil_Pr1384483009e_form ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Nil_eq_concat_conv
% 0.16/0.43  thf(fact_241_Nil__eq__concat__conv,axiom,
% 0.16/0.43      ! [Xss2: list_list_nat] :
% 0.16/0.43        ( ( nil_nat
% 0.16/0.43          = ( concat_nat @ Xss2 ) )
% 0.16/0.43        = ( ! [X3: list_nat] :
% 0.16/0.43              ( ( member_list_nat @ X3 @ ( set_list_nat2 @ Xss2 ) )
% 0.16/0.43             => ( X3 = nil_nat ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Nil_eq_concat_conv
% 0.16/0.43  thf(fact_242_concat__append,axiom,
% 0.16/0.43      ! [Xs: list_l461858535e_form,Ys: list_l461858535e_form] :
% 0.16/0.43        ( ( concat1664984646e_form @ ( append1797078012e_form @ Xs @ Ys ) )
% 0.16/0.43        = ( append1038020460e_form @ ( concat1664984646e_form @ Xs ) @ ( concat1664984646e_form @ Ys ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % concat_append
% 0.16/0.43  thf(fact_243_concat__append,axiom,
% 0.16/0.43      ! [Xs: list_list_nat,Ys: list_list_nat] :
% 0.16/0.43        ( ( concat_nat @ ( append_list_nat @ Xs @ Ys ) )
% 0.16/0.43        = ( append_nat @ ( concat_nat @ Xs ) @ ( concat_nat @ Ys ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % concat_append
% 0.16/0.43  thf(fact_244_Cons__listrel1__Cons,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,Y: prover1687215943e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ ( cons_P1475164433e_form @ Y @ Ys ) ) @ ( listre502458152e_form @ R ) )
% 0.16/0.43        = ( ( ( member189065477e_form @ ( produc1018812320e_form @ X2 @ Y ) @ R )
% 0.16/0.43            & ( Xs = Ys ) )
% 0.16/0.43          | ( ( X2 = Y )
% 0.16/0.43            & ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre502458152e_form @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Cons_listrel1_Cons
% 0.16/0.43  thf(fact_245_Cons__listrel1__Cons,axiom,
% 0.16/0.43      ! [X2: nat,Xs: list_nat,Y: nat,Ys: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X2 @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( listrel1_nat @ R ) )
% 0.16/0.43        = ( ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ R )
% 0.16/0.43            & ( Xs = Ys ) )
% 0.16/0.43          | ( ( X2 = Y )
% 0.16/0.43            & ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Cons_listrel1_Cons
% 0.16/0.43  thf(fact_246_lexord__cons__cons,axiom,
% 0.16/0.43      ! [A: prover1687215943e_form,X2: list_P512754263e_form,B: prover1687215943e_form,Y: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ A @ X2 ) @ ( cons_P1475164433e_form @ B @ Y ) ) @ ( lexord1848469012e_form @ R ) )
% 0.16/0.43        = ( ( member189065477e_form @ ( produc1018812320e_form @ A @ B ) @ R )
% 0.16/0.43          | ( ( A = B )
% 0.16/0.43            & ( member650892795e_form @ ( produc891809686e_form @ X2 @ Y ) @ ( lexord1848469012e_form @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_cons_cons
% 0.16/0.43  thf(fact_247_lexord__cons__cons,axiom,
% 0.16/0.43      ! [A: nat,X2: list_nat,B: nat,Y: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ A @ X2 ) @ ( cons_nat @ B @ Y ) ) @ ( lexord_nat @ R ) )
% 0.16/0.43        = ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.16/0.43          | ( ( A = B )
% 0.16/0.43            & ( member1926390090st_nat @ ( produc1625736153st_nat @ X2 @ Y ) @ ( lexord_nat @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_cons_cons
% 0.16/0.43  thf(fact_248_lexord__Nil__left,axiom,
% 0.16/0.43      ! [Y: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ nil_Pr1384483009e_form @ Y ) @ ( lexord1848469012e_form @ R ) )
% 0.16/0.43        = ( ? [A6: prover1687215943e_form,X3: list_P512754263e_form] :
% 0.16/0.43              ( Y
% 0.16/0.43              = ( cons_P1475164433e_form @ A6 @ X3 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_Nil_left
% 0.16/0.43  thf(fact_249_lexord__Nil__left,axiom,
% 0.16/0.43      ! [Y: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ nil_nat @ Y ) @ ( lexord_nat @ R ) )
% 0.16/0.43        = ( ? [A6: nat,X3: list_nat] :
% 0.16/0.43              ( Y
% 0.16/0.43              = ( cons_nat @ A6 @ X3 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_Nil_left
% 0.16/0.43  thf(fact_250_Cons__in__subseqsD,axiom,
% 0.16/0.43      ! [Y: prover1687215943e_form,Ys: list_P512754263e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( member1828782574e_form @ ( cons_P1475164433e_form @ Y @ Ys ) @ ( set_li1219651714e_form @ ( subseq1471997234e_form @ Xs ) ) )
% 0.16/0.43       => ( member1828782574e_form @ Ys @ ( set_li1219651714e_form @ ( subseq1471997234e_form @ Xs ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Cons_in_subseqsD
% 0.16/0.43  thf(fact_251_Cons__in__subseqsD,axiom,
% 0.16/0.43      ! [Y: nat,Ys: list_nat,Xs: list_nat] :
% 0.16/0.43        ( ( member_list_nat @ ( cons_nat @ Y @ Ys ) @ ( set_list_nat2 @ ( subseqs_nat @ Xs ) ) )
% 0.16/0.43       => ( member_list_nat @ Ys @ ( set_list_nat2 @ ( subseqs_nat @ Xs ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Cons_in_subseqsD
% 0.16/0.43  thf(fact_252_listrel1I2,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form,X2: prover1687215943e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre502458152e_form @ R ) )
% 0.16/0.43       => ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ ( cons_P1475164433e_form @ X2 @ Ys ) ) @ ( listre502458152e_form @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel1I2
% 0.16/0.43  thf(fact_253_listrel1I2,axiom,
% 0.16/0.43      ! [Xs: list_nat,Ys: list_nat,R: set_Pr1986765409at_nat,X2: nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) )
% 0.16/0.43       => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X2 @ Xs ) @ ( cons_nat @ X2 @ Ys ) ) @ ( listrel1_nat @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel1I2
% 0.16/0.43  thf(fact_254_not__listrel1__Nil,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ~ ( member650892795e_form @ ( produc891809686e_form @ Xs @ nil_Pr1384483009e_form ) @ ( listre502458152e_form @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % not_listrel1_Nil
% 0.16/0.43  thf(fact_255_not__listrel1__Nil,axiom,
% 0.16/0.43      ! [Xs: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ nil_nat ) @ ( listrel1_nat @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % not_listrel1_Nil
% 0.16/0.43  thf(fact_256_not__Nil__listrel1,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ~ ( member650892795e_form @ ( produc891809686e_form @ nil_Pr1384483009e_form @ Xs ) @ ( listre502458152e_form @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % not_Nil_listrel1
% 0.16/0.43  thf(fact_257_not__Nil__listrel1,axiom,
% 0.16/0.43      ! [Xs: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ nil_nat @ Xs ) @ ( listrel1_nat @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % not_Nil_listrel1
% 0.16/0.43  thf(fact_258_append__listrel1I,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form,Us2: list_P512754263e_form,Vs: list_P512754263e_form] :
% 0.16/0.43        ( ( ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre502458152e_form @ R ) )
% 0.16/0.43            & ( Us2 = Vs ) )
% 0.16/0.43          | ( ( Xs = Ys )
% 0.16/0.43            & ( member650892795e_form @ ( produc891809686e_form @ Us2 @ Vs ) @ ( listre502458152e_form @ R ) ) ) )
% 0.16/0.43       => ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ Us2 ) @ ( append1038020460e_form @ Ys @ Vs ) ) @ ( listre502458152e_form @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % append_listrel1I
% 0.16/0.43  thf(fact_259_append__listrel1I,axiom,
% 0.16/0.43      ! [Xs: list_nat,Ys: list_nat,R: set_Pr1986765409at_nat,Us2: list_nat,Vs: list_nat] :
% 0.16/0.43        ( ( ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) )
% 0.16/0.43            & ( Us2 = Vs ) )
% 0.16/0.43          | ( ( Xs = Ys )
% 0.16/0.43            & ( member1926390090st_nat @ ( produc1625736153st_nat @ Us2 @ Vs ) @ ( listrel1_nat @ R ) ) ) )
% 0.16/0.43       => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Us2 ) @ ( append_nat @ Ys @ Vs ) ) @ ( listrel1_nat @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % append_listrel1I
% 0.16/0.43  thf(fact_260_concat_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( concat1664984646e_form @ nil_li1393862353e_form )
% 0.16/0.43      = nil_Pr1384483009e_form ) ).
% 0.16/0.43  
% 0.16/0.43  % concat.simps(1)
% 0.16/0.43  thf(fact_261_concat_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( concat_nat @ nil_list_nat )
% 0.16/0.43      = nil_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % concat.simps(1)
% 0.16/0.43  thf(fact_262_concat_Osimps_I2_J,axiom,
% 0.16/0.43      ! [X2: list_P512754263e_form,Xs: list_l461858535e_form] :
% 0.16/0.43        ( ( concat1664984646e_form @ ( cons_l1379921697e_form @ X2 @ Xs ) )
% 0.16/0.43        = ( append1038020460e_form @ X2 @ ( concat1664984646e_form @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % concat.simps(2)
% 0.16/0.43  thf(fact_263_concat_Osimps_I2_J,axiom,
% 0.16/0.43      ! [X2: list_nat,Xs: list_list_nat] :
% 0.16/0.43        ( ( concat_nat @ ( cons_list_nat @ X2 @ Xs ) )
% 0.16/0.43        = ( append_nat @ X2 @ ( concat_nat @ Xs ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % concat.simps(2)
% 0.16/0.43  thf(fact_264_lexord__Nil__right,axiom,
% 0.16/0.43      ! [X2: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ~ ( member650892795e_form @ ( produc891809686e_form @ X2 @ nil_Pr1384483009e_form ) @ ( lexord1848469012e_form @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_Nil_right
% 0.16/0.43  thf(fact_265_lexord__Nil__right,axiom,
% 0.16/0.43      ! [X2: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ X2 @ nil_nat ) @ ( lexord_nat @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_Nil_right
% 0.16/0.43  thf(fact_266_lexord__append__leftI,axiom,
% 0.16/0.43      ! [U: list_P512754263e_form,V: list_P512754263e_form,R: set_Pr1189404964e_form,X2: list_P512754263e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ U @ V ) @ ( lexord1848469012e_form @ R ) )
% 0.16/0.43       => ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ X2 @ U ) @ ( append1038020460e_form @ X2 @ V ) ) @ ( lexord1848469012e_form @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_append_leftI
% 0.16/0.43  thf(fact_267_lexord__append__leftI,axiom,
% 0.16/0.43      ! [U: list_nat,V: list_nat,R: set_Pr1986765409at_nat,X2: list_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ U @ V ) @ ( lexord_nat @ R ) )
% 0.16/0.43       => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ X2 @ U ) @ ( append_nat @ X2 @ V ) ) @ ( lexord_nat @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_append_leftI
% 0.16/0.43  thf(fact_268_listrel1I1,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Y: prover1687215943e_form,R: set_Pr1189404964e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( member189065477e_form @ ( produc1018812320e_form @ X2 @ Y ) @ R )
% 0.16/0.43       => ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ ( cons_P1475164433e_form @ Y @ Xs ) ) @ ( listre502458152e_form @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel1I1
% 0.16/0.43  thf(fact_269_listrel1I1,axiom,
% 0.16/0.43      ! [X2: nat,Y: nat,R: set_Pr1986765409at_nat,Xs: list_nat] :
% 0.16/0.43        ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ R )
% 0.16/0.43       => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X2 @ Xs ) @ ( cons_nat @ Y @ Xs ) ) @ ( listrel1_nat @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel1I1
% 0.16/0.43  thf(fact_270_Cons__listrel1E1,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ Ys ) @ ( listre502458152e_form @ R ) )
% 0.16/0.43       => ( ! [Y2: prover1687215943e_form] :
% 0.16/0.43              ( ( Ys
% 0.16/0.43                = ( cons_P1475164433e_form @ Y2 @ Xs ) )
% 0.16/0.43             => ~ ( member189065477e_form @ ( produc1018812320e_form @ X2 @ Y2 ) @ R ) )
% 0.16/0.43         => ~ ! [Zs: list_P512754263e_form] :
% 0.16/0.43                ( ( Ys
% 0.16/0.43                  = ( cons_P1475164433e_form @ X2 @ Zs ) )
% 0.16/0.43               => ~ ( member650892795e_form @ ( produc891809686e_form @ Xs @ Zs ) @ ( listre502458152e_form @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Cons_listrel1E1
% 0.16/0.43  thf(fact_271_Cons__listrel1E1,axiom,
% 0.16/0.43      ! [X2: nat,Xs: list_nat,Ys: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X2 @ Xs ) @ Ys ) @ ( listrel1_nat @ R ) )
% 0.16/0.43       => ( ! [Y2: nat] :
% 0.16/0.43              ( ( Ys
% 0.16/0.43                = ( cons_nat @ Y2 @ Xs ) )
% 0.16/0.43             => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ R ) )
% 0.16/0.43         => ~ ! [Zs: list_nat] :
% 0.16/0.43                ( ( Ys
% 0.16/0.43                  = ( cons_nat @ X2 @ Zs ) )
% 0.16/0.43               => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Zs ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Cons_listrel1E1
% 0.16/0.43  thf(fact_272_Cons__listrel1E2,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,Y: prover1687215943e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ ( cons_P1475164433e_form @ Y @ Ys ) ) @ ( listre502458152e_form @ R ) )
% 0.16/0.43       => ( ! [X: prover1687215943e_form] :
% 0.16/0.43              ( ( Xs
% 0.16/0.43                = ( cons_P1475164433e_form @ X @ Ys ) )
% 0.16/0.43             => ~ ( member189065477e_form @ ( produc1018812320e_form @ X @ Y ) @ R ) )
% 0.16/0.43         => ~ ! [Zs: list_P512754263e_form] :
% 0.16/0.43                ( ( Xs
% 0.16/0.43                  = ( cons_P1475164433e_form @ Y @ Zs ) )
% 0.16/0.43               => ~ ( member650892795e_form @ ( produc891809686e_form @ Zs @ Ys ) @ ( listre502458152e_form @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Cons_listrel1E2
% 0.16/0.43  thf(fact_273_Cons__listrel1E2,axiom,
% 0.16/0.43      ! [Xs: list_nat,Y: nat,Ys: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ ( cons_nat @ Y @ Ys ) ) @ ( listrel1_nat @ R ) )
% 0.16/0.43       => ( ! [X: nat] :
% 0.16/0.43              ( ( Xs
% 0.16/0.43                = ( cons_nat @ X @ Ys ) )
% 0.16/0.43             => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R ) )
% 0.16/0.43         => ~ ! [Zs: list_nat] :
% 0.16/0.43                ( ( Xs
% 0.16/0.43                  = ( cons_nat @ Y @ Zs ) )
% 0.16/0.43               => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Zs @ Ys ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Cons_listrel1E2
% 0.16/0.43  thf(fact_274_lexord__partial__trans,axiom,
% 0.16/0.43      ! [Xs: list_nat,R: set_Pr1986765409at_nat,Ys: list_nat,Zs2: list_nat] :
% 0.16/0.43        ( ! [X: nat,Y2: nat,Z: nat] :
% 0.16/0.43            ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.16/0.43           => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R )
% 0.16/0.43             => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y2 @ Z ) @ R )
% 0.16/0.43               => ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ R ) ) ) )
% 0.16/0.43       => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( lexord_nat @ R ) )
% 0.16/0.43         => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Zs2 ) @ ( lexord_nat @ R ) )
% 0.16/0.43           => ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Zs2 ) @ ( lexord_nat @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_partial_trans
% 0.16/0.43  thf(fact_275_lexord__append__leftD,axiom,
% 0.16/0.43      ! [X2: list_P512754263e_form,U: list_P512754263e_form,V: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ X2 @ U ) @ ( append1038020460e_form @ X2 @ V ) ) @ ( lexord1848469012e_form @ R ) )
% 0.16/0.43       => ( ! [A3: prover1687215943e_form] :
% 0.16/0.43              ~ ( member189065477e_form @ ( produc1018812320e_form @ A3 @ A3 ) @ R )
% 0.16/0.43         => ( member650892795e_form @ ( produc891809686e_form @ U @ V ) @ ( lexord1848469012e_form @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_append_leftD
% 0.16/0.43  thf(fact_276_lexord__append__leftD,axiom,
% 0.16/0.43      ! [X2: list_nat,U: list_nat,V: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ X2 @ U ) @ ( append_nat @ X2 @ V ) ) @ ( lexord_nat @ R ) )
% 0.16/0.43       => ( ! [A3: nat] :
% 0.16/0.43              ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A3 @ A3 ) @ R )
% 0.16/0.43         => ( member1926390090st_nat @ ( produc1625736153st_nat @ U @ V ) @ ( lexord_nat @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_append_leftD
% 0.16/0.43  thf(fact_277_lexord__append__rightI,axiom,
% 0.16/0.43      ! [Y: list_P512754263e_form,X2: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ? [B4: prover1687215943e_form,Z3: list_P512754263e_form] :
% 0.16/0.43            ( Y
% 0.16/0.43            = ( cons_P1475164433e_form @ B4 @ Z3 ) )
% 0.16/0.43       => ( member650892795e_form @ ( produc891809686e_form @ X2 @ ( append1038020460e_form @ X2 @ Y ) ) @ ( lexord1848469012e_form @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_append_rightI
% 0.16/0.43  thf(fact_278_lexord__append__rightI,axiom,
% 0.16/0.43      ! [Y: list_nat,X2: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ? [B4: nat,Z3: list_nat] :
% 0.16/0.43            ( Y
% 0.16/0.43            = ( cons_nat @ B4 @ Z3 ) )
% 0.16/0.43       => ( member1926390090st_nat @ ( produc1625736153st_nat @ X2 @ ( append_nat @ X2 @ Y ) ) @ ( lexord_nat @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_append_rightI
% 0.16/0.43  thf(fact_279_concat__eq__appendD,axiom,
% 0.16/0.43      ! [Xss2: list_l461858535e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.16/0.43        ( ( ( concat1664984646e_form @ Xss2 )
% 0.16/0.43          = ( append1038020460e_form @ Ys @ Zs2 ) )
% 0.16/0.43       => ( ( Xss2 != nil_li1393862353e_form )
% 0.16/0.43         => ? [Xss12: list_l461858535e_form,Xs2: list_P512754263e_form,Xs5: list_P512754263e_form,Xss23: list_l461858535e_form] :
% 0.16/0.43              ( ( Xss2
% 0.16/0.43                = ( append1797078012e_form @ Xss12 @ ( cons_l1379921697e_form @ ( append1038020460e_form @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.16/0.43              & ( Ys
% 0.16/0.43                = ( append1038020460e_form @ ( concat1664984646e_form @ Xss12 ) @ Xs2 ) )
% 0.16/0.43              & ( Zs2
% 0.16/0.43                = ( append1038020460e_form @ Xs5 @ ( concat1664984646e_form @ Xss23 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % concat_eq_appendD
% 0.16/0.43  thf(fact_280_concat__eq__appendD,axiom,
% 0.16/0.43      ! [Xss2: list_list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.16/0.43        ( ( ( concat_nat @ Xss2 )
% 0.16/0.43          = ( append_nat @ Ys @ Zs2 ) )
% 0.16/0.43       => ( ( Xss2 != nil_list_nat )
% 0.16/0.43         => ? [Xss12: list_list_nat,Xs2: list_nat,Xs5: list_nat,Xss23: list_list_nat] :
% 0.16/0.43              ( ( Xss2
% 0.16/0.43                = ( append_list_nat @ Xss12 @ ( cons_list_nat @ ( append_nat @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.16/0.43              & ( Ys
% 0.16/0.43                = ( append_nat @ ( concat_nat @ Xss12 ) @ Xs2 ) )
% 0.16/0.43              & ( Zs2
% 0.16/0.43                = ( append_nat @ Xs5 @ ( concat_nat @ Xss23 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % concat_eq_appendD
% 0.16/0.43  thf(fact_281_listrel1E,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre502458152e_form @ R ) )
% 0.16/0.43       => ~ ! [X: prover1687215943e_form,Y2: prover1687215943e_form] :
% 0.16/0.43              ( ( member189065477e_form @ ( produc1018812320e_form @ X @ Y2 ) @ R )
% 0.16/0.43             => ! [Us3: list_P512754263e_form,Vs2: list_P512754263e_form] :
% 0.16/0.43                  ( ( Xs
% 0.16/0.43                    = ( append1038020460e_form @ Us3 @ ( cons_P1475164433e_form @ X @ Vs2 ) ) )
% 0.16/0.43                 => ( Ys
% 0.16/0.43                   != ( append1038020460e_form @ Us3 @ ( cons_P1475164433e_form @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel1E
% 0.16/0.43  thf(fact_282_listrel1E,axiom,
% 0.16/0.43      ! [Xs: list_nat,Ys: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) )
% 0.16/0.43       => ~ ! [X: nat,Y2: nat] :
% 0.16/0.43              ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R )
% 0.16/0.43             => ! [Us3: list_nat,Vs2: list_nat] :
% 0.16/0.43                  ( ( Xs
% 0.16/0.43                    = ( append_nat @ Us3 @ ( cons_nat @ X @ Vs2 ) ) )
% 0.16/0.43                 => ( Ys
% 0.16/0.43                   != ( append_nat @ Us3 @ ( cons_nat @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel1E
% 0.16/0.43  thf(fact_283_listrel1I,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Y: prover1687215943e_form,R: set_Pr1189404964e_form,Xs: list_P512754263e_form,Us2: list_P512754263e_form,Vs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.43        ( ( member189065477e_form @ ( produc1018812320e_form @ X2 @ Y ) @ R )
% 0.16/0.43       => ( ( Xs
% 0.16/0.43            = ( append1038020460e_form @ Us2 @ ( cons_P1475164433e_form @ X2 @ Vs ) ) )
% 0.16/0.43         => ( ( Ys
% 0.16/0.43              = ( append1038020460e_form @ Us2 @ ( cons_P1475164433e_form @ Y @ Vs ) ) )
% 0.16/0.43           => ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre502458152e_form @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel1I
% 0.16/0.43  thf(fact_284_listrel1I,axiom,
% 0.16/0.43      ! [X2: nat,Y: nat,R: set_Pr1986765409at_nat,Xs: list_nat,Us2: list_nat,Vs: list_nat,Ys: list_nat] :
% 0.16/0.43        ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ R )
% 0.16/0.43       => ( ( Xs
% 0.16/0.43            = ( append_nat @ Us2 @ ( cons_nat @ X2 @ Vs ) ) )
% 0.16/0.43         => ( ( Ys
% 0.16/0.43              = ( append_nat @ Us2 @ ( cons_nat @ Y @ Vs ) ) )
% 0.16/0.43           => ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel1I
% 0.16/0.43  thf(fact_285_lexord__append__left__rightI,axiom,
% 0.16/0.43      ! [A: prover1687215943e_form,B: prover1687215943e_form,R: set_Pr1189404964e_form,U: list_P512754263e_form,X2: list_P512754263e_form,Y: list_P512754263e_form] :
% 0.16/0.43        ( ( member189065477e_form @ ( produc1018812320e_form @ A @ B ) @ R )
% 0.16/0.43       => ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ U @ ( cons_P1475164433e_form @ A @ X2 ) ) @ ( append1038020460e_form @ U @ ( cons_P1475164433e_form @ B @ Y ) ) ) @ ( lexord1848469012e_form @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_append_left_rightI
% 0.16/0.43  thf(fact_286_lexord__append__left__rightI,axiom,
% 0.16/0.43      ! [A: nat,B: nat,R: set_Pr1986765409at_nat,U: list_nat,X2: list_nat,Y: list_nat] :
% 0.16/0.43        ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.16/0.43       => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ U @ ( cons_nat @ A @ X2 ) ) @ ( append_nat @ U @ ( cons_nat @ B @ Y ) ) ) @ ( lexord_nat @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_append_left_rightI
% 0.16/0.43  thf(fact_287_lexord__same__pref__if__irrefl,axiom,
% 0.16/0.43      ! [R: set_Pr1189404964e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.16/0.43        ( ( irrefl2121388754e_form @ R )
% 0.16/0.43       => ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ Ys ) @ ( append1038020460e_form @ Xs @ Zs2 ) ) @ ( lexord1848469012e_form @ R ) )
% 0.16/0.43          = ( member650892795e_form @ ( produc891809686e_form @ Ys @ Zs2 ) @ ( lexord1848469012e_form @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_same_pref_if_irrefl
% 0.16/0.43  thf(fact_288_lexord__same__pref__if__irrefl,axiom,
% 0.16/0.43      ! [R: set_Pr1986765409at_nat,Xs: list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.16/0.43        ( ( irrefl_nat @ R )
% 0.16/0.43       => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Ys ) @ ( append_nat @ Xs @ Zs2 ) ) @ ( lexord_nat @ R ) )
% 0.16/0.43          = ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Zs2 ) @ ( lexord_nat @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lexord_same_pref_if_irrefl
% 0.16/0.43  thf(fact_289_listrel_Ocases,axiom,
% 0.16/0.43      ! [A1: list_P512754263e_form,A2: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ A1 @ A2 ) @ ( listre1908795590e_form @ R ) )
% 0.16/0.43       => ( ( ( A1 = nil_Pr1384483009e_form )
% 0.16/0.43           => ( A2 != nil_Pr1384483009e_form ) )
% 0.16/0.43         => ~ ! [X: prover1687215943e_form,Y2: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.16/0.43                ( ( A1
% 0.16/0.43                  = ( cons_P1475164433e_form @ X @ Xs2 ) )
% 0.16/0.43               => ! [Ys2: list_P512754263e_form] :
% 0.16/0.43                    ( ( A2
% 0.16/0.43                      = ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.16/0.43                   => ( ( member189065477e_form @ ( produc1018812320e_form @ X @ Y2 ) @ R )
% 0.16/0.43                     => ~ ( member650892795e_form @ ( produc891809686e_form @ Xs2 @ Ys2 ) @ ( listre1908795590e_form @ R ) ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.cases
% 0.16/0.43  thf(fact_290_listrel_Ocases,axiom,
% 0.16/0.43      ! [A1: list_P512754263e_form,A2: list_nat,R: set_Pr957084504rm_nat] :
% 0.16/0.43        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ A1 @ A2 ) @ ( listre483706378rm_nat @ R ) )
% 0.16/0.43       => ( ( ( A1 = nil_Pr1384483009e_form )
% 0.16/0.43           => ( A2 != nil_nat ) )
% 0.16/0.43         => ~ ! [X: prover1687215943e_form,Y2: nat,Xs2: list_P512754263e_form] :
% 0.16/0.43                ( ( A1
% 0.16/0.43                  = ( cons_P1475164433e_form @ X @ Xs2 ) )
% 0.16/0.43               => ! [Ys2: list_nat] :
% 0.16/0.43                    ( ( A2
% 0.16/0.43                      = ( cons_nat @ Y2 @ Ys2 ) )
% 0.16/0.43                   => ( ( member986698273rm_nat @ ( produc1041874352rm_nat @ X @ Y2 ) @ R )
% 0.16/0.43                     => ~ ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs2 @ Ys2 ) @ ( listre483706378rm_nat @ R ) ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.cases
% 0.16/0.43  thf(fact_291_listrel_Ocases,axiom,
% 0.16/0.43      ! [A1: list_nat,A2: list_P512754263e_form,R: set_Pr816919384e_form] :
% 0.16/0.43        ( ( member1471151041e_form @ ( produc1617574096e_form @ A1 @ A2 ) @ ( listre318297994e_form @ R ) )
% 0.16/0.43       => ( ( ( A1 = nil_nat )
% 0.16/0.43           => ( A2 != nil_Pr1384483009e_form ) )
% 0.16/0.43         => ~ ! [X: nat,Y2: prover1687215943e_form,Xs2: list_nat] :
% 0.16/0.43                ( ( A1
% 0.16/0.43                  = ( cons_nat @ X @ Xs2 ) )
% 0.16/0.43               => ! [Ys2: list_P512754263e_form] :
% 0.16/0.43                    ( ( A2
% 0.16/0.43                      = ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.16/0.43                   => ( ( member18158113e_form @ ( produc876465968e_form @ X @ Y2 ) @ R )
% 0.16/0.43                     => ~ ( member1471151041e_form @ ( produc1617574096e_form @ Xs2 @ Ys2 ) @ ( listre318297994e_form @ R ) ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.cases
% 0.16/0.43  thf(fact_292_listrel_Ocases,axiom,
% 0.16/0.43      ! [A1: list_nat,A2: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ A1 @ A2 ) @ ( listrel_nat_nat @ R ) )
% 0.16/0.43       => ( ( ( A1 = nil_nat )
% 0.16/0.43           => ( A2 != nil_nat ) )
% 0.16/0.43         => ~ ! [X: nat,Y2: nat,Xs2: list_nat] :
% 0.16/0.43                ( ( A1
% 0.16/0.43                  = ( cons_nat @ X @ Xs2 ) )
% 0.16/0.43               => ! [Ys2: list_nat] :
% 0.16/0.43                    ( ( A2
% 0.16/0.43                      = ( cons_nat @ Y2 @ Ys2 ) )
% 0.16/0.43                   => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R )
% 0.16/0.43                     => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs2 @ Ys2 ) @ ( listrel_nat_nat @ R ) ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.cases
% 0.16/0.43  thf(fact_293_listrel_Ocases,axiom,
% 0.16/0.43      ! [A1: list_s1200803384elle_U,A2: list_n2139828004le_U_o,R: set_Pr1072215906le_U_o] :
% 0.16/0.43        ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ A1 @ A2 ) @ ( listre290852044le_U_o @ R ) )
% 0.16/0.43       => ( ( ( A1 = nil_se944326968elle_U )
% 0.16/0.43           => ( A2 != nil_na1584420238le_U_o ) )
% 0.16/0.43         => ~ ! [X: set_Pr619177522elle_U,Y2: nat > list_P796095576elle_U > $o,Xs2: list_s1200803384elle_U] :
% 0.16/0.43                ( ( A1
% 0.16/0.43                  = ( cons_s32021736elle_U @ X @ Xs2 ) )
% 0.16/0.43               => ! [Ys2: list_n2139828004le_U_o] :
% 0.16/0.43                    ( ( A2
% 0.16/0.43                      = ( cons_n50929118le_U_o @ Y2 @ Ys2 ) )
% 0.16/0.43                   => ( ( member1933006123le_U_o @ ( produc1069574002le_U_o @ X @ Y2 ) @ R )
% 0.16/0.43                     => ~ ( member493452075le_U_o @ ( produc1377086578le_U_o @ Xs2 @ Ys2 ) @ ( listre290852044le_U_o @ R ) ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.cases
% 0.16/0.43  thf(fact_294_listrel_Osimps,axiom,
% 0.16/0.43      ! [A1: list_P512754263e_form,A2: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ A1 @ A2 ) @ ( listre1908795590e_form @ R ) )
% 0.16/0.43        = ( ( ( A1 = nil_Pr1384483009e_form )
% 0.16/0.43            & ( A2 = nil_Pr1384483009e_form ) )
% 0.16/0.43          | ? [X3: prover1687215943e_form,Y3: prover1687215943e_form,Xs4: list_P512754263e_form,Ys3: list_P512754263e_form] :
% 0.16/0.43              ( ( A1
% 0.16/0.43                = ( cons_P1475164433e_form @ X3 @ Xs4 ) )
% 0.16/0.43              & ( A2
% 0.16/0.43                = ( cons_P1475164433e_form @ Y3 @ Ys3 ) )
% 0.16/0.43              & ( member189065477e_form @ ( produc1018812320e_form @ X3 @ Y3 ) @ R )
% 0.16/0.43              & ( member650892795e_form @ ( produc891809686e_form @ Xs4 @ Ys3 ) @ ( listre1908795590e_form @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.simps
% 0.16/0.43  thf(fact_295_listrel_Osimps,axiom,
% 0.16/0.43      ! [A1: list_P512754263e_form,A2: list_nat,R: set_Pr957084504rm_nat] :
% 0.16/0.43        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ A1 @ A2 ) @ ( listre483706378rm_nat @ R ) )
% 0.16/0.43        = ( ( ( A1 = nil_Pr1384483009e_form )
% 0.16/0.43            & ( A2 = nil_nat ) )
% 0.16/0.43          | ? [X3: prover1687215943e_form,Y3: nat,Xs4: list_P512754263e_form,Ys3: list_nat] :
% 0.16/0.43              ( ( A1
% 0.16/0.43                = ( cons_P1475164433e_form @ X3 @ Xs4 ) )
% 0.16/0.43              & ( A2
% 0.16/0.43                = ( cons_nat @ Y3 @ Ys3 ) )
% 0.16/0.43              & ( member986698273rm_nat @ ( produc1041874352rm_nat @ X3 @ Y3 ) @ R )
% 0.16/0.43              & ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs4 @ Ys3 ) @ ( listre483706378rm_nat @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.simps
% 0.16/0.43  thf(fact_296_listrel_Osimps,axiom,
% 0.16/0.43      ! [A1: list_nat,A2: list_P512754263e_form,R: set_Pr816919384e_form] :
% 0.16/0.43        ( ( member1471151041e_form @ ( produc1617574096e_form @ A1 @ A2 ) @ ( listre318297994e_form @ R ) )
% 0.16/0.43        = ( ( ( A1 = nil_nat )
% 0.16/0.43            & ( A2 = nil_Pr1384483009e_form ) )
% 0.16/0.43          | ? [X3: nat,Y3: prover1687215943e_form,Xs4: list_nat,Ys3: list_P512754263e_form] :
% 0.16/0.43              ( ( A1
% 0.16/0.43                = ( cons_nat @ X3 @ Xs4 ) )
% 0.16/0.43              & ( A2
% 0.16/0.43                = ( cons_P1475164433e_form @ Y3 @ Ys3 ) )
% 0.16/0.43              & ( member18158113e_form @ ( produc876465968e_form @ X3 @ Y3 ) @ R )
% 0.16/0.43              & ( member1471151041e_form @ ( produc1617574096e_form @ Xs4 @ Ys3 ) @ ( listre318297994e_form @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.simps
% 0.16/0.43  thf(fact_297_listrel_Osimps,axiom,
% 0.16/0.43      ! [A1: list_nat,A2: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ A1 @ A2 ) @ ( listrel_nat_nat @ R ) )
% 0.16/0.43        = ( ( ( A1 = nil_nat )
% 0.16/0.43            & ( A2 = nil_nat ) )
% 0.16/0.43          | ? [X3: nat,Y3: nat,Xs4: list_nat,Ys3: list_nat] :
% 0.16/0.43              ( ( A1
% 0.16/0.43                = ( cons_nat @ X3 @ Xs4 ) )
% 0.16/0.43              & ( A2
% 0.16/0.43                = ( cons_nat @ Y3 @ Ys3 ) )
% 0.16/0.43              & ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
% 0.16/0.43              & ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs4 @ Ys3 ) @ ( listrel_nat_nat @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.simps
% 0.16/0.43  thf(fact_298_listrel_Osimps,axiom,
% 0.16/0.43      ! [A1: list_s1200803384elle_U,A2: list_n2139828004le_U_o,R: set_Pr1072215906le_U_o] :
% 0.16/0.43        ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ A1 @ A2 ) @ ( listre290852044le_U_o @ R ) )
% 0.16/0.43        = ( ( ( A1 = nil_se944326968elle_U )
% 0.16/0.43            & ( A2 = nil_na1584420238le_U_o ) )
% 0.16/0.43          | ? [X3: set_Pr619177522elle_U,Y3: nat > list_P796095576elle_U > $o,Xs4: list_s1200803384elle_U,Ys3: list_n2139828004le_U_o] :
% 0.16/0.43              ( ( A1
% 0.16/0.43                = ( cons_s32021736elle_U @ X3 @ Xs4 ) )
% 0.16/0.43              & ( A2
% 0.16/0.43                = ( cons_n50929118le_U_o @ Y3 @ Ys3 ) )
% 0.16/0.43              & ( member1933006123le_U_o @ ( produc1069574002le_U_o @ X3 @ Y3 ) @ R )
% 0.16/0.43              & ( member493452075le_U_o @ ( produc1377086578le_U_o @ Xs4 @ Ys3 ) @ ( listre290852044le_U_o @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.simps
% 0.16/0.43  thf(fact_299_listrel_Oinducts,axiom,
% 0.16/0.43      ! [X12: list_P512754263e_form,X24: list_P512754263e_form,R: set_Pr1189404964e_form,P: list_P512754263e_form > list_P512754263e_form > $o] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ X12 @ X24 ) @ ( listre1908795590e_form @ R ) )
% 0.16/0.43       => ( ( P @ nil_Pr1384483009e_form @ nil_Pr1384483009e_form )
% 0.16/0.43         => ( ! [X: prover1687215943e_form,Y2: prover1687215943e_form,Xs2: list_P512754263e_form,Ys2: list_P512754263e_form] :
% 0.16/0.43                ( ( member189065477e_form @ ( produc1018812320e_form @ X @ Y2 ) @ R )
% 0.16/0.43               => ( ( member650892795e_form @ ( produc891809686e_form @ Xs2 @ Ys2 ) @ ( listre1908795590e_form @ R ) )
% 0.16/0.43                 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.43                   => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) ) ) ) )
% 0.16/0.43           => ( P @ X12 @ X24 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.inducts
% 0.16/0.43  thf(fact_300_listrel_Oinducts,axiom,
% 0.16/0.43      ! [X12: list_P512754263e_form,X24: list_nat,R: set_Pr957084504rm_nat,P: list_P512754263e_form > list_nat > $o] :
% 0.16/0.43        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ X12 @ X24 ) @ ( listre483706378rm_nat @ R ) )
% 0.16/0.43       => ( ( P @ nil_Pr1384483009e_form @ nil_nat )
% 0.16/0.43         => ( ! [X: prover1687215943e_form,Y2: nat,Xs2: list_P512754263e_form,Ys2: list_nat] :
% 0.16/0.43                ( ( member986698273rm_nat @ ( produc1041874352rm_nat @ X @ Y2 ) @ R )
% 0.16/0.43               => ( ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs2 @ Ys2 ) @ ( listre483706378rm_nat @ R ) )
% 0.16/0.43                 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.43                   => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ ( cons_nat @ Y2 @ Ys2 ) ) ) ) )
% 0.16/0.43           => ( P @ X12 @ X24 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.inducts
% 0.16/0.43  thf(fact_301_listrel_Oinducts,axiom,
% 0.16/0.43      ! [X12: list_nat,X24: list_P512754263e_form,R: set_Pr816919384e_form,P: list_nat > list_P512754263e_form > $o] :
% 0.16/0.43        ( ( member1471151041e_form @ ( produc1617574096e_form @ X12 @ X24 ) @ ( listre318297994e_form @ R ) )
% 0.16/0.43       => ( ( P @ nil_nat @ nil_Pr1384483009e_form )
% 0.16/0.43         => ( ! [X: nat,Y2: prover1687215943e_form,Xs2: list_nat,Ys2: list_P512754263e_form] :
% 0.16/0.43                ( ( member18158113e_form @ ( produc876465968e_form @ X @ Y2 ) @ R )
% 0.16/0.43               => ( ( member1471151041e_form @ ( produc1617574096e_form @ Xs2 @ Ys2 ) @ ( listre318297994e_form @ R ) )
% 0.16/0.43                 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.43                   => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) ) ) ) )
% 0.16/0.43           => ( P @ X12 @ X24 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.inducts
% 0.16/0.43  thf(fact_302_listrel_Oinducts,axiom,
% 0.16/0.43      ! [X12: list_nat,X24: list_nat,R: set_Pr1986765409at_nat,P: list_nat > list_nat > $o] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ X12 @ X24 ) @ ( listrel_nat_nat @ R ) )
% 0.16/0.43       => ( ( P @ nil_nat @ nil_nat )
% 0.16/0.43         => ( ! [X: nat,Y2: nat,Xs2: list_nat,Ys2: list_nat] :
% 0.16/0.43                ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R )
% 0.16/0.43               => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs2 @ Ys2 ) @ ( listrel_nat_nat @ R ) )
% 0.16/0.43                 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.43                   => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y2 @ Ys2 ) ) ) ) )
% 0.16/0.43           => ( P @ X12 @ X24 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.inducts
% 0.16/0.43  thf(fact_303_listrel_Oinducts,axiom,
% 0.16/0.43      ! [X12: list_s1200803384elle_U,X24: list_n2139828004le_U_o,R: set_Pr1072215906le_U_o,P: list_s1200803384elle_U > list_n2139828004le_U_o > $o] :
% 0.16/0.43        ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ X12 @ X24 ) @ ( listre290852044le_U_o @ R ) )
% 0.16/0.43       => ( ( P @ nil_se944326968elle_U @ nil_na1584420238le_U_o )
% 0.16/0.43         => ( ! [X: set_Pr619177522elle_U,Y2: nat > list_P796095576elle_U > $o,Xs2: list_s1200803384elle_U,Ys2: list_n2139828004le_U_o] :
% 0.16/0.43                ( ( member1933006123le_U_o @ ( produc1069574002le_U_o @ X @ Y2 ) @ R )
% 0.16/0.43               => ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ Xs2 @ Ys2 ) @ ( listre290852044le_U_o @ R ) )
% 0.16/0.43                 => ( ( P @ Xs2 @ Ys2 )
% 0.16/0.43                   => ( P @ ( cons_s32021736elle_U @ X @ Xs2 ) @ ( cons_n50929118le_U_o @ Y2 @ Ys2 ) ) ) ) )
% 0.16/0.43           => ( P @ X12 @ X24 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.inducts
% 0.16/0.43  thf(fact_304_listrel_ONil,axiom,
% 0.16/0.43      ! [R: set_Pr1189404964e_form] : ( member650892795e_form @ ( produc891809686e_form @ nil_Pr1384483009e_form @ nil_Pr1384483009e_form ) @ ( listre1908795590e_form @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.Nil
% 0.16/0.43  thf(fact_305_listrel_ONil,axiom,
% 0.16/0.43      ! [R: set_Pr957084504rm_nat] : ( member1449753665st_nat @ ( produc1897654224st_nat @ nil_Pr1384483009e_form @ nil_nat ) @ ( listre483706378rm_nat @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.Nil
% 0.16/0.43  thf(fact_306_listrel_ONil,axiom,
% 0.16/0.43      ! [R: set_Pr816919384e_form] : ( member1471151041e_form @ ( produc1617574096e_form @ nil_nat @ nil_Pr1384483009e_form ) @ ( listre318297994e_form @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.Nil
% 0.16/0.43  thf(fact_307_listrel_ONil,axiom,
% 0.16/0.43      ! [R: set_Pr1986765409at_nat] : ( member1926390090st_nat @ ( produc1625736153st_nat @ nil_nat @ nil_nat ) @ ( listrel_nat_nat @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.Nil
% 0.16/0.43  thf(fact_308_listrel__Nil1,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ nil_Pr1384483009e_form @ Xs ) @ ( listre1908795590e_form @ R ) )
% 0.16/0.43       => ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Nil1
% 0.16/0.43  thf(fact_309_listrel__Nil1,axiom,
% 0.16/0.43      ! [Xs: list_nat,R: set_Pr957084504rm_nat] :
% 0.16/0.43        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ nil_Pr1384483009e_form @ Xs ) @ ( listre483706378rm_nat @ R ) )
% 0.16/0.43       => ( Xs = nil_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Nil1
% 0.16/0.43  thf(fact_310_listrel__Nil1,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,R: set_Pr816919384e_form] :
% 0.16/0.43        ( ( member1471151041e_form @ ( produc1617574096e_form @ nil_nat @ Xs ) @ ( listre318297994e_form @ R ) )
% 0.16/0.43       => ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Nil1
% 0.16/0.43  thf(fact_311_listrel__Nil1,axiom,
% 0.16/0.43      ! [Xs: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ nil_nat @ Xs ) @ ( listrel_nat_nat @ R ) )
% 0.16/0.43       => ( Xs = nil_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Nil1
% 0.16/0.43  thf(fact_312_listrel__Nil2,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ nil_Pr1384483009e_form ) @ ( listre1908795590e_form @ R ) )
% 0.16/0.43       => ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Nil2
% 0.16/0.43  thf(fact_313_listrel__Nil2,axiom,
% 0.16/0.43      ! [Xs: list_nat,R: set_Pr816919384e_form] :
% 0.16/0.43        ( ( member1471151041e_form @ ( produc1617574096e_form @ Xs @ nil_Pr1384483009e_form ) @ ( listre318297994e_form @ R ) )
% 0.16/0.43       => ( Xs = nil_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Nil2
% 0.16/0.43  thf(fact_314_listrel__Nil2,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,R: set_Pr957084504rm_nat] :
% 0.16/0.43        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs @ nil_nat ) @ ( listre483706378rm_nat @ R ) )
% 0.16/0.43       => ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Nil2
% 0.16/0.43  thf(fact_315_listrel__Nil2,axiom,
% 0.16/0.43      ! [Xs: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ nil_nat ) @ ( listrel_nat_nat @ R ) )
% 0.16/0.43       => ( Xs = nil_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Nil2
% 0.16/0.43  thf(fact_316_listrel__Cons2,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,Y: prover1687215943e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ ( cons_P1475164433e_form @ Y @ Ys ) ) @ ( listre1908795590e_form @ R ) )
% 0.16/0.43       => ~ ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.16/0.43              ( ( Xs
% 0.16/0.43                = ( cons_P1475164433e_form @ X @ Xs2 ) )
% 0.16/0.43             => ( ( member189065477e_form @ ( produc1018812320e_form @ X @ Y ) @ R )
% 0.16/0.43               => ~ ( member650892795e_form @ ( produc891809686e_form @ Xs2 @ Ys ) @ ( listre1908795590e_form @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Cons2
% 0.16/0.43  thf(fact_317_listrel__Cons2,axiom,
% 0.16/0.43      ! [Xs: list_nat,Y: prover1687215943e_form,Ys: list_P512754263e_form,R: set_Pr816919384e_form] :
% 0.16/0.43        ( ( member1471151041e_form @ ( produc1617574096e_form @ Xs @ ( cons_P1475164433e_form @ Y @ Ys ) ) @ ( listre318297994e_form @ R ) )
% 0.16/0.43       => ~ ! [X: nat,Xs2: list_nat] :
% 0.16/0.43              ( ( Xs
% 0.16/0.43                = ( cons_nat @ X @ Xs2 ) )
% 0.16/0.43             => ( ( member18158113e_form @ ( produc876465968e_form @ X @ Y ) @ R )
% 0.16/0.43               => ~ ( member1471151041e_form @ ( produc1617574096e_form @ Xs2 @ Ys ) @ ( listre318297994e_form @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Cons2
% 0.16/0.43  thf(fact_318_listrel__Cons2,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,Y: nat,Ys: list_nat,R: set_Pr957084504rm_nat] :
% 0.16/0.43        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs @ ( cons_nat @ Y @ Ys ) ) @ ( listre483706378rm_nat @ R ) )
% 0.16/0.43       => ~ ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.16/0.43              ( ( Xs
% 0.16/0.43                = ( cons_P1475164433e_form @ X @ Xs2 ) )
% 0.16/0.43             => ( ( member986698273rm_nat @ ( produc1041874352rm_nat @ X @ Y ) @ R )
% 0.16/0.43               => ~ ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs2 @ Ys ) @ ( listre483706378rm_nat @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Cons2
% 0.16/0.43  thf(fact_319_listrel__Cons2,axiom,
% 0.16/0.43      ! [Xs: list_nat,Y: nat,Ys: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_nat_nat @ R ) )
% 0.16/0.43       => ~ ! [X: nat,Xs2: list_nat] :
% 0.16/0.43              ( ( Xs
% 0.16/0.43                = ( cons_nat @ X @ Xs2 ) )
% 0.16/0.43             => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 0.16/0.43               => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs2 @ Ys ) @ ( listrel_nat_nat @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Cons2
% 0.16/0.43  thf(fact_320_listrel__Cons2,axiom,
% 0.16/0.43      ! [Xs: list_s1200803384elle_U,Y: nat > list_P796095576elle_U > $o,Ys: list_n2139828004le_U_o,R: set_Pr1072215906le_U_o] :
% 0.16/0.43        ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ Xs @ ( cons_n50929118le_U_o @ Y @ Ys ) ) @ ( listre290852044le_U_o @ R ) )
% 0.16/0.43       => ~ ! [X: set_Pr619177522elle_U,Xs2: list_s1200803384elle_U] :
% 0.16/0.43              ( ( Xs
% 0.16/0.43                = ( cons_s32021736elle_U @ X @ Xs2 ) )
% 0.16/0.43             => ( ( member1933006123le_U_o @ ( produc1069574002le_U_o @ X @ Y ) @ R )
% 0.16/0.43               => ~ ( member493452075le_U_o @ ( produc1377086578le_U_o @ Xs2 @ Ys ) @ ( listre290852044le_U_o @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Cons2
% 0.16/0.43  thf(fact_321_listrel__Cons1,axiom,
% 0.16/0.43      ! [Y: prover1687215943e_form,Ys: list_P512754263e_form,Xs: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ Y @ Ys ) @ Xs ) @ ( listre1908795590e_form @ R ) )
% 0.16/0.43       => ~ ! [Y2: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.16/0.43              ( ( Xs
% 0.16/0.43                = ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.16/0.43             => ( ( member189065477e_form @ ( produc1018812320e_form @ Y @ Y2 ) @ R )
% 0.16/0.43               => ~ ( member650892795e_form @ ( produc891809686e_form @ Ys @ Ys2 ) @ ( listre1908795590e_form @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Cons1
% 0.16/0.43  thf(fact_322_listrel__Cons1,axiom,
% 0.16/0.43      ! [Y: prover1687215943e_form,Ys: list_P512754263e_form,Xs: list_nat,R: set_Pr957084504rm_nat] :
% 0.16/0.43        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ ( cons_P1475164433e_form @ Y @ Ys ) @ Xs ) @ ( listre483706378rm_nat @ R ) )
% 0.16/0.43       => ~ ! [Y2: nat,Ys2: list_nat] :
% 0.16/0.43              ( ( Xs
% 0.16/0.43                = ( cons_nat @ Y2 @ Ys2 ) )
% 0.16/0.43             => ( ( member986698273rm_nat @ ( produc1041874352rm_nat @ Y @ Y2 ) @ R )
% 0.16/0.43               => ~ ( member1449753665st_nat @ ( produc1897654224st_nat @ Ys @ Ys2 ) @ ( listre483706378rm_nat @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Cons1
% 0.16/0.43  thf(fact_323_listrel__Cons1,axiom,
% 0.16/0.43      ! [Y: nat,Ys: list_nat,Xs: list_P512754263e_form,R: set_Pr816919384e_form] :
% 0.16/0.43        ( ( member1471151041e_form @ ( produc1617574096e_form @ ( cons_nat @ Y @ Ys ) @ Xs ) @ ( listre318297994e_form @ R ) )
% 0.16/0.43       => ~ ! [Y2: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.16/0.43              ( ( Xs
% 0.16/0.43                = ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.16/0.43             => ( ( member18158113e_form @ ( produc876465968e_form @ Y @ Y2 ) @ R )
% 0.16/0.43               => ~ ( member1471151041e_form @ ( produc1617574096e_form @ Ys @ Ys2 ) @ ( listre318297994e_form @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Cons1
% 0.16/0.43  thf(fact_324_listrel__Cons1,axiom,
% 0.16/0.43      ! [Y: nat,Ys: list_nat,Xs: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ Y @ Ys ) @ Xs ) @ ( listrel_nat_nat @ R ) )
% 0.16/0.43       => ~ ! [Y2: nat,Ys2: list_nat] :
% 0.16/0.43              ( ( Xs
% 0.16/0.43                = ( cons_nat @ Y2 @ Ys2 ) )
% 0.16/0.43             => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y @ Y2 ) @ R )
% 0.16/0.43               => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Ys2 ) @ ( listrel_nat_nat @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Cons1
% 0.16/0.43  thf(fact_325_listrel__Cons1,axiom,
% 0.16/0.43      ! [Y: set_Pr619177522elle_U,Ys: list_s1200803384elle_U,Xs: list_n2139828004le_U_o,R: set_Pr1072215906le_U_o] :
% 0.16/0.43        ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ ( cons_s32021736elle_U @ Y @ Ys ) @ Xs ) @ ( listre290852044le_U_o @ R ) )
% 0.16/0.43       => ~ ! [Y2: nat > list_P796095576elle_U > $o,Ys2: list_n2139828004le_U_o] :
% 0.16/0.43              ( ( Xs
% 0.16/0.43                = ( cons_n50929118le_U_o @ Y2 @ Ys2 ) )
% 0.16/0.43             => ( ( member1933006123le_U_o @ ( produc1069574002le_U_o @ Y @ Y2 ) @ R )
% 0.16/0.43               => ~ ( member493452075le_U_o @ ( produc1377086578le_U_o @ Ys @ Ys2 ) @ ( listre290852044le_U_o @ R ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel_Cons1
% 0.16/0.43  thf(fact_326_listrel_OCons,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Y: prover1687215943e_form,R: set_Pr1189404964e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.43        ( ( member189065477e_form @ ( produc1018812320e_form @ X2 @ Y ) @ R )
% 0.16/0.43       => ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre1908795590e_form @ R ) )
% 0.16/0.43         => ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ ( cons_P1475164433e_form @ Y @ Ys ) ) @ ( listre1908795590e_form @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.Cons
% 0.16/0.43  thf(fact_327_listrel_OCons,axiom,
% 0.16/0.43      ! [X2: prover1687215943e_form,Y: nat,R: set_Pr957084504rm_nat,Xs: list_P512754263e_form,Ys: list_nat] :
% 0.16/0.43        ( ( member986698273rm_nat @ ( produc1041874352rm_nat @ X2 @ Y ) @ R )
% 0.16/0.43       => ( ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs @ Ys ) @ ( listre483706378rm_nat @ R ) )
% 0.16/0.43         => ( member1449753665st_nat @ ( produc1897654224st_nat @ ( cons_P1475164433e_form @ X2 @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( listre483706378rm_nat @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.Cons
% 0.16/0.43  thf(fact_328_listrel_OCons,axiom,
% 0.16/0.43      ! [X2: nat,Y: prover1687215943e_form,R: set_Pr816919384e_form,Xs: list_nat,Ys: list_P512754263e_form] :
% 0.16/0.43        ( ( member18158113e_form @ ( produc876465968e_form @ X2 @ Y ) @ R )
% 0.16/0.43       => ( ( member1471151041e_form @ ( produc1617574096e_form @ Xs @ Ys ) @ ( listre318297994e_form @ R ) )
% 0.16/0.43         => ( member1471151041e_form @ ( produc1617574096e_form @ ( cons_nat @ X2 @ Xs ) @ ( cons_P1475164433e_form @ Y @ Ys ) ) @ ( listre318297994e_form @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.Cons
% 0.16/0.43  thf(fact_329_listrel_OCons,axiom,
% 0.16/0.43      ! [X2: nat,Y: nat,R: set_Pr1986765409at_nat,Xs: list_nat,Ys: list_nat] :
% 0.16/0.43        ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ R )
% 0.16/0.43       => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel_nat_nat @ R ) )
% 0.16/0.43         => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X2 @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_nat_nat @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.Cons
% 0.16/0.43  thf(fact_330_listrel_OCons,axiom,
% 0.16/0.43      ! [X2: set_Pr619177522elle_U,Y: nat > list_P796095576elle_U > $o,R: set_Pr1072215906le_U_o,Xs: list_s1200803384elle_U,Ys: list_n2139828004le_U_o] :
% 0.16/0.43        ( ( member1933006123le_U_o @ ( produc1069574002le_U_o @ X2 @ Y ) @ R )
% 0.16/0.43       => ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ Xs @ Ys ) @ ( listre290852044le_U_o @ R ) )
% 0.16/0.43         => ( member493452075le_U_o @ ( produc1377086578le_U_o @ ( cons_s32021736elle_U @ X2 @ Xs ) @ ( cons_n50929118le_U_o @ Y @ Ys ) ) @ ( listre290852044le_U_o @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % listrel.Cons
% 0.16/0.43  thf(fact_331_lenlex__append2,axiom,
% 0.16/0.43      ! [R2: set_Pr1189404964e_form,Us2: list_P512754263e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.16/0.43        ( ( irrefl2121388754e_form @ R2 )
% 0.16/0.43       => ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Us2 @ Xs ) @ ( append1038020460e_form @ Us2 @ Ys ) ) @ ( lenlex1927129340e_form @ R2 ) )
% 0.16/0.43          = ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( lenlex1927129340e_form @ R2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lenlex_append2
% 0.16/0.43  thf(fact_332_lenlex__append2,axiom,
% 0.16/0.43      ! [R2: set_Pr1986765409at_nat,Us2: list_nat,Xs: list_nat,Ys: list_nat] :
% 0.16/0.43        ( ( irrefl_nat @ R2 )
% 0.16/0.43       => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Us2 @ Xs ) @ ( append_nat @ Us2 @ Ys ) ) @ ( lenlex_nat @ R2 ) )
% 0.16/0.43          = ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( lenlex_nat @ R2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lenlex_append2
% 0.16/0.43  thf(fact_333_Nil__lenlex__iff1,axiom,
% 0.16/0.43      ! [Ns: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ nil_Pr1384483009e_form @ Ns ) @ ( lenlex1927129340e_form @ R ) )
% 0.16/0.43        = ( Ns != nil_Pr1384483009e_form ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Nil_lenlex_iff1
% 0.16/0.43  thf(fact_334_Nil__lenlex__iff1,axiom,
% 0.16/0.43      ! [Ns: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ nil_nat @ Ns ) @ ( lenlex_nat @ R ) )
% 0.16/0.43        = ( Ns != nil_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Nil_lenlex_iff1
% 0.16/0.43  thf(fact_335_Nil__lenlex__iff2,axiom,
% 0.16/0.43      ! [Ns: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ~ ( member650892795e_form @ ( produc891809686e_form @ Ns @ nil_Pr1384483009e_form ) @ ( lenlex1927129340e_form @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Nil_lenlex_iff2
% 0.16/0.43  thf(fact_336_Nil__lenlex__iff2,axiom,
% 0.16/0.43      ! [Ns: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Ns @ nil_nat ) @ ( lenlex_nat @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Nil_lenlex_iff2
% 0.16/0.43  thf(fact_337_list__ex1__simps_I1_J,axiom,
% 0.16/0.43      ! [P: prover1687215943e_form > $o] :
% 0.16/0.43        ~ ( list_e2123636798e_form @ P @ nil_Pr1384483009e_form ) ).
% 0.16/0.43  
% 0.16/0.43  % list_ex1_simps(1)
% 0.16/0.43  thf(fact_338_list__ex1__simps_I1_J,axiom,
% 0.16/0.43      ! [P: nat > $o] :
% 0.16/0.43        ~ ( list_ex1_nat @ P @ nil_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % list_ex1_simps(1)
% 0.16/0.43  thf(fact_339_list__ex1__iff,axiom,
% 0.16/0.43      ( list_ex1_nat
% 0.16/0.43      = ( ^ [P4: nat > $o,Xs4: list_nat] :
% 0.16/0.43          ? [X3: nat] :
% 0.16/0.43            ( ( member_nat @ X3 @ ( set_nat2 @ Xs4 ) )
% 0.16/0.43            & ( P4 @ X3 )
% 0.16/0.43            & ! [Y3: nat] :
% 0.16/0.43                ( ( ( member_nat @ Y3 @ ( set_nat2 @ Xs4 ) )
% 0.16/0.43                  & ( P4 @ Y3 ) )
% 0.16/0.43               => ( Y3 = X3 ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % list_ex1_iff
% 0.16/0.43  thf(fact_340_Nil__notin__lex,axiom,
% 0.16/0.43      ! [Ys: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ~ ( member650892795e_form @ ( produc891809686e_form @ nil_Pr1384483009e_form @ Ys ) @ ( lex_Pr233218909e_form @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Nil_notin_lex
% 0.16/0.43  thf(fact_341_Nil__notin__lex,axiom,
% 0.16/0.43      ! [Ys: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ nil_nat @ Ys ) @ ( lex_nat @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Nil_notin_lex
% 0.16/0.43  thf(fact_342_Nil2__notin__lex,axiom,
% 0.16/0.43      ! [Xs: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.16/0.43        ~ ( member650892795e_form @ ( produc891809686e_form @ Xs @ nil_Pr1384483009e_form ) @ ( lex_Pr233218909e_form @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Nil2_notin_lex
% 0.16/0.43  thf(fact_343_Nil2__notin__lex,axiom,
% 0.16/0.43      ! [Xs: list_nat,R: set_Pr1986765409at_nat] :
% 0.16/0.43        ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ nil_nat ) @ ( lex_nat @ R ) ) ).
% 0.16/0.43  
% 0.16/0.43  % Nil2_notin_lex
% 0.16/0.43  thf(fact_344_lex__append__leftI,axiom,
% 0.16/0.43      ! [Ys: list_P512754263e_form,Zs2: list_P512754263e_form,R: set_Pr1189404964e_form,Xs: list_P512754263e_form] :
% 0.16/0.43        ( ( member650892795e_form @ ( produc891809686e_form @ Ys @ Zs2 ) @ ( lex_Pr233218909e_form @ R ) )
% 0.16/0.43       => ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ Ys ) @ ( append1038020460e_form @ Xs @ Zs2 ) ) @ ( lex_Pr233218909e_form @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lex_append_leftI
% 0.16/0.43  thf(fact_345_lex__append__leftI,axiom,
% 0.16/0.43      ! [Ys: list_nat,Zs2: list_nat,R: set_Pr1986765409at_nat,Xs: list_nat] :
% 0.16/0.43        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Zs2 ) @ ( lex_nat @ R ) )
% 0.16/0.43       => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Ys ) @ ( append_nat @ Xs @ Zs2 ) ) @ ( lex_nat @ R ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lex_append_leftI
% 0.16/0.43  thf(fact_346_lex__append__left__iff,axiom,
% 0.16/0.43      ! [R: set_Pr1189404964e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.16/0.43        ( ! [X: prover1687215943e_form] :
% 0.16/0.43            ~ ( member189065477e_form @ ( produc1018812320e_form @ X @ X ) @ R )
% 0.16/0.43       => ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ Ys ) @ ( append1038020460e_form @ Xs @ Zs2 ) ) @ ( lex_Pr233218909e_form @ R ) )
% 0.16/0.43          = ( member650892795e_form @ ( produc891809686e_form @ Ys @ Zs2 ) @ ( lex_Pr233218909e_form @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lex_append_left_iff
% 0.16/0.43  thf(fact_347_lex__append__left__iff,axiom,
% 0.16/0.43      ! [R: set_Pr1986765409at_nat,Xs: list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.16/0.43        ( ! [X: nat] :
% 0.16/0.43            ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ X ) @ R )
% 0.16/0.43       => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Ys ) @ ( append_nat @ Xs @ Zs2 ) ) @ ( lex_nat @ R ) )
% 0.16/0.43          = ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Zs2 ) @ ( lex_nat @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lex_append_left_iff
% 0.16/0.43  thf(fact_348_lex__append__leftD,axiom,
% 0.16/0.43      ! [R: set_Pr1189404964e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.16/0.43        ( ! [X: prover1687215943e_form] :
% 0.16/0.43            ~ ( member189065477e_form @ ( produc1018812320e_form @ X @ X ) @ R )
% 0.16/0.43       => ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ Ys ) @ ( append1038020460e_form @ Xs @ Zs2 ) ) @ ( lex_Pr233218909e_form @ R ) )
% 0.16/0.43         => ( member650892795e_form @ ( produc891809686e_form @ Ys @ Zs2 ) @ ( lex_Pr233218909e_form @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lex_append_leftD
% 0.16/0.43  thf(fact_349_lex__append__leftD,axiom,
% 0.16/0.43      ! [R: set_Pr1986765409at_nat,Xs: list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.16/0.43        ( ! [X: nat] :
% 0.16/0.43            ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ X ) @ R )
% 0.16/0.43       => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Ys ) @ ( append_nat @ Xs @ Zs2 ) ) @ ( lex_nat @ R ) )
% 0.16/0.43         => ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Zs2 ) @ ( lex_nat @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % lex_append_leftD
% 0.16/0.43  thf(fact_350_can__select__set__list__ex1,axiom,
% 0.16/0.43      ! [P: nat > $o,A4: list_nat] :
% 0.16/0.43        ( ( can_select_nat @ P @ ( set_nat2 @ A4 ) )
% 0.16/0.43        = ( list_ex1_nat @ P @ A4 ) ) ).
% 0.16/0.43  
% 0.16/0.43  % can_select_set_list_ex1
% 0.16/0.43  thf(fact_351_maxvar_Osimps_I1_J,axiom,
% 0.16/0.43      ( ( prover1021675886maxvar @ nil_nat )
% 0.16/0.43      = zero_zero_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % maxvar.simps(1)
% 0.16/0.43  
% 0.16/0.43  % Helper facts (5)
% 0.16/0.43  thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.16/0.43      ! [X2: list_nat,Y: list_nat] :
% 0.16/0.43        ( ( if_list_nat @ $false @ X2 @ Y )
% 0.16/0.43        = Y ) ).
% 0.16/0.43  
% 0.16/0.43  thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.16/0.43      ! [X2: list_nat,Y: list_nat] :
% 0.16/0.43        ( ( if_list_nat @ $true @ X2 @ Y )
% 0.16/0.43        = X2 ) ).
% 0.16/0.43  
% 0.16/0.43  thf(help_If_3_1_If_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_T,axiom,
% 0.16/0.43      ! [P: $o] :
% 0.16/0.43        ( ( P = $true )
% 0.16/0.43        | ( P = $false ) ) ).
% 0.16/0.43  
% 0.16/0.43  thf(help_If_2_1_If_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_T,axiom,
% 0.16/0.43      ! [X2: list_P512754263e_form,Y: list_P512754263e_form] :
% 0.16/0.43        ( ( if_lis1812881937e_form @ $false @ X2 @ Y )
% 0.16/0.43        = Y ) ).
% 0.16/0.43  
% 0.16/0.43  thf(help_If_1_1_If_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_T,axiom,
% 0.16/0.43      ! [X2: list_P512754263e_form,Y: list_P512754263e_form] :
% 0.16/0.43        ( ( if_lis1812881937e_form @ $true @ X2 @ Y )
% 0.16/0.43        = X2 ) ).
% 0.16/0.43  
% 0.16/0.43  % Conjectures (3)
% 0.16/0.43  thf(conj_0,hypothesis,
% 0.16/0.43      ~ ( member_nat @ u @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  thf(conj_1,hypothesis,
% 0.16/0.43      ! [A7: set_Pr619177522elle_U,B4: nat > list_P796095576elle_U > $o,E4: nat > prover_Mirabelle_U] :
% 0.16/0.43        ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ A7 @ B4 ) @ E4 )
% 0.16/0.43       => ( prover1282070756_SEval @ ( produc1069574002le_U_o @ A7 @ B4 ) @ E4 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  thf(conj_2,conjecture,
% 0.16/0.43      ! [E5: nat > prover_Mirabelle_U] :
% 0.16/0.43        ( ~ ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ E5 )
% 0.16/0.43        | ( prover1282070756_SEval @ ( produc1069574002le_U_o @ a @ b ) @ E5 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  %------------------------------------------------------------------------------
% 0.16/0.43  ------------------------
% 0.25/1.50  ---- Embedded in THF ---
% 0.25/1.50  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.25/1.50  %%% Generated on Tue Feb 24 08:27:54 EST 2026
% 0.25/1.50  %%% using '$$dhol' embedding, version 1.3.0.
% 0.25/1.50  %%% Logic specification used:
% 0.25/1.50  %%% thf(spec, logic, $$dhol).
% 0.25/1.50  
% 0.25/1.50  % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2DTF19870.p
% See solution above
% 0.25/1.51  ------------------------
% 0.25/1.54  ---- Cleaned THF ---
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_J_Mt__List__Olist_I_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J_J_J,type,
% 0.25/1.54      set_Pr2099245410le_U_o: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_J_Mt__List__Olist_I_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J_J,type,
% 0.25/1.54      produc622718850le_U_o: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Product____Type__Oprod_I_062_It__Prover____Mirabelle____icshcajtjh__Oform_M_062_It__Prover____Mirabelle____icshcajtjh__Oform_M_Eo_J_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.25/1.54      produc957084248e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_M_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J_J,type,
% 0.25/1.54      set_Pr1072215906le_U_o: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_M_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J,type,
% 0.25/1.54      produc227817602le_U_o: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J_J,type,
% 0.25/1.54      set_Pr31825690e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.25/1.54      produc791938916e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
% 0.25/1.54      set_Pr1057005944st_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J_J,type,
% 0.25/1.54      set_Pr1174364408e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Prover____Mirabelle____icshcajtjh__Oform_Mt__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.25/1.54      set_Pr1189404964e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 0.25/1.54      produc1473535256st_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.25/1.54      produc1494932632e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Product____Type__Oprod_It__Prover____Mirabelle____icshcajtjh__Oform_Mt__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      produc825256814e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__List__Olist_I_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J,type,
% 0.25/1.54      list_n2139828004le_U_o: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 0.25/1.54      produc890077173st_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
% 0.25/1.54      set_Pr1560408065st_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Prover____Mirabelle____icshcajtjh__Oform_Mt__Nat__Onat_J_J,type,
% 0.25/1.54      set_Pr957084504rm_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.25/1.54      set_Pr816919384e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 0.25/1.54      produc1699244961st_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Product____Type__Oprod_It__Prover____Mirabelle____icshcajtjh__Oform_Mt__Nat__Onat_J,type,
% 0.25/1.54      produc117678584rm_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      produc1296622072e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__List__Olist_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.25/1.54      list_l461858535e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.25/1.54      set_li5074317e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__List__Olist_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_J,type,
% 0.25/1.54      list_s1200803384elle_U: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.25/1.54      set_Pr1986765409at_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      list_P512754263e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      set_Pr554570749e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J,type,
% 0.25/1.54      list_P796095576elle_U: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J,type,
% 0.25/1.54      set_Pr619177522elle_U: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.25/1.54      product_prod_nat_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.25/1.54      list_list_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.25/1.54      set_list_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      prover1687215943e_form: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Prover____Mirabelle____icshcajtjh__OU,type,
% 0.25/1.54      prover_Mirabelle_U: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.25/1.54      list_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.25/1.54      set_nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(ty_n_t__Nat__Onat,type,
% 0.25/1.54      nat: $tType ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.25/1.54      zero_zero_nat: nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_If_001t__List__Olist_It__Nat__Onat_J,type,
% 0.25/1.54      if_list_nat: $o > list_nat > list_nat > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_If_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      if_lis1812881937e_form: $o > list_P512754263e_form > list_P512754263e_form > list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Oappend_001t__List__Olist_It__Nat__Onat_J,type,
% 0.25/1.54      append_list_nat: list_list_nat > list_list_nat > list_list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Oappend_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      append1797078012e_form: list_l461858535e_form > list_l461858535e_form > list_l461858535e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 0.25/1.54      append_nat: list_nat > list_nat > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Oappend_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      append1038020460e_form: list_P512754263e_form > list_P512754263e_form > list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Obind_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.25/1.54      bind_nat_nat: list_nat > ( nat > list_nat ) > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Obind_001t__Nat__Onat_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      bind_n1193922848e_form: list_nat > ( nat > list_P512754263e_form ) > list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Obind_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Nat__Onat,type,
% 0.25/1.54      bind_P1359331232rm_nat: list_P512754263e_form > ( prover1687215943e_form > list_nat ) > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Obind_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      bind_P1054726576e_form: list_P512754263e_form > ( prover1687215943e_form > list_P512754263e_form ) > list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
% 0.25/1.54      butlast_nat: list_nat > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Obutlast_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      butlas664258165e_form: list_P512754263e_form > list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Ocan__select_001t__Nat__Onat,type,
% 0.25/1.54      can_select_nat: ( nat > $o ) > set_nat > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Oconcat_001t__Nat__Onat,type,
% 0.25/1.54      concat_nat: list_list_nat > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Oconcat_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      concat1664984646e_form: list_l461858535e_form > list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Oinsert_001t__Nat__Onat,type,
% 0.25/1.54      insert_nat: nat > list_nat > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Oinsert_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      insert697320747e_form: prover1687215943e_form > list_P512754263e_form > list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 0.25/1.54      last_nat: list_nat > nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olast_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      last_P1811260776e_form: list_P512754263e_form > prover1687215943e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olenlex_001t__Nat__Onat,type,
% 0.25/1.54      lenlex_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olenlex_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      lenlex1927129340e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olex_001t__Nat__Onat,type,
% 0.25/1.54      lex_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olex_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      lex_Pr233218909e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olexord_001t__Nat__Onat,type,
% 0.25/1.54      lexord_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olexord_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      lexord1848469012e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_OCons_001_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J,type,
% 0.25/1.54      cons_n50929118le_U_o: ( nat > list_P796095576elle_U > $o ) > list_n2139828004le_U_o > list_n2139828004le_U_o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Nat__Onat_J,type,
% 0.25/1.54      cons_list_nat: list_nat > list_list_nat > list_list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      cons_l1379921697e_form: list_P512754263e_form > list_l461858535e_form > list_l461858535e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 0.25/1.54      cons_nat: nat > list_nat > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_OCons_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      cons_P1475164433e_form: prover1687215943e_form > list_P512754263e_form > list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J,type,
% 0.25/1.54      cons_s32021736elle_U: set_Pr619177522elle_U > list_s1200803384elle_U > list_s1200803384elle_U ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_ONil_001_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J,type,
% 0.25/1.54      nil_na1584420238le_U_o: list_n2139828004le_U_o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Nat__Onat_J,type,
% 0.25/1.54      nil_list_nat: list_list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      nil_li1393862353e_form: list_l461858535e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 0.25/1.54      nil_nat: list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_ONil_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      nil_Pr1384483009e_form: list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_ONil_001t__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J,type,
% 0.25/1.54      nil_se944326968elle_U: list_s1200803384elle_U ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 0.25/1.54      set_list_nat2: list_list_nat > set_list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      set_li1219651714e_form: list_l461858535e_form > set_li5074317e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 0.25/1.54      set_nat2: list_nat > set_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist_Oset_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      set_Pr1105237746e_form: list_P512754263e_form > set_Pr554570749e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist__ex1_001t__Nat__Onat,type,
% 0.25/1.54      list_ex1_nat: ( nat > $o ) > list_nat > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olist__ex1_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      list_e2123636798e_form: ( prover1687215943e_form > $o ) > list_P512754263e_form > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olistrel1_001t__Nat__Onat,type,
% 0.25/1.54      listrel1_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olistrel1_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      listre502458152e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olistrel_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.25/1.54      listrel_nat_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olistrel_001t__Nat__Onat_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      listre318297994e_form: set_Pr816919384e_form > set_Pr1174364408e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olistrel_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Nat__Onat,type,
% 0.25/1.54      listre483706378rm_nat: set_Pr957084504rm_nat > set_Pr1057005944st_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olistrel_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      listre1908795590e_form: set_Pr1189404964e_form > set_Pr31825690e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Olistrel_001t__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_001_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J,type,
% 0.25/1.54      listre290852044le_U_o: set_Pr1072215906le_U_o > set_Pr2099245410le_U_o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Omaps_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.25/1.54      maps_nat_nat: ( nat > list_nat ) > list_nat > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Omaps_001t__Nat__Onat_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      maps_n1383976154e_form: ( nat > list_P512754263e_form ) > list_nat > list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Omaps_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Nat__Onat,type,
% 0.25/1.54      maps_P1549384538rm_nat: ( prover1687215943e_form > list_nat ) > list_P512754263e_form > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Omaps_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      maps_P2058952566e_form: ( prover1687215943e_form > list_P512754263e_form ) > list_P512754263e_form > list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Oproduct__lists_001t__Nat__Onat,type,
% 0.25/1.54      product_lists_nat: list_list_nat > list_list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Oproduct__lists_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      produc168439576e_form: list_l461858535e_form > list_l461858535e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 0.25/1.54      rotate1_nat: list_nat > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Orotate1_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      rotate650061876e_form: list_P512754263e_form > list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Osubseqs_001t__Nat__Onat,type,
% 0.25/1.54      subseqs_nat: list_nat > list_list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_List_Osubseqs_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      subseq1471997234e_form: list_P512754263e_form > list_l461858535e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001t__List__Olist_It__Nat__Onat_J,type,
% 0.25/1.54      produc939441135st_nat: ( nat > nat > $o ) > list_nat > produc890077173st_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Product__Type_OPair_001_062_It__Prover____Mirabelle____icshcajtjh__Oform_M_062_It__Prover____Mirabelle____icshcajtjh__Oform_M_Eo_J_J_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      produc54611594e_form: ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > produc957084248e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Nat__Onat_J,type,
% 0.25/1.54      produc1625736153st_nat: list_nat > list_nat > produc1699244961st_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Nat__Onat_J_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      produc1617574096e_form: list_nat > list_P512754263e_form > produc1494932632e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_001t__List__Olist_It__Nat__Onat_J,type,
% 0.25/1.54      produc1897654224st_nat: list_P512754263e_form > list_nat > produc1473535256st_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      produc891809686e_form: list_P512754263e_form > list_P512754263e_form > produc791938916e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Product__Type_OPair_001t__List__Olist_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_J_001t__List__Olist_I_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J,type,
% 0.25/1.54      produc1377086578le_U_o: list_s1200803384elle_U > list_n2139828004le_U_o > produc622718850le_U_o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.25/1.54      product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      produc876465968e_form: nat > prover1687215943e_form > produc1296622072e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Product__Type_OPair_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Nat__Onat,type,
% 0.25/1.54      produc1041874352rm_nat: prover1687215943e_form > nat > produc117678584rm_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Product__Type_OPair_001t__Prover____Mirabelle____icshcajtjh__Oform_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      produc1018812320e_form: prover1687215943e_form > prover1687215943e_form > produc825256814e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Product__Type_OPair_001t__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_001_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J,type,
% 0.25/1.54      produc1069574002le_U_o: set_Pr619177522elle_U > ( nat > list_P796095576elle_U > $o ) > produc227817602le_U_o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Prover__Mirabelle__icshcajtjh_OSEval,type,
% 0.25/1.54      prover1282070756_SEval: produc227817602le_U_o > ( nat > prover_Mirabelle_U ) > list_P512754263e_form > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Prover__Mirabelle__icshcajtjh_OSvalid,type,
% 0.25/1.54      prover1539709396Svalid: list_P512754263e_form > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Prover__Mirabelle__icshcajtjh_Ofinst,type,
% 0.25/1.54      prover1577896257_finst: prover1687215943e_form > nat > prover1687215943e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Prover__Mirabelle__icshcajtjh_Oflatten_001t__Nat__Onat,type,
% 0.25/1.54      prover886976490en_nat: list_list_nat > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Prover__Mirabelle__icshcajtjh_Oflatten_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      prover542312166e_form: list_l461858535e_form > list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Prover__Mirabelle__icshcajtjh_Oform_OFAll,type,
% 0.25/1.54      prover571163162e_FAll: prover1687215943e_form > prover1687215943e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Prover__Mirabelle__icshcajtjh_Ofv,type,
% 0.25/1.54      prover_Mirabelle_fv: prover1687215943e_form > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Prover__Mirabelle__icshcajtjh_Ois__env,type,
% 0.25/1.54      prover1847600056is_env: produc227817602le_U_o > ( nat > prover_Mirabelle_U ) > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Prover__Mirabelle__icshcajtjh_Omaxvar,type,
% 0.25/1.54      prover1021675886maxvar: list_nat > nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Prover__Mirabelle__icshcajtjh_OpreSuc,type,
% 0.25/1.54      prover2096325705preSuc: list_nat > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Prover__Mirabelle__icshcajtjh_Osfv,type,
% 0.25/1.54      prover_Mirabelle_sfv: list_P512754263e_form > list_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Relation_Oirrefl_001t__Nat__Onat,type,
% 0.25/1.54      irrefl_nat: set_Pr1986765409at_nat > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Relation_Oirrefl_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      irrefl2121388754e_form: set_Pr1189404964e_form > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.25/1.54      collect_nat: ( nat > $o ) > set_nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Set_Othe__elem_001t__Nat__Onat,type,
% 0.25/1.54      the_elem_nat: set_nat > nat ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_Set_Othe__elem_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      the_el969789074e_form: set_Pr554570749e_form > prover1687215943e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 0.25/1.54      member_list_nat: list_nat > set_list_nat > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      member1828782574e_form: list_P512754263e_form > set_li5074317e_form > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__Nat__Onat,type,
% 0.25/1.54      member_nat: nat > set_nat > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 0.25/1.54      member1926390090st_nat: produc1699244961st_nat > set_Pr1560408065st_nat > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.25/1.54      member1471151041e_form: produc1494932632e_form > set_Pr1174364408e_form > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 0.25/1.54      member1449753665st_nat: produc1473535256st_nat > set_Pr1057005944st_nat > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_Mt__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_J,type,
% 0.25/1.54      member650892795e_form: produc791938916e_form > set_Pr31825690e_form > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_J_Mt__List__Olist_I_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J_J,type,
% 0.25/1.54      member493452075le_U_o: produc622718850le_U_o > set_Pr2099245410le_U_o > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.25/1.54      member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      member18158113e_form: produc1296622072e_form > set_Pr816919384e_form > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__Product____Type__Oprod_It__Prover____Mirabelle____icshcajtjh__Oform_Mt__Nat__Onat_J,type,
% 0.25/1.54      member986698273rm_nat: produc117678584rm_nat > set_Pr957084504rm_nat > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__Product____Type__Oprod_It__Prover____Mirabelle____icshcajtjh__Oform_Mt__Prover____Mirabelle____icshcajtjh__Oform_J,type,
% 0.25/1.54      member189065477e_form: produc825256814e_form > set_Pr1189404964e_form > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Prover____Mirabelle____icshcajtjh__OU_J_M_062_It__Nat__Onat_M_062_It__List__Olist_It__Prover____Mirabelle____icshcajtjh__OU_J_M_Eo_J_J_J,type,
% 0.25/1.54      member1933006123le_U_o: produc227817602le_U_o > set_Pr1072215906le_U_o > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_c_member_001t__Prover____Mirabelle____icshcajtjh__Oform,type,
% 0.25/1.54      member1793840734e_form: prover1687215943e_form > set_Pr554570749e_form > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_v_a,type,
% 0.25/1.54      a: set_Pr619177522elle_U ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_v_b,type,
% 0.25/1.54      b: nat > list_P796095576elle_U > $o ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_v_f,type,
% 0.25/1.54      f: prover1687215943e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_v_s,type,
% 0.25/1.54      s: list_P512754263e_form ).
% 0.25/1.54  
% 0.25/1.54  thf(sy_v_u,type,
% 0.25/1.54      u: nat ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_0_form_Oinject_I5_J,axiom,
% 0.25/1.54      ! [X5: prover1687215943e_form,Y5: prover1687215943e_form] :
% 0.25/1.54        ( ( ( prover571163162e_FAll @ X5 )
% 0.25/1.54          = ( prover571163162e_FAll @ Y5 ) )
% 0.25/1.54        = ( X5 = Y5 ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_1_SEval_Osimps_I1_J,axiom,
% 0.25/1.54      ! [M: produc227817602le_U_o,E: nat > prover_Mirabelle_U] :
% 0.25/1.54        ~ ( prover1282070756_SEval @ M @ E @ nil_Pr1384483009e_form ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_2_SEval__cong,axiom,
% 0.25/1.54      ! [S: list_P512754263e_form,E1: nat > prover_Mirabelle_U,E2: nat > prover_Mirabelle_U,M: produc227817602le_U_o] :
% 0.25/1.54        ( ! [X: nat] :
% 0.25/1.54            ( ( member_nat @ X @ ( set_nat2 @ ( prover_Mirabelle_sfv @ S ) ) )
% 0.25/1.54           => ( ( E1 @ X )
% 0.25/1.54              = ( E2 @ X ) ) )
% 0.25/1.54       => ( ( prover1282070756_SEval @ M @ E1 @ S )
% 0.25/1.54          = ( prover1282070756_SEval @ M @ E2 @ S ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_3_SEval__append,axiom,
% 0.25/1.54      ! [M: produc227817602le_U_o,E: nat > prover_Mirabelle_U,Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.54        ( ( prover1282070756_SEval @ M @ E @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.25/1.54        = ( ( prover1282070756_SEval @ M @ E @ Xs )
% 0.25/1.54          | ( prover1282070756_SEval @ M @ E @ Ys ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_4_sound__FAll,axiom,
% 0.25/1.54      ! [U: nat,F: prover1687215943e_form,S: list_P512754263e_form] :
% 0.25/1.54        ( ~ ( member_nat @ U @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ F ) @ S ) ) ) )
% 0.25/1.54       => ( ( prover1539709396Svalid @ ( append1038020460e_form @ S @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ F @ U ) @ nil_Pr1384483009e_form ) ) )
% 0.25/1.54         => ( prover1539709396Svalid @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ F ) @ S ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_5_append1__eq__conv,axiom,
% 0.25/1.54      ! [Xs: list_nat,X2: nat,Ys: list_nat,Y: nat] :
% 0.25/1.54        ( ( ( append_nat @ Xs @ ( cons_nat @ X2 @ nil_nat ) )
% 0.25/1.54          = ( append_nat @ Ys @ ( cons_nat @ Y @ nil_nat ) ) )
% 0.25/1.54        = ( ( Xs = Ys )
% 0.25/1.54          & ( X2 = Y ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_6_append1__eq__conv,axiom,
% 0.25/1.54      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form,Ys: list_P512754263e_form,Y: prover1687215943e_form] :
% 0.25/1.54        ( ( ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) )
% 0.25/1.54          = ( append1038020460e_form @ Ys @ ( cons_P1475164433e_form @ Y @ nil_Pr1384483009e_form ) ) )
% 0.25/1.54        = ( ( Xs = Ys )
% 0.25/1.54          & ( X2 = Y ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_7_append__Nil2,axiom,
% 0.25/1.54      ! [Xs: list_P512754263e_form] :
% 0.25/1.54        ( ( append1038020460e_form @ Xs @ nil_Pr1384483009e_form )
% 0.25/1.54        = Xs ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_8_append__Nil2,axiom,
% 0.25/1.54      ! [Xs: list_nat] :
% 0.25/1.54        ( ( append_nat @ Xs @ nil_nat )
% 0.25/1.54        = Xs ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_9_append__self__conv,axiom,
% 0.25/1.54      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.54        ( ( ( append1038020460e_form @ Xs @ Ys )
% 0.25/1.54          = Xs )
% 0.25/1.54        = ( Ys = nil_Pr1384483009e_form ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_10_append__self__conv,axiom,
% 0.25/1.54      ! [Xs: list_nat,Ys: list_nat] :
% 0.25/1.54        ( ( ( append_nat @ Xs @ Ys )
% 0.25/1.54          = Xs )
% 0.25/1.54        = ( Ys = nil_nat ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_11_self__append__conv,axiom,
% 0.25/1.54      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.54        ( ( Xs
% 0.25/1.54          = ( append1038020460e_form @ Xs @ Ys ) )
% 0.25/1.54        = ( Ys = nil_Pr1384483009e_form ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_12_self__append__conv,axiom,
% 0.25/1.54      ! [Xs: list_nat,Ys: list_nat] :
% 0.25/1.54        ( ( Xs
% 0.25/1.54          = ( append_nat @ Xs @ Ys ) )
% 0.25/1.54        = ( Ys = nil_nat ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_13_append__self__conv2,axiom,
% 0.25/1.54      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.54        ( ( ( append1038020460e_form @ Xs @ Ys )
% 0.25/1.54          = Ys )
% 0.25/1.54        = ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_14_append__self__conv2,axiom,
% 0.25/1.54      ! [Xs: list_nat,Ys: list_nat] :
% 0.25/1.54        ( ( ( append_nat @ Xs @ Ys )
% 0.25/1.54          = Ys )
% 0.25/1.54        = ( Xs = nil_nat ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_15_self__append__conv2,axiom,
% 0.25/1.54      ! [Ys: list_P512754263e_form,Xs: list_P512754263e_form] :
% 0.25/1.54        ( ( Ys
% 0.25/1.54          = ( append1038020460e_form @ Xs @ Ys ) )
% 0.25/1.54        = ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_16_self__append__conv2,axiom,
% 0.25/1.54      ! [Ys: list_nat,Xs: list_nat] :
% 0.25/1.54        ( ( Ys
% 0.25/1.54          = ( append_nat @ Xs @ Ys ) )
% 0.25/1.54        = ( Xs = nil_nat ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_17_Nil__is__append__conv,axiom,
% 0.25/1.54      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.54        ( ( nil_Pr1384483009e_form
% 0.25/1.54          = ( append1038020460e_form @ Xs @ Ys ) )
% 0.25/1.54        = ( ( Xs = nil_Pr1384483009e_form )
% 0.25/1.54          & ( Ys = nil_Pr1384483009e_form ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_18_Nil__is__append__conv,axiom,
% 0.25/1.54      ! [Xs: list_nat,Ys: list_nat] :
% 0.25/1.54        ( ( nil_nat
% 0.25/1.54          = ( append_nat @ Xs @ Ys ) )
% 0.25/1.54        = ( ( Xs = nil_nat )
% 0.25/1.54          & ( Ys = nil_nat ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_19_append__is__Nil__conv,axiom,
% 0.25/1.54      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.54        ( ( ( append1038020460e_form @ Xs @ Ys )
% 0.25/1.54          = nil_Pr1384483009e_form )
% 0.25/1.54        = ( ( Xs = nil_Pr1384483009e_form )
% 0.25/1.54          & ( Ys = nil_Pr1384483009e_form ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_20_append__is__Nil__conv,axiom,
% 0.25/1.54      ! [Xs: list_nat,Ys: list_nat] :
% 0.25/1.54        ( ( ( append_nat @ Xs @ Ys )
% 0.25/1.54          = nil_nat )
% 0.25/1.54        = ( ( Xs = nil_nat )
% 0.25/1.54          & ( Ys = nil_nat ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_21_append_Oright__neutral,axiom,
% 0.25/1.54      ! [A: list_P512754263e_form] :
% 0.25/1.54        ( ( append1038020460e_form @ A @ nil_Pr1384483009e_form )
% 0.25/1.54        = A ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_22_append_Oright__neutral,axiom,
% 0.25/1.54      ! [A: list_nat] :
% 0.25/1.54        ( ( append_nat @ A @ nil_nat )
% 0.25/1.54        = A ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_23_Svalid__def,axiom,
% 0.25/1.54      ( prover1539709396Svalid
% 0.25/1.54      = ( ^ [S2: list_P512754263e_form] :
% 0.25/1.54          ! [MI: produc227817602le_U_o,E3: nat > prover_Mirabelle_U] :
% 0.25/1.54            ( ( prover1847600056is_env @ MI @ E3 )
% 0.25/1.54           => ( prover1282070756_SEval @ MI @ E3 @ S2 ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_24_split__list,axiom,
% 0.25/1.54      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.54        ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.54       => ? [Ys2: list_P512754263e_form,Zs: list_P512754263e_form] :
% 0.25/1.54            ( Xs
% 0.25/1.54            = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X2 @ Zs ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_25_split__list,axiom,
% 0.25/1.54      ! [X2: nat,Xs: list_nat] :
% 0.25/1.54        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.25/1.54       => ? [Ys2: list_nat,Zs: list_nat] :
% 0.25/1.54            ( Xs
% 0.25/1.54            = ( append_nat @ Ys2 @ ( cons_nat @ X2 @ Zs ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_26_list_Oinject,axiom,
% 0.25/1.54      ! [X21: prover1687215943e_form,X22: list_P512754263e_form,Y21: prover1687215943e_form,Y22: list_P512754263e_form] :
% 0.25/1.54        ( ( ( cons_P1475164433e_form @ X21 @ X22 )
% 0.25/1.54          = ( cons_P1475164433e_form @ Y21 @ Y22 ) )
% 0.25/1.54        = ( ( X21 = Y21 )
% 0.25/1.54          & ( X22 = Y22 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_27_list_Oinject,axiom,
% 0.25/1.54      ! [X21: nat,X22: list_nat,Y21: nat,Y22: list_nat] :
% 0.25/1.54        ( ( ( cons_nat @ X21 @ X22 )
% 0.25/1.54          = ( cons_nat @ Y21 @ Y22 ) )
% 0.25/1.54        = ( ( X21 = Y21 )
% 0.25/1.54          & ( X22 = Y22 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_28_same__append__eq,axiom,
% 0.25/1.54      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.25/1.54        ( ( ( append1038020460e_form @ Xs @ Ys )
% 0.25/1.54          = ( append1038020460e_form @ Xs @ Zs2 ) )
% 0.25/1.54        = ( Ys = Zs2 ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_29_same__append__eq,axiom,
% 0.25/1.54      ! [Xs: list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.25/1.54        ( ( ( append_nat @ Xs @ Ys )
% 0.25/1.54          = ( append_nat @ Xs @ Zs2 ) )
% 0.25/1.54        = ( Ys = Zs2 ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_30_append__same__eq,axiom,
% 0.25/1.54      ! [Ys: list_P512754263e_form,Xs: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.25/1.54        ( ( ( append1038020460e_form @ Ys @ Xs )
% 0.25/1.54          = ( append1038020460e_form @ Zs2 @ Xs ) )
% 0.25/1.54        = ( Ys = Zs2 ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_31_append__same__eq,axiom,
% 0.25/1.54      ! [Ys: list_nat,Xs: list_nat,Zs2: list_nat] :
% 0.25/1.54        ( ( ( append_nat @ Ys @ Xs )
% 0.25/1.54          = ( append_nat @ Zs2 @ Xs ) )
% 0.25/1.54        = ( Ys = Zs2 ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_32_append__assoc,axiom,
% 0.25/1.54      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.25/1.54        ( ( append1038020460e_form @ ( append1038020460e_form @ Xs @ Ys ) @ Zs2 )
% 0.25/1.54        = ( append1038020460e_form @ Xs @ ( append1038020460e_form @ Ys @ Zs2 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_33_append__assoc,axiom,
% 0.25/1.54      ! [Xs: list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.25/1.54        ( ( append_nat @ ( append_nat @ Xs @ Ys ) @ Zs2 )
% 0.25/1.54        = ( append_nat @ Xs @ ( append_nat @ Ys @ Zs2 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_34_append_Oassoc,axiom,
% 0.25/1.54      ! [A: list_P512754263e_form,B: list_P512754263e_form,C: list_P512754263e_form] :
% 0.25/1.54        ( ( append1038020460e_form @ ( append1038020460e_form @ A @ B ) @ C )
% 0.25/1.54        = ( append1038020460e_form @ A @ ( append1038020460e_form @ B @ C ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_35_append_Oassoc,axiom,
% 0.25/1.54      ! [A: list_nat,B: list_nat,C: list_nat] :
% 0.25/1.54        ( ( append_nat @ ( append_nat @ A @ B ) @ C )
% 0.25/1.54        = ( append_nat @ A @ ( append_nat @ B @ C ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_36_not__Cons__self2,axiom,
% 0.25/1.54      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.54        ( ( cons_P1475164433e_form @ X2 @ Xs )
% 0.25/1.54       != Xs ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_37_not__Cons__self2,axiom,
% 0.25/1.54      ! [X2: nat,Xs: list_nat] :
% 0.25/1.54        ( ( cons_nat @ X2 @ Xs )
% 0.25/1.54       != Xs ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_38_sfv__nil,axiom,
% 0.25/1.54      ( ( prover_Mirabelle_sfv @ nil_Pr1384483009e_form )
% 0.25/1.54      = nil_nat ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_39_append__eq__append__conv2,axiom,
% 0.25/1.54      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form,Ts: list_P512754263e_form] :
% 0.25/1.54        ( ( ( append1038020460e_form @ Xs @ Ys )
% 0.25/1.54          = ( append1038020460e_form @ Zs2 @ Ts ) )
% 0.25/1.54        = ( ? [Us: list_P512754263e_form] :
% 0.25/1.54              ( ( ( Xs
% 0.25/1.54                  = ( append1038020460e_form @ Zs2 @ Us ) )
% 0.25/1.54                & ( ( append1038020460e_form @ Us @ Ys )
% 0.25/1.54                  = Ts ) )
% 0.25/1.54              | ( ( ( append1038020460e_form @ Xs @ Us )
% 0.25/1.54                  = Zs2 )
% 0.25/1.54                & ( Ys
% 0.25/1.54                  = ( append1038020460e_form @ Us @ Ts ) ) ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_40_append__eq__append__conv2,axiom,
% 0.25/1.54      ! [Xs: list_nat,Ys: list_nat,Zs2: list_nat,Ts: list_nat] :
% 0.25/1.54        ( ( ( append_nat @ Xs @ Ys )
% 0.25/1.54          = ( append_nat @ Zs2 @ Ts ) )
% 0.25/1.54        = ( ? [Us: list_nat] :
% 0.25/1.54              ( ( ( Xs
% 0.25/1.54                  = ( append_nat @ Zs2 @ Us ) )
% 0.25/1.54                & ( ( append_nat @ Us @ Ys )
% 0.25/1.54                  = Ts ) )
% 0.25/1.54              | ( ( ( append_nat @ Xs @ Us )
% 0.25/1.54                  = Zs2 )
% 0.25/1.54                & ( Ys
% 0.25/1.54                  = ( append_nat @ Us @ Ts ) ) ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_41_append__eq__appendI,axiom,
% 0.25/1.54      ! [Xs: list_P512754263e_form,Xs1: list_P512754263e_form,Zs2: list_P512754263e_form,Ys: list_P512754263e_form,Us2: list_P512754263e_form] :
% 0.25/1.54        ( ( ( append1038020460e_form @ Xs @ Xs1 )
% 0.25/1.54          = Zs2 )
% 0.25/1.54       => ( ( Ys
% 0.25/1.54            = ( append1038020460e_form @ Xs1 @ Us2 ) )
% 0.25/1.54         => ( ( append1038020460e_form @ Xs @ Ys )
% 0.25/1.54            = ( append1038020460e_form @ Zs2 @ Us2 ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_42_append__eq__appendI,axiom,
% 0.25/1.54      ! [Xs: list_nat,Xs1: list_nat,Zs2: list_nat,Ys: list_nat,Us2: list_nat] :
% 0.25/1.54        ( ( ( append_nat @ Xs @ Xs1 )
% 0.25/1.54          = Zs2 )
% 0.25/1.54       => ( ( Ys
% 0.25/1.54            = ( append_nat @ Xs1 @ Us2 ) )
% 0.25/1.54         => ( ( append_nat @ Xs @ Ys )
% 0.25/1.54            = ( append_nat @ Zs2 @ Us2 ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_43_strict__sorted_Oinduct,axiom,
% 0.25/1.54      ! [P: list_nat > $o,A0: list_nat] :
% 0.25/1.54        ( ( P @ nil_nat )
% 0.25/1.54       => ( ! [X: nat,Ys2: list_nat] :
% 0.25/1.54              ( ( P @ Ys2 )
% 0.25/1.54             => ( P @ ( cons_nat @ X @ Ys2 ) ) )
% 0.25/1.54         => ( P @ A0 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_44_strict__sorted_Ocases,axiom,
% 0.25/1.54      ! [X2: list_nat] :
% 0.25/1.54        ( ( X2 != nil_nat )
% 0.25/1.54       => ~ ! [X: nat,Ys2: list_nat] :
% 0.25/1.54              ( X2
% 0.25/1.54             != ( cons_nat @ X @ Ys2 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_45_map__tailrec__rev_Oinduct,axiom,
% 0.25/1.54      ! [P: ( prover1687215943e_form > prover1687215943e_form ) > list_P512754263e_form > list_P512754263e_form > $o,A0: prover1687215943e_form > prover1687215943e_form,A1: list_P512754263e_form,A2: list_P512754263e_form] :
% 0.25/1.54        ( ! [F2: prover1687215943e_form > prover1687215943e_form,X_1: list_P512754263e_form] : ( P @ F2 @ nil_Pr1384483009e_form @ X_1 )
% 0.25/1.54       => ( ! [F2: prover1687215943e_form > prover1687215943e_form,A3: prover1687215943e_form,As: list_P512754263e_form,Bs: list_P512754263e_form] :
% 0.25/1.54              ( ( P @ F2 @ As @ ( cons_P1475164433e_form @ ( F2 @ A3 ) @ Bs ) )
% 0.25/1.54             => ( P @ F2 @ ( cons_P1475164433e_form @ A3 @ As ) @ Bs ) )
% 0.25/1.54         => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_46_map__tailrec__rev_Oinduct,axiom,
% 0.25/1.54      ! [P: ( nat > prover1687215943e_form ) > list_nat > list_P512754263e_form > $o,A0: nat > prover1687215943e_form,A1: list_nat,A2: list_P512754263e_form] :
% 0.25/1.54        ( ! [F2: nat > prover1687215943e_form,X_1: list_P512754263e_form] : ( P @ F2 @ nil_nat @ X_1 )
% 0.25/1.54       => ( ! [F2: nat > prover1687215943e_form,A3: nat,As: list_nat,Bs: list_P512754263e_form] :
% 0.25/1.54              ( ( P @ F2 @ As @ ( cons_P1475164433e_form @ ( F2 @ A3 ) @ Bs ) )
% 0.25/1.54             => ( P @ F2 @ ( cons_nat @ A3 @ As ) @ Bs ) )
% 0.25/1.54         => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_47_map__tailrec__rev_Oinduct,axiom,
% 0.25/1.54      ! [P: ( prover1687215943e_form > nat ) > list_P512754263e_form > list_nat > $o,A0: prover1687215943e_form > nat,A1: list_P512754263e_form,A2: list_nat] :
% 0.25/1.54        ( ! [F2: prover1687215943e_form > nat,X_1: list_nat] : ( P @ F2 @ nil_Pr1384483009e_form @ X_1 )
% 0.25/1.54       => ( ! [F2: prover1687215943e_form > nat,A3: prover1687215943e_form,As: list_P512754263e_form,Bs: list_nat] :
% 0.25/1.54              ( ( P @ F2 @ As @ ( cons_nat @ ( F2 @ A3 ) @ Bs ) )
% 0.25/1.54             => ( P @ F2 @ ( cons_P1475164433e_form @ A3 @ As ) @ Bs ) )
% 0.25/1.54         => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_48_map__tailrec__rev_Oinduct,axiom,
% 0.25/1.54      ! [P: ( nat > nat ) > list_nat > list_nat > $o,A0: nat > nat,A1: list_nat,A2: list_nat] :
% 0.25/1.54        ( ! [F2: nat > nat,X_1: list_nat] : ( P @ F2 @ nil_nat @ X_1 )
% 0.25/1.54       => ( ! [F2: nat > nat,A3: nat,As: list_nat,Bs: list_nat] :
% 0.25/1.54              ( ( P @ F2 @ As @ ( cons_nat @ ( F2 @ A3 ) @ Bs ) )
% 0.25/1.54             => ( P @ F2 @ ( cons_nat @ A3 @ As ) @ Bs ) )
% 0.25/1.54         => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_49_list__nonempty__induct,axiom,
% 0.25/1.54      ! [Xs: list_P512754263e_form,P: list_P512754263e_form > $o] :
% 0.25/1.54        ( ( Xs != nil_Pr1384483009e_form )
% 0.25/1.54       => ( ! [X: prover1687215943e_form] : ( P @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) )
% 0.25/1.54         => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.25/1.54                ( ( Xs2 != nil_Pr1384483009e_form )
% 0.25/1.54               => ( ( P @ Xs2 )
% 0.25/1.54                 => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) ) ) )
% 0.25/1.54           => ( P @ Xs ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_50_list__nonempty__induct,axiom,
% 0.25/1.54      ! [Xs: list_nat,P: list_nat > $o] :
% 0.25/1.54        ( ( Xs != nil_nat )
% 0.25/1.54       => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 0.25/1.54         => ( ! [X: nat,Xs2: list_nat] :
% 0.25/1.54                ( ( Xs2 != nil_nat )
% 0.25/1.54               => ( ( P @ Xs2 )
% 0.25/1.54                 => ( P @ ( cons_nat @ X @ Xs2 ) ) ) )
% 0.25/1.54           => ( P @ Xs ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_51_successively_Oinduct,axiom,
% 0.25/1.54      ! [P: ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o,A0: prover1687215943e_form > prover1687215943e_form > $o,A1: list_P512754263e_form] :
% 0.25/1.54        ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o] : ( P @ P2 @ nil_Pr1384483009e_form )
% 0.25/1.54       => ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o,X: prover1687215943e_form] : ( P @ P2 @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) )
% 0.25/1.54         => ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o,X: prover1687215943e_form,Y2: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.25/1.54                ( ( P @ P2 @ ( cons_P1475164433e_form @ Y2 @ Xs2 ) )
% 0.25/1.54               => ( P @ P2 @ ( cons_P1475164433e_form @ X @ ( cons_P1475164433e_form @ Y2 @ Xs2 ) ) ) )
% 0.25/1.54           => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_52_successively_Oinduct,axiom,
% 0.25/1.54      ! [P: ( nat > nat > $o ) > list_nat > $o,A0: nat > nat > $o,A1: list_nat] :
% 0.25/1.54        ( ! [P2: nat > nat > $o] : ( P @ P2 @ nil_nat )
% 0.25/1.54       => ( ! [P2: nat > nat > $o,X: nat] : ( P @ P2 @ ( cons_nat @ X @ nil_nat ) )
% 0.25/1.54         => ( ! [P2: nat > nat > $o,X: nat,Y2: nat,Xs2: list_nat] :
% 0.25/1.54                ( ( P @ P2 @ ( cons_nat @ Y2 @ Xs2 ) )
% 0.25/1.54               => ( P @ P2 @ ( cons_nat @ X @ ( cons_nat @ Y2 @ Xs2 ) ) ) )
% 0.25/1.54           => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_53_remdups__adj_Oinduct,axiom,
% 0.25/1.54      ! [P: list_P512754263e_form > $o,A0: list_P512754263e_form] :
% 0.25/1.54        ( ( P @ nil_Pr1384483009e_form )
% 0.25/1.54       => ( ! [X: prover1687215943e_form] : ( P @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) )
% 0.25/1.54         => ( ! [X: prover1687215943e_form,Y2: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.25/1.54                ( ( ( X = Y2 )
% 0.25/1.54                 => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) ) )
% 0.25/1.54               => ( ( ( X != Y2 )
% 0.25/1.54                   => ( P @ ( cons_P1475164433e_form @ Y2 @ Xs2 ) ) )
% 0.25/1.54                 => ( P @ ( cons_P1475164433e_form @ X @ ( cons_P1475164433e_form @ Y2 @ Xs2 ) ) ) ) )
% 0.25/1.54           => ( P @ A0 ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_54_remdups__adj_Oinduct,axiom,
% 0.25/1.54      ! [P: list_nat > $o,A0: list_nat] :
% 0.25/1.54        ( ( P @ nil_nat )
% 0.25/1.54       => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 0.25/1.54         => ( ! [X: nat,Y2: nat,Xs2: list_nat] :
% 0.25/1.54                ( ( ( X = Y2 )
% 0.25/1.54                 => ( P @ ( cons_nat @ X @ Xs2 ) ) )
% 0.25/1.54               => ( ( ( X != Y2 )
% 0.25/1.54                   => ( P @ ( cons_nat @ Y2 @ Xs2 ) ) )
% 0.25/1.54                 => ( P @ ( cons_nat @ X @ ( cons_nat @ Y2 @ Xs2 ) ) ) ) )
% 0.25/1.54           => ( P @ A0 ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_55_sorted__wrt_Oinduct,axiom,
% 0.25/1.54      ! [P: ( prover1687215943e_form > prover1687215943e_form > $o ) > list_P512754263e_form > $o,A0: prover1687215943e_form > prover1687215943e_form > $o,A1: list_P512754263e_form] :
% 0.25/1.54        ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o] : ( P @ P2 @ nil_Pr1384483009e_form )
% 0.25/1.54       => ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o,X: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.25/1.54              ( ( P @ P2 @ Ys2 )
% 0.25/1.54             => ( P @ P2 @ ( cons_P1475164433e_form @ X @ Ys2 ) ) )
% 0.25/1.54         => ( P @ A0 @ A1 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_56_sorted__wrt_Oinduct,axiom,
% 0.25/1.54      ! [P: ( nat > nat > $o ) > list_nat > $o,A0: nat > nat > $o,A1: list_nat] :
% 0.25/1.54        ( ! [P2: nat > nat > $o] : ( P @ P2 @ nil_nat )
% 0.25/1.54       => ( ! [P2: nat > nat > $o,X: nat,Ys2: list_nat] :
% 0.25/1.54              ( ( P @ P2 @ Ys2 )
% 0.25/1.54             => ( P @ P2 @ ( cons_nat @ X @ Ys2 ) ) )
% 0.25/1.54         => ( P @ A0 @ A1 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_57_remdups__adj_Ocases,axiom,
% 0.25/1.54      ! [X2: list_P512754263e_form] :
% 0.25/1.54        ( ( X2 != nil_Pr1384483009e_form )
% 0.25/1.54       => ( ! [X: prover1687215943e_form] :
% 0.25/1.54              ( X2
% 0.25/1.54             != ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) )
% 0.25/1.54         => ~ ! [X: prover1687215943e_form,Y2: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.25/1.54                ( X2
% 0.25/1.54               != ( cons_P1475164433e_form @ X @ ( cons_P1475164433e_form @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_58_remdups__adj_Ocases,axiom,
% 0.25/1.54      ! [X2: list_nat] :
% 0.25/1.54        ( ( X2 != nil_nat )
% 0.25/1.54       => ( ! [X: nat] :
% 0.25/1.54              ( X2
% 0.25/1.54             != ( cons_nat @ X @ nil_nat ) )
% 0.25/1.54         => ~ ! [X: nat,Y2: nat,Xs2: list_nat] :
% 0.25/1.54                ( X2
% 0.25/1.54               != ( cons_nat @ X @ ( cons_nat @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_59_transpose_Ocases,axiom,
% 0.25/1.54      ! [X2: list_l461858535e_form] :
% 0.25/1.54        ( ( X2 != nil_li1393862353e_form )
% 0.25/1.54       => ( ! [Xss: list_l461858535e_form] :
% 0.25/1.54              ( X2
% 0.25/1.54             != ( cons_l1379921697e_form @ nil_Pr1384483009e_form @ Xss ) )
% 0.25/1.54         => ~ ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Xss: list_l461858535e_form] :
% 0.25/1.54                ( X2
% 0.25/1.54               != ( cons_l1379921697e_form @ ( cons_P1475164433e_form @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_60_transpose_Ocases,axiom,
% 0.25/1.54      ! [X2: list_list_nat] :
% 0.25/1.54        ( ( X2 != nil_list_nat )
% 0.25/1.54       => ( ! [Xss: list_list_nat] :
% 0.25/1.54              ( X2
% 0.25/1.54             != ( cons_list_nat @ nil_nat @ Xss ) )
% 0.25/1.54         => ~ ! [X: nat,Xs2: list_nat,Xss: list_list_nat] :
% 0.25/1.54                ( X2
% 0.25/1.54               != ( cons_list_nat @ ( cons_nat @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_61_shuffles_Oinduct,axiom,
% 0.25/1.54      ! [P: list_P512754263e_form > list_P512754263e_form > $o,A0: list_P512754263e_form,A1: list_P512754263e_form] :
% 0.25/1.54        ( ! [X_1: list_P512754263e_form] : ( P @ nil_Pr1384483009e_form @ X_1 )
% 0.25/1.54       => ( ! [Xs2: list_P512754263e_form] : ( P @ Xs2 @ nil_Pr1384483009e_form )
% 0.25/1.54         => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Y2: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.25/1.54                ( ( P @ Xs2 @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.25/1.54               => ( ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ Ys2 )
% 0.25/1.54                 => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) ) ) )
% 0.25/1.54           => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_62_shuffles_Oinduct,axiom,
% 0.25/1.54      ! [P: list_nat > list_nat > $o,A0: list_nat,A1: list_nat] :
% 0.25/1.54        ( ! [X_1: list_nat] : ( P @ nil_nat @ X_1 )
% 0.25/1.54       => ( ! [Xs2: list_nat] : ( P @ Xs2 @ nil_nat )
% 0.25/1.54         => ( ! [X: nat,Xs2: list_nat,Y2: nat,Ys2: list_nat] :
% 0.25/1.54                ( ( P @ Xs2 @ ( cons_nat @ Y2 @ Ys2 ) )
% 0.25/1.54               => ( ( P @ ( cons_nat @ X @ Xs2 ) @ Ys2 )
% 0.25/1.54                 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y2 @ Ys2 ) ) ) )
% 0.25/1.54           => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_63_min__list_Oinduct,axiom,
% 0.25/1.54      ! [P: list_nat > $o,A0: list_nat] :
% 0.25/1.54        ( ! [X: nat,Xs2: list_nat] :
% 0.25/1.54            ( ! [X212: nat,X222: list_nat] :
% 0.25/1.54                ( ( Xs2
% 0.25/1.54                  = ( cons_nat @ X212 @ X222 ) )
% 0.25/1.54               => ( P @ Xs2 ) )
% 0.25/1.54           => ( P @ ( cons_nat @ X @ Xs2 ) ) )
% 0.25/1.54       => ( ( P @ nil_nat )
% 0.25/1.54         => ( P @ A0 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_64_min__list_Ocases,axiom,
% 0.25/1.54      ! [X2: list_nat] :
% 0.25/1.54        ( ! [X: nat,Xs2: list_nat] :
% 0.25/1.54            ( X2
% 0.25/1.54           != ( cons_nat @ X @ Xs2 ) )
% 0.25/1.54       => ( X2 = nil_nat ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_65_induct__list012,axiom,
% 0.25/1.54      ! [P: list_P512754263e_form > $o,Xs: list_P512754263e_form] :
% 0.25/1.54        ( ( P @ nil_Pr1384483009e_form )
% 0.25/1.54       => ( ! [X: prover1687215943e_form] : ( P @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) )
% 0.25/1.54         => ( ! [X: prover1687215943e_form,Y2: prover1687215943e_form,Zs: list_P512754263e_form] :
% 0.25/1.54                ( ( P @ Zs )
% 0.25/1.54               => ( ( P @ ( cons_P1475164433e_form @ Y2 @ Zs ) )
% 0.25/1.54                 => ( P @ ( cons_P1475164433e_form @ X @ ( cons_P1475164433e_form @ Y2 @ Zs ) ) ) ) )
% 0.25/1.54           => ( P @ Xs ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_66_induct__list012,axiom,
% 0.25/1.54      ! [P: list_nat > $o,Xs: list_nat] :
% 0.25/1.54        ( ( P @ nil_nat )
% 0.25/1.54       => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 0.25/1.54         => ( ! [X: nat,Y2: nat,Zs: list_nat] :
% 0.25/1.54                ( ( P @ Zs )
% 0.25/1.54               => ( ( P @ ( cons_nat @ Y2 @ Zs ) )
% 0.25/1.54                 => ( P @ ( cons_nat @ X @ ( cons_nat @ Y2 @ Zs ) ) ) ) )
% 0.25/1.54           => ( P @ Xs ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_67_splice_Oinduct,axiom,
% 0.25/1.54      ! [P: list_P512754263e_form > list_P512754263e_form > $o,A0: list_P512754263e_form,A1: list_P512754263e_form] :
% 0.25/1.54        ( ! [X_1: list_P512754263e_form] : ( P @ nil_Pr1384483009e_form @ X_1 )
% 0.25/1.54       => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Ys2: list_P512754263e_form] :
% 0.25/1.54              ( ( P @ Ys2 @ Xs2 )
% 0.25/1.54             => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ Ys2 ) )
% 0.25/1.54         => ( P @ A0 @ A1 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_68_splice_Oinduct,axiom,
% 0.25/1.54      ! [P: list_nat > list_nat > $o,A0: list_nat,A1: list_nat] :
% 0.25/1.54        ( ! [X_1: list_nat] : ( P @ nil_nat @ X_1 )
% 0.25/1.54       => ( ! [X: nat,Xs2: list_nat,Ys2: list_nat] :
% 0.25/1.54              ( ( P @ Ys2 @ Xs2 )
% 0.25/1.54             => ( P @ ( cons_nat @ X @ Xs2 ) @ Ys2 ) )
% 0.25/1.54         => ( P @ A0 @ A1 ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_69_list__induct2_H,axiom,
% 0.25/1.54      ! [P: list_P512754263e_form > list_P512754263e_form > $o,Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.54        ( ( P @ nil_Pr1384483009e_form @ nil_Pr1384483009e_form )
% 0.25/1.54       => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] : ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ nil_Pr1384483009e_form )
% 0.25/1.54         => ( ! [Y2: prover1687215943e_form,Ys2: list_P512754263e_form] : ( P @ nil_Pr1384483009e_form @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.25/1.54           => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Y2: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.25/1.54                  ( ( P @ Xs2 @ Ys2 )
% 0.25/1.54                 => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) ) )
% 0.25/1.54             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_70_list__induct2_H,axiom,
% 0.25/1.54      ! [P: list_P512754263e_form > list_nat > $o,Xs: list_P512754263e_form,Ys: list_nat] :
% 0.25/1.54        ( ( P @ nil_Pr1384483009e_form @ nil_nat )
% 0.25/1.54       => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] : ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ nil_nat )
% 0.25/1.54         => ( ! [Y2: nat,Ys2: list_nat] : ( P @ nil_Pr1384483009e_form @ ( cons_nat @ Y2 @ Ys2 ) )
% 0.25/1.54           => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Y2: nat,Ys2: list_nat] :
% 0.25/1.54                  ( ( P @ Xs2 @ Ys2 )
% 0.25/1.54                 => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ ( cons_nat @ Y2 @ Ys2 ) ) )
% 0.25/1.54             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.25/1.54  
% 0.25/1.54  thf(fact_71_list__induct2_H,axiom,
% 0.25/1.54      ! [P: list_nat > list_P512754263e_form > $o,Xs: list_nat,Ys: list_P512754263e_form] :
% 0.25/1.54        ( ( P @ nil_nat @ nil_Pr1384483009e_form )
% 0.25/1.54       => ( ! [X: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X @ Xs2 ) @ nil_Pr1384483009e_form )
% 0.25/1.54         => ( ! [Y2: prover1687215943e_form,Ys2: list_P512754263e_form] : ( P @ nil_nat @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.25/1.55           => ( ! [X: nat,Xs2: list_nat,Y2: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.25/1.55                  ( ( P @ Xs2 @ Ys2 )
% 0.25/1.55                 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) ) )
% 0.25/1.55             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_72_list__induct2_H,axiom,
% 0.25/1.55      ! [P: list_nat > list_nat > $o,Xs: list_nat,Ys: list_nat] :
% 0.25/1.55        ( ( P @ nil_nat @ nil_nat )
% 0.25/1.55       => ( ! [X: nat,Xs2: list_nat] : ( P @ ( cons_nat @ X @ Xs2 ) @ nil_nat )
% 0.25/1.55         => ( ! [Y2: nat,Ys2: list_nat] : ( P @ nil_nat @ ( cons_nat @ Y2 @ Ys2 ) )
% 0.25/1.55           => ( ! [X: nat,Xs2: list_nat,Y2: nat,Ys2: list_nat] :
% 0.25/1.55                  ( ( P @ Xs2 @ Ys2 )
% 0.25/1.55                 => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y2 @ Ys2 ) ) )
% 0.25/1.55             => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_73_neq__Nil__conv,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( Xs != nil_Pr1384483009e_form )
% 0.25/1.55        = ( ? [Y3: prover1687215943e_form,Ys3: list_P512754263e_form] :
% 0.25/1.55              ( Xs
% 0.25/1.55              = ( cons_P1475164433e_form @ Y3 @ Ys3 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_74_neq__Nil__conv,axiom,
% 0.25/1.55      ! [Xs: list_nat] :
% 0.25/1.55        ( ( Xs != nil_nat )
% 0.25/1.55        = ( ? [Y3: nat,Ys3: list_nat] :
% 0.25/1.55              ( Xs
% 0.25/1.55              = ( cons_nat @ Y3 @ Ys3 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_75_list_Oinducts,axiom,
% 0.25/1.55      ! [P: list_P512754263e_form > $o,List: list_P512754263e_form] :
% 0.25/1.55        ( ( P @ nil_Pr1384483009e_form )
% 0.25/1.55       => ( ! [X1: prover1687215943e_form,X23: list_P512754263e_form] :
% 0.25/1.55              ( ( P @ X23 )
% 0.25/1.55             => ( P @ ( cons_P1475164433e_form @ X1 @ X23 ) ) )
% 0.25/1.55         => ( P @ List ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_76_list_Oinducts,axiom,
% 0.25/1.55      ! [P: list_nat > $o,List: list_nat] :
% 0.25/1.55        ( ( P @ nil_nat )
% 0.25/1.55       => ( ! [X1: nat,X23: list_nat] :
% 0.25/1.55              ( ( P @ X23 )
% 0.25/1.55             => ( P @ ( cons_nat @ X1 @ X23 ) ) )
% 0.25/1.55         => ( P @ List ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_77_list_Oexhaust,axiom,
% 0.25/1.55      ! [Y: list_P512754263e_form] :
% 0.25/1.55        ( ( Y != nil_Pr1384483009e_form )
% 0.25/1.55       => ~ ! [X213: prover1687215943e_form,X223: list_P512754263e_form] :
% 0.25/1.55              ( Y
% 0.25/1.55             != ( cons_P1475164433e_form @ X213 @ X223 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_78_list_Oexhaust,axiom,
% 0.25/1.55      ! [Y: list_nat] :
% 0.25/1.55        ( ( Y != nil_nat )
% 0.25/1.55       => ~ ! [X213: nat,X223: list_nat] :
% 0.25/1.55              ( Y
% 0.25/1.55             != ( cons_nat @ X213 @ X223 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_79_mem__Collect__eq,axiom,
% 0.25/1.55      ! [A: nat,P: nat > $o] :
% 0.25/1.55        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.25/1.55        = ( P @ A ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_80_Collect__mem__eq,axiom,
% 0.25/1.55      ! [A4: set_nat] :
% 0.25/1.55        ( ( collect_nat
% 0.25/1.55          @ ^ [X3: nat] : ( member_nat @ X3 @ A4 ) )
% 0.25/1.55        = A4 ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_81_list_OdiscI,axiom,
% 0.25/1.55      ! [List: list_P512754263e_form,X21: prover1687215943e_form,X22: list_P512754263e_form] :
% 0.25/1.55        ( ( List
% 0.25/1.55          = ( cons_P1475164433e_form @ X21 @ X22 ) )
% 0.25/1.55       => ( List != nil_Pr1384483009e_form ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_82_list_OdiscI,axiom,
% 0.25/1.55      ! [List: list_nat,X21: nat,X22: list_nat] :
% 0.25/1.55        ( ( List
% 0.25/1.55          = ( cons_nat @ X21 @ X22 ) )
% 0.25/1.55       => ( List != nil_nat ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_83_list_Odistinct_I1_J,axiom,
% 0.25/1.55      ! [X21: prover1687215943e_form,X22: list_P512754263e_form] :
% 0.25/1.55        ( nil_Pr1384483009e_form
% 0.25/1.55       != ( cons_P1475164433e_form @ X21 @ X22 ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_84_list_Odistinct_I1_J,axiom,
% 0.25/1.55      ! [X21: nat,X22: list_nat] :
% 0.25/1.55        ( nil_nat
% 0.25/1.55       != ( cons_nat @ X21 @ X22 ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_85_list_Oset__cases,axiom,
% 0.25/1.55      ! [E: prover1687215943e_form,A: list_P512754263e_form] :
% 0.25/1.55        ( ( member1793840734e_form @ E @ ( set_Pr1105237746e_form @ A ) )
% 0.25/1.55       => ( ! [Z2: list_P512754263e_form] :
% 0.25/1.55              ( A
% 0.25/1.55             != ( cons_P1475164433e_form @ E @ Z2 ) )
% 0.25/1.55         => ~ ! [Z1: prover1687215943e_form,Z2: list_P512754263e_form] :
% 0.25/1.55                ( ( A
% 0.25/1.55                  = ( cons_P1475164433e_form @ Z1 @ Z2 ) )
% 0.25/1.55               => ~ ( member1793840734e_form @ E @ ( set_Pr1105237746e_form @ Z2 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_86_list_Oset__cases,axiom,
% 0.25/1.55      ! [E: nat,A: list_nat] :
% 0.25/1.55        ( ( member_nat @ E @ ( set_nat2 @ A ) )
% 0.25/1.55       => ( ! [Z2: list_nat] :
% 0.25/1.55              ( A
% 0.25/1.55             != ( cons_nat @ E @ Z2 ) )
% 0.25/1.55         => ~ ! [Z1: nat,Z2: list_nat] :
% 0.25/1.55                ( ( A
% 0.25/1.55                  = ( cons_nat @ Z1 @ Z2 ) )
% 0.25/1.55               => ~ ( member_nat @ E @ ( set_nat2 @ Z2 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_87_set__ConsD,axiom,
% 0.25/1.55      ! [Y: prover1687215943e_form,X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( member1793840734e_form @ Y @ ( set_Pr1105237746e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) ) )
% 0.25/1.55       => ( ( Y = X2 )
% 0.25/1.55          | ( member1793840734e_form @ Y @ ( set_Pr1105237746e_form @ Xs ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_88_set__ConsD,axiom,
% 0.25/1.55      ! [Y: nat,X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ( member_nat @ Y @ ( set_nat2 @ ( cons_nat @ X2 @ Xs ) ) )
% 0.25/1.55       => ( ( Y = X2 )
% 0.25/1.55          | ( member_nat @ Y @ ( set_nat2 @ Xs ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_89_list_Oset__intros_I1_J,axiom,
% 0.25/1.55      ! [X21: prover1687215943e_form,X22: list_P512754263e_form] : ( member1793840734e_form @ X21 @ ( set_Pr1105237746e_form @ ( cons_P1475164433e_form @ X21 @ X22 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_90_list_Oset__intros_I1_J,axiom,
% 0.25/1.55      ! [X21: nat,X22: list_nat] : ( member_nat @ X21 @ ( set_nat2 @ ( cons_nat @ X21 @ X22 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_91_list_Oset__intros_I2_J,axiom,
% 0.25/1.55      ! [Y: prover1687215943e_form,X22: list_P512754263e_form,X21: prover1687215943e_form] :
% 0.25/1.55        ( ( member1793840734e_form @ Y @ ( set_Pr1105237746e_form @ X22 ) )
% 0.25/1.55       => ( member1793840734e_form @ Y @ ( set_Pr1105237746e_form @ ( cons_P1475164433e_form @ X21 @ X22 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_92_list_Oset__intros_I2_J,axiom,
% 0.25/1.55      ! [Y: nat,X22: list_nat,X21: nat] :
% 0.25/1.55        ( ( member_nat @ Y @ ( set_nat2 @ X22 ) )
% 0.25/1.55       => ( member_nat @ Y @ ( set_nat2 @ ( cons_nat @ X21 @ X22 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_93_append__Cons,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.55        ( ( append1038020460e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ Ys )
% 0.25/1.55        = ( cons_P1475164433e_form @ X2 @ ( append1038020460e_form @ Xs @ Ys ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_94_append__Cons,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat,Ys: list_nat] :
% 0.25/1.55        ( ( append_nat @ ( cons_nat @ X2 @ Xs ) @ Ys )
% 0.25/1.55        = ( cons_nat @ X2 @ ( append_nat @ Xs @ Ys ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_95_Cons__eq__appendI,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs1: list_P512754263e_form,Ys: list_P512754263e_form,Xs: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.25/1.55        ( ( ( cons_P1475164433e_form @ X2 @ Xs1 )
% 0.25/1.55          = Ys )
% 0.25/1.55       => ( ( Xs
% 0.25/1.55            = ( append1038020460e_form @ Xs1 @ Zs2 ) )
% 0.25/1.55         => ( ( cons_P1475164433e_form @ X2 @ Xs )
% 0.25/1.55            = ( append1038020460e_form @ Ys @ Zs2 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_96_Cons__eq__appendI,axiom,
% 0.25/1.55      ! [X2: nat,Xs1: list_nat,Ys: list_nat,Xs: list_nat,Zs2: list_nat] :
% 0.25/1.55        ( ( ( cons_nat @ X2 @ Xs1 )
% 0.25/1.55          = Ys )
% 0.25/1.55       => ( ( Xs
% 0.25/1.55            = ( append_nat @ Xs1 @ Zs2 ) )
% 0.25/1.55         => ( ( cons_nat @ X2 @ Xs )
% 0.25/1.55            = ( append_nat @ Ys @ Zs2 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_97_append_Oleft__neutral,axiom,
% 0.25/1.55      ! [A: list_P512754263e_form] :
% 0.25/1.55        ( ( append1038020460e_form @ nil_Pr1384483009e_form @ A )
% 0.25/1.55        = A ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_98_append_Oleft__neutral,axiom,
% 0.25/1.55      ! [A: list_nat] :
% 0.25/1.55        ( ( append_nat @ nil_nat @ A )
% 0.25/1.55        = A ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_99_append__Nil,axiom,
% 0.25/1.55      ! [Ys: list_P512754263e_form] :
% 0.25/1.55        ( ( append1038020460e_form @ nil_Pr1384483009e_form @ Ys )
% 0.25/1.55        = Ys ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_100_append__Nil,axiom,
% 0.25/1.55      ! [Ys: list_nat] :
% 0.25/1.55        ( ( append_nat @ nil_nat @ Ys )
% 0.25/1.55        = Ys ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_101_eq__Nil__appendI,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.55        ( ( Xs = Ys )
% 0.25/1.55       => ( Xs
% 0.25/1.55          = ( append1038020460e_form @ nil_Pr1384483009e_form @ Ys ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_102_eq__Nil__appendI,axiom,
% 0.25/1.55      ! [Xs: list_nat,Ys: list_nat] :
% 0.25/1.55        ( ( Xs = Ys )
% 0.25/1.55       => ( Xs
% 0.25/1.55          = ( append_nat @ nil_nat @ Ys ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_103_rev__nonempty__induct,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,P: list_P512754263e_form > $o] :
% 0.25/1.55        ( ( Xs != nil_Pr1384483009e_form )
% 0.25/1.55       => ( ! [X: prover1687215943e_form] : ( P @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) )
% 0.25/1.55         => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.25/1.55                ( ( Xs2 != nil_Pr1384483009e_form )
% 0.25/1.55               => ( ( P @ Xs2 )
% 0.25/1.55                 => ( P @ ( append1038020460e_form @ Xs2 @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) ) ) ) )
% 0.25/1.55           => ( P @ Xs ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_104_rev__nonempty__induct,axiom,
% 0.25/1.55      ! [Xs: list_nat,P: list_nat > $o] :
% 0.25/1.55        ( ( Xs != nil_nat )
% 0.25/1.55       => ( ! [X: nat] : ( P @ ( cons_nat @ X @ nil_nat ) )
% 0.25/1.55         => ( ! [X: nat,Xs2: list_nat] :
% 0.25/1.55                ( ( Xs2 != nil_nat )
% 0.25/1.55               => ( ( P @ Xs2 )
% 0.25/1.55                 => ( P @ ( append_nat @ Xs2 @ ( cons_nat @ X @ nil_nat ) ) ) ) )
% 0.25/1.55           => ( P @ Xs ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_105_append__eq__Cons__conv,axiom,
% 0.25/1.55      ! [Ys: list_P512754263e_form,Zs2: list_P512754263e_form,X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( ( append1038020460e_form @ Ys @ Zs2 )
% 0.25/1.55          = ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.25/1.55        = ( ( ( Ys = nil_Pr1384483009e_form )
% 0.25/1.55            & ( Zs2
% 0.25/1.55              = ( cons_P1475164433e_form @ X2 @ Xs ) ) )
% 0.25/1.55          | ? [Ys4: list_P512754263e_form] :
% 0.25/1.55              ( ( Ys
% 0.25/1.55                = ( cons_P1475164433e_form @ X2 @ Ys4 ) )
% 0.25/1.55              & ( ( append1038020460e_form @ Ys4 @ Zs2 )
% 0.25/1.55                = Xs ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_106_append__eq__Cons__conv,axiom,
% 0.25/1.55      ! [Ys: list_nat,Zs2: list_nat,X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ( ( append_nat @ Ys @ Zs2 )
% 0.25/1.55          = ( cons_nat @ X2 @ Xs ) )
% 0.25/1.55        = ( ( ( Ys = nil_nat )
% 0.25/1.55            & ( Zs2
% 0.25/1.55              = ( cons_nat @ X2 @ Xs ) ) )
% 0.25/1.55          | ? [Ys4: list_nat] :
% 0.25/1.55              ( ( Ys
% 0.25/1.55                = ( cons_nat @ X2 @ Ys4 ) )
% 0.25/1.55              & ( ( append_nat @ Ys4 @ Zs2 )
% 0.25/1.55                = Xs ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_107_Cons__eq__append__conv,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.25/1.55        ( ( ( cons_P1475164433e_form @ X2 @ Xs )
% 0.25/1.55          = ( append1038020460e_form @ Ys @ Zs2 ) )
% 0.25/1.55        = ( ( ( Ys = nil_Pr1384483009e_form )
% 0.25/1.55            & ( ( cons_P1475164433e_form @ X2 @ Xs )
% 0.25/1.55              = Zs2 ) )
% 0.25/1.55          | ? [Ys4: list_P512754263e_form] :
% 0.25/1.55              ( ( ( cons_P1475164433e_form @ X2 @ Ys4 )
% 0.25/1.55                = Ys )
% 0.25/1.55              & ( Xs
% 0.25/1.55                = ( append1038020460e_form @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_108_Cons__eq__append__conv,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.25/1.55        ( ( ( cons_nat @ X2 @ Xs )
% 0.25/1.55          = ( append_nat @ Ys @ Zs2 ) )
% 0.25/1.55        = ( ( ( Ys = nil_nat )
% 0.25/1.55            & ( ( cons_nat @ X2 @ Xs )
% 0.25/1.55              = Zs2 ) )
% 0.25/1.55          | ? [Ys4: list_nat] :
% 0.25/1.55              ( ( ( cons_nat @ X2 @ Ys4 )
% 0.25/1.55                = Ys )
% 0.25/1.55              & ( Xs
% 0.25/1.55                = ( append_nat @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_109_rev__exhaust,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( Xs != nil_Pr1384483009e_form )
% 0.25/1.55       => ~ ! [Ys2: list_P512754263e_form,Y2: prover1687215943e_form] :
% 0.25/1.55              ( Xs
% 0.25/1.55             != ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ Y2 @ nil_Pr1384483009e_form ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_110_rev__exhaust,axiom,
% 0.25/1.55      ! [Xs: list_nat] :
% 0.25/1.55        ( ( Xs != nil_nat )
% 0.25/1.55       => ~ ! [Ys2: list_nat,Y2: nat] :
% 0.25/1.55              ( Xs
% 0.25/1.55             != ( append_nat @ Ys2 @ ( cons_nat @ Y2 @ nil_nat ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_111_rev__induct,axiom,
% 0.25/1.55      ! [P: list_P512754263e_form > $o,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( P @ nil_Pr1384483009e_form )
% 0.25/1.55       => ( ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.25/1.55              ( ( P @ Xs2 )
% 0.25/1.55             => ( P @ ( append1038020460e_form @ Xs2 @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) ) ) )
% 0.25/1.55         => ( P @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_112_rev__induct,axiom,
% 0.25/1.55      ! [P: list_nat > $o,Xs: list_nat] :
% 0.25/1.55        ( ( P @ nil_nat )
% 0.25/1.55       => ( ! [X: nat,Xs2: list_nat] :
% 0.25/1.55              ( ( P @ Xs2 )
% 0.25/1.55             => ( P @ ( append_nat @ Xs2 @ ( cons_nat @ X @ nil_nat ) ) ) )
% 0.25/1.55         => ( P @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_113_split__list__first__prop__iff,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.25/1.55        ( ( ? [X3: prover1687215943e_form] :
% 0.25/1.55              ( ( member1793840734e_form @ X3 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55              & ( P @ X3 ) ) )
% 0.25/1.55        = ( ? [Ys3: list_P512754263e_form,X3: prover1687215943e_form] :
% 0.25/1.55              ( ? [Zs3: list_P512754263e_form] :
% 0.25/1.55                  ( Xs
% 0.25/1.55                  = ( append1038020460e_form @ Ys3 @ ( cons_P1475164433e_form @ X3 @ Zs3 ) ) )
% 0.25/1.55              & ( P @ X3 )
% 0.25/1.55              & ! [Y3: prover1687215943e_form] :
% 0.25/1.55                  ( ( member1793840734e_form @ Y3 @ ( set_Pr1105237746e_form @ Ys3 ) )
% 0.25/1.55                 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_114_split__list__first__prop__iff,axiom,
% 0.25/1.55      ! [Xs: list_nat,P: nat > $o] :
% 0.25/1.55        ( ( ? [X3: nat] :
% 0.25/1.55              ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.25/1.55              & ( P @ X3 ) ) )
% 0.25/1.55        = ( ? [Ys3: list_nat,X3: nat] :
% 0.25/1.55              ( ? [Zs3: list_nat] :
% 0.25/1.55                  ( Xs
% 0.25/1.55                  = ( append_nat @ Ys3 @ ( cons_nat @ X3 @ Zs3 ) ) )
% 0.25/1.55              & ( P @ X3 )
% 0.25/1.55              & ! [Y3: nat] :
% 0.25/1.55                  ( ( member_nat @ Y3 @ ( set_nat2 @ Ys3 ) )
% 0.25/1.55                 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_115_split__list__last__prop__iff,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.25/1.55        ( ( ? [X3: prover1687215943e_form] :
% 0.25/1.55              ( ( member1793840734e_form @ X3 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55              & ( P @ X3 ) ) )
% 0.25/1.55        = ( ? [Ys3: list_P512754263e_form,X3: prover1687215943e_form,Zs3: list_P512754263e_form] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( append1038020460e_form @ Ys3 @ ( cons_P1475164433e_form @ X3 @ Zs3 ) ) )
% 0.25/1.55              & ( P @ X3 )
% 0.25/1.55              & ! [Y3: prover1687215943e_form] :
% 0.25/1.55                  ( ( member1793840734e_form @ Y3 @ ( set_Pr1105237746e_form @ Zs3 ) )
% 0.25/1.55                 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_116_split__list__last__prop__iff,axiom,
% 0.25/1.55      ! [Xs: list_nat,P: nat > $o] :
% 0.25/1.55        ( ( ? [X3: nat] :
% 0.25/1.55              ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.25/1.55              & ( P @ X3 ) ) )
% 0.25/1.55        = ( ? [Ys3: list_nat,X3: nat,Zs3: list_nat] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( append_nat @ Ys3 @ ( cons_nat @ X3 @ Zs3 ) ) )
% 0.25/1.55              & ( P @ X3 )
% 0.25/1.55              & ! [Y3: nat] :
% 0.25/1.55                  ( ( member_nat @ Y3 @ ( set_nat2 @ Zs3 ) )
% 0.25/1.55                 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_117_in__set__conv__decomp__first,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55        = ( ? [Ys3: list_P512754263e_form,Zs3: list_P512754263e_form] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( append1038020460e_form @ Ys3 @ ( cons_P1475164433e_form @ X2 @ Zs3 ) ) )
% 0.25/1.55              & ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Ys3 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_118_in__set__conv__decomp__first,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.25/1.55        = ( ? [Ys3: list_nat,Zs3: list_nat] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( append_nat @ Ys3 @ ( cons_nat @ X2 @ Zs3 ) ) )
% 0.25/1.55              & ~ ( member_nat @ X2 @ ( set_nat2 @ Ys3 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_119_in__set__conv__decomp__last,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55        = ( ? [Ys3: list_P512754263e_form,Zs3: list_P512754263e_form] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( append1038020460e_form @ Ys3 @ ( cons_P1475164433e_form @ X2 @ Zs3 ) ) )
% 0.25/1.55              & ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Zs3 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_120_in__set__conv__decomp__last,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.25/1.55        = ( ? [Ys3: list_nat,Zs3: list_nat] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( append_nat @ Ys3 @ ( cons_nat @ X2 @ Zs3 ) ) )
% 0.25/1.55              & ~ ( member_nat @ X2 @ ( set_nat2 @ Zs3 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_121_split__list__first__propE,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.25/1.55        ( ? [X4: prover1687215943e_form] :
% 0.25/1.55            ( ( member1793840734e_form @ X4 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55            & ( P @ X4 ) )
% 0.25/1.55       => ~ ! [Ys2: list_P512754263e_form,X: prover1687215943e_form] :
% 0.25/1.55              ( ? [Zs: list_P512754263e_form] :
% 0.25/1.55                  ( Xs
% 0.25/1.55                  = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X @ Zs ) ) )
% 0.25/1.55             => ( ( P @ X )
% 0.25/1.55               => ~ ! [Xa: prover1687215943e_form] :
% 0.25/1.55                      ( ( member1793840734e_form @ Xa @ ( set_Pr1105237746e_form @ Ys2 ) )
% 0.25/1.55                     => ~ ( P @ Xa ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_122_split__list__first__propE,axiom,
% 0.25/1.55      ! [Xs: list_nat,P: nat > $o] :
% 0.25/1.55        ( ? [X4: nat] :
% 0.25/1.55            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.25/1.55            & ( P @ X4 ) )
% 0.25/1.55       => ~ ! [Ys2: list_nat,X: nat] :
% 0.25/1.55              ( ? [Zs: list_nat] :
% 0.25/1.55                  ( Xs
% 0.25/1.55                  = ( append_nat @ Ys2 @ ( cons_nat @ X @ Zs ) ) )
% 0.25/1.55             => ( ( P @ X )
% 0.25/1.55               => ~ ! [Xa: nat] :
% 0.25/1.55                      ( ( member_nat @ Xa @ ( set_nat2 @ Ys2 ) )
% 0.25/1.55                     => ~ ( P @ Xa ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_123_split__list__last__propE,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.25/1.55        ( ? [X4: prover1687215943e_form] :
% 0.25/1.55            ( ( member1793840734e_form @ X4 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55            & ( P @ X4 ) )
% 0.25/1.55       => ~ ! [Ys2: list_P512754263e_form,X: prover1687215943e_form,Zs: list_P512754263e_form] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X @ Zs ) ) )
% 0.25/1.55             => ( ( P @ X )
% 0.25/1.55               => ~ ! [Xa: prover1687215943e_form] :
% 0.25/1.55                      ( ( member1793840734e_form @ Xa @ ( set_Pr1105237746e_form @ Zs ) )
% 0.25/1.55                     => ~ ( P @ Xa ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_124_split__list__last__propE,axiom,
% 0.25/1.55      ! [Xs: list_nat,P: nat > $o] :
% 0.25/1.55        ( ? [X4: nat] :
% 0.25/1.55            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.25/1.55            & ( P @ X4 ) )
% 0.25/1.55       => ~ ! [Ys2: list_nat,X: nat,Zs: list_nat] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( append_nat @ Ys2 @ ( cons_nat @ X @ Zs ) ) )
% 0.25/1.55             => ( ( P @ X )
% 0.25/1.55               => ~ ! [Xa: nat] :
% 0.25/1.55                      ( ( member_nat @ Xa @ ( set_nat2 @ Zs ) )
% 0.25/1.55                     => ~ ( P @ Xa ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_125_split__list__first__prop,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.25/1.55        ( ? [X4: prover1687215943e_form] :
% 0.25/1.55            ( ( member1793840734e_form @ X4 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55            & ( P @ X4 ) )
% 0.25/1.55       => ? [Ys2: list_P512754263e_form,X: prover1687215943e_form] :
% 0.25/1.55            ( ? [Zs: list_P512754263e_form] :
% 0.25/1.55                ( Xs
% 0.25/1.55                = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X @ Zs ) ) )
% 0.25/1.55            & ( P @ X )
% 0.25/1.55            & ! [Xa: prover1687215943e_form] :
% 0.25/1.55                ( ( member1793840734e_form @ Xa @ ( set_Pr1105237746e_form @ Ys2 ) )
% 0.25/1.55               => ~ ( P @ Xa ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_126_split__list__first__prop,axiom,
% 0.25/1.55      ! [Xs: list_nat,P: nat > $o] :
% 0.25/1.55        ( ? [X4: nat] :
% 0.25/1.55            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.25/1.55            & ( P @ X4 ) )
% 0.25/1.55       => ? [Ys2: list_nat,X: nat] :
% 0.25/1.55            ( ? [Zs: list_nat] :
% 0.25/1.55                ( Xs
% 0.25/1.55                = ( append_nat @ Ys2 @ ( cons_nat @ X @ Zs ) ) )
% 0.25/1.55            & ( P @ X )
% 0.25/1.55            & ! [Xa: nat] :
% 0.25/1.55                ( ( member_nat @ Xa @ ( set_nat2 @ Ys2 ) )
% 0.25/1.55               => ~ ( P @ Xa ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_127_split__list__last__prop,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.25/1.55        ( ? [X4: prover1687215943e_form] :
% 0.25/1.55            ( ( member1793840734e_form @ X4 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55            & ( P @ X4 ) )
% 0.25/1.55       => ? [Ys2: list_P512754263e_form,X: prover1687215943e_form,Zs: list_P512754263e_form] :
% 0.25/1.55            ( ( Xs
% 0.25/1.55              = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X @ Zs ) ) )
% 0.25/1.55            & ( P @ X )
% 0.25/1.55            & ! [Xa: prover1687215943e_form] :
% 0.25/1.55                ( ( member1793840734e_form @ Xa @ ( set_Pr1105237746e_form @ Zs ) )
% 0.25/1.55               => ~ ( P @ Xa ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_128_split__list__last__prop,axiom,
% 0.25/1.55      ! [Xs: list_nat,P: nat > $o] :
% 0.25/1.55        ( ? [X4: nat] :
% 0.25/1.55            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.25/1.55            & ( P @ X4 ) )
% 0.25/1.55       => ? [Ys2: list_nat,X: nat,Zs: list_nat] :
% 0.25/1.55            ( ( Xs
% 0.25/1.55              = ( append_nat @ Ys2 @ ( cons_nat @ X @ Zs ) ) )
% 0.25/1.55            & ( P @ X )
% 0.25/1.55            & ! [Xa: nat] :
% 0.25/1.55                ( ( member_nat @ Xa @ ( set_nat2 @ Zs ) )
% 0.25/1.55               => ~ ( P @ Xa ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_129_in__set__conv__decomp,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55        = ( ? [Ys3: list_P512754263e_form,Zs3: list_P512754263e_form] :
% 0.25/1.55              ( Xs
% 0.25/1.55              = ( append1038020460e_form @ Ys3 @ ( cons_P1475164433e_form @ X2 @ Zs3 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_130_in__set__conv__decomp,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.25/1.55        = ( ? [Ys3: list_nat,Zs3: list_nat] :
% 0.25/1.55              ( Xs
% 0.25/1.55              = ( append_nat @ Ys3 @ ( cons_nat @ X2 @ Zs3 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_131_append__Cons__eq__iff,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form,Xs3: list_P512754263e_form,Ys5: list_P512754263e_form] :
% 0.25/1.55        ( ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55       => ( ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Ys ) )
% 0.25/1.55         => ( ( ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ Ys ) )
% 0.25/1.55              = ( append1038020460e_form @ Xs3 @ ( cons_P1475164433e_form @ X2 @ Ys5 ) ) )
% 0.25/1.55            = ( ( Xs = Xs3 )
% 0.25/1.55              & ( Ys = Ys5 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_132_append__Cons__eq__iff,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat,Ys: list_nat,Xs3: list_nat,Ys5: list_nat] :
% 0.25/1.55        ( ~ ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.25/1.55       => ( ~ ( member_nat @ X2 @ ( set_nat2 @ Ys ) )
% 0.25/1.55         => ( ( ( append_nat @ Xs @ ( cons_nat @ X2 @ Ys ) )
% 0.25/1.55              = ( append_nat @ Xs3 @ ( cons_nat @ X2 @ Ys5 ) ) )
% 0.25/1.55            = ( ( Xs = Xs3 )
% 0.25/1.55              & ( Ys = Ys5 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_133_split__list__propE,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.25/1.55        ( ? [X4: prover1687215943e_form] :
% 0.25/1.55            ( ( member1793840734e_form @ X4 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55            & ( P @ X4 ) )
% 0.25/1.55       => ~ ! [Ys2: list_P512754263e_form,X: prover1687215943e_form] :
% 0.25/1.55              ( ? [Zs: list_P512754263e_form] :
% 0.25/1.55                  ( Xs
% 0.25/1.55                  = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X @ Zs ) ) )
% 0.25/1.55             => ~ ( P @ X ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_134_split__list__propE,axiom,
% 0.25/1.55      ! [Xs: list_nat,P: nat > $o] :
% 0.25/1.55        ( ? [X4: nat] :
% 0.25/1.55            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.25/1.55            & ( P @ X4 ) )
% 0.25/1.55       => ~ ! [Ys2: list_nat,X: nat] :
% 0.25/1.55              ( ? [Zs: list_nat] :
% 0.25/1.55                  ( Xs
% 0.25/1.55                  = ( append_nat @ Ys2 @ ( cons_nat @ X @ Zs ) ) )
% 0.25/1.55             => ~ ( P @ X ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_135_split__list__first,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55       => ? [Ys2: list_P512754263e_form,Zs: list_P512754263e_form] :
% 0.25/1.55            ( ( Xs
% 0.25/1.55              = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X2 @ Zs ) ) )
% 0.25/1.55            & ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Ys2 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_136_split__list__first,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.25/1.55       => ? [Ys2: list_nat,Zs: list_nat] :
% 0.25/1.55            ( ( Xs
% 0.25/1.55              = ( append_nat @ Ys2 @ ( cons_nat @ X2 @ Zs ) ) )
% 0.25/1.55            & ~ ( member_nat @ X2 @ ( set_nat2 @ Ys2 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_137_split__list__prop,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,P: prover1687215943e_form > $o] :
% 0.25/1.55        ( ? [X4: prover1687215943e_form] :
% 0.25/1.55            ( ( member1793840734e_form @ X4 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55            & ( P @ X4 ) )
% 0.25/1.55       => ? [Ys2: list_P512754263e_form,X: prover1687215943e_form] :
% 0.25/1.55            ( ? [Zs: list_P512754263e_form] :
% 0.25/1.55                ( Xs
% 0.25/1.55                = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X @ Zs ) ) )
% 0.25/1.55            & ( P @ X ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_138_split__list__prop,axiom,
% 0.25/1.55      ! [Xs: list_nat,P: nat > $o] :
% 0.25/1.55        ( ? [X4: nat] :
% 0.25/1.55            ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 0.25/1.55            & ( P @ X4 ) )
% 0.25/1.55       => ? [Ys2: list_nat,X: nat] :
% 0.25/1.55            ( ? [Zs: list_nat] :
% 0.25/1.55                ( Xs
% 0.25/1.55                = ( append_nat @ Ys2 @ ( cons_nat @ X @ Zs ) ) )
% 0.25/1.55            & ( P @ X ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_139_split__list__last,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55       => ? [Ys2: list_P512754263e_form,Zs: list_P512754263e_form] :
% 0.25/1.55            ( ( Xs
% 0.25/1.55              = ( append1038020460e_form @ Ys2 @ ( cons_P1475164433e_form @ X2 @ Zs ) ) )
% 0.25/1.55            & ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Zs ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_140_split__list__last,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.25/1.55       => ? [Ys2: list_nat,Zs: list_nat] :
% 0.25/1.55            ( ( Xs
% 0.25/1.55              = ( append_nat @ Ys2 @ ( cons_nat @ X2 @ Zs ) ) )
% 0.25/1.55            & ~ ( member_nat @ X2 @ ( set_nat2 @ Zs ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_141_old_Oprod_Oinject,axiom,
% 0.25/1.55      ! [A: set_Pr619177522elle_U,B: nat > list_P796095576elle_U > $o,A5: set_Pr619177522elle_U,B2: nat > list_P796095576elle_U > $o] :
% 0.25/1.55        ( ( ( produc1069574002le_U_o @ A @ B )
% 0.25/1.55          = ( produc1069574002le_U_o @ A5 @ B2 ) )
% 0.25/1.55        = ( ( A = A5 )
% 0.25/1.55          & ( B = B2 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_142_prod_Oinject,axiom,
% 0.25/1.55      ! [X12: set_Pr619177522elle_U,X24: nat > list_P796095576elle_U > $o,Y1: set_Pr619177522elle_U,Y23: nat > list_P796095576elle_U > $o] :
% 0.25/1.55        ( ( ( produc1069574002le_U_o @ X12 @ X24 )
% 0.25/1.55          = ( produc1069574002le_U_o @ Y1 @ Y23 ) )
% 0.25/1.55        = ( ( X12 = Y1 )
% 0.25/1.55          & ( X24 = Y23 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_143_the__elem__set,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form] :
% 0.25/1.55        ( ( the_el969789074e_form @ ( set_Pr1105237746e_form @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) ) )
% 0.25/1.55        = X2 ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_144_the__elem__set,axiom,
% 0.25/1.55      ! [X2: nat] :
% 0.25/1.55        ( ( the_elem_nat @ ( set_nat2 @ ( cons_nat @ X2 @ nil_nat ) ) )
% 0.25/1.55        = X2 ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_145_bind__simps_I2_J,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,F: prover1687215943e_form > list_P512754263e_form] :
% 0.25/1.55        ( ( bind_P1054726576e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ F )
% 0.25/1.55        = ( append1038020460e_form @ ( F @ X2 ) @ ( bind_P1054726576e_form @ Xs @ F ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_146_bind__simps_I2_J,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,F: prover1687215943e_form > list_nat] :
% 0.25/1.55        ( ( bind_P1359331232rm_nat @ ( cons_P1475164433e_form @ X2 @ Xs ) @ F )
% 0.25/1.55        = ( append_nat @ ( F @ X2 ) @ ( bind_P1359331232rm_nat @ Xs @ F ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_147_bind__simps_I2_J,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat,F: nat > list_P512754263e_form] :
% 0.25/1.55        ( ( bind_n1193922848e_form @ ( cons_nat @ X2 @ Xs ) @ F )
% 0.25/1.55        = ( append1038020460e_form @ ( F @ X2 ) @ ( bind_n1193922848e_form @ Xs @ F ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_148_bind__simps_I2_J,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat,F: nat > list_nat] :
% 0.25/1.55        ( ( bind_nat_nat @ ( cons_nat @ X2 @ Xs ) @ F )
% 0.25/1.55        = ( append_nat @ ( F @ X2 ) @ ( bind_nat_nat @ Xs @ F ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_149_maps__simps_I1_J,axiom,
% 0.25/1.55      ! [F: prover1687215943e_form > list_P512754263e_form,X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( maps_P2058952566e_form @ F @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.25/1.55        = ( append1038020460e_form @ ( F @ X2 ) @ ( maps_P2058952566e_form @ F @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_150_maps__simps_I1_J,axiom,
% 0.25/1.55      ! [F: prover1687215943e_form > list_nat,X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( maps_P1549384538rm_nat @ F @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.25/1.55        = ( append_nat @ ( F @ X2 ) @ ( maps_P1549384538rm_nat @ F @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_151_maps__simps_I1_J,axiom,
% 0.25/1.55      ! [F: nat > list_P512754263e_form,X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ( maps_n1383976154e_form @ F @ ( cons_nat @ X2 @ Xs ) )
% 0.25/1.55        = ( append1038020460e_form @ ( F @ X2 ) @ ( maps_n1383976154e_form @ F @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_152_maps__simps_I1_J,axiom,
% 0.25/1.55      ! [F: nat > list_nat,X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ( maps_nat_nat @ F @ ( cons_nat @ X2 @ Xs ) )
% 0.25/1.55        = ( append_nat @ ( F @ X2 ) @ ( maps_nat_nat @ F @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_153_not__in__set__insert,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ~ ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55       => ( ( insert697320747e_form @ X2 @ Xs )
% 0.25/1.55          = ( cons_P1475164433e_form @ X2 @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_154_not__in__set__insert,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ~ ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.25/1.55       => ( ( insert_nat @ X2 @ Xs )
% 0.25/1.55          = ( cons_nat @ X2 @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_155_insert__Nil,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form] :
% 0.25/1.55        ( ( insert697320747e_form @ X2 @ nil_Pr1384483009e_form )
% 0.25/1.55        = ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_156_insert__Nil,axiom,
% 0.25/1.55      ! [X2: nat] :
% 0.25/1.55        ( ( insert_nat @ X2 @ nil_nat )
% 0.25/1.55        = ( cons_nat @ X2 @ nil_nat ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_157_sfv__cons,axiom,
% 0.25/1.55      ! [A: prover1687215943e_form,List: list_P512754263e_form] :
% 0.25/1.55        ( ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ A @ List ) )
% 0.25/1.55        = ( append_nat @ ( prover_Mirabelle_fv @ A ) @ ( prover_Mirabelle_sfv @ List ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_158_rotate1_Osimps_I2_J,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( rotate650061876e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.25/1.55        = ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_159_rotate1_Osimps_I2_J,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ( rotate1_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.25/1.55        = ( append_nat @ Xs @ ( cons_nat @ X2 @ nil_nat ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_160_butlast__snoc,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form] :
% 0.25/1.55        ( ( butlas664258165e_form @ ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) ) )
% 0.25/1.55        = Xs ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_161_butlast__snoc,axiom,
% 0.25/1.55      ! [Xs: list_nat,X2: nat] :
% 0.25/1.55        ( ( butlast_nat @ ( append_nat @ Xs @ ( cons_nat @ X2 @ nil_nat ) ) )
% 0.25/1.55        = Xs ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_162_rotate1__is__Nil__conv,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( ( rotate650061876e_form @ Xs )
% 0.25/1.55          = nil_Pr1384483009e_form )
% 0.25/1.55        = ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_163_rotate1__is__Nil__conv,axiom,
% 0.25/1.55      ! [Xs: list_nat] :
% 0.25/1.55        ( ( ( rotate1_nat @ Xs )
% 0.25/1.55          = nil_nat )
% 0.25/1.55        = ( Xs = nil_nat ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_164_set__rotate1,axiom,
% 0.25/1.55      ! [Xs: list_nat] :
% 0.25/1.55        ( ( set_nat2 @ ( rotate1_nat @ Xs ) )
% 0.25/1.55        = ( set_nat2 @ Xs ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_165_in__set__insert,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 0.25/1.55       => ( ( insert_nat @ X2 @ Xs )
% 0.25/1.55          = Xs ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_166_bind__simps_I1_J,axiom,
% 0.25/1.55      ! [F: prover1687215943e_form > list_P512754263e_form] :
% 0.25/1.55        ( ( bind_P1054726576e_form @ nil_Pr1384483009e_form @ F )
% 0.25/1.55        = nil_Pr1384483009e_form ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_167_bind__simps_I1_J,axiom,
% 0.25/1.55      ! [F: prover1687215943e_form > list_nat] :
% 0.25/1.55        ( ( bind_P1359331232rm_nat @ nil_Pr1384483009e_form @ F )
% 0.25/1.55        = nil_nat ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_168_bind__simps_I1_J,axiom,
% 0.25/1.55      ! [F: nat > list_P512754263e_form] :
% 0.25/1.55        ( ( bind_n1193922848e_form @ nil_nat @ F )
% 0.25/1.55        = nil_Pr1384483009e_form ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_169_bind__simps_I1_J,axiom,
% 0.25/1.55      ! [F: nat > list_nat] :
% 0.25/1.55        ( ( bind_nat_nat @ nil_nat @ F )
% 0.25/1.55        = nil_nat ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_170_butlast_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( butlas664258165e_form @ nil_Pr1384483009e_form )
% 0.25/1.55      = nil_Pr1384483009e_form ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_171_butlast_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( butlast_nat @ nil_nat )
% 0.25/1.55      = nil_nat ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_172_in__set__butlastD,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat] :
% 0.25/1.55        ( ( member_nat @ X2 @ ( set_nat2 @ ( butlast_nat @ Xs ) ) )
% 0.25/1.55       => ( member_nat @ X2 @ ( set_nat2 @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_173_rotate1_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( rotate650061876e_form @ nil_Pr1384483009e_form )
% 0.25/1.55      = nil_Pr1384483009e_form ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_174_rotate1_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( rotate1_nat @ nil_nat )
% 0.25/1.55      = nil_nat ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_175_sorted__wrt_Ocases,axiom,
% 0.25/1.55      ! [X2: produc957084248e_form] :
% 0.25/1.55        ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o] :
% 0.25/1.55            ( X2
% 0.25/1.55           != ( produc54611594e_form @ P2 @ nil_Pr1384483009e_form ) )
% 0.25/1.55       => ~ ! [P2: prover1687215943e_form > prover1687215943e_form > $o,X: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.25/1.55              ( X2
% 0.25/1.55             != ( produc54611594e_form @ P2 @ ( cons_P1475164433e_form @ X @ Ys2 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_176_sorted__wrt_Ocases,axiom,
% 0.25/1.55      ! [X2: produc890077173st_nat] :
% 0.25/1.55        ( ! [P2: nat > nat > $o] :
% 0.25/1.55            ( X2
% 0.25/1.55           != ( produc939441135st_nat @ P2 @ nil_nat ) )
% 0.25/1.55       => ~ ! [P2: nat > nat > $o,X: nat,Ys2: list_nat] :
% 0.25/1.55              ( X2
% 0.25/1.55             != ( produc939441135st_nat @ P2 @ ( cons_nat @ X @ Ys2 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_177_successively_Ocases,axiom,
% 0.25/1.55      ! [X2: produc957084248e_form] :
% 0.25/1.55        ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o] :
% 0.25/1.55            ( X2
% 0.25/1.55           != ( produc54611594e_form @ P2 @ nil_Pr1384483009e_form ) )
% 0.25/1.55       => ( ! [P2: prover1687215943e_form > prover1687215943e_form > $o,X: prover1687215943e_form] :
% 0.25/1.55              ( X2
% 0.25/1.55             != ( produc54611594e_form @ P2 @ ( cons_P1475164433e_form @ X @ nil_Pr1384483009e_form ) ) )
% 0.25/1.55         => ~ ! [P2: prover1687215943e_form > prover1687215943e_form > $o,X: prover1687215943e_form,Y2: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.25/1.55                ( X2
% 0.25/1.55               != ( produc54611594e_form @ P2 @ ( cons_P1475164433e_form @ X @ ( cons_P1475164433e_form @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_178_successively_Ocases,axiom,
% 0.25/1.55      ! [X2: produc890077173st_nat] :
% 0.25/1.55        ( ! [P2: nat > nat > $o] :
% 0.25/1.55            ( X2
% 0.25/1.55           != ( produc939441135st_nat @ P2 @ nil_nat ) )
% 0.25/1.55       => ( ! [P2: nat > nat > $o,X: nat] :
% 0.25/1.55              ( X2
% 0.25/1.55             != ( produc939441135st_nat @ P2 @ ( cons_nat @ X @ nil_nat ) ) )
% 0.25/1.55         => ~ ! [P2: nat > nat > $o,X: nat,Y2: nat,Xs2: list_nat] :
% 0.25/1.55                ( X2
% 0.25/1.55               != ( produc939441135st_nat @ P2 @ ( cons_nat @ X @ ( cons_nat @ Y2 @ Xs2 ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_179_splice_Ocases,axiom,
% 0.25/1.55      ! [X2: produc791938916e_form] :
% 0.25/1.55        ( ! [Ys2: list_P512754263e_form] :
% 0.25/1.55            ( X2
% 0.25/1.55           != ( produc891809686e_form @ nil_Pr1384483009e_form @ Ys2 ) )
% 0.25/1.55       => ~ ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Ys2: list_P512754263e_form] :
% 0.25/1.55              ( X2
% 0.25/1.55             != ( produc891809686e_form @ ( cons_P1475164433e_form @ X @ Xs2 ) @ Ys2 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_180_splice_Ocases,axiom,
% 0.25/1.55      ! [X2: produc1699244961st_nat] :
% 0.25/1.55        ( ! [Ys2: list_nat] :
% 0.25/1.55            ( X2
% 0.25/1.55           != ( produc1625736153st_nat @ nil_nat @ Ys2 ) )
% 0.25/1.55       => ~ ! [X: nat,Xs2: list_nat,Ys2: list_nat] :
% 0.25/1.55              ( X2
% 0.25/1.55             != ( produc1625736153st_nat @ ( cons_nat @ X @ Xs2 ) @ Ys2 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_181_shuffles_Ocases,axiom,
% 0.25/1.55      ! [X2: produc791938916e_form] :
% 0.25/1.55        ( ! [Ys2: list_P512754263e_form] :
% 0.25/1.55            ( X2
% 0.25/1.55           != ( produc891809686e_form @ nil_Pr1384483009e_form @ Ys2 ) )
% 0.25/1.55       => ( ! [Xs2: list_P512754263e_form] :
% 0.25/1.55              ( X2
% 0.25/1.55             != ( produc891809686e_form @ Xs2 @ nil_Pr1384483009e_form ) )
% 0.25/1.55         => ~ ! [X: prover1687215943e_form,Xs2: list_P512754263e_form,Y2: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.25/1.55                ( X2
% 0.25/1.55               != ( produc891809686e_form @ ( cons_P1475164433e_form @ X @ Xs2 ) @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_182_shuffles_Ocases,axiom,
% 0.25/1.55      ! [X2: produc1699244961st_nat] :
% 0.25/1.55        ( ! [Ys2: list_nat] :
% 0.25/1.55            ( X2
% 0.25/1.55           != ( produc1625736153st_nat @ nil_nat @ Ys2 ) )
% 0.25/1.55       => ( ! [Xs2: list_nat] :
% 0.25/1.55              ( X2
% 0.25/1.55             != ( produc1625736153st_nat @ Xs2 @ nil_nat ) )
% 0.25/1.55         => ~ ! [X: nat,Xs2: list_nat,Y2: nat,Ys2: list_nat] :
% 0.25/1.55                ( X2
% 0.25/1.55               != ( produc1625736153st_nat @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y2 @ Ys2 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_183_butlast_Osimps_I2_J,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form] :
% 0.25/1.55        ( ( ( Xs = nil_Pr1384483009e_form )
% 0.25/1.55         => ( ( butlas664258165e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.25/1.55            = nil_Pr1384483009e_form ) )
% 0.25/1.55        & ( ( Xs != nil_Pr1384483009e_form )
% 0.25/1.55         => ( ( butlas664258165e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.25/1.55            = ( cons_P1475164433e_form @ X2 @ ( butlas664258165e_form @ Xs ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_184_butlast_Osimps_I2_J,axiom,
% 0.25/1.55      ! [Xs: list_nat,X2: nat] :
% 0.25/1.55        ( ( ( Xs = nil_nat )
% 0.25/1.55         => ( ( butlast_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.25/1.55            = nil_nat ) )
% 0.25/1.55        & ( ( Xs != nil_nat )
% 0.25/1.55         => ( ( butlast_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.25/1.55            = ( cons_nat @ X2 @ ( butlast_nat @ Xs ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_185_butlast__append,axiom,
% 0.25/1.55      ! [Ys: list_P512754263e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( ( Ys = nil_Pr1384483009e_form )
% 0.25/1.55         => ( ( butlas664258165e_form @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.25/1.55            = ( butlas664258165e_form @ Xs ) ) )
% 0.25/1.55        & ( ( Ys != nil_Pr1384483009e_form )
% 0.25/1.55         => ( ( butlas664258165e_form @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.25/1.55            = ( append1038020460e_form @ Xs @ ( butlas664258165e_form @ Ys ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_186_butlast__append,axiom,
% 0.25/1.55      ! [Ys: list_nat,Xs: list_nat] :
% 0.25/1.55        ( ( ( Ys = nil_nat )
% 0.25/1.55         => ( ( butlast_nat @ ( append_nat @ Xs @ Ys ) )
% 0.25/1.55            = ( butlast_nat @ Xs ) ) )
% 0.25/1.55        & ( ( Ys != nil_nat )
% 0.25/1.55         => ( ( butlast_nat @ ( append_nat @ Xs @ Ys ) )
% 0.25/1.55            = ( append_nat @ Xs @ ( butlast_nat @ Ys ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_187_in__set__butlast__appendI,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.55        ( ( ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ ( butlas664258165e_form @ Xs ) ) )
% 0.25/1.55          | ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ ( butlas664258165e_form @ Ys ) ) ) )
% 0.25/1.55       => ( member1793840734e_form @ X2 @ ( set_Pr1105237746e_form @ ( butlas664258165e_form @ ( append1038020460e_form @ Xs @ Ys ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_188_in__set__butlast__appendI,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat,Ys: list_nat] :
% 0.25/1.55        ( ( ( member_nat @ X2 @ ( set_nat2 @ ( butlast_nat @ Xs ) ) )
% 0.25/1.55          | ( member_nat @ X2 @ ( set_nat2 @ ( butlast_nat @ Ys ) ) ) )
% 0.25/1.55       => ( member_nat @ X2 @ ( set_nat2 @ ( butlast_nat @ ( append_nat @ Xs @ Ys ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_189_maps__simps_I2_J,axiom,
% 0.25/1.55      ! [F: prover1687215943e_form > list_P512754263e_form] :
% 0.25/1.55        ( ( maps_P2058952566e_form @ F @ nil_Pr1384483009e_form )
% 0.25/1.55        = nil_Pr1384483009e_form ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_190_maps__simps_I2_J,axiom,
% 0.25/1.55      ! [F: prover1687215943e_form > list_nat] :
% 0.25/1.55        ( ( maps_P1549384538rm_nat @ F @ nil_Pr1384483009e_form )
% 0.25/1.55        = nil_nat ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_191_maps__simps_I2_J,axiom,
% 0.25/1.55      ! [F: nat > list_P512754263e_form] :
% 0.25/1.55        ( ( maps_n1383976154e_form @ F @ nil_nat )
% 0.25/1.55        = nil_Pr1384483009e_form ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_192_maps__simps_I2_J,axiom,
% 0.25/1.55      ! [F: nat > list_nat] :
% 0.25/1.55        ( ( maps_nat_nat @ F @ nil_nat )
% 0.25/1.55        = nil_nat ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_193_surj__pair,axiom,
% 0.25/1.55      ! [P3: produc227817602le_U_o] :
% 0.25/1.55      ? [X: set_Pr619177522elle_U,Y2: nat > list_P796095576elle_U > $o] :
% 0.25/1.55        ( P3
% 0.25/1.55        = ( produc1069574002le_U_o @ X @ Y2 ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_194_prod__cases,axiom,
% 0.25/1.55      ! [P: produc227817602le_U_o > $o,P3: produc227817602le_U_o] :
% 0.25/1.55        ( ! [A3: set_Pr619177522elle_U,B3: nat > list_P796095576elle_U > $o] : ( P @ ( produc1069574002le_U_o @ A3 @ B3 ) )
% 0.25/1.55       => ( P @ P3 ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_195_Pair__inject,axiom,
% 0.25/1.55      ! [A: set_Pr619177522elle_U,B: nat > list_P796095576elle_U > $o,A5: set_Pr619177522elle_U,B2: nat > list_P796095576elle_U > $o] :
% 0.25/1.55        ( ( ( produc1069574002le_U_o @ A @ B )
% 0.25/1.55          = ( produc1069574002le_U_o @ A5 @ B2 ) )
% 0.25/1.55       => ~ ( ( A = A5 )
% 0.25/1.55           => ( B != B2 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_196_old_Oprod_Oexhaust,axiom,
% 0.25/1.55      ! [Y: produc227817602le_U_o] :
% 0.25/1.55        ~ ! [A3: set_Pr619177522elle_U,B3: nat > list_P796095576elle_U > $o] :
% 0.25/1.55            ( Y
% 0.25/1.55           != ( produc1069574002le_U_o @ A3 @ B3 ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_197_old_Oprod_Oinducts,axiom,
% 0.25/1.55      ! [P: produc227817602le_U_o > $o,Prod: produc227817602le_U_o] :
% 0.25/1.55        ( ! [A3: set_Pr619177522elle_U,B3: nat > list_P796095576elle_U > $o] : ( P @ ( produc1069574002le_U_o @ A3 @ B3 ) )
% 0.25/1.55       => ( P @ Prod ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_198_List_Oinsert__def,axiom,
% 0.25/1.55      ( insert697320747e_form
% 0.25/1.55      = ( ^ [X3: prover1687215943e_form,Xs4: list_P512754263e_form] : ( if_lis1812881937e_form @ ( member1793840734e_form @ X3 @ ( set_Pr1105237746e_form @ Xs4 ) ) @ Xs4 @ ( cons_P1475164433e_form @ X3 @ Xs4 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_199_List_Oinsert__def,axiom,
% 0.25/1.55      ( insert_nat
% 0.25/1.55      = ( ^ [X3: nat,Xs4: list_nat] : ( if_list_nat @ ( member_nat @ X3 @ ( set_nat2 @ Xs4 ) ) @ Xs4 @ ( cons_nat @ X3 @ Xs4 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_200_flatten_Osimps_I2_J,axiom,
% 0.25/1.55      ! [A: list_P512754263e_form,List: list_l461858535e_form] :
% 0.25/1.55        ( ( prover542312166e_form @ ( cons_l1379921697e_form @ A @ List ) )
% 0.25/1.55        = ( append1038020460e_form @ A @ ( prover542312166e_form @ List ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_201_flatten_Osimps_I2_J,axiom,
% 0.25/1.55      ! [A: list_nat,List: list_list_nat] :
% 0.25/1.55        ( ( prover886976490en_nat @ ( cons_list_nat @ A @ List ) )
% 0.25/1.55        = ( append_nat @ A @ ( prover886976490en_nat @ List ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_202_flatten_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( prover542312166e_form @ nil_li1393862353e_form )
% 0.25/1.55      = nil_Pr1384483009e_form ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_203_flatten_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( prover886976490en_nat @ nil_list_nat )
% 0.25/1.55      = nil_nat ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_204_product__lists_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( produc168439576e_form @ nil_li1393862353e_form )
% 0.25/1.55      = ( cons_l1379921697e_form @ nil_Pr1384483009e_form @ nil_li1393862353e_form ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_205_product__lists_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( product_lists_nat @ nil_list_nat )
% 0.25/1.55      = ( cons_list_nat @ nil_nat @ nil_list_nat ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_206_append__butlast__last__id,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( Xs != nil_Pr1384483009e_form )
% 0.25/1.55       => ( ( append1038020460e_form @ ( butlas664258165e_form @ Xs ) @ ( cons_P1475164433e_form @ ( last_P1811260776e_form @ Xs ) @ nil_Pr1384483009e_form ) )
% 0.25/1.55          = Xs ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_207_append__butlast__last__id,axiom,
% 0.25/1.55      ! [Xs: list_nat] :
% 0.25/1.55        ( ( Xs != nil_nat )
% 0.25/1.55       => ( ( append_nat @ ( butlast_nat @ Xs ) @ ( cons_nat @ ( last_nat @ Xs ) @ nil_nat ) )
% 0.25/1.55          = Xs ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_208_fv_Osimps_I5_J,axiom,
% 0.25/1.55      ! [F: prover1687215943e_form] :
% 0.25/1.55        ( ( prover_Mirabelle_fv @ ( prover571163162e_FAll @ F ) )
% 0.25/1.55        = ( prover2096325705preSuc @ ( prover_Mirabelle_fv @ F ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_209_last__appendR,axiom,
% 0.25/1.55      ! [Ys: list_P512754263e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( Ys != nil_Pr1384483009e_form )
% 0.25/1.55       => ( ( last_P1811260776e_form @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.25/1.55          = ( last_P1811260776e_form @ Ys ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_210_last__appendR,axiom,
% 0.25/1.55      ! [Ys: list_nat,Xs: list_nat] :
% 0.25/1.55        ( ( Ys != nil_nat )
% 0.25/1.55       => ( ( last_nat @ ( append_nat @ Xs @ Ys ) )
% 0.25/1.55          = ( last_nat @ Ys ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_211_last__appendL,axiom,
% 0.25/1.55      ! [Ys: list_P512754263e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( Ys = nil_Pr1384483009e_form )
% 0.25/1.55       => ( ( last_P1811260776e_form @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.25/1.55          = ( last_P1811260776e_form @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_212_last__appendL,axiom,
% 0.25/1.55      ! [Ys: list_nat,Xs: list_nat] :
% 0.25/1.55        ( ( Ys = nil_nat )
% 0.25/1.55       => ( ( last_nat @ ( append_nat @ Xs @ Ys ) )
% 0.25/1.55          = ( last_nat @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_213_last__snoc,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form] :
% 0.25/1.55        ( ( last_P1811260776e_form @ ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) ) )
% 0.25/1.55        = X2 ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_214_last__snoc,axiom,
% 0.25/1.55      ! [Xs: list_nat,X2: nat] :
% 0.25/1.55        ( ( last_nat @ ( append_nat @ Xs @ ( cons_nat @ X2 @ nil_nat ) ) )
% 0.25/1.55        = X2 ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_215_last__ConsR,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form] :
% 0.25/1.55        ( ( Xs != nil_Pr1384483009e_form )
% 0.25/1.55       => ( ( last_P1811260776e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.25/1.55          = ( last_P1811260776e_form @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_216_last__ConsR,axiom,
% 0.25/1.55      ! [Xs: list_nat,X2: nat] :
% 0.25/1.55        ( ( Xs != nil_nat )
% 0.25/1.55       => ( ( last_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.25/1.55          = ( last_nat @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_217_last__ConsL,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form] :
% 0.25/1.55        ( ( Xs = nil_Pr1384483009e_form )
% 0.25/1.55       => ( ( last_P1811260776e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.25/1.55          = X2 ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_218_last__ConsL,axiom,
% 0.25/1.55      ! [Xs: list_nat,X2: nat] :
% 0.25/1.55        ( ( Xs = nil_nat )
% 0.25/1.55       => ( ( last_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.25/1.55          = X2 ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_219_last_Osimps,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form] :
% 0.25/1.55        ( ( ( Xs = nil_Pr1384483009e_form )
% 0.25/1.55         => ( ( last_P1811260776e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.25/1.55            = X2 ) )
% 0.25/1.55        & ( ( Xs != nil_Pr1384483009e_form )
% 0.25/1.55         => ( ( last_P1811260776e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) )
% 0.25/1.55            = ( last_P1811260776e_form @ Xs ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_220_last_Osimps,axiom,
% 0.25/1.55      ! [Xs: list_nat,X2: nat] :
% 0.25/1.55        ( ( ( Xs = nil_nat )
% 0.25/1.55         => ( ( last_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.25/1.55            = X2 ) )
% 0.25/1.55        & ( ( Xs != nil_nat )
% 0.25/1.55         => ( ( last_nat @ ( cons_nat @ X2 @ Xs ) )
% 0.25/1.55            = ( last_nat @ Xs ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_221_last__in__set,axiom,
% 0.25/1.55      ! [As2: list_P512754263e_form] :
% 0.25/1.55        ( ( As2 != nil_Pr1384483009e_form )
% 0.25/1.55       => ( member1793840734e_form @ ( last_P1811260776e_form @ As2 ) @ ( set_Pr1105237746e_form @ As2 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_222_last__in__set,axiom,
% 0.25/1.55      ! [As2: list_nat] :
% 0.25/1.55        ( ( As2 != nil_nat )
% 0.25/1.55       => ( member_nat @ ( last_nat @ As2 ) @ ( set_nat2 @ As2 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_223_longest__common__suffix,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.55      ? [Ss: list_P512754263e_form,Xs5: list_P512754263e_form,Ys6: list_P512754263e_form] :
% 0.25/1.55        ( ( Xs
% 0.25/1.55          = ( append1038020460e_form @ Xs5 @ Ss ) )
% 0.25/1.55        & ( Ys
% 0.25/1.55          = ( append1038020460e_form @ Ys6 @ Ss ) )
% 0.25/1.55        & ( ( Xs5 = nil_Pr1384483009e_form )
% 0.25/1.55          | ( Ys6 = nil_Pr1384483009e_form )
% 0.25/1.55          | ( ( last_P1811260776e_form @ Xs5 )
% 0.25/1.55           != ( last_P1811260776e_form @ Ys6 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_224_longest__common__suffix,axiom,
% 0.25/1.55      ! [Xs: list_nat,Ys: list_nat] :
% 0.25/1.55      ? [Ss: list_nat,Xs5: list_nat,Ys6: list_nat] :
% 0.25/1.55        ( ( Xs
% 0.25/1.55          = ( append_nat @ Xs5 @ Ss ) )
% 0.25/1.55        & ( Ys
% 0.25/1.55          = ( append_nat @ Ys6 @ Ss ) )
% 0.25/1.55        & ( ( Xs5 = nil_nat )
% 0.25/1.55          | ( Ys6 = nil_nat )
% 0.25/1.55          | ( ( last_nat @ Xs5 )
% 0.25/1.55           != ( last_nat @ Ys6 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_225_last__append,axiom,
% 0.25/1.55      ! [Ys: list_P512754263e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( ( Ys = nil_Pr1384483009e_form )
% 0.25/1.55         => ( ( last_P1811260776e_form @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.25/1.55            = ( last_P1811260776e_form @ Xs ) ) )
% 0.25/1.55        & ( ( Ys != nil_Pr1384483009e_form )
% 0.25/1.55         => ( ( last_P1811260776e_form @ ( append1038020460e_form @ Xs @ Ys ) )
% 0.25/1.55            = ( last_P1811260776e_form @ Ys ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_226_last__append,axiom,
% 0.25/1.55      ! [Ys: list_nat,Xs: list_nat] :
% 0.25/1.55        ( ( ( Ys = nil_nat )
% 0.25/1.55         => ( ( last_nat @ ( append_nat @ Xs @ Ys ) )
% 0.25/1.55            = ( last_nat @ Xs ) ) )
% 0.25/1.55        & ( ( Ys != nil_nat )
% 0.25/1.55         => ( ( last_nat @ ( append_nat @ Xs @ Ys ) )
% 0.25/1.55            = ( last_nat @ Ys ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_227_preSuc_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( prover2096325705preSuc @ nil_nat )
% 0.25/1.55      = nil_nat ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_228_snoc__eq__iff__butlast,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form,Ys: list_P512754263e_form] :
% 0.25/1.55        ( ( ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) )
% 0.25/1.55          = Ys )
% 0.25/1.55        = ( ( Ys != nil_Pr1384483009e_form )
% 0.25/1.55          & ( ( butlas664258165e_form @ Ys )
% 0.25/1.55            = Xs )
% 0.25/1.55          & ( ( last_P1811260776e_form @ Ys )
% 0.25/1.55            = X2 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_229_snoc__eq__iff__butlast,axiom,
% 0.25/1.55      ! [Xs: list_nat,X2: nat,Ys: list_nat] :
% 0.25/1.55        ( ( ( append_nat @ Xs @ ( cons_nat @ X2 @ nil_nat ) )
% 0.25/1.55          = Ys )
% 0.25/1.55        = ( ( Ys != nil_nat )
% 0.25/1.55          & ( ( butlast_nat @ Ys )
% 0.25/1.55            = Xs )
% 0.25/1.55          & ( ( last_nat @ Ys )
% 0.25/1.55            = X2 ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_230_snoc__listrel1__snoc__iff,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,X2: prover1687215943e_form,Ys: list_P512754263e_form,Y: prover1687215943e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ ( cons_P1475164433e_form @ X2 @ nil_Pr1384483009e_form ) ) @ ( append1038020460e_form @ Ys @ ( cons_P1475164433e_form @ Y @ nil_Pr1384483009e_form ) ) ) @ ( listre502458152e_form @ R ) )
% 0.25/1.55        = ( ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre502458152e_form @ R ) )
% 0.25/1.55            & ( X2 = Y ) )
% 0.25/1.55          | ( ( Xs = Ys )
% 0.25/1.55            & ( member189065477e_form @ ( produc1018812320e_form @ X2 @ Y ) @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_231_snoc__listrel1__snoc__iff,axiom,
% 0.25/1.55      ! [Xs: list_nat,X2: nat,Ys: list_nat,Y: nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ ( cons_nat @ X2 @ nil_nat ) ) @ ( append_nat @ Ys @ ( cons_nat @ Y @ nil_nat ) ) ) @ ( listrel1_nat @ R ) )
% 0.25/1.55        = ( ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) )
% 0.25/1.55            & ( X2 = Y ) )
% 0.25/1.55          | ( ( Xs = Ys )
% 0.25/1.55            & ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_232_subseqs_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( subseq1471997234e_form @ nil_Pr1384483009e_form )
% 0.25/1.55      = ( cons_l1379921697e_form @ nil_Pr1384483009e_form @ nil_li1393862353e_form ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_233_subseqs_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( subseqs_nat @ nil_nat )
% 0.25/1.55      = ( cons_list_nat @ nil_nat @ nil_list_nat ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_234_concat__eq__append__conv,axiom,
% 0.25/1.55      ! [Xss2: list_l461858535e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.25/1.55        ( ( ( concat1664984646e_form @ Xss2 )
% 0.25/1.55          = ( append1038020460e_form @ Ys @ Zs2 ) )
% 0.25/1.55        = ( ( ( Xss2 = nil_li1393862353e_form )
% 0.25/1.55           => ( ( Ys = nil_Pr1384483009e_form )
% 0.25/1.55              & ( Zs2 = nil_Pr1384483009e_form ) ) )
% 0.25/1.55          & ( ( Xss2 != nil_li1393862353e_form )
% 0.25/1.55           => ? [Xss1: list_l461858535e_form,Xs4: list_P512754263e_form,Xs6: list_P512754263e_form,Xss22: list_l461858535e_form] :
% 0.25/1.55                ( ( Xss2
% 0.25/1.55                  = ( append1797078012e_form @ Xss1 @ ( cons_l1379921697e_form @ ( append1038020460e_form @ Xs4 @ Xs6 ) @ Xss22 ) ) )
% 0.25/1.55                & ( Ys
% 0.25/1.55                  = ( append1038020460e_form @ ( concat1664984646e_form @ Xss1 ) @ Xs4 ) )
% 0.25/1.55                & ( Zs2
% 0.25/1.55                  = ( append1038020460e_form @ Xs6 @ ( concat1664984646e_form @ Xss22 ) ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_235_concat__eq__append__conv,axiom,
% 0.25/1.55      ! [Xss2: list_list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.25/1.55        ( ( ( concat_nat @ Xss2 )
% 0.25/1.55          = ( append_nat @ Ys @ Zs2 ) )
% 0.25/1.55        = ( ( ( Xss2 = nil_list_nat )
% 0.25/1.55           => ( ( Ys = nil_nat )
% 0.25/1.55              & ( Zs2 = nil_nat ) ) )
% 0.25/1.55          & ( ( Xss2 != nil_list_nat )
% 0.25/1.55           => ? [Xss1: list_list_nat,Xs4: list_nat,Xs6: list_nat,Xss22: list_list_nat] :
% 0.25/1.55                ( ( Xss2
% 0.25/1.55                  = ( append_list_nat @ Xss1 @ ( cons_list_nat @ ( append_nat @ Xs4 @ Xs6 ) @ Xss22 ) ) )
% 0.25/1.55                & ( Ys
% 0.25/1.55                  = ( append_nat @ ( concat_nat @ Xss1 ) @ Xs4 ) )
% 0.25/1.55                & ( Zs2
% 0.25/1.55                  = ( append_nat @ Xs6 @ ( concat_nat @ Xss22 ) ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_236_lexord__same__pref__iff,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ Ys ) @ ( append1038020460e_form @ Xs @ Zs2 ) ) @ ( lexord1848469012e_form @ R ) )
% 0.25/1.55        = ( ? [X3: prover1687215943e_form] :
% 0.25/1.55              ( ( member1793840734e_form @ X3 @ ( set_Pr1105237746e_form @ Xs ) )
% 0.25/1.55              & ( member189065477e_form @ ( produc1018812320e_form @ X3 @ X3 ) @ R ) )
% 0.25/1.55          | ( member650892795e_form @ ( produc891809686e_form @ Ys @ Zs2 ) @ ( lexord1848469012e_form @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_237_lexord__same__pref__iff,axiom,
% 0.25/1.55      ! [Xs: list_nat,Ys: list_nat,Zs2: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Ys ) @ ( append_nat @ Xs @ Zs2 ) ) @ ( lexord_nat @ R ) )
% 0.25/1.55        = ( ? [X3: nat] :
% 0.25/1.55              ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 0.25/1.55              & ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ R ) )
% 0.25/1.55          | ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Zs2 ) @ ( lexord_nat @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_238_concat__eq__Nil__conv,axiom,
% 0.25/1.55      ! [Xss2: list_l461858535e_form] :
% 0.25/1.55        ( ( ( concat1664984646e_form @ Xss2 )
% 0.25/1.55          = nil_Pr1384483009e_form )
% 0.25/1.55        = ( ! [X3: list_P512754263e_form] :
% 0.25/1.55              ( ( member1828782574e_form @ X3 @ ( set_li1219651714e_form @ Xss2 ) )
% 0.25/1.55             => ( X3 = nil_Pr1384483009e_form ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_239_concat__eq__Nil__conv,axiom,
% 0.25/1.55      ! [Xss2: list_list_nat] :
% 0.25/1.55        ( ( ( concat_nat @ Xss2 )
% 0.25/1.55          = nil_nat )
% 0.25/1.55        = ( ! [X3: list_nat] :
% 0.25/1.55              ( ( member_list_nat @ X3 @ ( set_list_nat2 @ Xss2 ) )
% 0.25/1.55             => ( X3 = nil_nat ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_240_Nil__eq__concat__conv,axiom,
% 0.25/1.55      ! [Xss2: list_l461858535e_form] :
% 0.25/1.55        ( ( nil_Pr1384483009e_form
% 0.25/1.55          = ( concat1664984646e_form @ Xss2 ) )
% 0.25/1.55        = ( ! [X3: list_P512754263e_form] :
% 0.25/1.55              ( ( member1828782574e_form @ X3 @ ( set_li1219651714e_form @ Xss2 ) )
% 0.25/1.55             => ( X3 = nil_Pr1384483009e_form ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_241_Nil__eq__concat__conv,axiom,
% 0.25/1.55      ! [Xss2: list_list_nat] :
% 0.25/1.55        ( ( nil_nat
% 0.25/1.55          = ( concat_nat @ Xss2 ) )
% 0.25/1.55        = ( ! [X3: list_nat] :
% 0.25/1.55              ( ( member_list_nat @ X3 @ ( set_list_nat2 @ Xss2 ) )
% 0.25/1.55             => ( X3 = nil_nat ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_242_concat__append,axiom,
% 0.25/1.55      ! [Xs: list_l461858535e_form,Ys: list_l461858535e_form] :
% 0.25/1.55        ( ( concat1664984646e_form @ ( append1797078012e_form @ Xs @ Ys ) )
% 0.25/1.55        = ( append1038020460e_form @ ( concat1664984646e_form @ Xs ) @ ( concat1664984646e_form @ Ys ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_243_concat__append,axiom,
% 0.25/1.55      ! [Xs: list_list_nat,Ys: list_list_nat] :
% 0.25/1.55        ( ( concat_nat @ ( append_list_nat @ Xs @ Ys ) )
% 0.25/1.55        = ( append_nat @ ( concat_nat @ Xs ) @ ( concat_nat @ Ys ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_244_Cons__listrel1__Cons,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,Y: prover1687215943e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ ( cons_P1475164433e_form @ Y @ Ys ) ) @ ( listre502458152e_form @ R ) )
% 0.25/1.55        = ( ( ( member189065477e_form @ ( produc1018812320e_form @ X2 @ Y ) @ R )
% 0.25/1.55            & ( Xs = Ys ) )
% 0.25/1.55          | ( ( X2 = Y )
% 0.25/1.55            & ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre502458152e_form @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_245_Cons__listrel1__Cons,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat,Y: nat,Ys: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X2 @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( listrel1_nat @ R ) )
% 0.25/1.55        = ( ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ R )
% 0.25/1.55            & ( Xs = Ys ) )
% 0.25/1.55          | ( ( X2 = Y )
% 0.25/1.55            & ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_246_lexord__cons__cons,axiom,
% 0.25/1.55      ! [A: prover1687215943e_form,X2: list_P512754263e_form,B: prover1687215943e_form,Y: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ A @ X2 ) @ ( cons_P1475164433e_form @ B @ Y ) ) @ ( lexord1848469012e_form @ R ) )
% 0.25/1.55        = ( ( member189065477e_form @ ( produc1018812320e_form @ A @ B ) @ R )
% 0.25/1.55          | ( ( A = B )
% 0.25/1.55            & ( member650892795e_form @ ( produc891809686e_form @ X2 @ Y ) @ ( lexord1848469012e_form @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_247_lexord__cons__cons,axiom,
% 0.25/1.55      ! [A: nat,X2: list_nat,B: nat,Y: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ A @ X2 ) @ ( cons_nat @ B @ Y ) ) @ ( lexord_nat @ R ) )
% 0.25/1.55        = ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.25/1.55          | ( ( A = B )
% 0.25/1.55            & ( member1926390090st_nat @ ( produc1625736153st_nat @ X2 @ Y ) @ ( lexord_nat @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_248_lexord__Nil__left,axiom,
% 0.25/1.55      ! [Y: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ nil_Pr1384483009e_form @ Y ) @ ( lexord1848469012e_form @ R ) )
% 0.25/1.55        = ( ? [A6: prover1687215943e_form,X3: list_P512754263e_form] :
% 0.25/1.55              ( Y
% 0.25/1.55              = ( cons_P1475164433e_form @ A6 @ X3 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_249_lexord__Nil__left,axiom,
% 0.25/1.55      ! [Y: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ nil_nat @ Y ) @ ( lexord_nat @ R ) )
% 0.25/1.55        = ( ? [A6: nat,X3: list_nat] :
% 0.25/1.55              ( Y
% 0.25/1.55              = ( cons_nat @ A6 @ X3 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_250_Cons__in__subseqsD,axiom,
% 0.25/1.55      ! [Y: prover1687215943e_form,Ys: list_P512754263e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( member1828782574e_form @ ( cons_P1475164433e_form @ Y @ Ys ) @ ( set_li1219651714e_form @ ( subseq1471997234e_form @ Xs ) ) )
% 0.25/1.55       => ( member1828782574e_form @ Ys @ ( set_li1219651714e_form @ ( subseq1471997234e_form @ Xs ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_251_Cons__in__subseqsD,axiom,
% 0.25/1.55      ! [Y: nat,Ys: list_nat,Xs: list_nat] :
% 0.25/1.55        ( ( member_list_nat @ ( cons_nat @ Y @ Ys ) @ ( set_list_nat2 @ ( subseqs_nat @ Xs ) ) )
% 0.25/1.55       => ( member_list_nat @ Ys @ ( set_list_nat2 @ ( subseqs_nat @ Xs ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_252_listrel1I2,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form,X2: prover1687215943e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre502458152e_form @ R ) )
% 0.25/1.55       => ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ ( cons_P1475164433e_form @ X2 @ Ys ) ) @ ( listre502458152e_form @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_253_listrel1I2,axiom,
% 0.25/1.55      ! [Xs: list_nat,Ys: list_nat,R: set_Pr1986765409at_nat,X2: nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) )
% 0.25/1.55       => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X2 @ Xs ) @ ( cons_nat @ X2 @ Ys ) ) @ ( listrel1_nat @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_254_not__listrel1__Nil,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ~ ( member650892795e_form @ ( produc891809686e_form @ Xs @ nil_Pr1384483009e_form ) @ ( listre502458152e_form @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_255_not__listrel1__Nil,axiom,
% 0.25/1.55      ! [Xs: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ nil_nat ) @ ( listrel1_nat @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_256_not__Nil__listrel1,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ~ ( member650892795e_form @ ( produc891809686e_form @ nil_Pr1384483009e_form @ Xs ) @ ( listre502458152e_form @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_257_not__Nil__listrel1,axiom,
% 0.25/1.55      ! [Xs: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ nil_nat @ Xs ) @ ( listrel1_nat @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_258_append__listrel1I,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form,Us2: list_P512754263e_form,Vs: list_P512754263e_form] :
% 0.25/1.55        ( ( ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre502458152e_form @ R ) )
% 0.25/1.55            & ( Us2 = Vs ) )
% 0.25/1.55          | ( ( Xs = Ys )
% 0.25/1.55            & ( member650892795e_form @ ( produc891809686e_form @ Us2 @ Vs ) @ ( listre502458152e_form @ R ) ) ) )
% 0.25/1.55       => ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ Us2 ) @ ( append1038020460e_form @ Ys @ Vs ) ) @ ( listre502458152e_form @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_259_append__listrel1I,axiom,
% 0.25/1.55      ! [Xs: list_nat,Ys: list_nat,R: set_Pr1986765409at_nat,Us2: list_nat,Vs: list_nat] :
% 0.25/1.55        ( ( ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) )
% 0.25/1.55            & ( Us2 = Vs ) )
% 0.25/1.55          | ( ( Xs = Ys )
% 0.25/1.55            & ( member1926390090st_nat @ ( produc1625736153st_nat @ Us2 @ Vs ) @ ( listrel1_nat @ R ) ) ) )
% 0.25/1.55       => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Us2 ) @ ( append_nat @ Ys @ Vs ) ) @ ( listrel1_nat @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_260_concat_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( concat1664984646e_form @ nil_li1393862353e_form )
% 0.25/1.55      = nil_Pr1384483009e_form ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_261_concat_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( concat_nat @ nil_list_nat )
% 0.25/1.55      = nil_nat ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_262_concat_Osimps_I2_J,axiom,
% 0.25/1.55      ! [X2: list_P512754263e_form,Xs: list_l461858535e_form] :
% 0.25/1.55        ( ( concat1664984646e_form @ ( cons_l1379921697e_form @ X2 @ Xs ) )
% 0.25/1.55        = ( append1038020460e_form @ X2 @ ( concat1664984646e_form @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_263_concat_Osimps_I2_J,axiom,
% 0.25/1.55      ! [X2: list_nat,Xs: list_list_nat] :
% 0.25/1.55        ( ( concat_nat @ ( cons_list_nat @ X2 @ Xs ) )
% 0.25/1.55        = ( append_nat @ X2 @ ( concat_nat @ Xs ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_264_lexord__Nil__right,axiom,
% 0.25/1.55      ! [X2: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ~ ( member650892795e_form @ ( produc891809686e_form @ X2 @ nil_Pr1384483009e_form ) @ ( lexord1848469012e_form @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_265_lexord__Nil__right,axiom,
% 0.25/1.55      ! [X2: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ X2 @ nil_nat ) @ ( lexord_nat @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_266_lexord__append__leftI,axiom,
% 0.25/1.55      ! [U: list_P512754263e_form,V: list_P512754263e_form,R: set_Pr1189404964e_form,X2: list_P512754263e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ U @ V ) @ ( lexord1848469012e_form @ R ) )
% 0.25/1.55       => ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ X2 @ U ) @ ( append1038020460e_form @ X2 @ V ) ) @ ( lexord1848469012e_form @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_267_lexord__append__leftI,axiom,
% 0.25/1.55      ! [U: list_nat,V: list_nat,R: set_Pr1986765409at_nat,X2: list_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ U @ V ) @ ( lexord_nat @ R ) )
% 0.25/1.55       => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ X2 @ U ) @ ( append_nat @ X2 @ V ) ) @ ( lexord_nat @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_268_listrel1I1,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Y: prover1687215943e_form,R: set_Pr1189404964e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( member189065477e_form @ ( produc1018812320e_form @ X2 @ Y ) @ R )
% 0.25/1.55       => ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ ( cons_P1475164433e_form @ Y @ Xs ) ) @ ( listre502458152e_form @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_269_listrel1I1,axiom,
% 0.25/1.55      ! [X2: nat,Y: nat,R: set_Pr1986765409at_nat,Xs: list_nat] :
% 0.25/1.55        ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ R )
% 0.25/1.55       => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X2 @ Xs ) @ ( cons_nat @ Y @ Xs ) ) @ ( listrel1_nat @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_270_Cons__listrel1E1,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ Ys ) @ ( listre502458152e_form @ R ) )
% 0.25/1.55       => ( ! [Y2: prover1687215943e_form] :
% 0.25/1.55              ( ( Ys
% 0.25/1.55                = ( cons_P1475164433e_form @ Y2 @ Xs ) )
% 0.25/1.55             => ~ ( member189065477e_form @ ( produc1018812320e_form @ X2 @ Y2 ) @ R ) )
% 0.25/1.55         => ~ ! [Zs: list_P512754263e_form] :
% 0.25/1.55                ( ( Ys
% 0.25/1.55                  = ( cons_P1475164433e_form @ X2 @ Zs ) )
% 0.25/1.55               => ~ ( member650892795e_form @ ( produc891809686e_form @ Xs @ Zs ) @ ( listre502458152e_form @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_271_Cons__listrel1E1,axiom,
% 0.25/1.55      ! [X2: nat,Xs: list_nat,Ys: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X2 @ Xs ) @ Ys ) @ ( listrel1_nat @ R ) )
% 0.25/1.55       => ( ! [Y2: nat] :
% 0.25/1.55              ( ( Ys
% 0.25/1.55                = ( cons_nat @ Y2 @ Xs ) )
% 0.25/1.55             => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y2 ) @ R ) )
% 0.25/1.55         => ~ ! [Zs: list_nat] :
% 0.25/1.55                ( ( Ys
% 0.25/1.55                  = ( cons_nat @ X2 @ Zs ) )
% 0.25/1.55               => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Zs ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_272_Cons__listrel1E2,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,Y: prover1687215943e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ ( cons_P1475164433e_form @ Y @ Ys ) ) @ ( listre502458152e_form @ R ) )
% 0.25/1.55       => ( ! [X: prover1687215943e_form] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( cons_P1475164433e_form @ X @ Ys ) )
% 0.25/1.55             => ~ ( member189065477e_form @ ( produc1018812320e_form @ X @ Y ) @ R ) )
% 0.25/1.55         => ~ ! [Zs: list_P512754263e_form] :
% 0.25/1.55                ( ( Xs
% 0.25/1.55                  = ( cons_P1475164433e_form @ Y @ Zs ) )
% 0.25/1.55               => ~ ( member650892795e_form @ ( produc891809686e_form @ Zs @ Ys ) @ ( listre502458152e_form @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_273_Cons__listrel1E2,axiom,
% 0.25/1.55      ! [Xs: list_nat,Y: nat,Ys: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ ( cons_nat @ Y @ Ys ) ) @ ( listrel1_nat @ R ) )
% 0.25/1.55       => ( ! [X: nat] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( cons_nat @ X @ Ys ) )
% 0.25/1.55             => ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R ) )
% 0.25/1.55         => ~ ! [Zs: list_nat] :
% 0.25/1.55                ( ( Xs
% 0.25/1.55                  = ( cons_nat @ Y @ Zs ) )
% 0.25/1.55               => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Zs @ Ys ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_274_lexord__partial__trans,axiom,
% 0.25/1.55      ! [Xs: list_nat,R: set_Pr1986765409at_nat,Ys: list_nat,Zs2: list_nat] :
% 0.25/1.55        ( ! [X: nat,Y2: nat,Z: nat] :
% 0.25/1.55            ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 0.25/1.55           => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R )
% 0.25/1.55             => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y2 @ Z ) @ R )
% 0.25/1.55               => ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Z ) @ R ) ) ) )
% 0.25/1.55       => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( lexord_nat @ R ) )
% 0.25/1.55         => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Zs2 ) @ ( lexord_nat @ R ) )
% 0.25/1.55           => ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Zs2 ) @ ( lexord_nat @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_275_lexord__append__leftD,axiom,
% 0.25/1.55      ! [X2: list_P512754263e_form,U: list_P512754263e_form,V: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ X2 @ U ) @ ( append1038020460e_form @ X2 @ V ) ) @ ( lexord1848469012e_form @ R ) )
% 0.25/1.55       => ( ! [A3: prover1687215943e_form] :
% 0.25/1.55              ~ ( member189065477e_form @ ( produc1018812320e_form @ A3 @ A3 ) @ R )
% 0.25/1.55         => ( member650892795e_form @ ( produc891809686e_form @ U @ V ) @ ( lexord1848469012e_form @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_276_lexord__append__leftD,axiom,
% 0.25/1.55      ! [X2: list_nat,U: list_nat,V: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ X2 @ U ) @ ( append_nat @ X2 @ V ) ) @ ( lexord_nat @ R ) )
% 0.25/1.55       => ( ! [A3: nat] :
% 0.25/1.55              ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ A3 @ A3 ) @ R )
% 0.25/1.55         => ( member1926390090st_nat @ ( produc1625736153st_nat @ U @ V ) @ ( lexord_nat @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_277_lexord__append__rightI,axiom,
% 0.25/1.55      ! [Y: list_P512754263e_form,X2: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ? [B4: prover1687215943e_form,Z3: list_P512754263e_form] :
% 0.25/1.55            ( Y
% 0.25/1.55            = ( cons_P1475164433e_form @ B4 @ Z3 ) )
% 0.25/1.55       => ( member650892795e_form @ ( produc891809686e_form @ X2 @ ( append1038020460e_form @ X2 @ Y ) ) @ ( lexord1848469012e_form @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_278_lexord__append__rightI,axiom,
% 0.25/1.55      ! [Y: list_nat,X2: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ? [B4: nat,Z3: list_nat] :
% 0.25/1.55            ( Y
% 0.25/1.55            = ( cons_nat @ B4 @ Z3 ) )
% 0.25/1.55       => ( member1926390090st_nat @ ( produc1625736153st_nat @ X2 @ ( append_nat @ X2 @ Y ) ) @ ( lexord_nat @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_279_concat__eq__appendD,axiom,
% 0.25/1.55      ! [Xss2: list_l461858535e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.25/1.55        ( ( ( concat1664984646e_form @ Xss2 )
% 0.25/1.55          = ( append1038020460e_form @ Ys @ Zs2 ) )
% 0.25/1.55       => ( ( Xss2 != nil_li1393862353e_form )
% 0.25/1.55         => ? [Xss12: list_l461858535e_form,Xs2: list_P512754263e_form,Xs5: list_P512754263e_form,Xss23: list_l461858535e_form] :
% 0.25/1.55              ( ( Xss2
% 0.25/1.55                = ( append1797078012e_form @ Xss12 @ ( cons_l1379921697e_form @ ( append1038020460e_form @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.25/1.55              & ( Ys
% 0.25/1.55                = ( append1038020460e_form @ ( concat1664984646e_form @ Xss12 ) @ Xs2 ) )
% 0.25/1.55              & ( Zs2
% 0.25/1.55                = ( append1038020460e_form @ Xs5 @ ( concat1664984646e_form @ Xss23 ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_280_concat__eq__appendD,axiom,
% 0.25/1.55      ! [Xss2: list_list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.25/1.55        ( ( ( concat_nat @ Xss2 )
% 0.25/1.55          = ( append_nat @ Ys @ Zs2 ) )
% 0.25/1.55       => ( ( Xss2 != nil_list_nat )
% 0.25/1.55         => ? [Xss12: list_list_nat,Xs2: list_nat,Xs5: list_nat,Xss23: list_list_nat] :
% 0.25/1.55              ( ( Xss2
% 0.25/1.55                = ( append_list_nat @ Xss12 @ ( cons_list_nat @ ( append_nat @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.25/1.55              & ( Ys
% 0.25/1.55                = ( append_nat @ ( concat_nat @ Xss12 ) @ Xs2 ) )
% 0.25/1.55              & ( Zs2
% 0.25/1.55                = ( append_nat @ Xs5 @ ( concat_nat @ Xss23 ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_281_listrel1E,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre502458152e_form @ R ) )
% 0.25/1.55       => ~ ! [X: prover1687215943e_form,Y2: prover1687215943e_form] :
% 0.25/1.55              ( ( member189065477e_form @ ( produc1018812320e_form @ X @ Y2 ) @ R )
% 0.25/1.55             => ! [Us3: list_P512754263e_form,Vs2: list_P512754263e_form] :
% 0.25/1.55                  ( ( Xs
% 0.25/1.55                    = ( append1038020460e_form @ Us3 @ ( cons_P1475164433e_form @ X @ Vs2 ) ) )
% 0.25/1.55                 => ( Ys
% 0.25/1.55                   != ( append1038020460e_form @ Us3 @ ( cons_P1475164433e_form @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_282_listrel1E,axiom,
% 0.25/1.55      ! [Xs: list_nat,Ys: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) )
% 0.25/1.55       => ~ ! [X: nat,Y2: nat] :
% 0.25/1.55              ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R )
% 0.25/1.55             => ! [Us3: list_nat,Vs2: list_nat] :
% 0.25/1.55                  ( ( Xs
% 0.25/1.55                    = ( append_nat @ Us3 @ ( cons_nat @ X @ Vs2 ) ) )
% 0.25/1.55                 => ( Ys
% 0.25/1.55                   != ( append_nat @ Us3 @ ( cons_nat @ Y2 @ Vs2 ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_283_listrel1I,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Y: prover1687215943e_form,R: set_Pr1189404964e_form,Xs: list_P512754263e_form,Us2: list_P512754263e_form,Vs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.55        ( ( member189065477e_form @ ( produc1018812320e_form @ X2 @ Y ) @ R )
% 0.25/1.55       => ( ( Xs
% 0.25/1.55            = ( append1038020460e_form @ Us2 @ ( cons_P1475164433e_form @ X2 @ Vs ) ) )
% 0.25/1.55         => ( ( Ys
% 0.25/1.55              = ( append1038020460e_form @ Us2 @ ( cons_P1475164433e_form @ Y @ Vs ) ) )
% 0.25/1.55           => ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre502458152e_form @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_284_listrel1I,axiom,
% 0.25/1.55      ! [X2: nat,Y: nat,R: set_Pr1986765409at_nat,Xs: list_nat,Us2: list_nat,Vs: list_nat,Ys: list_nat] :
% 0.25/1.55        ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ R )
% 0.25/1.55       => ( ( Xs
% 0.25/1.55            = ( append_nat @ Us2 @ ( cons_nat @ X2 @ Vs ) ) )
% 0.25/1.55         => ( ( Ys
% 0.25/1.55              = ( append_nat @ Us2 @ ( cons_nat @ Y @ Vs ) ) )
% 0.25/1.55           => ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel1_nat @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_285_lexord__append__left__rightI,axiom,
% 0.25/1.55      ! [A: prover1687215943e_form,B: prover1687215943e_form,R: set_Pr1189404964e_form,U: list_P512754263e_form,X2: list_P512754263e_form,Y: list_P512754263e_form] :
% 0.25/1.55        ( ( member189065477e_form @ ( produc1018812320e_form @ A @ B ) @ R )
% 0.25/1.55       => ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ U @ ( cons_P1475164433e_form @ A @ X2 ) ) @ ( append1038020460e_form @ U @ ( cons_P1475164433e_form @ B @ Y ) ) ) @ ( lexord1848469012e_form @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_286_lexord__append__left__rightI,axiom,
% 0.25/1.55      ! [A: nat,B: nat,R: set_Pr1986765409at_nat,U: list_nat,X2: list_nat,Y: list_nat] :
% 0.25/1.55        ( ( member701585322at_nat @ ( product_Pair_nat_nat @ A @ B ) @ R )
% 0.25/1.55       => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ U @ ( cons_nat @ A @ X2 ) ) @ ( append_nat @ U @ ( cons_nat @ B @ Y ) ) ) @ ( lexord_nat @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_287_lexord__same__pref__if__irrefl,axiom,
% 0.25/1.55      ! [R: set_Pr1189404964e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.25/1.55        ( ( irrefl2121388754e_form @ R )
% 0.25/1.55       => ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ Ys ) @ ( append1038020460e_form @ Xs @ Zs2 ) ) @ ( lexord1848469012e_form @ R ) )
% 0.25/1.55          = ( member650892795e_form @ ( produc891809686e_form @ Ys @ Zs2 ) @ ( lexord1848469012e_form @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_288_lexord__same__pref__if__irrefl,axiom,
% 0.25/1.55      ! [R: set_Pr1986765409at_nat,Xs: list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.25/1.55        ( ( irrefl_nat @ R )
% 0.25/1.55       => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Ys ) @ ( append_nat @ Xs @ Zs2 ) ) @ ( lexord_nat @ R ) )
% 0.25/1.55          = ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Zs2 ) @ ( lexord_nat @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_289_listrel_Ocases,axiom,
% 0.25/1.55      ! [A1: list_P512754263e_form,A2: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ A1 @ A2 ) @ ( listre1908795590e_form @ R ) )
% 0.25/1.55       => ( ( ( A1 = nil_Pr1384483009e_form )
% 0.25/1.55           => ( A2 != nil_Pr1384483009e_form ) )
% 0.25/1.55         => ~ ! [X: prover1687215943e_form,Y2: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.25/1.55                ( ( A1
% 0.25/1.55                  = ( cons_P1475164433e_form @ X @ Xs2 ) )
% 0.25/1.55               => ! [Ys2: list_P512754263e_form] :
% 0.25/1.55                    ( ( A2
% 0.25/1.55                      = ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.25/1.55                   => ( ( member189065477e_form @ ( produc1018812320e_form @ X @ Y2 ) @ R )
% 0.25/1.55                     => ~ ( member650892795e_form @ ( produc891809686e_form @ Xs2 @ Ys2 ) @ ( listre1908795590e_form @ R ) ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_290_listrel_Ocases,axiom,
% 0.25/1.55      ! [A1: list_P512754263e_form,A2: list_nat,R: set_Pr957084504rm_nat] :
% 0.25/1.55        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ A1 @ A2 ) @ ( listre483706378rm_nat @ R ) )
% 0.25/1.55       => ( ( ( A1 = nil_Pr1384483009e_form )
% 0.25/1.55           => ( A2 != nil_nat ) )
% 0.25/1.55         => ~ ! [X: prover1687215943e_form,Y2: nat,Xs2: list_P512754263e_form] :
% 0.25/1.55                ( ( A1
% 0.25/1.55                  = ( cons_P1475164433e_form @ X @ Xs2 ) )
% 0.25/1.55               => ! [Ys2: list_nat] :
% 0.25/1.55                    ( ( A2
% 0.25/1.55                      = ( cons_nat @ Y2 @ Ys2 ) )
% 0.25/1.55                   => ( ( member986698273rm_nat @ ( produc1041874352rm_nat @ X @ Y2 ) @ R )
% 0.25/1.55                     => ~ ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs2 @ Ys2 ) @ ( listre483706378rm_nat @ R ) ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_291_listrel_Ocases,axiom,
% 0.25/1.55      ! [A1: list_nat,A2: list_P512754263e_form,R: set_Pr816919384e_form] :
% 0.25/1.55        ( ( member1471151041e_form @ ( produc1617574096e_form @ A1 @ A2 ) @ ( listre318297994e_form @ R ) )
% 0.25/1.55       => ( ( ( A1 = nil_nat )
% 0.25/1.55           => ( A2 != nil_Pr1384483009e_form ) )
% 0.25/1.55         => ~ ! [X: nat,Y2: prover1687215943e_form,Xs2: list_nat] :
% 0.25/1.55                ( ( A1
% 0.25/1.55                  = ( cons_nat @ X @ Xs2 ) )
% 0.25/1.55               => ! [Ys2: list_P512754263e_form] :
% 0.25/1.55                    ( ( A2
% 0.25/1.55                      = ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.25/1.55                   => ( ( member18158113e_form @ ( produc876465968e_form @ X @ Y2 ) @ R )
% 0.25/1.55                     => ~ ( member1471151041e_form @ ( produc1617574096e_form @ Xs2 @ Ys2 ) @ ( listre318297994e_form @ R ) ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_292_listrel_Ocases,axiom,
% 0.25/1.55      ! [A1: list_nat,A2: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ A1 @ A2 ) @ ( listrel_nat_nat @ R ) )
% 0.25/1.55       => ( ( ( A1 = nil_nat )
% 0.25/1.55           => ( A2 != nil_nat ) )
% 0.25/1.55         => ~ ! [X: nat,Y2: nat,Xs2: list_nat] :
% 0.25/1.55                ( ( A1
% 0.25/1.55                  = ( cons_nat @ X @ Xs2 ) )
% 0.25/1.55               => ! [Ys2: list_nat] :
% 0.25/1.55                    ( ( A2
% 0.25/1.55                      = ( cons_nat @ Y2 @ Ys2 ) )
% 0.25/1.55                   => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R )
% 0.25/1.55                     => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs2 @ Ys2 ) @ ( listrel_nat_nat @ R ) ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_293_listrel_Ocases,axiom,
% 0.25/1.55      ! [A1: list_s1200803384elle_U,A2: list_n2139828004le_U_o,R: set_Pr1072215906le_U_o] :
% 0.25/1.55        ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ A1 @ A2 ) @ ( listre290852044le_U_o @ R ) )
% 0.25/1.55       => ( ( ( A1 = nil_se944326968elle_U )
% 0.25/1.55           => ( A2 != nil_na1584420238le_U_o ) )
% 0.25/1.55         => ~ ! [X: set_Pr619177522elle_U,Y2: nat > list_P796095576elle_U > $o,Xs2: list_s1200803384elle_U] :
% 0.25/1.55                ( ( A1
% 0.25/1.55                  = ( cons_s32021736elle_U @ X @ Xs2 ) )
% 0.25/1.55               => ! [Ys2: list_n2139828004le_U_o] :
% 0.25/1.55                    ( ( A2
% 0.25/1.55                      = ( cons_n50929118le_U_o @ Y2 @ Ys2 ) )
% 0.25/1.55                   => ( ( member1933006123le_U_o @ ( produc1069574002le_U_o @ X @ Y2 ) @ R )
% 0.25/1.55                     => ~ ( member493452075le_U_o @ ( produc1377086578le_U_o @ Xs2 @ Ys2 ) @ ( listre290852044le_U_o @ R ) ) ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_294_listrel_Osimps,axiom,
% 0.25/1.55      ! [A1: list_P512754263e_form,A2: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ A1 @ A2 ) @ ( listre1908795590e_form @ R ) )
% 0.25/1.55        = ( ( ( A1 = nil_Pr1384483009e_form )
% 0.25/1.55            & ( A2 = nil_Pr1384483009e_form ) )
% 0.25/1.55          | ? [X3: prover1687215943e_form,Y3: prover1687215943e_form,Xs4: list_P512754263e_form,Ys3: list_P512754263e_form] :
% 0.25/1.55              ( ( A1
% 0.25/1.55                = ( cons_P1475164433e_form @ X3 @ Xs4 ) )
% 0.25/1.55              & ( A2
% 0.25/1.55                = ( cons_P1475164433e_form @ Y3 @ Ys3 ) )
% 0.25/1.55              & ( member189065477e_form @ ( produc1018812320e_form @ X3 @ Y3 ) @ R )
% 0.25/1.55              & ( member650892795e_form @ ( produc891809686e_form @ Xs4 @ Ys3 ) @ ( listre1908795590e_form @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_295_listrel_Osimps,axiom,
% 0.25/1.55      ! [A1: list_P512754263e_form,A2: list_nat,R: set_Pr957084504rm_nat] :
% 0.25/1.55        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ A1 @ A2 ) @ ( listre483706378rm_nat @ R ) )
% 0.25/1.55        = ( ( ( A1 = nil_Pr1384483009e_form )
% 0.25/1.55            & ( A2 = nil_nat ) )
% 0.25/1.55          | ? [X3: prover1687215943e_form,Y3: nat,Xs4: list_P512754263e_form,Ys3: list_nat] :
% 0.25/1.55              ( ( A1
% 0.25/1.55                = ( cons_P1475164433e_form @ X3 @ Xs4 ) )
% 0.25/1.55              & ( A2
% 0.25/1.55                = ( cons_nat @ Y3 @ Ys3 ) )
% 0.25/1.55              & ( member986698273rm_nat @ ( produc1041874352rm_nat @ X3 @ Y3 ) @ R )
% 0.25/1.55              & ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs4 @ Ys3 ) @ ( listre483706378rm_nat @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_296_listrel_Osimps,axiom,
% 0.25/1.55      ! [A1: list_nat,A2: list_P512754263e_form,R: set_Pr816919384e_form] :
% 0.25/1.55        ( ( member1471151041e_form @ ( produc1617574096e_form @ A1 @ A2 ) @ ( listre318297994e_form @ R ) )
% 0.25/1.55        = ( ( ( A1 = nil_nat )
% 0.25/1.55            & ( A2 = nil_Pr1384483009e_form ) )
% 0.25/1.55          | ? [X3: nat,Y3: prover1687215943e_form,Xs4: list_nat,Ys3: list_P512754263e_form] :
% 0.25/1.55              ( ( A1
% 0.25/1.55                = ( cons_nat @ X3 @ Xs4 ) )
% 0.25/1.55              & ( A2
% 0.25/1.55                = ( cons_P1475164433e_form @ Y3 @ Ys3 ) )
% 0.25/1.55              & ( member18158113e_form @ ( produc876465968e_form @ X3 @ Y3 ) @ R )
% 0.25/1.55              & ( member1471151041e_form @ ( produc1617574096e_form @ Xs4 @ Ys3 ) @ ( listre318297994e_form @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_297_listrel_Osimps,axiom,
% 0.25/1.55      ! [A1: list_nat,A2: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ A1 @ A2 ) @ ( listrel_nat_nat @ R ) )
% 0.25/1.55        = ( ( ( A1 = nil_nat )
% 0.25/1.55            & ( A2 = nil_nat ) )
% 0.25/1.55          | ? [X3: nat,Y3: nat,Xs4: list_nat,Ys3: list_nat] :
% 0.25/1.55              ( ( A1
% 0.25/1.55                = ( cons_nat @ X3 @ Xs4 ) )
% 0.25/1.55              & ( A2
% 0.25/1.55                = ( cons_nat @ Y3 @ Ys3 ) )
% 0.25/1.55              & ( member701585322at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
% 0.25/1.55              & ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs4 @ Ys3 ) @ ( listrel_nat_nat @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_298_listrel_Osimps,axiom,
% 0.25/1.55      ! [A1: list_s1200803384elle_U,A2: list_n2139828004le_U_o,R: set_Pr1072215906le_U_o] :
% 0.25/1.55        ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ A1 @ A2 ) @ ( listre290852044le_U_o @ R ) )
% 0.25/1.55        = ( ( ( A1 = nil_se944326968elle_U )
% 0.25/1.55            & ( A2 = nil_na1584420238le_U_o ) )
% 0.25/1.55          | ? [X3: set_Pr619177522elle_U,Y3: nat > list_P796095576elle_U > $o,Xs4: list_s1200803384elle_U,Ys3: list_n2139828004le_U_o] :
% 0.25/1.55              ( ( A1
% 0.25/1.55                = ( cons_s32021736elle_U @ X3 @ Xs4 ) )
% 0.25/1.55              & ( A2
% 0.25/1.55                = ( cons_n50929118le_U_o @ Y3 @ Ys3 ) )
% 0.25/1.55              & ( member1933006123le_U_o @ ( produc1069574002le_U_o @ X3 @ Y3 ) @ R )
% 0.25/1.55              & ( member493452075le_U_o @ ( produc1377086578le_U_o @ Xs4 @ Ys3 ) @ ( listre290852044le_U_o @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_299_listrel_Oinducts,axiom,
% 0.25/1.55      ! [X12: list_P512754263e_form,X24: list_P512754263e_form,R: set_Pr1189404964e_form,P: list_P512754263e_form > list_P512754263e_form > $o] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ X12 @ X24 ) @ ( listre1908795590e_form @ R ) )
% 0.25/1.55       => ( ( P @ nil_Pr1384483009e_form @ nil_Pr1384483009e_form )
% 0.25/1.55         => ( ! [X: prover1687215943e_form,Y2: prover1687215943e_form,Xs2: list_P512754263e_form,Ys2: list_P512754263e_form] :
% 0.25/1.55                ( ( member189065477e_form @ ( produc1018812320e_form @ X @ Y2 ) @ R )
% 0.25/1.55               => ( ( member650892795e_form @ ( produc891809686e_form @ Xs2 @ Ys2 ) @ ( listre1908795590e_form @ R ) )
% 0.25/1.55                 => ( ( P @ Xs2 @ Ys2 )
% 0.25/1.55                   => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) ) ) ) )
% 0.25/1.55           => ( P @ X12 @ X24 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_300_listrel_Oinducts,axiom,
% 0.25/1.55      ! [X12: list_P512754263e_form,X24: list_nat,R: set_Pr957084504rm_nat,P: list_P512754263e_form > list_nat > $o] :
% 0.25/1.55        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ X12 @ X24 ) @ ( listre483706378rm_nat @ R ) )
% 0.25/1.55       => ( ( P @ nil_Pr1384483009e_form @ nil_nat )
% 0.25/1.55         => ( ! [X: prover1687215943e_form,Y2: nat,Xs2: list_P512754263e_form,Ys2: list_nat] :
% 0.25/1.55                ( ( member986698273rm_nat @ ( produc1041874352rm_nat @ X @ Y2 ) @ R )
% 0.25/1.55               => ( ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs2 @ Ys2 ) @ ( listre483706378rm_nat @ R ) )
% 0.25/1.55                 => ( ( P @ Xs2 @ Ys2 )
% 0.25/1.55                   => ( P @ ( cons_P1475164433e_form @ X @ Xs2 ) @ ( cons_nat @ Y2 @ Ys2 ) ) ) ) )
% 0.25/1.55           => ( P @ X12 @ X24 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_301_listrel_Oinducts,axiom,
% 0.25/1.55      ! [X12: list_nat,X24: list_P512754263e_form,R: set_Pr816919384e_form,P: list_nat > list_P512754263e_form > $o] :
% 0.25/1.55        ( ( member1471151041e_form @ ( produc1617574096e_form @ X12 @ X24 ) @ ( listre318297994e_form @ R ) )
% 0.25/1.55       => ( ( P @ nil_nat @ nil_Pr1384483009e_form )
% 0.25/1.55         => ( ! [X: nat,Y2: prover1687215943e_form,Xs2: list_nat,Ys2: list_P512754263e_form] :
% 0.25/1.55                ( ( member18158113e_form @ ( produc876465968e_form @ X @ Y2 ) @ R )
% 0.25/1.55               => ( ( member1471151041e_form @ ( produc1617574096e_form @ Xs2 @ Ys2 ) @ ( listre318297994e_form @ R ) )
% 0.25/1.55                 => ( ( P @ Xs2 @ Ys2 )
% 0.25/1.55                   => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_P1475164433e_form @ Y2 @ Ys2 ) ) ) ) )
% 0.25/1.55           => ( P @ X12 @ X24 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_302_listrel_Oinducts,axiom,
% 0.25/1.55      ! [X12: list_nat,X24: list_nat,R: set_Pr1986765409at_nat,P: list_nat > list_nat > $o] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ X12 @ X24 ) @ ( listrel_nat_nat @ R ) )
% 0.25/1.55       => ( ( P @ nil_nat @ nil_nat )
% 0.25/1.55         => ( ! [X: nat,Y2: nat,Xs2: list_nat,Ys2: list_nat] :
% 0.25/1.55                ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y2 ) @ R )
% 0.25/1.55               => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs2 @ Ys2 ) @ ( listrel_nat_nat @ R ) )
% 0.25/1.55                 => ( ( P @ Xs2 @ Ys2 )
% 0.25/1.55                   => ( P @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y2 @ Ys2 ) ) ) ) )
% 0.25/1.55           => ( P @ X12 @ X24 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_303_listrel_Oinducts,axiom,
% 0.25/1.55      ! [X12: list_s1200803384elle_U,X24: list_n2139828004le_U_o,R: set_Pr1072215906le_U_o,P: list_s1200803384elle_U > list_n2139828004le_U_o > $o] :
% 0.25/1.55        ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ X12 @ X24 ) @ ( listre290852044le_U_o @ R ) )
% 0.25/1.55       => ( ( P @ nil_se944326968elle_U @ nil_na1584420238le_U_o )
% 0.25/1.55         => ( ! [X: set_Pr619177522elle_U,Y2: nat > list_P796095576elle_U > $o,Xs2: list_s1200803384elle_U,Ys2: list_n2139828004le_U_o] :
% 0.25/1.55                ( ( member1933006123le_U_o @ ( produc1069574002le_U_o @ X @ Y2 ) @ R )
% 0.25/1.55               => ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ Xs2 @ Ys2 ) @ ( listre290852044le_U_o @ R ) )
% 0.25/1.55                 => ( ( P @ Xs2 @ Ys2 )
% 0.25/1.55                   => ( P @ ( cons_s32021736elle_U @ X @ Xs2 ) @ ( cons_n50929118le_U_o @ Y2 @ Ys2 ) ) ) ) )
% 0.25/1.55           => ( P @ X12 @ X24 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_304_listrel_ONil,axiom,
% 0.25/1.55      ! [R: set_Pr1189404964e_form] : ( member650892795e_form @ ( produc891809686e_form @ nil_Pr1384483009e_form @ nil_Pr1384483009e_form ) @ ( listre1908795590e_form @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_305_listrel_ONil,axiom,
% 0.25/1.55      ! [R: set_Pr957084504rm_nat] : ( member1449753665st_nat @ ( produc1897654224st_nat @ nil_Pr1384483009e_form @ nil_nat ) @ ( listre483706378rm_nat @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_306_listrel_ONil,axiom,
% 0.25/1.55      ! [R: set_Pr816919384e_form] : ( member1471151041e_form @ ( produc1617574096e_form @ nil_nat @ nil_Pr1384483009e_form ) @ ( listre318297994e_form @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_307_listrel_ONil,axiom,
% 0.25/1.55      ! [R: set_Pr1986765409at_nat] : ( member1926390090st_nat @ ( produc1625736153st_nat @ nil_nat @ nil_nat ) @ ( listrel_nat_nat @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_308_listrel__Nil1,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ nil_Pr1384483009e_form @ Xs ) @ ( listre1908795590e_form @ R ) )
% 0.25/1.55       => ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_309_listrel__Nil1,axiom,
% 0.25/1.55      ! [Xs: list_nat,R: set_Pr957084504rm_nat] :
% 0.25/1.55        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ nil_Pr1384483009e_form @ Xs ) @ ( listre483706378rm_nat @ R ) )
% 0.25/1.55       => ( Xs = nil_nat ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_310_listrel__Nil1,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,R: set_Pr816919384e_form] :
% 0.25/1.55        ( ( member1471151041e_form @ ( produc1617574096e_form @ nil_nat @ Xs ) @ ( listre318297994e_form @ R ) )
% 0.25/1.55       => ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_311_listrel__Nil1,axiom,
% 0.25/1.55      ! [Xs: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ nil_nat @ Xs ) @ ( listrel_nat_nat @ R ) )
% 0.25/1.55       => ( Xs = nil_nat ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_312_listrel__Nil2,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ nil_Pr1384483009e_form ) @ ( listre1908795590e_form @ R ) )
% 0.25/1.55       => ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_313_listrel__Nil2,axiom,
% 0.25/1.55      ! [Xs: list_nat,R: set_Pr816919384e_form] :
% 0.25/1.55        ( ( member1471151041e_form @ ( produc1617574096e_form @ Xs @ nil_Pr1384483009e_form ) @ ( listre318297994e_form @ R ) )
% 0.25/1.55       => ( Xs = nil_nat ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_314_listrel__Nil2,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,R: set_Pr957084504rm_nat] :
% 0.25/1.55        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs @ nil_nat ) @ ( listre483706378rm_nat @ R ) )
% 0.25/1.55       => ( Xs = nil_Pr1384483009e_form ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_315_listrel__Nil2,axiom,
% 0.25/1.55      ! [Xs: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ nil_nat ) @ ( listrel_nat_nat @ R ) )
% 0.25/1.55       => ( Xs = nil_nat ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_316_listrel__Cons2,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,Y: prover1687215943e_form,Ys: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ ( cons_P1475164433e_form @ Y @ Ys ) ) @ ( listre1908795590e_form @ R ) )
% 0.25/1.55       => ~ ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( cons_P1475164433e_form @ X @ Xs2 ) )
% 0.25/1.55             => ( ( member189065477e_form @ ( produc1018812320e_form @ X @ Y ) @ R )
% 0.25/1.55               => ~ ( member650892795e_form @ ( produc891809686e_form @ Xs2 @ Ys ) @ ( listre1908795590e_form @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_317_listrel__Cons2,axiom,
% 0.25/1.55      ! [Xs: list_nat,Y: prover1687215943e_form,Ys: list_P512754263e_form,R: set_Pr816919384e_form] :
% 0.25/1.55        ( ( member1471151041e_form @ ( produc1617574096e_form @ Xs @ ( cons_P1475164433e_form @ Y @ Ys ) ) @ ( listre318297994e_form @ R ) )
% 0.25/1.55       => ~ ! [X: nat,Xs2: list_nat] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( cons_nat @ X @ Xs2 ) )
% 0.25/1.55             => ( ( member18158113e_form @ ( produc876465968e_form @ X @ Y ) @ R )
% 0.25/1.55               => ~ ( member1471151041e_form @ ( produc1617574096e_form @ Xs2 @ Ys ) @ ( listre318297994e_form @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_318_listrel__Cons2,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,Y: nat,Ys: list_nat,R: set_Pr957084504rm_nat] :
% 0.25/1.55        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs @ ( cons_nat @ Y @ Ys ) ) @ ( listre483706378rm_nat @ R ) )
% 0.25/1.55       => ~ ! [X: prover1687215943e_form,Xs2: list_P512754263e_form] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( cons_P1475164433e_form @ X @ Xs2 ) )
% 0.25/1.55             => ( ( member986698273rm_nat @ ( produc1041874352rm_nat @ X @ Y ) @ R )
% 0.25/1.55               => ~ ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs2 @ Ys ) @ ( listre483706378rm_nat @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_319_listrel__Cons2,axiom,
% 0.25/1.55      ! [Xs: list_nat,Y: nat,Ys: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_nat_nat @ R ) )
% 0.25/1.55       => ~ ! [X: nat,Xs2: list_nat] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( cons_nat @ X @ Xs2 ) )
% 0.25/1.55             => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 0.25/1.55               => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs2 @ Ys ) @ ( listrel_nat_nat @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_320_listrel__Cons2,axiom,
% 0.25/1.55      ! [Xs: list_s1200803384elle_U,Y: nat > list_P796095576elle_U > $o,Ys: list_n2139828004le_U_o,R: set_Pr1072215906le_U_o] :
% 0.25/1.55        ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ Xs @ ( cons_n50929118le_U_o @ Y @ Ys ) ) @ ( listre290852044le_U_o @ R ) )
% 0.25/1.55       => ~ ! [X: set_Pr619177522elle_U,Xs2: list_s1200803384elle_U] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( cons_s32021736elle_U @ X @ Xs2 ) )
% 0.25/1.55             => ( ( member1933006123le_U_o @ ( produc1069574002le_U_o @ X @ Y ) @ R )
% 0.25/1.55               => ~ ( member493452075le_U_o @ ( produc1377086578le_U_o @ Xs2 @ Ys ) @ ( listre290852044le_U_o @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_321_listrel__Cons1,axiom,
% 0.25/1.55      ! [Y: prover1687215943e_form,Ys: list_P512754263e_form,Xs: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ Y @ Ys ) @ Xs ) @ ( listre1908795590e_form @ R ) )
% 0.25/1.55       => ~ ! [Y2: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.25/1.55             => ( ( member189065477e_form @ ( produc1018812320e_form @ Y @ Y2 ) @ R )
% 0.25/1.55               => ~ ( member650892795e_form @ ( produc891809686e_form @ Ys @ Ys2 ) @ ( listre1908795590e_form @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_322_listrel__Cons1,axiom,
% 0.25/1.55      ! [Y: prover1687215943e_form,Ys: list_P512754263e_form,Xs: list_nat,R: set_Pr957084504rm_nat] :
% 0.25/1.55        ( ( member1449753665st_nat @ ( produc1897654224st_nat @ ( cons_P1475164433e_form @ Y @ Ys ) @ Xs ) @ ( listre483706378rm_nat @ R ) )
% 0.25/1.55       => ~ ! [Y2: nat,Ys2: list_nat] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( cons_nat @ Y2 @ Ys2 ) )
% 0.25/1.55             => ( ( member986698273rm_nat @ ( produc1041874352rm_nat @ Y @ Y2 ) @ R )
% 0.25/1.55               => ~ ( member1449753665st_nat @ ( produc1897654224st_nat @ Ys @ Ys2 ) @ ( listre483706378rm_nat @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_323_listrel__Cons1,axiom,
% 0.25/1.55      ! [Y: nat,Ys: list_nat,Xs: list_P512754263e_form,R: set_Pr816919384e_form] :
% 0.25/1.55        ( ( member1471151041e_form @ ( produc1617574096e_form @ ( cons_nat @ Y @ Ys ) @ Xs ) @ ( listre318297994e_form @ R ) )
% 0.25/1.55       => ~ ! [Y2: prover1687215943e_form,Ys2: list_P512754263e_form] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( cons_P1475164433e_form @ Y2 @ Ys2 ) )
% 0.25/1.55             => ( ( member18158113e_form @ ( produc876465968e_form @ Y @ Y2 ) @ R )
% 0.25/1.55               => ~ ( member1471151041e_form @ ( produc1617574096e_form @ Ys @ Ys2 ) @ ( listre318297994e_form @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_324_listrel__Cons1,axiom,
% 0.25/1.55      ! [Y: nat,Ys: list_nat,Xs: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ Y @ Ys ) @ Xs ) @ ( listrel_nat_nat @ R ) )
% 0.25/1.55       => ~ ! [Y2: nat,Ys2: list_nat] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( cons_nat @ Y2 @ Ys2 ) )
% 0.25/1.55             => ( ( member701585322at_nat @ ( product_Pair_nat_nat @ Y @ Y2 ) @ R )
% 0.25/1.55               => ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Ys2 ) @ ( listrel_nat_nat @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_325_listrel__Cons1,axiom,
% 0.25/1.55      ! [Y: set_Pr619177522elle_U,Ys: list_s1200803384elle_U,Xs: list_n2139828004le_U_o,R: set_Pr1072215906le_U_o] :
% 0.25/1.55        ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ ( cons_s32021736elle_U @ Y @ Ys ) @ Xs ) @ ( listre290852044le_U_o @ R ) )
% 0.25/1.55       => ~ ! [Y2: nat > list_P796095576elle_U > $o,Ys2: list_n2139828004le_U_o] :
% 0.25/1.55              ( ( Xs
% 0.25/1.55                = ( cons_n50929118le_U_o @ Y2 @ Ys2 ) )
% 0.25/1.55             => ( ( member1933006123le_U_o @ ( produc1069574002le_U_o @ Y @ Y2 ) @ R )
% 0.25/1.55               => ~ ( member493452075le_U_o @ ( produc1377086578le_U_o @ Ys @ Ys2 ) @ ( listre290852044le_U_o @ R ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_326_listrel_OCons,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Y: prover1687215943e_form,R: set_Pr1189404964e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.55        ( ( member189065477e_form @ ( produc1018812320e_form @ X2 @ Y ) @ R )
% 0.25/1.55       => ( ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( listre1908795590e_form @ R ) )
% 0.25/1.55         => ( member650892795e_form @ ( produc891809686e_form @ ( cons_P1475164433e_form @ X2 @ Xs ) @ ( cons_P1475164433e_form @ Y @ Ys ) ) @ ( listre1908795590e_form @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_327_listrel_OCons,axiom,
% 0.25/1.55      ! [X2: prover1687215943e_form,Y: nat,R: set_Pr957084504rm_nat,Xs: list_P512754263e_form,Ys: list_nat] :
% 0.25/1.55        ( ( member986698273rm_nat @ ( produc1041874352rm_nat @ X2 @ Y ) @ R )
% 0.25/1.55       => ( ( member1449753665st_nat @ ( produc1897654224st_nat @ Xs @ Ys ) @ ( listre483706378rm_nat @ R ) )
% 0.25/1.55         => ( member1449753665st_nat @ ( produc1897654224st_nat @ ( cons_P1475164433e_form @ X2 @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( listre483706378rm_nat @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_328_listrel_OCons,axiom,
% 0.25/1.55      ! [X2: nat,Y: prover1687215943e_form,R: set_Pr816919384e_form,Xs: list_nat,Ys: list_P512754263e_form] :
% 0.25/1.55        ( ( member18158113e_form @ ( produc876465968e_form @ X2 @ Y ) @ R )
% 0.25/1.55       => ( ( member1471151041e_form @ ( produc1617574096e_form @ Xs @ Ys ) @ ( listre318297994e_form @ R ) )
% 0.25/1.55         => ( member1471151041e_form @ ( produc1617574096e_form @ ( cons_nat @ X2 @ Xs ) @ ( cons_P1475164433e_form @ Y @ Ys ) ) @ ( listre318297994e_form @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_329_listrel_OCons,axiom,
% 0.25/1.55      ! [X2: nat,Y: nat,R: set_Pr1986765409at_nat,Xs: list_nat,Ys: list_nat] :
% 0.25/1.55        ( ( member701585322at_nat @ ( product_Pair_nat_nat @ X2 @ Y ) @ R )
% 0.25/1.55       => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( listrel_nat_nat @ R ) )
% 0.25/1.55         => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( cons_nat @ X2 @ Xs ) @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_nat_nat @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_330_listrel_OCons,axiom,
% 0.25/1.55      ! [X2: set_Pr619177522elle_U,Y: nat > list_P796095576elle_U > $o,R: set_Pr1072215906le_U_o,Xs: list_s1200803384elle_U,Ys: list_n2139828004le_U_o] :
% 0.25/1.55        ( ( member1933006123le_U_o @ ( produc1069574002le_U_o @ X2 @ Y ) @ R )
% 0.25/1.55       => ( ( member493452075le_U_o @ ( produc1377086578le_U_o @ Xs @ Ys ) @ ( listre290852044le_U_o @ R ) )
% 0.25/1.55         => ( member493452075le_U_o @ ( produc1377086578le_U_o @ ( cons_s32021736elle_U @ X2 @ Xs ) @ ( cons_n50929118le_U_o @ Y @ Ys ) ) @ ( listre290852044le_U_o @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_331_lenlex__append2,axiom,
% 0.25/1.55      ! [R2: set_Pr1189404964e_form,Us2: list_P512754263e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form] :
% 0.25/1.55        ( ( irrefl2121388754e_form @ R2 )
% 0.25/1.55       => ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Us2 @ Xs ) @ ( append1038020460e_form @ Us2 @ Ys ) ) @ ( lenlex1927129340e_form @ R2 ) )
% 0.25/1.55          = ( member650892795e_form @ ( produc891809686e_form @ Xs @ Ys ) @ ( lenlex1927129340e_form @ R2 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_332_lenlex__append2,axiom,
% 0.25/1.55      ! [R2: set_Pr1986765409at_nat,Us2: list_nat,Xs: list_nat,Ys: list_nat] :
% 0.25/1.55        ( ( irrefl_nat @ R2 )
% 0.25/1.55       => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Us2 @ Xs ) @ ( append_nat @ Us2 @ Ys ) ) @ ( lenlex_nat @ R2 ) )
% 0.25/1.55          = ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ Ys ) @ ( lenlex_nat @ R2 ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_333_Nil__lenlex__iff1,axiom,
% 0.25/1.55      ! [Ns: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ nil_Pr1384483009e_form @ Ns ) @ ( lenlex1927129340e_form @ R ) )
% 0.25/1.55        = ( Ns != nil_Pr1384483009e_form ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_334_Nil__lenlex__iff1,axiom,
% 0.25/1.55      ! [Ns: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ nil_nat @ Ns ) @ ( lenlex_nat @ R ) )
% 0.25/1.55        = ( Ns != nil_nat ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_335_Nil__lenlex__iff2,axiom,
% 0.25/1.55      ! [Ns: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ~ ( member650892795e_form @ ( produc891809686e_form @ Ns @ nil_Pr1384483009e_form ) @ ( lenlex1927129340e_form @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_336_Nil__lenlex__iff2,axiom,
% 0.25/1.55      ! [Ns: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Ns @ nil_nat ) @ ( lenlex_nat @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_337_list__ex1__simps_I1_J,axiom,
% 0.25/1.55      ! [P: prover1687215943e_form > $o] :
% 0.25/1.55        ~ ( list_e2123636798e_form @ P @ nil_Pr1384483009e_form ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_338_list__ex1__simps_I1_J,axiom,
% 0.25/1.55      ! [P: nat > $o] :
% 0.25/1.55        ~ ( list_ex1_nat @ P @ nil_nat ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_339_list__ex1__iff,axiom,
% 0.25/1.55      ( list_ex1_nat
% 0.25/1.55      = ( ^ [P4: nat > $o,Xs4: list_nat] :
% 0.25/1.55          ? [X3: nat] :
% 0.25/1.55            ( ( member_nat @ X3 @ ( set_nat2 @ Xs4 ) )
% 0.25/1.55            & ( P4 @ X3 )
% 0.25/1.55            & ! [Y3: nat] :
% 0.25/1.55                ( ( ( member_nat @ Y3 @ ( set_nat2 @ Xs4 ) )
% 0.25/1.55                  & ( P4 @ Y3 ) )
% 0.25/1.55               => ( Y3 = X3 ) ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_340_Nil__notin__lex,axiom,
% 0.25/1.55      ! [Ys: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ~ ( member650892795e_form @ ( produc891809686e_form @ nil_Pr1384483009e_form @ Ys ) @ ( lex_Pr233218909e_form @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_341_Nil__notin__lex,axiom,
% 0.25/1.55      ! [Ys: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ nil_nat @ Ys ) @ ( lex_nat @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_342_Nil2__notin__lex,axiom,
% 0.25/1.55      ! [Xs: list_P512754263e_form,R: set_Pr1189404964e_form] :
% 0.25/1.55        ~ ( member650892795e_form @ ( produc891809686e_form @ Xs @ nil_Pr1384483009e_form ) @ ( lex_Pr233218909e_form @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_343_Nil2__notin__lex,axiom,
% 0.25/1.55      ! [Xs: list_nat,R: set_Pr1986765409at_nat] :
% 0.25/1.55        ~ ( member1926390090st_nat @ ( produc1625736153st_nat @ Xs @ nil_nat ) @ ( lex_nat @ R ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_344_lex__append__leftI,axiom,
% 0.25/1.55      ! [Ys: list_P512754263e_form,Zs2: list_P512754263e_form,R: set_Pr1189404964e_form,Xs: list_P512754263e_form] :
% 0.25/1.55        ( ( member650892795e_form @ ( produc891809686e_form @ Ys @ Zs2 ) @ ( lex_Pr233218909e_form @ R ) )
% 0.25/1.55       => ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ Ys ) @ ( append1038020460e_form @ Xs @ Zs2 ) ) @ ( lex_Pr233218909e_form @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_345_lex__append__leftI,axiom,
% 0.25/1.55      ! [Ys: list_nat,Zs2: list_nat,R: set_Pr1986765409at_nat,Xs: list_nat] :
% 0.25/1.55        ( ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Zs2 ) @ ( lex_nat @ R ) )
% 0.25/1.55       => ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Ys ) @ ( append_nat @ Xs @ Zs2 ) ) @ ( lex_nat @ R ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_346_lex__append__left__iff,axiom,
% 0.25/1.55      ! [R: set_Pr1189404964e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.25/1.55        ( ! [X: prover1687215943e_form] :
% 0.25/1.55            ~ ( member189065477e_form @ ( produc1018812320e_form @ X @ X ) @ R )
% 0.25/1.55       => ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ Ys ) @ ( append1038020460e_form @ Xs @ Zs2 ) ) @ ( lex_Pr233218909e_form @ R ) )
% 0.25/1.55          = ( member650892795e_form @ ( produc891809686e_form @ Ys @ Zs2 ) @ ( lex_Pr233218909e_form @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_347_lex__append__left__iff,axiom,
% 0.25/1.55      ! [R: set_Pr1986765409at_nat,Xs: list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.25/1.55        ( ! [X: nat] :
% 0.25/1.55            ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ X ) @ R )
% 0.25/1.55       => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Ys ) @ ( append_nat @ Xs @ Zs2 ) ) @ ( lex_nat @ R ) )
% 0.25/1.55          = ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Zs2 ) @ ( lex_nat @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_348_lex__append__leftD,axiom,
% 0.25/1.55      ! [R: set_Pr1189404964e_form,Xs: list_P512754263e_form,Ys: list_P512754263e_form,Zs2: list_P512754263e_form] :
% 0.25/1.55        ( ! [X: prover1687215943e_form] :
% 0.25/1.55            ~ ( member189065477e_form @ ( produc1018812320e_form @ X @ X ) @ R )
% 0.25/1.55       => ( ( member650892795e_form @ ( produc891809686e_form @ ( append1038020460e_form @ Xs @ Ys ) @ ( append1038020460e_form @ Xs @ Zs2 ) ) @ ( lex_Pr233218909e_form @ R ) )
% 0.25/1.55         => ( member650892795e_form @ ( produc891809686e_form @ Ys @ Zs2 ) @ ( lex_Pr233218909e_form @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_349_lex__append__leftD,axiom,
% 0.25/1.55      ! [R: set_Pr1986765409at_nat,Xs: list_nat,Ys: list_nat,Zs2: list_nat] :
% 0.25/1.55        ( ! [X: nat] :
% 0.25/1.55            ~ ( member701585322at_nat @ ( product_Pair_nat_nat @ X @ X ) @ R )
% 0.25/1.55       => ( ( member1926390090st_nat @ ( produc1625736153st_nat @ ( append_nat @ Xs @ Ys ) @ ( append_nat @ Xs @ Zs2 ) ) @ ( lex_nat @ R ) )
% 0.25/1.55         => ( member1926390090st_nat @ ( produc1625736153st_nat @ Ys @ Zs2 ) @ ( lex_nat @ R ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_350_can__select__set__list__ex1,axiom,
% 0.25/1.55      ! [P: nat > $o,A4: list_nat] :
% 0.25/1.55        ( ( can_select_nat @ P @ ( set_nat2 @ A4 ) )
% 0.25/1.55        = ( list_ex1_nat @ P @ A4 ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(fact_351_maxvar_Osimps_I1_J,axiom,
% 0.25/1.55      ( ( prover1021675886maxvar @ nil_nat )
% 0.25/1.55      = zero_zero_nat ) ).
% 0.25/1.55  
% 0.25/1.55  thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.25/1.55      ! [X2: list_nat,Y: list_nat] :
% 0.25/1.55        ( ( if_list_nat @ $false @ X2 @ Y )
% 0.25/1.55        = Y ) ).
% 0.25/1.55  
% 0.25/1.55  thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.25/1.55      ! [X2: list_nat,Y: list_nat] :
% 0.25/1.55        ( ( if_list_nat @ $true @ X2 @ Y )
% 0.25/1.55        = X2 ) ).
% 0.25/1.55  
% 0.25/1.55  thf(help_If_3_1_If_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_T,axiom,
% 0.25/1.55      ! [P: $o] :
% 0.25/1.55        ( ( P = $true )
% 0.25/1.55        | ( P = $false ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(help_If_2_1_If_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_T,axiom,
% 0.25/1.55      ! [X2: list_P512754263e_form,Y: list_P512754263e_form] :
% 0.25/1.55        ( ( if_lis1812881937e_form @ $false @ X2 @ Y )
% 0.25/1.55        = Y ) ).
% 0.25/1.55  
% 0.25/1.55  thf(help_If_1_1_If_001t__List__Olist_It__Prover____Mirabelle____icshcajtjh__Oform_J_T,axiom,
% 0.25/1.55      ! [X2: list_P512754263e_form,Y: list_P512754263e_form] :
% 0.25/1.55        ( ( if_lis1812881937e_form @ $true @ X2 @ Y )
% 0.25/1.55        = X2 ) ).
% 0.25/1.55  
% 0.25/1.55  thf(conj_0,hypothesis,
% 0.25/1.55      ~ ( member_nat @ u @ ( set_nat2 @ ( prover_Mirabelle_sfv @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(conj_1,hypothesis,
% 0.25/1.55      ! [A7: set_Pr619177522elle_U,B4: nat > list_P796095576elle_U > $o,E4: nat > prover_Mirabelle_U] :
% 0.25/1.55        ( ( prover1847600056is_env @ ( produc1069574002le_U_o @ A7 @ B4 ) @ E4 )
% 0.25/1.55       => ( prover1282070756_SEval @ ( produc1069574002le_U_o @ A7 @ B4 ) @ E4 @ ( append1038020460e_form @ s @ ( cons_P1475164433e_form @ ( prover1577896257_finst @ f @ u ) @ nil_Pr1384483009e_form ) ) ) ) ).
% 0.25/1.55  
% 0.25/1.55  thf(conj_2,conjecture,
% 0.25/1.55      ! [E5: nat > prover_Mirabelle_U] :
% 0.25/1.55        ( ~ ( prover1847600056is_env @ ( produc1069574002le_U_o @ a @ b ) @ E5 )
% 0.25/1.55        | ( prover1282070756_SEval @ ( produc1069574002le_U_o @ a @ b ) @ E5 @ ( cons_P1475164433e_form @ ( prover571163162e_FAll @ f ) @ s ) ) ) ).
% 0.25/1.55  ------------------------
% 0.25/1.58  % (19974)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/183Mi)
% 0.25/1.58  % (19975)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/4Mi)
% 0.25/1.58  % (19979)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/275Mi)
% 0.25/1.58  % (19978)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/2Mi)
% 0.25/1.58  % (19977)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/2Mi)
% 0.25/1.58  % (19976)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/27Mi)
% 0.25/1.58  % (19980)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/18Mi)
% 0.25/1.58  % (19977)Instruction limit reached!
% 0.25/1.58  % (19977)------------------------------
% 0.25/1.58  % (19977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.59  % (19977)Termination reason: Unknown
% 0.25/1.59  % (19978)Instruction limit reached!
% 0.25/1.59  % (19978)------------------------------
% 0.25/1.59  % (19978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.59  % (19978)Termination reason: Unknown
% 0.25/1.59  % (19978)Termination phase: shuffling
% 0.25/1.59  
% 0.25/1.59  % (19978)Memory used [KB]: 1663
% 0.25/1.59  % (19978)Time elapsed: 0.003 s
% 0.25/1.59  % (19978)Instructions burned: 3 (million)
% 0.25/1.59  % (19978)------------------------------
% 0.25/1.59  % (19978)------------------------------
% 0.25/1.59  % (19977)Termination phase: shuffling
% 0.25/1.59  
% 0.25/1.59  % (19977)Memory used [KB]: 1663
% 0.25/1.59  % (19977)Time elapsed: 0.003 s
% 0.25/1.59  % (19977)Instructions burned: 2 (million)
% 0.25/1.59  % (19977)------------------------------
% 0.25/1.59  % (19977)------------------------------
% 0.25/1.59  % (19975)Instruction limit reached!
% 0.25/1.59  % (19975)------------------------------
% 0.25/1.59  % (19975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.59  % (19975)Termination reason: Unknown
% 0.25/1.59  % (19975)Termination phase: shuffling
% 0.25/1.59  
% 0.25/1.59  % (19975)Memory used [KB]: 1791
% 0.25/1.59  % (19975)Time elapsed: 0.004 s
% 0.25/1.59  % (19975)Instructions burned: 5 (million)
% 0.25/1.59  % (19975)------------------------------
% 0.25/1.59  % (19975)------------------------------
% 0.25/1.59  % (19980)Instruction limit reached!
% 0.25/1.59  % (19980)------------------------------
% 0.25/1.59  % (19980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.25/1.59  % (19980)Termination reason: Unknown
% 0.25/1.59  % (19980)Termination phase: shuffling
% 0.25/1.59  
% 0.25/1.59  % (19980)Memory used [KB]: 1918
% 0.25/1.59  % (19980)Time elapsed: 0.011 s
% 0.25/1.59  % (19980)Instructions burned: 18 (million)
% 0.25/1.59  % (19980)------------------------------
% 0.25/1.59  % (19980)------------------------------
% 3.02/1.60  % (19976)Instruction limit reached!
% 3.02/1.60  % (19976)------------------------------
% 3.02/1.60  % (19976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.60  % (19976)Termination reason: Unknown
% 3.02/1.60  % (19976)Termination phase: shuffling
% 3.02/1.60  
% 3.02/1.60  % (19976)Memory used [KB]: 2174
% 3.02/1.60  % (19976)Time elapsed: 0.015 s
% 3.02/1.60  % (19976)Instructions burned: 27 (million)
% 3.02/1.60  % (19976)------------------------------
% 3.02/1.60  % (19976)------------------------------
% 3.02/1.60  % (19981)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/3Mi)
% 3.02/1.60  % (19983)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/15Mi)
% 3.02/1.60  % (19982)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/37Mi)
% 3.02/1.60  % (19981)Instruction limit reached!
% 3.02/1.60  % (19981)------------------------------
% 3.02/1.60  % (19981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.60  % (19981)Termination reason: Unknown
% 3.02/1.60  % (19981)Termination phase: shuffling
% 3.02/1.60  
% 3.02/1.60  % (19981)Memory used [KB]: 1663
% 3.02/1.60  % (19981)Time elapsed: 0.003 s
% 3.02/1.60  % (19981)Instructions burned: 3 (million)
% 3.02/1.60  % (19981)------------------------------
% 3.02/1.60  % (19981)------------------------------
% 3.02/1.61  % (19984)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/3Mi)
% 3.02/1.61  % (19983)Instruction limit reached!
% 3.02/1.61  % (19983)------------------------------
% 3.02/1.61  % (19983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.61  % (19983)Termination reason: Unknown
% 3.02/1.61  % (19983)Termination phase: shuffling
% 3.02/1.61  
% 3.02/1.61  % (19983)Memory used [KB]: 1918
% 3.02/1.61  % (19983)Time elapsed: 0.009 s
% 3.02/1.61  % (19983)Instructions burned: 16 (million)
% 3.02/1.61  % (19983)------------------------------
% 3.02/1.61  % (19983)------------------------------
% 3.02/1.61  % (19984)Instruction limit reached!
% 3.02/1.61  % (19984)------------------------------
% 3.02/1.61  % (19984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.61  % (19984)Termination reason: Unknown
% 3.02/1.61  % (19984)Termination phase: shuffling
% 3.02/1.61  
% 3.02/1.61  % (19984)Memory used [KB]: 1663
% 3.02/1.61  % (19984)Time elapsed: 0.003 s
% 3.02/1.61  % (19984)Instructions burned: 3 (million)
% 3.02/1.61  % (19984)------------------------------
% 3.02/1.61  % (19984)------------------------------
% 3.02/1.62  % (19985)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/1041Mi)
% 3.02/1.62  % (19982)Instruction limit reached!
% 3.02/1.62  % (19982)------------------------------
% 3.02/1.62  % (19982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.62  % (19982)Termination reason: Unknown
% 3.02/1.62  % (19982)Termination phase: shuffling
% 3.02/1.62  
% 3.02/1.62  % (19982)Memory used [KB]: 2302
% 3.02/1.62  % (19982)Time elapsed: 0.019 s
% 3.02/1.62  % (19982)Instructions burned: 38 (million)
% 3.02/1.62  % (19982)------------------------------
% 3.02/1.62  % (19982)------------------------------
% 3.02/1.62  % (19986)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/7Mi)
% 3.02/1.62  % (19986)Instruction limit reached!
% 3.02/1.62  % (19986)------------------------------
% 3.02/1.62  % (19986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.62  % (19986)Termination reason: Unknown
% 3.02/1.62  % (19986)Termination phase: shuffling
% 3.02/1.62  
% 3.02/1.62  % (19986)Memory used [KB]: 1791
% 3.02/1.62  % (19986)Time elapsed: 0.005 s
% 3.02/1.62  % (19986)Instructions burned: 7 (million)
% 3.02/1.62  % (19986)------------------------------
% 3.02/1.62  % (19986)------------------------------
% 3.02/1.63  % (19987)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/16Mi)
% 3.02/1.63  % (19988)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/3Mi)
% 3.02/1.63  % (19988)Instruction limit reached!
% 3.02/1.63  % (19988)------------------------------
% 3.02/1.63  % (19988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.63  % (19988)Termination reason: Unknown
% 3.02/1.63  % (19988)Termination phase: shuffling
% 3.02/1.63  
% 3.02/1.63  % (19988)Memory used [KB]: 1663
% 3.02/1.63  % (19988)Time elapsed: 0.003 s
% 3.02/1.63  % (19988)Instructions burned: 3 (million)
% 3.02/1.63  % (19988)------------------------------
% 3.02/1.63  % (19988)------------------------------
% 3.02/1.63  % (19974)Instruction limit reached!
% 3.02/1.63  % (19974)------------------------------
% 3.02/1.63  % (19974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.63  % (19974)Termination reason: Unknown
% 3.02/1.63  % (19974)Termination phase: Saturation
% 3.02/1.63  
% 3.02/1.63  % (19974)Memory used [KB]: 7931
% 3.02/1.63  % (19974)Time elapsed: 0.053 s
% 3.02/1.63  % (19974)Instructions burned: 185 (million)
% 3.02/1.63  % (19974)------------------------------
% 3.02/1.63  % (19974)------------------------------
% 3.02/1.63  % (19987)Instruction limit reached!
% 3.02/1.63  % (19987)------------------------------
% 3.02/1.63  % (19987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.63  % (19987)Termination reason: Unknown
% 3.02/1.63  % (19987)Termination phase: shuffling
% 3.02/1.63  
% 3.02/1.63  % (19987)Memory used [KB]: 1918
% 3.02/1.63  % (19987)Time elapsed: 0.009 s
% 3.02/1.63  % (19987)Instructions burned: 16 (million)
% 3.02/1.63  % (19987)------------------------------
% 3.02/1.63  % (19987)------------------------------
% 3.02/1.63  % (19989)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/3Mi)
% 3.02/1.64  % (19989)Instruction limit reached!
% 3.02/1.64  % (19989)------------------------------
% 3.02/1.64  % (19989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.64  % (19989)Termination reason: Unknown
% 3.02/1.64  % (19989)Termination phase: shuffling
% 3.02/1.64  
% 3.02/1.64  % (19989)Memory used [KB]: 1663
% 3.02/1.64  % (19989)Time elapsed: 0.004 s
% 3.02/1.64  % (19989)Instructions burned: 4 (million)
% 3.02/1.64  % (19989)------------------------------
% 3.02/1.64  % (19989)------------------------------
% 3.02/1.64  % (19990)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/7Mi)
% 3.02/1.64  % (19992)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/3Mi)
% 3.02/1.64  % (19992)Instruction limit reached!
% 3.02/1.64  % (19992)------------------------------
% 3.02/1.64  % (19992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.64  % (19992)Termination reason: Unknown
% 3.02/1.64  % (19992)Termination phase: shuffling
% 3.02/1.64  
% 3.02/1.64  % (19992)Memory used [KB]: 1663
% 3.02/1.64  % (19992)Time elapsed: 0.002 s
% 3.02/1.64  % (19992)Instructions burned: 3 (million)
% 3.02/1.64  % (19992)------------------------------
% 3.02/1.64  % (19992)------------------------------
% 3.02/1.64  % (19990)Instruction limit reached!
% 3.02/1.64  % (19990)------------------------------
% 3.02/1.64  % (19990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.64  % (19990)Termination reason: Unknown
% 3.02/1.64  % (19990)Termination phase: shuffling
% 3.02/1.64  
% 3.02/1.64  % (19990)Memory used [KB]: 1791
% 3.02/1.64  % (19990)Time elapsed: 0.005 s
% 3.02/1.64  % (19990)Instructions burned: 7 (million)
% 3.02/1.64  % (19990)------------------------------
% 3.02/1.64  % (19990)------------------------------
% 3.02/1.65  % (19993)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/4Mi)
% 3.02/1.65  % (19993)Instruction limit reached!
% 3.02/1.65  % (19993)------------------------------
% 3.02/1.65  % (19993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.65  % (19993)Termination reason: Unknown
% 3.02/1.65  % (19993)Termination phase: shuffling
% 3.02/1.65  
% 3.02/1.65  % (19993)Memory used [KB]: 1791
% 3.02/1.65  % (19993)Time elapsed: 0.004 s
% 3.02/1.65  % (19993)Instructions burned: 5 (million)
% 3.02/1.65  % (19993)------------------------------
% 3.02/1.65  % (19993)------------------------------
% 3.02/1.65  % (19994)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/18Mi)
% 3.02/1.65  % (19996)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/6Mi)
% 3.02/1.65  % (19996)Instruction limit reached!
% 3.02/1.65  % (19996)------------------------------
% 3.02/1.65  % (19996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.65  % (19996)Termination reason: Unknown
% 3.02/1.65  % (19996)Termination phase: shuffling
% 3.02/1.65  
% 3.02/1.65  % (19996)Memory used [KB]: 1791
% 3.02/1.65  % (19996)Time elapsed: 0.003 s
% 3.02/1.65  % (19996)Instructions burned: 6 (million)
% 3.02/1.65  % (19996)------------------------------
% 3.02/1.65  % (19996)------------------------------
% 3.02/1.65  % (19995)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/710Mi)
% 3.02/1.66  % (19997)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/902Mi)
% 3.02/1.66  % (19994)Instruction limit reached!
% 3.02/1.66  % (19994)------------------------------
% 3.02/1.66  % (19994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.66  % (19994)Termination reason: Unknown
% 3.02/1.66  % (19994)Termination phase: shuffling
% 3.02/1.66  
% 3.02/1.66  % (19994)Memory used [KB]: 1918
% 3.02/1.66  % (19994)Time elapsed: 0.011 s
% 3.02/1.66  % (19994)Instructions burned: 19 (million)
% 3.02/1.66  % (19994)------------------------------
% 3.02/1.66  % (19994)------------------------------
% 3.02/1.66  % (19999)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/5Mi)
% 3.02/1.66  % (19999)Instruction limit reached!
% 3.02/1.66  % (19999)------------------------------
% 3.02/1.66  % (19999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.66  % (19999)Termination reason: Unknown
% 3.02/1.66  % (19999)Termination phase: shuffling
% 3.02/1.66  
% 3.02/1.66  % (19999)Memory used [KB]: 1791
% 3.02/1.66  % (19999)Time elapsed: 0.003 s
% 3.02/1.66  % (19999)Instructions burned: 7 (million)
% 3.02/1.66  % (19999)------------------------------
% 3.02/1.66  % (19999)------------------------------
% 3.02/1.66  % (19998)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/21Mi)
% 3.02/1.67  % (20001)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19870 for (2998ds/377Mi)
% 3.02/1.67  % (19998)Instruction limit reached!
% 3.02/1.67  % (19998)------------------------------
% 3.02/1.67  % (19998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.67  % (19998)Termination reason: Unknown
% 3.02/1.67  % (19998)Termination phase: shuffling
% 3.02/1.67  
% 3.02/1.67  % (19998)Memory used [KB]: 2046
% 3.02/1.67  % (19998)Time elapsed: 0.012 s
% 3.02/1.67  % (19998)Instructions burned: 21 (million)
% 3.02/1.67  % (19998)------------------------------
% 3.02/1.67  % (19998)------------------------------
% 3.02/1.67  % (20000)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_19870 for (2999ds/6Mi)
% 3.02/1.68  % (20000)Instruction limit reached!
% 3.02/1.68  % (20000)------------------------------
% 3.02/1.68  % (20000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.68  % (20000)Termination reason: Unknown
% 3.02/1.68  % (20000)Termination phase: shuffling
% 3.02/1.68  
% 3.02/1.68  % (20000)Memory used [KB]: 1791
% 3.02/1.68  % (20000)Time elapsed: 0.005 s
% 3.02/1.68  % (20000)Instructions burned: 8 (million)
% 3.02/1.68  % (20000)------------------------------
% 3.02/1.68  % (20000)------------------------------
% 3.02/1.69  % (20002)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_19870 for (2998ds/779Mi)
% 3.02/1.69  % (20003)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_19870 for (2998ds/19Mi)
% 3.02/1.70  % (20003)Instruction limit reached!
% 3.02/1.70  % (20003)------------------------------
% 3.02/1.70  % (20003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.70  % (20003)Termination reason: Unknown
% 3.02/1.70  % (20003)Termination phase: shuffling
% 3.02/1.70  
% 3.02/1.70  % (20003)Memory used [KB]: 2046
% 3.02/1.70  % (20003)Time elapsed: 0.007 s
% 3.02/1.70  % (20003)Instructions burned: 19 (million)
% 3.02/1.70  % (20003)------------------------------
% 3.02/1.70  % (20003)------------------------------
% 3.02/1.71  % (20004)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_19870 for (2998ds/879Mi)
% 3.02/1.71  % (19979)Instruction limit reached!
% 3.02/1.71  % (19979)------------------------------
% 3.02/1.71  % (19979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.71  % (19979)Termination reason: Unknown
% 3.02/1.71  % (19979)Termination phase: Saturation
% 3.02/1.71  
% 3.02/1.71  % (19979)Memory used [KB]: 7931
% 3.02/1.71  % (19979)Time elapsed: 0.130 s
% 3.02/1.71  % (19979)Instructions burned: 276 (million)
% 3.02/1.71  % (19979)------------------------------
% 3.02/1.71  % (19979)------------------------------
% 3.02/1.74  % (20005)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_19870 for (2998ds/17Mi)
% 3.02/1.75  % (20005)Instruction limit reached!
% 3.02/1.75  % (20005)------------------------------
% 3.02/1.75  % (20005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.75  % (20005)Termination reason: Unknown
% 3.02/1.75  % (20005)Termination phase: shuffling
% 3.02/1.75  
% 3.02/1.75  % (20005)Memory used [KB]: 1918
% 3.02/1.75  % (20005)Time elapsed: 0.009 s
% 3.02/1.75  % (20005)Instructions burned: 17 (million)
% 3.02/1.75  % (20005)------------------------------
% 3.02/1.75  % (20005)------------------------------
% 3.02/1.77  % (20006)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_19870 for (2998ds/3Mi)
% 3.02/1.77  % (20006)Instruction limit reached!
% 3.02/1.77  % (20006)------------------------------
% 3.02/1.77  % (20006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.77  % (20006)Termination reason: Unknown
% 3.02/1.77  % (20006)Termination phase: shuffling
% 3.02/1.77  
% 3.02/1.77  % (20006)Memory used [KB]: 1663
% 3.02/1.77  % (20006)Time elapsed: 0.004 s
% 3.02/1.77  % (20006)Instructions burned: 4 (million)
% 3.02/1.77  % (20006)------------------------------
% 3.02/1.77  % (20006)------------------------------
% 3.02/1.79  % (20007)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_19870 for (2997ds/30Mi)
% 3.02/1.80  % (20007)Instruction limit reached!
% 3.02/1.80  % (20007)------------------------------
% 3.02/1.80  % (20007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.80  % (20007)Termination reason: Unknown
% 3.02/1.80  % (20007)Termination phase: shuffling
% 3.02/1.80  
% 3.02/1.80  % (20007)Memory used [KB]: 2302
% 3.02/1.80  % (20007)Time elapsed: 0.011 s
% 3.02/1.80  % (20007)Instructions burned: 30 (million)
% 3.02/1.80  % (20007)------------------------------
% 3.02/1.80  % (20007)------------------------------
% 3.02/1.81  % (20008)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_19870 for (2997ds/127Mi)
% 3.02/1.84  % (20001)Instruction limit reached!
% 3.02/1.84  % (20001)------------------------------
% 3.02/1.84  % (20001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.84  % (20001)Termination reason: Unknown
% 3.02/1.84  % (20001)Termination phase: Saturation
% 3.02/1.84  
% 3.02/1.84  % (20001)Memory used [KB]: 9210
% 3.02/1.84  % (20001)Time elapsed: 0.171 s
% 3.02/1.84  % (20001)Instructions burned: 378 (million)
% 3.02/1.84  % (20001)------------------------------
% 3.02/1.84  % (20001)------------------------------
% 3.02/1.85  % (20008)Instruction limit reached!
% 3.02/1.85  % (20008)------------------------------
% 3.02/1.85  % (20008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.85  % (20008)Termination reason: Unknown
% 3.02/1.85  % (20008)Termination phase: Function definition elimination
% 3.02/1.85  
% 3.02/1.85  % (20008)Memory used [KB]: 3070
% 3.02/1.85  % (20008)Time elapsed: 0.038 s
% 3.02/1.85  % (20008)Instructions burned: 131 (million)
% 3.02/1.85  % (20008)------------------------------
% 3.02/1.85  % (20008)------------------------------
% 3.02/1.86  % (20010)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_19870 for (2997ds/3Mi)
% 3.02/1.86  % (20009)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_19870 for (2997ds/100Mi)
% 3.02/1.86  % (20010)Instruction limit reached!
% 3.02/1.86  % (20010)------------------------------
% 3.02/1.86  % (20010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.86  % (20010)Termination reason: Unknown
% 3.02/1.86  % (20010)Termination phase: shuffling
% 3.02/1.86  
% 3.02/1.86  % (20010)Memory used [KB]: 1791
% 3.02/1.86  % (20010)Time elapsed: 0.003 s
% 3.02/1.86  % (20010)Instructions burned: 6 (million)
% 3.02/1.86  % (20010)------------------------------
% 3.02/1.86  % (20010)------------------------------
% 3.02/1.87  % (20011)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_19870 for (2997ds/20Mi)
% 3.02/1.88  % (20011)Instruction limit reached!
% 3.02/1.88  % (20011)------------------------------
% 3.02/1.88  % (20011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.88  % (20011)Termination reason: Unknown
% 3.02/1.88  % (20011)Termination phase: shuffling
% 3.02/1.88  
% 3.02/1.88  % (20011)Memory used [KB]: 2046
% 3.02/1.88  % (20011)Time elapsed: 0.012 s
% 3.02/1.88  % (20011)Instructions burned: 21 (million)
% 3.02/1.88  % (20011)------------------------------
% 3.02/1.88  % (20011)------------------------------
% 3.02/1.90  % (20012)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_19870 for (2996ds/86Mi)
% 3.02/1.90  % (20009)Instruction limit reached!
% 3.02/1.90  % (20009)------------------------------
% 3.02/1.90  % (20009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.90  % (20009)Termination reason: Unknown
% 3.02/1.90  % (20009)Termination phase: Property scanning
% 3.02/1.90  
% 3.02/1.90  % (20009)Memory used [KB]: 3070
% 3.02/1.90  % (20009)Time elapsed: 0.047 s
% 3.02/1.90  % (20009)Instructions burned: 100 (million)
% 3.02/1.90  % (20009)------------------------------
% 3.02/1.90  % (20009)------------------------------
% 3.02/1.93  % (20013)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_19870 for (2996ds/107Mi)
% 3.02/1.94  % (20012)Instruction limit reached!
% 3.02/1.94  % (20012)------------------------------
% 3.02/1.94  % (20012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.94  % (20012)Termination reason: Unknown
% 3.02/1.94  % (20012)Termination phase: Preprocessing 3
% 3.02/1.94  
% 3.02/1.94  % (20012)Memory used [KB]: 2942
% 3.02/1.94  % (20012)Time elapsed: 0.043 s
% 3.02/1.94  % (20012)Instructions burned: 86 (million)
% 3.02/1.94  % (20012)------------------------------
% 3.02/1.94  % (20012)------------------------------
% 3.02/1.96  % (20013)Instruction limit reached!
% 3.02/1.96  % (20013)------------------------------
% 3.02/1.96  % (20013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.96  % (20013)Termination reason: Unknown
% 3.02/1.96  % (20013)Termination phase: Property scanning
% 3.02/1.96  
% 3.02/1.96  % (20013)Memory used [KB]: 3070
% 3.02/1.96  % (20013)Time elapsed: 0.032 s
% 3.02/1.96  % (20013)Instructions burned: 107 (million)
% 3.02/1.96  % (20013)------------------------------
% 3.02/1.96  % (20013)------------------------------
% 3.02/1.96  % (20014)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_19870 for (2996ds/39Mi)
% 3.02/1.97  % (20015)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_19870 for (2995ds/448Mi)
% 3.02/1.98  % (20014)Instruction limit reached!
% 3.02/1.98  % (20014)------------------------------
% 3.02/1.98  % (20014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/1.98  % (20014)Termination reason: Unknown
% 3.02/1.98  % (20014)Termination phase: shuffling
% 3.02/1.98  
% 3.02/1.98  % (20014)Memory used [KB]: 2430
% 3.02/1.98  % (20014)Time elapsed: 0.020 s
% 3.02/1.98  % (20014)Instructions burned: 40 (million)
% 3.02/1.98  % (20014)------------------------------
% 3.02/1.98  % (20014)------------------------------
% 3.02/1.99  % (20016)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_19870 for (2995ds/46Mi)
% 3.02/2.00  % (19995)Instruction limit reached!
% 3.02/2.00  % (19995)------------------------------
% 3.02/2.00  % (19995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/2.00  % (19995)Termination reason: Unknown
% 3.02/2.00  % (19995)Termination phase: Saturation
% 3.02/2.00  
% 3.02/2.00  % (19995)Memory used [KB]: 8187
% 3.02/2.00  % (19995)Time elapsed: 0.354 s
% 3.02/2.00  % (19995)Instructions burned: 712 (million)
% 3.02/2.00  % (19995)------------------------------
% 3.02/2.00  % (19995)------------------------------
% 3.02/2.02  % (20016)Instruction limit reached!
% 3.02/2.02  % (20016)------------------------------
% 3.02/2.02  % (20016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.02/2.02  % (20016)Termination reason: Unknown
% 3.02/2.02  % (20016)Termination phase: Property scanning
% 3.02/2.02  
% 3.02/2.02  % (20016)Memory used [KB]: 2302
% 3.02/2.02  % (20016)Time elapsed: 0.025 s
% 3.02/2.02  % (20016)Instructions burned: 46 (million)
% 3.02/2.02  % (20016)------------------------------
% 3.02/2.02  % (20016)------------------------------
% 6.03/2.03  % (20017)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_19870 for (2995ds/98Mi)
% 6.03/2.03  % (20018)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_19870 for (2995ds/507Mi)
% 6.03/2.05  % (20017)Instruction limit reached!
% 6.03/2.05  % (20017)------------------------------
% 6.03/2.05  % (20017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.05  % (20017)Termination reason: Unknown
% 6.03/2.05  % (20017)Termination phase: Property scanning
% 6.03/2.05  
% 6.03/2.05  % (20017)Memory used [KB]: 3070
% 6.03/2.05  % (20017)Time elapsed: 0.028 s
% 6.03/2.05  % (20017)Instructions burned: 101 (million)
% 6.03/2.05  % (20017)------------------------------
% 6.03/2.05  % (20017)------------------------------
% 6.03/2.06  % (20002)Instruction limit reached!
% 6.03/2.06  % (20002)------------------------------
% 6.03/2.06  % (20002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.06  % (20002)Termination reason: Unknown
% 6.03/2.06  % (20002)Termination phase: Saturation
% 6.03/2.06  
% 6.03/2.06  % (20002)Memory used [KB]: 9978
% 6.03/2.06  % (20002)Time elapsed: 0.373 s
% 6.03/2.06  % (20002)Instructions burned: 779 (million)
% 6.03/2.06  % (20002)------------------------------
% 6.03/2.06  % (20002)------------------------------
% 6.03/2.06  % (20019)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/149Mi)
% 6.03/2.08  % (19997)Instruction limit reached!
% 6.03/2.08  % (19997)------------------------------
% 6.03/2.08  % (19997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.08  % (19997)Termination reason: Unknown
% 6.03/2.08  % (19997)Termination phase: Saturation
% 6.03/2.08  
% 6.03/2.08  % (19997)Memory used [KB]: 9594
% 6.03/2.08  % (19997)Time elapsed: 0.422 s
% 6.03/2.08  % (19997)Instructions burned: 902 (million)
% 6.03/2.08  % (19997)------------------------------
% 6.03/2.08  % (19997)------------------------------
% 6.03/2.08  % (20020)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/39Mi)
% 6.03/2.10  % (20004)Instruction limit reached!
% 6.03/2.10  % (20004)------------------------------
% 6.03/2.10  % (20004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.10  % (20004)Termination reason: Unknown
% 6.03/2.10  % (20004)Termination phase: Saturation
% 6.03/2.10  
% 6.03/2.10  % (20004)Memory used [KB]: 8187
% 6.03/2.10  % (20004)Time elapsed: 0.406 s
% 6.03/2.10  % (20004)Instructions burned: 880 (million)
% 6.03/2.10  % (20004)------------------------------
% 6.03/2.10  % (20004)------------------------------
% 6.03/2.10  % (20020)Instruction limit reached!
% 6.03/2.10  % (20020)------------------------------
% 6.03/2.10  % (20020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.10  % (20020)Termination reason: Unknown
% 6.03/2.10  % (20020)Termination phase: Property scanning
% 6.03/2.10  
% 6.03/2.10  % (20020)Memory used [KB]: 2302
% 6.03/2.10  % (20020)Time elapsed: 0.021 s
% 6.03/2.10  % (20020)Instructions burned: 39 (million)
% 6.03/2.10  % (20020)------------------------------
% 6.03/2.10  % (20020)------------------------------
% 6.03/2.10  % (19985)Instruction limit reached!
% 6.03/2.10  % (19985)------------------------------
% 6.03/2.10  % (19985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.10  % (19985)Termination reason: Unknown
% 6.03/2.10  % (19985)Termination phase: Saturation
% 6.03/2.10  
% 6.03/2.10  % (19985)Memory used [KB]: 10490
% 6.03/2.10  % (19985)Time elapsed: 0.498 s
% 6.03/2.10  % (19985)Instructions burned: 1041 (million)
% 6.03/2.10  % (19985)------------------------------
% 6.03/2.10  % (19985)------------------------------
% 6.03/2.10  % (20021)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/6Mi)
% 6.03/2.11  % (20021)Instruction limit reached!
% 6.03/2.11  % (20021)------------------------------
% 6.03/2.11  % (20021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.11  % (20021)Termination reason: Unknown
% 6.03/2.11  % (20021)Termination phase: shuffling
% 6.03/2.11  
% 6.03/2.11  % (20021)Memory used [KB]: 1791
% 6.03/2.11  % (20021)Time elapsed: 0.005 s
% 6.03/2.11  % (20021)Instructions burned: 6 (million)
% 6.03/2.11  % (20021)------------------------------
% 6.03/2.11  % (20021)------------------------------
% 6.03/2.11  % (20019)Instruction limit reached!
% 6.03/2.11  % (20019)------------------------------
% 6.03/2.11  % (20019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.03/2.11  % (20019)Termination reason: Unknown
% 6.03/2.11  % (20019)Termination phase: Property scanning
% 6.03/2.11  
% 6.03/2.11  % (20019)Memory used [KB]: 3454
% 6.03/2.11  % (20019)Time elapsed: 0.052 s
% 6.03/2.11  % (20019)Instructions burned: 151 (million)
% 6.03/2.11  % (20019)------------------------------
% 6.03/2.11  % (20019)------------------------------
% 6.03/2.12  % (20023)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/47Mi)
% 6.03/2.12  % (20024)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/44Mi)
% 6.03/2.12  % (20022)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/1087Mi)
% 6.03/2.12  % (20025)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/432Mi)
% 6.60/2.13  % (20026)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/62Mi)
% 6.60/2.14  % (20024)Instruction limit reached!
% 6.60/2.14  % (20024)------------------------------
% 6.60/2.14  % (20024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.14  % (20024)Termination reason: Unknown
% 6.60/2.14  % (20024)Termination phase: shuffling
% 6.60/2.14  
% 6.60/2.14  % (20024)Memory used [KB]: 2430
% 6.60/2.14  % (20024)Time elapsed: 0.022 s
% 6.60/2.14  % (20024)Instructions burned: 45 (million)
% 6.60/2.14  % (20024)------------------------------
% 6.60/2.14  % (20024)------------------------------
% 6.60/2.14  % (20023)Instruction limit reached!
% 6.60/2.14  % (20023)------------------------------
% 6.60/2.14  % (20023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.14  % (20023)Termination reason: Unknown
% 6.60/2.14  % (20023)Termination phase: Property scanning
% 6.60/2.14  
% 6.60/2.14  % (20023)Memory used [KB]: 2302
% 6.60/2.14  % (20023)Time elapsed: 0.025 s
% 6.60/2.14  % (20023)Instructions burned: 48 (million)
% 6.60/2.14  % (20023)------------------------------
% 6.60/2.14  % (20023)------------------------------
% 6.60/2.16  % (20027)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/31Mi)
% 6.60/2.16  % (20026)Instruction limit reached!
% 6.60/2.16  % (20026)------------------------------
% 6.60/2.16  % (20026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.16  % (20026)Termination reason: Unknown
% 6.60/2.16  % (20026)Termination phase: shuffling
% 6.60/2.16  
% 6.60/2.16  % (20026)Memory used [KB]: 2814
% 6.60/2.16  % (20026)Time elapsed: 0.030 s
% 6.60/2.16  % (20026)Instructions burned: 64 (million)
% 6.60/2.16  % (20026)------------------------------
% 6.60/2.16  % (20026)------------------------------
% 6.60/2.16  % (20015)Instruction limit reached!
% 6.60/2.16  % (20015)------------------------------
% 6.60/2.16  % (20015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.16  % (20015)Termination reason: Unknown
% 6.60/2.16  % (20015)Termination phase: Saturation
% 6.60/2.16  
% 6.60/2.16  % (20015)Memory used [KB]: 9722
% 6.60/2.16  % (20015)Time elapsed: 0.184 s
% 6.60/2.16  % (20015)Instructions burned: 448 (million)
% 6.60/2.16  % (20015)------------------------------
% 6.60/2.16  % (20015)------------------------------
% 6.60/2.16  % (20028)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_19870 for (2994ds/96Mi)
% 6.60/2.17  % (20027)Instruction limit reached!
% 6.60/2.17  % (20027)------------------------------
% 6.60/2.17  % (20027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.17  % (20027)Termination reason: Unknown
% 6.60/2.17  % (20027)Termination phase: shuffling
% 6.60/2.17  
% 6.60/2.17  % (20027)Memory used [KB]: 2302
% 6.60/2.17  % (20027)Time elapsed: 0.017 s
% 6.60/2.17  % (20027)Instructions burned: 31 (million)
% 6.60/2.17  % (20027)------------------------------
% 6.60/2.17  % (20027)------------------------------
% 6.60/2.17  % (20029)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_19870 for (2993ds/453Mi)
% 6.60/2.18  % (20031)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_19870 for (2993ds/71Mi)
% 6.60/2.19  % (20032)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_19870 for (2993ds/83Mi)
% 6.60/2.19  % (20028)Instruction limit reached!
% 6.60/2.19  % (20028)------------------------------
% 6.60/2.19  % (20028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.60/2.19  % (20028)Termination reason: Unknown
% 6.60/2.19  % (20028)Termination phase: Property scanning
% 6.60/2.19  
% 6.60/2.19  % (20028)Memory used [KB]: 3070
% 6.60/2.19  % (20028)Time elapsed: 0.029 s
% 6.60/2.19  % (20028)Instructions burned: 97 (million)
% 6.60/2.19  % (20028)------------------------------
% 6.60/2.19  % (20028)------------------------------
% 6.82/2.20  % (20033)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_19870 for (2993ds/11Mi)
% 6.82/2.21  % (20033)Instruction limit reached!
% 6.82/2.21  % (20033)------------------------------
% 6.82/2.21  % (20033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.21  % (20033)Termination reason: Unknown
% 6.82/2.21  % (20033)Termination phase: shuffling
% 6.82/2.21  
% 6.82/2.21  % (20033)Memory used [KB]: 1918
% 6.82/2.21  % (20033)Time elapsed: 0.005 s
% 6.82/2.21  % (20033)Instructions burned: 14 (million)
% 6.82/2.21  % (20033)------------------------------
% 6.82/2.21  % (20033)------------------------------
% 6.82/2.21  % (20031)Instruction limit reached!
% 6.82/2.21  % (20031)------------------------------
% 6.82/2.21  % (20031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.21  % (20031)Termination reason: Unknown
% 6.82/2.21  % (20031)Termination phase: Preprocessing 2
% 6.82/2.21  
% 6.82/2.21  % (20031)Memory used [KB]: 2558
% 6.82/2.21  % (20031)Time elapsed: 0.036 s
% 6.82/2.21  % (20031)Instructions burned: 72 (million)
% 6.82/2.21  % (20031)------------------------------
% 6.82/2.21  % (20031)------------------------------
% 6.82/2.21  % (20034)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_19870 for (2993ds/41Mi)
% 6.82/2.23  % (20035)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19870 for (2993ds/6Mi)
% 6.82/2.23  % (20032)Instruction limit reached!
% 6.82/2.23  % (20032)------------------------------
% 6.82/2.23  % (20032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.23  % (20032)Termination reason: Unknown
% 6.82/2.23  % (20032)Termination phase: Preprocessing 3
% 6.82/2.23  
% 6.82/2.23  % (20032)Memory used [KB]: 2558
% 6.82/2.23  % (20032)Time elapsed: 0.042 s
% 6.82/2.23  % (20032)Instructions burned: 84 (million)
% 6.82/2.23  % (20032)------------------------------
% 6.82/2.23  % (20032)------------------------------
% 6.82/2.23  % (20034)Instruction limit reached!
% 6.82/2.23  % (20034)------------------------------
% 6.82/2.23  % (20034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.23  % (20034)Termination reason: Unknown
% 6.82/2.23  % (20034)Termination phase: shuffling
% 6.82/2.23  
% 6.82/2.23  % (20034)Memory used [KB]: 2430
% 6.82/2.23  % (20034)Time elapsed: 0.015 s
% 6.82/2.23  % (20034)Instructions burned: 41 (million)
% 6.82/2.23  % (20034)------------------------------
% 6.82/2.23  % (20034)------------------------------
% 6.82/2.23  % (20035)Instruction limit reached!
% 6.82/2.23  % (20035)------------------------------
% 6.82/2.23  % (20035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.23  % (20035)Termination reason: Unknown
% 6.82/2.23  % (20035)Termination phase: shuffling
% 6.82/2.23  
% 6.82/2.23  % (20035)Memory used [KB]: 1791
% 6.82/2.23  % (20035)Time elapsed: 0.005 s
% 6.82/2.23  % (20035)Instructions burned: 6 (million)
% 6.82/2.23  % (20035)------------------------------
% 6.82/2.23  % (20035)------------------------------
% 6.82/2.24  % (20036)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_19870 for (2993ds/150Mi)
% 6.82/2.24  % (20037)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_19870 for (2993ds/343Mi)
% 6.82/2.25  % (20038)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_19870 for (2993ds/109Mi)
% 6.82/2.25  % (20018)Instruction limit reached!
% 6.82/2.25  % (20018)------------------------------
% 6.82/2.25  % (20018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.25  % (20018)Termination reason: Unknown
% 6.82/2.25  % (20018)Termination phase: Saturation
% 6.82/2.25  
% 6.82/2.25  % (20018)Memory used [KB]: 9978
% 6.82/2.25  % (20018)Time elapsed: 0.208 s
% 6.82/2.25  % (20018)Instructions burned: 507 (million)
% 6.82/2.25  % (20018)------------------------------
% 6.82/2.25  % (20018)------------------------------
% 6.82/2.27  % (20039)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_19870 for (2993ds/253Mi)
% 7.21/2.30  % (20038)Instruction limit reached!
% 7.21/2.30  % (20038)------------------------------
% 7.21/2.30  % (20038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.30  % (20038)Termination reason: Unknown
% 7.21/2.30  % (20038)Termination phase: Property scanning
% 7.21/2.30  
% 7.21/2.30  % (20038)Memory used [KB]: 3070
% 7.21/2.30  % (20038)Time elapsed: 0.054 s
% 7.21/2.30  % (20038)Instructions burned: 110 (million)
% 7.21/2.30  % (20038)------------------------------
% 7.21/2.30  % (20038)------------------------------
% 7.21/2.31  % (20040)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_19870 for (2992ds/140Mi)
% 7.21/2.32  % (20036)Instruction limit reached!
% 7.21/2.32  % (20036)------------------------------
% 7.21/2.32  % (20036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.32  % (20036)Termination reason: Unknown
% 7.21/2.32  % (20036)Termination phase: Property scanning
% 7.21/2.32  
% 7.21/2.32  % (20036)Memory used [KB]: 3837
% 7.21/2.32  % (20036)Time elapsed: 0.073 s
% 7.21/2.32  % (20036)Instructions burned: 151 (million)
% 7.21/2.32  % (20036)------------------------------
% 7.21/2.32  % (20036)------------------------------
% 7.21/2.33  % (20025)Instruction limit reached!
% 7.21/2.33  % (20025)------------------------------
% 7.21/2.33  % (20025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.33  % (20025)Termination reason: Unknown
% 7.21/2.33  % (20025)Termination phase: Saturation
% 7.21/2.33  
% 7.21/2.33  % (20025)Memory used [KB]: 4733
% 7.21/2.33  % (20025)Time elapsed: 0.204 s
% 7.21/2.33  % (20025)Instructions burned: 433 (million)
% 7.21/2.33  % (20025)------------------------------
% 7.21/2.33  % (20025)------------------------------
% 7.21/2.34  % (20041)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_19870 for (2992ds/614Mi)
% 7.21/2.34  % (20042)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_19870 for (2992ds/202Mi)
% 7.21/2.37  % (20040)Instruction limit reached!
% 7.21/2.37  % (20040)------------------------------
% 7.21/2.37  % (20040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.37  % (20040)Termination reason: Unknown
% 7.21/2.37  % (20040)Termination phase: Saturation
% 7.21/2.37  
% 7.21/2.37  % (20040)Memory used [KB]: 7547
% 7.21/2.37  % (20040)Time elapsed: 0.059 s
% 7.21/2.37  % (20040)Instructions burned: 140 (million)
% 7.21/2.37  % (20040)------------------------------
% 7.21/2.37  % (20040)------------------------------
% 7.21/2.38  % (20029)Instruction limit reached!
% 7.21/2.38  % (20029)------------------------------
% 7.21/2.38  % (20029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.38  % (20029)Termination reason: Unknown
% 7.21/2.38  % (20029)Termination phase: Saturation
% 7.21/2.38  
% 7.21/2.38  % (20029)Memory used [KB]: 8571
% 7.21/2.38  % (20029)Time elapsed: 0.209 s
% 7.21/2.38  % (20029)Instructions burned: 453 (million)
% 7.21/2.38  % (20029)------------------------------
% 7.21/2.38  % (20029)------------------------------
% 7.21/2.39  % (20043)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_19870 for (2991ds/339Mi)
% 7.21/2.39  % (20039)Instruction limit reached!
% 7.21/2.39  % (20039)------------------------------
% 7.21/2.39  % (20039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.21/2.39  % (20039)Termination reason: Unknown
% 7.21/2.39  % (20039)Termination phase: Saturation
% 7.21/2.39  
% 7.21/2.39  % (20039)Memory used [KB]: 8571
% 7.21/2.39  % (20039)Time elapsed: 0.126 s
% 7.21/2.39  % (20039)Instructions burned: 253 (million)
% 7.21/2.39  % (20039)------------------------------
% 7.21/2.39  % (20039)------------------------------
% 8.03/2.40  % (20044)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_19870 for (2991ds/283Mi)
% 8.03/2.41  % (20037)Instruction limit reached!
% 8.03/2.41  % (20037)------------------------------
% 8.03/2.41  % (20037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.41  % (20037)Termination reason: Unknown
% 8.03/2.41  % (20037)Termination phase: Saturation
% 8.03/2.41  
% 8.03/2.41  % (20037)Memory used [KB]: 8827
% 8.03/2.41  % (20037)Time elapsed: 0.166 s
% 8.03/2.41  % (20037)Instructions burned: 343 (million)
% 8.03/2.41  % (20037)------------------------------
% 8.03/2.41  % (20037)------------------------------
% 8.03/2.42  % (20045)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_19870 for (2991ds/134Mi)
% 8.03/2.43  % (20046)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_19870 for (2991ds/298Mi)
% 8.03/2.44  % (20042)Instruction limit reached!
% 8.03/2.44  % (20042)------------------------------
% 8.03/2.44  % (20042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.44  % (20042)Termination reason: Unknown
% 8.03/2.44  % (20042)Termination phase: Saturation
% 8.03/2.44  
% 8.03/2.44  % (20042)Memory used [KB]: 8443
% 8.03/2.44  % (20042)Time elapsed: 0.099 s
% 8.03/2.44  % (20042)Instructions burned: 202 (million)
% 8.03/2.44  % (20042)------------------------------
% 8.03/2.44  % (20042)------------------------------
% 8.03/2.46  % (20047)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_19870 for (2991ds/192Mi)
% 8.03/2.47  % (20045)Instruction limit reached!
% 8.03/2.47  % (20045)------------------------------
% 8.03/2.47  % (20045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.47  % (20045)Termination reason: Unknown
% 8.03/2.47  % (20045)Termination phase: Property scanning
% 8.03/2.47  
% 8.03/2.47  % (20045)Memory used [KB]: 3454
% 8.03/2.47  % (20045)Time elapsed: 0.041 s
% 8.03/2.47  % (20045)Instructions burned: 137 (million)
% 8.03/2.47  % (20045)------------------------------
% 8.03/2.47  % (20045)------------------------------
% 8.03/2.48  % (20048)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_19870 for (2990ds/258Mi)
% 8.36/2.51  % (20044)Instruction limit reached!
% 8.36/2.51  % (20044)------------------------------
% 8.36/2.51  % (20044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.51  % (20044)Termination reason: Unknown
% 8.36/2.51  % (20044)Termination phase: Saturation
% 8.36/2.51  
% 8.36/2.51  % (20044)Memory used [KB]: 7931
% 8.36/2.51  % (20044)Time elapsed: 0.116 s
% 8.36/2.51  % (20044)Instructions burned: 284 (million)
% 8.36/2.51  % (20044)------------------------------
% 8.36/2.51  % (20044)------------------------------
% 8.36/2.52  % (20049)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_19870 for (2990ds/90Mi)
% 8.36/2.54  % (20043)Instruction limit reached!
% 8.36/2.54  % (20043)------------------------------
% 8.36/2.54  % (20043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.54  % (20043)Termination reason: Unknown
% 8.36/2.54  % (20043)Termination phase: Saturation
% 8.36/2.54  
% 8.36/2.54  % (20043)Memory used [KB]: 8315
% 8.36/2.54  % (20043)Time elapsed: 0.158 s
% 8.36/2.54  % (20043)Instructions burned: 340 (million)
% 8.36/2.54  % (20043)------------------------------
% 8.36/2.54  % (20043)------------------------------
% 8.36/2.55  % (20047)Instruction limit reached!
% 8.36/2.55  % (20047)------------------------------
% 8.36/2.55  % (20047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.55  % (20047)Termination reason: Unknown
% 8.36/2.55  % (20047)Termination phase: Saturation
% 8.36/2.55  
% 8.36/2.55  % (20047)Memory used [KB]: 3965
% 8.36/2.55  % (20047)Time elapsed: 0.091 s
% 8.36/2.55  % (20047)Instructions burned: 193 (million)
% 8.36/2.55  % (20047)------------------------------
% 8.36/2.55  % (20047)------------------------------
% 8.36/2.56  % (20046)Instruction limit reached!
% 8.36/2.56  % (20046)------------------------------
% 8.36/2.56  % (20046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.56  % (20046)Termination reason: Unknown
% 8.36/2.56  % (20046)Termination phase: Saturation
% 8.36/2.56  
% 8.36/2.56  % (20046)Memory used [KB]: 8571
% 8.36/2.56  % (20046)Time elapsed: 0.133 s
% 8.36/2.56  % (20046)Instructions burned: 298 (million)
% 8.36/2.56  % (20046)------------------------------
% 8.36/2.56  % (20046)------------------------------
% 8.36/2.56  % (20049)Instruction limit reached!
% 8.36/2.56  % (20049)------------------------------
% 8.36/2.56  % (20049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.56  % (20049)Termination reason: Unknown
% 8.36/2.56  % (20049)Termination phase: Clausification
% 8.36/2.56  
% 8.36/2.56  % (20049)Memory used [KB]: 3070
% 8.36/2.56  % (20049)Time elapsed: 0.035 s
% 8.36/2.56  % (20049)Instructions burned: 90 (million)
% 8.36/2.56  % (20049)------------------------------
% 8.36/2.56  % (20049)------------------------------
% 8.36/2.56  % (20050)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_19870 for (2990ds/231Mi)
% 8.36/2.56  % (20051)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_19870 for (2990ds/458Mi)
% 8.36/2.57  % (20053)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_19870 for (2990ds/297Mi)
% 8.36/2.58  % (20052)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19870 for (2990ds/31Mi)
% 8.36/2.59  % (20041)Instruction limit reached!
% 8.36/2.59  % (20041)------------------------------
% 8.36/2.59  % (20041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.36/2.59  % (20041)Termination reason: Unknown
% 8.36/2.59  % (20041)Termination phase: Saturation
% 8.36/2.59  
% 8.36/2.59  % (20041)Memory used [KB]: 9594
% 8.36/2.59  % (20041)Time elapsed: 0.262 s
% 8.36/2.59  % (20041)Instructions burned: 616 (million)
% 8.36/2.59  % (20041)------------------------------
% 8.36/2.59  % (20041)------------------------------
% 9.20/2.60  % (20048)Instruction limit reached!
% 9.20/2.60  % (20048)------------------------------
% 9.20/2.60  % (20048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.20/2.60  % (20048)Termination reason: Unknown
% 9.20/2.60  % (20048)Termination phase: Saturation
% 9.20/2.60  
% 9.20/2.60  % (20048)Memory used [KB]: 8443
% 9.20/2.60  % (20048)Time elapsed: 0.118 s
% 9.20/2.60  % (20048)Instructions burned: 259 (million)
% 9.20/2.60  % (20048)------------------------------
% 9.20/2.60  % (20048)------------------------------
% 9.20/2.60  % (20052)Instruction limit reached!
% 9.20/2.60  % (20052)------------------------------
% 9.20/2.60  % (20052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.20/2.60  % (20052)Termination reason: Unknown
% 9.20/2.60  % (20052)Termination phase: shuffling
% 9.20/2.60  
% 9.20/2.60  % (20052)Memory used [KB]: 2302
% 9.20/2.60  % (20052)Time elapsed: 0.012 s
% 9.20/2.60  % (20052)Instructions burned: 31 (million)
% 9.20/2.60  % (20052)------------------------------
% 9.20/2.60  % (20052)------------------------------
% 9.20/2.61  % (20055)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_19870 for (2989ds/182Mi)
% 9.20/2.61  % (20054)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_19870 for (2989ds/987Mi)
% 9.20/2.61  % (20056)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_19870 for (2989ds/182Mi)
% 9.20/2.64  % (20022)Instruction limit reached!
% 9.20/2.64  % (20022)------------------------------
% 9.20/2.64  % (20022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.20/2.64  % (20022)Termination reason: Unknown
% 9.20/2.64  % (20022)Termination phase: Saturation
% 9.20/2.64  
% 9.20/2.64  % (20022)Memory used [KB]: 8955
% 9.20/2.64  % (20022)Time elapsed: 0.518 s
% 9.20/2.64  % (20022)Instructions burned: 1087 (million)
% 9.20/2.64  % (20022)------------------------------
% 9.20/2.64  % (20022)------------------------------
% 9.20/2.66  % (20057)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_19870 for (2989ds/154Mi)
% 9.20/2.66  % (20055)Instruction limit reached!
% 9.20/2.66  % (20055)------------------------------
% 9.20/2.66  % (20055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.20/2.66  % (20055)Termination reason: Unknown
% 9.20/2.66  % (20055)Termination phase: Saturation
% 9.20/2.66  
% 9.20/2.66  % (20055)Memory used [KB]: 7931
% 9.20/2.66  % (20055)Time elapsed: 0.051 s
% 9.20/2.66  % (20055)Instructions burned: 183 (million)
% 9.20/2.66  % (20055)------------------------------
% 9.20/2.66  % (20055)------------------------------
% 9.20/2.66  % (20050)Instruction limit reached!
% 9.20/2.66  % (20050)------------------------------
% 9.20/2.66  % (20050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.20/2.66  % (20050)Termination reason: Unknown
% 9.20/2.66  % (20050)Termination phase: Saturation
% 9.20/2.66  
% 9.20/2.66  % (20050)Memory used [KB]: 7803
% 9.20/2.66  % (20050)Time elapsed: 0.105 s
% 9.20/2.66  % (20050)Instructions burned: 233 (million)
% 9.20/2.66  % (20050)------------------------------
% 9.20/2.66  % (20050)------------------------------
% 9.20/2.67  % (20058)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_19870 for (2988ds/79Mi)
% 9.20/2.69  % (20059)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_19870 for (2988ds/216Mi)
% 9.20/2.69  % (20058)Instruction limit reached!
% 9.20/2.69  % (20058)------------------------------
% 9.20/2.69  % (20058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.20/2.69  % (20058)Termination reason: Unknown
% 9.20/2.69  % (20058)Termination phase: Preprocessing 3
% 9.20/2.69  
% 9.20/2.69  % (20058)Memory used [KB]: 2814
% 9.20/2.69  % (20058)Time elapsed: 0.025 s
% 9.20/2.69  % (20058)Instructions burned: 82 (million)
% 9.20/2.69  % (20058)------------------------------
% 9.20/2.69  % (20058)------------------------------
% 10.09/2.70  % (20056)Instruction limit reached!
% 10.09/2.70  % (20056)------------------------------
% 10.09/2.70  % (20056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.70  % (20056)Termination reason: Unknown
% 10.09/2.70  % (20056)Termination phase: Property scanning
% 10.09/2.70  
% 10.09/2.70  % (20056)Memory used [KB]: 3454
% 10.09/2.70  % (20056)Time elapsed: 0.085 s
% 10.09/2.70  % (20056)Instructions burned: 183 (million)
% 10.09/2.70  % (20056)------------------------------
% 10.09/2.70  % (20056)------------------------------
% 10.09/2.70  % (20060)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_19870 for (2988ds/114Mi)
% 10.09/2.71  % (20053)Instruction limit reached!
% 10.09/2.71  % (20053)------------------------------
% 10.09/2.71  % (20053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.71  % (20053)Termination reason: Unknown
% 10.09/2.71  % (20053)Termination phase: Saturation
% 10.09/2.71  
% 10.09/2.71  % (20053)Memory used [KB]: 8059
% 10.09/2.71  % (20053)Time elapsed: 0.162 s
% 10.09/2.71  % (20053)Instructions burned: 297 (million)
% 10.09/2.71  % (20053)------------------------------
% 10.09/2.71  % (20053)------------------------------
% 10.09/2.71  % (20061)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_19870 for (2988ds/922Mi)
% 10.09/2.73  % (20057)Instruction limit reached!
% 10.09/2.73  % (20057)------------------------------
% 10.09/2.73  % (20057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.73  % (20057)Termination reason: Unknown
% 10.09/2.73  % (20057)Termination phase: Property scanning
% 10.09/2.73  
% 10.09/2.73  % (20057)Memory used [KB]: 3198
% 10.09/2.73  % (20057)Time elapsed: 0.072 s
% 10.09/2.73  % (20057)Instructions burned: 155 (million)
% 10.09/2.73  % (20057)------------------------------
% 10.09/2.73  % (20057)------------------------------
% 10.09/2.73  % (20062)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_19870 for (2988ds/182Mi)
% 10.09/2.75  % (20063)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_19870 for (2988ds/164Mi)
% 10.09/2.75  % (20060)Instruction limit reached!
% 10.09/2.75  % (20060)------------------------------
% 10.09/2.75  % (20060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.75  % (20060)Termination reason: Unknown
% 10.09/2.75  % (20060)Termination phase: Property scanning
% 10.09/2.75  
% 10.09/2.75  % (20060)Memory used [KB]: 3070
% 10.09/2.75  % (20060)Time elapsed: 0.054 s
% 10.09/2.75  % (20060)Instructions burned: 115 (million)
% 10.09/2.75  % (20060)------------------------------
% 10.09/2.75  % (20060)------------------------------
% 10.09/2.77  % (20064)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_19870 for (2987ds/50Mi)
% 10.09/2.78  % (20059)Instruction limit reached!
% 10.09/2.78  % (20059)------------------------------
% 10.09/2.78  % (20059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.78  % (20059)Termination reason: Unknown
% 10.09/2.78  % (20059)Termination phase: Saturation
% 10.09/2.78  
% 10.09/2.78  % (20059)Memory used [KB]: 7675
% 10.09/2.78  % (20059)Time elapsed: 0.097 s
% 10.09/2.78  % (20059)Instructions burned: 217 (million)
% 10.09/2.78  % (20059)------------------------------
% 10.09/2.78  % (20059)------------------------------
% 10.09/2.79  % (20051)Instruction limit reached!
% 10.09/2.79  % (20051)------------------------------
% 10.09/2.79  % (20051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.79  % (20051)Termination reason: Unknown
% 10.09/2.79  % (20051)Termination phase: Saturation
% 10.09/2.79  
% 10.09/2.79  % (20051)Memory used [KB]: 9466
% 10.09/2.79  % (20051)Time elapsed: 0.202 s
% 10.09/2.79  % (20051)Instructions burned: 460 (million)
% 10.09/2.79  % (20051)------------------------------
% 10.09/2.79  % (20051)------------------------------
% 10.09/2.79  % (20064)Instruction limit reached!
% 10.09/2.79  % (20064)------------------------------
% 10.09/2.79  % (20064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.79  % (20064)Termination reason: Unknown
% 10.09/2.79  % (20064)Termination phase: shuffling
% 10.09/2.79  
% 10.09/2.79  % (20064)Memory used [KB]: 2686
% 10.09/2.79  % (20064)Time elapsed: 0.025 s
% 10.09/2.79  % (20064)Instructions burned: 51 (million)
% 10.09/2.79  % (20064)------------------------------
% 10.09/2.79  % (20064)------------------------------
% 10.86/2.80  % (20065)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_19870 for (2987ds/368Mi)
% 10.86/2.80  % (20066)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_19870 for (2987ds/1021Mi)
% 10.86/2.81  % (20062)Instruction limit reached!
% 10.86/2.81  % (20062)------------------------------
% 10.86/2.81  % (20062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.86/2.81  % (20062)Termination reason: Unknown
% 10.86/2.81  % (20062)Termination phase: Function definition elimination
% 10.86/2.81  
% 10.86/2.81  % (20062)Memory used [KB]: 3326
% 10.86/2.81  % (20062)Time elapsed: 0.083 s
% 10.86/2.81  % (20062)Instructions burned: 182 (million)
% 10.86/2.81  % (20062)------------------------------
% 10.86/2.81  % (20062)------------------------------
% 10.86/2.82  % (20067)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_19870 for (2987ds/267Mi)
% 10.86/2.83  % (20068)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_19870 for (2987ds/204Mi)
% 10.86/2.83  % (20063)Instruction limit reached!
% 10.86/2.83  % (20063)------------------------------
% 10.86/2.83  % (20063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.86/2.83  % (20063)Termination reason: Unknown
% 10.86/2.83  % (20063)Termination phase: Property scanning
% 10.86/2.83  
% 10.86/2.83  % (20063)Memory used [KB]: 3070
% 10.86/2.83  % (20063)Time elapsed: 0.048 s
% 10.86/2.83  % (20063)Instructions burned: 166 (million)
% 10.86/2.83  % (20063)------------------------------
% 10.86/2.83  % (20063)------------------------------
% 10.86/2.84  % (20069)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_19870 for (2987ds/26Mi)
% 10.86/2.86  % (20069)Instruction limit reached!
% 10.86/2.86  % (20069)------------------------------
% 10.86/2.86  % (20069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.86/2.86  % (20069)Termination reason: Unknown
% 10.86/2.86  % (20069)Termination phase: shuffling
% 10.86/2.86  
% 10.86/2.86  % (20069)Memory used [KB]: 2174
% 10.86/2.86  % (20069)Time elapsed: 0.014 s
% 10.86/2.86  % (20069)Instructions burned: 27 (million)
% 10.86/2.86  % (20069)------------------------------
% 10.86/2.86  % (20069)------------------------------
% 10.86/2.88  % (20070)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_19870 for (2987ds/53Mi)
% 11.04/2.91  % (20070)Instruction limit reached!
% 11.04/2.91  % (20070)------------------------------
% 11.04/2.91  % (20070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.04/2.91  % (20070)Termination reason: Unknown
% 11.04/2.91  % (20070)Termination phase: shuffling
% 11.04/2.91  
% 11.04/2.91  % (20070)Memory used [KB]: 2686
% 11.04/2.91  % (20070)Time elapsed: 0.017 s
% 11.04/2.91  % (20070)Instructions burned: 55 (million)
% 11.04/2.91  % (20070)------------------------------
% 11.04/2.91  % (20070)------------------------------
% 11.04/2.92  % (20067)Instruction limit reached!
% 11.04/2.92  % (20067)------------------------------
% 11.04/2.92  % (20067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.04/2.92  % (20067)Termination reason: Unknown
% 11.04/2.92  % (20067)Termination phase: Saturation
% 11.04/2.92  
% 11.04/2.92  % (20067)Memory used [KB]: 7803
% 11.04/2.92  % (20067)Time elapsed: 0.124 s
% 11.04/2.92  % (20067)Instructions burned: 269 (million)
% 11.04/2.92  % (20067)------------------------------
% 11.04/2.92  % (20067)------------------------------
% 11.04/2.92  % (20068)Instruction limit reached!
% 11.04/2.92  % (20068)------------------------------
% 11.04/2.92  % (20068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.04/2.92  % (20068)Termination reason: Unknown
% 11.04/2.92  % (20068)Termination phase: Saturation
% 11.04/2.92  
% 11.04/2.92  % (20068)Memory used [KB]: 7931
% 11.04/2.92  % (20068)Time elapsed: 0.096 s
% 11.04/2.92  % (20068)Instructions burned: 204 (million)
% 11.04/2.92  % (20068)------------------------------
% 11.04/2.92  % (20068)------------------------------
% 11.04/2.92  % (20071)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_19870 for (2986ds/4436Mi)
% 11.04/2.93  % (20072)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_19870 for (2986ds/1539Mi)
% 11.04/2.95  % (20073)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_19870 for (2986ds/408Mi)
% 11.04/2.98  % (20065)Instruction limit reached!
% 11.04/2.98  % (20065)------------------------------
% 11.04/2.98  % (20065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.04/2.98  % (20065)Termination reason: Unknown
% 11.04/2.98  % (20065)Termination phase: Saturation
% 11.04/2.98  
% 11.04/2.98  % (20065)Memory used [KB]: 9083
% 11.04/2.98  % (20065)Time elapsed: 0.177 s
% 11.04/2.98  % (20065)Instructions burned: 369 (million)
% 11.04/2.98  % (20065)------------------------------
% 11.04/2.98  % (20065)------------------------------
% 11.04/2.99  % (20074)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_19870 for (2985ds/5205Mi)
% 12.66/3.07  % (20054)Instruction limit reached!
% 12.66/3.07  % (20054)------------------------------
% 12.66/3.07  % (20054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.66/3.07  % (20054)Termination reason: Unknown
% 12.66/3.07  % (20054)Termination phase: Saturation
% 12.66/3.07  
% 12.66/3.07  % (20054)Memory used [KB]: 9850
% 12.66/3.07  % (20054)Time elapsed: 0.481 s
% 12.66/3.07  % (20054)Instructions burned: 987 (million)
% 12.66/3.07  % (20054)------------------------------
% 12.66/3.07  % (20054)------------------------------
% 12.66/3.08  % (20075)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_19870 for (2984ds/1913Mi)
% 12.66/3.12  % (20073)Instruction limit reached!
% 12.66/3.12  % (20073)------------------------------
% 12.66/3.12  % (20073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.66/3.12  % (20073)Termination reason: Unknown
% 12.66/3.12  % (20073)Termination phase: Saturation
% 12.66/3.12  
% 12.66/3.12  % (20073)Memory used [KB]: 10618
% 12.66/3.12  % (20073)Time elapsed: 0.194 s
% 12.66/3.12  % (20073)Instructions burned: 409 (million)
% 12.66/3.12  % (20073)------------------------------
% 12.66/3.12  % (20073)------------------------------
% 13.33/3.13  % (20076)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_19870 for (2984ds/4350Mi)
% 13.33/3.17  % (20061)Instruction limit reached!
% 13.33/3.17  % (20061)------------------------------
% 13.33/3.17  % (20061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.33/3.17  % (20061)Termination reason: Unknown
% 13.33/3.17  % (20061)Termination phase: Saturation
% 13.33/3.17  
% 13.33/3.17  % (20061)Memory used [KB]: 8827
% 13.33/3.17  % (20061)Time elapsed: 0.459 s
% 13.33/3.17  % (20061)Instructions burned: 922 (million)
% 13.33/3.17  % (20061)------------------------------
% 13.33/3.17  % (20061)------------------------------
% 13.33/3.19  % (20077)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_19870 for (2983ds/68Mi)
% 13.67/3.22  % (20077)Instruction limit reached!
% 13.67/3.22  % (20077)------------------------------
% 13.67/3.22  % (20077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.67/3.22  % (20077)Termination reason: Unknown
% 13.67/3.22  % (20077)Termination phase: SInE selection
% 13.67/3.22  
% 13.67/3.22  % (20077)Memory used [KB]: 2430
% 13.67/3.22  % (20077)Time elapsed: 0.035 s
% 13.67/3.22  % (20077)Instructions burned: 68 (million)
% 13.67/3.22  % (20077)------------------------------
% 13.67/3.22  % (20077)------------------------------
% 13.67/3.24  % (20078)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_19870 for (2983ds/358Mi)
% 13.67/3.29  % (20066)Instruction limit reached!
% 13.67/3.29  % (20066)------------------------------
% 13.67/3.29  % (20066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.67/3.29  % (20066)Termination reason: Unknown
% 13.67/3.29  % (20066)Termination phase: Saturation
% 13.67/3.29  
% 13.67/3.29  % (20066)Memory used [KB]: 10490
% 13.67/3.29  % (20066)Time elapsed: 0.492 s
% 13.67/3.29  % (20066)Instructions burned: 1021 (million)
% 13.67/3.29  % (20066)------------------------------
% 13.67/3.29  % (20066)------------------------------
% 14.12/3.31  % (20079)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19870 for (2982ds/31Mi)
% 14.12/3.32  % (20079)Instruction limit reached!
% 14.12/3.32  % (20079)------------------------------
% 14.12/3.32  % (20079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.12/3.32  % (20079)Termination reason: Unknown
% 14.12/3.32  % (20079)Termination phase: shuffling
% 14.12/3.32  
% 14.12/3.32  % (20079)Memory used [KB]: 2302
% 14.12/3.32  % (20079)Time elapsed: 0.017 s
% 14.12/3.32  % (20079)Instructions burned: 31 (million)
% 14.12/3.32  % (20079)------------------------------
% 14.12/3.32  % (20079)------------------------------
% 14.12/3.34  % (20080)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_19870 for (2982ds/279Mi)
% 14.46/3.41  % (20078)Instruction limit reached!
% 14.46/3.41  % (20078)------------------------------
% 14.46/3.41  % (20078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.46/3.41  % (20078)Termination reason: Unknown
% 14.46/3.41  % (20078)Termination phase: Saturation
% 14.46/3.41  
% 14.46/3.41  % (20078)Memory used [KB]: 8443
% 14.46/3.41  % (20078)Time elapsed: 0.171 s
% 14.46/3.41  % (20078)Instructions burned: 359 (million)
% 14.46/3.41  % (20078)------------------------------
% 14.46/3.41  % (20078)------------------------------
% 14.46/3.42  % (20082)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_19870 for (2981ds/258Mi)
% 14.46/3.43  % (20080)Refutation not found, incomplete strategy
% 14.46/3.43  % (20080)------------------------------
% 14.46/3.43  % (20080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.46/3.43  % (20080)Termination reason: Refutation not found, incomplete strategy
% 14.46/3.43  
% 14.46/3.43  
% 14.46/3.43  % (20080)Memory used [KB]: 7803
% 14.46/3.43  % (20080)Time elapsed: 0.089 s
% 14.46/3.43  % (20080)Instructions burned: 197 (million)
% 14.46/3.43  % (20080)------------------------------
% 14.46/3.43  % (20080)------------------------------
% 14.46/3.45  % (20083)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_19870 for (2981ds/26Mi)
% 14.46/3.46  % (20083)Instruction limit reached!
% 14.46/3.46  % (20083)------------------------------
% 14.46/3.46  % (20083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.46/3.46  % (20083)Termination reason: Unknown
% 14.46/3.46  % (20083)Termination phase: shuffling
% 14.46/3.46  
% 14.46/3.46  % (20083)Memory used [KB]: 2174
% 14.46/3.46  % (20083)Time elapsed: 0.014 s
% 14.46/3.46  % (20083)Instructions burned: 26 (million)
% 14.46/3.46  % (20083)------------------------------
% 14.46/3.46  % (20083)------------------------------
% 14.46/3.48  % (20084)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_19870 for (2981ds/995Mi)
% 15.07/3.52  % (20082)Instruction limit reached!
% 15.07/3.52  % (20082)------------------------------
% 15.07/3.52  % (20082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.07/3.52  % (20082)Termination reason: Unknown
% 15.07/3.52  % (20082)Termination phase: Saturation
% 15.07/3.52  
% 15.07/3.52  % (20082)Memory used [KB]: 8571
% 15.07/3.52  % (20082)Time elapsed: 0.096 s
% 15.07/3.52  % (20082)Instructions burned: 259 (million)
% 15.07/3.52  % (20082)------------------------------
% 15.07/3.52  % (20082)------------------------------
% 15.07/3.53  % (20085)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_19870 for (2980ds/373Mi)
% 15.50/3.61  % (20075)Instruction limit reached!
% 15.50/3.61  % (20075)------------------------------
% 15.50/3.61  % (20075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.50/3.61  % (20075)Termination reason: Unknown
% 15.50/3.61  % (20075)Termination phase: Saturation
% 15.50/3.61  
% 15.50/3.61  % (20075)Memory used [KB]: 3965
% 15.50/3.61  % (20075)Time elapsed: 0.537 s
% 15.50/3.61  % (20075)Instructions burned: 1914 (million)
% 15.50/3.61  % (20075)------------------------------
% 15.50/3.61  % (20075)------------------------------
% 15.50/3.63  % (20086)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_19870 for (2979ds/253Mi)
% 15.50/3.65  % (20072)Instruction limit reached!
% 15.50/3.65  % (20072)------------------------------
% 15.50/3.65  % (20072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.50/3.65  % (20072)Termination reason: Unknown
% 15.50/3.65  % (20072)Termination phase: Saturation
% 15.50/3.65  
% 15.50/3.65  % (20072)Memory used [KB]: 11129
% 15.50/3.65  % (20072)Time elapsed: 0.737 s
% 15.50/3.65  % (20072)Instructions burned: 1540 (million)
% 15.50/3.65  % (20072)------------------------------
% 15.50/3.65  % (20072)------------------------------
% 15.50/3.68  % (20087)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_19870 for (2979ds/832Mi)
% 16.30/3.71  % (20085)Instruction limit reached!
% 16.30/3.71  % (20085)------------------------------
% 16.30/3.71  % (20085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.30/3.71  % (20085)Termination reason: Unknown
% 16.30/3.71  % (20085)Termination phase: Saturation
% 16.30/3.71  
% 16.30/3.71  % (20085)Memory used [KB]: 9083
% 16.30/3.71  % (20085)Time elapsed: 0.180 s
% 16.30/3.71  % (20085)Instructions burned: 373 (million)
% 16.30/3.71  % (20085)------------------------------
% 16.30/3.71  % (20085)------------------------------
% 16.30/3.72  % (20088)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_19870 for (2978ds/668Mi)
% 16.30/3.74  % (20086)Instruction limit reached!
% 16.30/3.74  % (20086)------------------------------
% 16.30/3.74  % (20086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.30/3.74  % (20086)Termination reason: Unknown
% 16.30/3.74  % (20086)Termination phase: Saturation
% 16.30/3.74  
% 16.30/3.74  % (20086)Memory used [KB]: 7803
% 16.30/3.74  % (20086)Time elapsed: 0.115 s
% 16.30/3.74  % (20086)Instructions burned: 255 (million)
% 16.30/3.74  % (20086)------------------------------
% 16.30/3.74  % (20086)------------------------------
% 16.30/3.76  % (20090)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_19870 for (2978ds/40Mi)
% 16.30/3.78  % (20090)Instruction limit reached!
% 16.30/3.78  % (20090)------------------------------
% 16.30/3.78  % (20090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.30/3.78  % (20090)Termination reason: Unknown
% 16.30/3.78  % (20090)Termination phase: shuffling
% 16.30/3.78  
% 16.30/3.78  % (20090)Memory used [KB]: 2430
% 16.30/3.78  % (20090)Time elapsed: 0.020 s
% 16.30/3.78  % (20090)Instructions burned: 40 (million)
% 16.30/3.78  % (20090)------------------------------
% 16.30/3.78  % (20090)------------------------------
% 16.30/3.79  % (20091)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_19870 for (2977ds/294Mi)
% 16.86/3.88  % (20084)Instruction limit reached!
% 16.86/3.88  % (20084)------------------------------
% 16.86/3.88  % (20084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.86/3.88  % (20084)Termination reason: Unknown
% 16.86/3.88  % (20084)Termination phase: Saturation
% 16.86/3.88  
% 16.86/3.88  % (20084)Memory used [KB]: 12409
% 16.86/3.88  % (20084)Time elapsed: 0.373 s
% 16.86/3.88  % (20084)Instructions burned: 996 (million)
% 16.86/3.88  % (20084)------------------------------
% 16.86/3.88  % (20084)------------------------------
% 17.44/3.90  % (20092)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_19870 for (2976ds/187Mi)
% 17.44/3.92  % (20091)Instruction limit reached!
% 17.44/3.92  % (20091)------------------------------
% 17.44/3.92  % (20091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.92  % (20091)Termination reason: Unknown
% 17.44/3.92  % (20091)Termination phase: Saturation
% 17.44/3.92  
% 17.44/3.92  % (20091)Memory used [KB]: 7931
% 17.44/3.92  % (20091)Time elapsed: 0.145 s
% 17.44/3.92  % (20091)Instructions burned: 294 (million)
% 17.44/3.92  % (20091)------------------------------
% 17.44/3.92  % (20091)------------------------------
% 17.44/3.93  % (20093)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_19870 for (2976ds/371Mi)
% 17.44/3.99  % (20092)Instruction limit reached!
% 17.44/3.99  % (20092)------------------------------
% 17.44/3.99  % (20092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.99  % (20092)Termination reason: Unknown
% 17.44/3.99  % (20092)Termination phase: Saturation
% 17.44/3.99  
% 17.44/3.99  % (20092)Memory used [KB]: 7931
% 17.44/3.99  % (20092)Time elapsed: 0.088 s
% 17.44/3.99  % (20092)Instructions burned: 188 (million)
% 17.44/3.99  % (20092)------------------------------
% 17.44/3.99  % (20092)------------------------------
% 17.44/4.00  % (20088)Instruction limit reached!
% 17.44/4.00  % (20088)------------------------------
% 17.44/4.00  % (20088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/4.00  % (20088)Termination reason: Unknown
% 17.44/4.00  % (20088)Termination phase: Saturation
% 17.44/4.00  
% 17.44/4.00  % (20088)Memory used [KB]: 16502
% 17.44/4.00  % (20088)Time elapsed: 0.277 s
% 17.44/4.00  % (20088)Instructions burned: 668 (million)
% 17.44/4.00  % (20088)------------------------------
% 17.44/4.00  % (20088)------------------------------
% 17.44/4.00  % (20094)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_19870 for (2975ds/1827Mi)
% 17.44/4.01  % (20095)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_19870 for (2975ds/70Mi)
% 19.54/4.03  % (20095)Instruction limit reached!
% 19.54/4.03  % (20095)------------------------------
% 19.54/4.03  % (20095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.54/4.03  % (20095)Termination reason: Unknown
% 19.54/4.03  % (20095)Termination phase: shuffling
% 19.54/4.03  
% 19.54/4.03  % (20095)Memory used [KB]: 2942
% 19.54/4.03  % (20095)Time elapsed: 0.021 s
% 19.54/4.03  % (20095)Instructions burned: 71 (million)
% 19.54/4.03  % (20095)------------------------------
% 19.54/4.03  % (20095)------------------------------
% 19.54/4.04  % (20087)Instruction limit reached!
% 19.54/4.04  % (20087)------------------------------
% 19.54/4.04  % (20087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.54/4.04  % (20087)Termination reason: Unknown
% 19.54/4.04  % (20087)Termination phase: Saturation
% 19.54/4.04  
% 19.54/4.04  % (20087)Memory used [KB]: 10106
% 19.54/4.04  % (20087)Time elapsed: 0.388 s
% 19.54/4.04  % (20087)Instructions burned: 835 (million)
% 19.54/4.04  % (20087)------------------------------
% 19.54/4.04  % (20087)------------------------------
% 19.54/4.04  % (20096)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_19870 for (2975ds/316Mi)
% 19.54/4.07  % (20097)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_19870 for (2975ds/932Mi)
% 19.54/4.11  % (20093)Instruction limit reached!
% 19.54/4.11  % (20093)------------------------------
% 19.54/4.11  % (20093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.54/4.11  % (20093)Termination reason: Unknown
% 19.54/4.11  % (20093)Termination phase: Saturation
% 19.54/4.11  
% 19.54/4.11  % (20093)Memory used [KB]: 9338
% 19.54/4.11  % (20093)Time elapsed: 0.181 s
% 19.54/4.11  % (20093)Instructions burned: 371 (million)
% 19.54/4.11  % (20093)------------------------------
% 19.54/4.11  % (20093)------------------------------
% 20.12/4.13  % (20098)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_19870 for (2974ds/4714Mi)
% 20.12/4.15  % (20096)Refutation not found, incomplete strategy
% 20.12/4.15  % (20096)------------------------------
% 20.12/4.15  % (20096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.12/4.15  % (20096)Termination reason: Refutation not found, incomplete strategy
% 20.12/4.15  
% 20.12/4.15  
% 20.12/4.15  % (20096)Memory used [KB]: 8187
% 20.12/4.15  % (20096)Time elapsed: 0.112 s
% 20.12/4.15  % (20096)Instructions burned: 288 (million)
% 20.12/4.15  % (20096)------------------------------
% 20.12/4.15  % (20096)------------------------------
% 20.12/4.17  % (20099)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_19870 for (2974ds/8250Mi)
% 20.52/4.25  % (20098)Refutation not found, incomplete strategy
% 20.52/4.25  % (20098)------------------------------
% 20.52/4.25  % (20098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.52/4.25  % (20098)Termination reason: Refutation not found, incomplete strategy
% 20.52/4.25  
% 20.52/4.25  
% 20.52/4.25  % (20098)Memory used [KB]: 8315
% 20.52/4.25  % (20098)Time elapsed: 0.125 s
% 20.52/4.25  % (20098)Instructions burned: 297 (million)
% 20.52/4.25  % (20098)------------------------------
% 20.52/4.25  % (20098)------------------------------
% 20.52/4.27  % (20100)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_19870 for (2972ds/770Mi)
% 21.86/4.51  % (20097)Instruction limit reached!
% 21.86/4.51  % (20097)------------------------------
% 21.86/4.51  % (20097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.86/4.51  % (20097)Termination reason: Unknown
% 21.86/4.51  % (20097)Termination phase: Saturation
% 21.86/4.51  
% 21.86/4.51  % (20097)Memory used [KB]: 10362
% 21.86/4.51  % (20097)Time elapsed: 0.447 s
% 21.86/4.51  % (20097)Instructions burned: 933 (million)
% 21.86/4.51  % (20097)------------------------------
% 21.86/4.51  % (20097)------------------------------
% 21.86/4.53  % (20101)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_19870 for (2970ds/794Mi)
% 22.73/4.63  % (20100)Instruction limit reached!
% 22.73/4.63  % (20100)------------------------------
% 22.73/4.63  % (20100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.73/4.63  % (20100)Termination reason: Unknown
% 22.73/4.63  % (20100)Termination phase: Saturation
% 22.73/4.63  
% 22.73/4.63  % (20100)Memory used [KB]: 8699
% 22.73/4.63  % (20100)Time elapsed: 0.360 s
% 22.73/4.63  % (20100)Instructions burned: 771 (million)
% 22.73/4.63  % (20100)------------------------------
% 22.73/4.63  % (20100)------------------------------
% 22.73/4.64  % (20102)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_19870 for (2969ds/464Mi)
% 22.73/4.68  % (20076)First to succeed.
% 22.73/4.68  % (20076)Refutation found. Thanks to Tanya!
% 22.73/4.68  % SZS status Theorem for DTF2THF_19870
% 22.73/4.68  % SZS output start Proof for DTF2THF_19870
% 22.73/4.68  thf(type_def_5, type, nat: $tType).
% 22.73/4.68  thf(type_def_6, type, list_nat: $tType).
% 22.73/4.68  thf(type_def_8, type, list_P512754263e_form: $tType).
% 22.73/4.68  thf(type_def_9, type, list_list_nat: $tType).
% 22.73/4.68  thf(type_def_10, type, list_l461858535e_form: $tType).
% 22.73/4.68  thf(type_def_11, type, prover1687215943e_form: $tType).
% 22.73/4.68  thf(type_def_12, type, set_nat: $tType).
% 22.73/4.68  thf(type_def_13, type, set_Pr1986765409at_nat: $tType).
% 22.73/4.68  thf(type_def_14, type, set_Pr1560408065st_nat: $tType).
% 22.73/4.68  thf(type_def_15, type, set_Pr1189404964e_form: $tType).
% 22.73/4.68  thf(type_def_16, type, set_Pr31825690e_form: $tType).
% 22.73/4.68  thf(type_def_17, type, list_P796095576elle_U: $tType).
% 22.73/4.68  thf(type_def_18, type, list_n2139828004le_U_o: $tType).
% 22.73/4.68  thf(type_def_19, type, set_Pr619177522elle_U: $tType).
% 22.73/4.68  thf(type_def_20, type, list_s1200803384elle_U: $tType).
% 22.73/4.68  thf(type_def_21, type, set_list_nat: $tType).
% 22.73/4.68  thf(type_def_22, type, set_li5074317e_form: $tType).
% 22.73/4.68  thf(type_def_23, type, set_Pr554570749e_form: $tType).
% 22.73/4.68  thf(type_def_24, type, set_Pr816919384e_form: $tType).
% 22.73/4.68  thf(type_def_25, type, set_Pr1174364408e_form: $tType).
% 22.73/4.68  thf(type_def_26, type, set_Pr957084504rm_nat: $tType).
% 22.73/4.68  thf(type_def_27, type, set_Pr1057005944st_nat: $tType).
% 22.73/4.68  thf(type_def_28, type, set_Pr1072215906le_U_o: $tType).
% 22.73/4.68  thf(type_def_29, type, set_Pr2099245410le_U_o: $tType).
% 22.73/4.68  thf(type_def_30, type, produc890077173st_nat: $tType).
% 22.73/4.68  thf(type_def_31, type, produc957084248e_form: $tType).
% 22.73/4.68  thf(type_def_32, type, produc1699244961st_nat: $tType).
% 22.73/4.68  thf(type_def_33, type, produc1494932632e_form: $tType).
% 22.73/4.68  thf(type_def_34, type, produc1473535256st_nat: $tType).
% 22.73/4.68  thf(type_def_35, type, produc791938916e_form: $tType).
% 22.73/4.68  thf(type_def_36, type, produc622718850le_U_o: $tType).
% 22.73/4.68  thf(type_def_37, type, product_prod_nat_nat: $tType).
% 22.73/4.68  thf(type_def_38, type, produc1296622072e_form: $tType).
% 22.73/4.68  thf(type_def_39, type, produc117678584rm_nat: $tType).
% 22.73/4.68  thf(type_def_40, type, produc825256814e_form: $tType).
% 22.73/4.68  thf(type_def_41, type, produc227817602le_U_o: $tType).
% 22.73/4.68  thf(type_def_42, type, prover_Mirabelle_U: $tType).
% 22.73/4.68  thf(func_def_0, type, set_Pr2099245410le_U_o: $tType).
% 22.73/4.68  thf(func_def_1, type, produc622718850le_U_o: $tType).
% 22.73/4.68  thf(func_def_2, type, produc957084248e_form: $tType).
% 22.73/4.68  thf(func_def_3, type, set_Pr1072215906le_U_o: $tType).
% 22.73/4.68  thf(func_def_4, type, produc227817602le_U_o: $tType).
% 22.73/4.68  thf(func_def_5, type, set_Pr31825690e_form: $tType).
% 22.73/4.68  thf(func_def_6, type, produc791938916e_form: $tType).
% 22.73/4.68  thf(func_def_7, type, set_Pr1057005944st_nat: $tType).
% 22.73/4.68  thf(func_def_8, type, set_Pr1174364408e_form: $tType).
% 22.73/4.68  thf(func_def_9, type, set_Pr1189404964e_form: $tType).
% 22.73/4.68  thf(func_def_10, type, produc1473535256st_nat: $tType).
% 22.73/4.68  thf(func_def_11, type, produc1494932632e_form: $tType).
% 22.73/4.68  thf(func_def_12, type, produc825256814e_form: $tType).
% 22.73/4.68  thf(func_def_13, type, list_n2139828004le_U_o: $tType).
% 22.73/4.68  thf(func_def_14, type, produc890077173st_nat: $tType).
% 22.73/4.68  thf(func_def_15, type, set_Pr1560408065st_nat: $tType).
% 22.73/4.68  thf(func_def_16, type, set_Pr957084504rm_nat: $tType).
% 22.73/4.68  thf(func_def_17, type, set_Pr816919384e_form: $tType).
% 22.73/4.68  thf(func_def_18, type, produc1699244961st_nat: $tType).
% 22.73/4.68  thf(func_def_19, type, produc117678584rm_nat: $tType).
% 22.73/4.68  thf(func_def_20, type, produc1296622072e_form: $tType).
% 22.73/4.68  thf(func_def_21, type, list_l461858535e_form: $tType).
% 22.73/4.68  thf(func_def_22, type, set_li5074317e_form: $tType).
% 22.73/4.68  thf(func_def_23, type, list_s1200803384elle_U: $tType).
% 22.73/4.68  thf(func_def_24, type, set_Pr1986765409at_nat: $tType).
% 22.73/4.68  thf(func_def_25, type, list_P512754263e_form: $tType).
% 22.73/4.68  thf(func_def_26, type, set_Pr554570749e_form: $tType).
% 22.73/4.68  thf(func_def_27, type, list_P796095576elle_U: $tType).
% 22.73/4.68  thf(func_def_28, type, set_Pr619177522elle_U: $tType).
% 22.73/4.68  thf(func_def_29, type, product_prod_nat_nat: $tType).
% 22.73/4.68  thf(func_def_30, type, list_list_nat: $tType).
% 22.73/4.68  thf(func_def_31, type, set_list_nat: $tType).
% 22.73/4.68  thf(func_def_32, type, prover1687215943e_form: $tType).
% 22.73/4.68  thf(func_def_33, type, prover_Mirabelle_U: $tType).
% 22.73/4.68  thf(func_def_34, type, list_nat: $tType).
% 22.73/4.68  thf(func_def_35, type, set_nat: $tType).
% 22.73/4.68  thf(func_def_36, type, nat: $tType).
% 22.73/4.68  thf(func_def_37, type, zero_zero_nat: nat).
% 22.73/4.68  thf(func_def_38, type, if_list_nat: $o > list_nat > list_nat > list_nat).
% 22.73/4.68  thf(func_def_39, type, if_lis1812881937e_form: $o > list_P512754263e_form > list_P512754263e_form > list_P512754263e_form).
% 22.73/4.68  thf(func_def_40, type, append_list_nat: list_list_nat > list_list_nat > list_list_nat).
% 22.73/4.68  thf(func_def_41, type, append1797078012e_form: list_l461858535e_form > list_l461858535e_form > list_l461858535e_form).
% 22.73/4.68  thf(func_def_42, type, append_nat: list_nat > list_nat > list_nat).
% 22.73/4.68  thf(func_def_43, type, append1038020460e_form: list_P512754263e_form > list_P512754263e_form > list_P512754263e_form).
% 22.73/4.68  thf(func_def_44, type, bind_nat_nat: list_nat > (nat > list_nat) > list_nat).
% 22.73/4.68  thf(func_def_45, type, bind_n1193922848e_form: list_nat > (nat > list_P512754263e_form) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_46, type, bind_P1359331232rm_nat: list_P512754263e_form > (prover1687215943e_form > list_nat) > list_nat).
% 22.73/4.68  thf(func_def_47, type, bind_P1054726576e_form: list_P512754263e_form > (prover1687215943e_form > list_P512754263e_form) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_48, type, butlast_nat: list_nat > list_nat).
% 22.73/4.68  thf(func_def_49, type, butlas664258165e_form: list_P512754263e_form > list_P512754263e_form).
% 22.73/4.68  thf(func_def_50, type, can_select_nat: (nat > $o) > set_nat > $o).
% 22.73/4.68  thf(func_def_51, type, concat_nat: list_list_nat > list_nat).
% 22.73/4.68  thf(func_def_52, type, concat1664984646e_form: list_l461858535e_form > list_P512754263e_form).
% 22.73/4.68  thf(func_def_53, type, insert_nat: nat > list_nat > list_nat).
% 22.73/4.68  thf(func_def_54, type, insert697320747e_form: prover1687215943e_form > list_P512754263e_form > list_P512754263e_form).
% 22.73/4.68  thf(func_def_55, type, last_nat: list_nat > nat).
% 22.73/4.68  thf(func_def_56, type, last_P1811260776e_form: list_P512754263e_form > prover1687215943e_form).
% 22.73/4.68  thf(func_def_57, type, lenlex_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat).
% 22.73/4.68  thf(func_def_58, type, lenlex1927129340e_form: set_Pr1189404964e_form > set_Pr31825690e_form).
% 22.73/4.68  thf(func_def_59, type, lex_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat).
% 22.73/4.68  thf(func_def_60, type, lex_Pr233218909e_form: set_Pr1189404964e_form > set_Pr31825690e_form).
% 22.73/4.68  thf(func_def_61, type, lexord_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat).
% 22.73/4.68  thf(func_def_62, type, lexord1848469012e_form: set_Pr1189404964e_form > set_Pr31825690e_form).
% 22.73/4.68  thf(func_def_63, type, cons_n50929118le_U_o: (nat > list_P796095576elle_U > $o) > list_n2139828004le_U_o > list_n2139828004le_U_o).
% 22.73/4.68  thf(func_def_64, type, cons_list_nat: list_nat > list_list_nat > list_list_nat).
% 22.73/4.68  thf(func_def_65, type, cons_l1379921697e_form: list_P512754263e_form > list_l461858535e_form > list_l461858535e_form).
% 22.73/4.68  thf(func_def_66, type, cons_nat: nat > list_nat > list_nat).
% 22.73/4.68  thf(func_def_67, type, cons_P1475164433e_form: prover1687215943e_form > list_P512754263e_form > list_P512754263e_form).
% 22.73/4.68  thf(func_def_68, type, cons_s32021736elle_U: set_Pr619177522elle_U > list_s1200803384elle_U > list_s1200803384elle_U).
% 22.73/4.68  thf(func_def_69, type, nil_na1584420238le_U_o: list_n2139828004le_U_o).
% 22.73/4.68  thf(func_def_70, type, nil_list_nat: list_list_nat).
% 22.73/4.68  thf(func_def_71, type, nil_li1393862353e_form: list_l461858535e_form).
% 22.73/4.68  thf(func_def_72, type, nil_nat: list_nat).
% 22.73/4.68  thf(func_def_73, type, nil_Pr1384483009e_form: list_P512754263e_form).
% 22.73/4.68  thf(func_def_74, type, nil_se944326968elle_U: list_s1200803384elle_U).
% 22.73/4.68  thf(func_def_75, type, set_list_nat2: list_list_nat > set_list_nat).
% 22.73/4.68  thf(func_def_76, type, set_li1219651714e_form: list_l461858535e_form > set_li5074317e_form).
% 22.73/4.68  thf(func_def_77, type, set_nat2: list_nat > set_nat).
% 22.73/4.68  thf(func_def_78, type, set_Pr1105237746e_form: list_P512754263e_form > set_Pr554570749e_form).
% 22.73/4.68  thf(func_def_79, type, list_ex1_nat: (nat > $o) > list_nat > $o).
% 22.73/4.68  thf(func_def_80, type, list_e2123636798e_form: (prover1687215943e_form > $o) > list_P512754263e_form > $o).
% 22.73/4.68  thf(func_def_81, type, listrel1_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat).
% 22.73/4.68  thf(func_def_82, type, listre502458152e_form: set_Pr1189404964e_form > set_Pr31825690e_form).
% 22.73/4.68  thf(func_def_83, type, listrel_nat_nat: set_Pr1986765409at_nat > set_Pr1560408065st_nat).
% 22.73/4.68  thf(func_def_84, type, listre318297994e_form: set_Pr816919384e_form > set_Pr1174364408e_form).
% 22.73/4.68  thf(func_def_85, type, listre483706378rm_nat: set_Pr957084504rm_nat > set_Pr1057005944st_nat).
% 22.73/4.68  thf(func_def_86, type, listre1908795590e_form: set_Pr1189404964e_form > set_Pr31825690e_form).
% 22.73/4.68  thf(func_def_87, type, listre290852044le_U_o: set_Pr1072215906le_U_o > set_Pr2099245410le_U_o).
% 22.73/4.68  thf(func_def_88, type, maps_nat_nat: (nat > list_nat) > list_nat > list_nat).
% 22.73/4.68  thf(func_def_89, type, maps_n1383976154e_form: (nat > list_P512754263e_form) > list_nat > list_P512754263e_form).
% 22.73/4.68  thf(func_def_90, type, maps_P1549384538rm_nat: (prover1687215943e_form > list_nat) > list_P512754263e_form > list_nat).
% 22.73/4.68  thf(func_def_91, type, maps_P2058952566e_form: (prover1687215943e_form > list_P512754263e_form) > list_P512754263e_form > list_P512754263e_form).
% 22.73/4.68  thf(func_def_92, type, product_lists_nat: list_list_nat > list_list_nat).
% 22.73/4.68  thf(func_def_93, type, produc168439576e_form: list_l461858535e_form > list_l461858535e_form).
% 22.73/4.68  thf(func_def_94, type, rotate1_nat: list_nat > list_nat).
% 22.73/4.68  thf(func_def_95, type, rotate650061876e_form: list_P512754263e_form > list_P512754263e_form).
% 22.73/4.68  thf(func_def_96, type, subseqs_nat: list_nat > list_list_nat).
% 22.73/4.68  thf(func_def_97, type, subseq1471997234e_form: list_P512754263e_form > list_l461858535e_form).
% 22.73/4.68  thf(func_def_98, type, produc939441135st_nat: (nat > nat > $o) > list_nat > produc890077173st_nat).
% 22.73/4.68  thf(func_def_99, type, produc54611594e_form: (prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > produc957084248e_form).
% 22.73/4.68  thf(func_def_100, type, produc1625736153st_nat: list_nat > list_nat > produc1699244961st_nat).
% 22.73/4.68  thf(func_def_101, type, produc1617574096e_form: list_nat > list_P512754263e_form > produc1494932632e_form).
% 22.73/4.68  thf(func_def_102, type, produc1897654224st_nat: list_P512754263e_form > list_nat > produc1473535256st_nat).
% 22.73/4.68  thf(func_def_103, type, produc891809686e_form: list_P512754263e_form > list_P512754263e_form > produc791938916e_form).
% 22.73/4.68  thf(func_def_104, type, produc1377086578le_U_o: list_s1200803384elle_U > list_n2139828004le_U_o > produc622718850le_U_o).
% 22.73/4.68  thf(func_def_105, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 22.73/4.68  thf(func_def_106, type, produc876465968e_form: nat > prover1687215943e_form > produc1296622072e_form).
% 22.73/4.68  thf(func_def_107, type, produc1041874352rm_nat: prover1687215943e_form > nat > produc117678584rm_nat).
% 22.73/4.68  thf(func_def_108, type, produc1018812320e_form: prover1687215943e_form > prover1687215943e_form > produc825256814e_form).
% 22.73/4.68  thf(func_def_109, type, produc1069574002le_U_o: set_Pr619177522elle_U > (nat > list_P796095576elle_U > $o) > produc227817602le_U_o).
% 22.73/4.68  thf(func_def_110, type, prover1282070756_SEval: produc227817602le_U_o > (nat > prover_Mirabelle_U) > list_P512754263e_form > $o).
% 22.73/4.68  thf(func_def_111, type, prover1539709396Svalid: list_P512754263e_form > $o).
% 22.73/4.68  thf(func_def_112, type, prover1577896257_finst: prover1687215943e_form > nat > prover1687215943e_form).
% 22.73/4.68  thf(func_def_113, type, prover886976490en_nat: list_list_nat > list_nat).
% 22.73/4.68  thf(func_def_114, type, prover542312166e_form: list_l461858535e_form > list_P512754263e_form).
% 22.73/4.68  thf(func_def_115, type, prover571163162e_FAll: prover1687215943e_form > prover1687215943e_form).
% 22.73/4.68  thf(func_def_116, type, prover_Mirabelle_fv: prover1687215943e_form > list_nat).
% 22.73/4.68  thf(func_def_117, type, prover1847600056is_env: produc227817602le_U_o > (nat > prover_Mirabelle_U) > $o).
% 22.73/4.68  thf(func_def_118, type, prover1021675886maxvar: list_nat > nat).
% 22.73/4.68  thf(func_def_119, type, prover2096325705preSuc: list_nat > list_nat).
% 22.73/4.68  thf(func_def_120, type, prover_Mirabelle_sfv: list_P512754263e_form > list_nat).
% 22.73/4.68  thf(func_def_121, type, irrefl_nat: set_Pr1986765409at_nat > $o).
% 22.73/4.68  thf(func_def_122, type, irrefl2121388754e_form: set_Pr1189404964e_form > $o).
% 22.73/4.68  thf(func_def_123, type, collect_nat: (nat > $o) > set_nat).
% 22.73/4.68  thf(func_def_124, type, the_elem_nat: set_nat > nat).
% 22.73/4.68  thf(func_def_125, type, the_el969789074e_form: set_Pr554570749e_form > prover1687215943e_form).
% 22.73/4.68  thf(func_def_126, type, member_list_nat: list_nat > set_list_nat > $o).
% 22.73/4.68  thf(func_def_127, type, member1828782574e_form: list_P512754263e_form > set_li5074317e_form > $o).
% 22.73/4.68  thf(func_def_128, type, member_nat: nat > set_nat > $o).
% 22.73/4.68  thf(func_def_129, type, member1926390090st_nat: produc1699244961st_nat > set_Pr1560408065st_nat > $o).
% 22.73/4.68  thf(func_def_130, type, member1471151041e_form: produc1494932632e_form > set_Pr1174364408e_form > $o).
% 22.73/4.68  thf(func_def_131, type, member1449753665st_nat: produc1473535256st_nat > set_Pr1057005944st_nat > $o).
% 22.73/4.68  thf(func_def_132, type, member650892795e_form: produc791938916e_form > set_Pr31825690e_form > $o).
% 22.73/4.68  thf(func_def_133, type, member493452075le_U_o: produc622718850le_U_o > set_Pr2099245410le_U_o > $o).
% 22.73/4.68  thf(func_def_134, type, member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o).
% 22.73/4.68  thf(func_def_135, type, member18158113e_form: produc1296622072e_form > set_Pr816919384e_form > $o).
% 22.73/4.68  thf(func_def_136, type, member986698273rm_nat: produc117678584rm_nat > set_Pr957084504rm_nat > $o).
% 22.73/4.68  thf(func_def_137, type, member189065477e_form: produc825256814e_form > set_Pr1189404964e_form > $o).
% 22.73/4.68  thf(func_def_138, type, member1933006123le_U_o: produc227817602le_U_o > set_Pr1072215906le_U_o > $o).
% 22.73/4.68  thf(func_def_139, type, member1793840734e_form: prover1687215943e_form > set_Pr554570749e_form > $o).
% 22.73/4.68  thf(func_def_140, type, a: set_Pr619177522elle_U).
% 22.73/4.68  thf(func_def_141, type, b: nat > list_P796095576elle_U > $o).
% 22.73/4.68  thf(func_def_142, type, f: prover1687215943e_form).
% 22.73/4.68  thf(func_def_143, type, s: list_P512754263e_form).
% 22.73/4.68  thf(func_def_144, type, u: nat).
% 22.73/4.68  thf(func_def_160, type, sK0: produc227817602le_U_o > nat > list_P796095576elle_U > $o).
% 22.73/4.68  thf(func_def_161, type, sK1: produc227817602le_U_o > set_Pr619177522elle_U).
% 22.73/4.68  thf(func_def_162, type, sK2: list_nat > (nat > $o) > nat).
% 22.73/4.68  thf(func_def_163, type, sK3: list_nat > (nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_164, type, sK4: list_nat > (nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_165, type, sK5: ((prover1687215943e_form > prover1687215943e_form) > list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_166, type, sK6: ((prover1687215943e_form > prover1687215943e_form) > list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form).
% 22.73/4.68  thf(func_def_167, type, sK7: ((prover1687215943e_form > prover1687215943e_form) > list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_168, type, sK8: ((prover1687215943e_form > prover1687215943e_form) > list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form).
% 22.73/4.68  thf(func_def_169, type, sK9: ((prover1687215943e_form > prover1687215943e_form) > list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_170, type, sK10: ((prover1687215943e_form > prover1687215943e_form) > list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_171, type, sK11: (list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_172, type, sK12: (list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_173, type, sK13: (list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_174, type, sK14: (list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_175, type, sK15: list_nat > (nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_176, type, sK16: list_nat > (nat > $o) > nat).
% 22.73/4.68  thf(func_def_177, type, sK17: list_nat > (nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_178, type, sK18: ((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form > $o).
% 22.73/4.68  thf(func_def_179, type, sK19: ((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_180, type, sK20: ((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_181, type, sK21: ((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_182, type, sK22: ((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_183, type, sK23: ((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form > $o).
% 22.73/4.68  thf(func_def_184, type, sK24: ((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form > $o).
% 22.73/4.68  thf(func_def_185, type, sK25: list_nat > (nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_186, type, sK26: list_nat > (nat > $o) > nat).
% 22.73/4.68  thf(func_def_187, type, sK27: list_nat > (nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_188, type, sK28: ((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_189, type, sK29: ((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form > $o).
% 22.73/4.68  thf(func_def_190, type, sK30: ((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_191, type, sK31: ((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form > $o).
% 22.73/4.68  thf(func_def_192, type, sK32: (produc227817602le_U_o > $o) > nat > list_P796095576elle_U > $o).
% 22.73/4.68  thf(func_def_193, type, sK33: (produc227817602le_U_o > $o) > set_Pr619177522elle_U).
% 22.73/4.68  thf(func_def_194, type, sK34: nat > prover_Mirabelle_U).
% 22.73/4.68  thf(func_def_195, type, sK35: ((prover1687215943e_form > nat) > list_P512754263e_form > list_nat > $o) > prover1687215943e_form > nat).
% 22.73/4.68  thf(func_def_196, type, sK36: ((prover1687215943e_form > nat) > list_P512754263e_form > list_nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_197, type, sK37: ((prover1687215943e_form > nat) > list_P512754263e_form > list_nat > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_198, type, sK38: ((prover1687215943e_form > nat) > list_P512754263e_form > list_nat > $o) > prover1687215943e_form > nat).
% 22.73/4.68  thf(func_def_199, type, sK39: ((prover1687215943e_form > nat) > list_P512754263e_form > list_nat > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_200, type, sK40: ((prover1687215943e_form > nat) > list_P512754263e_form > list_nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_201, type, sK41: list_P512754263e_form > list_P512754263e_form).
% 22.73/4.68  thf(func_def_202, type, sK42: list_P512754263e_form > prover1687215943e_form).
% 22.73/4.68  thf(func_def_203, type, sK43: list_nat > nat > list_nat).
% 22.73/4.68  thf(func_def_204, type, sK44: list_nat > nat > list_nat).
% 22.73/4.68  thf(func_def_205, type, sK45: (list_nat > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_206, type, sK46: (list_nat > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_207, type, sK47: (list_nat > list_P512754263e_form > $o) > list_nat).
% 22.73/4.68  thf(func_def_208, type, sK48: (list_nat > list_P512754263e_form > $o) > nat).
% 22.73/4.68  thf(func_def_209, type, sK49: (list_nat > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_210, type, sK50: (list_nat > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_211, type, sK51: (list_nat > list_P512754263e_form > $o) > nat).
% 22.73/4.68  thf(func_def_212, type, sK52: (list_nat > list_P512754263e_form > $o) > list_nat).
% 22.73/4.68  thf(func_def_213, type, sK53: set_Pr1072215906le_U_o > (nat > list_P796095576elle_U > $o) > list_s1200803384elle_U > list_n2139828004le_U_o > list_s1200803384elle_U).
% 22.73/4.68  thf(func_def_214, type, sK54: set_Pr1072215906le_U_o > (nat > list_P796095576elle_U > $o) > list_s1200803384elle_U > list_n2139828004le_U_o > set_Pr619177522elle_U).
% 22.73/4.68  thf(func_def_215, type, sK55: list_nat > nat > list_nat).
% 22.73/4.68  thf(func_def_216, type, sK56: list_nat > nat > list_nat).
% 22.73/4.68  thf(func_def_217, type, sK57: (nat > prover_Mirabelle_U) > list_P512754263e_form > (nat > prover_Mirabelle_U) > nat).
% 22.73/4.68  thf(func_def_218, type, sK58: (list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_219, type, sK59: (list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_220, type, sK60: (list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_221, type, sK61: (list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_222, type, sK62: (list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_223, type, sK63: (list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_224, type, sK64: (list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_225, type, sK65: (list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_226, type, sK66: (list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_227, type, sK67: (list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_228, type, sK68: (list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_229, type, sK69: (list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_230, type, sK70: (list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_231, type, sK71: set_Pr1072215906le_U_o > list_s1200803384elle_U > list_n2139828004le_U_o > list_s1200803384elle_U).
% 22.73/4.68  thf(func_def_232, type, sK72: set_Pr1072215906le_U_o > list_s1200803384elle_U > list_n2139828004le_U_o > nat > list_P796095576elle_U > $o).
% 22.73/4.68  thf(func_def_233, type, sK73: set_Pr1072215906le_U_o > list_s1200803384elle_U > list_n2139828004le_U_o > set_Pr619177522elle_U).
% 22.73/4.68  thf(func_def_234, type, sK74: set_Pr1072215906le_U_o > list_s1200803384elle_U > list_n2139828004le_U_o > list_n2139828004le_U_o).
% 22.73/4.68  thf(func_def_235, type, sK75: list_nat > (nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_236, type, sK76: list_nat > (nat > $o) > nat).
% 22.73/4.68  thf(func_def_237, type, sK77: list_nat > (nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_238, type, sK78: (list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_239, type, sK79: (list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_240, type, sK80: (list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_241, type, sK81: (list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_242, type, sK82: (list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_243, type, sK83: (list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_244, type, sK84: (list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_245, type, sK85: (list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_246, type, sK86: (list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_247, type, sK87: (list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_248, type, sK88: list_nat > (nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_249, type, sK89: list_nat > (nat > $o) > nat).
% 22.73/4.68  thf(func_def_250, type, sK90: list_nat > (nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_251, type, sK91: list_P512754263e_form > prover1687215943e_form).
% 22.73/4.68  thf(func_def_252, type, sK92: list_P512754263e_form > prover1687215943e_form).
% 22.73/4.68  thf(func_def_253, type, sK93: list_P512754263e_form > list_P512754263e_form).
% 22.73/4.68  thf(func_def_254, type, sK94: list_P512754263e_form > prover1687215943e_form).
% 22.73/4.68  thf(func_def_255, type, sK95: nat > list_nat > list_nat).
% 22.73/4.68  thf(func_def_256, type, sK96: nat > list_nat > list_nat).
% 22.73/4.68  thf(func_def_257, type, sK97: (nat > $o) > list_nat > nat).
% 22.73/4.68  thf(func_def_258, type, sK98: (nat > $o) > list_nat > list_nat).
% 22.73/4.68  thf(func_def_259, type, sK99: (nat > $o) > list_nat > list_nat).
% 22.73/4.68  thf(func_def_260, type, sK100: set_Pr1072215906le_U_o > (list_s1200803384elle_U > list_n2139828004le_U_o > $o) > list_s1200803384elle_U).
% 22.73/4.68  thf(func_def_261, type, sK101: set_Pr1072215906le_U_o > (list_s1200803384elle_U > list_n2139828004le_U_o > $o) > set_Pr619177522elle_U).
% 22.73/4.68  thf(func_def_262, type, sK102: set_Pr1072215906le_U_o > (list_s1200803384elle_U > list_n2139828004le_U_o > $o) > nat > list_P796095576elle_U > $o).
% 22.73/4.68  thf(func_def_263, type, sK103: set_Pr1072215906le_U_o > (list_s1200803384elle_U > list_n2139828004le_U_o > $o) > list_n2139828004le_U_o).
% 22.73/4.68  thf(func_def_264, type, sK104: produc227817602le_U_o > set_Pr619177522elle_U).
% 22.73/4.68  thf(func_def_265, type, sK105: produc227817602le_U_o > nat > list_P796095576elle_U > $o).
% 22.73/4.68  thf(func_def_266, type, sK106: (produc227817602le_U_o > $o) > nat > list_P796095576elle_U > $o).
% 22.73/4.68  thf(func_def_267, type, sK107: (produc227817602le_U_o > $o) > set_Pr619177522elle_U).
% 22.73/4.68  thf(func_def_268, type, sK108: (list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_269, type, sK109: (list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_270, type, sK110: list_n2139828004le_U_o > set_Pr1072215906le_U_o > set_Pr619177522elle_U > list_s1200803384elle_U > nat > list_P796095576elle_U > $o).
% 22.73/4.68  thf(func_def_271, type, sK111: list_n2139828004le_U_o > set_Pr1072215906le_U_o > set_Pr619177522elle_U > list_s1200803384elle_U > list_n2139828004le_U_o).
% 22.73/4.68  thf(func_def_272, type, sK112: list_P512754263e_form > list_P512754263e_form).
% 22.73/4.68  thf(func_def_273, type, sK113: list_P512754263e_form > prover1687215943e_form).
% 22.73/4.68  thf(func_def_274, type, sK114: (list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_275, type, sK115: (list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_276, type, sK116: (list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_277, type, sK117: (list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_278, type, sK118: (list_P512754263e_form > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_279, type, sK119: (list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_280, type, sK120: (list_P512754263e_form > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_281, type, sK121: (list_P512754263e_form > list_nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_282, type, sK122: (list_P512754263e_form > list_nat > $o) > nat).
% 22.73/4.68  thf(func_def_283, type, sK123: (list_P512754263e_form > list_nat > $o) > list_nat).
% 22.73/4.68  thf(func_def_284, type, sK124: (list_P512754263e_form > list_nat > $o) > nat).
% 22.73/4.68  thf(func_def_285, type, sK125: (list_P512754263e_form > list_nat > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_286, type, sK126: (list_P512754263e_form > list_nat > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_287, type, sK127: (list_P512754263e_form > list_nat > $o) > prover1687215943e_form).
% 22.73/4.68  thf(func_def_288, type, sK128: (list_P512754263e_form > list_nat > $o) > list_P512754263e_form).
% 22.73/4.68  thf(func_def_289, type, sK129: list_nat > nat > list_nat).
% 22.73/4.68  thf(func_def_290, type, sK130: list_nat > nat > nat).
% 22.73/4.68  thf(func_def_291, type, sK131: list_nat > nat > list_nat).
% 22.73/4.68  thf(func_def_293, type, ph133: !>[X0: $tType]:(X0)).
% 22.73/4.68  thf(func_def_295, type, sK134: nat > prover_Mirabelle_U).
% 22.73/4.68  thf(func_def_296, type, sK135: produc227817602le_U_o).
% 22.73/4.68  thf(f3302,plain,(
% 22.73/4.68    $false),
% 22.73/4.68    inference(avatar_sat_refutation,[status(thm)],[f1765,f1770,f3070,f3301])).
% 22.73/4.68  thf(f3301,plain,(
% 22.73/4.68    ~spl132_1 | ~spl132_3),
% 22.73/4.68    inference(avatar_contradiction_clause,[status(thm)],[f3300])).
% 22.73/4.68  thf(f3300,plain,(
% 22.73/4.68    $false | (~spl132_1 | ~spl132_3)),
% 22.73/4.68    inference(subsumption_resolution,[status(thm)],[f3284,f1769])).
% 22.73/4.68  thf(f1769,plain,(
% 22.73/4.68    ((prover1847600056is_env @ sK135 @ sK134) = $true) | ~spl132_3),
% 22.73/4.68    inference(avatar_component_clause,[status(thm)],[f1767])).
% 22.73/4.68  thf(f1767,definition,(
% 22.73/4.68    spl132_3 <=> ((prover1847600056is_env @ sK135 @ sK134) = $true)),
% 22.73/4.68    introduced(definition,[new_symbols(naming,[spl132_3])],[avatar_definition])).
% 22.73/4.68  thf(f3284,plain,(
% 22.73/4.68    ((prover1847600056is_env @ sK135 @ sK134) != $true) | ~spl132_1),
% 22.73/4.68    inference(trivial_inequality_removal,[status(thm)],[f3209])).
% 22.73/4.68  thf(f3209,plain,(
% 22.73/4.68    ($false = $true) | ((prover1847600056is_env @ sK135 @ sK134) != $true) | ~spl132_1),
% 22.73/4.68    inference(superposition,[status(thm)],[f2688,f1761])).
% 22.73/4.68  thf(f1761,plain,(
% 22.73/4.68    ($false = (prover1282070756_SEval @ sK135 @ sK134 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))) | ~spl132_1),
% 22.73/4.68    inference(avatar_component_clause,[status(thm)],[f1759])).
% 22.73/4.68  thf(f1759,definition,(
% 22.73/4.68    spl132_1 <=> ($false = (prover1282070756_SEval @ sK135 @ sK134 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))),
% 22.73/4.68    introduced(definition,[new_symbols(naming,[spl132_1])],[avatar_definition])).
% 22.73/4.68  thf(f2688,plain,(
% 22.73/4.68    ( ! [X0 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : (((prover1282070756_SEval @ X0 @ X1 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))) = $true) | ((prover1847600056is_env @ X0 @ X1) != $true)) )),
% 22.73/4.68    inference(superposition,[status(thm)],[f1148,f1153])).
% 22.73/4.68  thf(f1153,plain,(
% 22.73/4.68    ( ! [X0 : produc227817602le_U_o] : (((produc1069574002le_U_o @ (sK104 @ X0) @ (sK105 @ X0)) = X0)) )),
% 22.73/4.68    inference(cnf_transformation,[status(thm)],[f1042])).
% 22.73/4.68  thf(f1042,plain,(
% 22.73/4.68    ! [X0 : produc227817602le_U_o] : ((produc1069574002le_U_o @ (sK104 @ X0) @ (sK105 @ X0)) = X0)),
% 22.73/4.68    inference(skolemisation,[status(esa),new_symbols(skolem,[sK104,sK105])],[f892,f1041])).
% 22.73/4.68  thf(f1041,plain,(
% 22.73/4.68    ! [X0 : produc227817602le_U_o] : (? [X1 : set_Pr619177522elle_U,X2 : nat > list_P796095576elle_U > $o] : ((produc1069574002le_U_o @ X1 @ X2) = X0) => ((produc1069574002le_U_o @ (sK104 @ X0) @ (sK105 @ X0)) = X0))),
% 22.73/4.68    introduced(definition,[],[choice_axiom])).
% 22.73/4.68  thf(f892,plain,(
% 22.73/4.68    ! [X0 : produc227817602le_U_o] : ? [X1 : set_Pr619177522elle_U,X2 : nat > list_P796095576elle_U > $o] : ((produc1069574002le_U_o @ X1 @ X2) = X0)),
% 22.73/4.68    inference(ennf_transformation,[status(thm)],[f846])).
% 22.73/4.68  thf(f846,plain,(
% 22.73/4.68    ! [X0 : produc227817602le_U_o] : ~! [X1 : set_Pr619177522elle_U,X2 : nat > list_P796095576elle_U > $o] : ((produc1069574002le_U_o @ X1 @ X2) != X0)),
% 22.73/4.68    inference(rectify,[status(thm)],[f197])).
% 22.73/4.68  thf(f197,axiom,(
% 22.73/4.68    ! [X13 : produc227817602le_U_o] : ~! [X37 : set_Pr619177522elle_U,X70 : nat > list_P796095576elle_U > $o] : ((produc1069574002le_U_o @ X37 @ X70) != X13)),
% 22.73/4.68    file('/export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2THF_19870.p',fact_196_old_Oprod_Oexhaust)).
% 22.73/4.68  thf(f1148,plain,(
% 22.73/4.68    ( ! [X2 : nat > prover_Mirabelle_U,X0 : nat > list_P796095576elle_U > $o,X1 : set_Pr619177522elle_U] : (((prover1282070756_SEval @ (produc1069574002le_U_o @ X1 @ X0) @ X2 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))) = $true) | ((prover1847600056is_env @ (produc1069574002le_U_o @ X1 @ X0) @ X2) != $true)) )),
% 22.73/4.68    inference(cnf_transformation,[status(thm)],[f910])).
% 22.73/4.68  thf(f910,plain,(
% 22.73/4.68    ! [X0 : nat > list_P796095576elle_U > $o,X1 : set_Pr619177522elle_U,X2 : nat > prover_Mirabelle_U] : (((prover1282070756_SEval @ (produc1069574002le_U_o @ X1 @ X0) @ X2 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))) = $true) | ((prover1847600056is_env @ (produc1069574002le_U_o @ X1 @ X0) @ X2) != $true))),
% 22.73/4.68    inference(ennf_transformation,[status(thm)],[f448])).
% 22.73/4.68  thf(f448,plain,(
% 22.73/4.68    ! [X0 : nat > list_P796095576elle_U > $o,X1 : set_Pr619177522elle_U,X2 : nat > prover_Mirabelle_U] : (((prover1847600056is_env @ (produc1069574002le_U_o @ X1 @ X0) @ X2) = $true) => ((prover1282070756_SEval @ (produc1069574002le_U_o @ X1 @ X0) @ X2 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))) = $true))),
% 22.73/4.68    inference(fool_elimination,[status(thm)],[f447])).
% 22.73/4.68  thf(f447,plain,(
% 22.73/4.68    ! [X0 : nat > list_P796095576elle_U > $o,X1 : set_Pr619177522elle_U,X2 : nat > prover_Mirabelle_U] : ((prover1847600056is_env @ (produc1069574002le_U_o @ X1 @ X0) @ X2) => (prover1282070756_SEval @ (produc1069574002le_U_o @ X1 @ X0) @ X2 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))),
% 22.73/4.68    inference(rectify,[status(thm)],[f359])).
% 22.73/4.68  thf(f359,axiom,(
% 22.73/4.68    ! [X86 : nat > list_P796095576elle_U > $o,X95 : set_Pr619177522elle_U,X96 : nat > prover_Mirabelle_U] : ((prover1847600056is_env @ (produc1069574002le_U_o @ X95 @ X86) @ X96) => (prover1282070756_SEval @ (produc1069574002le_U_o @ X95 @ X86) @ X96 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))),
% 22.73/4.68    file('/export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2THF_19870.p',conj_1)).
% 22.73/4.68  thf(f3070,plain,(
% 22.73/4.68    ~spl132_2),
% 22.73/4.68    inference(avatar_contradiction_clause,[status(thm)],[f3069])).
% 22.73/4.68  thf(f3069,plain,(
% 22.73/4.68    $false | ~spl132_2),
% 22.73/4.68    inference(trivial_inequality_removal,[status(thm)],[f3005])).
% 22.73/4.68  thf(f3005,plain,(
% 22.73/4.68    ($false = $true) | ~spl132_2),
% 22.73/4.68    inference(superposition,[status(thm)],[f2633,f1096])).
% 22.73/4.68  thf(f1096,plain,(
% 22.73/4.68    ((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ sK34) = $true)),
% 22.73/4.68    inference(cnf_transformation,[status(thm)],[f981])).
% 22.73/4.68  thf(f981,plain,(
% 22.73/4.68    ((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ sK34) = $true) & ((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ sK34 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)) != $true)),
% 22.73/4.68    inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f933,f980])).
% 22.73/4.68  thf(f980,plain,(
% 22.73/4.68    ? [X0 : nat > prover_Mirabelle_U] : (((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X0) = $true) & ((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)) != $true)) => (((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ sK34) = $true) & ((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ sK34 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)) != $true))),
% 22.73/4.68    introduced(definition,[],[choice_axiom])).
% 22.73/4.68  thf(f933,plain,(
% 22.73/4.68    ? [X0 : nat > prover_Mirabelle_U] : (((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X0) = $true) & ((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)) != $true))),
% 22.73/4.68    inference(ennf_transformation,[status(thm)],[f841])).
% 22.73/4.68  thf(f841,plain,(
% 22.73/4.68    ~! [X0 : nat > prover_Mirabelle_U] : (((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X0) != $true) | ((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)) = $true))),
% 22.73/4.68    inference(flattening,[status(thm)],[f827])).
% 22.73/4.68  thf(f827,plain,(
% 22.73/4.68    ~! [X0 : nat > prover_Mirabelle_U] : (~((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X0) = $true) | ((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)) = $true))),
% 22.73/4.68    inference(fool_elimination,[status(thm)],[f826])).
% 22.73/4.68  thf(f826,plain,(
% 22.73/4.68    ~! [X0 : nat > prover_Mirabelle_U] : (~(prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X0) | (prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))),
% 22.73/4.68    inference(rectify,[status(thm)],[f361])).
% 22.73/4.68  thf(f361,negated_conjecture,(
% 22.73/4.68    ~! [X97 : nat > prover_Mirabelle_U] : (~(prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X97) | (prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X97 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))),
% 22.73/4.68    inference(negated_conjecture,[status(cth)],[f360])).
% 22.73/4.68  thf(f360,conjecture,(
% 22.73/4.68    ! [X97 : nat > prover_Mirabelle_U] : (~(prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X97) | (prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X97 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))),
% 22.73/4.68    file('/export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2THF_19870.p',conj_2)).
% 22.73/4.68  thf(f2633,plain,(
% 22.73/4.68    ($false = (prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ sK34)) | ~spl132_2),
% 22.73/4.68    inference(trivial_inequality_removal,[status(thm)],[f2374])).
% 22.73/4.68  thf(f2374,plain,(
% 22.73/4.68    ($true != $true) | ($false = (prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ sK34)) | ~spl132_2),
% 22.73/4.68    inference(superposition,[status(thm)],[f1095,f1764])).
% 22.73/4.68  thf(f1764,plain,(
% 22.73/4.68    ( ! [X2 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : (((prover1282070756_SEval @ X2 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)) = $true) | ($false = (prover1847600056is_env @ X2 @ X1))) ) | ~spl132_2),
% 22.73/4.68    inference(avatar_component_clause,[status(thm)],[f1763])).
% 22.73/4.68  thf(f1763,definition,(
% 22.73/4.68    spl132_2 <=> ! [X2 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : (($false = (prover1847600056is_env @ X2 @ X1)) | ((prover1282070756_SEval @ X2 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)) = $true))),
% 22.73/4.68    introduced(definition,[new_symbols(naming,[spl132_2])],[avatar_definition])).
% 22.73/4.68  thf(f1095,plain,(
% 22.73/4.68    ((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ sK34 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)) != $true)),
% 22.73/4.68    inference(cnf_transformation,[status(thm)],[f981])).
% 22.73/4.68  thf(f1770,plain,(
% 22.73/4.68    spl132_2 | spl132_3),
% 22.73/4.68    inference(avatar_split_clause,[status(thm)],[f1683,f1767,f1763])).
% 22.73/4.68  thf(f1683,plain,(
% 22.73/4.68    ( ! [X2 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : (((prover1847600056is_env @ sK135 @ sK134) = $true) | ((prover1282070756_SEval @ X2 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)) = $true) | ($false = (prover1847600056is_env @ X2 @ X1))) )),
% 22.73/4.68    inference(binary_proxy_clausification,[status(thm)],[f1682])).
% 22.73/4.68  thf(f1682,plain,(
% 22.73/4.68    ( ! [X2 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : (((prover1847600056is_env @ sK135 @ sK134) = $true) | (((prover1847600056is_env @ X2 @ X1) => (prover1282070756_SEval @ X2 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true)) )),
% 22.73/4.68    inference(binary_proxy_clausification,[status(thm)],[f1680])).
% 22.73/4.68  thf(f1680,plain,(
% 22.73/4.68    ( ! [X2 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : (($false = ((prover1847600056is_env @ sK135 @ sK134) => (prover1282070756_SEval @ sK135 @ sK134 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))) | (((prover1847600056is_env @ X2 @ X1) => (prover1282070756_SEval @ X2 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true)) )),
% 22.73/4.68    inference(beta_eta_normalization,[status(thm)],[f1679])).
% 22.73/4.68  thf(f1679,plain,(
% 22.73/4.68    ( ! [X2 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : (($false = ((^[Y0 : produc227817602le_U_o]: ((prover1847600056is_env @ Y0 @ sK134) => (prover1282070756_SEval @ Y0 @ sK134 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))) @ sK135)) | (((prover1847600056is_env @ X2 @ X1) => (prover1282070756_SEval @ X2 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true)) )),
% 22.73/4.68    inference(sigma_clausification,[status(thm)],[f1678])).
% 22.73/4.68  thf(f1678,plain,(
% 22.73/4.68    ( ! [X2 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : (($false = (!! @ produc227817602le_U_o @ (^[Y0 : produc227817602le_U_o]: ((prover1847600056is_env @ Y0 @ sK134) => (prover1282070756_SEval @ Y0 @ sK134 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))))) | (((prover1847600056is_env @ X2 @ X1) => (prover1282070756_SEval @ X2 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true)) )),
% 22.73/4.68    inference(beta_eta_normalization,[status(thm)],[f1677])).
% 22.73/4.68  thf(f1677,plain,(
% 22.73/4.68    ( ! [X2 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : ((((prover1847600056is_env @ X2 @ X1) => (prover1282070756_SEval @ X2 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true) | ($false = ((^[Y0 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: ((prover1847600056is_env @ Y1 @ Y0) => (prover1282070756_SEval @ Y1 @ Y0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))))) @ sK134))) )),
% 22.73/4.68    inference(sigma_clausification,[status(thm)],[f1676])).
% 22.73/4.68  thf(f1676,plain,(
% 22.73/4.68    ( ! [X2 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : (((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: ((prover1847600056is_env @ Y1 @ Y0) => (prover1282070756_SEval @ Y1 @ Y0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))))))) != $true) | (((prover1847600056is_env @ X2 @ X1) => (prover1282070756_SEval @ X2 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true)) )),
% 22.73/4.68    inference(beta_eta_normalization,[status(thm)],[f1675])).
% 22.73/4.68  thf(f1675,plain,(
% 22.73/4.68    ( ! [X2 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : (((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: ((prover1847600056is_env @ Y1 @ Y0) => (prover1282070756_SEval @ Y1 @ Y0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))))))) != $true) | (((^[Y0 : produc227817602le_U_o]: ((prover1847600056is_env @ Y0 @ X1) => (prover1282070756_SEval @ Y0 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))) @ X2) = $true)) )),
% 22.73/4.68    inference(pi_clausification,[status(thm)],[f1674])).
% 22.73/4.68  thf(f1674,plain,(
% 22.73/4.68    ( ! [X1 : nat > prover_Mirabelle_U] : (($true = (!! @ produc227817602le_U_o @ (^[Y0 : produc227817602le_U_o]: ((prover1847600056is_env @ Y0 @ X1) => (prover1282070756_SEval @ Y0 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))))) | ((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: ((prover1847600056is_env @ Y1 @ Y0) => (prover1282070756_SEval @ Y1 @ Y0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))))))) != $true)) )),
% 22.73/4.68    inference(beta_eta_normalization,[status(thm)],[f1673])).
% 22.73/4.68  thf(f1673,plain,(
% 22.73/4.68    ( ! [X1 : nat > prover_Mirabelle_U] : (((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: ((prover1847600056is_env @ Y1 @ Y0) => (prover1282070756_SEval @ Y1 @ Y0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))))))) != $true) | (((^[Y0 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: ((prover1847600056is_env @ Y1 @ Y0) => (prover1282070756_SEval @ Y1 @ Y0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))))) @ X1) = $true)) )),
% 22.73/4.68    inference(pi_clausification,[status(thm)],[f1672])).
% 22.73/4.68  thf(f1672,plain,(
% 22.73/4.68    ((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: ((prover1847600056is_env @ Y1 @ Y0) => (prover1282070756_SEval @ Y1 @ Y0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))))))) = $true) | ((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: ((prover1847600056is_env @ Y1 @ Y0) => (prover1282070756_SEval @ Y1 @ Y0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))))))) != $true)),
% 22.73/4.68    inference(trivial_inequality_removal,[status(thm)],[f1500])).
% 22.73/4.68  thf(f1500,plain,(
% 22.73/4.68    ((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: ((prover1847600056is_env @ Y1 @ Y0) => (prover1282070756_SEval @ Y1 @ Y0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))))))) != $true) | ((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: ((prover1847600056is_env @ Y1 @ Y0) => (prover1282070756_SEval @ Y1 @ Y0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))))))) = $true) | ($true != $true)),
% 22.73/4.68    inference(superposition,[status(thm)],[f1164,f1199])).
% 22.73/4.68  thf(f1199,plain,(
% 22.73/4.68    ( ! [X2 : list_P512754263e_form,X0 : prover1687215943e_form,X1 : nat] : (((member_nat @ X1 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)))) = $true) | ($true != (!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: ((prover1847600056is_env @ Y1 @ Y0) => (prover1282070756_SEval @ Y1 @ Y0 @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X0 @ X1) @ nil_Pr1384483009e_form))))))))) | ((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: ((prover1847600056is_env @ Y1 @ Y0) => (prover1282070756_SEval @ Y1 @ Y0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2))))))) = $true)) )),
% 22.73/4.68    inference(beta_eta_normalization,[status(thm)],[f1190])).
% 22.73/4.68  thf(f1190,plain,(
% 22.73/4.68    ( ! [X2 : list_P512754263e_form,X0 : prover1687215943e_form,X1 : nat] : (((member_nat @ X1 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)))) = $true) | (((^[Y0 : list_P512754263e_form]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y2 : produc227817602le_U_o]: ((prover1847600056is_env @ Y2 @ Y1) => (prover1282070756_SEval @ Y2 @ Y1 @ Y0))))))) @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X0 @ X1) @ nil_Pr1384483009e_form))) != $true) | (((^[Y0 : list_P512754263e_form]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y2 : produc227817602le_U_o]: ((prover1847600056is_env @ Y2 @ Y1) => (prover1282070756_SEval @ Y2 @ Y1 @ Y0))))))) @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)) = $true)) )),
% 22.73/4.68    inference(definition_unfolding,[status(thm)],[f1159,f1069,f1069])).
% 22.73/4.68  thf(f1069,plain,(
% 22.73/4.68    (prover1539709396Svalid = (^[Y0 : list_P512754263e_form]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y2 : produc227817602le_U_o]: ((prover1847600056is_env @ Y2 @ Y1) => (prover1282070756_SEval @ Y2 @ Y1 @ Y0))))))))),
% 22.73/4.68    inference(cnf_transformation,[status(thm)],[f711])).
% 22.73/4.68  thf(f711,plain,(
% 22.73/4.68    (prover1539709396Svalid = (^[Y0 : list_P512754263e_form]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: (!! @ produc227817602le_U_o @ (^[Y2 : produc227817602le_U_o]: ((prover1847600056is_env @ Y2 @ Y1) => (prover1282070756_SEval @ Y2 @ Y1 @ Y0))))))))),
% 22.73/4.68    inference(fool_elimination,[status(thm)],[f710])).
% 22.73/4.68  thf(f710,plain,(
% 22.73/4.68    ((^[X0 : list_P512754263e_form] : (! [X1 : produc227817602le_U_o,X2 : nat > prover_Mirabelle_U] : ((prover1847600056is_env @ X1 @ X2) => (prover1282070756_SEval @ X1 @ X2 @ X0)))) = prover1539709396Svalid)),
% 22.73/4.68    inference(rectify,[status(thm)],[f24])).
% 22.73/4.68  thf(f24,axiom,(
% 22.73/4.68    ((^[X15 : list_P512754263e_form] : (! [X16 : produc227817602le_U_o,X17 : nat > prover_Mirabelle_U] : ((prover1847600056is_env @ X16 @ X17) => (prover1282070756_SEval @ X16 @ X17 @ X15)))) = prover1539709396Svalid)),
% 22.73/4.68    file('/export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2THF_19870.p',fact_23_Svalid__def)).
% 22.73/4.68  thf(f1159,plain,(
% 22.73/4.68    ( ! [X2 : list_P512754263e_form,X0 : prover1687215943e_form,X1 : nat] : (((prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)) = $true) | ((member_nat @ X1 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)))) = $true) | ((prover1539709396Svalid @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X0 @ X1) @ nil_Pr1384483009e_form))) != $true)) )),
% 22.73/4.68    inference(cnf_transformation,[status(thm)],[f880])).
% 22.73/4.68  thf(f880,plain,(
% 22.73/4.68    ! [X0 : prover1687215943e_form,X1 : nat,X2 : list_P512754263e_form] : (((prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)) = $true) | ((member_nat @ X1 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)))) = $true) | ((prover1539709396Svalid @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X0 @ X1) @ nil_Pr1384483009e_form))) != $true))),
% 22.73/4.68    inference(flattening,[status(thm)],[f879])).
% 22.73/4.68  thf(f879,plain,(
% 22.73/4.68    ! [X0 : prover1687215943e_form,X1 : nat,X2 : list_P512754263e_form] : ((((prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)) = $true) | ((prover1539709396Svalid @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X0 @ X1) @ nil_Pr1384483009e_form))) != $true)) | ((member_nat @ X1 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)))) = $true))),
% 22.73/4.68    inference(ennf_transformation,[status(thm)],[f865])).
% 22.73/4.68  thf(f865,plain,(
% 22.73/4.68    ! [X0 : prover1687215943e_form,X1 : nat,X2 : list_P512754263e_form] : (((member_nat @ X1 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)))) != $true) => (((prover1539709396Svalid @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X0 @ X1) @ nil_Pr1384483009e_form))) = $true) => ((prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)) = $true)))),
% 22.73/4.68    inference(flattening,[status(thm)],[f761])).
% 22.73/4.68  thf(f761,plain,(
% 22.73/4.68    ! [X0 : prover1687215943e_form,X1 : nat,X2 : list_P512754263e_form] : (~((member_nat @ X1 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)))) = $true) => (((prover1539709396Svalid @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X0 @ X1) @ nil_Pr1384483009e_form))) = $true) => ((prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)) = $true)))),
% 22.73/4.68    inference(fool_elimination,[status(thm)],[f760])).
% 22.73/4.68  thf(f760,plain,(
% 22.73/4.68    ! [X0 : prover1687215943e_form,X1 : nat,X2 : list_P512754263e_form] : (~(member_nat @ X1 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)))) => ((prover1539709396Svalid @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X0 @ X1) @ nil_Pr1384483009e_form))) => (prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2))))),
% 22.73/4.68    inference(rectify,[status(thm)],[f5])).
% 22.73/4.68  thf(f5,axiom,(
% 22.73/4.68    ! [X11 : prover1687215943e_form,X10 : nat,X4 : list_P512754263e_form] : (~(member_nat @ X10 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X11) @ X4)))) => ((prover1539709396Svalid @ (append1038020460e_form @ X4 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X11 @ X10) @ nil_Pr1384483009e_form))) => (prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X11) @ X4))))),
% 22.73/4.68    file('/export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2THF_19870.p',fact_4_sound__FAll)).
% 22.73/4.68  thf(f1164,plain,(
% 22.73/4.68    ((member_nat @ u @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))) != $true)),
% 22.73/4.68    inference(cnf_transformation,[status(thm)],[f840])).
% 22.73/4.68  thf(f840,plain,(
% 22.73/4.68    ((member_nat @ u @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))) != $true)),
% 22.73/4.68    inference(flattening,[status(thm)],[f492])).
% 22.73/4.68  thf(f492,plain,(
% 22.73/4.68    ~((member_nat @ u @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))) = $true)),
% 22.73/4.68    inference(fool_elimination,[status(thm)],[f491])).
% 22.73/4.68  thf(f491,plain,(
% 22.73/4.68    ~(member_nat @ u @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))))),
% 22.73/4.68    inference(rectify,[status(thm)],[f358])).
% 22.73/4.68  thf(f358,axiom,(
% 22.73/4.68    ~(member_nat @ u @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))))),
% 22.73/4.68    file('/export/starexec/sandbox2/tmp/tmp.BPFx4rpRT8/DTF2THF_19870.p',conj_0)).
% 22.73/4.68  thf(f1765,plain,(
% 22.73/4.68    spl132_1 | spl132_2),
% 22.73/4.68    inference(avatar_split_clause,[status(thm)],[f1684,f1763,f1759])).
% 22.73/4.68  thf(f1684,plain,(
% 22.73/4.68    ( ! [X2 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : (($false = (prover1847600056is_env @ X2 @ X1)) | ($false = (prover1282070756_SEval @ sK135 @ sK134 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))) | ((prover1282070756_SEval @ X2 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)) = $true)) )),
% 22.73/4.68    inference(binary_proxy_clausification,[status(thm)],[f1681])).
% 22.73/4.68  thf(f1681,plain,(
% 22.73/4.68    ( ! [X2 : produc227817602le_U_o,X1 : nat > prover_Mirabelle_U] : ((((prover1847600056is_env @ X2 @ X1) => (prover1282070756_SEval @ X2 @ X1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true) | ($false = (prover1282070756_SEval @ sK135 @ sK134 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))) )),
% 22.73/4.68    inference(binary_proxy_clausification,[status(thm)],[f1680])).
% 22.73/4.68  % SZS output end Proof for DTF2THF_19870
% 22.73/4.68  % (20076)------------------------------
% 22.73/4.68  % (20076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.73/4.68  % (20076)Termination reason: Refutation
% 22.73/4.68  
% 22.73/4.68  % (20076)Memory used [KB]: 13176
% 22.73/4.68  % (20076)Time elapsed: 1.547 s
% 22.73/4.68  % (20076)Instructions burned: 3747 (million)
% 22.73/4.68  % (20076)------------------------------
% 22.73/4.68  % (20076)------------------------------
% 22.73/4.68  % (19973)Success in time 3.127 s
%------------------------------------------------------------------------------