DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP136^1 : 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 : n029.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 08:55:50 AM UTC 2026

% Result   : Theorem 3.14s 1.64s
% Output   : Refutation 3.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   16 (  12 unt;   0 typ;   0 def)
%            Number of atoms       :   38 (  23 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   69 (   9   ~;   4   |;   1   &;  54   @)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Number of types       :   37 (  36 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  170 ( 167 usr;  15 con; 0-3 aty)
%            Number of variables   :    9 (   0   ^;   9   !;   0   ?;   9   :)

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

thf(type_def_7,type,
    set_nat: $tType ).

thf(type_def_8,type,
    paraco1605129243lle_tv: $tType ).

thf(type_def_9,type,
    set_Pa1764573435lle_tv: $tType ).

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

thf(type_def_11,type,
    set_Pr1986765409at_nat: $tType ).

thf(type_def_12,type,
    produc270694976lle_tv: $tType ).

thf(type_def_13,type,
    set_Pr13445366lle_tv: $tType ).

thf(type_def_14,type,
    produc194167194tv_nat: $tType ).

thf(type_def_15,type,
    set_Pr1725653840tv_nat: $tType ).

thf(type_def_16,type,
    produc1647334210lle_tv: $tType ).

thf(type_def_17,type,
    set_Pr2014382200lle_tv: $tType ).

thf(type_def_18,type,
    set_Pr2061825550lle_tv: $tType ).

thf(type_def_19,type,
    set_Pr2120184979lle_fm: $tType ).

thf(type_def_20,type,
    set_Pr1357842111at_nat: $tType ).

thf(type_def_21,type,
    set_Pr560526279lle_tv: $tType ).

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

thf(type_def_23,type,
    produc931990033lle_tv: $tType ).

thf(type_def_24,type,
    paraco1604210848lle_fm: $tType ).

thf(type_def_25,type,
    produc1852595672lle_tv: $tType ).

thf(type_def_26,type,
    produc696645085lle_fm: $tType ).

thf(type_def_27,type,
    produc1281043295at_nat: $tType ).

thf(type_def_28,type,
    produc1443694919lle_tv: $tType ).

thf(type_def_29,type,
    produc450659916lle_fm: $tType ).

thf(type_def_30,type,
    produc596913417at_nat: $tType ).

thf(type_def_31,type,
    produc1250255278lle_fm: $tType ).

thf(type_def_32,type,
    produc1720769084lle_tv: $tType ).

thf(type_def_33,type,
    set_Pr1490359111at_nat: $tType ).

thf(type_def_34,type,
    set_Pr292927124lle_tv: $tType ).

thf(type_def_35,type,
    set_Pr1943077434tv_nat: $tType ).

thf(type_def_36,type,
    set_Pr2012908090lle_tv: $tType ).

thf(type_def_37,type,
    set_Pr1723822845lle_tv: $tType ).

thf(type_def_38,type,
    set_Pr840833727at_nat: $tType ).

thf(type_def_39,type,
    set_Pr1019238018lle_fm: $tType ).

thf(type_def_40,type,
    set_Pr1475944804lle_fm: $tType ).

thf(type_def_41,type,
    set_Pr698334450lle_tv: $tType ).

thf(func_def_0,type,
    set_Pr1475944804lle_fm: $tType ).

thf(func_def_1,type,
    produc1250255278lle_fm: $tType ).

thf(func_def_2,type,
    set_Pr2012908090lle_tv: $tType ).

thf(func_def_3,type,
    set_Pr698334450lle_tv: $tType ).

thf(func_def_4,type,
    produc1720769084lle_tv: $tType ).

thf(func_def_5,type,
    set_Pr2061825550lle_tv: $tType ).

thf(func_def_6,type,
    set_Pr1943077434tv_nat: $tType ).

thf(func_def_7,type,
    set_Pr292927124lle_tv: $tType ).

thf(func_def_8,type,
    produc1852595672lle_tv: $tType ).

thf(func_def_9,type,
    set_Pr1723822845lle_tv: $tType ).

thf(func_def_10,type,
    set_Pr2120184979lle_fm: $tType ).

thf(func_def_11,type,
    produc1443694919lle_tv: $tType ).

thf(func_def_12,type,
    produc696645085lle_fm: $tType ).

thf(func_def_13,type,
    set_Pr1490359111at_nat: $tType ).

thf(func_def_14,type,
    set_Pr2014382200lle_tv: $tType ).

thf(func_def_15,type,
    set_Pr1019238018lle_fm: $tType ).

thf(func_def_16,type,
    set_Pr840833727at_nat: $tType ).

thf(func_def_17,type,
    set_Pr560526279lle_tv: $tType ).

thf(func_def_18,type,
    produc1647334210lle_tv: $tType ).

thf(func_def_19,type,
    produc450659916lle_fm: $tType ).

thf(func_def_20,type,
    set_Pr1357842111at_nat: $tType ).

thf(func_def_21,type,
    produc596913417at_nat: $tType ).

thf(func_def_22,type,
    produc931990033lle_tv: $tType ).

thf(func_def_23,type,
    set_Pr1725653840tv_nat: $tType ).

thf(func_def_24,type,
    set_Pr13445366lle_tv: $tType ).

thf(func_def_25,type,
    produc1281043295at_nat: $tType ).

thf(func_def_26,type,
    produc194167194tv_nat: $tType ).

thf(func_def_27,type,
    produc270694976lle_tv: $tType ).

thf(func_def_28,type,
    set_Pr1986765409at_nat: $tType ).

thf(func_def_29,type,
    set_Pa1764573435lle_tv: $tType ).

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

thf(func_def_31,type,
    paraco1605129243lle_tv: $tType ).

thf(func_def_32,type,
    paraco1604210848lle_fm: $tType ).

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

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

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

thf(func_def_36,type,
    inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).

thf(func_def_37,type,
    inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).

thf(func_def_38,type,
    inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).

thf(func_def_39,type,
    inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).

thf(func_def_40,type,
    inj_on26176689at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > $o ).

thf(func_def_41,type,
    inj_on1745913142lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > $o ).

thf(func_def_42,type,
    inj_on552895452tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > $o ).

thf(func_def_43,type,
    inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).

thf(func_def_44,type,
    the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).

thf(func_def_45,type,
    the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).

thf(func_def_46,type,
    if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ).

thf(func_def_47,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(func_def_48,type,
    ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).

thf(func_def_49,type,
    top_top_nat_o: nat > $o ).

thf(func_def_50,type,
    top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).

thf(func_def_51,type,
    top_to632227436_nat_o: product_prod_nat_nat > $o ).

thf(func_def_52,type,
    top_to1889334367e_tv_o: produc270694976lle_tv > $o ).

thf(func_def_53,type,
    top_to900819589_nat_o: produc194167194tv_nat > $o ).

thf(func_def_55,type,
    top_top_set_nat: set_nat ).

thf(func_def_56,type,
    top_to1057771083lle_tv: set_Pa1764573435lle_tv ).

thf(func_def_57,type,
    top_to138697918lle_tv: set_Pr2061825550lle_tv ).

thf(func_def_58,type,
    top_to775056195lle_fm: set_Pr2120184979lle_fm ).

thf(func_def_59,type,
    top_to1541413903at_nat: set_Pr1357842111at_nat ).

thf(func_def_60,type,
    top_to449985143lle_tv: set_Pr560526279lle_tv ).

thf(func_def_61,type,
    top_to1555900337at_nat: set_Pr1986765409at_nat ).

thf(func_def_62,type,
    top_to1411004326lle_tv: set_Pr13445366lle_tv ).

thf(func_def_63,type,
    top_to975729152tv_nat: set_Pr1725653840tv_nat ).

thf(func_def_64,type,
    top_to1871154984lle_tv: set_Pr2014382200lle_tv ).

thf(func_def_65,type,
    paraco761681009ge_int: ( nat > nat ) > ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ).

thf(func_def_66,type,
    paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).

thf(func_def_67,type,
    paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o ).

thf(func_def_68,type,
    paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).

thf(func_def_69,type,
    paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_70,type,
    paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_71,type,
    paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_72,type,
    paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_73,type,
    paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).

thf(func_def_74,type,
    paraco367965286_Truth: paraco1604210848lle_fm ).

thf(func_def_75,type,
    paraco1344940915le_Det: $o > paraco1605129243lle_tv ).

thf(func_def_76,type,
    paraco793048302_Indet: nat > paraco1605129243lle_tv ).

thf(func_def_77,type,
    paraco2051596139lle_tv: ( $o > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).

thf(func_def_78,type,
    paraco327635598_valid: paraco1604210848lle_fm > $o ).

thf(func_def_79,type,
    paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).

thf(func_def_80,type,
    produc1297923922lle_tv: ( list_char > paraco1605129243lle_tv ) > ( list_char > paraco1605129243lle_tv ) > produc1852595672lle_tv ).

thf(func_def_81,type,
    produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).

thf(func_def_82,type,
    produc780837143at_nat: ( nat > nat ) > ( nat > nat ) > produc1281043295at_nat ).

thf(func_def_83,type,
    produc1680557635lle_tv: ( nat > nat ) > paraco1605129243lle_tv > produc931990033lle_tv ).

thf(func_def_84,type,
    produc1943344577lle_tv: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc1443694919lle_tv ).

thf(func_def_85,type,
    produc1126104134lle_fm: paraco1604210848lle_fm > paraco1604210848lle_fm > produc450659916lle_fm ).

thf(func_def_86,type,
    produc1633679363at_nat: paraco1605129243lle_tv > ( nat > nat ) > produc596913417at_nat ).

thf(func_def_87,type,
    produc2058540732lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv ).

thf(func_def_88,type,
    produc407632608lle_fm: produc696645085lle_fm > produc696645085lle_fm > produc1250255278lle_fm ).

thf(func_def_89,type,
    produc2057188974lle_tv: produc931990033lle_tv > produc931990033lle_tv > produc1720769084lle_tv ).

thf(func_def_90,type,
    produc1942165868lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > produc696645085lle_fm > produc696645085lle_fm ).

thf(func_def_91,type,
    produc939316703lle_tv: ( ( nat > nat ) > nat > nat ) > produc931990033lle_tv > produc931990033lle_tv ).

thf(func_def_92,type,
    produc1807466521lle_tv: ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).

thf(func_def_93,type,
    produc109093078at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).

thf(func_def_94,type,
    produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv ).

thf(func_def_95,type,
    produc275353523e_fm_o: ( produc696645085lle_fm > $o ) > ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o ).

thf(func_def_96,type,
    produc752649287e_tv_o: ( produc931990033lle_tv > $o ) > ( nat > nat ) > paraco1605129243lle_tv > $o ).

thf(func_def_97,type,
    produc1900967599lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).

thf(func_def_98,type,
    produc1566550641lle_tv: ( ( list_char > paraco1605129243lle_tv ) > nat > nat ) > ( paraco1604210848lle_fm > paraco1605129243lle_tv ) > produc696645085lle_fm > produc931990033lle_tv ).

thf(func_def_99,type,
    produc951033137lle_fm: ( ( nat > nat ) > list_char > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1604210848lle_fm ) > produc931990033lle_tv > produc696645085lle_fm ).

thf(func_def_100,type,
    produc532909085lle_tv: ( ( nat > nat ) > nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).

thf(func_def_101,type,
    produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_102,type,
    produc313957681lle_tv: ( nat > nat ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc270694976lle_tv ).

thf(func_def_103,type,
    produc1685803475tv_nat: ( nat > nat ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > product_prod_nat_nat ).

thf(func_def_104,type,
    produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).

thf(func_def_105,type,
    produc1250721397at_nat: ( nat > paraco1605129243lle_tv ) > ( nat > nat ) > product_prod_nat_nat > produc194167194tv_nat ).

thf(func_def_106,type,
    produc210389789lle_tv: ( nat > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc1647334210lle_tv ).

thf(func_def_107,type,
    produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).

thf(func_def_108,type,
    produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).

thf(func_def_109,type,
    produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).

thf(func_def_110,type,
    produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).

thf(func_def_111,type,
    produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).

thf(func_def_112,type,
    produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).

thf(func_def_113,type,
    produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_114,type,
    produc1636169559lle_tv: produc931990033lle_tv > nat > nat ).

thf(func_def_115,type,
    produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm ).

thf(func_def_116,type,
    produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv ).

thf(func_def_117,type,
    produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm ).

thf(func_def_118,type,
    produc547496597lle_tv: produc931990033lle_tv > paraco1605129243lle_tv ).

thf(func_def_119,type,
    produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv ).

thf(func_def_120,type,
    produc500618325at_nat: produc596913417at_nat > nat > nat ).

thf(func_def_121,type,
    produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv ).

thf(func_def_122,type,
    produc225513635lle_tv: produc931990033lle_tv > produc596913417at_nat ).

thf(func_def_123,type,
    produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm ).

thf(func_def_124,type,
    produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv ).

thf(func_def_125,type,
    inv_image_nat_nat: set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).

thf(func_def_126,type,
    inv_im1292588663lle_tv: set_Pr1986765409at_nat > ( paraco1605129243lle_tv > nat ) > set_Pr2014382200lle_tv ).

thf(func_def_127,type,
    inv_im516950809tv_nat: set_Pr2014382200lle_tv > ( nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat ).

thf(func_def_128,type,
    inv_im719552961lle_tv: set_Pr2014382200lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pr2014382200lle_tv ).

thf(func_def_129,type,
    total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).

thf(func_def_130,type,
    total_1781621663lle_tv: set_Pa1764573435lle_tv > set_Pr2014382200lle_tv > $o ).

thf(func_def_131,type,
    total_1775715973at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).

thf(func_def_132,type,
    total_517371324lle_tv: set_Pr13445366lle_tv > set_Pr292927124lle_tv > $o ).

thf(func_def_133,type,
    total_440843542tv_nat: set_Pr1725653840tv_nat > set_Pr1943077434tv_nat > $o ).

thf(func_def_134,type,
    total_92239038lle_tv: set_Pr2014382200lle_tv > set_Pr2012908090lle_tv > $o ).

thf(func_def_135,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(func_def_136,type,
    collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).

thf(func_def_137,type,
    collec1102043437lle_tv: ( produc1852595672lle_tv > $o ) > set_Pr2061825550lle_tv ).

thf(func_def_138,type,
    collec835549234lle_fm: ( produc696645085lle_fm > $o ) > set_Pr2120184979lle_fm ).

thf(func_def_139,type,
    collec791369802at_nat: ( produc1281043295at_nat > $o ) > set_Pr1357842111at_nat ).

thf(func_def_140,type,
    collec1624074086lle_tv: ( produc931990033lle_tv > $o ) > set_Pr560526279lle_tv ).

thf(func_def_141,type,
    collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).

thf(func_def_142,type,
    collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).

thf(func_def_143,type,
    collec848462447tv_nat: ( produc194167194tv_nat > $o ) > set_Pr1725653840tv_nat ).

thf(func_def_144,type,
    image_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_145,type,
    image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).

thf(func_def_146,type,
    image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).

thf(func_def_147,type,
    image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).

thf(func_def_148,type,
    image_807538418lle_fm: ( produc696645085lle_fm > produc696645085lle_fm ) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm ).

thf(func_def_149,type,
    image_1154804148lle_tv: ( produc696645085lle_fm > produc931990033lle_tv ) > set_Pr2120184979lle_fm > set_Pr560526279lle_tv ).

thf(func_def_150,type,
    image_924970994lle_tv: ( produc696645085lle_fm > produc1443694919lle_tv ) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv ).

thf(func_def_151,type,
    image_1585092542lle_fm: ( produc931990033lle_tv > produc696645085lle_fm ) > set_Pr560526279lle_tv > set_Pr2120184979lle_fm ).

thf(func_def_152,type,
    image_1751508608lle_tv: ( produc931990033lle_tv > produc931990033lle_tv ) > set_Pr560526279lle_tv > set_Pr560526279lle_tv ).

thf(func_def_153,type,
    image_1724396928at_nat: ( produc931990033lle_tv > produc596913417at_nat ) > set_Pr560526279lle_tv > set_Pr840833727at_nat ).

thf(func_def_154,type,
    image_815163717at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).

thf(func_def_155,type,
    image_1674248956lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > set_Pr13445366lle_tv ).

thf(func_def_156,type,
    image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).

thf(func_def_157,type,
    image_1507992062lle_tv: ( product_prod_nat_nat > produc1647334210lle_tv ) > set_Pr1986765409at_nat > set_Pr2014382200lle_tv ).

thf(func_def_158,type,
    image_1787705850at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > set_Pr1986765409at_nat ).

thf(func_def_159,type,
    image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).

thf(func_def_160,type,
    image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).

thf(func_def_161,type,
    image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).

thf(func_def_162,type,
    image_326034184lle_fm: ( produc1443694919lle_tv > produc696645085lle_fm ) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm ).

thf(func_def_163,type,
    image_769496456lle_tv: ( produc596913417at_nat > produc931990033lle_tv ) > set_Pr840833727at_nat > set_Pr560526279lle_tv ).

thf(func_def_164,type,
    image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).

thf(func_def_165,type,
    image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).

thf(func_def_166,type,
    image_1221801032lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv ).

thf(func_def_167,type,
    accp_P2085826120lle_tv: ( produc931990033lle_tv > produc931990033lle_tv > $o ) > produc931990033lle_tv > $o ).

thf(func_def_168,type,
    lex_pr2001015487lle_fm: set_Pr2061825550lle_tv > set_Pr1019238018lle_fm > set_Pr1475944804lle_fm ).

thf(func_def_169,type,
    lex_pr1093414955lle_tv: set_Pr1357842111at_nat > set_Pr2014382200lle_tv > set_Pr698334450lle_tv ).

thf(func_def_170,type,
    lex_prod_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1490359111at_nat ).

thf(func_def_171,type,
    lex_pr413684186lle_tv: set_Pr1986765409at_nat > set_Pr2014382200lle_tv > set_Pr292927124lle_tv ).

thf(func_def_172,type,
    lex_pr1785529980tv_nat: set_Pr2014382200lle_tv > set_Pr1986765409at_nat > set_Pr1943077434tv_nat ).

thf(func_def_173,type,
    lex_pr567812260lle_tv: set_Pr2014382200lle_tv > set_Pr2014382200lle_tv > set_Pr2012908090lle_tv ).

thf(func_def_174,type,
    wf_nat: set_Pr1986765409at_nat > $o ).

thf(func_def_175,type,
    wf_Par1378404612lle_tv: set_Pr2014382200lle_tv > $o ).

thf(func_def_176,type,
    same_f1581085506lle_fm: ( ( list_char > paraco1605129243lle_tv ) > $o ) > ( ( list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm ) > set_Pr1475944804lle_fm ).

thf(func_def_177,type,
    same_f1138187694lle_tv: ( ( nat > nat ) > $o ) > ( ( nat > nat ) > set_Pr2014382200lle_tv ) > set_Pr698334450lle_tv ).

thf(func_def_178,type,
    member_nat: nat > set_nat > $o ).

thf(func_def_179,type,
    member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).

thf(func_def_180,type,
    member146333935lle_tv: produc1852595672lle_tv > set_Pr2061825550lle_tv > $o ).

thf(func_def_181,type,
    member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o ).

thf(func_def_182,type,
    member112824072at_nat: produc1281043295at_nat > set_Pr1357842111at_nat > $o ).

thf(func_def_183,type,
    member1569366824lle_tv: produc931990033lle_tv > set_Pr560526279lle_tv > $o ).

thf(func_def_184,type,
    member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).

thf(func_def_185,type,
    member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).

thf(func_def_186,type,
    member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o ).

thf(func_def_187,type,
    member334644067lle_fm: produc450659916lle_fm > set_Pr1019238018lle_fm > $o ).

thf(func_def_188,type,
    member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o ).

thf(func_def_189,type,
    member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).

thf(func_def_190,type,
    member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).

thf(func_def_191,type,
    member1592865093lle_fm: produc1250255278lle_fm > set_Pr1475944804lle_fm > $o ).

thf(func_def_192,type,
    member1339857875lle_tv: produc1720769084lle_tv > set_Pr698334450lle_tv > $o ).

thf(func_def_193,type,
    f: nat > nat ).

thf(func_def_194,type,
    i: list_char > paraco1605129243lle_tv ).

thf(func_def_195,type,
    p1: paraco1604210848lle_fm ).

thf(func_def_196,type,
    p2: paraco1604210848lle_fm ).

thf(func_def_208,type,
    sK0: ( nat > nat ) > nat ).

thf(func_def_209,type,
    sK1: ( nat > nat ) > nat ).

thf(func_def_210,type,
    sK2: ( nat > nat ) > nat ).

thf(func_def_211,type,
    sK3: ( nat > nat ) > nat ).

thf(func_def_212,type,
    sK4: paraco1605129243lle_tv > paraco1605129243lle_tv > $o ).

thf(func_def_213,type,
    sK5: paraco1605129243lle_tv > ( nat > nat ) > paraco1605129243lle_tv > nat ).

thf(func_def_215,type,
    ph7: 
      !>[X0: $tType] : X0 ).

thf(f931,plain,
    $false,
    inference(trivial_inequality_removal,[status(thm)],[f930]) ).

thf(f930,plain,
    $false = $true,
    inference(equality_resolution,[status(thm)],[f927]) ).

thf(f927,plain,
    ! [X0: $o] :
      ( ( ( paraco1344940915le_Det @ X0 )
       != ( paraco1344940915le_Det @ $false ) )
      | ( $true = X0 ) ),
    inference(superposition,[status(thm)],[f894,f924]) ).

thf(f924,plain,
    ( ( paraco1344940915le_Det @ $true )
    = ( paraco1344940915le_Det @ $false ) ),
    inference(forward_demodulation,[status(thm)],[f895,f892]) ).

thf(f892,plain,
    ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
    = ( paraco1344940915le_Det @ $false ) ),
    inference(cnf_transformation,[status(thm)],[f714]) ).

thf(f714,plain,
    ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
    = ( paraco1344940915le_Det @ $false ) ),
    inference(fool_elimination,[status(thm)],[f7]) ).

thf(f7,axiom,
    ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
    = ( paraco1344940915le_Det @ $false ) ),
    file('/export/starexec/sandbox2/tmp/tmp.b6Vcvump8L/DTF2THF_12469.p',fact_6_b) ).

thf(f895,plain,
    ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
    = ( paraco1344940915le_Det @ $true ) ),
    inference(cnf_transformation,[status(thm)],[f851]) ).

thf(f851,plain,
    ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
    = ( paraco1344940915le_Det @ $true ) ),
    inference(flattening,[status(thm)],[f387]) ).

thf(f387,plain,
    ~ ( ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
       != ( paraco1344940915le_Det @ $true ) ) ),
    inference(fool_elimination,[status(thm)],[f359]) ).

thf(f359,negated_conjecture,
    ~ ( ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
       != ( paraco1344940915le_Det @ $true ) ) ),
    inference(negated_conjecture,[status(cth)],[f358]) ).

thf(f358,conjecture,
    ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
   != ( paraco1344940915le_Det @ $true ) ),
    file('/export/starexec/sandbox2/tmp/tmp.b6Vcvump8L/DTF2THF_12469.p',conj_0) ).

thf(f894,plain,
    ! [X0: $o,X1: $o] :
      ( ( ( paraco1344940915le_Det @ X0 )
       != ( paraco1344940915le_Det @ X1 ) )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[status(thm)],[f868]) ).

thf(f868,plain,
    ! [X0: $o,X1: $o] :
      ( ( ( X0 = X1 )
        | ( ( paraco1344940915le_Det @ X0 )
         != ( paraco1344940915le_Det @ X1 ) ) )
      & ( ( ( paraco1344940915le_Det @ X0 )
          = ( paraco1344940915le_Det @ X1 ) )
        | ( X0 != X1 ) ) ),
    inference(nnf_transformation,[status(thm)],[f407]) ).

thf(f407,plain,
    ! [X0: $o,X1: $o] :
      ( ( X0 = X1 )
    <=> ( ( paraco1344940915le_Det @ X0 )
        = ( paraco1344940915le_Det @ X1 ) ) ),
    inference(fool_elimination,[status(thm)],[f9]) ).

thf(f9,axiom,
    ! [X0: $o,X1: $o] :
      ( ( ( paraco1344940915le_Det @ X0 )
        = ( paraco1344940915le_Det @ X1 ) )
      = ( X0 = X1 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.b6Vcvump8L/DTF2THF_12469.p',fact_8_tv_Oinject_I1_J) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP136^1 : TPTP v9.2.1. Released v7.5.0.
% 0.10/0.13  % Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.33  % Computer : n029.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Tue Feb 24 08:35:59 EST 2026
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  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     : ITP136^1 : TPTP v9.2.1. Released v7.5.0.
% 0.16/0.42  % Domain   : Interactive Theorem Proving
% 0.16/0.42  % Problem  : Sledgehammer Paraconsistency problem prob_1104__3276536_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    : Paraconsistency/prob_1104__3276536_1 [Des21]
% 0.16/0.42  
% 0.16/0.42  % Status   : Theorem
% 0.16/0.42  % Rating   : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.18 v7.5.0
% 0.16/0.42  % Syntax   : Number of formulae    :  555 ( 175 unt; 197 typ;   0 def)
% 0.16/0.42  %            Number of atoms       :  955 ( 534 equ;   0 cnn)
% 0.16/0.42  %            Maximal formula atoms :   16 (   2 avg)
% 0.16/0.42  %            Number of connectives : 2679 ( 116   ~;   4   |;  29   &;2112   @)
% 0.16/0.42  %                                         (   0 <=>; 418  =>;   0  <=;   0 <~>)
% 0.16/0.42  %            Maximal formula depth :   16 (   6 avg)
% 0.16/0.42  %            Number of types       :   37 (  36 usr)
% 0.16/0.42  %            Number of type conns  :  797 ( 797   >;   0   *;   0   +;   0  <<)
% 0.16/0.42  %            Number of symbols     :  164 ( 161 usr;  16 con; 0-3 aty)
% 0.16/0.42  %            Number of variables   :  986 (  25   ^; 934   !;  27   ?; 986   :)
% 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 15:40:22.190
% 0.16/0.42  %------------------------------------------------------------------------------
% 0.16/0.42  % Could-be-implicit typings (36)
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J_J,type,
% 0.16/0.42      set_Pr1475944804lle_fm: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 0.16/0.42      produc1250255278lle_fm: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 0.16/0.42      set_Pr2012908090lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 0.16/0.42      set_Pr698334450lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      produc1720769084lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 0.16/0.42      set_Pr2061825550lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J_J,type,
% 0.16/0.42      set_Pr1943077434tv_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 0.16/0.42      set_Pr292927124lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      produc1852595672lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 0.16/0.42      set_Pr1723822845lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 0.16/0.42      set_Pr2120184979lle_fm: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      produc1443694919lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 0.16/0.42      produc696645085lle_fm: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.16/0.42      set_Pr1490359111at_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      set_Pr2014382200lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 0.16/0.42      set_Pr1019238018lle_fm: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.16/0.42      set_Pr840833727at_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      set_Pr560526279lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      produc1647334210lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 0.16/0.42      produc450659916lle_fm: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.16/0.42      set_Pr1357842111at_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.16/0.42      produc596913417at_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      produc931990033lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J,type,
% 0.16/0.42      set_Pr1725653840tv_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      set_Pr13445366lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.16/0.42      produc1281043295at_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.16/0.42      produc194167194tv_nat: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      produc270694976lle_tv: $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__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      set_Pa1764573435lle_tv: $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__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      paraco1605129243lle_tv: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.16/0.42      paraco1604210848lle_fm: $tType ).
% 0.16/0.42  
% 0.16/0.42  thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
% 0.16/0.42      list_char: $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 (161)
% 0.16/0.42  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.16/0.42      inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      inj_on26176689at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      inj_on1745913142lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.16/0.42      inj_on552895452tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Fun_Othe__inv__into_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Fun_Othe__inv__into_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.16/0.42      ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.16/0.42      top_top_nat_o: nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_Eo_J,type,
% 0.16/0.42      top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.16/0.42      top_to632227436_nat_o: product_prod_nat_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_Eo_J,type,
% 0.16/0.42      top_to1889334367e_tv_o: produc270694976lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.16/0.42      top_to900819589_nat_o: produc194167194tv_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001_Eo,type,
% 0.16/0.42      top_top_o: $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.16/0.42      top_top_set_nat: set_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 0.16/0.42      top_to138697918lle_tv: set_Pr2061825550lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 0.16/0.42      top_to775056195lle_fm: set_Pr2120184979lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.16/0.42      top_to1541413903at_nat: set_Pr1357842111at_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      top_to449985143lle_tv: set_Pr560526279lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.16/0.42      top_to1555900337at_nat: set_Pr1986765409at_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      top_to1411004326lle_tv: set_Pr13445366lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J,type,
% 0.16/0.42      top_to975729152tv_nat: set_Pr1725653840tv_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      top_to1871154984lle_tv: set_Pr2014382200lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__int,type,
% 0.16/0.42      paraco761681009ge_int: ( nat > nat ) > ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv,type,
% 0.16/0.42      paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv__rel,type,
% 0.16/0.42      paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Oeval,type,
% 0.16/0.42      paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OCon_H,type,
% 0.16/0.42      paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql,type,
% 0.16/0.42      paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql_H,type,
% 0.16/0.42      paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_ONeg_H,type,
% 0.16/0.42      paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OPro,type,
% 0.16/0.42      paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OTruth,type,
% 0.16/0.42      paraco367965286_Truth: paraco1604210848lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_ODet,type,
% 0.16/0.42      paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_OIndet,type,
% 0.16/0.42      paraco793048302_Indet: nat > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_Ocase__tv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      paraco2051596139lle_tv: ( $o > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid,type,
% 0.16/0.42      paraco327635598_valid: paraco1604210848lle_fm > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid__in,type,
% 0.16/0.42      paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      produc1297923922lle_tv: ( list_char > paraco1605129243lle_tv ) > ( list_char > paraco1605129243lle_tv ) > produc1852595672lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.16/0.42      produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      produc780837143at_nat: ( nat > nat ) > ( nat > nat ) > produc1281043295at_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc1680557635lle_tv: ( nat > nat ) > paraco1605129243lle_tv > produc931990033lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      produc1943344577lle_tv: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc1443694919lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.16/0.42      produc1126104134lle_fm: paraco1604210848lle_fm > paraco1604210848lle_fm > produc450659916lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      produc1633679363at_nat: paraco1605129243lle_tv > ( nat > nat ) > produc596913417at_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc2058540732lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 0.16/0.42      produc407632608lle_fm: produc696645085lle_fm > produc696645085lle_fm > produc1250255278lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      produc2057188974lle_tv: produc931990033lle_tv > produc931990033lle_tv > produc1720769084lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oapfst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.16/0.42      produc1942165868lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > produc696645085lle_fm > produc696645085lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oapfst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc939316703lle_tv: ( ( nat > nat ) > nat > nat ) > produc931990033lle_tv > produc931990033lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oapsnd_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      produc1807466521lle_tv: ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oapsnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      produc109093078at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Obool_Ocase__bool_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Ocurry_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_Eo,type,
% 0.16/0.42      produc275353523e_fm_o: ( produc696645085lle_fm > $o ) > ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Ocurry_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_Eo,type,
% 0.16/0.42      produc752649287e_tv_o: ( produc931990033lle_tv > $o ) > ( nat > nat ) > paraco1605129243lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.16/0.42      produc1900967599lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc1566550641lle_tv: ( ( list_char > paraco1605129243lle_tv ) > nat > nat ) > ( paraco1604210848lle_fm > paraco1605129243lle_tv ) > produc696645085lle_fm > produc931990033lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.16/0.42      produc951033137lle_fm: ( ( nat > nat ) > list_char > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1604210848lle_fm ) > produc931990033lle_tv > produc696645085lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc532909085lle_tv: ( ( nat > nat ) > nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc313957681lle_tv: ( nat > nat ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc270694976lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.16/0.42      produc1685803475tv_nat: ( nat > nat ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > product_prod_nat_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      produc1250721397at_nat: ( nat > paraco1605129243lle_tv ) > ( nat > nat ) > product_prod_nat_nat > produc194167194tv_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc210389789lle_tv: ( nat > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc1647334210lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.16/0.42      produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.16/0.42      produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc1636169559lle_tv: produc931990033lle_tv > nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Ofst_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Ofst_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.16/0.42      produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc547496597lle_tv: produc931990033lle_tv > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Osnd_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Osnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      produc500618325at_nat: produc596913417at_nat > nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.16/0.42      produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      produc225513635lle_tv: produc931990033lle_tv > produc596913417at_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Oswap_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Product__Type_Oprod_Oswap_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      inv_image_nat_nat: set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      inv_im1292588663lle_tv: set_Pr1986765409at_nat > ( paraco1605129243lle_tv > nat ) > set_Pr2014382200lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Relation_Oinv__image_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.16/0.42      inv_im516950809tv_nat: set_Pr2014382200lle_tv > ( nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Relation_Oinv__image_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      inv_im719552961lle_tv: set_Pr2014382200lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pr2014382200lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Relation_Ototal__on_001t__Nat__Onat,type,
% 0.16/0.42      total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Relation_Ototal__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      total_1781621663lle_tv: set_Pa1764573435lle_tv > set_Pr2014382200lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      total_1775715973at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      total_517371324lle_tv: set_Pr13445366lle_tv > set_Pr292927124lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.16/0.42      total_440843542tv_nat: set_Pr1725653840tv_nat > set_Pr1943077434tv_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      total_92239038lle_tv: set_Pr2014382200lle_tv > set_Pr2012908090lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
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% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_OCollect_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      collec1102043437lle_tv: ( produc1852595672lle_tv > $o ) > set_Pr2061825550lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 0.16/0.42      collec835549234lle_fm: ( produc696645085lle_fm > $o ) > set_Pr2120184979lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      collec1624074086lle_tv: ( produc931990033lle_tv > $o ) > set_Pr560526279lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
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% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.16/0.42      image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 0.16/0.42      image_807538418lle_fm: ( produc696645085lle_fm > produc696645085lle_fm ) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      image_1154804148lle_tv: ( produc696645085lle_fm > produc931990033lle_tv ) > set_Pr2120184979lle_fm > set_Pr560526279lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      image_924970994lle_tv: ( produc696645085lle_fm > produc1443694919lle_tv ) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 0.16/0.42      image_1585092542lle_fm: ( produc931990033lle_tv > produc696645085lle_fm ) > set_Pr560526279lle_tv > set_Pr2120184979lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
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% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 0.16/0.42  
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% 0.16/0.42      image_815163717at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      image_1674248956lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > set_Pr13445366lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.16/0.42      image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      image_1507992062lle_tv: ( product_prod_nat_nat > produc1647334210lle_tv ) > set_Pr1986765409at_nat > set_Pr2014382200lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      image_1787705850at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > set_Pr1986765409at_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.16/0.42      image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 0.16/0.42      image_326034184lle_fm: ( produc1443694919lle_tv > produc696645085lle_fm ) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm ).
% 0.16/0.42  
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% 0.16/0.42      image_769496456lle_tv: ( produc596913417at_nat > produc931990033lle_tv ) > set_Pr840833727at_nat > set_Pr560526279lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.16/0.42      image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
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% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      accp_P2085826120lle_tv: ( produc931990033lle_tv > produc931990033lle_tv > $o ) > produc931990033lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Wellfounded_Olex__prod_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.16/0.42      lex_pr2001015487lle_fm: set_Pr2061825550lle_tv > set_Pr1019238018lle_fm > set_Pr1475944804lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Wellfounded_Olex__prod_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      lex_pr1093414955lle_tv: set_Pr1357842111at_nat > set_Pr2014382200lle_tv > set_Pr698334450lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.16/0.42      lex_prod_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1490359111at_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.16/0.42      lex_pr413684186lle_tv: set_Pr1986765409at_nat > set_Pr2014382200lle_tv > set_Pr292927124lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Wellfounded_Olex__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.16/0.42      lex_pr1785529980tv_nat: set_Pr2014382200lle_tv > set_Pr1986765409at_nat > set_Pr1943077434tv_nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Wellfounded_Olex__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 0.16/0.42      wf_nat: set_Pr1986765409at_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Wellfounded_Owf_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Wfrec_Osame__fst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
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% 0.16/0.42  
% 0.16/0.42  thf(sy_c_Wfrec_Osame__fst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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% 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  
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% 0.16/0.42  
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% 0.16/0.42  
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% 0.16/0.42  
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% 0.16/0.42  
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% 0.16/0.42  
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% 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__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 0.16/0.42      member334644067lle_fm: produc450659916lle_fm > set_Pr1019238018lle_fm > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.16/0.42      member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.16/0.42      member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.16/0.42      member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 0.16/0.42      member1592865093lle_fm: produc1250255278lle_fm > set_Pr1475944804lle_fm > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.16/0.42      member1339857875lle_tv: produc1720769084lle_tv > set_Pr698334450lle_tv > $o ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_v_f,type,
% 0.16/0.42      f: nat > nat ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_v_i,type,
% 0.16/0.42      i: list_char > paraco1605129243lle_tv ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_v_p1____,type,
% 0.16/0.42      p1: paraco1604210848lle_fm ).
% 0.16/0.42  
% 0.16/0.42  thf(sy_v_p2____,type,
% 0.16/0.42      p2: paraco1604210848lle_fm ).
% 0.16/0.42  
% 0.16/0.42  % Relevant facts (354)
% 0.16/0.42  thf(fact_0_a_H_H_H,axiom,
% 0.16/0.42      ( ( paraco1325918602e_eval @ i @ p2 )
% 0.16/0.42     != ( paraco1344940915le_Det @ $true ) ) ).
% 0.16/0.42  
% 0.16/0.42  % a'''
% 0.16/0.42  thf(fact_1_a_H_H,axiom,
% 0.16/0.42      ( ( paraco1325918602e_eval @ i @ p1 )
% 0.16/0.42     != ( paraco1344940915le_Det @ $true ) ) ).
% 0.16/0.42  
% 0.16/0.42  % a''
% 0.16/0.42  thf(fact_2_a_H_H_H_H,axiom,
% 0.16/0.42      ( ( paraco1325918602e_eval @ i @ p1 )
% 0.16/0.42     != ( paraco1344940915le_Det @ $false ) ) ).
% 0.16/0.42  
% 0.16/0.42  % a''''
% 0.16/0.42  thf(fact_3_b_H_H,axiom,
% 0.16/0.42      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 0.16/0.42     != ( paraco1344940915le_Det @ $true ) ) ).
% 0.16/0.42  
% 0.16/0.42  % b''
% 0.16/0.42  thf(fact_4_a,axiom,
% 0.16/0.42      ( ( paraco1325918602e_eval @ i @ p2 )
% 0.16/0.42      = ( paraco1344940915le_Det @ $false ) ) ).
% 0.16/0.42  
% 0.16/0.42  % a
% 0.16/0.42  thf(fact_5_a_H,axiom,
% 0.16/0.42      ( ( paraco1325918602e_eval @ i @ p1 )
% 0.16/0.42     != ( paraco1325918602e_eval @ i @ p2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % a'
% 0.16/0.42  thf(fact_6_b,axiom,
% 0.16/0.42      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
% 0.16/0.42      = ( paraco1344940915le_Det @ $false ) ) ).
% 0.16/0.42  
% 0.16/0.42  % b
% 0.16/0.42  thf(fact_7_b_H,axiom,
% 0.16/0.42      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 0.16/0.42     != ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % b'
% 0.16/0.42  thf(fact_8_tv_Oinject_I1_J,axiom,
% 0.16/0.42      ! [X1: $o,Y1: $o] :
% 0.16/0.42        ( ( ( paraco1344940915le_Det @ X1 )
% 0.16/0.42          = ( paraco1344940915le_Det @ Y1 ) )
% 0.16/0.42        = ( X1 = Y1 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % tv.inject(1)
% 0.16/0.42  thf(fact_9_ih2,axiom,
% 0.16/0.42      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
% 0.16/0.42      = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % ih2
% 0.16/0.42  thf(fact_10_ih1,axiom,
% 0.16/0.42      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 0.16/0.42      = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p1 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % ih1
% 0.16/0.42  thf(fact_11__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_AFalse_092_060close_062,axiom,
% 0.16/0.42      ( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
% 0.16/0.42      = ( paraco1344940915le_Det @ $false ) ) ).
% 0.16/0.42  
% 0.16/0.42  % \<open>change_tv f (eval i p2) = Det False\<close>
% 0.16/0.42  thf(fact_12_valid__def,axiom,
% 0.16/0.42      ( paraco327635598_valid
% 0.16/0.42      = ( ^ [P: paraco1604210848lle_fm] :
% 0.16/0.42          ! [I: list_char > paraco1605129243lle_tv] :
% 0.16/0.42            ( ( paraco1325918602e_eval @ I @ P )
% 0.16/0.42            = ( paraco1344940915le_Det @ $true ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % valid_def
% 0.16/0.42  thf(fact_13_yes,axiom,
% 0.16/0.42      ( ( paraco1325918602e_eval @ i @ ( paraco1745535428le_Eql @ p1 @ p2 ) )
% 0.16/0.42      = ( paraco1325918602e_eval @ i @ ( paraco445776468le_Neg @ p1 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % yes
% 0.16/0.42  thf(fact_14_eval_Osimps_I2_J,axiom,
% 0.16/0.42      ! [I2: list_char > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( paraco1325918602e_eval @ I2 @ paraco367965286_Truth )
% 0.16/0.42        = ( paraco1344940915le_Det @ $true ) ) ).
% 0.16/0.42  
% 0.16/0.42  % eval.simps(2)
% 0.16/0.42  thf(fact_15_eval_Osimps_I5_J,axiom,
% 0.16/0.42      ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42            = ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.16/0.42         => ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
% 0.16/0.42            = ( paraco1344940915le_Det @ $true ) ) )
% 0.16/0.42        & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42           != ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.16/0.42         => ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
% 0.16/0.42            = ( paraco1344940915le_Det @ $false ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % eval.simps(5)
% 0.16/0.42  thf(fact_16_eval__equality__simplify,axiom,
% 0.16/0.42      ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
% 0.16/0.42        = ( paraco1344940915le_Det
% 0.16/0.42          @ ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42            = ( paraco1325918602e_eval @ I2 @ Q ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % eval_equality_simplify
% 0.16/0.42  thf(fact_17_change__int__def,axiom,
% 0.16/0.42      ( paraco761681009ge_int
% 0.16/0.42      = ( ^ [F: nat > nat,I: list_char > paraco1605129243lle_tv,S: list_char] : ( paraco1147068288nge_tv @ F @ ( I @ S ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % change_int_def
% 0.16/0.42  thf(fact_18_eval_Osimps_I4_J,axiom,
% 0.16/0.42      ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42            = ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.16/0.42         => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.16/0.42            = ( paraco1325918602e_eval @ I2 @ P2 ) ) )
% 0.16/0.42        & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42           != ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.16/0.42         => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42                = ( paraco1344940915le_Det @ $true ) )
% 0.16/0.42             => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.16/0.42                = ( paraco1325918602e_eval @ I2 @ Q ) ) )
% 0.16/0.42            & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42               != ( paraco1344940915le_Det @ $true ) )
% 0.16/0.42             => ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.16/0.42                    = ( paraco1344940915le_Det @ $true ) )
% 0.16/0.42                 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.16/0.42                    = ( paraco1325918602e_eval @ I2 @ P2 ) ) )
% 0.16/0.42                & ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.16/0.42                   != ( paraco1344940915le_Det @ $true ) )
% 0.16/0.42                 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.16/0.42                    = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % eval.simps(4)
% 0.16/0.42  thf(fact_19_tv_Osimps_I5_J,axiom,
% 0.16/0.42      ! [F1: $o > paraco1605129243lle_tv,F2: nat > paraco1605129243lle_tv,X1: $o] :
% 0.16/0.42        ( ( paraco2051596139lle_tv @ F1 @ F2 @ ( paraco1344940915le_Det @ X1 ) )
% 0.16/0.42        = ( F1 @ X1 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % tv.simps(5)
% 0.16/0.42  thf(fact_20_eval__negation,axiom,
% 0.16/0.42      ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42            = ( paraco1344940915le_Det @ $false ) )
% 0.16/0.42         => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 0.16/0.42            = ( paraco1344940915le_Det @ $true ) ) )
% 0.16/0.42        & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42           != ( paraco1344940915le_Det @ $false ) )
% 0.16/0.42         => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42                = ( paraco1344940915le_Det @ $true ) )
% 0.16/0.42             => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 0.16/0.42                = ( paraco1344940915le_Det @ $false ) ) )
% 0.16/0.42            & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42               != ( paraco1344940915le_Det @ $true ) )
% 0.16/0.42             => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 0.16/0.42                = ( paraco1325918602e_eval @ I2 @ P2 ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % eval_negation
% 0.16/0.42  thf(fact_21_assms,axiom,
% 0.16/0.42      inj_on_nat_nat @ f @ top_top_set_nat ).
% 0.16/0.42  
% 0.16/0.42  % assms
% 0.16/0.42  thf(fact_22_change__tv_Osimps_I1_J,axiom,
% 0.16/0.42      ! [F3: nat > nat,B: $o] :
% 0.16/0.42        ( ( paraco1147068288nge_tv @ F3 @ ( paraco1344940915le_Det @ B ) )
% 0.16/0.42        = ( paraco1344940915le_Det @ B ) ) ).
% 0.16/0.42  
% 0.16/0.42  % change_tv.simps(1)
% 0.16/0.42  thf(fact_23_fm_Oinject_I2_J,axiom,
% 0.16/0.42      ! [X3: paraco1604210848lle_fm,Y3: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( ( paraco445776468le_Neg @ X3 )
% 0.16/0.42          = ( paraco445776468le_Neg @ Y3 ) )
% 0.16/0.42        = ( X3 = Y3 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.inject(2)
% 0.16/0.42  thf(fact_24_fm_Oinject_I3_J,axiom,
% 0.16/0.42      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,Y41: paraco1604210848lle_fm,Y42: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.16/0.42          = ( paraco69239110le_Con @ Y41 @ Y42 ) )
% 0.16/0.42        = ( ( X41 = Y41 )
% 0.16/0.42          & ( X42 = Y42 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.inject(3)
% 0.16/0.42  thf(fact_25_fm_Oinject_I5_J,axiom,
% 0.16/0.42      ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm,Y61: paraco1604210848lle_fm,Y62: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( ( paraco1745535428le_Eql @ X61 @ X62 )
% 0.16/0.42          = ( paraco1745535428le_Eql @ Y61 @ Y62 ) )
% 0.16/0.42        = ( ( X61 = Y61 )
% 0.16/0.42          & ( X62 = Y62 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.inject(5)
% 0.16/0.42  thf(fact_26_fm_Oinject_I4_J,axiom,
% 0.16/0.42      ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,Y51: paraco1604210848lle_fm,Y52: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 0.16/0.42          = ( paraco1389086619le_Eql @ Y51 @ Y52 ) )
% 0.16/0.42        = ( ( X51 = Y51 )
% 0.16/0.42          & ( X52 = Y52 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.inject(4)
% 0.16/0.42  thf(fact_27_fm_Odistinct_I29_J,axiom,
% 0.16/0.42      ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 0.16/0.42       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(29)
% 0.16/0.42  thf(fact_28_fm_Odistinct_I27_J,axiom,
% 0.16/0.42      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.16/0.42       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(27)
% 0.16/0.42  thf(fact_29_fm_Odistinct_I25_J,axiom,
% 0.16/0.42      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.16/0.42       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(25)
% 0.16/0.42  thf(fact_30_fm_Odistinct_I23_J,axiom,
% 0.16/0.42      ! [X3: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco445776468le_Neg @ X3 )
% 0.16/0.42       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(23)
% 0.16/0.42  thf(fact_31_fm_Odistinct_I21_J,axiom,
% 0.16/0.42      ! [X3: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco445776468le_Neg @ X3 )
% 0.16/0.42       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(21)
% 0.16/0.42  thf(fact_32_fm_Odistinct_I19_J,axiom,
% 0.16/0.42      ! [X3: paraco1604210848lle_fm,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco445776468le_Neg @ X3 )
% 0.16/0.42       != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(19)
% 0.16/0.42  thf(fact_33_fm_Odistinct_I17_J,axiom,
% 0.16/0.42      ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.16/0.42        ( paraco367965286_Truth
% 0.16/0.42       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(17)
% 0.16/0.42  thf(fact_34_fm_Odistinct_I15_J,axiom,
% 0.16/0.42      ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.16/0.42        ( paraco367965286_Truth
% 0.16/0.42       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(15)
% 0.16/0.42  thf(fact_35_fm_Odistinct_I13_J,axiom,
% 0.16/0.42      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.16/0.42        ( paraco367965286_Truth
% 0.16/0.42       != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(13)
% 0.16/0.42  thf(fact_36_fm_Odistinct_I11_J,axiom,
% 0.16/0.42      ! [X3: paraco1604210848lle_fm] :
% 0.16/0.42        ( paraco367965286_Truth
% 0.16/0.42       != ( paraco445776468le_Neg @ X3 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(11)
% 0.16/0.42  thf(fact_37_conjunction,axiom,
% 0.16/0.42      ! [P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco327635598_valid @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.16/0.42        = ( ( paraco327635598_valid @ P2 )
% 0.16/0.42          & ( paraco327635598_valid @ Q ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % conjunction
% 0.16/0.42  thf(fact_38_eval__equality,axiom,
% 0.16/0.42      ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42            = ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.16/0.42         => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.16/0.42            = ( paraco1344940915le_Det @ $true ) ) )
% 0.16/0.42        & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42           != ( paraco1325918602e_eval @ I2 @ Q ) )
% 0.16/0.42         => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42                = ( paraco1344940915le_Det @ $true ) )
% 0.16/0.42             => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.16/0.42                = ( paraco1325918602e_eval @ I2 @ Q ) ) )
% 0.16/0.42            & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42               != ( paraco1344940915le_Det @ $true ) )
% 0.16/0.42             => ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.16/0.42                    = ( paraco1344940915le_Det @ $true ) )
% 0.16/0.42                 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.16/0.42                    = ( paraco1325918602e_eval @ I2 @ P2 ) ) )
% 0.16/0.42                & ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.16/0.42                   != ( paraco1344940915le_Det @ $true ) )
% 0.16/0.42                 => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42                        = ( paraco1344940915le_Det @ $false ) )
% 0.16/0.42                     => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.16/0.42                        = ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ Q ) ) ) )
% 0.16/0.42                    & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.16/0.42                       != ( paraco1344940915le_Det @ $false ) )
% 0.16/0.42                     => ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.16/0.42                            = ( paraco1344940915le_Det @ $false ) )
% 0.16/0.42                         => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.16/0.42                            = ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) ) ) )
% 0.16/0.42                        & ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 0.16/0.42                           != ( paraco1344940915le_Det @ $false ) )
% 0.16/0.42                         => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 0.16/0.42                            = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % eval_equality
% 0.16/0.42  thf(fact_39_double__negation,axiom,
% 0.16/0.42      ( paraco1325918602e_eval
% 0.16/0.42      = ( ^ [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ P ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % double_negation
% 0.16/0.42  thf(fact_40_UNIV__I,axiom,
% 0.16/0.42      ! [X: produc696645085lle_fm] : ( member1474794996lle_fm @ X @ top_to775056195lle_fm ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_I
% 0.16/0.42  thf(fact_41_UNIV__I,axiom,
% 0.16/0.42      ! [X: produc1852595672lle_tv] : ( member146333935lle_tv @ X @ top_to138697918lle_tv ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_I
% 0.16/0.42  thf(fact_42_UNIV__I,axiom,
% 0.16/0.42      ! [X: produc931990033lle_tv] : ( member1569366824lle_tv @ X @ top_to449985143lle_tv ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_I
% 0.16/0.42  thf(fact_43_UNIV__I,axiom,
% 0.16/0.42      ! [X: produc1281043295at_nat] : ( member112824072at_nat @ X @ top_to1541413903at_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_I
% 0.16/0.42  thf(fact_44_UNIV__I,axiom,
% 0.16/0.42      ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_I
% 0.16/0.42  thf(fact_45_UNIV__I,axiom,
% 0.16/0.42      ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_I
% 0.16/0.42  thf(fact_46_UNIV__I,axiom,
% 0.16/0.42      ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_I
% 0.16/0.42  thf(fact_47_UNIV__I,axiom,
% 0.16/0.42      ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_I
% 0.16/0.42  thf(fact_48_UNIV__I,axiom,
% 0.16/0.42      ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_I
% 0.16/0.42  thf(fact_49_iso__tuple__UNIV__I,axiom,
% 0.16/0.42      ! [X: produc696645085lle_fm] : ( member1474794996lle_fm @ X @ top_to775056195lle_fm ) ).
% 0.16/0.42  
% 0.16/0.42  % iso_tuple_UNIV_I
% 0.16/0.42  thf(fact_50_iso__tuple__UNIV__I,axiom,
% 0.16/0.42      ! [X: produc1852595672lle_tv] : ( member146333935lle_tv @ X @ top_to138697918lle_tv ) ).
% 0.16/0.42  
% 0.16/0.42  % iso_tuple_UNIV_I
% 0.16/0.42  thf(fact_51_iso__tuple__UNIV__I,axiom,
% 0.16/0.42      ! [X: produc931990033lle_tv] : ( member1569366824lle_tv @ X @ top_to449985143lle_tv ) ).
% 0.16/0.42  
% 0.16/0.42  % iso_tuple_UNIV_I
% 0.16/0.42  thf(fact_52_iso__tuple__UNIV__I,axiom,
% 0.16/0.42      ! [X: produc1281043295at_nat] : ( member112824072at_nat @ X @ top_to1541413903at_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % iso_tuple_UNIV_I
% 0.16/0.42  thf(fact_53_iso__tuple__UNIV__I,axiom,
% 0.16/0.42      ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % iso_tuple_UNIV_I
% 0.16/0.42  thf(fact_54_iso__tuple__UNIV__I,axiom,
% 0.16/0.42      ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 0.16/0.42  
% 0.16/0.42  % iso_tuple_UNIV_I
% 0.16/0.42  thf(fact_55_iso__tuple__UNIV__I,axiom,
% 0.16/0.42      ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % iso_tuple_UNIV_I
% 0.16/0.42  thf(fact_56_iso__tuple__UNIV__I,axiom,
% 0.16/0.42      ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % iso_tuple_UNIV_I
% 0.16/0.42  thf(fact_57_iso__tuple__UNIV__I,axiom,
% 0.16/0.42      ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 0.16/0.42  
% 0.16/0.42  % iso_tuple_UNIV_I
% 0.16/0.42  thf(fact_58_top__apply,axiom,
% 0.16/0.42      ( top_to1299250770e_tv_o
% 0.16/0.42      = ( ^ [X2: paraco1605129243lle_tv] : top_top_o ) ) ).
% 0.16/0.42  
% 0.16/0.42  % top_apply
% 0.16/0.42  thf(fact_59_top__apply,axiom,
% 0.16/0.42      ( top_top_nat_o
% 0.16/0.42      = ( ^ [X2: nat] : top_top_o ) ) ).
% 0.16/0.42  
% 0.16/0.42  % top_apply
% 0.16/0.42  thf(fact_60_injD,axiom,
% 0.16/0.42      ! [F3: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.16/0.42        ( ( inj_on2112487900lle_tv @ F3 @ top_to1871154984lle_tv )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42         => ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injD
% 0.16/0.42  thf(fact_61_injD,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 0.16/0.42        ( ( inj_on1955349912lle_tv @ F3 @ top_top_set_nat )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42         => ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injD
% 0.16/0.42  thf(fact_62_injD,axiom,
% 0.16/0.42      ! [F3: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.16/0.42        ( ( inj_on552895452tv_nat @ F3 @ top_to975729152tv_nat )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42         => ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injD
% 0.16/0.42  thf(fact_63_injD,axiom,
% 0.16/0.42      ! [F3: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.16/0.42        ( ( inj_on1745913142lle_tv @ F3 @ top_to1411004326lle_tv )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42         => ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injD
% 0.16/0.42  thf(fact_64_injD,axiom,
% 0.16/0.42      ! [F3: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.16/0.42        ( ( inj_on26176689at_nat @ F3 @ top_to1555900337at_nat )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42         => ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injD
% 0.16/0.42  thf(fact_65_injD,axiom,
% 0.16/0.42      ! [F3: nat > nat,X: nat,Y: nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42         => ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injD
% 0.16/0.42  thf(fact_66_injD,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42         => ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injD
% 0.16/0.42  thf(fact_67_mem__Collect__eq,axiom,
% 0.16/0.42      ! [A: produc696645085lle_fm,P3: produc696645085lle_fm > $o] :
% 0.16/0.42        ( ( member1474794996lle_fm @ A @ ( collec835549234lle_fm @ P3 ) )
% 0.16/0.42        = ( P3 @ A ) ) ).
% 0.16/0.42  
% 0.16/0.42  % mem_Collect_eq
% 0.16/0.42  thf(fact_68_mem__Collect__eq,axiom,
% 0.16/0.42      ! [A: produc1852595672lle_tv,P3: produc1852595672lle_tv > $o] :
% 0.16/0.42        ( ( member146333935lle_tv @ A @ ( collec1102043437lle_tv @ P3 ) )
% 0.16/0.42        = ( P3 @ A ) ) ).
% 0.16/0.42  
% 0.16/0.42  % mem_Collect_eq
% 0.16/0.42  thf(fact_69_mem__Collect__eq,axiom,
% 0.16/0.42      ! [A: produc931990033lle_tv,P3: produc931990033lle_tv > $o] :
% 0.16/0.42        ( ( member1569366824lle_tv @ A @ ( collec1624074086lle_tv @ P3 ) )
% 0.16/0.42        = ( P3 @ A ) ) ).
% 0.16/0.42  
% 0.16/0.42  % mem_Collect_eq
% 0.16/0.42  thf(fact_70_mem__Collect__eq,axiom,
% 0.16/0.42      ! [A: produc1281043295at_nat,P3: produc1281043295at_nat > $o] :
% 0.16/0.42        ( ( member112824072at_nat @ A @ ( collec791369802at_nat @ P3 ) )
% 0.16/0.42        = ( P3 @ A ) ) ).
% 0.16/0.42  
% 0.16/0.42  % mem_Collect_eq
% 0.16/0.42  thf(fact_71_mem__Collect__eq,axiom,
% 0.16/0.42      ! [A: paraco1605129243lle_tv,P3: paraco1605129243lle_tv > $o] :
% 0.16/0.42        ( ( member266900804lle_tv @ A @ ( collec1111687558lle_tv @ P3 ) )
% 0.16/0.42        = ( P3 @ A ) ) ).
% 0.16/0.42  
% 0.16/0.42  % mem_Collect_eq
% 0.16/0.42  thf(fact_72_mem__Collect__eq,axiom,
% 0.16/0.42      ! [A: nat,P3: nat > $o] :
% 0.16/0.42        ( ( member_nat @ A @ ( collect_nat @ P3 ) )
% 0.16/0.42        = ( P3 @ A ) ) ).
% 0.16/0.42  
% 0.16/0.42  % mem_Collect_eq
% 0.16/0.42  thf(fact_73_Collect__mem__eq,axiom,
% 0.16/0.42      ! [A2: set_Pr2120184979lle_fm] :
% 0.16/0.42        ( ( collec835549234lle_fm
% 0.16/0.42          @ ^ [X2: produc696645085lle_fm] : ( member1474794996lle_fm @ X2 @ A2 ) )
% 0.16/0.42        = A2 ) ).
% 0.16/0.42  
% 0.16/0.42  % Collect_mem_eq
% 0.16/0.42  thf(fact_74_Collect__mem__eq,axiom,
% 0.16/0.42      ! [A2: set_Pr2061825550lle_tv] :
% 0.16/0.42        ( ( collec1102043437lle_tv
% 0.16/0.42          @ ^ [X2: produc1852595672lle_tv] : ( member146333935lle_tv @ X2 @ A2 ) )
% 0.16/0.42        = A2 ) ).
% 0.16/0.42  
% 0.16/0.42  % Collect_mem_eq
% 0.16/0.42  thf(fact_75_Collect__mem__eq,axiom,
% 0.16/0.42      ! [A2: set_Pr560526279lle_tv] :
% 0.16/0.42        ( ( collec1624074086lle_tv
% 0.16/0.42          @ ^ [X2: produc931990033lle_tv] : ( member1569366824lle_tv @ X2 @ A2 ) )
% 0.16/0.42        = A2 ) ).
% 0.16/0.42  
% 0.16/0.42  % Collect_mem_eq
% 0.16/0.42  thf(fact_76_Collect__mem__eq,axiom,
% 0.16/0.42      ! [A2: set_Pr1357842111at_nat] :
% 0.16/0.42        ( ( collec791369802at_nat
% 0.16/0.42          @ ^ [X2: produc1281043295at_nat] : ( member112824072at_nat @ X2 @ A2 ) )
% 0.16/0.42        = A2 ) ).
% 0.16/0.42  
% 0.16/0.42  % Collect_mem_eq
% 0.16/0.42  thf(fact_77_Collect__mem__eq,axiom,
% 0.16/0.42      ! [A2: set_Pa1764573435lle_tv] :
% 0.16/0.42        ( ( collec1111687558lle_tv
% 0.16/0.42          @ ^ [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ A2 ) )
% 0.16/0.42        = A2 ) ).
% 0.16/0.42  
% 0.16/0.42  % Collect_mem_eq
% 0.16/0.42  thf(fact_78_Collect__mem__eq,axiom,
% 0.16/0.42      ! [A2: set_nat] :
% 0.16/0.42        ( ( collect_nat
% 0.16/0.42          @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 0.16/0.42        = A2 ) ).
% 0.16/0.42  
% 0.16/0.42  % Collect_mem_eq
% 0.16/0.42  thf(fact_79_Collect__cong,axiom,
% 0.16/0.42      ! [P3: paraco1605129243lle_tv > $o,Q2: paraco1605129243lle_tv > $o] :
% 0.16/0.42        ( ! [X4: paraco1605129243lle_tv] :
% 0.16/0.42            ( ( P3 @ X4 )
% 0.16/0.42            = ( Q2 @ X4 ) )
% 0.16/0.42       => ( ( collec1111687558lle_tv @ P3 )
% 0.16/0.42          = ( collec1111687558lle_tv @ Q2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % Collect_cong
% 0.16/0.42  thf(fact_80_Collect__cong,axiom,
% 0.16/0.42      ! [P3: nat > $o,Q2: nat > $o] :
% 0.16/0.42        ( ! [X4: nat] :
% 0.16/0.42            ( ( P3 @ X4 )
% 0.16/0.42            = ( Q2 @ X4 ) )
% 0.16/0.42       => ( ( collect_nat @ P3 )
% 0.16/0.42          = ( collect_nat @ Q2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % Collect_cong
% 0.16/0.42  thf(fact_81_injI,axiom,
% 0.16/0.42      ! [F3: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.16/0.42        ( ! [X4: produc1647334210lle_tv,Y2: produc1647334210lle_tv] :
% 0.16/0.42            ( ( ( F3 @ X4 )
% 0.16/0.42              = ( F3 @ Y2 ) )
% 0.16/0.42           => ( X4 = Y2 ) )
% 0.16/0.42       => ( inj_on2112487900lle_tv @ F3 @ top_to1871154984lle_tv ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injI
% 0.16/0.42  thf(fact_82_injI,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [X4: nat,Y2: nat] :
% 0.16/0.42            ( ( ( F3 @ X4 )
% 0.16/0.42              = ( F3 @ Y2 ) )
% 0.16/0.42           => ( X4 = Y2 ) )
% 0.16/0.42       => ( inj_on1955349912lle_tv @ F3 @ top_top_set_nat ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injI
% 0.16/0.42  thf(fact_83_injI,axiom,
% 0.16/0.42      ! [F3: produc194167194tv_nat > produc194167194tv_nat] :
% 0.16/0.42        ( ! [X4: produc194167194tv_nat,Y2: produc194167194tv_nat] :
% 0.16/0.42            ( ( ( F3 @ X4 )
% 0.16/0.42              = ( F3 @ Y2 ) )
% 0.16/0.42           => ( X4 = Y2 ) )
% 0.16/0.42       => ( inj_on552895452tv_nat @ F3 @ top_to975729152tv_nat ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injI
% 0.16/0.42  thf(fact_84_injI,axiom,
% 0.16/0.42      ! [F3: produc270694976lle_tv > produc270694976lle_tv] :
% 0.16/0.42        ( ! [X4: produc270694976lle_tv,Y2: produc270694976lle_tv] :
% 0.16/0.42            ( ( ( F3 @ X4 )
% 0.16/0.42              = ( F3 @ Y2 ) )
% 0.16/0.42           => ( X4 = Y2 ) )
% 0.16/0.42       => ( inj_on1745913142lle_tv @ F3 @ top_to1411004326lle_tv ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injI
% 0.16/0.42  thf(fact_85_injI,axiom,
% 0.16/0.42      ! [F3: product_prod_nat_nat > product_prod_nat_nat] :
% 0.16/0.42        ( ! [X4: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.16/0.42            ( ( ( F3 @ X4 )
% 0.16/0.42              = ( F3 @ Y2 ) )
% 0.16/0.42           => ( X4 = Y2 ) )
% 0.16/0.42       => ( inj_on26176689at_nat @ F3 @ top_to1555900337at_nat ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injI
% 0.16/0.42  thf(fact_86_injI,axiom,
% 0.16/0.42      ! [F3: nat > nat] :
% 0.16/0.42        ( ! [X4: nat,Y2: nat] :
% 0.16/0.42            ( ( ( F3 @ X4 )
% 0.16/0.42              = ( F3 @ Y2 ) )
% 0.16/0.42           => ( X4 = Y2 ) )
% 0.16/0.42       => ( inj_on_nat_nat @ F3 @ top_top_set_nat ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injI
% 0.16/0.42  thf(fact_87_injI,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [X4: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
% 0.16/0.42            ( ( ( F3 @ X4 )
% 0.16/0.42              = ( F3 @ Y2 ) )
% 0.16/0.42           => ( X4 = Y2 ) )
% 0.16/0.42       => ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv ) ) ).
% 0.16/0.42  
% 0.16/0.42  % injI
% 0.16/0.42  thf(fact_88_inj__eq,axiom,
% 0.16/0.42      ! [F3: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.16/0.42        ( ( inj_on2112487900lle_tv @ F3 @ top_to1871154984lle_tv )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42          = ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_eq
% 0.16/0.42  thf(fact_89_inj__eq,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 0.16/0.42        ( ( inj_on1955349912lle_tv @ F3 @ top_top_set_nat )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42          = ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_eq
% 0.16/0.42  thf(fact_90_inj__eq,axiom,
% 0.16/0.42      ! [F3: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.16/0.42        ( ( inj_on552895452tv_nat @ F3 @ top_to975729152tv_nat )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42          = ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_eq
% 0.16/0.42  thf(fact_91_inj__eq,axiom,
% 0.16/0.42      ! [F3: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.16/0.42        ( ( inj_on1745913142lle_tv @ F3 @ top_to1411004326lle_tv )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42          = ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_eq
% 0.16/0.42  thf(fact_92_inj__eq,axiom,
% 0.16/0.42      ! [F3: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.16/0.42        ( ( inj_on26176689at_nat @ F3 @ top_to1555900337at_nat )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42          = ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_eq
% 0.16/0.42  thf(fact_93_inj__eq,axiom,
% 0.16/0.42      ! [F3: nat > nat,X: nat,Y: nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42          = ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_eq
% 0.16/0.42  thf(fact_94_inj__eq,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42          = ( X = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_eq
% 0.16/0.42  thf(fact_95_inj__def,axiom,
% 0.16/0.42      ! [F3: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.16/0.42        ( ( inj_on2112487900lle_tv @ F3 @ top_to1871154984lle_tv )
% 0.16/0.42        = ( ! [X2: produc1647334210lle_tv,Y4: produc1647334210lle_tv] :
% 0.16/0.42              ( ( ( F3 @ X2 )
% 0.16/0.42                = ( F3 @ Y4 ) )
% 0.16/0.42             => ( X2 = Y4 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_def
% 0.16/0.42  thf(fact_96_inj__def,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on1955349912lle_tv @ F3 @ top_top_set_nat )
% 0.16/0.42        = ( ! [X2: nat,Y4: nat] :
% 0.16/0.42              ( ( ( F3 @ X2 )
% 0.16/0.42                = ( F3 @ Y4 ) )
% 0.16/0.42             => ( X2 = Y4 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_def
% 0.16/0.42  thf(fact_97_inj__def,axiom,
% 0.16/0.42      ! [F3: produc194167194tv_nat > produc194167194tv_nat] :
% 0.16/0.42        ( ( inj_on552895452tv_nat @ F3 @ top_to975729152tv_nat )
% 0.16/0.42        = ( ! [X2: produc194167194tv_nat,Y4: produc194167194tv_nat] :
% 0.16/0.42              ( ( ( F3 @ X2 )
% 0.16/0.42                = ( F3 @ Y4 ) )
% 0.16/0.42             => ( X2 = Y4 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_def
% 0.16/0.42  thf(fact_98_inj__def,axiom,
% 0.16/0.42      ! [F3: produc270694976lle_tv > produc270694976lle_tv] :
% 0.16/0.42        ( ( inj_on1745913142lle_tv @ F3 @ top_to1411004326lle_tv )
% 0.16/0.42        = ( ! [X2: produc270694976lle_tv,Y4: produc270694976lle_tv] :
% 0.16/0.42              ( ( ( F3 @ X2 )
% 0.16/0.42                = ( F3 @ Y4 ) )
% 0.16/0.42             => ( X2 = Y4 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_def
% 0.16/0.42  thf(fact_99_inj__def,axiom,
% 0.16/0.42      ! [F3: product_prod_nat_nat > product_prod_nat_nat] :
% 0.16/0.42        ( ( inj_on26176689at_nat @ F3 @ top_to1555900337at_nat )
% 0.16/0.42        = ( ! [X2: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 0.16/0.42              ( ( ( F3 @ X2 )
% 0.16/0.42                = ( F3 @ Y4 ) )
% 0.16/0.42             => ( X2 = Y4 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_def
% 0.16/0.42  thf(fact_100_inj__def,axiom,
% 0.16/0.42      ! [F3: nat > nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42        = ( ! [X2: nat,Y4: nat] :
% 0.16/0.42              ( ( ( F3 @ X2 )
% 0.16/0.42                = ( F3 @ Y4 ) )
% 0.16/0.42             => ( X2 = Y4 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_def
% 0.16/0.42  thf(fact_101_inj__def,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42        = ( ! [X2: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
% 0.16/0.42              ( ( ( F3 @ X2 )
% 0.16/0.42                = ( F3 @ Y4 ) )
% 0.16/0.42             => ( X2 = Y4 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_def
% 0.16/0.42  thf(fact_102_fm_Oinduct,axiom,
% 0.16/0.42      ! [P3: paraco1604210848lle_fm > $o,Fm: paraco1604210848lle_fm] :
% 0.16/0.42        ( ! [X4: list_char] : ( P3 @ ( paraco1480028776le_Pro @ X4 ) )
% 0.16/0.42       => ( ( P3 @ paraco367965286_Truth )
% 0.16/0.42         => ( ! [X4: paraco1604210848lle_fm] :
% 0.16/0.42                ( ( P3 @ X4 )
% 0.16/0.42               => ( P3 @ ( paraco445776468le_Neg @ X4 ) ) )
% 0.16/0.42           => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.16/0.42                  ( ( P3 @ X1a )
% 0.16/0.42                 => ( ( P3 @ X22 )
% 0.16/0.42                   => ( P3 @ ( paraco69239110le_Con @ X1a @ X22 ) ) ) )
% 0.16/0.42             => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.16/0.42                    ( ( P3 @ X1a )
% 0.16/0.42                   => ( ( P3 @ X22 )
% 0.16/0.42                     => ( P3 @ ( paraco1389086619le_Eql @ X1a @ X22 ) ) ) )
% 0.16/0.42               => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.16/0.42                      ( ( P3 @ X1a )
% 0.16/0.42                     => ( ( P3 @ X22 )
% 0.16/0.42                       => ( P3 @ ( paraco1745535428le_Eql @ X1a @ X22 ) ) ) )
% 0.16/0.42                 => ( P3 @ Fm ) ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.induct
% 0.16/0.42  thf(fact_103_fm_Oexhaust,axiom,
% 0.16/0.42      ! [Y: paraco1604210848lle_fm] :
% 0.16/0.42        ( ! [X12: list_char] :
% 0.16/0.42            ( Y
% 0.16/0.42           != ( paraco1480028776le_Pro @ X12 ) )
% 0.16/0.42       => ( ( Y != paraco367965286_Truth )
% 0.16/0.42         => ( ! [X32: paraco1604210848lle_fm] :
% 0.16/0.42                ( Y
% 0.16/0.42               != ( paraco445776468le_Neg @ X32 ) )
% 0.16/0.42           => ( ! [X412: paraco1604210848lle_fm,X422: paraco1604210848lle_fm] :
% 0.16/0.42                  ( Y
% 0.16/0.42                 != ( paraco69239110le_Con @ X412 @ X422 ) )
% 0.16/0.42             => ( ! [X512: paraco1604210848lle_fm,X522: paraco1604210848lle_fm] :
% 0.16/0.42                    ( Y
% 0.16/0.42                   != ( paraco1389086619le_Eql @ X512 @ X522 ) )
% 0.16/0.42               => ~ ! [X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 0.16/0.42                      ( Y
% 0.16/0.42                     != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.exhaust
% 0.16/0.42  thf(fact_104_props_Ocases,axiom,
% 0.16/0.42      ! [X: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( X != paraco367965286_Truth )
% 0.16/0.42       => ( ! [S2: list_char] :
% 0.16/0.42              ( X
% 0.16/0.42             != ( paraco1480028776le_Pro @ S2 ) )
% 0.16/0.42         => ( ! [P4: paraco1604210848lle_fm] :
% 0.16/0.42                ( X
% 0.16/0.42               != ( paraco445776468le_Neg @ P4 ) )
% 0.16/0.42           => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.16/0.42                  ( X
% 0.16/0.42                 != ( paraco69239110le_Con @ P4 @ Q3 ) )
% 0.16/0.42             => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.16/0.42                    ( X
% 0.16/0.42                   != ( paraco1389086619le_Eql @ P4 @ Q3 ) )
% 0.16/0.42               => ~ ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.16/0.42                      ( X
% 0.16/0.42                     != ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % props.cases
% 0.16/0.42  thf(fact_105_fm_Oinject_I1_J,axiom,
% 0.16/0.42      ! [X1: list_char,Y1: list_char] :
% 0.16/0.42        ( ( ( paraco1480028776le_Pro @ X1 )
% 0.16/0.42          = ( paraco1480028776le_Pro @ Y1 ) )
% 0.16/0.42        = ( X1 = Y1 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.inject(1)
% 0.16/0.42  thf(fact_106_top__set__def,axiom,
% 0.16/0.42      ( top_to975729152tv_nat
% 0.16/0.42      = ( collec848462447tv_nat @ top_to900819589_nat_o ) ) ).
% 0.16/0.42  
% 0.16/0.42  % top_set_def
% 0.16/0.42  thf(fact_107_top__set__def,axiom,
% 0.16/0.42      ( top_to1411004326lle_tv
% 0.16/0.42      = ( collec924990229lle_tv @ top_to1889334367e_tv_o ) ) ).
% 0.16/0.42  
% 0.16/0.42  % top_set_def
% 0.16/0.42  thf(fact_108_top__set__def,axiom,
% 0.16/0.42      ( top_to1555900337at_nat
% 0.16/0.42      = ( collec7649004at_nat @ top_to632227436_nat_o ) ) ).
% 0.16/0.42  
% 0.16/0.42  % top_set_def
% 0.16/0.42  thf(fact_109_top__set__def,axiom,
% 0.16/0.42      ( top_top_set_nat
% 0.16/0.42      = ( collect_nat @ top_top_nat_o ) ) ).
% 0.16/0.42  
% 0.16/0.42  % top_set_def
% 0.16/0.42  thf(fact_110_top__set__def,axiom,
% 0.16/0.42      ( top_to1057771083lle_tv
% 0.16/0.42      = ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ) ).
% 0.16/0.42  
% 0.16/0.42  % top_set_def
% 0.16/0.42  thf(fact_111_eval_Osimps_I1_J,axiom,
% 0.16/0.42      ! [I2: list_char > paraco1605129243lle_tv,S3: list_char] :
% 0.16/0.42        ( ( paraco1325918602e_eval @ I2 @ ( paraco1480028776le_Pro @ S3 ) )
% 0.16/0.42        = ( I2 @ S3 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % eval.simps(1)
% 0.16/0.42  thf(fact_112_fm_Odistinct_I3_J,axiom,
% 0.16/0.42      ! [X1: list_char,X3: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco1480028776le_Pro @ X1 )
% 0.16/0.42       != ( paraco445776468le_Neg @ X3 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(3)
% 0.16/0.42  thf(fact_113_fm_Odistinct_I5_J,axiom,
% 0.16/0.42      ! [X1: list_char,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco1480028776le_Pro @ X1 )
% 0.16/0.42       != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(5)
% 0.16/0.42  thf(fact_114_fm_Odistinct_I9_J,axiom,
% 0.16/0.42      ! [X1: list_char,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco1480028776le_Pro @ X1 )
% 0.16/0.42       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(9)
% 0.16/0.42  thf(fact_115_fm_Odistinct_I7_J,axiom,
% 0.16/0.42      ! [X1: list_char,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco1480028776le_Pro @ X1 )
% 0.16/0.42       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(7)
% 0.16/0.42  thf(fact_116_fm_Odistinct_I1_J,axiom,
% 0.16/0.42      ! [X1: list_char] :
% 0.16/0.42        ( ( paraco1480028776le_Pro @ X1 )
% 0.16/0.42       != paraco367965286_Truth ) ).
% 0.16/0.42  
% 0.16/0.42  % fm.distinct(1)
% 0.16/0.42  thf(fact_117_change__tv__injection,axiom,
% 0.16/0.42      ! [F3: nat > nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42       => ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ F3 ) @ top_to1057771083lle_tv ) ) ).
% 0.16/0.42  
% 0.16/0.42  % change_tv_injection
% 0.16/0.42  thf(fact_118_UNIV__witness,axiom,
% 0.16/0.42      ? [X4: produc696645085lle_fm] : ( member1474794996lle_fm @ X4 @ top_to775056195lle_fm ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_witness
% 0.16/0.42  thf(fact_119_UNIV__witness,axiom,
% 0.16/0.42      ? [X4: produc1852595672lle_tv] : ( member146333935lle_tv @ X4 @ top_to138697918lle_tv ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_witness
% 0.16/0.42  thf(fact_120_UNIV__witness,axiom,
% 0.16/0.42      ? [X4: produc931990033lle_tv] : ( member1569366824lle_tv @ X4 @ top_to449985143lle_tv ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_witness
% 0.16/0.42  thf(fact_121_UNIV__witness,axiom,
% 0.16/0.42      ? [X4: produc1281043295at_nat] : ( member112824072at_nat @ X4 @ top_to1541413903at_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_witness
% 0.16/0.42  thf(fact_122_UNIV__witness,axiom,
% 0.16/0.42      ? [X4: produc194167194tv_nat] : ( member737151281tv_nat @ X4 @ top_to975729152tv_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_witness
% 0.16/0.42  thf(fact_123_UNIV__witness,axiom,
% 0.16/0.42      ? [X4: produc270694976lle_tv] : ( member813679063lle_tv @ X4 @ top_to1411004326lle_tv ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_witness
% 0.16/0.42  thf(fact_124_UNIV__witness,axiom,
% 0.16/0.42      ? [X4: product_prod_nat_nat] : ( member701585322at_nat @ X4 @ top_to1555900337at_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_witness
% 0.16/0.42  thf(fact_125_UNIV__witness,axiom,
% 0.16/0.42      ? [X4: nat] : ( member_nat @ X4 @ top_top_set_nat ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_witness
% 0.16/0.42  thf(fact_126_UNIV__witness,axiom,
% 0.16/0.42      ? [X4: paraco1605129243lle_tv] : ( member266900804lle_tv @ X4 @ top_to1057771083lle_tv ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_witness
% 0.16/0.42  thf(fact_127_UNIV__eq__I,axiom,
% 0.16/0.42      ! [A2: set_Pr2120184979lle_fm] :
% 0.16/0.42        ( ! [X4: produc696645085lle_fm] : ( member1474794996lle_fm @ X4 @ A2 )
% 0.16/0.42       => ( top_to775056195lle_fm = A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_eq_I
% 0.16/0.42  thf(fact_128_UNIV__eq__I,axiom,
% 0.16/0.42      ! [A2: set_Pr2061825550lle_tv] :
% 0.16/0.42        ( ! [X4: produc1852595672lle_tv] : ( member146333935lle_tv @ X4 @ A2 )
% 0.16/0.42       => ( top_to138697918lle_tv = A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_eq_I
% 0.16/0.42  thf(fact_129_UNIV__eq__I,axiom,
% 0.16/0.42      ! [A2: set_Pr560526279lle_tv] :
% 0.16/0.42        ( ! [X4: produc931990033lle_tv] : ( member1569366824lle_tv @ X4 @ A2 )
% 0.16/0.42       => ( top_to449985143lle_tv = A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_eq_I
% 0.16/0.42  thf(fact_130_UNIV__eq__I,axiom,
% 0.16/0.42      ! [A2: set_Pr1357842111at_nat] :
% 0.16/0.42        ( ! [X4: produc1281043295at_nat] : ( member112824072at_nat @ X4 @ A2 )
% 0.16/0.42       => ( top_to1541413903at_nat = A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_eq_I
% 0.16/0.42  thf(fact_131_UNIV__eq__I,axiom,
% 0.16/0.42      ! [A2: set_Pr1725653840tv_nat] :
% 0.16/0.42        ( ! [X4: produc194167194tv_nat] : ( member737151281tv_nat @ X4 @ A2 )
% 0.16/0.42       => ( top_to975729152tv_nat = A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_eq_I
% 0.16/0.42  thf(fact_132_UNIV__eq__I,axiom,
% 0.16/0.42      ! [A2: set_Pr13445366lle_tv] :
% 0.16/0.42        ( ! [X4: produc270694976lle_tv] : ( member813679063lle_tv @ X4 @ A2 )
% 0.16/0.42       => ( top_to1411004326lle_tv = A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_eq_I
% 0.16/0.42  thf(fact_133_UNIV__eq__I,axiom,
% 0.16/0.42      ! [A2: set_Pr1986765409at_nat] :
% 0.16/0.42        ( ! [X4: product_prod_nat_nat] : ( member701585322at_nat @ X4 @ A2 )
% 0.16/0.42       => ( top_to1555900337at_nat = A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_eq_I
% 0.16/0.42  thf(fact_134_UNIV__eq__I,axiom,
% 0.16/0.42      ! [A2: set_nat] :
% 0.16/0.42        ( ! [X4: nat] : ( member_nat @ X4 @ A2 )
% 0.16/0.42       => ( top_top_set_nat = A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_eq_I
% 0.16/0.42  thf(fact_135_UNIV__eq__I,axiom,
% 0.16/0.42      ! [A2: set_Pa1764573435lle_tv] :
% 0.16/0.42        ( ! [X4: paraco1605129243lle_tv] : ( member266900804lle_tv @ X4 @ A2 )
% 0.16/0.42       => ( top_to1057771083lle_tv = A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % UNIV_eq_I
% 0.16/0.42  thf(fact_136_inj__on__inverseI,axiom,
% 0.16/0.42      ! [A2: set_Pr2014382200lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv,F3: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.16/0.42        ( ! [X4: produc1647334210lle_tv] :
% 0.16/0.42            ( ( member1531318361lle_tv @ X4 @ A2 )
% 0.16/0.42           => ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42              = X4 ) )
% 0.16/0.42       => ( inj_on2112487900lle_tv @ F3 @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_inverseI
% 0.16/0.42  thf(fact_137_inj__on__inverseI,axiom,
% 0.16/0.42      ! [A2: set_Pr1725653840tv_nat,G: produc194167194tv_nat > produc194167194tv_nat,F3: produc194167194tv_nat > produc194167194tv_nat] :
% 0.16/0.42        ( ! [X4: produc194167194tv_nat] :
% 0.16/0.42            ( ( member737151281tv_nat @ X4 @ A2 )
% 0.16/0.42           => ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42              = X4 ) )
% 0.16/0.42       => ( inj_on552895452tv_nat @ F3 @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_inverseI
% 0.16/0.42  thf(fact_138_inj__on__inverseI,axiom,
% 0.16/0.42      ! [A2: set_Pr13445366lle_tv,G: produc270694976lle_tv > produc270694976lle_tv,F3: produc270694976lle_tv > produc270694976lle_tv] :
% 0.16/0.42        ( ! [X4: produc270694976lle_tv] :
% 0.16/0.42            ( ( member813679063lle_tv @ X4 @ A2 )
% 0.16/0.42           => ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42              = X4 ) )
% 0.16/0.42       => ( inj_on1745913142lle_tv @ F3 @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_inverseI
% 0.16/0.42  thf(fact_139_inj__on__inverseI,axiom,
% 0.16/0.42      ! [A2: set_Pr1986765409at_nat,G: product_prod_nat_nat > product_prod_nat_nat,F3: product_prod_nat_nat > product_prod_nat_nat] :
% 0.16/0.42        ( ! [X4: product_prod_nat_nat] :
% 0.16/0.42            ( ( member701585322at_nat @ X4 @ A2 )
% 0.16/0.42           => ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42              = X4 ) )
% 0.16/0.42       => ( inj_on26176689at_nat @ F3 @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_inverseI
% 0.16/0.42  thf(fact_140_inj__on__inverseI,axiom,
% 0.16/0.42      ! [A2: set_nat,G: paraco1605129243lle_tv > nat,F3: nat > paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [X4: nat] :
% 0.16/0.42            ( ( member_nat @ X4 @ A2 )
% 0.16/0.42           => ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42              = X4 ) )
% 0.16/0.42       => ( inj_on1955349912lle_tv @ F3 @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_inverseI
% 0.16/0.42  thf(fact_141_inj__on__inverseI,axiom,
% 0.16/0.42      ! [A2: set_nat,G: nat > nat,F3: nat > nat] :
% 0.16/0.42        ( ! [X4: nat] :
% 0.16/0.42            ( ( member_nat @ X4 @ A2 )
% 0.16/0.42           => ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42              = X4 ) )
% 0.16/0.42       => ( inj_on_nat_nat @ F3 @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_inverseI
% 0.16/0.42  thf(fact_142_inj__on__inverseI,axiom,
% 0.16/0.42      ! [A2: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [X4: paraco1605129243lle_tv] :
% 0.16/0.42            ( ( member266900804lle_tv @ X4 @ A2 )
% 0.16/0.42           => ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42              = X4 ) )
% 0.16/0.42       => ( inj_on772319074lle_tv @ F3 @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_inverseI
% 0.16/0.42  thf(fact_143_inj__on__contraD,axiom,
% 0.16/0.42      ! [F3: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.16/0.42        ( ( inj_on2112487900lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( X != Y )
% 0.16/0.42         => ( ( member1531318361lle_tv @ X @ A2 )
% 0.16/0.42           => ( ( member1531318361lle_tv @ Y @ A2 )
% 0.16/0.42             => ( ( F3 @ X )
% 0.16/0.42               != ( F3 @ Y ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_contraD
% 0.16/0.42  thf(fact_144_inj__on__contraD,axiom,
% 0.16/0.42      ! [F3: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.16/0.42        ( ( inj_on552895452tv_nat @ F3 @ A2 )
% 0.16/0.42       => ( ( X != Y )
% 0.16/0.42         => ( ( member737151281tv_nat @ X @ A2 )
% 0.16/0.42           => ( ( member737151281tv_nat @ Y @ A2 )
% 0.16/0.42             => ( ( F3 @ X )
% 0.16/0.42               != ( F3 @ Y ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_contraD
% 0.16/0.42  thf(fact_145_inj__on__contraD,axiom,
% 0.16/0.42      ! [F3: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.16/0.42        ( ( inj_on1745913142lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( X != Y )
% 0.16/0.42         => ( ( member813679063lle_tv @ X @ A2 )
% 0.16/0.42           => ( ( member813679063lle_tv @ Y @ A2 )
% 0.16/0.42             => ( ( F3 @ X )
% 0.16/0.42               != ( F3 @ Y ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_contraD
% 0.16/0.42  thf(fact_146_inj__on__contraD,axiom,
% 0.16/0.42      ! [F3: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.16/0.42        ( ( inj_on26176689at_nat @ F3 @ A2 )
% 0.16/0.42       => ( ( X != Y )
% 0.16/0.42         => ( ( member701585322at_nat @ X @ A2 )
% 0.16/0.42           => ( ( member701585322at_nat @ Y @ A2 )
% 0.16/0.42             => ( ( F3 @ X )
% 0.16/0.42               != ( F3 @ Y ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_contraD
% 0.16/0.42  thf(fact_147_inj__on__contraD,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 0.16/0.42        ( ( inj_on1955349912lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( X != Y )
% 0.16/0.42         => ( ( member_nat @ X @ A2 )
% 0.16/0.42           => ( ( member_nat @ Y @ A2 )
% 0.16/0.42             => ( ( F3 @ X )
% 0.16/0.42               != ( F3 @ Y ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_contraD
% 0.16/0.42  thf(fact_148_inj__on__contraD,axiom,
% 0.16/0.42      ! [F3: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ A2 )
% 0.16/0.42       => ( ( X != Y )
% 0.16/0.42         => ( ( member_nat @ X @ A2 )
% 0.16/0.42           => ( ( member_nat @ Y @ A2 )
% 0.16/0.42             => ( ( F3 @ X )
% 0.16/0.42               != ( F3 @ Y ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_contraD
% 0.16/0.42  thf(fact_149_inj__on__contraD,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( X != Y )
% 0.16/0.42         => ( ( member266900804lle_tv @ X @ A2 )
% 0.16/0.42           => ( ( member266900804lle_tv @ Y @ A2 )
% 0.16/0.42             => ( ( F3 @ X )
% 0.16/0.42               != ( F3 @ Y ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_contraD
% 0.16/0.42  thf(fact_150_inj__on__eq__iff,axiom,
% 0.16/0.42      ! [F3: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.16/0.42        ( ( inj_on2112487900lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( member1531318361lle_tv @ X @ A2 )
% 0.16/0.42         => ( ( member1531318361lle_tv @ Y @ A2 )
% 0.16/0.42           => ( ( ( F3 @ X )
% 0.16/0.42                = ( F3 @ Y ) )
% 0.16/0.42              = ( X = Y ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_eq_iff
% 0.16/0.42  thf(fact_151_inj__on__eq__iff,axiom,
% 0.16/0.42      ! [F3: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.16/0.42        ( ( inj_on552895452tv_nat @ F3 @ A2 )
% 0.16/0.42       => ( ( member737151281tv_nat @ X @ A2 )
% 0.16/0.42         => ( ( member737151281tv_nat @ Y @ A2 )
% 0.16/0.42           => ( ( ( F3 @ X )
% 0.16/0.42                = ( F3 @ Y ) )
% 0.16/0.42              = ( X = Y ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_eq_iff
% 0.16/0.42  thf(fact_152_inj__on__eq__iff,axiom,
% 0.16/0.42      ! [F3: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.16/0.42        ( ( inj_on1745913142lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( member813679063lle_tv @ X @ A2 )
% 0.16/0.42         => ( ( member813679063lle_tv @ Y @ A2 )
% 0.16/0.42           => ( ( ( F3 @ X )
% 0.16/0.42                = ( F3 @ Y ) )
% 0.16/0.42              = ( X = Y ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_eq_iff
% 0.16/0.42  thf(fact_153_inj__on__eq__iff,axiom,
% 0.16/0.42      ! [F3: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.16/0.42        ( ( inj_on26176689at_nat @ F3 @ A2 )
% 0.16/0.42       => ( ( member701585322at_nat @ X @ A2 )
% 0.16/0.42         => ( ( member701585322at_nat @ Y @ A2 )
% 0.16/0.42           => ( ( ( F3 @ X )
% 0.16/0.42                = ( F3 @ Y ) )
% 0.16/0.42              = ( X = Y ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_eq_iff
% 0.16/0.42  thf(fact_154_inj__on__eq__iff,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 0.16/0.42        ( ( inj_on1955349912lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( member_nat @ X @ A2 )
% 0.16/0.42         => ( ( member_nat @ Y @ A2 )
% 0.16/0.42           => ( ( ( F3 @ X )
% 0.16/0.42                = ( F3 @ Y ) )
% 0.16/0.42              = ( X = Y ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_eq_iff
% 0.16/0.42  thf(fact_155_inj__on__eq__iff,axiom,
% 0.16/0.42      ! [F3: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ A2 )
% 0.16/0.42       => ( ( member_nat @ X @ A2 )
% 0.16/0.42         => ( ( member_nat @ Y @ A2 )
% 0.16/0.42           => ( ( ( F3 @ X )
% 0.16/0.42                = ( F3 @ Y ) )
% 0.16/0.42              = ( X = Y ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_eq_iff
% 0.16/0.42  thf(fact_156_inj__on__eq__iff,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( member266900804lle_tv @ X @ A2 )
% 0.16/0.42         => ( ( member266900804lle_tv @ Y @ A2 )
% 0.16/0.42           => ( ( ( F3 @ X )
% 0.16/0.42                = ( F3 @ Y ) )
% 0.16/0.42              = ( X = Y ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_eq_iff
% 0.16/0.42  thf(fact_157_inj__on__cong,axiom,
% 0.16/0.42      ! [A2: set_Pr2014382200lle_tv,F3: produc1647334210lle_tv > produc1647334210lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.16/0.42        ( ! [A3: produc1647334210lle_tv] :
% 0.16/0.42            ( ( member1531318361lle_tv @ A3 @ A2 )
% 0.16/0.42           => ( ( F3 @ A3 )
% 0.16/0.42              = ( G @ A3 ) ) )
% 0.16/0.42       => ( ( inj_on2112487900lle_tv @ F3 @ A2 )
% 0.16/0.42          = ( inj_on2112487900lle_tv @ G @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_cong
% 0.16/0.42  thf(fact_158_inj__on__cong,axiom,
% 0.16/0.42      ! [A2: set_Pr1725653840tv_nat,F3: produc194167194tv_nat > produc194167194tv_nat,G: produc194167194tv_nat > produc194167194tv_nat] :
% 0.16/0.42        ( ! [A3: produc194167194tv_nat] :
% 0.16/0.42            ( ( member737151281tv_nat @ A3 @ A2 )
% 0.16/0.42           => ( ( F3 @ A3 )
% 0.16/0.42              = ( G @ A3 ) ) )
% 0.16/0.42       => ( ( inj_on552895452tv_nat @ F3 @ A2 )
% 0.16/0.42          = ( inj_on552895452tv_nat @ G @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_cong
% 0.16/0.42  thf(fact_159_inj__on__cong,axiom,
% 0.16/0.42      ! [A2: set_Pr13445366lle_tv,F3: produc270694976lle_tv > produc270694976lle_tv,G: produc270694976lle_tv > produc270694976lle_tv] :
% 0.16/0.42        ( ! [A3: produc270694976lle_tv] :
% 0.16/0.42            ( ( member813679063lle_tv @ A3 @ A2 )
% 0.16/0.42           => ( ( F3 @ A3 )
% 0.16/0.42              = ( G @ A3 ) ) )
% 0.16/0.42       => ( ( inj_on1745913142lle_tv @ F3 @ A2 )
% 0.16/0.42          = ( inj_on1745913142lle_tv @ G @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_cong
% 0.16/0.42  thf(fact_160_inj__on__cong,axiom,
% 0.16/0.42      ! [A2: set_Pr1986765409at_nat,F3: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat] :
% 0.16/0.42        ( ! [A3: product_prod_nat_nat] :
% 0.16/0.42            ( ( member701585322at_nat @ A3 @ A2 )
% 0.16/0.42           => ( ( F3 @ A3 )
% 0.16/0.42              = ( G @ A3 ) ) )
% 0.16/0.42       => ( ( inj_on26176689at_nat @ F3 @ A2 )
% 0.16/0.42          = ( inj_on26176689at_nat @ G @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_cong
% 0.16/0.42  thf(fact_161_inj__on__cong,axiom,
% 0.16/0.42      ! [A2: set_nat,F3: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [A3: nat] :
% 0.16/0.42            ( ( member_nat @ A3 @ A2 )
% 0.16/0.42           => ( ( F3 @ A3 )
% 0.16/0.42              = ( G @ A3 ) ) )
% 0.16/0.42       => ( ( inj_on1955349912lle_tv @ F3 @ A2 )
% 0.16/0.42          = ( inj_on1955349912lle_tv @ G @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_cong
% 0.16/0.42  thf(fact_162_inj__on__cong,axiom,
% 0.16/0.42      ! [A2: set_nat,F3: nat > nat,G: nat > nat] :
% 0.16/0.42        ( ! [A3: nat] :
% 0.16/0.42            ( ( member_nat @ A3 @ A2 )
% 0.16/0.42           => ( ( F3 @ A3 )
% 0.16/0.42              = ( G @ A3 ) ) )
% 0.16/0.42       => ( ( inj_on_nat_nat @ F3 @ A2 )
% 0.16/0.42          = ( inj_on_nat_nat @ G @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_cong
% 0.16/0.42  thf(fact_163_inj__on__cong,axiom,
% 0.16/0.42      ! [A2: set_Pa1764573435lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [A3: paraco1605129243lle_tv] :
% 0.16/0.42            ( ( member266900804lle_tv @ A3 @ A2 )
% 0.16/0.42           => ( ( F3 @ A3 )
% 0.16/0.42              = ( G @ A3 ) ) )
% 0.16/0.42       => ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 0.16/0.42          = ( inj_on772319074lle_tv @ G @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_cong
% 0.16/0.42  thf(fact_164_inj__on__def,axiom,
% 0.16/0.42      ( inj_on_nat_nat
% 0.16/0.42      = ( ^ [F: nat > nat,A4: set_nat] :
% 0.16/0.42          ! [X2: nat] :
% 0.16/0.42            ( ( member_nat @ X2 @ A4 )
% 0.16/0.42           => ! [Y4: nat] :
% 0.16/0.42                ( ( member_nat @ Y4 @ A4 )
% 0.16/0.42               => ( ( ( F @ X2 )
% 0.16/0.42                    = ( F @ Y4 ) )
% 0.16/0.42                 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_def
% 0.16/0.42  thf(fact_165_inj__on__def,axiom,
% 0.16/0.42      ( inj_on772319074lle_tv
% 0.16/0.42      = ( ^ [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A4: set_Pa1764573435lle_tv] :
% 0.16/0.42          ! [X2: paraco1605129243lle_tv] :
% 0.16/0.42            ( ( member266900804lle_tv @ X2 @ A4 )
% 0.16/0.42           => ! [Y4: paraco1605129243lle_tv] :
% 0.16/0.42                ( ( member266900804lle_tv @ Y4 @ A4 )
% 0.16/0.42               => ( ( ( F @ X2 )
% 0.16/0.42                    = ( F @ Y4 ) )
% 0.16/0.42                 => ( X2 = Y4 ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_def
% 0.16/0.42  thf(fact_166_inj__onI,axiom,
% 0.16/0.42      ! [A2: set_nat,F3: nat > nat] :
% 0.16/0.42        ( ! [X4: nat,Y2: nat] :
% 0.16/0.42            ( ( member_nat @ X4 @ A2 )
% 0.16/0.42           => ( ( member_nat @ Y2 @ A2 )
% 0.16/0.42             => ( ( ( F3 @ X4 )
% 0.16/0.42                  = ( F3 @ Y2 ) )
% 0.16/0.42               => ( X4 = Y2 ) ) ) )
% 0.16/0.42       => ( inj_on_nat_nat @ F3 @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_onI
% 0.16/0.42  thf(fact_167_inj__onI,axiom,
% 0.16/0.42      ! [A2: set_Pa1764573435lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [X4: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
% 0.16/0.42            ( ( member266900804lle_tv @ X4 @ A2 )
% 0.16/0.42           => ( ( member266900804lle_tv @ Y2 @ A2 )
% 0.16/0.42             => ( ( ( F3 @ X4 )
% 0.16/0.42                  = ( F3 @ Y2 ) )
% 0.16/0.42               => ( X4 = Y2 ) ) ) )
% 0.16/0.42       => ( inj_on772319074lle_tv @ F3 @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_onI
% 0.16/0.42  thf(fact_168_inj__onD,axiom,
% 0.16/0.42      ! [F3: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ A2 )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42         => ( ( member_nat @ X @ A2 )
% 0.16/0.42           => ( ( member_nat @ Y @ A2 )
% 0.16/0.42             => ( X = Y ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_onD
% 0.16/0.42  thf(fact_169_inj__onD,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = ( F3 @ Y ) )
% 0.16/0.42         => ( ( member266900804lle_tv @ X @ A2 )
% 0.16/0.42           => ( ( member266900804lle_tv @ Y @ A2 )
% 0.16/0.42             => ( X = Y ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_onD
% 0.16/0.42  thf(fact_170_props_Oinduct,axiom,
% 0.16/0.42      ! [P3: paraco1604210848lle_fm > $o,A0: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( P3 @ paraco367965286_Truth )
% 0.16/0.42       => ( ! [S2: list_char] : ( P3 @ ( paraco1480028776le_Pro @ S2 ) )
% 0.16/0.42         => ( ! [P4: paraco1604210848lle_fm] :
% 0.16/0.42                ( ( P3 @ P4 )
% 0.16/0.42               => ( P3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 0.16/0.42           => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.16/0.42                  ( ( P3 @ P4 )
% 0.16/0.42                 => ( ( P3 @ Q3 )
% 0.16/0.42                   => ( P3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) ) )
% 0.16/0.42             => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.16/0.42                    ( ( P3 @ P4 )
% 0.16/0.42                   => ( ( P3 @ Q3 )
% 0.16/0.42                     => ( P3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) ) )
% 0.16/0.42               => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.16/0.42                      ( ( P3 @ P4 )
% 0.16/0.42                     => ( ( P3 @ Q3 )
% 0.16/0.42                       => ( P3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) )
% 0.16/0.42                 => ( P3 @ A0 ) ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % props.induct
% 0.16/0.42  thf(fact_171_eval_Ocases,axiom,
% 0.16/0.42      ! [X: produc696645085lle_fm] :
% 0.16/0.42        ( ! [I3: list_char > paraco1605129243lle_tv,S2: list_char] :
% 0.16/0.42            ( X
% 0.16/0.42           != ( produc1710735575lle_fm @ I3 @ ( paraco1480028776le_Pro @ S2 ) ) )
% 0.16/0.42       => ( ! [I3: list_char > paraco1605129243lle_tv] :
% 0.16/0.42              ( X
% 0.16/0.42             != ( produc1710735575lle_fm @ I3 @ paraco367965286_Truth ) )
% 0.16/0.42         => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm] :
% 0.16/0.42                ( X
% 0.16/0.42               != ( produc1710735575lle_fm @ I3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 0.16/0.42           => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.16/0.42                  ( X
% 0.16/0.42                 != ( produc1710735575lle_fm @ I3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) )
% 0.16/0.42             => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.16/0.42                    ( X
% 0.16/0.42                   != ( produc1710735575lle_fm @ I3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) )
% 0.16/0.42               => ~ ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.16/0.42                      ( X
% 0.16/0.42                     != ( produc1710735575lle_fm @ I3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % eval.cases
% 0.16/0.42  thf(fact_172_top__empty__eq,axiom,
% 0.16/0.42      ( top_top_nat_o
% 0.16/0.42      = ( ^ [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % top_empty_eq
% 0.16/0.42  thf(fact_173_top__empty__eq,axiom,
% 0.16/0.42      ( top_to1299250770e_tv_o
% 0.16/0.42      = ( ^ [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ top_to1057771083lle_tv ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % top_empty_eq
% 0.16/0.42  thf(fact_174_change__tv_Oelims,axiom,
% 0.16/0.42      ! [X: nat > nat,Xa: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( paraco1147068288nge_tv @ X @ Xa )
% 0.16/0.42          = Y )
% 0.16/0.42       => ( ! [B2: $o] :
% 0.16/0.42              ( ( Xa
% 0.16/0.42                = ( paraco1344940915le_Det @ B2 ) )
% 0.16/0.42             => ( Y
% 0.16/0.42               != ( paraco1344940915le_Det @ B2 ) ) )
% 0.16/0.42         => ~ ! [N: nat] :
% 0.16/0.42                ( ( Xa
% 0.16/0.42                  = ( paraco793048302_Indet @ N ) )
% 0.16/0.42               => ( Y
% 0.16/0.42                 != ( paraco793048302_Indet @ ( X @ N ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % change_tv.elims
% 0.16/0.42  thf(fact_175_valid__valid__in,axiom,
% 0.16/0.42      ! [P2: paraco1604210848lle_fm,U: set_nat] :
% 0.16/0.42        ( ( paraco327635598_valid @ P2 )
% 0.16/0.42       => ( paraco55203475lid_in @ U @ P2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % valid_valid_in
% 0.16/0.42  thf(fact_176_transfer,axiom,
% 0.16/0.42      ! [U: set_nat,P2: paraco1604210848lle_fm] :
% 0.16/0.42        ( ~ ( paraco55203475lid_in @ U @ P2 )
% 0.16/0.42       => ~ ( paraco327635598_valid @ P2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % transfer
% 0.16/0.42  thf(fact_177_the__inv__f__f,axiom,
% 0.16/0.42      ! [F3: nat > nat,X: nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42       => ( ( the_inv_into_nat_nat @ top_top_set_nat @ F3 @ ( F3 @ X ) )
% 0.16/0.42          = X ) ) ).
% 0.16/0.42  
% 0.16/0.42  % the_inv_f_f
% 0.16/0.42  thf(fact_178_the__inv__f__f,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42       => ( ( the_in452116896lle_tv @ top_to1057771083lle_tv @ F3 @ ( F3 @ X ) )
% 0.16/0.42          = X ) ) ).
% 0.16/0.42  
% 0.16/0.42  % the_inv_f_f
% 0.16/0.42  thf(fact_179_conjunction__in,axiom,
% 0.16/0.42      ! [U: set_nat,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco55203475lid_in @ U @ ( paraco69239110le_Con @ P2 @ Q ) )
% 0.16/0.42        = ( ( paraco55203475lid_in @ U @ P2 )
% 0.16/0.42          & ( paraco55203475lid_in @ U @ Q ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % conjunction_in
% 0.16/0.42  thf(fact_180_tv_Oinject_I2_J,axiom,
% 0.16/0.42      ! [X23: nat,Y22: nat] :
% 0.16/0.42        ( ( ( paraco793048302_Indet @ X23 )
% 0.16/0.42          = ( paraco793048302_Indet @ Y22 ) )
% 0.16/0.42        = ( X23 = Y22 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % tv.inject(2)
% 0.16/0.42  thf(fact_181_string__tv_Oinduct,axiom,
% 0.16/0.42      ! [P3: paraco1605129243lle_tv > $o,A0: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( P3 @ ( paraco1344940915le_Det @ $true ) )
% 0.16/0.42       => ( ( P3 @ ( paraco1344940915le_Det @ $false ) )
% 0.16/0.42         => ( ! [N: nat] : ( P3 @ ( paraco793048302_Indet @ N ) )
% 0.16/0.42           => ( P3 @ A0 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % string_tv.induct
% 0.16/0.42  thf(fact_182_change__tv_Oinduct,axiom,
% 0.16/0.42      ! [P3: ( nat > nat ) > paraco1605129243lle_tv > $o,A0: nat > nat,A1: paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [F4: nat > nat,B2: $o] : ( P3 @ F4 @ ( paraco1344940915le_Det @ B2 ) )
% 0.16/0.42       => ( ! [F4: nat > nat,N: nat] : ( P3 @ F4 @ ( paraco793048302_Indet @ N ) )
% 0.16/0.42         => ( P3 @ A0 @ A1 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % change_tv.induct
% 0.16/0.42  thf(fact_183_string__tv_Ocases,axiom,
% 0.16/0.42      ! [X: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( X
% 0.16/0.42         != ( paraco1344940915le_Det @ $true ) )
% 0.16/0.42       => ( ( X
% 0.16/0.42           != ( paraco1344940915le_Det @ $false ) )
% 0.16/0.42         => ~ ! [N: nat] :
% 0.16/0.42                ( X
% 0.16/0.42               != ( paraco793048302_Indet @ N ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % string_tv.cases
% 0.16/0.42  thf(fact_184_tv_Oexhaust,axiom,
% 0.16/0.42      ! [Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [X12: $o] :
% 0.16/0.42            ( Y
% 0.16/0.42           != ( paraco1344940915le_Det @ X12 ) )
% 0.16/0.42       => ~ ! [X22: nat] :
% 0.16/0.42              ( Y
% 0.16/0.42             != ( paraco793048302_Indet @ X22 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % tv.exhaust
% 0.16/0.42  thf(fact_185_tv_Oinduct,axiom,
% 0.16/0.42      ! [P3: paraco1605129243lle_tv > $o,Tv: paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [X4: $o] : ( P3 @ ( paraco1344940915le_Det @ X4 ) )
% 0.16/0.42       => ( ! [X4: nat] : ( P3 @ ( paraco793048302_Indet @ X4 ) )
% 0.16/0.42         => ( P3 @ Tv ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % tv.induct
% 0.16/0.42  thf(fact_186_tv_Odistinct_I1_J,axiom,
% 0.16/0.42      ! [X1: $o,X23: nat] :
% 0.16/0.42        ( ( paraco1344940915le_Det @ X1 )
% 0.16/0.42       != ( paraco793048302_Indet @ X23 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % tv.distinct(1)
% 0.16/0.42  thf(fact_187_the__inv__into__f__f,axiom,
% 0.16/0.42      ! [F3: nat > nat,A2: set_nat,X: nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ A2 )
% 0.16/0.42       => ( ( member_nat @ X @ A2 )
% 0.16/0.42         => ( ( the_inv_into_nat_nat @ A2 @ F3 @ ( F3 @ X ) )
% 0.16/0.42            = X ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % the_inv_into_f_f
% 0.16/0.42  thf(fact_188_the__inv__into__f__f,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( member266900804lle_tv @ X @ A2 )
% 0.16/0.42         => ( ( the_in452116896lle_tv @ A2 @ F3 @ ( F3 @ X ) )
% 0.16/0.42            = X ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % the_inv_into_f_f
% 0.16/0.42  thf(fact_189_the__inv__into__f__eq,axiom,
% 0.16/0.42      ! [F3: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ A2 )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = Y )
% 0.16/0.42         => ( ( member_nat @ X @ A2 )
% 0.16/0.42           => ( ( the_inv_into_nat_nat @ A2 @ F3 @ Y )
% 0.16/0.42              = X ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % the_inv_into_f_eq
% 0.16/0.42  thf(fact_190_the__inv__into__f__eq,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( ( F3 @ X )
% 0.16/0.42            = Y )
% 0.16/0.42         => ( ( member266900804lle_tv @ X @ A2 )
% 0.16/0.42           => ( ( the_in452116896lle_tv @ A2 @ F3 @ Y )
% 0.16/0.42              = X ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % the_inv_into_f_eq
% 0.16/0.42  thf(fact_191_tv_Osimps_I6_J,axiom,
% 0.16/0.42      ! [F1: $o > paraco1605129243lle_tv,F2: nat > paraco1605129243lle_tv,X23: nat] :
% 0.16/0.42        ( ( paraco2051596139lle_tv @ F1 @ F2 @ ( paraco793048302_Indet @ X23 ) )
% 0.16/0.42        = ( F2 @ X23 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % tv.simps(6)
% 0.16/0.42  thf(fact_192_change__tv_Osimps_I2_J,axiom,
% 0.16/0.42      ! [F3: nat > nat,N2: nat] :
% 0.16/0.42        ( ( paraco1147068288nge_tv @ F3 @ ( paraco793048302_Indet @ N2 ) )
% 0.16/0.42        = ( paraco793048302_Indet @ ( F3 @ N2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % change_tv.simps(2)
% 0.16/0.42  thf(fact_193_prod_Oinject,axiom,
% 0.16/0.42      ! [X1: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm,Y1: list_char > paraco1605129243lle_tv,Y22: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( ( produc1710735575lle_fm @ X1 @ X23 )
% 0.16/0.42          = ( produc1710735575lle_fm @ Y1 @ Y22 ) )
% 0.16/0.42        = ( ( X1 = Y1 )
% 0.16/0.42          & ( X23 = Y22 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod.inject
% 0.16/0.42  thf(fact_194_prod_Oinject,axiom,
% 0.16/0.42      ! [X1: nat > nat,X23: paraco1605129243lle_tv,Y1: nat > nat,Y22: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( produc1680557635lle_tv @ X1 @ X23 )
% 0.16/0.42          = ( produc1680557635lle_tv @ Y1 @ Y22 ) )
% 0.16/0.42        = ( ( X1 = Y1 )
% 0.16/0.42          & ( X23 = Y22 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod.inject
% 0.16/0.42  thf(fact_195_old_Oprod_Oinject,axiom,
% 0.16/0.42      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( ( produc1710735575lle_fm @ A @ B )
% 0.16/0.42          = ( produc1710735575lle_fm @ A5 @ B3 ) )
% 0.16/0.42        = ( ( A = A5 )
% 0.16/0.42          & ( B = B3 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % old.prod.inject
% 0.16/0.42  thf(fact_196_old_Oprod_Oinject,axiom,
% 0.16/0.42      ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( produc1680557635lle_tv @ A @ B )
% 0.16/0.42          = ( produc1680557635lle_tv @ A5 @ B3 ) )
% 0.16/0.42        = ( ( A = A5 )
% 0.16/0.42          & ( B = B3 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % old.prod.inject
% 0.16/0.42  thf(fact_197_eval_Osimps_I3_J,axiom,
% 0.16/0.42      ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 0.16/0.42        = ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1344940915le_Det @ $false ) @ ( paraco1344940915le_Det @ $true ) ) @ paraco793048302_Indet @ ( paraco1325918602e_eval @ I2 @ P2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % eval.simps(3)
% 0.16/0.42  thf(fact_198_surj__pair,axiom,
% 0.16/0.42      ! [P2: produc696645085lle_fm] :
% 0.16/0.42      ? [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 0.16/0.42        ( P2
% 0.16/0.42        = ( produc1710735575lle_fm @ X4 @ Y2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surj_pair
% 0.16/0.42  thf(fact_199_surj__pair,axiom,
% 0.16/0.42      ! [P2: produc931990033lle_tv] :
% 0.16/0.42      ? [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 0.16/0.42        ( P2
% 0.16/0.42        = ( produc1680557635lle_tv @ X4 @ Y2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surj_pair
% 0.16/0.42  thf(fact_200_bool_Osplit__sel__asm,axiom,
% 0.16/0.42      ! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv,Bool: $o] :
% 0.16/0.42        ( ( P3 @ ( produc234482697lle_tv @ F1 @ F2 @ Bool ) )
% 0.16/0.42        = ( ~ ( ( Bool
% 0.16/0.42                & ~ ( P3 @ F1 ) )
% 0.16/0.42              | ( ~ Bool
% 0.16/0.42                & ~ ( P3 @ F2 ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % bool.split_sel_asm
% 0.16/0.42  thf(fact_201_bool_Ocase__distrib,axiom,
% 0.16/0.42      ! [H: paraco1605129243lle_tv > paraco1605129243lle_tv,F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv,Bool: $o] :
% 0.16/0.42        ( ( H @ ( produc234482697lle_tv @ F1 @ F2 @ Bool ) )
% 0.16/0.42        = ( produc234482697lle_tv @ ( H @ F1 ) @ ( H @ F2 ) @ Bool ) ) ).
% 0.16/0.42  
% 0.16/0.42  % bool.case_distrib
% 0.16/0.42  thf(fact_202_bool_Ocase__eq__if,axiom,
% 0.16/0.42      ( produc234482697lle_tv
% 0.16/0.42      = ( ^ [F12: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool2: $o] : ( if_Par1134130401lle_tv @ Bool2 @ F12 @ F22 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % bool.case_eq_if
% 0.16/0.42  thf(fact_203_bool_Osplit__sel,axiom,
% 0.16/0.42      ! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv,Bool: $o] :
% 0.16/0.42        ( ( P3 @ ( produc234482697lle_tv @ F1 @ F2 @ Bool ) )
% 0.16/0.42        = ( ( Bool
% 0.16/0.42           => ( P3 @ F1 ) )
% 0.16/0.42          & ( ~ Bool
% 0.16/0.42           => ( P3 @ F2 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % bool.split_sel
% 0.16/0.42  thf(fact_204_old_Obool_Osimps_I3_J,axiom,
% 0.16/0.42      ! [F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( produc234482697lle_tv @ F1 @ F2 @ $true )
% 0.16/0.42        = F1 ) ).
% 0.16/0.42  
% 0.16/0.42  % old.bool.simps(3)
% 0.16/0.42  thf(fact_205_old_Obool_Osimps_I4_J,axiom,
% 0.16/0.42      ! [F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( produc234482697lle_tv @ F1 @ F2 @ $false )
% 0.16/0.42        = F2 ) ).
% 0.16/0.42  
% 0.16/0.42  % old.bool.simps(4)
% 0.16/0.42  thf(fact_206_change__tv_Ocases,axiom,
% 0.16/0.42      ! [X: produc931990033lle_tv] :
% 0.16/0.42        ( ! [F4: nat > nat,B2: $o] :
% 0.16/0.42            ( X
% 0.16/0.42           != ( produc1680557635lle_tv @ F4 @ ( paraco1344940915le_Det @ B2 ) ) )
% 0.16/0.42       => ~ ! [F4: nat > nat,N: nat] :
% 0.16/0.42              ( X
% 0.16/0.42             != ( produc1680557635lle_tv @ F4 @ ( paraco793048302_Indet @ N ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % change_tv.cases
% 0.16/0.42  thf(fact_207_old_Oprod_Oinducts,axiom,
% 0.16/0.42      ! [P3: produc696645085lle_fm > $o,Prod: produc696645085lle_fm] :
% 0.16/0.42        ( ! [A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A3 @ B2 ) )
% 0.16/0.42       => ( P3 @ Prod ) ) ).
% 0.16/0.42  
% 0.16/0.42  % old.prod.inducts
% 0.16/0.42  thf(fact_208_old_Oprod_Oinducts,axiom,
% 0.16/0.42      ! [P3: produc931990033lle_tv > $o,Prod: produc931990033lle_tv] :
% 0.16/0.42        ( ! [A3: nat > nat,B2: paraco1605129243lle_tv] : ( P3 @ ( produc1680557635lle_tv @ A3 @ B2 ) )
% 0.16/0.42       => ( P3 @ Prod ) ) ).
% 0.16/0.42  
% 0.16/0.42  % old.prod.inducts
% 0.16/0.42  thf(fact_209_old_Oprod_Oexhaust,axiom,
% 0.16/0.42      ! [Y: produc696645085lle_fm] :
% 0.16/0.42        ~ ! [A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] :
% 0.16/0.42            ( Y
% 0.16/0.42           != ( produc1710735575lle_fm @ A3 @ B2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % old.prod.exhaust
% 0.16/0.42  thf(fact_210_old_Oprod_Oexhaust,axiom,
% 0.16/0.42      ! [Y: produc931990033lle_tv] :
% 0.16/0.42        ~ ! [A3: nat > nat,B2: paraco1605129243lle_tv] :
% 0.16/0.42            ( Y
% 0.16/0.42           != ( produc1680557635lle_tv @ A3 @ B2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % old.prod.exhaust
% 0.16/0.42  thf(fact_211_Pair__inject,axiom,
% 0.16/0.42      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( ( produc1710735575lle_fm @ A @ B )
% 0.16/0.42          = ( produc1710735575lle_fm @ A5 @ B3 ) )
% 0.16/0.42       => ~ ( ( A = A5 )
% 0.16/0.42           => ( B != B3 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % Pair_inject
% 0.16/0.42  thf(fact_212_Pair__inject,axiom,
% 0.16/0.42      ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( produc1680557635lle_tv @ A @ B )
% 0.16/0.42          = ( produc1680557635lle_tv @ A5 @ B3 ) )
% 0.16/0.42       => ~ ( ( A = A5 )
% 0.16/0.42           => ( B != B3 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % Pair_inject
% 0.16/0.42  thf(fact_213_prod__cases,axiom,
% 0.16/0.42      ! [P3: produc696645085lle_fm > $o,P2: produc696645085lle_fm] :
% 0.16/0.42        ( ! [A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A3 @ B2 ) )
% 0.16/0.42       => ( P3 @ P2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod_cases
% 0.16/0.42  thf(fact_214_prod__cases,axiom,
% 0.16/0.42      ! [P3: produc931990033lle_tv > $o,P2: produc931990033lle_tv] :
% 0.16/0.42        ( ! [A3: nat > nat,B2: paraco1605129243lle_tv] : ( P3 @ ( produc1680557635lle_tv @ A3 @ B2 ) )
% 0.16/0.42       => ( P3 @ P2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod_cases
% 0.16/0.42  thf(fact_215_ssubst__Pair__rhs,axiom,
% 0.16/0.42      ! [R: list_char > paraco1605129243lle_tv,S3: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,S4: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S3 ) @ R2 )
% 0.16/0.42       => ( ( S4 = S3 )
% 0.16/0.42         => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S4 ) @ R2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % ssubst_Pair_rhs
% 0.16/0.42  thf(fact_216_ssubst__Pair__rhs,axiom,
% 0.16/0.42      ! [R: nat > nat,S3: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,S4: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ R @ S3 ) @ R2 )
% 0.16/0.42       => ( ( S4 = S3 )
% 0.16/0.42         => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ R @ S4 ) @ R2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % ssubst_Pair_rhs
% 0.16/0.42  thf(fact_217_apfst__conv,axiom,
% 0.16/0.42      ! [F3: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( produc1942165868lle_fm @ F3 @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.16/0.42        = ( produc1710735575lle_fm @ ( F3 @ X ) @ Y ) ) ).
% 0.16/0.42  
% 0.16/0.42  % apfst_conv
% 0.16/0.42  thf(fact_218_apfst__conv,axiom,
% 0.16/0.42      ! [F3: ( nat > nat ) > nat > nat,X: nat > nat,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( produc939316703lle_tv @ F3 @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.16/0.42        = ( produc1680557635lle_tv @ ( F3 @ X ) @ Y ) ) ).
% 0.16/0.42  
% 0.16/0.42  % apfst_conv
% 0.16/0.42  thf(fact_219_apsnd__conv,axiom,
% 0.16/0.42      ! [F3: paraco1604210848lle_fm > paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( produc1807466521lle_tv @ F3 @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.16/0.42        = ( produc1710735575lle_fm @ X @ ( F3 @ Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % apsnd_conv
% 0.16/0.42  thf(fact_220_apsnd__conv,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,X: nat > nat,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( produc109093078at_nat @ F3 @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.16/0.42        = ( produc1680557635lle_tv @ X @ ( F3 @ Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % apsnd_conv
% 0.16/0.42  thf(fact_221_change__tv_Opelims,axiom,
% 0.16/0.42      ! [X: nat > nat,Xa: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( paraco1147068288nge_tv @ X @ Xa )
% 0.16/0.42          = Y )
% 0.16/0.42       => ( ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ Xa ) )
% 0.16/0.42         => ( ! [B2: $o] :
% 0.16/0.42                ( ( Xa
% 0.16/0.42                  = ( paraco1344940915le_Det @ B2 ) )
% 0.16/0.42               => ( ( Y
% 0.16/0.42                    = ( paraco1344940915le_Det @ B2 ) )
% 0.16/0.42                 => ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ ( paraco1344940915le_Det @ B2 ) ) ) ) )
% 0.16/0.42           => ~ ! [N: nat] :
% 0.16/0.42                  ( ( Xa
% 0.16/0.42                    = ( paraco793048302_Indet @ N ) )
% 0.16/0.42                 => ( ( Y
% 0.16/0.42                      = ( paraco793048302_Indet @ ( X @ N ) ) )
% 0.16/0.42                   => ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ ( paraco793048302_Indet @ N ) ) ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % change_tv.pelims
% 0.16/0.42  thf(fact_222_prod_Oinj__map,axiom,
% 0.16/0.42      ! [F1: nat > nat,F2: nat > nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 0.16/0.42       => ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.16/0.42         => ( inj_on26176689at_nat @ ( produc505105722at_nat @ F1 @ F2 ) @ top_to1555900337at_nat ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod.inj_map
% 0.16/0.42  thf(fact_223_prod_Oinj__map,axiom,
% 0.16/0.42      ! [F1: nat > nat,F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 0.16/0.42       => ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.16/0.42         => ( inj_on1745913142lle_tv @ ( produc2101297531lle_tv @ F1 @ F2 ) @ top_to1411004326lle_tv ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod.inj_map
% 0.16/0.42  thf(fact_224_prod_Oinj__map,axiom,
% 0.16/0.42      ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F2: nat > nat] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 0.16/0.42       => ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 0.16/0.42         => ( inj_on552895452tv_nat @ ( produc42536895at_nat @ F1 @ F2 ) @ top_to975729152tv_nat ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod.inj_map
% 0.16/0.42  thf(fact_225_prod_Oinj__map,axiom,
% 0.16/0.42      ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 0.16/0.42       => ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 0.16/0.42         => ( inj_on2112487900lle_tv @ ( produc1345917071lle_tv @ F1 @ F2 ) @ top_to1871154984lle_tv ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod.inj_map
% 0.16/0.42  thf(fact_226_curryI,axiom,
% 0.16/0.42      ! [F3: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( F3 @ ( produc1710735575lle_fm @ A @ B ) )
% 0.16/0.42       => ( produc275353523e_fm_o @ F3 @ A @ B ) ) ).
% 0.16/0.42  
% 0.16/0.42  % curryI
% 0.16/0.42  thf(fact_227_curryI,axiom,
% 0.16/0.42      ! [F3: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( F3 @ ( produc1680557635lle_tv @ A @ B ) )
% 0.16/0.42       => ( produc752649287e_tv_o @ F3 @ A @ B ) ) ).
% 0.16/0.42  
% 0.16/0.42  % curryI
% 0.16/0.42  thf(fact_228_map__prod__simp,axiom,
% 0.16/0.42      ! [F3: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( produc1900967599lle_fm @ F3 @ G @ ( produc1710735575lle_fm @ A @ B ) )
% 0.16/0.42        = ( produc1710735575lle_fm @ ( F3 @ A ) @ ( G @ B ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_simp
% 0.16/0.42  thf(fact_229_map__prod__simp,axiom,
% 0.16/0.42      ! [F3: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( produc1566550641lle_tv @ F3 @ G @ ( produc1710735575lle_fm @ A @ B ) )
% 0.16/0.42        = ( produc1680557635lle_tv @ ( F3 @ A ) @ ( G @ B ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_simp
% 0.16/0.42  thf(fact_230_map__prod__simp,axiom,
% 0.16/0.42      ! [F3: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( produc951033137lle_fm @ F3 @ G @ ( produc1680557635lle_tv @ A @ B ) )
% 0.16/0.42        = ( produc1710735575lle_fm @ ( F3 @ A ) @ ( G @ B ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_simp
% 0.16/0.42  thf(fact_231_map__prod__simp,axiom,
% 0.16/0.42      ! [F3: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( produc532909085lle_tv @ F3 @ G @ ( produc1680557635lle_tv @ A @ B ) )
% 0.16/0.42        = ( produc1680557635lle_tv @ ( F3 @ A ) @ ( G @ B ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_simp
% 0.16/0.42  thf(fact_232_curryD,axiom,
% 0.16/0.42      ! [F3: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( produc275353523e_fm_o @ F3 @ A @ B )
% 0.16/0.42       => ( F3 @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % curryD
% 0.16/0.42  thf(fact_233_curryD,axiom,
% 0.16/0.42      ! [F3: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( produc752649287e_tv_o @ F3 @ A @ B )
% 0.16/0.42       => ( F3 @ ( produc1680557635lle_tv @ A @ B ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % curryD
% 0.16/0.42  thf(fact_234_curryE,axiom,
% 0.16/0.42      ! [F3: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( produc275353523e_fm_o @ F3 @ A @ B )
% 0.16/0.42       => ( F3 @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % curryE
% 0.16/0.42  thf(fact_235_curryE,axiom,
% 0.16/0.42      ! [F3: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( produc752649287e_tv_o @ F3 @ A @ B )
% 0.16/0.42       => ( F3 @ ( produc1680557635lle_tv @ A @ B ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % curryE
% 0.16/0.42  thf(fact_236_the__inv__into__onto,axiom,
% 0.16/0.42      ! [F3: nat > nat,A2: set_nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ A2 )
% 0.16/0.42       => ( ( image_nat_nat @ ( the_inv_into_nat_nat @ A2 @ F3 ) @ ( image_nat_nat @ F3 @ A2 ) )
% 0.16/0.42          = A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % the_inv_into_onto
% 0.16/0.42  thf(fact_237_the__inv__into__onto,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( image_335818702lle_tv @ ( the_in452116896lle_tv @ A2 @ F3 ) @ ( image_335818702lle_tv @ F3 @ A2 ) )
% 0.16/0.42          = A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % the_inv_into_onto
% 0.16/0.42  thf(fact_238_map__prod__imageI,axiom,
% 0.16/0.42      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm] :
% 0.16/0.42        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
% 0.16/0.42       => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F3 @ A ) @ ( G @ B ) ) @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F3 @ G ) @ R2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_imageI
% 0.16/0.42  thf(fact_239_map__prod__imageI,axiom,
% 0.16/0.42      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
% 0.16/0.42       => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ ( F3 @ A ) @ ( G @ B ) ) @ ( image_1154804148lle_tv @ ( produc1566550641lle_tv @ F3 @ G ) @ R2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_imageI
% 0.16/0.42  thf(fact_240_map__prod__imageI,axiom,
% 0.16/0.42      ! [A: nat > nat,B: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,F3: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm] :
% 0.16/0.42        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ R2 )
% 0.16/0.42       => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F3 @ A ) @ ( G @ B ) ) @ ( image_1585092542lle_fm @ ( produc951033137lle_fm @ F3 @ G ) @ R2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_imageI
% 0.16/0.42  thf(fact_241_map__prod__imageI,axiom,
% 0.16/0.42      ! [A: nat > nat,B: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,F3: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ R2 )
% 0.16/0.42       => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ ( F3 @ A ) @ ( G @ B ) ) @ ( image_1751508608lle_tv @ ( produc532909085lle_tv @ F3 @ G ) @ R2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_imageI
% 0.16/0.42  thf(fact_242_swap__simp,axiom,
% 0.16/0.42      ! [X: paraco1604210848lle_fm,Y: list_char > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( produc1232814113lle_tv @ ( produc1943344577lle_tv @ X @ Y ) )
% 0.16/0.42        = ( produc1710735575lle_fm @ Y @ X ) ) ).
% 0.16/0.42  
% 0.16/0.42  % swap_simp
% 0.16/0.42  thf(fact_243_swap__simp,axiom,
% 0.16/0.42      ! [X: paraco1605129243lle_tv,Y: nat > nat] :
% 0.16/0.42        ( ( produc178635363at_nat @ ( produc1633679363at_nat @ X @ Y ) )
% 0.16/0.42        = ( produc1680557635lle_tv @ Y @ X ) ) ).
% 0.16/0.42  
% 0.16/0.42  % swap_simp
% 0.16/0.42  thf(fact_244_swap__simp,axiom,
% 0.16/0.42      ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 0.16/0.42        ( ( produc1000205111lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.16/0.42        = ( produc1943344577lle_tv @ Y @ X ) ) ).
% 0.16/0.42  
% 0.16/0.42  % swap_simp
% 0.16/0.42  thf(fact_245_swap__simp,axiom,
% 0.16/0.42      ! [X: nat > nat,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( produc225513635lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.16/0.42        = ( produc1633679363at_nat @ Y @ X ) ) ).
% 0.16/0.42  
% 0.16/0.42  % swap_simp
% 0.16/0.42  thf(fact_246_pair__in__swap__image,axiom,
% 0.16/0.42      ! [Y: paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv,A2: set_Pr2120184979lle_fm] :
% 0.16/0.42        ( ( member74361182lle_tv @ ( produc1943344577lle_tv @ Y @ X ) @ ( image_924970994lle_tv @ produc1000205111lle_fm @ A2 ) )
% 0.16/0.42        = ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X @ Y ) @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % pair_in_swap_image
% 0.16/0.42  thf(fact_247_pair__in__swap__image,axiom,
% 0.16/0.42      ! [Y: paraco1605129243lle_tv,X: nat > nat,A2: set_Pr560526279lle_tv] :
% 0.16/0.42        ( ( member1234290208at_nat @ ( produc1633679363at_nat @ Y @ X ) @ ( image_1724396928at_nat @ produc225513635lle_tv @ A2 ) )
% 0.16/0.42        = ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X @ Y ) @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % pair_in_swap_image
% 0.16/0.42  thf(fact_248_pair__in__swap__image,axiom,
% 0.16/0.42      ! [Y: list_char > paraco1605129243lle_tv,X: paraco1604210848lle_fm,A2: set_Pr1723822845lle_tv] :
% 0.16/0.42        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ Y @ X ) @ ( image_326034184lle_fm @ produc1232814113lle_tv @ A2 ) )
% 0.16/0.42        = ( member74361182lle_tv @ ( produc1943344577lle_tv @ X @ Y ) @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % pair_in_swap_image
% 0.16/0.42  thf(fact_249_pair__in__swap__image,axiom,
% 0.16/0.42      ! [Y: nat > nat,X: paraco1605129243lle_tv,A2: set_Pr840833727at_nat] :
% 0.16/0.42        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ Y @ X ) @ ( image_769496456lle_tv @ produc178635363at_nat @ A2 ) )
% 0.16/0.42        = ( member1234290208at_nat @ ( produc1633679363at_nat @ X @ Y ) @ A2 ) ) ).
% 0.16/0.42  
% 0.16/0.42  % pair_in_swap_image
% 0.16/0.42  thf(fact_250_map__prod__surj,axiom,
% 0.16/0.42      ! [F3: nat > nat,G: nat > nat] :
% 0.16/0.42        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_top_set_nat )
% 0.16/0.42       => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.16/0.42            = top_top_set_nat )
% 0.16/0.42         => ( ( image_815163717at_nat @ ( produc505105722at_nat @ F3 @ G ) @ top_to1555900337at_nat )
% 0.16/0.42            = top_to1555900337at_nat ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_surj
% 0.16/0.42  thf(fact_251_map__prod__surj,axiom,
% 0.16/0.42      ! [F3: nat > nat,G: nat > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_top_set_nat )
% 0.16/0.42       => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.16/0.42            = top_to1057771083lle_tv )
% 0.16/0.42         => ( ( image_1674248956lle_tv @ ( produc313957681lle_tv @ F3 @ G ) @ top_to1555900337at_nat )
% 0.16/0.42            = top_to1411004326lle_tv ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_surj
% 0.16/0.42  thf(fact_252_map__prod__surj,axiom,
% 0.16/0.42      ! [F3: nat > nat,G: paraco1605129243lle_tv > nat] :
% 0.16/0.42        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_top_set_nat )
% 0.16/0.42       => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.16/0.42            = top_top_set_nat )
% 0.16/0.42         => ( ( image_1787705850at_nat @ ( produc1685803475tv_nat @ F3 @ G ) @ top_to1411004326lle_tv )
% 0.16/0.42            = top_to1555900337at_nat ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_surj
% 0.16/0.42  thf(fact_253_map__prod__surj,axiom,
% 0.16/0.42      ! [F3: nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_top_set_nat )
% 0.16/0.42       => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.16/0.42            = top_to1057771083lle_tv )
% 0.16/0.42         => ( ( image_149830562lle_tv @ ( produc2101297531lle_tv @ F3 @ G ) @ top_to1411004326lle_tv )
% 0.16/0.42            = top_to1411004326lle_tv ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_surj
% 0.16/0.42  thf(fact_254_map__prod__surj,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv,G: nat > nat] :
% 0.16/0.42        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_to1057771083lle_tv )
% 0.16/0.42       => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.16/0.42            = top_top_set_nat )
% 0.16/0.42         => ( ( image_1597721174tv_nat @ ( produc1250721397at_nat @ F3 @ G ) @ top_to1555900337at_nat )
% 0.16/0.42            = top_to975729152tv_nat ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_surj
% 0.16/0.42  thf(fact_255_map__prod__surj,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_to1057771083lle_tv )
% 0.16/0.42       => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.16/0.42            = top_to1057771083lle_tv )
% 0.16/0.42         => ( ( image_1507992062lle_tv @ ( produc210389789lle_tv @ F3 @ G ) @ top_to1555900337at_nat )
% 0.16/0.42            = top_to1871154984lle_tv ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_surj
% 0.16/0.42  thf(fact_256_map__prod__surj,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > nat] :
% 0.16/0.42        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_to1057771083lle_tv )
% 0.16/0.42       => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.16/0.42            = top_top_set_nat )
% 0.16/0.42         => ( ( image_53754658tv_nat @ ( produc189459613tv_nat @ F3 @ G ) @ top_to1411004326lle_tv )
% 0.16/0.42            = top_to975729152tv_nat ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_surj
% 0.16/0.42  thf(fact_257_map__prod__surj,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_to1057771083lle_tv )
% 0.16/0.42       => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.16/0.42            = top_to1057771083lle_tv )
% 0.16/0.42         => ( ( image_988201162lle_tv @ ( produc1975500101lle_tv @ F3 @ G ) @ top_to1411004326lle_tv )
% 0.16/0.42            = top_to1871154984lle_tv ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_surj
% 0.16/0.42  thf(fact_258_map__prod__surj,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > nat,G: nat > nat] :
% 0.16/0.42        ( ( ( image_376325286tv_nat @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42          = top_top_set_nat )
% 0.16/0.42       => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.16/0.42            = top_top_set_nat )
% 0.16/0.42         => ( ( image_1805124128at_nat @ ( produc386540311at_nat @ F3 @ G ) @ top_to975729152tv_nat )
% 0.16/0.42            = top_to1555900337at_nat ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_surj
% 0.16/0.42  thf(fact_259_map__prod__surj,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > nat,G: nat > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( image_376325286tv_nat @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42          = top_top_set_nat )
% 0.16/0.42       => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.16/0.42            = top_to1057771083lle_tv )
% 0.16/0.42         => ( ( image_1200372424lle_tv @ ( produc72207551lle_tv @ F3 @ G ) @ top_to975729152tv_nat )
% 0.16/0.42            = top_to1411004326lle_tv ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % map_prod_surj
% 0.16/0.42  thf(fact_260_inj__on__image__iff,axiom,
% 0.16/0.42      ! [A2: set_nat,G: nat > nat,F3: nat > nat] :
% 0.16/0.42        ( ! [X4: nat] :
% 0.16/0.42            ( ( member_nat @ X4 @ A2 )
% 0.16/0.42           => ! [Xa2: nat] :
% 0.16/0.42                ( ( member_nat @ Xa2 @ A2 )
% 0.16/0.42               => ( ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42                    = ( G @ ( F3 @ Xa2 ) ) )
% 0.16/0.42                  = ( ( G @ X4 )
% 0.16/0.42                    = ( G @ Xa2 ) ) ) ) )
% 0.16/0.42       => ( ( inj_on_nat_nat @ F3 @ A2 )
% 0.16/0.42         => ( ( inj_on_nat_nat @ G @ ( image_nat_nat @ F3 @ A2 ) )
% 0.16/0.42            = ( inj_on_nat_nat @ G @ A2 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_image_iff
% 0.16/0.42  thf(fact_261_inj__on__image__iff,axiom,
% 0.16/0.42      ! [A2: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [X4: paraco1605129243lle_tv] :
% 0.16/0.42            ( ( member266900804lle_tv @ X4 @ A2 )
% 0.16/0.42           => ! [Xa2: paraco1605129243lle_tv] :
% 0.16/0.42                ( ( member266900804lle_tv @ Xa2 @ A2 )
% 0.16/0.42               => ( ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42                    = ( G @ ( F3 @ Xa2 ) ) )
% 0.16/0.42                  = ( ( G @ X4 )
% 0.16/0.42                    = ( G @ Xa2 ) ) ) ) )
% 0.16/0.42       => ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 0.16/0.42         => ( ( inj_on772319074lle_tv @ G @ ( image_335818702lle_tv @ F3 @ A2 ) )
% 0.16/0.42            = ( inj_on772319074lle_tv @ G @ A2 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_image_iff
% 0.16/0.42  thf(fact_262_surjD,axiom,
% 0.16/0.42      ! [F3: nat > nat,Y: nat] :
% 0.16/0.42        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_top_set_nat )
% 0.16/0.42       => ? [X4: nat] :
% 0.16/0.42            ( Y
% 0.16/0.42            = ( F3 @ X4 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surjD
% 0.16/0.42  thf(fact_263_surjD,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_to1057771083lle_tv )
% 0.16/0.42       => ? [X4: nat] :
% 0.16/0.42            ( Y
% 0.16/0.42            = ( F3 @ X4 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surjD
% 0.16/0.42  thf(fact_264_surjD,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > nat,Y: nat] :
% 0.16/0.42        ( ( ( image_376325286tv_nat @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42          = top_top_set_nat )
% 0.16/0.42       => ? [X4: paraco1605129243lle_tv] :
% 0.16/0.42            ( Y
% 0.16/0.42            = ( F3 @ X4 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surjD
% 0.16/0.42  thf(fact_265_surjD,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( image_335818702lle_tv @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42          = top_to1057771083lle_tv )
% 0.16/0.42       => ? [X4: paraco1605129243lle_tv] :
% 0.16/0.42            ( Y
% 0.16/0.42            = ( F3 @ X4 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surjD
% 0.16/0.42  thf(fact_266_surjE,axiom,
% 0.16/0.42      ! [F3: nat > nat,Y: nat] :
% 0.16/0.42        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_top_set_nat )
% 0.16/0.42       => ~ ! [X4: nat] :
% 0.16/0.42              ( Y
% 0.16/0.42             != ( F3 @ X4 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surjE
% 0.16/0.42  thf(fact_267_surjE,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_to1057771083lle_tv )
% 0.16/0.42       => ~ ! [X4: nat] :
% 0.16/0.42              ( Y
% 0.16/0.42             != ( F3 @ X4 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surjE
% 0.16/0.42  thf(fact_268_surjE,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > nat,Y: nat] :
% 0.16/0.42        ( ( ( image_376325286tv_nat @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42          = top_top_set_nat )
% 0.16/0.42       => ~ ! [X4: paraco1605129243lle_tv] :
% 0.16/0.42              ( Y
% 0.16/0.42             != ( F3 @ X4 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surjE
% 0.16/0.42  thf(fact_269_surjE,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( image_335818702lle_tv @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42          = top_to1057771083lle_tv )
% 0.16/0.42       => ~ ! [X4: paraco1605129243lle_tv] :
% 0.16/0.42              ( Y
% 0.16/0.42             != ( F3 @ X4 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surjE
% 0.16/0.42  thf(fact_270_surjI,axiom,
% 0.16/0.42      ! [G: nat > nat,F3: nat > nat] :
% 0.16/0.42        ( ! [X4: nat] :
% 0.16/0.42            ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42            = X4 )
% 0.16/0.42       => ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.16/0.42          = top_top_set_nat ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surjI
% 0.16/0.42  thf(fact_271_surjI,axiom,
% 0.16/0.42      ! [G: nat > paraco1605129243lle_tv,F3: paraco1605129243lle_tv > nat] :
% 0.16/0.42        ( ! [X4: paraco1605129243lle_tv] :
% 0.16/0.42            ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42            = X4 )
% 0.16/0.42       => ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.16/0.42          = top_to1057771083lle_tv ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surjI
% 0.16/0.42  thf(fact_272_surjI,axiom,
% 0.16/0.42      ! [G: paraco1605129243lle_tv > nat,F3: nat > paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [X4: nat] :
% 0.16/0.42            ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42            = X4 )
% 0.16/0.42       => ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.16/0.42          = top_top_set_nat ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surjI
% 0.16/0.42  thf(fact_273_surjI,axiom,
% 0.16/0.42      ! [G: paraco1605129243lle_tv > paraco1605129243lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ! [X4: paraco1605129243lle_tv] :
% 0.16/0.42            ( ( G @ ( F3 @ X4 ) )
% 0.16/0.42            = X4 )
% 0.16/0.42       => ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.16/0.42          = top_to1057771083lle_tv ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surjI
% 0.16/0.42  thf(fact_274_surj__def,axiom,
% 0.16/0.42      ! [F3: nat > nat] :
% 0.16/0.42        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_top_set_nat )
% 0.16/0.42        = ( ! [Y4: nat] :
% 0.16/0.42            ? [X2: nat] :
% 0.16/0.42              ( Y4
% 0.16/0.42              = ( F3 @ X2 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surj_def
% 0.16/0.42  thf(fact_275_surj__def,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 0.16/0.42          = top_to1057771083lle_tv )
% 0.16/0.42        = ( ! [Y4: paraco1605129243lle_tv] :
% 0.16/0.42            ? [X2: nat] :
% 0.16/0.42              ( Y4
% 0.16/0.42              = ( F3 @ X2 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surj_def
% 0.16/0.42  thf(fact_276_surj__def,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > nat] :
% 0.16/0.42        ( ( ( image_376325286tv_nat @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42          = top_top_set_nat )
% 0.16/0.42        = ( ! [Y4: nat] :
% 0.16/0.42            ? [X2: paraco1605129243lle_tv] :
% 0.16/0.42              ( Y4
% 0.16/0.42              = ( F3 @ X2 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surj_def
% 0.16/0.42  thf(fact_277_surj__def,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( image_335818702lle_tv @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42          = top_to1057771083lle_tv )
% 0.16/0.42        = ( ! [Y4: paraco1605129243lle_tv] :
% 0.16/0.42            ? [X2: paraco1605129243lle_tv] :
% 0.16/0.42              ( Y4
% 0.16/0.42              = ( F3 @ X2 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % surj_def
% 0.16/0.42  thf(fact_278_range__ex1__eq,axiom,
% 0.16/0.42      ! [F3: nat > nat,B: nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42       => ( ( member_nat @ B @ ( image_nat_nat @ F3 @ top_top_set_nat ) )
% 0.16/0.42          = ( ? [X2: nat] :
% 0.16/0.42                ( ( B
% 0.16/0.42                  = ( F3 @ X2 ) )
% 0.16/0.42                & ! [Y4: nat] :
% 0.16/0.42                    ( ( B
% 0.16/0.42                      = ( F3 @ Y4 ) )
% 0.16/0.42                   => ( Y4 = X2 ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % range_ex1_eq
% 0.16/0.42  thf(fact_279_range__ex1__eq,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42       => ( ( member266900804lle_tv @ B @ ( image_335818702lle_tv @ F3 @ top_to1057771083lle_tv ) )
% 0.16/0.42          = ( ? [X2: paraco1605129243lle_tv] :
% 0.16/0.42                ( ( B
% 0.16/0.42                  = ( F3 @ X2 ) )
% 0.16/0.42                & ! [Y4: paraco1605129243lle_tv] :
% 0.16/0.42                    ( ( B
% 0.16/0.42                      = ( F3 @ Y4 ) )
% 0.16/0.42                   => ( Y4 = X2 ) ) ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % range_ex1_eq
% 0.16/0.42  thf(fact_280_inj__image__eq__iff,axiom,
% 0.16/0.42      ! [F3: nat > nat,A2: set_nat,B4: set_nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42       => ( ( ( image_nat_nat @ F3 @ A2 )
% 0.16/0.42            = ( image_nat_nat @ F3 @ B4 ) )
% 0.16/0.42          = ( A2 = B4 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_image_eq_iff
% 0.16/0.42  thf(fact_281_inj__image__eq__iff,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42       => ( ( ( image_335818702lle_tv @ F3 @ A2 )
% 0.16/0.42            = ( image_335818702lle_tv @ F3 @ B4 ) )
% 0.16/0.42          = ( A2 = B4 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_image_eq_iff
% 0.16/0.42  thf(fact_282_inj__image__mem__iff,axiom,
% 0.16/0.42      ! [F3: nat > nat,A: nat,A2: set_nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42       => ( ( member_nat @ ( F3 @ A ) @ ( image_nat_nat @ F3 @ A2 ) )
% 0.16/0.42          = ( member_nat @ A @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_image_mem_iff
% 0.16/0.42  thf(fact_283_inj__image__mem__iff,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42       => ( ( member266900804lle_tv @ ( F3 @ A ) @ ( image_335818702lle_tv @ F3 @ A2 ) )
% 0.16/0.42          = ( member266900804lle_tv @ A @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_image_mem_iff
% 0.16/0.42  thf(fact_284_prod__fun__imageE,axiom,
% 0.16/0.42      ! [C: produc696645085lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm] :
% 0.16/0.42        ( ( member1474794996lle_fm @ C @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F3 @ G ) @ R2 ) )
% 0.16/0.42       => ~ ! [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 0.16/0.42              ( ( C
% 0.16/0.42                = ( produc1710735575lle_fm @ ( F3 @ X4 ) @ ( G @ Y2 ) ) )
% 0.16/0.42             => ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y2 ) @ R2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod_fun_imageE
% 0.16/0.42  thf(fact_285_prod__fun__imageE,axiom,
% 0.16/0.42      ! [C: produc696645085lle_fm,F3: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,R2: set_Pr560526279lle_tv] :
% 0.16/0.42        ( ( member1474794996lle_fm @ C @ ( image_1585092542lle_fm @ ( produc951033137lle_fm @ F3 @ G ) @ R2 ) )
% 0.16/0.42       => ~ ! [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 0.16/0.42              ( ( C
% 0.16/0.42                = ( produc1710735575lle_fm @ ( F3 @ X4 ) @ ( G @ Y2 ) ) )
% 0.16/0.42             => ~ ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X4 @ Y2 ) @ R2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod_fun_imageE
% 0.16/0.42  thf(fact_286_prod__fun__imageE,axiom,
% 0.16/0.42      ! [C: produc931990033lle_tv,F3: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv,R2: set_Pr2120184979lle_fm] :
% 0.16/0.42        ( ( member1569366824lle_tv @ C @ ( image_1154804148lle_tv @ ( produc1566550641lle_tv @ F3 @ G ) @ R2 ) )
% 0.16/0.42       => ~ ! [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 0.16/0.42              ( ( C
% 0.16/0.42                = ( produc1680557635lle_tv @ ( F3 @ X4 ) @ ( G @ Y2 ) ) )
% 0.16/0.42             => ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y2 ) @ R2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod_fun_imageE
% 0.16/0.42  thf(fact_287_prod__fun__imageE,axiom,
% 0.16/0.42      ! [C: produc931990033lle_tv,F3: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv,R2: set_Pr560526279lle_tv] :
% 0.16/0.42        ( ( member1569366824lle_tv @ C @ ( image_1751508608lle_tv @ ( produc532909085lle_tv @ F3 @ G ) @ R2 ) )
% 0.16/0.42       => ~ ! [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 0.16/0.42              ( ( C
% 0.16/0.42                = ( produc1680557635lle_tv @ ( F3 @ X4 ) @ ( G @ Y2 ) ) )
% 0.16/0.42             => ~ ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X4 @ Y2 ) @ R2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod_fun_imageE
% 0.16/0.42  thf(fact_288_f__the__inv__into__f,axiom,
% 0.16/0.42      ! [F3: nat > nat,A2: set_nat,Y: nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ A2 )
% 0.16/0.42       => ( ( member_nat @ Y @ ( image_nat_nat @ F3 @ A2 ) )
% 0.16/0.42         => ( ( F3 @ ( the_inv_into_nat_nat @ A2 @ F3 @ Y ) )
% 0.16/0.42            = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % f_the_inv_into_f
% 0.16/0.42  thf(fact_289_f__the__inv__into__f,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( ( member266900804lle_tv @ Y @ ( image_335818702lle_tv @ F3 @ A2 ) )
% 0.16/0.42         => ( ( F3 @ ( the_in452116896lle_tv @ A2 @ F3 @ Y ) )
% 0.16/0.42            = Y ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % f_the_inv_into_f
% 0.16/0.42  thf(fact_290_inj__on__the__inv__into,axiom,
% 0.16/0.42      ! [F3: nat > nat,A2: set_nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ A2 )
% 0.16/0.42       => ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ A2 @ F3 ) @ ( image_nat_nat @ F3 @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_the_inv_into
% 0.16/0.42  thf(fact_291_inj__on__the__inv__into,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 0.16/0.42       => ( inj_on772319074lle_tv @ ( the_in452116896lle_tv @ A2 @ F3 ) @ ( image_335818702lle_tv @ F3 @ A2 ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % inj_on_the_inv_into
% 0.16/0.42  thf(fact_292_total__inv__image,axiom,
% 0.16/0.42      ! [F3: nat > nat,R: set_Pr1986765409at_nat] :
% 0.16/0.42        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.42       => ( ( total_on_nat @ top_top_set_nat @ R )
% 0.16/0.42         => ( total_on_nat @ top_top_set_nat @ ( inv_image_nat_nat @ R @ F3 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % total_inv_image
% 0.16/0.42  thf(fact_293_total__inv__image,axiom,
% 0.16/0.42      ! [F3: nat > paraco1605129243lle_tv,R: set_Pr2014382200lle_tv] :
% 0.16/0.42        ( ( inj_on1955349912lle_tv @ F3 @ top_top_set_nat )
% 0.16/0.42       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 0.16/0.42         => ( total_on_nat @ top_top_set_nat @ ( inv_im516950809tv_nat @ R @ F3 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % total_inv_image
% 0.16/0.42  thf(fact_294_total__inv__image,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > nat,R: set_Pr1986765409at_nat] :
% 0.16/0.42        ( ( inj_on1179712058tv_nat @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42       => ( ( total_on_nat @ top_top_set_nat @ R )
% 0.16/0.42         => ( total_1781621663lle_tv @ top_to1057771083lle_tv @ ( inv_im1292588663lle_tv @ R @ F3 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % total_inv_image
% 0.16/0.42  thf(fact_295_total__inv__image,axiom,
% 0.16/0.42      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,R: set_Pr2014382200lle_tv] :
% 0.16/0.42        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 0.16/0.42       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 0.16/0.42         => ( total_1781621663lle_tv @ top_to1057771083lle_tv @ ( inv_im719552961lle_tv @ R @ F3 ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % total_inv_image
% 0.16/0.42  thf(fact_296_prod_Ocollapse,axiom,
% 0.16/0.42      ! [Prod: produc696645085lle_fm] :
% 0.16/0.42        ( ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) )
% 0.16/0.42        = Prod ) ).
% 0.16/0.42  
% 0.16/0.42  % prod.collapse
% 0.16/0.42  thf(fact_297_prod_Ocollapse,axiom,
% 0.16/0.42      ! [Prod: produc931990033lle_tv] :
% 0.16/0.42        ( ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ Prod ) @ ( produc547496597lle_tv @ Prod ) )
% 0.16/0.42        = Prod ) ).
% 0.16/0.42  
% 0.16/0.42  % prod.collapse
% 0.16/0.42  thf(fact_298_prod_Oswap__def,axiom,
% 0.16/0.42      ( produc1232814113lle_tv
% 0.16/0.42      = ( ^ [P: produc1443694919lle_tv] : ( produc1710735575lle_fm @ ( produc381314067lle_tv @ P ) @ ( produc262413013lle_tv @ P ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod.swap_def
% 0.16/0.42  thf(fact_299_prod_Oswap__def,axiom,
% 0.16/0.42      ( produc178635363at_nat
% 0.16/0.42      = ( ^ [P: produc596913417at_nat] : ( produc1680557635lle_tv @ ( produc500618325at_nat @ P ) @ ( produc1589291287at_nat @ P ) ) ) ) ).
% 0.16/0.42  
% 0.16/0.42  % prod.swap_def
% 0.16/0.42  thf(fact_300_fst__eqD,axiom,
% 0.16/0.42      ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv] :
% 0.16/0.42        ( ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.16/0.42          = A )
% 0.16/0.42       => ( X = A ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fst_eqD
% 0.16/0.42  thf(fact_301_fst__eqD,axiom,
% 0.16/0.42      ! [X: nat > nat,Y: paraco1605129243lle_tv,A: nat > nat] :
% 0.16/0.42        ( ( ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.16/0.42          = A )
% 0.16/0.42       => ( X = A ) ) ).
% 0.16/0.42  
% 0.16/0.42  % fst_eqD
% 0.16/0.42  thf(fact_302_snd__eqD,axiom,
% 0.16/0.42      ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: paraco1604210848lle_fm] :
% 0.16/0.43        ( ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.16/0.43          = A )
% 0.16/0.43       => ( Y = A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % snd_eqD
% 0.16/0.43  thf(fact_303_snd__eqD,axiom,
% 0.16/0.43      ! [X: nat > nat,Y: paraco1605129243lle_tv,A: paraco1605129243lle_tv] :
% 0.16/0.43        ( ( ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.16/0.43          = A )
% 0.16/0.43       => ( Y = A ) ) ).
% 0.16/0.43  
% 0.16/0.43  % snd_eqD
% 0.16/0.43  thf(fact_304_fst__conv,axiom,
% 0.16/0.43      ! [X1: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm] :
% 0.16/0.43        ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X1 @ X23 ) )
% 0.16/0.43        = X1 ) ).
% 0.16/0.43  
% 0.16/0.43  % fst_conv
% 0.16/0.43  thf(fact_305_fst__conv,axiom,
% 0.16/0.43      ! [X1: nat > nat,X23: paraco1605129243lle_tv] :
% 0.16/0.43        ( ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X1 @ X23 ) )
% 0.16/0.43        = X1 ) ).
% 0.16/0.43  
% 0.16/0.43  % fst_conv
% 0.16/0.43  thf(fact_306_snd__conv,axiom,
% 0.16/0.43      ! [X1: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm] :
% 0.16/0.43        ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X1 @ X23 ) )
% 0.16/0.43        = X23 ) ).
% 0.16/0.43  
% 0.16/0.43  % snd_conv
% 0.16/0.43  thf(fact_307_snd__conv,axiom,
% 0.16/0.43      ! [X1: nat > nat,X23: paraco1605129243lle_tv] :
% 0.16/0.43        ( ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X1 @ X23 ) )
% 0.16/0.43        = X23 ) ).
% 0.16/0.43  
% 0.16/0.43  % snd_conv
% 0.16/0.43  thf(fact_308_prod_Oexhaust__sel,axiom,
% 0.16/0.43      ! [Prod: produc696645085lle_fm] :
% 0.16/0.43        ( Prod
% 0.16/0.43        = ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % prod.exhaust_sel
% 0.16/0.43  thf(fact_309_prod_Oexhaust__sel,axiom,
% 0.16/0.43      ! [Prod: produc931990033lle_tv] :
% 0.16/0.43        ( Prod
% 0.16/0.43        = ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ Prod ) @ ( produc547496597lle_tv @ Prod ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % prod.exhaust_sel
% 0.16/0.43  thf(fact_310_surjective__pairing,axiom,
% 0.16/0.43      ! [T: produc696645085lle_fm] :
% 0.16/0.43        ( T
% 0.16/0.43        = ( produc1710735575lle_fm @ ( produc29804011lle_fm @ T ) @ ( produc148705065lle_fm @ T ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % surjective_pairing
% 0.16/0.43  thf(fact_311_surjective__pairing,axiom,
% 0.16/0.43      ! [T: produc931990033lle_tv] :
% 0.16/0.43        ( T
% 0.16/0.43        = ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ T ) @ ( produc547496597lle_tv @ T ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % surjective_pairing
% 0.16/0.43  thf(fact_312_exI__realizer,axiom,
% 0.16/0.43      ! [P3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > $o,Y: paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv] :
% 0.16/0.43        ( ( P3 @ Y @ X )
% 0.16/0.43       => ( P3 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X @ Y ) ) @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X @ Y ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % exI_realizer
% 0.16/0.43  thf(fact_313_exI__realizer,axiom,
% 0.16/0.43      ! [P3: paraco1605129243lle_tv > ( nat > nat ) > $o,Y: paraco1605129243lle_tv,X: nat > nat] :
% 0.16/0.43        ( ( P3 @ Y @ X )
% 0.16/0.43       => ( P3 @ ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X @ Y ) ) @ ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X @ Y ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % exI_realizer
% 0.16/0.43  thf(fact_314_conjI__realizer,axiom,
% 0.16/0.43      ! [P3: ( list_char > paraco1605129243lle_tv ) > $o,P2: list_char > paraco1605129243lle_tv,Q2: paraco1604210848lle_fm > $o,Q: paraco1604210848lle_fm] :
% 0.16/0.43        ( ( P3 @ P2 )
% 0.16/0.43       => ( ( Q2 @ Q )
% 0.16/0.43         => ( ( P3 @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ P2 @ Q ) ) )
% 0.16/0.43            & ( Q2 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ P2 @ Q ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % conjI_realizer
% 0.16/0.43  thf(fact_315_conjI__realizer,axiom,
% 0.16/0.43      ! [P3: ( nat > nat ) > $o,P2: nat > nat,Q2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv] :
% 0.16/0.43        ( ( P3 @ P2 )
% 0.16/0.43       => ( ( Q2 @ Q )
% 0.16/0.43         => ( ( P3 @ ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ P2 @ Q ) ) )
% 0.16/0.43            & ( Q2 @ ( produc547496597lle_tv @ ( produc1680557635lle_tv @ P2 @ Q ) ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % conjI_realizer
% 0.16/0.43  thf(fact_316_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.16/0.43      ! [P3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: produc696645085lle_fm] :
% 0.16/0.43        ( ( P3 @ X @ Y )
% 0.16/0.43       => ( ( A
% 0.16/0.43            = ( produc1710735575lle_fm @ X @ Y ) )
% 0.16/0.43         => ( P3 @ ( produc29804011lle_fm @ A ) @ ( produc148705065lle_fm @ A ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % BNF_Greatest_Fixpoint.subst_Pair
% 0.16/0.43  thf(fact_317_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.16/0.43      ! [P3: ( nat > nat ) > paraco1605129243lle_tv > $o,X: nat > nat,Y: paraco1605129243lle_tv,A: produc931990033lle_tv] :
% 0.16/0.43        ( ( P3 @ X @ Y )
% 0.16/0.43       => ( ( A
% 0.16/0.43            = ( produc1680557635lle_tv @ X @ Y ) )
% 0.16/0.43         => ( P3 @ ( produc1636169559lle_tv @ A ) @ ( produc547496597lle_tv @ A ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % BNF_Greatest_Fixpoint.subst_Pair
% 0.16/0.43  thf(fact_318_eq__snd__iff,axiom,
% 0.16/0.43      ! [B: paraco1604210848lle_fm,P2: produc696645085lle_fm] :
% 0.16/0.43        ( ( B
% 0.16/0.43          = ( produc148705065lle_fm @ P2 ) )
% 0.16/0.43        = ( ? [A6: list_char > paraco1605129243lle_tv] :
% 0.16/0.43              ( P2
% 0.16/0.43              = ( produc1710735575lle_fm @ A6 @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % eq_snd_iff
% 0.16/0.43  thf(fact_319_eq__snd__iff,axiom,
% 0.16/0.43      ! [B: paraco1605129243lle_tv,P2: produc931990033lle_tv] :
% 0.16/0.43        ( ( B
% 0.16/0.43          = ( produc547496597lle_tv @ P2 ) )
% 0.16/0.43        = ( ? [A6: nat > nat] :
% 0.16/0.43              ( P2
% 0.16/0.43              = ( produc1680557635lle_tv @ A6 @ B ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % eq_snd_iff
% 0.16/0.43  thf(fact_320_sndI,axiom,
% 0.16/0.43      ! [X: produc696645085lle_fm,Y: list_char > paraco1605129243lle_tv,Z: paraco1604210848lle_fm] :
% 0.16/0.43        ( ( X
% 0.16/0.43          = ( produc1710735575lle_fm @ Y @ Z ) )
% 0.16/0.43       => ( ( produc148705065lle_fm @ X )
% 0.16/0.43          = Z ) ) ).
% 0.16/0.43  
% 0.16/0.43  % sndI
% 0.16/0.43  thf(fact_321_sndI,axiom,
% 0.16/0.43      ! [X: produc931990033lle_tv,Y: nat > nat,Z: paraco1605129243lle_tv] :
% 0.16/0.43        ( ( X
% 0.16/0.43          = ( produc1680557635lle_tv @ Y @ Z ) )
% 0.16/0.43       => ( ( produc547496597lle_tv @ X )
% 0.16/0.43          = Z ) ) ).
% 0.16/0.43  
% 0.16/0.43  % sndI
% 0.16/0.43  thf(fact_322_fstI,axiom,
% 0.16/0.43      ! [X: produc696645085lle_fm,Y: list_char > paraco1605129243lle_tv,Z: paraco1604210848lle_fm] :
% 0.16/0.43        ( ( X
% 0.16/0.43          = ( produc1710735575lle_fm @ Y @ Z ) )
% 0.16/0.43       => ( ( produc29804011lle_fm @ X )
% 0.16/0.43          = Y ) ) ).
% 0.16/0.43  
% 0.16/0.43  % fstI
% 0.16/0.43  thf(fact_323_fstI,axiom,
% 0.16/0.43      ! [X: produc931990033lle_tv,Y: nat > nat,Z: paraco1605129243lle_tv] :
% 0.16/0.43        ( ( X
% 0.16/0.43          = ( produc1680557635lle_tv @ Y @ Z ) )
% 0.16/0.43       => ( ( produc1636169559lle_tv @ X )
% 0.16/0.43          = Y ) ) ).
% 0.16/0.43  
% 0.16/0.43  % fstI
% 0.16/0.43  thf(fact_324_eq__fst__iff,axiom,
% 0.16/0.43      ! [A: list_char > paraco1605129243lle_tv,P2: produc696645085lle_fm] :
% 0.16/0.43        ( ( A
% 0.16/0.43          = ( produc29804011lle_fm @ P2 ) )
% 0.16/0.43        = ( ? [B5: paraco1604210848lle_fm] :
% 0.16/0.43              ( P2
% 0.16/0.43              = ( produc1710735575lle_fm @ A @ B5 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % eq_fst_iff
% 0.16/0.43  thf(fact_325_eq__fst__iff,axiom,
% 0.16/0.43      ! [A: nat > nat,P2: produc931990033lle_tv] :
% 0.16/0.43        ( ( A
% 0.16/0.43          = ( produc1636169559lle_tv @ P2 ) )
% 0.16/0.43        = ( ? [B5: paraco1605129243lle_tv] :
% 0.16/0.43              ( P2
% 0.16/0.43              = ( produc1680557635lle_tv @ A @ B5 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % eq_fst_iff
% 0.16/0.43  thf(fact_326_total__lex__prod,axiom,
% 0.16/0.43      ! [R: set_Pr1986765409at_nat,S3: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( total_on_nat @ top_top_set_nat @ R )
% 0.16/0.43       => ( ( total_on_nat @ top_top_set_nat @ S3 )
% 0.16/0.43         => ( total_1775715973at_nat @ top_to1555900337at_nat @ ( lex_prod_nat_nat @ R @ S3 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % total_lex_prod
% 0.16/0.43  thf(fact_327_total__lex__prod,axiom,
% 0.16/0.43      ! [R: set_Pr1986765409at_nat,S3: set_Pr2014382200lle_tv] :
% 0.16/0.43        ( ( total_on_nat @ top_top_set_nat @ R )
% 0.16/0.43       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ S3 )
% 0.16/0.43         => ( total_517371324lle_tv @ top_to1411004326lle_tv @ ( lex_pr413684186lle_tv @ R @ S3 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % total_lex_prod
% 0.16/0.43  thf(fact_328_total__lex__prod,axiom,
% 0.16/0.43      ! [R: set_Pr2014382200lle_tv,S3: set_Pr1986765409at_nat] :
% 0.16/0.43        ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 0.16/0.43       => ( ( total_on_nat @ top_top_set_nat @ S3 )
% 0.16/0.43         => ( total_440843542tv_nat @ top_to975729152tv_nat @ ( lex_pr1785529980tv_nat @ R @ S3 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % total_lex_prod
% 0.16/0.43  thf(fact_329_total__lex__prod,axiom,
% 0.16/0.43      ! [R: set_Pr2014382200lle_tv,S3: set_Pr2014382200lle_tv] :
% 0.16/0.43        ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 0.16/0.43       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ S3 )
% 0.16/0.43         => ( total_92239038lle_tv @ top_to1871154984lle_tv @ ( lex_pr567812260lle_tv @ R @ S3 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % total_lex_prod
% 0.16/0.43  thf(fact_330_in__lex__prod,axiom,
% 0.16/0.43      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm,R: set_Pr2061825550lle_tv,S3: set_Pr1019238018lle_fm] :
% 0.16/0.43        ( ( member1592865093lle_fm @ ( produc407632608lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ ( produc1710735575lle_fm @ A5 @ B3 ) ) @ ( lex_pr2001015487lle_fm @ R @ S3 ) )
% 0.16/0.43        = ( ( member146333935lle_tv @ ( produc1297923922lle_tv @ A @ A5 ) @ R )
% 0.16/0.43          | ( ( A = A5 )
% 0.16/0.43            & ( member334644067lle_fm @ ( produc1126104134lle_fm @ B @ B3 ) @ S3 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % in_lex_prod
% 0.16/0.43  thf(fact_331_in__lex__prod,axiom,
% 0.16/0.43      ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv,R: set_Pr1357842111at_nat,S3: set_Pr2014382200lle_tv] :
% 0.16/0.43        ( ( member1339857875lle_tv @ ( produc2057188974lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ ( produc1680557635lle_tv @ A5 @ B3 ) ) @ ( lex_pr1093414955lle_tv @ R @ S3 ) )
% 0.16/0.43        = ( ( member112824072at_nat @ ( produc780837143at_nat @ A @ A5 ) @ R )
% 0.16/0.43          | ( ( A = A5 )
% 0.16/0.43            & ( member1531318361lle_tv @ ( produc2058540732lle_tv @ B @ B3 ) @ S3 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % in_lex_prod
% 0.16/0.43  thf(fact_332_wf__map__prod__image,axiom,
% 0.16/0.43      ! [R: set_Pr1986765409at_nat,F3: nat > nat] :
% 0.16/0.43        ( ( wf_nat @ R )
% 0.16/0.43       => ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 0.16/0.43         => ( wf_nat @ ( image_815163717at_nat @ ( produc505105722at_nat @ F3 @ F3 ) @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % wf_map_prod_image
% 0.16/0.43  thf(fact_333_wf__map__prod__image,axiom,
% 0.16/0.43      ! [R: set_Pr2014382200lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.16/0.43        ( ( wf_Par1378404612lle_tv @ R )
% 0.16/0.43       => ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 0.16/0.43         => ( wf_Par1378404612lle_tv @ ( image_1221801032lle_tv @ ( produc1345917071lle_tv @ F3 @ F3 ) @ R ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % wf_map_prod_image
% 0.16/0.43  thf(fact_334_same__fstI,axiom,
% 0.16/0.43      ! [P3: ( list_char > paraco1605129243lle_tv ) > $o,X: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm,Y: paraco1604210848lle_fm,R2: ( list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm] :
% 0.16/0.43        ( ( P3 @ X )
% 0.16/0.43       => ( ( member334644067lle_fm @ ( produc1126104134lle_fm @ Y5 @ Y ) @ ( R2 @ X ) )
% 0.16/0.43         => ( member1592865093lle_fm @ ( produc407632608lle_fm @ ( produc1710735575lle_fm @ X @ Y5 ) @ ( produc1710735575lle_fm @ X @ Y ) ) @ ( same_f1581085506lle_fm @ P3 @ R2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % same_fstI
% 0.16/0.43  thf(fact_335_same__fstI,axiom,
% 0.16/0.43      ! [P3: ( nat > nat ) > $o,X: nat > nat,Y5: paraco1605129243lle_tv,Y: paraco1605129243lle_tv,R2: ( nat > nat ) > set_Pr2014382200lle_tv] :
% 0.16/0.43        ( ( P3 @ X )
% 0.16/0.43       => ( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ Y5 @ Y ) @ ( R2 @ X ) )
% 0.16/0.43         => ( member1339857875lle_tv @ ( produc2057188974lle_tv @ ( produc1680557635lle_tv @ X @ Y5 ) @ ( produc1680557635lle_tv @ X @ Y ) ) @ ( same_f1138187694lle_tv @ P3 @ R2 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % same_fstI
% 0.16/0.43  thf(fact_336_the__inv__into__into,axiom,
% 0.16/0.43      ! [F3: nat > nat,A2: set_nat,X: nat,B4: set_nat] :
% 0.16/0.43        ( ( inj_on_nat_nat @ F3 @ A2 )
% 0.16/0.43       => ( ( member_nat @ X @ ( image_nat_nat @ F3 @ A2 ) )
% 0.16/0.43         => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 0.16/0.43           => ( member_nat @ ( the_inv_into_nat_nat @ A2 @ F3 @ X ) @ B4 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % the_inv_into_into
% 0.16/0.43  thf(fact_337_the__inv__into__into,axiom,
% 0.16/0.43      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.16/0.43        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 0.16/0.43       => ( ( member266900804lle_tv @ X @ ( image_335818702lle_tv @ F3 @ A2 ) )
% 0.16/0.43         => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 0.16/0.43           => ( member266900804lle_tv @ ( the_in452116896lle_tv @ A2 @ F3 @ X ) @ B4 ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % the_inv_into_into
% 0.16/0.43  thf(fact_338_inj__on__image__eq__iff,axiom,
% 0.16/0.43      ! [F3: nat > nat,C2: set_nat,A2: set_nat,B4: set_nat] :
% 0.16/0.43        ( ( inj_on_nat_nat @ F3 @ C2 )
% 0.16/0.43       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.16/0.43         => ( ( ord_less_eq_set_nat @ B4 @ C2 )
% 0.16/0.43           => ( ( ( image_nat_nat @ F3 @ A2 )
% 0.16/0.43                = ( image_nat_nat @ F3 @ B4 ) )
% 0.16/0.43              = ( A2 = B4 ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % inj_on_image_eq_iff
% 0.16/0.43  thf(fact_339_inj__on__image__eq__iff,axiom,
% 0.16/0.43      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,C2: set_Pa1764573435lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.16/0.43        ( ( inj_on772319074lle_tv @ F3 @ C2 )
% 0.16/0.43       => ( ( ord_le241064091lle_tv @ A2 @ C2 )
% 0.16/0.43         => ( ( ord_le241064091lle_tv @ B4 @ C2 )
% 0.16/0.43           => ( ( ( image_335818702lle_tv @ F3 @ A2 )
% 0.16/0.43                = ( image_335818702lle_tv @ F3 @ B4 ) )
% 0.16/0.43              = ( A2 = B4 ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % inj_on_image_eq_iff
% 0.16/0.43  thf(fact_340_inj__on__image__mem__iff,axiom,
% 0.16/0.43      ! [F3: nat > nat,B4: set_nat,A: nat,A2: set_nat] :
% 0.16/0.43        ( ( inj_on_nat_nat @ F3 @ B4 )
% 0.16/0.43       => ( ( member_nat @ A @ B4 )
% 0.16/0.43         => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 0.16/0.43           => ( ( member_nat @ ( F3 @ A ) @ ( image_nat_nat @ F3 @ A2 ) )
% 0.16/0.43              = ( member_nat @ A @ A2 ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % inj_on_image_mem_iff
% 0.16/0.43  thf(fact_341_inj__on__image__mem__iff,axiom,
% 0.16/0.43      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv,A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.16/0.43        ( ( inj_on772319074lle_tv @ F3 @ B4 )
% 0.16/0.43       => ( ( member266900804lle_tv @ A @ B4 )
% 0.16/0.43         => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 0.16/0.43           => ( ( member266900804lle_tv @ ( F3 @ A ) @ ( image_335818702lle_tv @ F3 @ A2 ) )
% 0.16/0.43              = ( member266900804lle_tv @ A @ A2 ) ) ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % inj_on_image_mem_iff
% 0.16/0.43  thf(fact_342_top_Oextremum__uniqueI,axiom,
% 0.16/0.43      ! [A: set_nat] :
% 0.16/0.43        ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
% 0.16/0.43       => ( A = top_top_set_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % top.extremum_uniqueI
% 0.16/0.43  thf(fact_343_top_Oextremum__uniqueI,axiom,
% 0.16/0.43      ! [A: set_Pa1764573435lle_tv] :
% 0.16/0.43        ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
% 0.16/0.43       => ( A = top_to1057771083lle_tv ) ) ).
% 0.16/0.43  
% 0.16/0.43  % top.extremum_uniqueI
% 0.16/0.43  thf(fact_344_top_Oextremum__unique,axiom,
% 0.16/0.43      ! [A: set_nat] :
% 0.16/0.43        ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
% 0.16/0.43        = ( A = top_top_set_nat ) ) ).
% 0.16/0.43  
% 0.16/0.43  % top.extremum_unique
% 0.16/0.43  thf(fact_345_top_Oextremum__unique,axiom,
% 0.16/0.43      ! [A: set_Pa1764573435lle_tv] :
% 0.16/0.43        ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
% 0.16/0.43        = ( A = top_to1057771083lle_tv ) ) ).
% 0.16/0.43  
% 0.16/0.43  % top.extremum_unique
% 0.16/0.43  thf(fact_346_top__greatest,axiom,
% 0.16/0.43      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % top_greatest
% 0.16/0.43  thf(fact_347_top__greatest,axiom,
% 0.16/0.43      ! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ) ).
% 0.16/0.43  
% 0.16/0.43  % top_greatest
% 0.16/0.43  thf(fact_348_subset__UNIV,axiom,
% 0.16/0.43      ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ top_top_set_nat ) ).
% 0.16/0.43  
% 0.16/0.43  % subset_UNIV
% 0.16/0.43  thf(fact_349_subset__UNIV,axiom,
% 0.16/0.43      ! [A2: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A2 @ top_to1057771083lle_tv ) ).
% 0.16/0.43  
% 0.16/0.43  % subset_UNIV
% 0.16/0.43  thf(fact_350_inj__on__subset,axiom,
% 0.16/0.43      ! [F3: nat > nat,A2: set_nat,B4: set_nat] :
% 0.16/0.43        ( ( inj_on_nat_nat @ F3 @ A2 )
% 0.16/0.43       => ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 0.16/0.43         => ( inj_on_nat_nat @ F3 @ B4 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % inj_on_subset
% 0.16/0.43  thf(fact_351_inj__on__subset,axiom,
% 0.16/0.43      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.16/0.43        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 0.16/0.43       => ( ( ord_le241064091lle_tv @ B4 @ A2 )
% 0.16/0.43         => ( inj_on772319074lle_tv @ F3 @ B4 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % inj_on_subset
% 0.16/0.43  thf(fact_352_subset__inj__on,axiom,
% 0.16/0.43      ! [F3: nat > nat,B4: set_nat,A2: set_nat] :
% 0.16/0.43        ( ( inj_on_nat_nat @ F3 @ B4 )
% 0.16/0.43       => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 0.16/0.43         => ( inj_on_nat_nat @ F3 @ A2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % subset_inj_on
% 0.16/0.43  thf(fact_353_subset__inj__on,axiom,
% 0.16/0.43      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.16/0.43        ( ( inj_on772319074lle_tv @ F3 @ B4 )
% 0.16/0.43       => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 0.16/0.43         => ( inj_on772319074lle_tv @ F3 @ A2 ) ) ) ).
% 0.16/0.43  
% 0.16/0.43  % subset_inj_on
% 0.16/0.43  
% 0.16/0.43  % Helper facts (3)
% 0.16/0.43  thf(help_If_3_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 0.16/0.43      ! [P3: $o] :
% 0.16/0.43        ( ( P3 = $true )
% 0.16/0.43        | ( P3 = $false ) ) ).
% 0.16/0.43  
% 0.16/0.43  thf(help_If_2_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 0.16/0.43      ! [X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.43        ( ( if_Par1134130401lle_tv @ $false @ X @ Y )
% 0.16/0.43        = Y ) ).
% 0.16/0.43  
% 0.16/0.43  thf(help_If_1_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 0.16/0.43      ! [X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.16/0.43        ( ( if_Par1134130401lle_tv @ $true @ X @ Y )
% 0.16/0.43        = X ) ).
% 0.16/0.43  
% 0.16/0.43  % Conjectures (1)
% 0.16/0.43  thf(conj_0,conjecture,
% 0.16/0.43      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
% 0.16/0.43     != ( paraco1344940915le_Det @ $true ) ) ).
% 0.16/0.43  
% 0.16/0.43  %------------------------------------------------------------------------------
% 0.16/0.43  ------------------------
% 3.06/1.52  ---- Embedded in THF ---
% 3.06/1.52  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.06/1.52  %%% Generated on Tue Feb 24 08:36:00 EST 2026
% 3.06/1.52  %%% using '$$dhol' embedding, version 1.3.0.
% 3.06/1.52  %%% Logic specification used:
% 3.06/1.52  %%% thf(spec, logic, $$dhol).
% 3.06/1.52  
% 3.06/1.52  % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.b6Vcvump8L/DTF2DTF12469.p
% See solution above
% 3.06/1.52  ------------------------
% 3.06/1.58  ---- Cleaned THF ---
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J_J,type,
% 3.06/1.58      set_Pr1475944804lle_fm: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 3.06/1.58      produc1250255278lle_fm: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 3.06/1.58      set_Pr2012908090lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 3.06/1.58      set_Pr698334450lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      produc1720769084lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 3.06/1.58      set_Pr2061825550lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J_J,type,
% 3.06/1.58      set_Pr1943077434tv_nat: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 3.06/1.58      set_Pr292927124lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      produc1852595672lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 3.06/1.58      set_Pr1723822845lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 3.06/1.58      set_Pr2120184979lle_fm: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      produc1443694919lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 3.06/1.58      produc696645085lle_fm: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 3.06/1.58      set_Pr1490359111at_nat: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      set_Pr2014382200lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 3.06/1.58      set_Pr1019238018lle_fm: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 3.06/1.58      set_Pr840833727at_nat: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      set_Pr560526279lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      produc1647334210lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 3.06/1.58      produc450659916lle_fm: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 3.06/1.58      set_Pr1357842111at_nat: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.06/1.58      produc596913417at_nat: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      produc931990033lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J,type,
% 3.06/1.58      set_Pr1725653840tv_nat: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      set_Pr13445366lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.06/1.58      produc1281043295at_nat: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 3.06/1.58      produc194167194tv_nat: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      produc270694976lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.06/1.58      set_Pr1986765409at_nat: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      set_Pa1764573435lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      product_prod_nat_nat: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      paraco1605129243lle_tv: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 3.06/1.58      paraco1604210848lle_fm: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
% 3.06/1.58      list_char: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 3.06/1.58      set_nat: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(ty_n_t__Nat__Onat,type,
% 3.06/1.58      nat: $tType ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.06/1.58      inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.06/1.58      inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      inj_on26176689at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      inj_on1745913142lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 3.06/1.58      inj_on552895452tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Fun_Oinj__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Fun_Othe__inv__into_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.06/1.58      the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Fun_Othe__inv__into_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 3.06/1.58      ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
% 3.06/1.58      top_top_nat_o: nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_Eo_J,type,
% 3.06/1.58      top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 3.06/1.58      top_to632227436_nat_o: product_prod_nat_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_Eo_J,type,
% 3.06/1.58      top_to1889334367e_tv_o: produc270694976lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_M_Eo_J,type,
% 3.06/1.58      top_to900819589_nat_o: produc194167194tv_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001_Eo,type,
% 3.06/1.58      top_top_o: $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 3.06/1.58      top_top_set_nat: set_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_J,type,
% 3.06/1.58      top_to138697918lle_tv: set_Pr2061825550lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 3.06/1.58      top_to775056195lle_fm: set_Pr2120184979lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 3.06/1.58      top_to1541413903at_nat: set_Pr1357842111at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      top_to449985143lle_tv: set_Pr560526279lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.06/1.58      top_to1555900337at_nat: set_Pr1986765409at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      top_to1411004326lle_tv: set_Pr13445366lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J,type,
% 3.06/1.58      top_to975729152tv_nat: set_Pr1725653840tv_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      top_to1871154984lle_tv: set_Pr2014382200lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__int,type,
% 3.06/1.58      paraco761681009ge_int: ( nat > nat ) > ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv,type,
% 3.06/1.58      paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv__rel,type,
% 3.06/1.58      paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Oeval,type,
% 3.06/1.58      paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OCon_H,type,
% 3.06/1.58      paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql,type,
% 3.06/1.58      paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql_H,type,
% 3.06/1.58      paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_ONeg_H,type,
% 3.06/1.58      paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OPro,type,
% 3.06/1.58      paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OTruth,type,
% 3.06/1.58      paraco367965286_Truth: paraco1604210848lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_ODet,type,
% 3.06/1.58      paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_OIndet,type,
% 3.06/1.58      paraco793048302_Indet: nat > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_Ocase__tv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      paraco2051596139lle_tv: ( $o > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid,type,
% 3.06/1.58      paraco327635598_valid: paraco1604210848lle_fm > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid__in,type,
% 3.06/1.58      paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      produc1297923922lle_tv: ( list_char > paraco1605129243lle_tv ) > ( list_char > paraco1605129243lle_tv ) > produc1852595672lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_OPair_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 3.06/1.58      produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      produc780837143at_nat: ( nat > nat ) > ( nat > nat ) > produc1281043295at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc1680557635lle_tv: ( nat > nat ) > paraco1605129243lle_tv > produc931990033lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      produc1943344577lle_tv: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc1443694919lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 3.06/1.58      produc1126104134lle_fm: paraco1604210848lle_fm > paraco1604210848lle_fm > produc450659916lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      produc1633679363at_nat: paraco1605129243lle_tv > ( nat > nat ) > produc596913417at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc2058540732lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 3.06/1.58      produc407632608lle_fm: produc696645085lle_fm > produc696645085lle_fm > produc1250255278lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_OPair_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      produc2057188974lle_tv: produc931990033lle_tv > produc931990033lle_tv > produc1720769084lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oapfst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 3.06/1.58      produc1942165868lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > produc696645085lle_fm > produc696645085lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oapfst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc939316703lle_tv: ( ( nat > nat ) > nat > nat ) > produc931990033lle_tv > produc931990033lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oapsnd_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      produc1807466521lle_tv: ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oapsnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      produc109093078at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Obool_Ocase__bool_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Ocurry_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_Eo,type,
% 3.06/1.58      produc275353523e_fm_o: ( produc696645085lle_fm > $o ) > ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Ocurry_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_Eo,type,
% 3.06/1.58      produc752649287e_tv_o: ( produc931990033lle_tv > $o ) > ( nat > nat ) > paraco1605129243lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 3.06/1.58      produc1900967599lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc1566550641lle_tv: ( ( list_char > paraco1605129243lle_tv ) > nat > nat ) > ( paraco1604210848lle_fm > paraco1605129243lle_tv ) > produc696645085lle_fm > produc931990033lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 3.06/1.58      produc951033137lle_fm: ( ( nat > nat ) > list_char > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1604210848lle_fm ) > produc931990033lle_tv > produc696645085lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc532909085lle_tv: ( ( nat > nat ) > nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.06/1.58      produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc313957681lle_tv: ( nat > nat ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc270694976lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.06/1.58      produc1685803475tv_nat: ( nat > nat ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > product_prod_nat_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.06/1.58      produc1250721397at_nat: ( nat > paraco1605129243lle_tv ) > ( nat > nat ) > product_prod_nat_nat > produc194167194tv_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc210389789lle_tv: ( nat > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc1647334210lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.06/1.58      produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.06/1.58      produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.06/1.58      produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 3.06/1.58      produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc1636169559lle_tv: produc931990033lle_tv > nat > nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oprod_Ofst_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oprod_Ofst_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 3.06/1.58      produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc547496597lle_tv: produc931990033lle_tv > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oprod_Osnd_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oprod_Osnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      produc500618325at_nat: produc596913417at_nat > nat > nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 3.06/1.58      produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      produc225513635lle_tv: produc931990033lle_tv > produc596913417at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oprod_Oswap_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Product__Type_Oprod_Oswap_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.06/1.58      inv_image_nat_nat: set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      inv_im1292588663lle_tv: set_Pr1986765409at_nat > ( paraco1605129243lle_tv > nat ) > set_Pr2014382200lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Relation_Oinv__image_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.06/1.58      inv_im516950809tv_nat: set_Pr2014382200lle_tv > ( nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Relation_Oinv__image_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      inv_im719552961lle_tv: set_Pr2014382200lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pr2014382200lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Relation_Ototal__on_001t__Nat__Onat,type,
% 3.06/1.58      total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Relation_Ototal__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      total_1781621663lle_tv: set_Pa1764573435lle_tv > set_Pr2014382200lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      total_1775715973at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      total_517371324lle_tv: set_Pr13445366lle_tv > set_Pr292927124lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 3.06/1.58      total_440843542tv_nat: set_Pr1725653840tv_nat > set_Pr1943077434tv_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      total_92239038lle_tv: set_Pr2014382200lle_tv > set_Pr2012908090lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 3.06/1.58      collect_nat: ( nat > $o ) > set_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_OCollect_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      collec1102043437lle_tv: ( produc1852595672lle_tv > $o ) > set_Pr2061825550lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 3.06/1.58      collec835549234lle_fm: ( produc696645085lle_fm > $o ) > set_Pr2120184979lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.06/1.58      collec791369802at_nat: ( produc1281043295at_nat > $o ) > set_Pr1357842111at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      collec1624074086lle_tv: ( produc931990033lle_tv > $o ) > set_Pr560526279lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 3.06/1.58      collec848462447tv_nat: ( produc194167194tv_nat > $o ) > set_Pr1725653840tv_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.06/1.58      image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.06/1.58      image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 3.06/1.58      image_807538418lle_fm: ( produc696645085lle_fm > produc696645085lle_fm ) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      image_1154804148lle_tv: ( produc696645085lle_fm > produc931990033lle_tv ) > set_Pr2120184979lle_fm > set_Pr560526279lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      image_924970994lle_tv: ( produc696645085lle_fm > produc1443694919lle_tv ) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 3.06/1.58      image_1585092542lle_fm: ( produc931990033lle_tv > produc696645085lle_fm ) > set_Pr560526279lle_tv > set_Pr2120184979lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      image_1751508608lle_tv: ( produc931990033lle_tv > produc931990033lle_tv ) > set_Pr560526279lle_tv > set_Pr560526279lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.06/1.58      image_1724396928at_nat: ( produc931990033lle_tv > produc596913417at_nat ) > set_Pr560526279lle_tv > set_Pr840833727at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      image_815163717at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      image_1674248956lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > set_Pr13445366lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 3.06/1.58      image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      image_1507992062lle_tv: ( product_prod_nat_nat > produc1647334210lle_tv ) > set_Pr1986765409at_nat > set_Pr2014382200lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      image_1787705850at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > set_Pr1986765409at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 3.06/1.58      image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 3.06/1.58      image_326034184lle_fm: ( produc1443694919lle_tv > produc696645085lle_fm ) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      image_769496456lle_tv: ( produc596913417at_nat > produc931990033lle_tv ) > set_Pr840833727at_nat > set_Pr560526279lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      image_1221801032lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      accp_P2085826120lle_tv: ( produc931990033lle_tv > produc931990033lle_tv > $o ) > produc931990033lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Wellfounded_Olex__prod_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 3.06/1.58      lex_pr2001015487lle_fm: set_Pr2061825550lle_tv > set_Pr1019238018lle_fm > set_Pr1475944804lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Wellfounded_Olex__prod_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      lex_pr1093414955lle_tv: set_Pr1357842111at_nat > set_Pr2014382200lle_tv > set_Pr698334450lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Nat__Onat,type,
% 3.06/1.58      lex_prod_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1490359111at_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      lex_pr413684186lle_tv: set_Pr1986765409at_nat > set_Pr2014382200lle_tv > set_Pr292927124lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Wellfounded_Olex__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 3.06/1.58      lex_pr1785529980tv_nat: set_Pr2014382200lle_tv > set_Pr1986765409at_nat > set_Pr1943077434tv_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Wellfounded_Olex__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      lex_pr567812260lle_tv: set_Pr2014382200lle_tv > set_Pr2014382200lle_tv > set_Pr2012908090lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 3.06/1.58      wf_nat: set_Pr1986765409at_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Wellfounded_Owf_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      wf_Par1378404612lle_tv: set_Pr2014382200lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Wfrec_Osame__fst_001_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 3.06/1.58      same_f1581085506lle_fm: ( ( list_char > paraco1605129243lle_tv ) > $o ) > ( ( list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm ) > set_Pr1475944804lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_Wfrec_Osame__fst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      same_f1138187694lle_tv: ( ( nat > nat ) > $o ) > ( ( nat > nat ) > set_Pr2014382200lle_tv ) > set_Pr698334450lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Nat__Onat,type,
% 3.06/1.58      member_nat: nat > set_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 3.06/1.58      member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      member146333935lle_tv: produc1852595672lle_tv > set_Pr2061825550lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 3.06/1.58      member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.06/1.58      member112824072at_nat: produc1281043295at_nat > set_Pr1357842111at_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      member1569366824lle_tv: produc931990033lle_tv > set_Pr560526279lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 3.06/1.58      member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_M_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 3.06/1.58      member334644067lle_fm: produc450659916lle_fm > set_Pr1019238018lle_fm > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 3.06/1.58      member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 3.06/1.58      member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 3.06/1.58      member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_Mt__Product____Type__Oprod_I_062_It__List__Olist_It__String__Ochar_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 3.06/1.58      member1592865093lle_fm: produc1250255278lle_fm > set_Pr1475944804lle_fm > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_Mt__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 3.06/1.58      member1339857875lle_tv: produc1720769084lle_tv > set_Pr698334450lle_tv > $o ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_v_f,type,
% 3.06/1.58      f: nat > nat ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_v_i,type,
% 3.06/1.58      i: list_char > paraco1605129243lle_tv ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_v_p1____,type,
% 3.06/1.58      p1: paraco1604210848lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(sy_v_p2____,type,
% 3.06/1.58      p2: paraco1604210848lle_fm ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_0_a_H_H_H,axiom,
% 3.06/1.58      ( ( paraco1325918602e_eval @ i @ p2 )
% 3.06/1.58     != ( paraco1344940915le_Det @ $true ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_1_a_H_H,axiom,
% 3.06/1.58      ( ( paraco1325918602e_eval @ i @ p1 )
% 3.06/1.58     != ( paraco1344940915le_Det @ $true ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_2_a_H_H_H_H,axiom,
% 3.06/1.58      ( ( paraco1325918602e_eval @ i @ p1 )
% 3.06/1.58     != ( paraco1344940915le_Det @ $false ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_3_b_H_H,axiom,
% 3.06/1.58      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 3.06/1.58     != ( paraco1344940915le_Det @ $true ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_4_a,axiom,
% 3.06/1.58      ( ( paraco1325918602e_eval @ i @ p2 )
% 3.06/1.58      = ( paraco1344940915le_Det @ $false ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_5_a_H,axiom,
% 3.06/1.58      ( ( paraco1325918602e_eval @ i @ p1 )
% 3.06/1.58     != ( paraco1325918602e_eval @ i @ p2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_6_b,axiom,
% 3.06/1.58      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
% 3.06/1.58      = ( paraco1344940915le_Det @ $false ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_7_b_H,axiom,
% 3.06/1.58      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 3.06/1.58     != ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_8_tv_Oinject_I1_J,axiom,
% 3.06/1.58      ! [X1: $o,Y1: $o] :
% 3.06/1.58        ( ( ( paraco1344940915le_Det @ X1 )
% 3.06/1.58          = ( paraco1344940915le_Det @ Y1 ) )
% 3.06/1.58        = ( X1 = Y1 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_9_ih2,axiom,
% 3.06/1.58      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
% 3.06/1.58      = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_10_ih1,axiom,
% 3.06/1.58      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 3.06/1.58      = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p1 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_11__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_AFalse_092_060close_062,axiom,
% 3.06/1.58      ( ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) )
% 3.06/1.58      = ( paraco1344940915le_Det @ $false ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_12_valid__def,axiom,
% 3.06/1.58      ( paraco327635598_valid
% 3.06/1.58      = ( ^ [P: paraco1604210848lle_fm] :
% 3.06/1.58          ! [I: list_char > paraco1605129243lle_tv] :
% 3.06/1.58            ( ( paraco1325918602e_eval @ I @ P )
% 3.06/1.58            = ( paraco1344940915le_Det @ $true ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_13_yes,axiom,
% 3.06/1.58      ( ( paraco1325918602e_eval @ i @ ( paraco1745535428le_Eql @ p1 @ p2 ) )
% 3.06/1.58      = ( paraco1325918602e_eval @ i @ ( paraco445776468le_Neg @ p1 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_14_eval_Osimps_I2_J,axiom,
% 3.06/1.58      ! [I2: list_char > paraco1605129243lle_tv] :
% 3.06/1.58        ( ( paraco1325918602e_eval @ I2 @ paraco367965286_Truth )
% 3.06/1.58        = ( paraco1344940915le_Det @ $true ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_15_eval_Osimps_I5_J,axiom,
% 3.06/1.58      ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58            = ( paraco1325918602e_eval @ I2 @ Q ) )
% 3.06/1.58         => ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
% 3.06/1.58            = ( paraco1344940915le_Det @ $true ) ) )
% 3.06/1.58        & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58           != ( paraco1325918602e_eval @ I2 @ Q ) )
% 3.06/1.58         => ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
% 3.06/1.58            = ( paraco1344940915le_Det @ $false ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_16_eval__equality__simplify,axiom,
% 3.06/1.58      ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( paraco1325918602e_eval @ I2 @ ( paraco1389086619le_Eql @ P2 @ Q ) )
% 3.06/1.58        = ( paraco1344940915le_Det
% 3.06/1.58          @ ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58            = ( paraco1325918602e_eval @ I2 @ Q ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_17_change__int__def,axiom,
% 3.06/1.58      ( paraco761681009ge_int
% 3.06/1.58      = ( ^ [F: nat > nat,I: list_char > paraco1605129243lle_tv,S: list_char] : ( paraco1147068288nge_tv @ F @ ( I @ S ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_18_eval_Osimps_I4_J,axiom,
% 3.06/1.58      ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58            = ( paraco1325918602e_eval @ I2 @ Q ) )
% 3.06/1.58         => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 3.06/1.58            = ( paraco1325918602e_eval @ I2 @ P2 ) ) )
% 3.06/1.58        & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58           != ( paraco1325918602e_eval @ I2 @ Q ) )
% 3.06/1.58         => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58                = ( paraco1344940915le_Det @ $true ) )
% 3.06/1.58             => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 3.06/1.58                = ( paraco1325918602e_eval @ I2 @ Q ) ) )
% 3.06/1.58            & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58               != ( paraco1344940915le_Det @ $true ) )
% 3.06/1.58             => ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 3.06/1.58                    = ( paraco1344940915le_Det @ $true ) )
% 3.06/1.58                 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 3.06/1.58                    = ( paraco1325918602e_eval @ I2 @ P2 ) ) )
% 3.06/1.58                & ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 3.06/1.58                   != ( paraco1344940915le_Det @ $true ) )
% 3.06/1.58                 => ( ( paraco1325918602e_eval @ I2 @ ( paraco69239110le_Con @ P2 @ Q ) )
% 3.06/1.58                    = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_19_tv_Osimps_I5_J,axiom,
% 3.06/1.58      ! [F1: $o > paraco1605129243lle_tv,F2: nat > paraco1605129243lle_tv,X1: $o] :
% 3.06/1.58        ( ( paraco2051596139lle_tv @ F1 @ F2 @ ( paraco1344940915le_Det @ X1 ) )
% 3.06/1.58        = ( F1 @ X1 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_20_eval__negation,axiom,
% 3.06/1.58      ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58            = ( paraco1344940915le_Det @ $false ) )
% 3.06/1.58         => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 3.06/1.58            = ( paraco1344940915le_Det @ $true ) ) )
% 3.06/1.58        & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58           != ( paraco1344940915le_Det @ $false ) )
% 3.06/1.58         => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58                = ( paraco1344940915le_Det @ $true ) )
% 3.06/1.58             => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 3.06/1.58                = ( paraco1344940915le_Det @ $false ) ) )
% 3.06/1.58            & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58               != ( paraco1344940915le_Det @ $true ) )
% 3.06/1.58             => ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 3.06/1.58                = ( paraco1325918602e_eval @ I2 @ P2 ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_21_assms,axiom,
% 3.06/1.58      inj_on_nat_nat @ f @ top_top_set_nat ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_22_change__tv_Osimps_I1_J,axiom,
% 3.06/1.58      ! [F3: nat > nat,B: $o] :
% 3.06/1.58        ( ( paraco1147068288nge_tv @ F3 @ ( paraco1344940915le_Det @ B ) )
% 3.06/1.58        = ( paraco1344940915le_Det @ B ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_23_fm_Oinject_I2_J,axiom,
% 3.06/1.58      ! [X3: paraco1604210848lle_fm,Y3: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( ( paraco445776468le_Neg @ X3 )
% 3.06/1.58          = ( paraco445776468le_Neg @ Y3 ) )
% 3.06/1.58        = ( X3 = Y3 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_24_fm_Oinject_I3_J,axiom,
% 3.06/1.58      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,Y41: paraco1604210848lle_fm,Y42: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( ( paraco69239110le_Con @ X41 @ X42 )
% 3.06/1.58          = ( paraco69239110le_Con @ Y41 @ Y42 ) )
% 3.06/1.58        = ( ( X41 = Y41 )
% 3.06/1.58          & ( X42 = Y42 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_25_fm_Oinject_I5_J,axiom,
% 3.06/1.58      ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm,Y61: paraco1604210848lle_fm,Y62: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( ( paraco1745535428le_Eql @ X61 @ X62 )
% 3.06/1.58          = ( paraco1745535428le_Eql @ Y61 @ Y62 ) )
% 3.06/1.58        = ( ( X61 = Y61 )
% 3.06/1.58          & ( X62 = Y62 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_26_fm_Oinject_I4_J,axiom,
% 3.06/1.58      ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,Y51: paraco1604210848lle_fm,Y52: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 3.06/1.58          = ( paraco1389086619le_Eql @ Y51 @ Y52 ) )
% 3.06/1.58        = ( ( X51 = Y51 )
% 3.06/1.58          & ( X52 = Y52 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_27_fm_Odistinct_I29_J,axiom,
% 3.06/1.58      ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 3.06/1.58       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_28_fm_Odistinct_I27_J,axiom,
% 3.06/1.58      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( paraco69239110le_Con @ X41 @ X42 )
% 3.06/1.58       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_29_fm_Odistinct_I25_J,axiom,
% 3.06/1.58      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( paraco69239110le_Con @ X41 @ X42 )
% 3.06/1.58       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_30_fm_Odistinct_I23_J,axiom,
% 3.06/1.58      ! [X3: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( paraco445776468le_Neg @ X3 )
% 3.06/1.58       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_31_fm_Odistinct_I21_J,axiom,
% 3.06/1.58      ! [X3: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( paraco445776468le_Neg @ X3 )
% 3.06/1.58       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_32_fm_Odistinct_I19_J,axiom,
% 3.06/1.58      ! [X3: paraco1604210848lle_fm,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( paraco445776468le_Neg @ X3 )
% 3.06/1.58       != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_33_fm_Odistinct_I17_J,axiom,
% 3.06/1.58      ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 3.06/1.58        ( paraco367965286_Truth
% 3.06/1.58       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_34_fm_Odistinct_I15_J,axiom,
% 3.06/1.58      ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 3.06/1.58        ( paraco367965286_Truth
% 3.06/1.58       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_35_fm_Odistinct_I13_J,axiom,
% 3.06/1.58      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 3.06/1.58        ( paraco367965286_Truth
% 3.06/1.58       != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_36_fm_Odistinct_I11_J,axiom,
% 3.06/1.58      ! [X3: paraco1604210848lle_fm] :
% 3.06/1.58        ( paraco367965286_Truth
% 3.06/1.58       != ( paraco445776468le_Neg @ X3 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_37_conjunction,axiom,
% 3.06/1.58      ! [P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( paraco327635598_valid @ ( paraco69239110le_Con @ P2 @ Q ) )
% 3.06/1.58        = ( ( paraco327635598_valid @ P2 )
% 3.06/1.58          & ( paraco327635598_valid @ Q ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_38_eval__equality,axiom,
% 3.06/1.58      ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58            = ( paraco1325918602e_eval @ I2 @ Q ) )
% 3.06/1.58         => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 3.06/1.58            = ( paraco1344940915le_Det @ $true ) ) )
% 3.06/1.58        & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58           != ( paraco1325918602e_eval @ I2 @ Q ) )
% 3.06/1.58         => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58                = ( paraco1344940915le_Det @ $true ) )
% 3.06/1.58             => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 3.06/1.58                = ( paraco1325918602e_eval @ I2 @ Q ) ) )
% 3.06/1.58            & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58               != ( paraco1344940915le_Det @ $true ) )
% 3.06/1.58             => ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 3.06/1.58                    = ( paraco1344940915le_Det @ $true ) )
% 3.06/1.58                 => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 3.06/1.58                    = ( paraco1325918602e_eval @ I2 @ P2 ) ) )
% 3.06/1.58                & ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 3.06/1.58                   != ( paraco1344940915le_Det @ $true ) )
% 3.06/1.58                 => ( ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58                        = ( paraco1344940915le_Det @ $false ) )
% 3.06/1.58                     => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 3.06/1.58                        = ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ Q ) ) ) )
% 3.06/1.58                    & ( ( ( paraco1325918602e_eval @ I2 @ P2 )
% 3.06/1.58                       != ( paraco1344940915le_Det @ $false ) )
% 3.06/1.58                     => ( ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 3.06/1.58                            = ( paraco1344940915le_Det @ $false ) )
% 3.06/1.58                         => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 3.06/1.58                            = ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) ) ) )
% 3.06/1.58                        & ( ( ( paraco1325918602e_eval @ I2 @ Q )
% 3.06/1.58                           != ( paraco1344940915le_Det @ $false ) )
% 3.06/1.58                         => ( ( paraco1325918602e_eval @ I2 @ ( paraco1745535428le_Eql @ P2 @ Q ) )
% 3.06/1.58                            = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_39_double__negation,axiom,
% 3.06/1.58      ( paraco1325918602e_eval
% 3.06/1.58      = ( ^ [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ P ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_40_UNIV__I,axiom,
% 3.06/1.58      ! [X: produc696645085lle_fm] : ( member1474794996lle_fm @ X @ top_to775056195lle_fm ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_41_UNIV__I,axiom,
% 3.06/1.58      ! [X: produc1852595672lle_tv] : ( member146333935lle_tv @ X @ top_to138697918lle_tv ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_42_UNIV__I,axiom,
% 3.06/1.58      ! [X: produc931990033lle_tv] : ( member1569366824lle_tv @ X @ top_to449985143lle_tv ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_43_UNIV__I,axiom,
% 3.06/1.58      ! [X: produc1281043295at_nat] : ( member112824072at_nat @ X @ top_to1541413903at_nat ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_44_UNIV__I,axiom,
% 3.06/1.58      ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_45_UNIV__I,axiom,
% 3.06/1.58      ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_46_UNIV__I,axiom,
% 3.06/1.58      ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_47_UNIV__I,axiom,
% 3.06/1.58      ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_48_UNIV__I,axiom,
% 3.06/1.58      ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_49_iso__tuple__UNIV__I,axiom,
% 3.06/1.58      ! [X: produc696645085lle_fm] : ( member1474794996lle_fm @ X @ top_to775056195lle_fm ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_50_iso__tuple__UNIV__I,axiom,
% 3.06/1.58      ! [X: produc1852595672lle_tv] : ( member146333935lle_tv @ X @ top_to138697918lle_tv ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_51_iso__tuple__UNIV__I,axiom,
% 3.06/1.58      ! [X: produc931990033lle_tv] : ( member1569366824lle_tv @ X @ top_to449985143lle_tv ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_52_iso__tuple__UNIV__I,axiom,
% 3.06/1.58      ! [X: produc1281043295at_nat] : ( member112824072at_nat @ X @ top_to1541413903at_nat ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_53_iso__tuple__UNIV__I,axiom,
% 3.06/1.58      ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_54_iso__tuple__UNIV__I,axiom,
% 3.06/1.58      ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_55_iso__tuple__UNIV__I,axiom,
% 3.06/1.58      ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_56_iso__tuple__UNIV__I,axiom,
% 3.06/1.58      ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_57_iso__tuple__UNIV__I,axiom,
% 3.06/1.58      ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_58_top__apply,axiom,
% 3.06/1.58      ( top_to1299250770e_tv_o
% 3.06/1.58      = ( ^ [X2: paraco1605129243lle_tv] : top_top_o ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_59_top__apply,axiom,
% 3.06/1.58      ( top_top_nat_o
% 3.06/1.58      = ( ^ [X2: nat] : top_top_o ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_60_injD,axiom,
% 3.06/1.58      ! [F3: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 3.06/1.58        ( ( inj_on2112487900lle_tv @ F3 @ top_to1871154984lle_tv )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58         => ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_61_injD,axiom,
% 3.06/1.58      ! [F3: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 3.06/1.58        ( ( inj_on1955349912lle_tv @ F3 @ top_top_set_nat )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58         => ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_62_injD,axiom,
% 3.06/1.58      ! [F3: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 3.06/1.58        ( ( inj_on552895452tv_nat @ F3 @ top_to975729152tv_nat )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58         => ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_63_injD,axiom,
% 3.06/1.58      ! [F3: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 3.06/1.58        ( ( inj_on1745913142lle_tv @ F3 @ top_to1411004326lle_tv )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58         => ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_64_injD,axiom,
% 3.06/1.58      ! [F3: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 3.06/1.58        ( ( inj_on26176689at_nat @ F3 @ top_to1555900337at_nat )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58         => ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_65_injD,axiom,
% 3.06/1.58      ! [F3: nat > nat,X: nat,Y: nat] :
% 3.06/1.58        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58         => ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_66_injD,axiom,
% 3.06/1.58      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.58        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58         => ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_67_mem__Collect__eq,axiom,
% 3.06/1.58      ! [A: produc696645085lle_fm,P3: produc696645085lle_fm > $o] :
% 3.06/1.58        ( ( member1474794996lle_fm @ A @ ( collec835549234lle_fm @ P3 ) )
% 3.06/1.58        = ( P3 @ A ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_68_mem__Collect__eq,axiom,
% 3.06/1.58      ! [A: produc1852595672lle_tv,P3: produc1852595672lle_tv > $o] :
% 3.06/1.58        ( ( member146333935lle_tv @ A @ ( collec1102043437lle_tv @ P3 ) )
% 3.06/1.58        = ( P3 @ A ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_69_mem__Collect__eq,axiom,
% 3.06/1.58      ! [A: produc931990033lle_tv,P3: produc931990033lle_tv > $o] :
% 3.06/1.58        ( ( member1569366824lle_tv @ A @ ( collec1624074086lle_tv @ P3 ) )
% 3.06/1.58        = ( P3 @ A ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_70_mem__Collect__eq,axiom,
% 3.06/1.58      ! [A: produc1281043295at_nat,P3: produc1281043295at_nat > $o] :
% 3.06/1.58        ( ( member112824072at_nat @ A @ ( collec791369802at_nat @ P3 ) )
% 3.06/1.58        = ( P3 @ A ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_71_mem__Collect__eq,axiom,
% 3.06/1.58      ! [A: paraco1605129243lle_tv,P3: paraco1605129243lle_tv > $o] :
% 3.06/1.58        ( ( member266900804lle_tv @ A @ ( collec1111687558lle_tv @ P3 ) )
% 3.06/1.58        = ( P3 @ A ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_72_mem__Collect__eq,axiom,
% 3.06/1.58      ! [A: nat,P3: nat > $o] :
% 3.06/1.58        ( ( member_nat @ A @ ( collect_nat @ P3 ) )
% 3.06/1.58        = ( P3 @ A ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_73_Collect__mem__eq,axiom,
% 3.06/1.58      ! [A2: set_Pr2120184979lle_fm] :
% 3.06/1.58        ( ( collec835549234lle_fm
% 3.06/1.58          @ ^ [X2: produc696645085lle_fm] : ( member1474794996lle_fm @ X2 @ A2 ) )
% 3.06/1.58        = A2 ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_74_Collect__mem__eq,axiom,
% 3.06/1.58      ! [A2: set_Pr2061825550lle_tv] :
% 3.06/1.58        ( ( collec1102043437lle_tv
% 3.06/1.58          @ ^ [X2: produc1852595672lle_tv] : ( member146333935lle_tv @ X2 @ A2 ) )
% 3.06/1.58        = A2 ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_75_Collect__mem__eq,axiom,
% 3.06/1.58      ! [A2: set_Pr560526279lle_tv] :
% 3.06/1.58        ( ( collec1624074086lle_tv
% 3.06/1.58          @ ^ [X2: produc931990033lle_tv] : ( member1569366824lle_tv @ X2 @ A2 ) )
% 3.06/1.58        = A2 ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_76_Collect__mem__eq,axiom,
% 3.06/1.58      ! [A2: set_Pr1357842111at_nat] :
% 3.06/1.58        ( ( collec791369802at_nat
% 3.06/1.58          @ ^ [X2: produc1281043295at_nat] : ( member112824072at_nat @ X2 @ A2 ) )
% 3.06/1.58        = A2 ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_77_Collect__mem__eq,axiom,
% 3.06/1.58      ! [A2: set_Pa1764573435lle_tv] :
% 3.06/1.58        ( ( collec1111687558lle_tv
% 3.06/1.58          @ ^ [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ A2 ) )
% 3.06/1.58        = A2 ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_78_Collect__mem__eq,axiom,
% 3.06/1.58      ! [A2: set_nat] :
% 3.06/1.58        ( ( collect_nat
% 3.06/1.58          @ ^ [X2: nat] : ( member_nat @ X2 @ A2 ) )
% 3.06/1.58        = A2 ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_79_Collect__cong,axiom,
% 3.06/1.58      ! [P3: paraco1605129243lle_tv > $o,Q2: paraco1605129243lle_tv > $o] :
% 3.06/1.58        ( ! [X4: paraco1605129243lle_tv] :
% 3.06/1.58            ( ( P3 @ X4 )
% 3.06/1.58            = ( Q2 @ X4 ) )
% 3.06/1.58       => ( ( collec1111687558lle_tv @ P3 )
% 3.06/1.58          = ( collec1111687558lle_tv @ Q2 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_80_Collect__cong,axiom,
% 3.06/1.58      ! [P3: nat > $o,Q2: nat > $o] :
% 3.06/1.58        ( ! [X4: nat] :
% 3.06/1.58            ( ( P3 @ X4 )
% 3.06/1.58            = ( Q2 @ X4 ) )
% 3.06/1.58       => ( ( collect_nat @ P3 )
% 3.06/1.58          = ( collect_nat @ Q2 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_81_injI,axiom,
% 3.06/1.58      ! [F3: produc1647334210lle_tv > produc1647334210lle_tv] :
% 3.06/1.58        ( ! [X4: produc1647334210lle_tv,Y2: produc1647334210lle_tv] :
% 3.06/1.58            ( ( ( F3 @ X4 )
% 3.06/1.58              = ( F3 @ Y2 ) )
% 3.06/1.58           => ( X4 = Y2 ) )
% 3.06/1.58       => ( inj_on2112487900lle_tv @ F3 @ top_to1871154984lle_tv ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_82_injI,axiom,
% 3.06/1.58      ! [F3: nat > paraco1605129243lle_tv] :
% 3.06/1.58        ( ! [X4: nat,Y2: nat] :
% 3.06/1.58            ( ( ( F3 @ X4 )
% 3.06/1.58              = ( F3 @ Y2 ) )
% 3.06/1.58           => ( X4 = Y2 ) )
% 3.06/1.58       => ( inj_on1955349912lle_tv @ F3 @ top_top_set_nat ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_83_injI,axiom,
% 3.06/1.58      ! [F3: produc194167194tv_nat > produc194167194tv_nat] :
% 3.06/1.58        ( ! [X4: produc194167194tv_nat,Y2: produc194167194tv_nat] :
% 3.06/1.58            ( ( ( F3 @ X4 )
% 3.06/1.58              = ( F3 @ Y2 ) )
% 3.06/1.58           => ( X4 = Y2 ) )
% 3.06/1.58       => ( inj_on552895452tv_nat @ F3 @ top_to975729152tv_nat ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_84_injI,axiom,
% 3.06/1.58      ! [F3: produc270694976lle_tv > produc270694976lle_tv] :
% 3.06/1.58        ( ! [X4: produc270694976lle_tv,Y2: produc270694976lle_tv] :
% 3.06/1.58            ( ( ( F3 @ X4 )
% 3.06/1.58              = ( F3 @ Y2 ) )
% 3.06/1.58           => ( X4 = Y2 ) )
% 3.06/1.58       => ( inj_on1745913142lle_tv @ F3 @ top_to1411004326lle_tv ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_85_injI,axiom,
% 3.06/1.58      ! [F3: product_prod_nat_nat > product_prod_nat_nat] :
% 3.06/1.58        ( ! [X4: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 3.06/1.58            ( ( ( F3 @ X4 )
% 3.06/1.58              = ( F3 @ Y2 ) )
% 3.06/1.58           => ( X4 = Y2 ) )
% 3.06/1.58       => ( inj_on26176689at_nat @ F3 @ top_to1555900337at_nat ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_86_injI,axiom,
% 3.06/1.58      ! [F3: nat > nat] :
% 3.06/1.58        ( ! [X4: nat,Y2: nat] :
% 3.06/1.58            ( ( ( F3 @ X4 )
% 3.06/1.58              = ( F3 @ Y2 ) )
% 3.06/1.58           => ( X4 = Y2 ) )
% 3.06/1.58       => ( inj_on_nat_nat @ F3 @ top_top_set_nat ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_87_injI,axiom,
% 3.06/1.58      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.58        ( ! [X4: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
% 3.06/1.58            ( ( ( F3 @ X4 )
% 3.06/1.58              = ( F3 @ Y2 ) )
% 3.06/1.58           => ( X4 = Y2 ) )
% 3.06/1.58       => ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_88_inj__eq,axiom,
% 3.06/1.58      ! [F3: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 3.06/1.58        ( ( inj_on2112487900lle_tv @ F3 @ top_to1871154984lle_tv )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58          = ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_89_inj__eq,axiom,
% 3.06/1.58      ! [F3: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 3.06/1.58        ( ( inj_on1955349912lle_tv @ F3 @ top_top_set_nat )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58          = ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_90_inj__eq,axiom,
% 3.06/1.58      ! [F3: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 3.06/1.58        ( ( inj_on552895452tv_nat @ F3 @ top_to975729152tv_nat )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58          = ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_91_inj__eq,axiom,
% 3.06/1.58      ! [F3: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 3.06/1.58        ( ( inj_on1745913142lle_tv @ F3 @ top_to1411004326lle_tv )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58          = ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_92_inj__eq,axiom,
% 3.06/1.58      ! [F3: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 3.06/1.58        ( ( inj_on26176689at_nat @ F3 @ top_to1555900337at_nat )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58          = ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_93_inj__eq,axiom,
% 3.06/1.58      ! [F3: nat > nat,X: nat,Y: nat] :
% 3.06/1.58        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58          = ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_94_inj__eq,axiom,
% 3.06/1.58      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.58        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 3.06/1.58       => ( ( ( F3 @ X )
% 3.06/1.58            = ( F3 @ Y ) )
% 3.06/1.58          = ( X = Y ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_95_inj__def,axiom,
% 3.06/1.58      ! [F3: produc1647334210lle_tv > produc1647334210lle_tv] :
% 3.06/1.58        ( ( inj_on2112487900lle_tv @ F3 @ top_to1871154984lle_tv )
% 3.06/1.58        = ( ! [X2: produc1647334210lle_tv,Y4: produc1647334210lle_tv] :
% 3.06/1.58              ( ( ( F3 @ X2 )
% 3.06/1.58                = ( F3 @ Y4 ) )
% 3.06/1.58             => ( X2 = Y4 ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_96_inj__def,axiom,
% 3.06/1.58      ! [F3: nat > paraco1605129243lle_tv] :
% 3.06/1.58        ( ( inj_on1955349912lle_tv @ F3 @ top_top_set_nat )
% 3.06/1.58        = ( ! [X2: nat,Y4: nat] :
% 3.06/1.58              ( ( ( F3 @ X2 )
% 3.06/1.58                = ( F3 @ Y4 ) )
% 3.06/1.58             => ( X2 = Y4 ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_97_inj__def,axiom,
% 3.06/1.58      ! [F3: produc194167194tv_nat > produc194167194tv_nat] :
% 3.06/1.58        ( ( inj_on552895452tv_nat @ F3 @ top_to975729152tv_nat )
% 3.06/1.58        = ( ! [X2: produc194167194tv_nat,Y4: produc194167194tv_nat] :
% 3.06/1.58              ( ( ( F3 @ X2 )
% 3.06/1.58                = ( F3 @ Y4 ) )
% 3.06/1.58             => ( X2 = Y4 ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_98_inj__def,axiom,
% 3.06/1.58      ! [F3: produc270694976lle_tv > produc270694976lle_tv] :
% 3.06/1.58        ( ( inj_on1745913142lle_tv @ F3 @ top_to1411004326lle_tv )
% 3.06/1.58        = ( ! [X2: produc270694976lle_tv,Y4: produc270694976lle_tv] :
% 3.06/1.58              ( ( ( F3 @ X2 )
% 3.06/1.58                = ( F3 @ Y4 ) )
% 3.06/1.58             => ( X2 = Y4 ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_99_inj__def,axiom,
% 3.06/1.58      ! [F3: product_prod_nat_nat > product_prod_nat_nat] :
% 3.06/1.58        ( ( inj_on26176689at_nat @ F3 @ top_to1555900337at_nat )
% 3.06/1.58        = ( ! [X2: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 3.06/1.58              ( ( ( F3 @ X2 )
% 3.06/1.58                = ( F3 @ Y4 ) )
% 3.06/1.58             => ( X2 = Y4 ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_100_inj__def,axiom,
% 3.06/1.58      ! [F3: nat > nat] :
% 3.06/1.58        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.58        = ( ! [X2: nat,Y4: nat] :
% 3.06/1.58              ( ( ( F3 @ X2 )
% 3.06/1.58                = ( F3 @ Y4 ) )
% 3.06/1.58             => ( X2 = Y4 ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_101_inj__def,axiom,
% 3.06/1.58      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.58        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 3.06/1.58        = ( ! [X2: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
% 3.06/1.58              ( ( ( F3 @ X2 )
% 3.06/1.58                = ( F3 @ Y4 ) )
% 3.06/1.58             => ( X2 = Y4 ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_102_fm_Oinduct,axiom,
% 3.06/1.58      ! [P3: paraco1604210848lle_fm > $o,Fm: paraco1604210848lle_fm] :
% 3.06/1.58        ( ! [X4: list_char] : ( P3 @ ( paraco1480028776le_Pro @ X4 ) )
% 3.06/1.58       => ( ( P3 @ paraco367965286_Truth )
% 3.06/1.58         => ( ! [X4: paraco1604210848lle_fm] :
% 3.06/1.58                ( ( P3 @ X4 )
% 3.06/1.58               => ( P3 @ ( paraco445776468le_Neg @ X4 ) ) )
% 3.06/1.58           => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 3.06/1.58                  ( ( P3 @ X1a )
% 3.06/1.58                 => ( ( P3 @ X22 )
% 3.06/1.58                   => ( P3 @ ( paraco69239110le_Con @ X1a @ X22 ) ) ) )
% 3.06/1.58             => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 3.06/1.58                    ( ( P3 @ X1a )
% 3.06/1.58                   => ( ( P3 @ X22 )
% 3.06/1.58                     => ( P3 @ ( paraco1389086619le_Eql @ X1a @ X22 ) ) ) )
% 3.06/1.58               => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 3.06/1.58                      ( ( P3 @ X1a )
% 3.06/1.58                     => ( ( P3 @ X22 )
% 3.06/1.58                       => ( P3 @ ( paraco1745535428le_Eql @ X1a @ X22 ) ) ) )
% 3.06/1.58                 => ( P3 @ Fm ) ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_103_fm_Oexhaust,axiom,
% 3.06/1.58      ! [Y: paraco1604210848lle_fm] :
% 3.06/1.58        ( ! [X12: list_char] :
% 3.06/1.58            ( Y
% 3.06/1.58           != ( paraco1480028776le_Pro @ X12 ) )
% 3.06/1.58       => ( ( Y != paraco367965286_Truth )
% 3.06/1.58         => ( ! [X32: paraco1604210848lle_fm] :
% 3.06/1.58                ( Y
% 3.06/1.58               != ( paraco445776468le_Neg @ X32 ) )
% 3.06/1.58           => ( ! [X412: paraco1604210848lle_fm,X422: paraco1604210848lle_fm] :
% 3.06/1.58                  ( Y
% 3.06/1.58                 != ( paraco69239110le_Con @ X412 @ X422 ) )
% 3.06/1.58             => ( ! [X512: paraco1604210848lle_fm,X522: paraco1604210848lle_fm] :
% 3.06/1.58                    ( Y
% 3.06/1.58                   != ( paraco1389086619le_Eql @ X512 @ X522 ) )
% 3.06/1.58               => ~ ! [X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 3.06/1.58                      ( Y
% 3.06/1.58                     != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_104_props_Ocases,axiom,
% 3.06/1.58      ! [X: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( X != paraco367965286_Truth )
% 3.06/1.58       => ( ! [S2: list_char] :
% 3.06/1.58              ( X
% 3.06/1.58             != ( paraco1480028776le_Pro @ S2 ) )
% 3.06/1.58         => ( ! [P4: paraco1604210848lle_fm] :
% 3.06/1.58                ( X
% 3.06/1.58               != ( paraco445776468le_Neg @ P4 ) )
% 3.06/1.58           => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 3.06/1.58                  ( X
% 3.06/1.58                 != ( paraco69239110le_Con @ P4 @ Q3 ) )
% 3.06/1.58             => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 3.06/1.58                    ( X
% 3.06/1.58                   != ( paraco1389086619le_Eql @ P4 @ Q3 ) )
% 3.06/1.58               => ~ ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 3.06/1.58                      ( X
% 3.06/1.58                     != ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_105_fm_Oinject_I1_J,axiom,
% 3.06/1.58      ! [X1: list_char,Y1: list_char] :
% 3.06/1.58        ( ( ( paraco1480028776le_Pro @ X1 )
% 3.06/1.58          = ( paraco1480028776le_Pro @ Y1 ) )
% 3.06/1.58        = ( X1 = Y1 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_106_top__set__def,axiom,
% 3.06/1.58      ( top_to975729152tv_nat
% 3.06/1.58      = ( collec848462447tv_nat @ top_to900819589_nat_o ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_107_top__set__def,axiom,
% 3.06/1.58      ( top_to1411004326lle_tv
% 3.06/1.58      = ( collec924990229lle_tv @ top_to1889334367e_tv_o ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_108_top__set__def,axiom,
% 3.06/1.58      ( top_to1555900337at_nat
% 3.06/1.58      = ( collec7649004at_nat @ top_to632227436_nat_o ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_109_top__set__def,axiom,
% 3.06/1.58      ( top_top_set_nat
% 3.06/1.58      = ( collect_nat @ top_top_nat_o ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_110_top__set__def,axiom,
% 3.06/1.58      ( top_to1057771083lle_tv
% 3.06/1.58      = ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_111_eval_Osimps_I1_J,axiom,
% 3.06/1.58      ! [I2: list_char > paraco1605129243lle_tv,S3: list_char] :
% 3.06/1.58        ( ( paraco1325918602e_eval @ I2 @ ( paraco1480028776le_Pro @ S3 ) )
% 3.06/1.58        = ( I2 @ S3 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_112_fm_Odistinct_I3_J,axiom,
% 3.06/1.58      ! [X1: list_char,X3: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( paraco1480028776le_Pro @ X1 )
% 3.06/1.58       != ( paraco445776468le_Neg @ X3 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_113_fm_Odistinct_I5_J,axiom,
% 3.06/1.58      ! [X1: list_char,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( paraco1480028776le_Pro @ X1 )
% 3.06/1.58       != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_114_fm_Odistinct_I9_J,axiom,
% 3.06/1.58      ! [X1: list_char,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( paraco1480028776le_Pro @ X1 )
% 3.06/1.58       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_115_fm_Odistinct_I7_J,axiom,
% 3.06/1.58      ! [X1: list_char,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 3.06/1.58        ( ( paraco1480028776le_Pro @ X1 )
% 3.06/1.58       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_116_fm_Odistinct_I1_J,axiom,
% 3.06/1.58      ! [X1: list_char] :
% 3.06/1.58        ( ( paraco1480028776le_Pro @ X1 )
% 3.06/1.58       != paraco367965286_Truth ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_117_change__tv__injection,axiom,
% 3.06/1.58      ! [F3: nat > nat] :
% 3.06/1.58        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.58       => ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ F3 ) @ top_to1057771083lle_tv ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_118_UNIV__witness,axiom,
% 3.06/1.58      ? [X4: produc696645085lle_fm] : ( member1474794996lle_fm @ X4 @ top_to775056195lle_fm ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_119_UNIV__witness,axiom,
% 3.06/1.58      ? [X4: produc1852595672lle_tv] : ( member146333935lle_tv @ X4 @ top_to138697918lle_tv ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_120_UNIV__witness,axiom,
% 3.06/1.58      ? [X4: produc931990033lle_tv] : ( member1569366824lle_tv @ X4 @ top_to449985143lle_tv ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_121_UNIV__witness,axiom,
% 3.06/1.58      ? [X4: produc1281043295at_nat] : ( member112824072at_nat @ X4 @ top_to1541413903at_nat ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_122_UNIV__witness,axiom,
% 3.06/1.58      ? [X4: produc194167194tv_nat] : ( member737151281tv_nat @ X4 @ top_to975729152tv_nat ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_123_UNIV__witness,axiom,
% 3.06/1.58      ? [X4: produc270694976lle_tv] : ( member813679063lle_tv @ X4 @ top_to1411004326lle_tv ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_124_UNIV__witness,axiom,
% 3.06/1.58      ? [X4: product_prod_nat_nat] : ( member701585322at_nat @ X4 @ top_to1555900337at_nat ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_125_UNIV__witness,axiom,
% 3.06/1.58      ? [X4: nat] : ( member_nat @ X4 @ top_top_set_nat ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_126_UNIV__witness,axiom,
% 3.06/1.58      ? [X4: paraco1605129243lle_tv] : ( member266900804lle_tv @ X4 @ top_to1057771083lle_tv ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_127_UNIV__eq__I,axiom,
% 3.06/1.58      ! [A2: set_Pr2120184979lle_fm] :
% 3.06/1.58        ( ! [X4: produc696645085lle_fm] : ( member1474794996lle_fm @ X4 @ A2 )
% 3.06/1.58       => ( top_to775056195lle_fm = A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_128_UNIV__eq__I,axiom,
% 3.06/1.58      ! [A2: set_Pr2061825550lle_tv] :
% 3.06/1.58        ( ! [X4: produc1852595672lle_tv] : ( member146333935lle_tv @ X4 @ A2 )
% 3.06/1.58       => ( top_to138697918lle_tv = A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_129_UNIV__eq__I,axiom,
% 3.06/1.58      ! [A2: set_Pr560526279lle_tv] :
% 3.06/1.58        ( ! [X4: produc931990033lle_tv] : ( member1569366824lle_tv @ X4 @ A2 )
% 3.06/1.58       => ( top_to449985143lle_tv = A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_130_UNIV__eq__I,axiom,
% 3.06/1.58      ! [A2: set_Pr1357842111at_nat] :
% 3.06/1.58        ( ! [X4: produc1281043295at_nat] : ( member112824072at_nat @ X4 @ A2 )
% 3.06/1.58       => ( top_to1541413903at_nat = A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_131_UNIV__eq__I,axiom,
% 3.06/1.58      ! [A2: set_Pr1725653840tv_nat] :
% 3.06/1.58        ( ! [X4: produc194167194tv_nat] : ( member737151281tv_nat @ X4 @ A2 )
% 3.06/1.58       => ( top_to975729152tv_nat = A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_132_UNIV__eq__I,axiom,
% 3.06/1.58      ! [A2: set_Pr13445366lle_tv] :
% 3.06/1.58        ( ! [X4: produc270694976lle_tv] : ( member813679063lle_tv @ X4 @ A2 )
% 3.06/1.58       => ( top_to1411004326lle_tv = A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_133_UNIV__eq__I,axiom,
% 3.06/1.58      ! [A2: set_Pr1986765409at_nat] :
% 3.06/1.58        ( ! [X4: product_prod_nat_nat] : ( member701585322at_nat @ X4 @ A2 )
% 3.06/1.58       => ( top_to1555900337at_nat = A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_134_UNIV__eq__I,axiom,
% 3.06/1.58      ! [A2: set_nat] :
% 3.06/1.58        ( ! [X4: nat] : ( member_nat @ X4 @ A2 )
% 3.06/1.58       => ( top_top_set_nat = A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_135_UNIV__eq__I,axiom,
% 3.06/1.58      ! [A2: set_Pa1764573435lle_tv] :
% 3.06/1.58        ( ! [X4: paraco1605129243lle_tv] : ( member266900804lle_tv @ X4 @ A2 )
% 3.06/1.58       => ( top_to1057771083lle_tv = A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_136_inj__on__inverseI,axiom,
% 3.06/1.58      ! [A2: set_Pr2014382200lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv,F3: produc1647334210lle_tv > produc1647334210lle_tv] :
% 3.06/1.58        ( ! [X4: produc1647334210lle_tv] :
% 3.06/1.58            ( ( member1531318361lle_tv @ X4 @ A2 )
% 3.06/1.58           => ( ( G @ ( F3 @ X4 ) )
% 3.06/1.58              = X4 ) )
% 3.06/1.58       => ( inj_on2112487900lle_tv @ F3 @ A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_137_inj__on__inverseI,axiom,
% 3.06/1.58      ! [A2: set_Pr1725653840tv_nat,G: produc194167194tv_nat > produc194167194tv_nat,F3: produc194167194tv_nat > produc194167194tv_nat] :
% 3.06/1.58        ( ! [X4: produc194167194tv_nat] :
% 3.06/1.58            ( ( member737151281tv_nat @ X4 @ A2 )
% 3.06/1.58           => ( ( G @ ( F3 @ X4 ) )
% 3.06/1.58              = X4 ) )
% 3.06/1.58       => ( inj_on552895452tv_nat @ F3 @ A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_138_inj__on__inverseI,axiom,
% 3.06/1.58      ! [A2: set_Pr13445366lle_tv,G: produc270694976lle_tv > produc270694976lle_tv,F3: produc270694976lle_tv > produc270694976lle_tv] :
% 3.06/1.58        ( ! [X4: produc270694976lle_tv] :
% 3.06/1.58            ( ( member813679063lle_tv @ X4 @ A2 )
% 3.06/1.58           => ( ( G @ ( F3 @ X4 ) )
% 3.06/1.58              = X4 ) )
% 3.06/1.58       => ( inj_on1745913142lle_tv @ F3 @ A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_139_inj__on__inverseI,axiom,
% 3.06/1.58      ! [A2: set_Pr1986765409at_nat,G: product_prod_nat_nat > product_prod_nat_nat,F3: product_prod_nat_nat > product_prod_nat_nat] :
% 3.06/1.58        ( ! [X4: product_prod_nat_nat] :
% 3.06/1.58            ( ( member701585322at_nat @ X4 @ A2 )
% 3.06/1.58           => ( ( G @ ( F3 @ X4 ) )
% 3.06/1.58              = X4 ) )
% 3.06/1.58       => ( inj_on26176689at_nat @ F3 @ A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_140_inj__on__inverseI,axiom,
% 3.06/1.58      ! [A2: set_nat,G: paraco1605129243lle_tv > nat,F3: nat > paraco1605129243lle_tv] :
% 3.06/1.58        ( ! [X4: nat] :
% 3.06/1.58            ( ( member_nat @ X4 @ A2 )
% 3.06/1.58           => ( ( G @ ( F3 @ X4 ) )
% 3.06/1.58              = X4 ) )
% 3.06/1.58       => ( inj_on1955349912lle_tv @ F3 @ A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_141_inj__on__inverseI,axiom,
% 3.06/1.58      ! [A2: set_nat,G: nat > nat,F3: nat > nat] :
% 3.06/1.58        ( ! [X4: nat] :
% 3.06/1.58            ( ( member_nat @ X4 @ A2 )
% 3.06/1.58           => ( ( G @ ( F3 @ X4 ) )
% 3.06/1.58              = X4 ) )
% 3.06/1.58       => ( inj_on_nat_nat @ F3 @ A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_142_inj__on__inverseI,axiom,
% 3.06/1.58      ! [A2: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.58        ( ! [X4: paraco1605129243lle_tv] :
% 3.06/1.58            ( ( member266900804lle_tv @ X4 @ A2 )
% 3.06/1.58           => ( ( G @ ( F3 @ X4 ) )
% 3.06/1.58              = X4 ) )
% 3.06/1.58       => ( inj_on772319074lle_tv @ F3 @ A2 ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_143_inj__on__contraD,axiom,
% 3.06/1.58      ! [F3: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 3.06/1.58        ( ( inj_on2112487900lle_tv @ F3 @ A2 )
% 3.06/1.58       => ( ( X != Y )
% 3.06/1.58         => ( ( member1531318361lle_tv @ X @ A2 )
% 3.06/1.58           => ( ( member1531318361lle_tv @ Y @ A2 )
% 3.06/1.58             => ( ( F3 @ X )
% 3.06/1.58               != ( F3 @ Y ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_144_inj__on__contraD,axiom,
% 3.06/1.58      ! [F3: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 3.06/1.58        ( ( inj_on552895452tv_nat @ F3 @ A2 )
% 3.06/1.58       => ( ( X != Y )
% 3.06/1.58         => ( ( member737151281tv_nat @ X @ A2 )
% 3.06/1.58           => ( ( member737151281tv_nat @ Y @ A2 )
% 3.06/1.58             => ( ( F3 @ X )
% 3.06/1.58               != ( F3 @ Y ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_145_inj__on__contraD,axiom,
% 3.06/1.58      ! [F3: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 3.06/1.58        ( ( inj_on1745913142lle_tv @ F3 @ A2 )
% 3.06/1.58       => ( ( X != Y )
% 3.06/1.58         => ( ( member813679063lle_tv @ X @ A2 )
% 3.06/1.58           => ( ( member813679063lle_tv @ Y @ A2 )
% 3.06/1.58             => ( ( F3 @ X )
% 3.06/1.58               != ( F3 @ Y ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_146_inj__on__contraD,axiom,
% 3.06/1.58      ! [F3: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 3.06/1.58        ( ( inj_on26176689at_nat @ F3 @ A2 )
% 3.06/1.58       => ( ( X != Y )
% 3.06/1.58         => ( ( member701585322at_nat @ X @ A2 )
% 3.06/1.58           => ( ( member701585322at_nat @ Y @ A2 )
% 3.06/1.58             => ( ( F3 @ X )
% 3.06/1.58               != ( F3 @ Y ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_147_inj__on__contraD,axiom,
% 3.06/1.58      ! [F3: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 3.06/1.58        ( ( inj_on1955349912lle_tv @ F3 @ A2 )
% 3.06/1.58       => ( ( X != Y )
% 3.06/1.58         => ( ( member_nat @ X @ A2 )
% 3.06/1.58           => ( ( member_nat @ Y @ A2 )
% 3.06/1.58             => ( ( F3 @ X )
% 3.06/1.58               != ( F3 @ Y ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_148_inj__on__contraD,axiom,
% 3.06/1.58      ! [F3: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 3.06/1.58        ( ( inj_on_nat_nat @ F3 @ A2 )
% 3.06/1.58       => ( ( X != Y )
% 3.06/1.58         => ( ( member_nat @ X @ A2 )
% 3.06/1.58           => ( ( member_nat @ Y @ A2 )
% 3.06/1.58             => ( ( F3 @ X )
% 3.06/1.58               != ( F3 @ Y ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_149_inj__on__contraD,axiom,
% 3.06/1.58      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.58        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 3.06/1.58       => ( ( X != Y )
% 3.06/1.58         => ( ( member266900804lle_tv @ X @ A2 )
% 3.06/1.58           => ( ( member266900804lle_tv @ Y @ A2 )
% 3.06/1.58             => ( ( F3 @ X )
% 3.06/1.58               != ( F3 @ Y ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_150_inj__on__eq__iff,axiom,
% 3.06/1.58      ! [F3: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 3.06/1.58        ( ( inj_on2112487900lle_tv @ F3 @ A2 )
% 3.06/1.58       => ( ( member1531318361lle_tv @ X @ A2 )
% 3.06/1.58         => ( ( member1531318361lle_tv @ Y @ A2 )
% 3.06/1.58           => ( ( ( F3 @ X )
% 3.06/1.58                = ( F3 @ Y ) )
% 3.06/1.58              = ( X = Y ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_151_inj__on__eq__iff,axiom,
% 3.06/1.58      ! [F3: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 3.06/1.58        ( ( inj_on552895452tv_nat @ F3 @ A2 )
% 3.06/1.58       => ( ( member737151281tv_nat @ X @ A2 )
% 3.06/1.58         => ( ( member737151281tv_nat @ Y @ A2 )
% 3.06/1.58           => ( ( ( F3 @ X )
% 3.06/1.58                = ( F3 @ Y ) )
% 3.06/1.58              = ( X = Y ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_152_inj__on__eq__iff,axiom,
% 3.06/1.58      ! [F3: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 3.06/1.58        ( ( inj_on1745913142lle_tv @ F3 @ A2 )
% 3.06/1.58       => ( ( member813679063lle_tv @ X @ A2 )
% 3.06/1.58         => ( ( member813679063lle_tv @ Y @ A2 )
% 3.06/1.58           => ( ( ( F3 @ X )
% 3.06/1.58                = ( F3 @ Y ) )
% 3.06/1.58              = ( X = Y ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_153_inj__on__eq__iff,axiom,
% 3.06/1.58      ! [F3: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 3.06/1.58        ( ( inj_on26176689at_nat @ F3 @ A2 )
% 3.06/1.58       => ( ( member701585322at_nat @ X @ A2 )
% 3.06/1.58         => ( ( member701585322at_nat @ Y @ A2 )
% 3.06/1.58           => ( ( ( F3 @ X )
% 3.06/1.58                = ( F3 @ Y ) )
% 3.06/1.58              = ( X = Y ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_154_inj__on__eq__iff,axiom,
% 3.06/1.58      ! [F3: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 3.06/1.58        ( ( inj_on1955349912lle_tv @ F3 @ A2 )
% 3.06/1.58       => ( ( member_nat @ X @ A2 )
% 3.06/1.58         => ( ( member_nat @ Y @ A2 )
% 3.06/1.58           => ( ( ( F3 @ X )
% 3.06/1.58                = ( F3 @ Y ) )
% 3.06/1.58              = ( X = Y ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_155_inj__on__eq__iff,axiom,
% 3.06/1.58      ! [F3: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 3.06/1.58        ( ( inj_on_nat_nat @ F3 @ A2 )
% 3.06/1.58       => ( ( member_nat @ X @ A2 )
% 3.06/1.58         => ( ( member_nat @ Y @ A2 )
% 3.06/1.58           => ( ( ( F3 @ X )
% 3.06/1.58                = ( F3 @ Y ) )
% 3.06/1.58              = ( X = Y ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_156_inj__on__eq__iff,axiom,
% 3.06/1.58      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.58        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 3.06/1.58       => ( ( member266900804lle_tv @ X @ A2 )
% 3.06/1.58         => ( ( member266900804lle_tv @ Y @ A2 )
% 3.06/1.58           => ( ( ( F3 @ X )
% 3.06/1.58                = ( F3 @ Y ) )
% 3.06/1.58              = ( X = Y ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_157_inj__on__cong,axiom,
% 3.06/1.58      ! [A2: set_Pr2014382200lle_tv,F3: produc1647334210lle_tv > produc1647334210lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv] :
% 3.06/1.58        ( ! [A3: produc1647334210lle_tv] :
% 3.06/1.58            ( ( member1531318361lle_tv @ A3 @ A2 )
% 3.06/1.58           => ( ( F3 @ A3 )
% 3.06/1.58              = ( G @ A3 ) ) )
% 3.06/1.58       => ( ( inj_on2112487900lle_tv @ F3 @ A2 )
% 3.06/1.58          = ( inj_on2112487900lle_tv @ G @ A2 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_158_inj__on__cong,axiom,
% 3.06/1.58      ! [A2: set_Pr1725653840tv_nat,F3: produc194167194tv_nat > produc194167194tv_nat,G: produc194167194tv_nat > produc194167194tv_nat] :
% 3.06/1.58        ( ! [A3: produc194167194tv_nat] :
% 3.06/1.58            ( ( member737151281tv_nat @ A3 @ A2 )
% 3.06/1.58           => ( ( F3 @ A3 )
% 3.06/1.58              = ( G @ A3 ) ) )
% 3.06/1.58       => ( ( inj_on552895452tv_nat @ F3 @ A2 )
% 3.06/1.58          = ( inj_on552895452tv_nat @ G @ A2 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_159_inj__on__cong,axiom,
% 3.06/1.58      ! [A2: set_Pr13445366lle_tv,F3: produc270694976lle_tv > produc270694976lle_tv,G: produc270694976lle_tv > produc270694976lle_tv] :
% 3.06/1.58        ( ! [A3: produc270694976lle_tv] :
% 3.06/1.58            ( ( member813679063lle_tv @ A3 @ A2 )
% 3.06/1.58           => ( ( F3 @ A3 )
% 3.06/1.58              = ( G @ A3 ) ) )
% 3.06/1.58       => ( ( inj_on1745913142lle_tv @ F3 @ A2 )
% 3.06/1.58          = ( inj_on1745913142lle_tv @ G @ A2 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_160_inj__on__cong,axiom,
% 3.06/1.58      ! [A2: set_Pr1986765409at_nat,F3: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat] :
% 3.06/1.58        ( ! [A3: product_prod_nat_nat] :
% 3.06/1.58            ( ( member701585322at_nat @ A3 @ A2 )
% 3.06/1.58           => ( ( F3 @ A3 )
% 3.06/1.58              = ( G @ A3 ) ) )
% 3.06/1.58       => ( ( inj_on26176689at_nat @ F3 @ A2 )
% 3.06/1.58          = ( inj_on26176689at_nat @ G @ A2 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_161_inj__on__cong,axiom,
% 3.06/1.58      ! [A2: set_nat,F3: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 3.06/1.58        ( ! [A3: nat] :
% 3.06/1.58            ( ( member_nat @ A3 @ A2 )
% 3.06/1.58           => ( ( F3 @ A3 )
% 3.06/1.58              = ( G @ A3 ) ) )
% 3.06/1.58       => ( ( inj_on1955349912lle_tv @ F3 @ A2 )
% 3.06/1.58          = ( inj_on1955349912lle_tv @ G @ A2 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_162_inj__on__cong,axiom,
% 3.06/1.58      ! [A2: set_nat,F3: nat > nat,G: nat > nat] :
% 3.06/1.58        ( ! [A3: nat] :
% 3.06/1.58            ( ( member_nat @ A3 @ A2 )
% 3.06/1.58           => ( ( F3 @ A3 )
% 3.06/1.58              = ( G @ A3 ) ) )
% 3.06/1.58       => ( ( inj_on_nat_nat @ F3 @ A2 )
% 3.06/1.58          = ( inj_on_nat_nat @ G @ A2 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_163_inj__on__cong,axiom,
% 3.06/1.58      ! [A2: set_Pa1764573435lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.58        ( ! [A3: paraco1605129243lle_tv] :
% 3.06/1.58            ( ( member266900804lle_tv @ A3 @ A2 )
% 3.06/1.58           => ( ( F3 @ A3 )
% 3.06/1.58              = ( G @ A3 ) ) )
% 3.06/1.58       => ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 3.06/1.58          = ( inj_on772319074lle_tv @ G @ A2 ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_164_inj__on__def,axiom,
% 3.06/1.58      ( inj_on_nat_nat
% 3.06/1.58      = ( ^ [F: nat > nat,A4: set_nat] :
% 3.06/1.58          ! [X2: nat] :
% 3.06/1.58            ( ( member_nat @ X2 @ A4 )
% 3.06/1.58           => ! [Y4: nat] :
% 3.06/1.58                ( ( member_nat @ Y4 @ A4 )
% 3.06/1.58               => ( ( ( F @ X2 )
% 3.06/1.58                    = ( F @ Y4 ) )
% 3.06/1.58                 => ( X2 = Y4 ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_165_inj__on__def,axiom,
% 3.06/1.58      ( inj_on772319074lle_tv
% 3.06/1.58      = ( ^ [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A4: set_Pa1764573435lle_tv] :
% 3.06/1.58          ! [X2: paraco1605129243lle_tv] :
% 3.06/1.58            ( ( member266900804lle_tv @ X2 @ A4 )
% 3.06/1.58           => ! [Y4: paraco1605129243lle_tv] :
% 3.06/1.58                ( ( member266900804lle_tv @ Y4 @ A4 )
% 3.06/1.58               => ( ( ( F @ X2 )
% 3.06/1.58                    = ( F @ Y4 ) )
% 3.06/1.58                 => ( X2 = Y4 ) ) ) ) ) ) ).
% 3.06/1.58  
% 3.06/1.58  thf(fact_166_inj__onI,axiom,
% 3.06/1.58      ! [A2: set_nat,F3: nat > nat] :
% 3.06/1.58        ( ! [X4: nat,Y2: nat] :
% 3.06/1.58            ( ( member_nat @ X4 @ A2 )
% 3.06/1.58           => ( ( member_nat @ Y2 @ A2 )
% 3.06/1.59             => ( ( ( F3 @ X4 )
% 3.06/1.59                  = ( F3 @ Y2 ) )
% 3.06/1.59               => ( X4 = Y2 ) ) ) )
% 3.06/1.59       => ( inj_on_nat_nat @ F3 @ A2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_167_inj__onI,axiom,
% 3.06/1.59      ! [A2: set_Pa1764573435lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.59        ( ! [X4: paraco1605129243lle_tv,Y2: paraco1605129243lle_tv] :
% 3.06/1.59            ( ( member266900804lle_tv @ X4 @ A2 )
% 3.06/1.59           => ( ( member266900804lle_tv @ Y2 @ A2 )
% 3.06/1.59             => ( ( ( F3 @ X4 )
% 3.06/1.59                  = ( F3 @ Y2 ) )
% 3.06/1.59               => ( X4 = Y2 ) ) ) )
% 3.06/1.59       => ( inj_on772319074lle_tv @ F3 @ A2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_168_inj__onD,axiom,
% 3.06/1.59      ! [F3: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ A2 )
% 3.06/1.59       => ( ( ( F3 @ X )
% 3.06/1.59            = ( F3 @ Y ) )
% 3.06/1.59         => ( ( member_nat @ X @ A2 )
% 3.06/1.59           => ( ( member_nat @ Y @ A2 )
% 3.06/1.59             => ( X = Y ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_169_inj__onD,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 3.06/1.59       => ( ( ( F3 @ X )
% 3.06/1.59            = ( F3 @ Y ) )
% 3.06/1.59         => ( ( member266900804lle_tv @ X @ A2 )
% 3.06/1.59           => ( ( member266900804lle_tv @ Y @ A2 )
% 3.06/1.59             => ( X = Y ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_170_props_Oinduct,axiom,
% 3.06/1.59      ! [P3: paraco1604210848lle_fm > $o,A0: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( P3 @ paraco367965286_Truth )
% 3.06/1.59       => ( ! [S2: list_char] : ( P3 @ ( paraco1480028776le_Pro @ S2 ) )
% 3.06/1.59         => ( ! [P4: paraco1604210848lle_fm] :
% 3.06/1.59                ( ( P3 @ P4 )
% 3.06/1.59               => ( P3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 3.06/1.59           => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 3.06/1.59                  ( ( P3 @ P4 )
% 3.06/1.59                 => ( ( P3 @ Q3 )
% 3.06/1.59                   => ( P3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) ) )
% 3.06/1.59             => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 3.06/1.59                    ( ( P3 @ P4 )
% 3.06/1.59                   => ( ( P3 @ Q3 )
% 3.06/1.59                     => ( P3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) ) )
% 3.06/1.59               => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 3.06/1.59                      ( ( P3 @ P4 )
% 3.06/1.59                     => ( ( P3 @ Q3 )
% 3.06/1.59                       => ( P3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) )
% 3.06/1.59                 => ( P3 @ A0 ) ) ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_171_eval_Ocases,axiom,
% 3.06/1.59      ! [X: produc696645085lle_fm] :
% 3.06/1.59        ( ! [I3: list_char > paraco1605129243lle_tv,S2: list_char] :
% 3.06/1.59            ( X
% 3.06/1.59           != ( produc1710735575lle_fm @ I3 @ ( paraco1480028776le_Pro @ S2 ) ) )
% 3.06/1.59       => ( ! [I3: list_char > paraco1605129243lle_tv] :
% 3.06/1.59              ( X
% 3.06/1.59             != ( produc1710735575lle_fm @ I3 @ paraco367965286_Truth ) )
% 3.06/1.59         => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm] :
% 3.06/1.59                ( X
% 3.06/1.59               != ( produc1710735575lle_fm @ I3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 3.06/1.59           => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 3.06/1.59                  ( X
% 3.06/1.59                 != ( produc1710735575lle_fm @ I3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) )
% 3.06/1.59             => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 3.06/1.59                    ( X
% 3.06/1.59                   != ( produc1710735575lle_fm @ I3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) )
% 3.06/1.59               => ~ ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 3.06/1.59                      ( X
% 3.06/1.59                     != ( produc1710735575lle_fm @ I3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_172_top__empty__eq,axiom,
% 3.06/1.59      ( top_top_nat_o
% 3.06/1.59      = ( ^ [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_173_top__empty__eq,axiom,
% 3.06/1.59      ( top_to1299250770e_tv_o
% 3.06/1.59      = ( ^ [X2: paraco1605129243lle_tv] : ( member266900804lle_tv @ X2 @ top_to1057771083lle_tv ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_174_change__tv_Oelims,axiom,
% 3.06/1.59      ! [X: nat > nat,Xa: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( paraco1147068288nge_tv @ X @ Xa )
% 3.06/1.59          = Y )
% 3.06/1.59       => ( ! [B2: $o] :
% 3.06/1.59              ( ( Xa
% 3.06/1.59                = ( paraco1344940915le_Det @ B2 ) )
% 3.06/1.59             => ( Y
% 3.06/1.59               != ( paraco1344940915le_Det @ B2 ) ) )
% 3.06/1.59         => ~ ! [N: nat] :
% 3.06/1.59                ( ( Xa
% 3.06/1.59                  = ( paraco793048302_Indet @ N ) )
% 3.06/1.59               => ( Y
% 3.06/1.59                 != ( paraco793048302_Indet @ ( X @ N ) ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_175_valid__valid__in,axiom,
% 3.06/1.59      ! [P2: paraco1604210848lle_fm,U: set_nat] :
% 3.06/1.59        ( ( paraco327635598_valid @ P2 )
% 3.06/1.59       => ( paraco55203475lid_in @ U @ P2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_176_transfer,axiom,
% 3.06/1.59      ! [U: set_nat,P2: paraco1604210848lle_fm] :
% 3.06/1.59        ( ~ ( paraco55203475lid_in @ U @ P2 )
% 3.06/1.59       => ~ ( paraco327635598_valid @ P2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_177_the__inv__f__f,axiom,
% 3.06/1.59      ! [F3: nat > nat,X: nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59       => ( ( the_inv_into_nat_nat @ top_top_set_nat @ F3 @ ( F3 @ X ) )
% 3.06/1.59          = X ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_178_the__inv__f__f,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59       => ( ( the_in452116896lle_tv @ top_to1057771083lle_tv @ F3 @ ( F3 @ X ) )
% 3.06/1.59          = X ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_179_conjunction__in,axiom,
% 3.06/1.59      ! [U: set_nat,P2: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( paraco55203475lid_in @ U @ ( paraco69239110le_Con @ P2 @ Q ) )
% 3.06/1.59        = ( ( paraco55203475lid_in @ U @ P2 )
% 3.06/1.59          & ( paraco55203475lid_in @ U @ Q ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_180_tv_Oinject_I2_J,axiom,
% 3.06/1.59      ! [X23: nat,Y22: nat] :
% 3.06/1.59        ( ( ( paraco793048302_Indet @ X23 )
% 3.06/1.59          = ( paraco793048302_Indet @ Y22 ) )
% 3.06/1.59        = ( X23 = Y22 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_181_string__tv_Oinduct,axiom,
% 3.06/1.59      ! [P3: paraco1605129243lle_tv > $o,A0: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( P3 @ ( paraco1344940915le_Det @ $true ) )
% 3.06/1.59       => ( ( P3 @ ( paraco1344940915le_Det @ $false ) )
% 3.06/1.59         => ( ! [N: nat] : ( P3 @ ( paraco793048302_Indet @ N ) )
% 3.06/1.59           => ( P3 @ A0 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_182_change__tv_Oinduct,axiom,
% 3.06/1.59      ! [P3: ( nat > nat ) > paraco1605129243lle_tv > $o,A0: nat > nat,A1: paraco1605129243lle_tv] :
% 3.06/1.59        ( ! [F4: nat > nat,B2: $o] : ( P3 @ F4 @ ( paraco1344940915le_Det @ B2 ) )
% 3.06/1.59       => ( ! [F4: nat > nat,N: nat] : ( P3 @ F4 @ ( paraco793048302_Indet @ N ) )
% 3.06/1.59         => ( P3 @ A0 @ A1 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_183_string__tv_Ocases,axiom,
% 3.06/1.59      ! [X: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( X
% 3.06/1.59         != ( paraco1344940915le_Det @ $true ) )
% 3.06/1.59       => ( ( X
% 3.06/1.59           != ( paraco1344940915le_Det @ $false ) )
% 3.06/1.59         => ~ ! [N: nat] :
% 3.06/1.59                ( X
% 3.06/1.59               != ( paraco793048302_Indet @ N ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_184_tv_Oexhaust,axiom,
% 3.06/1.59      ! [Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ! [X12: $o] :
% 3.06/1.59            ( Y
% 3.06/1.59           != ( paraco1344940915le_Det @ X12 ) )
% 3.06/1.59       => ~ ! [X22: nat] :
% 3.06/1.59              ( Y
% 3.06/1.59             != ( paraco793048302_Indet @ X22 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_185_tv_Oinduct,axiom,
% 3.06/1.59      ! [P3: paraco1605129243lle_tv > $o,Tv: paraco1605129243lle_tv] :
% 3.06/1.59        ( ! [X4: $o] : ( P3 @ ( paraco1344940915le_Det @ X4 ) )
% 3.06/1.59       => ( ! [X4: nat] : ( P3 @ ( paraco793048302_Indet @ X4 ) )
% 3.06/1.59         => ( P3 @ Tv ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_186_tv_Odistinct_I1_J,axiom,
% 3.06/1.59      ! [X1: $o,X23: nat] :
% 3.06/1.59        ( ( paraco1344940915le_Det @ X1 )
% 3.06/1.59       != ( paraco793048302_Indet @ X23 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_187_the__inv__into__f__f,axiom,
% 3.06/1.59      ! [F3: nat > nat,A2: set_nat,X: nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ A2 )
% 3.06/1.59       => ( ( member_nat @ X @ A2 )
% 3.06/1.59         => ( ( the_inv_into_nat_nat @ A2 @ F3 @ ( F3 @ X ) )
% 3.06/1.59            = X ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_188_the__inv__into__f__f,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 3.06/1.59       => ( ( member266900804lle_tv @ X @ A2 )
% 3.06/1.59         => ( ( the_in452116896lle_tv @ A2 @ F3 @ ( F3 @ X ) )
% 3.06/1.59            = X ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_189_the__inv__into__f__eq,axiom,
% 3.06/1.59      ! [F3: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ A2 )
% 3.06/1.59       => ( ( ( F3 @ X )
% 3.06/1.59            = Y )
% 3.06/1.59         => ( ( member_nat @ X @ A2 )
% 3.06/1.59           => ( ( the_inv_into_nat_nat @ A2 @ F3 @ Y )
% 3.06/1.59              = X ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_190_the__inv__into__f__eq,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 3.06/1.59       => ( ( ( F3 @ X )
% 3.06/1.59            = Y )
% 3.06/1.59         => ( ( member266900804lle_tv @ X @ A2 )
% 3.06/1.59           => ( ( the_in452116896lle_tv @ A2 @ F3 @ Y )
% 3.06/1.59              = X ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_191_tv_Osimps_I6_J,axiom,
% 3.06/1.59      ! [F1: $o > paraco1605129243lle_tv,F2: nat > paraco1605129243lle_tv,X23: nat] :
% 3.06/1.59        ( ( paraco2051596139lle_tv @ F1 @ F2 @ ( paraco793048302_Indet @ X23 ) )
% 3.06/1.59        = ( F2 @ X23 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_192_change__tv_Osimps_I2_J,axiom,
% 3.06/1.59      ! [F3: nat > nat,N2: nat] :
% 3.06/1.59        ( ( paraco1147068288nge_tv @ F3 @ ( paraco793048302_Indet @ N2 ) )
% 3.06/1.59        = ( paraco793048302_Indet @ ( F3 @ N2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_193_prod_Oinject,axiom,
% 3.06/1.59      ! [X1: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm,Y1: list_char > paraco1605129243lle_tv,Y22: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( ( produc1710735575lle_fm @ X1 @ X23 )
% 3.06/1.59          = ( produc1710735575lle_fm @ Y1 @ Y22 ) )
% 3.06/1.59        = ( ( X1 = Y1 )
% 3.06/1.59          & ( X23 = Y22 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_194_prod_Oinject,axiom,
% 3.06/1.59      ! [X1: nat > nat,X23: paraco1605129243lle_tv,Y1: nat > nat,Y22: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( produc1680557635lle_tv @ X1 @ X23 )
% 3.06/1.59          = ( produc1680557635lle_tv @ Y1 @ Y22 ) )
% 3.06/1.59        = ( ( X1 = Y1 )
% 3.06/1.59          & ( X23 = Y22 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_195_old_Oprod_Oinject,axiom,
% 3.06/1.59      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( ( produc1710735575lle_fm @ A @ B )
% 3.06/1.59          = ( produc1710735575lle_fm @ A5 @ B3 ) )
% 3.06/1.59        = ( ( A = A5 )
% 3.06/1.59          & ( B = B3 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_196_old_Oprod_Oinject,axiom,
% 3.06/1.59      ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( produc1680557635lle_tv @ A @ B )
% 3.06/1.59          = ( produc1680557635lle_tv @ A5 @ B3 ) )
% 3.06/1.59        = ( ( A = A5 )
% 3.06/1.59          & ( B = B3 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_197_eval_Osimps_I3_J,axiom,
% 3.06/1.59      ! [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ P2 ) )
% 3.06/1.59        = ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1344940915le_Det @ $false ) @ ( paraco1344940915le_Det @ $true ) ) @ paraco793048302_Indet @ ( paraco1325918602e_eval @ I2 @ P2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_198_surj__pair,axiom,
% 3.06/1.59      ! [P2: produc696645085lle_fm] :
% 3.06/1.59      ? [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 3.06/1.59        ( P2
% 3.06/1.59        = ( produc1710735575lle_fm @ X4 @ Y2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_199_surj__pair,axiom,
% 3.06/1.59      ! [P2: produc931990033lle_tv] :
% 3.06/1.59      ? [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 3.06/1.59        ( P2
% 3.06/1.59        = ( produc1680557635lle_tv @ X4 @ Y2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_200_bool_Osplit__sel__asm,axiom,
% 3.06/1.59      ! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv,Bool: $o] :
% 3.06/1.59        ( ( P3 @ ( produc234482697lle_tv @ F1 @ F2 @ Bool ) )
% 3.06/1.59        = ( ~ ( ( Bool
% 3.06/1.59                & ~ ( P3 @ F1 ) )
% 3.06/1.59              | ( ~ Bool
% 3.06/1.59                & ~ ( P3 @ F2 ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_201_bool_Ocase__distrib,axiom,
% 3.06/1.59      ! [H: paraco1605129243lle_tv > paraco1605129243lle_tv,F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv,Bool: $o] :
% 3.06/1.59        ( ( H @ ( produc234482697lle_tv @ F1 @ F2 @ Bool ) )
% 3.06/1.59        = ( produc234482697lle_tv @ ( H @ F1 ) @ ( H @ F2 ) @ Bool ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_202_bool_Ocase__eq__if,axiom,
% 3.06/1.59      ( produc234482697lle_tv
% 3.06/1.59      = ( ^ [F12: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool2: $o] : ( if_Par1134130401lle_tv @ Bool2 @ F12 @ F22 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_203_bool_Osplit__sel,axiom,
% 3.06/1.59      ! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv,Bool: $o] :
% 3.06/1.59        ( ( P3 @ ( produc234482697lle_tv @ F1 @ F2 @ Bool ) )
% 3.06/1.59        = ( ( Bool
% 3.06/1.59           => ( P3 @ F1 ) )
% 3.06/1.59          & ( ~ Bool
% 3.06/1.59           => ( P3 @ F2 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_204_old_Obool_Osimps_I3_J,axiom,
% 3.06/1.59      ! [F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( produc234482697lle_tv @ F1 @ F2 @ $true )
% 3.06/1.59        = F1 ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_205_old_Obool_Osimps_I4_J,axiom,
% 3.06/1.59      ! [F1: paraco1605129243lle_tv,F2: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( produc234482697lle_tv @ F1 @ F2 @ $false )
% 3.06/1.59        = F2 ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_206_change__tv_Ocases,axiom,
% 3.06/1.59      ! [X: produc931990033lle_tv] :
% 3.06/1.59        ( ! [F4: nat > nat,B2: $o] :
% 3.06/1.59            ( X
% 3.06/1.59           != ( produc1680557635lle_tv @ F4 @ ( paraco1344940915le_Det @ B2 ) ) )
% 3.06/1.59       => ~ ! [F4: nat > nat,N: nat] :
% 3.06/1.59              ( X
% 3.06/1.59             != ( produc1680557635lle_tv @ F4 @ ( paraco793048302_Indet @ N ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_207_old_Oprod_Oinducts,axiom,
% 3.06/1.59      ! [P3: produc696645085lle_fm > $o,Prod: produc696645085lle_fm] :
% 3.06/1.59        ( ! [A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A3 @ B2 ) )
% 3.06/1.59       => ( P3 @ Prod ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_208_old_Oprod_Oinducts,axiom,
% 3.06/1.59      ! [P3: produc931990033lle_tv > $o,Prod: produc931990033lle_tv] :
% 3.06/1.59        ( ! [A3: nat > nat,B2: paraco1605129243lle_tv] : ( P3 @ ( produc1680557635lle_tv @ A3 @ B2 ) )
% 3.06/1.59       => ( P3 @ Prod ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_209_old_Oprod_Oexhaust,axiom,
% 3.06/1.59      ! [Y: produc696645085lle_fm] :
% 3.06/1.59        ~ ! [A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] :
% 3.06/1.59            ( Y
% 3.06/1.59           != ( produc1710735575lle_fm @ A3 @ B2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_210_old_Oprod_Oexhaust,axiom,
% 3.06/1.59      ! [Y: produc931990033lle_tv] :
% 3.06/1.59        ~ ! [A3: nat > nat,B2: paraco1605129243lle_tv] :
% 3.06/1.59            ( Y
% 3.06/1.59           != ( produc1680557635lle_tv @ A3 @ B2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_211_Pair__inject,axiom,
% 3.06/1.59      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( ( produc1710735575lle_fm @ A @ B )
% 3.06/1.59          = ( produc1710735575lle_fm @ A5 @ B3 ) )
% 3.06/1.59       => ~ ( ( A = A5 )
% 3.06/1.59           => ( B != B3 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_212_Pair__inject,axiom,
% 3.06/1.59      ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( produc1680557635lle_tv @ A @ B )
% 3.06/1.59          = ( produc1680557635lle_tv @ A5 @ B3 ) )
% 3.06/1.59       => ~ ( ( A = A5 )
% 3.06/1.59           => ( B != B3 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_213_prod__cases,axiom,
% 3.06/1.59      ! [P3: produc696645085lle_fm > $o,P2: produc696645085lle_fm] :
% 3.06/1.59        ( ! [A3: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A3 @ B2 ) )
% 3.06/1.59       => ( P3 @ P2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_214_prod__cases,axiom,
% 3.06/1.59      ! [P3: produc931990033lle_tv > $o,P2: produc931990033lle_tv] :
% 3.06/1.59        ( ! [A3: nat > nat,B2: paraco1605129243lle_tv] : ( P3 @ ( produc1680557635lle_tv @ A3 @ B2 ) )
% 3.06/1.59       => ( P3 @ P2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_215_ssubst__Pair__rhs,axiom,
% 3.06/1.59      ! [R: list_char > paraco1605129243lle_tv,S3: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,S4: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S3 ) @ R2 )
% 3.06/1.59       => ( ( S4 = S3 )
% 3.06/1.59         => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S4 ) @ R2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_216_ssubst__Pair__rhs,axiom,
% 3.06/1.59      ! [R: nat > nat,S3: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,S4: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ R @ S3 ) @ R2 )
% 3.06/1.59       => ( ( S4 = S3 )
% 3.06/1.59         => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ R @ S4 ) @ R2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_217_apfst__conv,axiom,
% 3.06/1.59      ! [F3: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( produc1942165868lle_fm @ F3 @ ( produc1710735575lle_fm @ X @ Y ) )
% 3.06/1.59        = ( produc1710735575lle_fm @ ( F3 @ X ) @ Y ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_218_apfst__conv,axiom,
% 3.06/1.59      ! [F3: ( nat > nat ) > nat > nat,X: nat > nat,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( produc939316703lle_tv @ F3 @ ( produc1680557635lle_tv @ X @ Y ) )
% 3.06/1.59        = ( produc1680557635lle_tv @ ( F3 @ X ) @ Y ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_219_apsnd__conv,axiom,
% 3.06/1.59      ! [F3: paraco1604210848lle_fm > paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( produc1807466521lle_tv @ F3 @ ( produc1710735575lle_fm @ X @ Y ) )
% 3.06/1.59        = ( produc1710735575lle_fm @ X @ ( F3 @ Y ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_220_apsnd__conv,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,X: nat > nat,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( produc109093078at_nat @ F3 @ ( produc1680557635lle_tv @ X @ Y ) )
% 3.06/1.59        = ( produc1680557635lle_tv @ X @ ( F3 @ Y ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_221_change__tv_Opelims,axiom,
% 3.06/1.59      ! [X: nat > nat,Xa: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( paraco1147068288nge_tv @ X @ Xa )
% 3.06/1.59          = Y )
% 3.06/1.59       => ( ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ Xa ) )
% 3.06/1.59         => ( ! [B2: $o] :
% 3.06/1.59                ( ( Xa
% 3.06/1.59                  = ( paraco1344940915le_Det @ B2 ) )
% 3.06/1.59               => ( ( Y
% 3.06/1.59                    = ( paraco1344940915le_Det @ B2 ) )
% 3.06/1.59                 => ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ ( paraco1344940915le_Det @ B2 ) ) ) ) )
% 3.06/1.59           => ~ ! [N: nat] :
% 3.06/1.59                  ( ( Xa
% 3.06/1.59                    = ( paraco793048302_Indet @ N ) )
% 3.06/1.59                 => ( ( Y
% 3.06/1.59                      = ( paraco793048302_Indet @ ( X @ N ) ) )
% 3.06/1.59                   => ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ ( paraco793048302_Indet @ N ) ) ) ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_222_prod_Oinj__map,axiom,
% 3.06/1.59      ! [F1: nat > nat,F2: nat > nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 3.06/1.59       => ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 3.06/1.59         => ( inj_on26176689at_nat @ ( produc505105722at_nat @ F1 @ F2 ) @ top_to1555900337at_nat ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_223_prod_Oinj__map,axiom,
% 3.06/1.59      ! [F1: nat > nat,F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 3.06/1.59       => ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 3.06/1.59         => ( inj_on1745913142lle_tv @ ( produc2101297531lle_tv @ F1 @ F2 ) @ top_to1411004326lle_tv ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_224_prod_Oinj__map,axiom,
% 3.06/1.59      ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F2: nat > nat] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 3.06/1.59       => ( ( inj_on_nat_nat @ F2 @ top_top_set_nat )
% 3.06/1.59         => ( inj_on552895452tv_nat @ ( produc42536895at_nat @ F1 @ F2 ) @ top_to975729152tv_nat ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_225_prod_Oinj__map,axiom,
% 3.06/1.59      ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F2: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 3.06/1.59       => ( ( inj_on772319074lle_tv @ F2 @ top_to1057771083lle_tv )
% 3.06/1.59         => ( inj_on2112487900lle_tv @ ( produc1345917071lle_tv @ F1 @ F2 ) @ top_to1871154984lle_tv ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_226_curryI,axiom,
% 3.06/1.59      ! [F3: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( F3 @ ( produc1710735575lle_fm @ A @ B ) )
% 3.06/1.59       => ( produc275353523e_fm_o @ F3 @ A @ B ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_227_curryI,axiom,
% 3.06/1.59      ! [F3: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( F3 @ ( produc1680557635lle_tv @ A @ B ) )
% 3.06/1.59       => ( produc752649287e_tv_o @ F3 @ A @ B ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_228_map__prod__simp,axiom,
% 3.06/1.59      ! [F3: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( produc1900967599lle_fm @ F3 @ G @ ( produc1710735575lle_fm @ A @ B ) )
% 3.06/1.59        = ( produc1710735575lle_fm @ ( F3 @ A ) @ ( G @ B ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_229_map__prod__simp,axiom,
% 3.06/1.59      ! [F3: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( produc1566550641lle_tv @ F3 @ G @ ( produc1710735575lle_fm @ A @ B ) )
% 3.06/1.59        = ( produc1680557635lle_tv @ ( F3 @ A ) @ ( G @ B ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_230_map__prod__simp,axiom,
% 3.06/1.59      ! [F3: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,A: nat > nat,B: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( produc951033137lle_fm @ F3 @ G @ ( produc1680557635lle_tv @ A @ B ) )
% 3.06/1.59        = ( produc1710735575lle_fm @ ( F3 @ A ) @ ( G @ B ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_231_map__prod__simp,axiom,
% 3.06/1.59      ! [F3: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv,A: nat > nat,B: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( produc532909085lle_tv @ F3 @ G @ ( produc1680557635lle_tv @ A @ B ) )
% 3.06/1.59        = ( produc1680557635lle_tv @ ( F3 @ A ) @ ( G @ B ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_232_curryD,axiom,
% 3.06/1.59      ! [F3: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( produc275353523e_fm_o @ F3 @ A @ B )
% 3.06/1.59       => ( F3 @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_233_curryD,axiom,
% 3.06/1.59      ! [F3: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( produc752649287e_tv_o @ F3 @ A @ B )
% 3.06/1.59       => ( F3 @ ( produc1680557635lle_tv @ A @ B ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_234_curryE,axiom,
% 3.06/1.59      ! [F3: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( produc275353523e_fm_o @ F3 @ A @ B )
% 3.06/1.59       => ( F3 @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_235_curryE,axiom,
% 3.06/1.59      ! [F3: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( produc752649287e_tv_o @ F3 @ A @ B )
% 3.06/1.59       => ( F3 @ ( produc1680557635lle_tv @ A @ B ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_236_the__inv__into__onto,axiom,
% 3.06/1.59      ! [F3: nat > nat,A2: set_nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ A2 )
% 3.06/1.59       => ( ( image_nat_nat @ ( the_inv_into_nat_nat @ A2 @ F3 ) @ ( image_nat_nat @ F3 @ A2 ) )
% 3.06/1.59          = A2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_237_the__inv__into__onto,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 3.06/1.59       => ( ( image_335818702lle_tv @ ( the_in452116896lle_tv @ A2 @ F3 ) @ ( image_335818702lle_tv @ F3 @ A2 ) )
% 3.06/1.59          = A2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_238_map__prod__imageI,axiom,
% 3.06/1.59      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm] :
% 3.06/1.59        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
% 3.06/1.59       => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F3 @ A ) @ ( G @ B ) ) @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F3 @ G ) @ R2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_239_map__prod__imageI,axiom,
% 3.06/1.59      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
% 3.06/1.59       => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ ( F3 @ A ) @ ( G @ B ) ) @ ( image_1154804148lle_tv @ ( produc1566550641lle_tv @ F3 @ G ) @ R2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_240_map__prod__imageI,axiom,
% 3.06/1.59      ! [A: nat > nat,B: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,F3: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm] :
% 3.06/1.59        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ R2 )
% 3.06/1.59       => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F3 @ A ) @ ( G @ B ) ) @ ( image_1585092542lle_fm @ ( produc951033137lle_fm @ F3 @ G ) @ R2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_241_map__prod__imageI,axiom,
% 3.06/1.59      ! [A: nat > nat,B: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,F3: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ R2 )
% 3.06/1.59       => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ ( F3 @ A ) @ ( G @ B ) ) @ ( image_1751508608lle_tv @ ( produc532909085lle_tv @ F3 @ G ) @ R2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_242_swap__simp,axiom,
% 3.06/1.59      ! [X: paraco1604210848lle_fm,Y: list_char > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( produc1232814113lle_tv @ ( produc1943344577lle_tv @ X @ Y ) )
% 3.06/1.59        = ( produc1710735575lle_fm @ Y @ X ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_243_swap__simp,axiom,
% 3.06/1.59      ! [X: paraco1605129243lle_tv,Y: nat > nat] :
% 3.06/1.59        ( ( produc178635363at_nat @ ( produc1633679363at_nat @ X @ Y ) )
% 3.06/1.59        = ( produc1680557635lle_tv @ Y @ X ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_244_swap__simp,axiom,
% 3.06/1.59      ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( produc1000205111lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 3.06/1.59        = ( produc1943344577lle_tv @ Y @ X ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_245_swap__simp,axiom,
% 3.06/1.59      ! [X: nat > nat,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( produc225513635lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 3.06/1.59        = ( produc1633679363at_nat @ Y @ X ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_246_pair__in__swap__image,axiom,
% 3.06/1.59      ! [Y: paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv,A2: set_Pr2120184979lle_fm] :
% 3.06/1.59        ( ( member74361182lle_tv @ ( produc1943344577lle_tv @ Y @ X ) @ ( image_924970994lle_tv @ produc1000205111lle_fm @ A2 ) )
% 3.06/1.59        = ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X @ Y ) @ A2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_247_pair__in__swap__image,axiom,
% 3.06/1.59      ! [Y: paraco1605129243lle_tv,X: nat > nat,A2: set_Pr560526279lle_tv] :
% 3.06/1.59        ( ( member1234290208at_nat @ ( produc1633679363at_nat @ Y @ X ) @ ( image_1724396928at_nat @ produc225513635lle_tv @ A2 ) )
% 3.06/1.59        = ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X @ Y ) @ A2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_248_pair__in__swap__image,axiom,
% 3.06/1.59      ! [Y: list_char > paraco1605129243lle_tv,X: paraco1604210848lle_fm,A2: set_Pr1723822845lle_tv] :
% 3.06/1.59        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ Y @ X ) @ ( image_326034184lle_fm @ produc1232814113lle_tv @ A2 ) )
% 3.06/1.59        = ( member74361182lle_tv @ ( produc1943344577lle_tv @ X @ Y ) @ A2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_249_pair__in__swap__image,axiom,
% 3.06/1.59      ! [Y: nat > nat,X: paraco1605129243lle_tv,A2: set_Pr840833727at_nat] :
% 3.06/1.59        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ Y @ X ) @ ( image_769496456lle_tv @ produc178635363at_nat @ A2 ) )
% 3.06/1.59        = ( member1234290208at_nat @ ( produc1633679363at_nat @ X @ Y ) @ A2 ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_250_map__prod__surj,axiom,
% 3.06/1.59      ! [F3: nat > nat,G: nat > nat] :
% 3.06/1.59        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_top_set_nat )
% 3.06/1.59       => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 3.06/1.59            = top_top_set_nat )
% 3.06/1.59         => ( ( image_815163717at_nat @ ( produc505105722at_nat @ F3 @ G ) @ top_to1555900337at_nat )
% 3.06/1.59            = top_to1555900337at_nat ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_251_map__prod__surj,axiom,
% 3.06/1.59      ! [F3: nat > nat,G: nat > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_top_set_nat )
% 3.06/1.59       => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 3.06/1.59            = top_to1057771083lle_tv )
% 3.06/1.59         => ( ( image_1674248956lle_tv @ ( produc313957681lle_tv @ F3 @ G ) @ top_to1555900337at_nat )
% 3.06/1.59            = top_to1411004326lle_tv ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_252_map__prod__surj,axiom,
% 3.06/1.59      ! [F3: nat > nat,G: paraco1605129243lle_tv > nat] :
% 3.06/1.59        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_top_set_nat )
% 3.06/1.59       => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 3.06/1.59            = top_top_set_nat )
% 3.06/1.59         => ( ( image_1787705850at_nat @ ( produc1685803475tv_nat @ F3 @ G ) @ top_to1411004326lle_tv )
% 3.06/1.59            = top_to1555900337at_nat ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_253_map__prod__surj,axiom,
% 3.06/1.59      ! [F3: nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_top_set_nat )
% 3.06/1.59       => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 3.06/1.59            = top_to1057771083lle_tv )
% 3.06/1.59         => ( ( image_149830562lle_tv @ ( produc2101297531lle_tv @ F3 @ G ) @ top_to1411004326lle_tv )
% 3.06/1.59            = top_to1411004326lle_tv ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_254_map__prod__surj,axiom,
% 3.06/1.59      ! [F3: nat > paraco1605129243lle_tv,G: nat > nat] :
% 3.06/1.59        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_to1057771083lle_tv )
% 3.06/1.59       => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 3.06/1.59            = top_top_set_nat )
% 3.06/1.59         => ( ( image_1597721174tv_nat @ ( produc1250721397at_nat @ F3 @ G ) @ top_to1555900337at_nat )
% 3.06/1.59            = top_to975729152tv_nat ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_255_map__prod__surj,axiom,
% 3.06/1.59      ! [F3: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_to1057771083lle_tv )
% 3.06/1.59       => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 3.06/1.59            = top_to1057771083lle_tv )
% 3.06/1.59         => ( ( image_1507992062lle_tv @ ( produc210389789lle_tv @ F3 @ G ) @ top_to1555900337at_nat )
% 3.06/1.59            = top_to1871154984lle_tv ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_256_map__prod__surj,axiom,
% 3.06/1.59      ! [F3: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > nat] :
% 3.06/1.59        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_to1057771083lle_tv )
% 3.06/1.59       => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 3.06/1.59            = top_top_set_nat )
% 3.06/1.59         => ( ( image_53754658tv_nat @ ( produc189459613tv_nat @ F3 @ G ) @ top_to1411004326lle_tv )
% 3.06/1.59            = top_to975729152tv_nat ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_257_map__prod__surj,axiom,
% 3.06/1.59      ! [F3: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_to1057771083lle_tv )
% 3.06/1.59       => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 3.06/1.59            = top_to1057771083lle_tv )
% 3.06/1.59         => ( ( image_988201162lle_tv @ ( produc1975500101lle_tv @ F3 @ G ) @ top_to1411004326lle_tv )
% 3.06/1.59            = top_to1871154984lle_tv ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_258_map__prod__surj,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > nat,G: nat > nat] :
% 3.06/1.59        ( ( ( image_376325286tv_nat @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59          = top_top_set_nat )
% 3.06/1.59       => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 3.06/1.59            = top_top_set_nat )
% 3.06/1.59         => ( ( image_1805124128at_nat @ ( produc386540311at_nat @ F3 @ G ) @ top_to975729152tv_nat )
% 3.06/1.59            = top_to1555900337at_nat ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_259_map__prod__surj,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > nat,G: nat > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( image_376325286tv_nat @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59          = top_top_set_nat )
% 3.06/1.59       => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 3.06/1.59            = top_to1057771083lle_tv )
% 3.06/1.59         => ( ( image_1200372424lle_tv @ ( produc72207551lle_tv @ F3 @ G ) @ top_to975729152tv_nat )
% 3.06/1.59            = top_to1411004326lle_tv ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_260_inj__on__image__iff,axiom,
% 3.06/1.59      ! [A2: set_nat,G: nat > nat,F3: nat > nat] :
% 3.06/1.59        ( ! [X4: nat] :
% 3.06/1.59            ( ( member_nat @ X4 @ A2 )
% 3.06/1.59           => ! [Xa2: nat] :
% 3.06/1.59                ( ( member_nat @ Xa2 @ A2 )
% 3.06/1.59               => ( ( ( G @ ( F3 @ X4 ) )
% 3.06/1.59                    = ( G @ ( F3 @ Xa2 ) ) )
% 3.06/1.59                  = ( ( G @ X4 )
% 3.06/1.59                    = ( G @ Xa2 ) ) ) ) )
% 3.06/1.59       => ( ( inj_on_nat_nat @ F3 @ A2 )
% 3.06/1.59         => ( ( inj_on_nat_nat @ G @ ( image_nat_nat @ F3 @ A2 ) )
% 3.06/1.59            = ( inj_on_nat_nat @ G @ A2 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_261_inj__on__image__iff,axiom,
% 3.06/1.59      ! [A2: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.59        ( ! [X4: paraco1605129243lle_tv] :
% 3.06/1.59            ( ( member266900804lle_tv @ X4 @ A2 )
% 3.06/1.59           => ! [Xa2: paraco1605129243lle_tv] :
% 3.06/1.59                ( ( member266900804lle_tv @ Xa2 @ A2 )
% 3.06/1.59               => ( ( ( G @ ( F3 @ X4 ) )
% 3.06/1.59                    = ( G @ ( F3 @ Xa2 ) ) )
% 3.06/1.59                  = ( ( G @ X4 )
% 3.06/1.59                    = ( G @ Xa2 ) ) ) ) )
% 3.06/1.59       => ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 3.06/1.59         => ( ( inj_on772319074lle_tv @ G @ ( image_335818702lle_tv @ F3 @ A2 ) )
% 3.06/1.59            = ( inj_on772319074lle_tv @ G @ A2 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_262_surjD,axiom,
% 3.06/1.59      ! [F3: nat > nat,Y: nat] :
% 3.06/1.59        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_top_set_nat )
% 3.06/1.59       => ? [X4: nat] :
% 3.06/1.59            ( Y
% 3.06/1.59            = ( F3 @ X4 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_263_surjD,axiom,
% 3.06/1.59      ! [F3: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_to1057771083lle_tv )
% 3.06/1.59       => ? [X4: nat] :
% 3.06/1.59            ( Y
% 3.06/1.59            = ( F3 @ X4 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_264_surjD,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > nat,Y: nat] :
% 3.06/1.59        ( ( ( image_376325286tv_nat @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59          = top_top_set_nat )
% 3.06/1.59       => ? [X4: paraco1605129243lle_tv] :
% 3.06/1.59            ( Y
% 3.06/1.59            = ( F3 @ X4 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_265_surjD,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( image_335818702lle_tv @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59          = top_to1057771083lle_tv )
% 3.06/1.59       => ? [X4: paraco1605129243lle_tv] :
% 3.06/1.59            ( Y
% 3.06/1.59            = ( F3 @ X4 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_266_surjE,axiom,
% 3.06/1.59      ! [F3: nat > nat,Y: nat] :
% 3.06/1.59        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_top_set_nat )
% 3.06/1.59       => ~ ! [X4: nat] :
% 3.06/1.59              ( Y
% 3.06/1.59             != ( F3 @ X4 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_267_surjE,axiom,
% 3.06/1.59      ! [F3: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_to1057771083lle_tv )
% 3.06/1.59       => ~ ! [X4: nat] :
% 3.06/1.59              ( Y
% 3.06/1.59             != ( F3 @ X4 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_268_surjE,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > nat,Y: nat] :
% 3.06/1.59        ( ( ( image_376325286tv_nat @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59          = top_top_set_nat )
% 3.06/1.59       => ~ ! [X4: paraco1605129243lle_tv] :
% 3.06/1.59              ( Y
% 3.06/1.59             != ( F3 @ X4 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_269_surjE,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( image_335818702lle_tv @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59          = top_to1057771083lle_tv )
% 3.06/1.59       => ~ ! [X4: paraco1605129243lle_tv] :
% 3.06/1.59              ( Y
% 3.06/1.59             != ( F3 @ X4 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_270_surjI,axiom,
% 3.06/1.59      ! [G: nat > nat,F3: nat > nat] :
% 3.06/1.59        ( ! [X4: nat] :
% 3.06/1.59            ( ( G @ ( F3 @ X4 ) )
% 3.06/1.59            = X4 )
% 3.06/1.59       => ( ( image_nat_nat @ G @ top_top_set_nat )
% 3.06/1.59          = top_top_set_nat ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_271_surjI,axiom,
% 3.06/1.59      ! [G: nat > paraco1605129243lle_tv,F3: paraco1605129243lle_tv > nat] :
% 3.06/1.59        ( ! [X4: paraco1605129243lle_tv] :
% 3.06/1.59            ( ( G @ ( F3 @ X4 ) )
% 3.06/1.59            = X4 )
% 3.06/1.59       => ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 3.06/1.59          = top_to1057771083lle_tv ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_272_surjI,axiom,
% 3.06/1.59      ! [G: paraco1605129243lle_tv > nat,F3: nat > paraco1605129243lle_tv] :
% 3.06/1.59        ( ! [X4: nat] :
% 3.06/1.59            ( ( G @ ( F3 @ X4 ) )
% 3.06/1.59            = X4 )
% 3.06/1.59       => ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 3.06/1.59          = top_top_set_nat ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_273_surjI,axiom,
% 3.06/1.59      ! [G: paraco1605129243lle_tv > paraco1605129243lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.59        ( ! [X4: paraco1605129243lle_tv] :
% 3.06/1.59            ( ( G @ ( F3 @ X4 ) )
% 3.06/1.59            = X4 )
% 3.06/1.59       => ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 3.06/1.59          = top_to1057771083lle_tv ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_274_surj__def,axiom,
% 3.06/1.59      ! [F3: nat > nat] :
% 3.06/1.59        ( ( ( image_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_top_set_nat )
% 3.06/1.59        = ( ! [Y4: nat] :
% 3.06/1.59            ? [X2: nat] :
% 3.06/1.59              ( Y4
% 3.06/1.59              = ( F3 @ X2 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_275_surj__def,axiom,
% 3.06/1.59      ! [F3: nat > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( image_1151963140lle_tv @ F3 @ top_top_set_nat )
% 3.06/1.59          = top_to1057771083lle_tv )
% 3.06/1.59        = ( ! [Y4: paraco1605129243lle_tv] :
% 3.06/1.59            ? [X2: nat] :
% 3.06/1.59              ( Y4
% 3.06/1.59              = ( F3 @ X2 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_276_surj__def,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > nat] :
% 3.06/1.59        ( ( ( image_376325286tv_nat @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59          = top_top_set_nat )
% 3.06/1.59        = ( ! [Y4: nat] :
% 3.06/1.59            ? [X2: paraco1605129243lle_tv] :
% 3.06/1.59              ( Y4
% 3.06/1.59              = ( F3 @ X2 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_277_surj__def,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( image_335818702lle_tv @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59          = top_to1057771083lle_tv )
% 3.06/1.59        = ( ! [Y4: paraco1605129243lle_tv] :
% 3.06/1.59            ? [X2: paraco1605129243lle_tv] :
% 3.06/1.59              ( Y4
% 3.06/1.59              = ( F3 @ X2 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_278_range__ex1__eq,axiom,
% 3.06/1.59      ! [F3: nat > nat,B: nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59       => ( ( member_nat @ B @ ( image_nat_nat @ F3 @ top_top_set_nat ) )
% 3.06/1.59          = ( ? [X2: nat] :
% 3.06/1.59                ( ( B
% 3.06/1.59                  = ( F3 @ X2 ) )
% 3.06/1.59                & ! [Y4: nat] :
% 3.06/1.59                    ( ( B
% 3.06/1.59                      = ( F3 @ Y4 ) )
% 3.06/1.59                   => ( Y4 = X2 ) ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_279_range__ex1__eq,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59       => ( ( member266900804lle_tv @ B @ ( image_335818702lle_tv @ F3 @ top_to1057771083lle_tv ) )
% 3.06/1.59          = ( ? [X2: paraco1605129243lle_tv] :
% 3.06/1.59                ( ( B
% 3.06/1.59                  = ( F3 @ X2 ) )
% 3.06/1.59                & ! [Y4: paraco1605129243lle_tv] :
% 3.06/1.59                    ( ( B
% 3.06/1.59                      = ( F3 @ Y4 ) )
% 3.06/1.59                   => ( Y4 = X2 ) ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_280_inj__image__eq__iff,axiom,
% 3.06/1.59      ! [F3: nat > nat,A2: set_nat,B4: set_nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59       => ( ( ( image_nat_nat @ F3 @ A2 )
% 3.06/1.59            = ( image_nat_nat @ F3 @ B4 ) )
% 3.06/1.59          = ( A2 = B4 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_281_inj__image__eq__iff,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59       => ( ( ( image_335818702lle_tv @ F3 @ A2 )
% 3.06/1.59            = ( image_335818702lle_tv @ F3 @ B4 ) )
% 3.06/1.59          = ( A2 = B4 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_282_inj__image__mem__iff,axiom,
% 3.06/1.59      ! [F3: nat > nat,A: nat,A2: set_nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59       => ( ( member_nat @ ( F3 @ A ) @ ( image_nat_nat @ F3 @ A2 ) )
% 3.06/1.59          = ( member_nat @ A @ A2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_283_inj__image__mem__iff,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59       => ( ( member266900804lle_tv @ ( F3 @ A ) @ ( image_335818702lle_tv @ F3 @ A2 ) )
% 3.06/1.59          = ( member266900804lle_tv @ A @ A2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_284_prod__fun__imageE,axiom,
% 3.06/1.59      ! [C: produc696645085lle_fm,F3: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm] :
% 3.06/1.59        ( ( member1474794996lle_fm @ C @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F3 @ G ) @ R2 ) )
% 3.06/1.59       => ~ ! [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 3.06/1.59              ( ( C
% 3.06/1.59                = ( produc1710735575lle_fm @ ( F3 @ X4 ) @ ( G @ Y2 ) ) )
% 3.06/1.59             => ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y2 ) @ R2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_285_prod__fun__imageE,axiom,
% 3.06/1.59      ! [C: produc696645085lle_fm,F3: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,R2: set_Pr560526279lle_tv] :
% 3.06/1.59        ( ( member1474794996lle_fm @ C @ ( image_1585092542lle_fm @ ( produc951033137lle_fm @ F3 @ G ) @ R2 ) )
% 3.06/1.59       => ~ ! [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 3.06/1.59              ( ( C
% 3.06/1.59                = ( produc1710735575lle_fm @ ( F3 @ X4 ) @ ( G @ Y2 ) ) )
% 3.06/1.59             => ~ ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X4 @ Y2 ) @ R2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_286_prod__fun__imageE,axiom,
% 3.06/1.59      ! [C: produc931990033lle_tv,F3: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv,R2: set_Pr2120184979lle_fm] :
% 3.06/1.59        ( ( member1569366824lle_tv @ C @ ( image_1154804148lle_tv @ ( produc1566550641lle_tv @ F3 @ G ) @ R2 ) )
% 3.06/1.59       => ~ ! [X4: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 3.06/1.59              ( ( C
% 3.06/1.59                = ( produc1680557635lle_tv @ ( F3 @ X4 ) @ ( G @ Y2 ) ) )
% 3.06/1.59             => ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X4 @ Y2 ) @ R2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_287_prod__fun__imageE,axiom,
% 3.06/1.59      ! [C: produc931990033lle_tv,F3: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv,R2: set_Pr560526279lle_tv] :
% 3.06/1.59        ( ( member1569366824lle_tv @ C @ ( image_1751508608lle_tv @ ( produc532909085lle_tv @ F3 @ G ) @ R2 ) )
% 3.06/1.59       => ~ ! [X4: nat > nat,Y2: paraco1605129243lle_tv] :
% 3.06/1.59              ( ( C
% 3.06/1.59                = ( produc1680557635lle_tv @ ( F3 @ X4 ) @ ( G @ Y2 ) ) )
% 3.06/1.59             => ~ ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X4 @ Y2 ) @ R2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_288_f__the__inv__into__f,axiom,
% 3.06/1.59      ! [F3: nat > nat,A2: set_nat,Y: nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ A2 )
% 3.06/1.59       => ( ( member_nat @ Y @ ( image_nat_nat @ F3 @ A2 ) )
% 3.06/1.59         => ( ( F3 @ ( the_inv_into_nat_nat @ A2 @ F3 @ Y ) )
% 3.06/1.59            = Y ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_289_f__the__inv__into__f,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 3.06/1.59       => ( ( member266900804lle_tv @ Y @ ( image_335818702lle_tv @ F3 @ A2 ) )
% 3.06/1.59         => ( ( F3 @ ( the_in452116896lle_tv @ A2 @ F3 @ Y ) )
% 3.06/1.59            = Y ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_290_inj__on__the__inv__into,axiom,
% 3.06/1.59      ! [F3: nat > nat,A2: set_nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ A2 )
% 3.06/1.59       => ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ A2 @ F3 ) @ ( image_nat_nat @ F3 @ A2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_291_inj__on__the__inv__into,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 3.06/1.59       => ( inj_on772319074lle_tv @ ( the_in452116896lle_tv @ A2 @ F3 ) @ ( image_335818702lle_tv @ F3 @ A2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_292_total__inv__image,axiom,
% 3.06/1.59      ! [F3: nat > nat,R: set_Pr1986765409at_nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59       => ( ( total_on_nat @ top_top_set_nat @ R )
% 3.06/1.59         => ( total_on_nat @ top_top_set_nat @ ( inv_image_nat_nat @ R @ F3 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_293_total__inv__image,axiom,
% 3.06/1.59      ! [F3: nat > paraco1605129243lle_tv,R: set_Pr2014382200lle_tv] :
% 3.06/1.59        ( ( inj_on1955349912lle_tv @ F3 @ top_top_set_nat )
% 3.06/1.59       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 3.06/1.59         => ( total_on_nat @ top_top_set_nat @ ( inv_im516950809tv_nat @ R @ F3 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_294_total__inv__image,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > nat,R: set_Pr1986765409at_nat] :
% 3.06/1.59        ( ( inj_on1179712058tv_nat @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59       => ( ( total_on_nat @ top_top_set_nat @ R )
% 3.06/1.59         => ( total_1781621663lle_tv @ top_to1057771083lle_tv @ ( inv_im1292588663lle_tv @ R @ F3 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_295_total__inv__image,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,R: set_Pr2014382200lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 3.06/1.59         => ( total_1781621663lle_tv @ top_to1057771083lle_tv @ ( inv_im719552961lle_tv @ R @ F3 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_296_prod_Ocollapse,axiom,
% 3.06/1.59      ! [Prod: produc696645085lle_fm] :
% 3.06/1.59        ( ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) )
% 3.06/1.59        = Prod ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_297_prod_Ocollapse,axiom,
% 3.06/1.59      ! [Prod: produc931990033lle_tv] :
% 3.06/1.59        ( ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ Prod ) @ ( produc547496597lle_tv @ Prod ) )
% 3.06/1.59        = Prod ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_298_prod_Oswap__def,axiom,
% 3.06/1.59      ( produc1232814113lle_tv
% 3.06/1.59      = ( ^ [P: produc1443694919lle_tv] : ( produc1710735575lle_fm @ ( produc381314067lle_tv @ P ) @ ( produc262413013lle_tv @ P ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_299_prod_Oswap__def,axiom,
% 3.06/1.59      ( produc178635363at_nat
% 3.06/1.59      = ( ^ [P: produc596913417at_nat] : ( produc1680557635lle_tv @ ( produc500618325at_nat @ P ) @ ( produc1589291287at_nat @ P ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_300_fst__eqD,axiom,
% 3.06/1.59      ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 3.06/1.59          = A )
% 3.06/1.59       => ( X = A ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_301_fst__eqD,axiom,
% 3.06/1.59      ! [X: nat > nat,Y: paraco1605129243lle_tv,A: nat > nat] :
% 3.06/1.59        ( ( ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 3.06/1.59          = A )
% 3.06/1.59       => ( X = A ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_302_snd__eqD,axiom,
% 3.06/1.59      ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 3.06/1.59          = A )
% 3.06/1.59       => ( Y = A ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_303_snd__eqD,axiom,
% 3.06/1.59      ! [X: nat > nat,Y: paraco1605129243lle_tv,A: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 3.06/1.59          = A )
% 3.06/1.59       => ( Y = A ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_304_fst__conv,axiom,
% 3.06/1.59      ! [X1: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X1 @ X23 ) )
% 3.06/1.59        = X1 ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_305_fst__conv,axiom,
% 3.06/1.59      ! [X1: nat > nat,X23: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X1 @ X23 ) )
% 3.06/1.59        = X1 ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_306_snd__conv,axiom,
% 3.06/1.59      ! [X1: list_char > paraco1605129243lle_tv,X23: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X1 @ X23 ) )
% 3.06/1.59        = X23 ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_307_snd__conv,axiom,
% 3.06/1.59      ! [X1: nat > nat,X23: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X1 @ X23 ) )
% 3.06/1.59        = X23 ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_308_prod_Oexhaust__sel,axiom,
% 3.06/1.59      ! [Prod: produc696645085lle_fm] :
% 3.06/1.59        ( Prod
% 3.06/1.59        = ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_309_prod_Oexhaust__sel,axiom,
% 3.06/1.59      ! [Prod: produc931990033lle_tv] :
% 3.06/1.59        ( Prod
% 3.06/1.59        = ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ Prod ) @ ( produc547496597lle_tv @ Prod ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_310_surjective__pairing,axiom,
% 3.06/1.59      ! [T: produc696645085lle_fm] :
% 3.06/1.59        ( T
% 3.06/1.59        = ( produc1710735575lle_fm @ ( produc29804011lle_fm @ T ) @ ( produc148705065lle_fm @ T ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_311_surjective__pairing,axiom,
% 3.06/1.59      ! [T: produc931990033lle_tv] :
% 3.06/1.59        ( T
% 3.06/1.59        = ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ T ) @ ( produc547496597lle_tv @ T ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_312_exI__realizer,axiom,
% 3.06/1.59      ! [P3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > $o,Y: paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( P3 @ Y @ X )
% 3.06/1.59       => ( P3 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X @ Y ) ) @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X @ Y ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_313_exI__realizer,axiom,
% 3.06/1.59      ! [P3: paraco1605129243lle_tv > ( nat > nat ) > $o,Y: paraco1605129243lle_tv,X: nat > nat] :
% 3.06/1.59        ( ( P3 @ Y @ X )
% 3.06/1.59       => ( P3 @ ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X @ Y ) ) @ ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X @ Y ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_314_conjI__realizer,axiom,
% 3.06/1.59      ! [P3: ( list_char > paraco1605129243lle_tv ) > $o,P2: list_char > paraco1605129243lle_tv,Q2: paraco1604210848lle_fm > $o,Q: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( P3 @ P2 )
% 3.06/1.59       => ( ( Q2 @ Q )
% 3.06/1.59         => ( ( P3 @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ P2 @ Q ) ) )
% 3.06/1.59            & ( Q2 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ P2 @ Q ) ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_315_conjI__realizer,axiom,
% 3.06/1.59      ! [P3: ( nat > nat ) > $o,P2: nat > nat,Q2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( P3 @ P2 )
% 3.06/1.59       => ( ( Q2 @ Q )
% 3.06/1.59         => ( ( P3 @ ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ P2 @ Q ) ) )
% 3.06/1.59            & ( Q2 @ ( produc547496597lle_tv @ ( produc1680557635lle_tv @ P2 @ Q ) ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_316_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.06/1.59      ! [P3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: produc696645085lle_fm] :
% 3.06/1.59        ( ( P3 @ X @ Y )
% 3.06/1.59       => ( ( A
% 3.06/1.59            = ( produc1710735575lle_fm @ X @ Y ) )
% 3.06/1.59         => ( P3 @ ( produc29804011lle_fm @ A ) @ ( produc148705065lle_fm @ A ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_317_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.06/1.59      ! [P3: ( nat > nat ) > paraco1605129243lle_tv > $o,X: nat > nat,Y: paraco1605129243lle_tv,A: produc931990033lle_tv] :
% 3.06/1.59        ( ( P3 @ X @ Y )
% 3.06/1.59       => ( ( A
% 3.06/1.59            = ( produc1680557635lle_tv @ X @ Y ) )
% 3.06/1.59         => ( P3 @ ( produc1636169559lle_tv @ A ) @ ( produc547496597lle_tv @ A ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_318_eq__snd__iff,axiom,
% 3.06/1.59      ! [B: paraco1604210848lle_fm,P2: produc696645085lle_fm] :
% 3.06/1.59        ( ( B
% 3.06/1.59          = ( produc148705065lle_fm @ P2 ) )
% 3.06/1.59        = ( ? [A6: list_char > paraco1605129243lle_tv] :
% 3.06/1.59              ( P2
% 3.06/1.59              = ( produc1710735575lle_fm @ A6 @ B ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_319_eq__snd__iff,axiom,
% 3.06/1.59      ! [B: paraco1605129243lle_tv,P2: produc931990033lle_tv] :
% 3.06/1.59        ( ( B
% 3.06/1.59          = ( produc547496597lle_tv @ P2 ) )
% 3.06/1.59        = ( ? [A6: nat > nat] :
% 3.06/1.59              ( P2
% 3.06/1.59              = ( produc1680557635lle_tv @ A6 @ B ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_320_sndI,axiom,
% 3.06/1.59      ! [X: produc696645085lle_fm,Y: list_char > paraco1605129243lle_tv,Z: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( X
% 3.06/1.59          = ( produc1710735575lle_fm @ Y @ Z ) )
% 3.06/1.59       => ( ( produc148705065lle_fm @ X )
% 3.06/1.59          = Z ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_321_sndI,axiom,
% 3.06/1.59      ! [X: produc931990033lle_tv,Y: nat > nat,Z: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( X
% 3.06/1.59          = ( produc1680557635lle_tv @ Y @ Z ) )
% 3.06/1.59       => ( ( produc547496597lle_tv @ X )
% 3.06/1.59          = Z ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_322_fstI,axiom,
% 3.06/1.59      ! [X: produc696645085lle_fm,Y: list_char > paraco1605129243lle_tv,Z: paraco1604210848lle_fm] :
% 3.06/1.59        ( ( X
% 3.06/1.59          = ( produc1710735575lle_fm @ Y @ Z ) )
% 3.06/1.59       => ( ( produc29804011lle_fm @ X )
% 3.06/1.59          = Y ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_323_fstI,axiom,
% 3.06/1.59      ! [X: produc931990033lle_tv,Y: nat > nat,Z: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( X
% 3.06/1.59          = ( produc1680557635lle_tv @ Y @ Z ) )
% 3.06/1.59       => ( ( produc1636169559lle_tv @ X )
% 3.06/1.59          = Y ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_324_eq__fst__iff,axiom,
% 3.06/1.59      ! [A: list_char > paraco1605129243lle_tv,P2: produc696645085lle_fm] :
% 3.06/1.59        ( ( A
% 3.06/1.59          = ( produc29804011lle_fm @ P2 ) )
% 3.06/1.59        = ( ? [B5: paraco1604210848lle_fm] :
% 3.06/1.59              ( P2
% 3.06/1.59              = ( produc1710735575lle_fm @ A @ B5 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_325_eq__fst__iff,axiom,
% 3.06/1.59      ! [A: nat > nat,P2: produc931990033lle_tv] :
% 3.06/1.59        ( ( A
% 3.06/1.59          = ( produc1636169559lle_tv @ P2 ) )
% 3.06/1.59        = ( ? [B5: paraco1605129243lle_tv] :
% 3.06/1.59              ( P2
% 3.06/1.59              = ( produc1680557635lle_tv @ A @ B5 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_326_total__lex__prod,axiom,
% 3.06/1.59      ! [R: set_Pr1986765409at_nat,S3: set_Pr1986765409at_nat] :
% 3.06/1.59        ( ( total_on_nat @ top_top_set_nat @ R )
% 3.06/1.59       => ( ( total_on_nat @ top_top_set_nat @ S3 )
% 3.06/1.59         => ( total_1775715973at_nat @ top_to1555900337at_nat @ ( lex_prod_nat_nat @ R @ S3 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_327_total__lex__prod,axiom,
% 3.06/1.59      ! [R: set_Pr1986765409at_nat,S3: set_Pr2014382200lle_tv] :
% 3.06/1.59        ( ( total_on_nat @ top_top_set_nat @ R )
% 3.06/1.59       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ S3 )
% 3.06/1.59         => ( total_517371324lle_tv @ top_to1411004326lle_tv @ ( lex_pr413684186lle_tv @ R @ S3 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_328_total__lex__prod,axiom,
% 3.06/1.59      ! [R: set_Pr2014382200lle_tv,S3: set_Pr1986765409at_nat] :
% 3.06/1.59        ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 3.06/1.59       => ( ( total_on_nat @ top_top_set_nat @ S3 )
% 3.06/1.59         => ( total_440843542tv_nat @ top_to975729152tv_nat @ ( lex_pr1785529980tv_nat @ R @ S3 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_329_total__lex__prod,axiom,
% 3.06/1.59      ! [R: set_Pr2014382200lle_tv,S3: set_Pr2014382200lle_tv] :
% 3.06/1.59        ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 3.06/1.59       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ S3 )
% 3.06/1.59         => ( total_92239038lle_tv @ top_to1871154984lle_tv @ ( lex_pr567812260lle_tv @ R @ S3 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_330_in__lex__prod,axiom,
% 3.06/1.59      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm,R: set_Pr2061825550lle_tv,S3: set_Pr1019238018lle_fm] :
% 3.06/1.59        ( ( member1592865093lle_fm @ ( produc407632608lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ ( produc1710735575lle_fm @ A5 @ B3 ) ) @ ( lex_pr2001015487lle_fm @ R @ S3 ) )
% 3.06/1.59        = ( ( member146333935lle_tv @ ( produc1297923922lle_tv @ A @ A5 ) @ R )
% 3.06/1.59          | ( ( A = A5 )
% 3.06/1.59            & ( member334644067lle_fm @ ( produc1126104134lle_fm @ B @ B3 ) @ S3 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_331_in__lex__prod,axiom,
% 3.06/1.59      ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv,R: set_Pr1357842111at_nat,S3: set_Pr2014382200lle_tv] :
% 3.06/1.59        ( ( member1339857875lle_tv @ ( produc2057188974lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ ( produc1680557635lle_tv @ A5 @ B3 ) ) @ ( lex_pr1093414955lle_tv @ R @ S3 ) )
% 3.06/1.59        = ( ( member112824072at_nat @ ( produc780837143at_nat @ A @ A5 ) @ R )
% 3.06/1.59          | ( ( A = A5 )
% 3.06/1.59            & ( member1531318361lle_tv @ ( produc2058540732lle_tv @ B @ B3 ) @ S3 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_332_wf__map__prod__image,axiom,
% 3.06/1.59      ! [R: set_Pr1986765409at_nat,F3: nat > nat] :
% 3.06/1.59        ( ( wf_nat @ R )
% 3.06/1.59       => ( ( inj_on_nat_nat @ F3 @ top_top_set_nat )
% 3.06/1.59         => ( wf_nat @ ( image_815163717at_nat @ ( produc505105722at_nat @ F3 @ F3 ) @ R ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_333_wf__map__prod__image,axiom,
% 3.06/1.59      ! [R: set_Pr2014382200lle_tv,F3: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.59        ( ( wf_Par1378404612lle_tv @ R )
% 3.06/1.59       => ( ( inj_on772319074lle_tv @ F3 @ top_to1057771083lle_tv )
% 3.06/1.59         => ( wf_Par1378404612lle_tv @ ( image_1221801032lle_tv @ ( produc1345917071lle_tv @ F3 @ F3 ) @ R ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_334_same__fstI,axiom,
% 3.06/1.59      ! [P3: ( list_char > paraco1605129243lle_tv ) > $o,X: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm,Y: paraco1604210848lle_fm,R2: ( list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm] :
% 3.06/1.59        ( ( P3 @ X )
% 3.06/1.59       => ( ( member334644067lle_fm @ ( produc1126104134lle_fm @ Y5 @ Y ) @ ( R2 @ X ) )
% 3.06/1.59         => ( member1592865093lle_fm @ ( produc407632608lle_fm @ ( produc1710735575lle_fm @ X @ Y5 ) @ ( produc1710735575lle_fm @ X @ Y ) ) @ ( same_f1581085506lle_fm @ P3 @ R2 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_335_same__fstI,axiom,
% 3.06/1.59      ! [P3: ( nat > nat ) > $o,X: nat > nat,Y5: paraco1605129243lle_tv,Y: paraco1605129243lle_tv,R2: ( nat > nat ) > set_Pr2014382200lle_tv] :
% 3.06/1.59        ( ( P3 @ X )
% 3.06/1.59       => ( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ Y5 @ Y ) @ ( R2 @ X ) )
% 3.06/1.59         => ( member1339857875lle_tv @ ( produc2057188974lle_tv @ ( produc1680557635lle_tv @ X @ Y5 ) @ ( produc1680557635lle_tv @ X @ Y ) ) @ ( same_f1138187694lle_tv @ P3 @ R2 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_336_the__inv__into__into,axiom,
% 3.06/1.59      ! [F3: nat > nat,A2: set_nat,X: nat,B4: set_nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ A2 )
% 3.06/1.59       => ( ( member_nat @ X @ ( image_nat_nat @ F3 @ A2 ) )
% 3.06/1.59         => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 3.06/1.59           => ( member_nat @ ( the_inv_into_nat_nat @ A2 @ F3 @ X ) @ B4 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_337_the__inv__into__into,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 3.06/1.59       => ( ( member266900804lle_tv @ X @ ( image_335818702lle_tv @ F3 @ A2 ) )
% 3.06/1.59         => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 3.06/1.59           => ( member266900804lle_tv @ ( the_in452116896lle_tv @ A2 @ F3 @ X ) @ B4 ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_338_inj__on__image__eq__iff,axiom,
% 3.06/1.59      ! [F3: nat > nat,C2: set_nat,A2: set_nat,B4: set_nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ C2 )
% 3.06/1.59       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 3.06/1.59         => ( ( ord_less_eq_set_nat @ B4 @ C2 )
% 3.06/1.59           => ( ( ( image_nat_nat @ F3 @ A2 )
% 3.06/1.59                = ( image_nat_nat @ F3 @ B4 ) )
% 3.06/1.59              = ( A2 = B4 ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_339_inj__on__image__eq__iff,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,C2: set_Pa1764573435lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ C2 )
% 3.06/1.59       => ( ( ord_le241064091lle_tv @ A2 @ C2 )
% 3.06/1.59         => ( ( ord_le241064091lle_tv @ B4 @ C2 )
% 3.06/1.59           => ( ( ( image_335818702lle_tv @ F3 @ A2 )
% 3.06/1.59                = ( image_335818702lle_tv @ F3 @ B4 ) )
% 3.06/1.59              = ( A2 = B4 ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_340_inj__on__image__mem__iff,axiom,
% 3.06/1.59      ! [F3: nat > nat,B4: set_nat,A: nat,A2: set_nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ B4 )
% 3.06/1.59       => ( ( member_nat @ A @ B4 )
% 3.06/1.59         => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 3.06/1.59           => ( ( member_nat @ ( F3 @ A ) @ ( image_nat_nat @ F3 @ A2 ) )
% 3.06/1.59              = ( member_nat @ A @ A2 ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_341_inj__on__image__mem__iff,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv,A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ B4 )
% 3.06/1.59       => ( ( member266900804lle_tv @ A @ B4 )
% 3.06/1.59         => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 3.06/1.59           => ( ( member266900804lle_tv @ ( F3 @ A ) @ ( image_335818702lle_tv @ F3 @ A2 ) )
% 3.06/1.59              = ( member266900804lle_tv @ A @ A2 ) ) ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_342_top_Oextremum__uniqueI,axiom,
% 3.06/1.59      ! [A: set_nat] :
% 3.06/1.59        ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
% 3.06/1.59       => ( A = top_top_set_nat ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_343_top_Oextremum__uniqueI,axiom,
% 3.06/1.59      ! [A: set_Pa1764573435lle_tv] :
% 3.06/1.59        ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
% 3.06/1.59       => ( A = top_to1057771083lle_tv ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_344_top_Oextremum__unique,axiom,
% 3.06/1.59      ! [A: set_nat] :
% 3.06/1.59        ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
% 3.06/1.59        = ( A = top_top_set_nat ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_345_top_Oextremum__unique,axiom,
% 3.06/1.59      ! [A: set_Pa1764573435lle_tv] :
% 3.06/1.59        ( ( ord_le241064091lle_tv @ top_to1057771083lle_tv @ A )
% 3.06/1.59        = ( A = top_to1057771083lle_tv ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_346_top__greatest,axiom,
% 3.06/1.59      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_347_top__greatest,axiom,
% 3.06/1.59      ! [A: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A @ top_to1057771083lle_tv ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_348_subset__UNIV,axiom,
% 3.06/1.59      ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ top_top_set_nat ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_349_subset__UNIV,axiom,
% 3.06/1.59      ! [A2: set_Pa1764573435lle_tv] : ( ord_le241064091lle_tv @ A2 @ top_to1057771083lle_tv ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_350_inj__on__subset,axiom,
% 3.06/1.59      ! [F3: nat > nat,A2: set_nat,B4: set_nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ A2 )
% 3.06/1.59       => ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 3.06/1.59         => ( inj_on_nat_nat @ F3 @ B4 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_351_inj__on__subset,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ A2 )
% 3.06/1.59       => ( ( ord_le241064091lle_tv @ B4 @ A2 )
% 3.06/1.59         => ( inj_on772319074lle_tv @ F3 @ B4 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_352_subset__inj__on,axiom,
% 3.06/1.59      ! [F3: nat > nat,B4: set_nat,A2: set_nat] :
% 3.06/1.59        ( ( inj_on_nat_nat @ F3 @ B4 )
% 3.06/1.59       => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 3.06/1.59         => ( inj_on_nat_nat @ F3 @ A2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(fact_353_subset__inj__on,axiom,
% 3.06/1.59      ! [F3: paraco1605129243lle_tv > paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv,A2: set_Pa1764573435lle_tv] :
% 3.06/1.59        ( ( inj_on772319074lle_tv @ F3 @ B4 )
% 3.06/1.59       => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 3.06/1.59         => ( inj_on772319074lle_tv @ F3 @ A2 ) ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(help_If_3_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 3.06/1.59      ! [P3: $o] :
% 3.06/1.59        ( ( P3 = $true )
% 3.06/1.59        | ( P3 = $false ) ) ).
% 3.06/1.59  
% 3.06/1.59  thf(help_If_2_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 3.06/1.59      ! [X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( if_Par1134130401lle_tv @ $false @ X @ Y )
% 3.06/1.59        = Y ) ).
% 3.06/1.59  
% 3.06/1.59  thf(help_If_1_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 3.06/1.59      ! [X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.59        ( ( if_Par1134130401lle_tv @ $true @ X @ Y )
% 3.06/1.59        = X ) ).
% 3.06/1.59  
% 3.06/1.59  thf(conj_0,conjecture,
% 3.06/1.59      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
% 3.06/1.59     != ( paraco1344940915le_Det @ $true ) ) ).
% 3.06/1.59  ------------------------
% 3.14/1.61  % (12571)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12469 for (2999ds/183Mi)
% 3.14/1.62  % (12575)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_12469 for (2999ds/2Mi)
% 3.14/1.62  % (12574)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12469 for (2999ds/2Mi)
% 3.14/1.62  % (12576)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_12469 for (2999ds/275Mi)
% 3.14/1.62  % (12572)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_12469 for (2999ds/4Mi)
% 3.14/1.62  % (12573)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_12469 for (2999ds/27Mi)
% 3.14/1.62  % (12577)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12469 for (2999ds/18Mi)
% 3.14/1.62  % (12574)Instruction limit reached!
% 3.14/1.62  % (12574)------------------------------
% 3.14/1.62  % (12574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.62  % (12574)Termination reason: Unknown
% 3.14/1.62  % (12575)Instruction limit reached!
% 3.14/1.62  % (12575)------------------------------
% 3.14/1.62  % (12575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.62  % (12574)Termination phase: shuffling
% 3.14/1.62  
% 3.14/1.62  % (12574)Memory used [KB]: 1535
% 3.14/1.62  % (12574)Time elapsed: 0.003 s
% 3.14/1.62  % (12574)Instructions burned: 3 (million)
% 3.14/1.62  % (12574)------------------------------
% 3.14/1.62  % (12574)------------------------------
% 3.14/1.62  % (12575)Termination reason: Unknown
% 3.14/1.62  % (12575)Termination phase: shuffling
% 3.14/1.62  
% 3.14/1.62  % (12575)Memory used [KB]: 1535
% 3.14/1.62  % (12575)Time elapsed: 0.003 s
% 3.14/1.62  % (12575)Instructions burned: 3 (million)
% 3.14/1.62  % (12575)------------------------------
% 3.14/1.62  % (12575)------------------------------
% 3.14/1.62  % (12572)Instruction limit reached!
% 3.14/1.62  % (12572)------------------------------
% 3.14/1.62  % (12572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.62  % (12572)Termination reason: Unknown
% 3.14/1.62  % (12572)Termination phase: shuffling
% 3.14/1.62  
% 3.14/1.62  % (12572)Memory used [KB]: 1663
% 3.14/1.62  % (12572)Time elapsed: 0.004 s
% 3.14/1.62  % (12572)Instructions burned: 5 (million)
% 3.14/1.62  % (12572)------------------------------
% 3.14/1.62  % (12572)------------------------------
% 3.14/1.63  % (12577)Instruction limit reached!
% 3.14/1.63  % (12577)------------------------------
% 3.14/1.63  % (12577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.63  % (12577)Termination reason: Unknown
% 3.14/1.63  % (12577)Termination phase: shuffling
% 3.14/1.63  
% 3.14/1.63  % (12577)Memory used [KB]: 1918
% 3.14/1.63  % (12577)Time elapsed: 0.011 s
% 3.14/1.63  % (12577)Instructions burned: 19 (million)
% 3.14/1.63  % (12577)------------------------------
% 3.14/1.63  % (12577)------------------------------
% 3.14/1.63  % (12573)Instruction limit reached!
% 3.14/1.63  % (12573)------------------------------
% 3.14/1.63  % (12573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.63  % (12573)Termination reason: Unknown
% 3.14/1.63  % (12573)Termination phase: Property scanning
% 3.14/1.63  
% 3.14/1.63  % (12573)Memory used [KB]: 1918
% 3.14/1.63  % (12573)Time elapsed: 0.015 s
% 3.14/1.63  % (12573)Instructions burned: 27 (million)
% 3.14/1.63  % (12573)------------------------------
% 3.14/1.63  % (12573)------------------------------
% 3.14/1.64  % (12578)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12469 for (2999ds/3Mi)
% 3.14/1.64  % (12579)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_12469 for (2999ds/37Mi)
% 3.14/1.64  % (12580)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_12469 for (2999ds/15Mi)
% 3.14/1.64  % (12578)Instruction limit reached!
% 3.14/1.64  % (12578)------------------------------
% 3.14/1.64  % (12578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.64  % (12578)Termination reason: Unknown
% 3.14/1.64  % (12578)Termination phase: shuffling
% 3.14/1.64  
% 3.14/1.64  % (12578)Memory used [KB]: 1535
% 3.14/1.64  % (12578)Time elapsed: 0.003 s
% 3.14/1.64  % (12578)Instructions burned: 3 (million)
% 3.14/1.64  % (12578)------------------------------
% 3.14/1.64  % (12578)------------------------------
% 3.14/1.64  % (12576)First to succeed.
% 3.14/1.64  % (12581)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_12469 for (2999ds/3Mi)
% 3.14/1.64  % (12580)Instruction limit reached!
% 3.14/1.64  % (12580)------------------------------
% 3.14/1.64  % (12580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.64  % (12580)Termination reason: Unknown
% 3.14/1.64  % (12580)Termination phase: shuffling
% 3.14/1.64  
% 3.14/1.64  % (12580)Memory used [KB]: 1918
% 3.14/1.64  % (12580)Time elapsed: 0.009 s
% 3.14/1.64  % (12580)Instructions burned: 15 (million)
% 3.14/1.64  % (12580)------------------------------
% 3.14/1.64  % (12580)------------------------------
% 3.14/1.64  % (12576)Refutation found. Thanks to Tanya!
% 3.14/1.64  % SZS status Theorem for DTF2THF_12469
% 3.14/1.64  % SZS output start Proof for DTF2THF_12469
% 3.14/1.64  thf(type_def_5, type, nat: $tType).
% 3.14/1.64  thf(type_def_7, type, set_nat: $tType).
% 3.14/1.64  thf(type_def_8, type, paraco1605129243lle_tv: $tType).
% 3.14/1.64  thf(type_def_9, type, set_Pa1764573435lle_tv: $tType).
% 3.14/1.64  thf(type_def_10, type, product_prod_nat_nat: $tType).
% 3.14/1.64  thf(type_def_11, type, set_Pr1986765409at_nat: $tType).
% 3.14/1.64  thf(type_def_12, type, produc270694976lle_tv: $tType).
% 3.14/1.64  thf(type_def_13, type, set_Pr13445366lle_tv: $tType).
% 3.14/1.64  thf(type_def_14, type, produc194167194tv_nat: $tType).
% 3.14/1.64  thf(type_def_15, type, set_Pr1725653840tv_nat: $tType).
% 3.14/1.64  thf(type_def_16, type, produc1647334210lle_tv: $tType).
% 3.14/1.64  thf(type_def_17, type, set_Pr2014382200lle_tv: $tType).
% 3.14/1.64  thf(type_def_18, type, set_Pr2061825550lle_tv: $tType).
% 3.14/1.64  thf(type_def_19, type, set_Pr2120184979lle_fm: $tType).
% 3.14/1.64  thf(type_def_20, type, set_Pr1357842111at_nat: $tType).
% 3.14/1.64  thf(type_def_21, type, set_Pr560526279lle_tv: $tType).
% 3.14/1.64  thf(type_def_22, type, list_char: $tType).
% 3.14/1.64  thf(type_def_23, type, produc931990033lle_tv: $tType).
% 3.14/1.64  thf(type_def_24, type, paraco1604210848lle_fm: $tType).
% 3.14/1.64  thf(type_def_25, type, produc1852595672lle_tv: $tType).
% 3.14/1.64  thf(type_def_26, type, produc696645085lle_fm: $tType).
% 3.14/1.64  thf(type_def_27, type, produc1281043295at_nat: $tType).
% 3.14/1.64  thf(type_def_28, type, produc1443694919lle_tv: $tType).
% 3.14/1.64  thf(type_def_29, type, produc450659916lle_fm: $tType).
% 3.14/1.64  thf(type_def_30, type, produc596913417at_nat: $tType).
% 3.14/1.64  thf(type_def_31, type, produc1250255278lle_fm: $tType).
% 3.14/1.64  thf(type_def_32, type, produc1720769084lle_tv: $tType).
% 3.14/1.64  thf(type_def_33, type, set_Pr1490359111at_nat: $tType).
% 3.14/1.64  thf(type_def_34, type, set_Pr292927124lle_tv: $tType).
% 3.14/1.64  thf(type_def_35, type, set_Pr1943077434tv_nat: $tType).
% 3.14/1.64  thf(type_def_36, type, set_Pr2012908090lle_tv: $tType).
% 3.14/1.64  thf(type_def_37, type, set_Pr1723822845lle_tv: $tType).
% 3.14/1.64  thf(type_def_38, type, set_Pr840833727at_nat: $tType).
% 3.14/1.64  thf(type_def_39, type, set_Pr1019238018lle_fm: $tType).
% 3.14/1.64  thf(type_def_40, type, set_Pr1475944804lle_fm: $tType).
% 3.14/1.64  thf(type_def_41, type, set_Pr698334450lle_tv: $tType).
% 3.14/1.64  thf(func_def_0, type, set_Pr1475944804lle_fm: $tType).
% 3.14/1.64  thf(func_def_1, type, produc1250255278lle_fm: $tType).
% 3.14/1.64  thf(func_def_2, type, set_Pr2012908090lle_tv: $tType).
% 3.14/1.64  thf(func_def_3, type, set_Pr698334450lle_tv: $tType).
% 3.14/1.64  thf(func_def_4, type, produc1720769084lle_tv: $tType).
% 3.14/1.64  thf(func_def_5, type, set_Pr2061825550lle_tv: $tType).
% 3.14/1.64  thf(func_def_6, type, set_Pr1943077434tv_nat: $tType).
% 3.14/1.64  thf(func_def_7, type, set_Pr292927124lle_tv: $tType).
% 3.14/1.64  thf(func_def_8, type, produc1852595672lle_tv: $tType).
% 3.14/1.64  thf(func_def_9, type, set_Pr1723822845lle_tv: $tType).
% 3.14/1.64  thf(func_def_10, type, set_Pr2120184979lle_fm: $tType).
% 3.14/1.64  thf(func_def_11, type, produc1443694919lle_tv: $tType).
% 3.14/1.64  thf(func_def_12, type, produc696645085lle_fm: $tType).
% 3.14/1.64  thf(func_def_13, type, set_Pr1490359111at_nat: $tType).
% 3.14/1.64  thf(func_def_14, type, set_Pr2014382200lle_tv: $tType).
% 3.14/1.64  thf(func_def_15, type, set_Pr1019238018lle_fm: $tType).
% 3.14/1.64  thf(func_def_16, type, set_Pr840833727at_nat: $tType).
% 3.14/1.64  thf(func_def_17, type, set_Pr560526279lle_tv: $tType).
% 3.14/1.64  thf(func_def_18, type, produc1647334210lle_tv: $tType).
% 3.14/1.64  thf(func_def_19, type, produc450659916lle_fm: $tType).
% 3.14/1.64  thf(func_def_20, type, set_Pr1357842111at_nat: $tType).
% 3.14/1.64  thf(func_def_21, type, produc596913417at_nat: $tType).
% 3.14/1.64  thf(func_def_22, type, produc931990033lle_tv: $tType).
% 3.14/1.64  thf(func_def_23, type, set_Pr1725653840tv_nat: $tType).
% 3.14/1.64  thf(func_def_24, type, set_Pr13445366lle_tv: $tType).
% 3.14/1.64  thf(func_def_25, type, produc1281043295at_nat: $tType).
% 3.14/1.64  thf(func_def_26, type, produc194167194tv_nat: $tType).
% 3.14/1.64  thf(func_def_27, type, produc270694976lle_tv: $tType).
% 3.14/1.64  thf(func_def_28, type, set_Pr1986765409at_nat: $tType).
% 3.14/1.64  thf(func_def_29, type, set_Pa1764573435lle_tv: $tType).
% 3.14/1.64  thf(func_def_30, type, product_prod_nat_nat: $tType).
% 3.14/1.64  thf(func_def_31, type, paraco1605129243lle_tv: $tType).
% 3.14/1.64  thf(func_def_32, type, paraco1604210848lle_fm: $tType).
% 3.14/1.64  thf(func_def_33, type, list_char: $tType).
% 3.14/1.64  thf(func_def_34, type, set_nat: $tType).
% 3.14/1.64  thf(func_def_35, type, nat: $tType).
% 3.14/1.64  thf(func_def_36, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 3.14/1.64  thf(func_def_37, type, inj_on1955349912lle_tv: (nat > paraco1605129243lle_tv) > set_nat > $o).
% 3.14/1.64  thf(func_def_38, type, inj_on1179712058tv_nat: (paraco1605129243lle_tv > nat) > set_Pa1764573435lle_tv > $o).
% 3.14/1.64  thf(func_def_39, type, inj_on772319074lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > $o).
% 3.14/1.64  thf(func_def_40, type, inj_on26176689at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1986765409at_nat > $o).
% 3.14/1.64  thf(func_def_41, type, inj_on1745913142lle_tv: (produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > $o).
% 3.14/1.64  thf(func_def_42, type, inj_on552895452tv_nat: (produc194167194tv_nat > produc194167194tv_nat) > set_Pr1725653840tv_nat > $o).
% 3.14/1.64  thf(func_def_43, type, inj_on2112487900lle_tv: (produc1647334210lle_tv > produc1647334210lle_tv) > set_Pr2014382200lle_tv > $o).
% 3.14/1.64  thf(func_def_44, type, the_inv_into_nat_nat: set_nat > (nat > nat) > nat > nat).
% 3.14/1.64  thf(func_def_45, type, the_in452116896lle_tv: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_46, type, if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_47, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 3.14/1.64  thf(func_def_48, type, ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o).
% 3.14/1.64  thf(func_def_49, type, top_top_nat_o: nat > $o).
% 3.14/1.64  thf(func_def_50, type, top_to1299250770e_tv_o: paraco1605129243lle_tv > $o).
% 3.14/1.64  thf(func_def_51, type, top_to632227436_nat_o: product_prod_nat_nat > $o).
% 3.14/1.64  thf(func_def_52, type, top_to1889334367e_tv_o: produc270694976lle_tv > $o).
% 3.14/1.64  thf(func_def_53, type, top_to900819589_nat_o: produc194167194tv_nat > $o).
% 3.14/1.64  thf(func_def_55, type, top_top_set_nat: set_nat).
% 3.14/1.64  thf(func_def_56, type, top_to1057771083lle_tv: set_Pa1764573435lle_tv).
% 3.14/1.64  thf(func_def_57, type, top_to138697918lle_tv: set_Pr2061825550lle_tv).
% 3.14/1.64  thf(func_def_58, type, top_to775056195lle_fm: set_Pr2120184979lle_fm).
% 3.14/1.64  thf(func_def_59, type, top_to1541413903at_nat: set_Pr1357842111at_nat).
% 3.14/1.64  thf(func_def_60, type, top_to449985143lle_tv: set_Pr560526279lle_tv).
% 3.14/1.64  thf(func_def_61, type, top_to1555900337at_nat: set_Pr1986765409at_nat).
% 3.14/1.64  thf(func_def_62, type, top_to1411004326lle_tv: set_Pr13445366lle_tv).
% 3.14/1.64  thf(func_def_63, type, top_to975729152tv_nat: set_Pr1725653840tv_nat).
% 3.14/1.64  thf(func_def_64, type, top_to1871154984lle_tv: set_Pr2014382200lle_tv).
% 3.14/1.64  thf(func_def_65, type, paraco761681009ge_int: (nat > nat) > (list_char > paraco1605129243lle_tv) > list_char > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_66, type, paraco1147068288nge_tv: (nat > nat) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_67, type, paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o).
% 3.14/1.64  thf(func_def_68, type, paraco1325918602e_eval: (list_char > paraco1605129243lle_tv) > paraco1604210848lle_fm > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_69, type, paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.14/1.64  thf(func_def_70, type, paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.14/1.64  thf(func_def_71, type, paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.14/1.64  thf(func_def_72, type, paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.14/1.64  thf(func_def_73, type, paraco1480028776le_Pro: list_char > paraco1604210848lle_fm).
% 3.14/1.64  thf(func_def_74, type, paraco367965286_Truth: paraco1604210848lle_fm).
% 3.14/1.64  thf(func_def_75, type, paraco1344940915le_Det: $o > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_76, type, paraco793048302_Indet: nat > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_77, type, paraco2051596139lle_tv: ($o > paraco1605129243lle_tv) > (nat > paraco1605129243lle_tv) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_78, type, paraco327635598_valid: paraco1604210848lle_fm > $o).
% 3.14/1.64  thf(func_def_79, type, paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o).
% 3.14/1.64  thf(func_def_80, type, produc1297923922lle_tv: (list_char > paraco1605129243lle_tv) > (list_char > paraco1605129243lle_tv) > produc1852595672lle_tv).
% 3.14/1.64  thf(func_def_81, type, produc1710735575lle_fm: (list_char > paraco1605129243lle_tv) > paraco1604210848lle_fm > produc696645085lle_fm).
% 3.14/1.64  thf(func_def_82, type, produc780837143at_nat: (nat > nat) > (nat > nat) > produc1281043295at_nat).
% 3.14/1.64  thf(func_def_83, type, produc1680557635lle_tv: (nat > nat) > paraco1605129243lle_tv > produc931990033lle_tv).
% 3.14/1.64  thf(func_def_84, type, produc1943344577lle_tv: paraco1604210848lle_fm > (list_char > paraco1605129243lle_tv) > produc1443694919lle_tv).
% 3.14/1.64  thf(func_def_85, type, produc1126104134lle_fm: paraco1604210848lle_fm > paraco1604210848lle_fm > produc450659916lle_fm).
% 3.14/1.64  thf(func_def_86, type, produc1633679363at_nat: paraco1605129243lle_tv > (nat > nat) > produc596913417at_nat).
% 3.14/1.64  thf(func_def_87, type, produc2058540732lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv).
% 3.14/1.64  thf(func_def_88, type, produc407632608lle_fm: produc696645085lle_fm > produc696645085lle_fm > produc1250255278lle_fm).
% 3.14/1.64  thf(func_def_89, type, produc2057188974lle_tv: produc931990033lle_tv > produc931990033lle_tv > produc1720769084lle_tv).
% 3.14/1.64  thf(func_def_90, type, produc1942165868lle_fm: ((list_char > paraco1605129243lle_tv) > list_char > paraco1605129243lle_tv) > produc696645085lle_fm > produc696645085lle_fm).
% 3.14/1.64  thf(func_def_91, type, produc939316703lle_tv: ((nat > nat) > nat > nat) > produc931990033lle_tv > produc931990033lle_tv).
% 3.14/1.64  thf(func_def_92, type, produc1807466521lle_tv: (paraco1604210848lle_fm > paraco1604210848lle_fm) > produc696645085lle_fm > produc696645085lle_fm).
% 3.14/1.64  thf(func_def_93, type, produc109093078at_nat: (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc931990033lle_tv > produc931990033lle_tv).
% 3.14/1.64  thf(func_def_94, type, produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_95, type, produc275353523e_fm_o: (produc696645085lle_fm > $o) > (list_char > paraco1605129243lle_tv) > paraco1604210848lle_fm > $o).
% 3.14/1.64  thf(func_def_96, type, produc752649287e_tv_o: (produc931990033lle_tv > $o) > (nat > nat) > paraco1605129243lle_tv > $o).
% 3.14/1.64  thf(func_def_97, type, produc1900967599lle_fm: ((list_char > paraco1605129243lle_tv) > list_char > paraco1605129243lle_tv) > (paraco1604210848lle_fm > paraco1604210848lle_fm) > produc696645085lle_fm > produc696645085lle_fm).
% 3.14/1.64  thf(func_def_98, type, produc1566550641lle_tv: ((list_char > paraco1605129243lle_tv) > nat > nat) > (paraco1604210848lle_fm > paraco1605129243lle_tv) > produc696645085lle_fm > produc931990033lle_tv).
% 3.14/1.64  thf(func_def_99, type, produc951033137lle_fm: ((nat > nat) > list_char > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1604210848lle_fm) > produc931990033lle_tv > produc696645085lle_fm).
% 3.14/1.64  thf(func_def_100, type, produc532909085lle_tv: ((nat > nat) > nat > nat) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc931990033lle_tv > produc931990033lle_tv).
% 3.14/1.64  thf(func_def_101, type, produc505105722at_nat: (nat > nat) > (nat > nat) > product_prod_nat_nat > product_prod_nat_nat).
% 3.14/1.64  thf(func_def_102, type, produc313957681lle_tv: (nat > nat) > (nat > paraco1605129243lle_tv) > product_prod_nat_nat > produc270694976lle_tv).
% 3.14/1.64  thf(func_def_103, type, produc1685803475tv_nat: (nat > nat) > (paraco1605129243lle_tv > nat) > produc270694976lle_tv > product_prod_nat_nat).
% 3.14/1.64  thf(func_def_104, type, produc2101297531lle_tv: (nat > nat) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc270694976lle_tv > produc270694976lle_tv).
% 3.14/1.64  thf(func_def_105, type, produc1250721397at_nat: (nat > paraco1605129243lle_tv) > (nat > nat) > product_prod_nat_nat > produc194167194tv_nat).
% 3.14/1.64  thf(func_def_106, type, produc210389789lle_tv: (nat > paraco1605129243lle_tv) > (nat > paraco1605129243lle_tv) > product_prod_nat_nat > produc1647334210lle_tv).
% 3.14/1.64  thf(func_def_107, type, produc189459613tv_nat: (nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > nat) > produc270694976lle_tv > produc194167194tv_nat).
% 3.14/1.64  thf(func_def_108, type, produc1975500101lle_tv: (nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc270694976lle_tv > produc1647334210lle_tv).
% 3.14/1.64  thf(func_def_109, type, produc386540311at_nat: (paraco1605129243lle_tv > nat) > (nat > nat) > produc194167194tv_nat > product_prod_nat_nat).
% 3.14/1.64  thf(func_def_110, type, produc72207551lle_tv: (paraco1605129243lle_tv > nat) > (nat > paraco1605129243lle_tv) > produc194167194tv_nat > produc270694976lle_tv).
% 3.14/1.64  thf(func_def_111, type, produc42536895at_nat: (paraco1605129243lle_tv > paraco1605129243lle_tv) > (nat > nat) > produc194167194tv_nat > produc194167194tv_nat).
% 3.14/1.64  thf(func_def_112, type, produc1345917071lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc1647334210lle_tv > produc1647334210lle_tv).
% 3.14/1.64  thf(func_def_113, type, produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_114, type, produc1636169559lle_tv: produc931990033lle_tv > nat > nat).
% 3.14/1.64  thf(func_def_115, type, produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm).
% 3.14/1.64  thf(func_def_116, type, produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_117, type, produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm).
% 3.14/1.64  thf(func_def_118, type, produc547496597lle_tv: produc931990033lle_tv > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_119, type, produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_120, type, produc500618325at_nat: produc596913417at_nat > nat > nat).
% 3.14/1.64  thf(func_def_121, type, produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv).
% 3.14/1.64  thf(func_def_122, type, produc225513635lle_tv: produc931990033lle_tv > produc596913417at_nat).
% 3.14/1.64  thf(func_def_123, type, produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm).
% 3.14/1.64  thf(func_def_124, type, produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv).
% 3.14/1.64  thf(func_def_125, type, inv_image_nat_nat: set_Pr1986765409at_nat > (nat > nat) > set_Pr1986765409at_nat).
% 3.14/1.64  thf(func_def_126, type, inv_im1292588663lle_tv: set_Pr1986765409at_nat > (paraco1605129243lle_tv > nat) > set_Pr2014382200lle_tv).
% 3.14/1.64  thf(func_def_127, type, inv_im516950809tv_nat: set_Pr2014382200lle_tv > (nat > paraco1605129243lle_tv) > set_Pr1986765409at_nat).
% 3.14/1.64  thf(func_def_128, type, inv_im719552961lle_tv: set_Pr2014382200lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pr2014382200lle_tv).
% 3.14/1.64  thf(func_def_129, type, total_on_nat: set_nat > set_Pr1986765409at_nat > $o).
% 3.14/1.64  thf(func_def_130, type, total_1781621663lle_tv: set_Pa1764573435lle_tv > set_Pr2014382200lle_tv > $o).
% 3.14/1.64  thf(func_def_131, type, total_1775715973at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o).
% 3.14/1.64  thf(func_def_132, type, total_517371324lle_tv: set_Pr13445366lle_tv > set_Pr292927124lle_tv > $o).
% 3.14/1.64  thf(func_def_133, type, total_440843542tv_nat: set_Pr1725653840tv_nat > set_Pr1943077434tv_nat > $o).
% 3.14/1.64  thf(func_def_134, type, total_92239038lle_tv: set_Pr2014382200lle_tv > set_Pr2012908090lle_tv > $o).
% 3.14/1.64  thf(func_def_135, type, collect_nat: (nat > $o) > set_nat).
% 3.14/1.64  thf(func_def_136, type, collec1111687558lle_tv: (paraco1605129243lle_tv > $o) > set_Pa1764573435lle_tv).
% 3.14/1.64  thf(func_def_137, type, collec1102043437lle_tv: (produc1852595672lle_tv > $o) > set_Pr2061825550lle_tv).
% 3.14/1.64  thf(func_def_138, type, collec835549234lle_fm: (produc696645085lle_fm > $o) > set_Pr2120184979lle_fm).
% 3.14/1.64  thf(func_def_139, type, collec791369802at_nat: (produc1281043295at_nat > $o) > set_Pr1357842111at_nat).
% 3.14/1.64  thf(func_def_140, type, collec1624074086lle_tv: (produc931990033lle_tv > $o) > set_Pr560526279lle_tv).
% 3.14/1.64  thf(func_def_141, type, collec7649004at_nat: (product_prod_nat_nat > $o) > set_Pr1986765409at_nat).
% 3.14/1.64  thf(func_def_142, type, collec924990229lle_tv: (produc270694976lle_tv > $o) > set_Pr13445366lle_tv).
% 3.14/1.64  thf(func_def_143, type, collec848462447tv_nat: (produc194167194tv_nat > $o) > set_Pr1725653840tv_nat).
% 3.14/1.64  thf(func_def_144, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 3.14/1.64  thf(func_def_145, type, image_1151963140lle_tv: (nat > paraco1605129243lle_tv) > set_nat > set_Pa1764573435lle_tv).
% 3.14/1.64  thf(func_def_146, type, image_376325286tv_nat: (paraco1605129243lle_tv > nat) > set_Pa1764573435lle_tv > set_nat).
% 3.14/1.64  thf(func_def_147, type, image_335818702lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv).
% 3.14/1.64  thf(func_def_148, type, image_807538418lle_fm: (produc696645085lle_fm > produc696645085lle_fm) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm).
% 3.14/1.64  thf(func_def_149, type, image_1154804148lle_tv: (produc696645085lle_fm > produc931990033lle_tv) > set_Pr2120184979lle_fm > set_Pr560526279lle_tv).
% 3.14/1.64  thf(func_def_150, type, image_924970994lle_tv: (produc696645085lle_fm > produc1443694919lle_tv) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv).
% 3.14/1.64  thf(func_def_151, type, image_1585092542lle_fm: (produc931990033lle_tv > produc696645085lle_fm) > set_Pr560526279lle_tv > set_Pr2120184979lle_fm).
% 3.14/1.64  thf(func_def_152, type, image_1751508608lle_tv: (produc931990033lle_tv > produc931990033lle_tv) > set_Pr560526279lle_tv > set_Pr560526279lle_tv).
% 3.14/1.64  thf(func_def_153, type, image_1724396928at_nat: (produc931990033lle_tv > produc596913417at_nat) > set_Pr560526279lle_tv > set_Pr840833727at_nat).
% 3.14/1.64  thf(func_def_154, type, image_815163717at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1986765409at_nat > set_Pr1986765409at_nat).
% 3.14/1.64  thf(func_def_155, type, image_1674248956lle_tv: (product_prod_nat_nat > produc270694976lle_tv) > set_Pr1986765409at_nat > set_Pr13445366lle_tv).
% 3.14/1.64  thf(func_def_156, type, image_1597721174tv_nat: (product_prod_nat_nat > produc194167194tv_nat) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat).
% 3.14/1.64  thf(func_def_157, type, image_1507992062lle_tv: (product_prod_nat_nat > produc1647334210lle_tv) > set_Pr1986765409at_nat > set_Pr2014382200lle_tv).
% 3.14/1.64  thf(func_def_158, type, image_1787705850at_nat: (produc270694976lle_tv > product_prod_nat_nat) > set_Pr13445366lle_tv > set_Pr1986765409at_nat).
% 3.14/1.64  thf(func_def_159, type, image_149830562lle_tv: (produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > set_Pr13445366lle_tv).
% 3.14/1.64  thf(func_def_160, type, image_53754658tv_nat: (produc270694976lle_tv > produc194167194tv_nat) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat).
% 3.14/1.64  thf(func_def_161, type, image_988201162lle_tv: (produc270694976lle_tv > produc1647334210lle_tv) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv).
% 3.14/1.64  thf(func_def_162, type, image_326034184lle_fm: (produc1443694919lle_tv > produc696645085lle_fm) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm).
% 3.14/1.64  thf(func_def_163, type, image_769496456lle_tv: (produc596913417at_nat > produc931990033lle_tv) > set_Pr840833727at_nat > set_Pr560526279lle_tv).
% 3.14/1.64  thf(func_def_164, type, image_1805124128at_nat: (produc194167194tv_nat > product_prod_nat_nat) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat).
% 3.14/1.64  thf(func_def_165, type, image_1200372424lle_tv: (produc194167194tv_nat > produc270694976lle_tv) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv).
% 3.14/1.64  thf(func_def_166, type, image_1221801032lle_tv: (produc1647334210lle_tv > produc1647334210lle_tv) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv).
% 3.14/1.64  thf(func_def_167, type, accp_P2085826120lle_tv: (produc931990033lle_tv > produc931990033lle_tv > $o) > produc931990033lle_tv > $o).
% 3.14/1.64  thf(func_def_168, type, lex_pr2001015487lle_fm: set_Pr2061825550lle_tv > set_Pr1019238018lle_fm > set_Pr1475944804lle_fm).
% 3.14/1.64  thf(func_def_169, type, lex_pr1093414955lle_tv: set_Pr1357842111at_nat > set_Pr2014382200lle_tv > set_Pr698334450lle_tv).
% 3.14/1.64  thf(func_def_170, type, lex_prod_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1490359111at_nat).
% 3.14/1.64  thf(func_def_171, type, lex_pr413684186lle_tv: set_Pr1986765409at_nat > set_Pr2014382200lle_tv > set_Pr292927124lle_tv).
% 3.14/1.64  thf(func_def_172, type, lex_pr1785529980tv_nat: set_Pr2014382200lle_tv > set_Pr1986765409at_nat > set_Pr1943077434tv_nat).
% 3.14/1.64  thf(func_def_173, type, lex_pr567812260lle_tv: set_Pr2014382200lle_tv > set_Pr2014382200lle_tv > set_Pr2012908090lle_tv).
% 3.14/1.64  thf(func_def_174, type, wf_nat: set_Pr1986765409at_nat > $o).
% 3.14/1.64  thf(func_def_175, type, wf_Par1378404612lle_tv: set_Pr2014382200lle_tv > $o).
% 3.14/1.64  thf(func_def_176, type, same_f1581085506lle_fm: ((list_char > paraco1605129243lle_tv) > $o) > ((list_char > paraco1605129243lle_tv) > set_Pr1019238018lle_fm) > set_Pr1475944804lle_fm).
% 3.14/1.64  thf(func_def_177, type, same_f1138187694lle_tv: ((nat > nat) > $o) > ((nat > nat) > set_Pr2014382200lle_tv) > set_Pr698334450lle_tv).
% 3.14/1.64  thf(func_def_178, type, member_nat: nat > set_nat > $o).
% 3.14/1.64  thf(func_def_179, type, member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o).
% 3.14/1.64  thf(func_def_180, type, member146333935lle_tv: produc1852595672lle_tv > set_Pr2061825550lle_tv > $o).
% 3.14/1.64  thf(func_def_181, type, member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o).
% 3.14/1.64  thf(func_def_182, type, member112824072at_nat: produc1281043295at_nat > set_Pr1357842111at_nat > $o).
% 3.14/1.64  thf(func_def_183, type, member1569366824lle_tv: produc931990033lle_tv > set_Pr560526279lle_tv > $o).
% 3.14/1.64  thf(func_def_184, type, member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o).
% 3.14/1.64  thf(func_def_185, type, member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o).
% 3.14/1.64  thf(func_def_186, type, member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o).
% 3.14/1.64  thf(func_def_187, type, member334644067lle_fm: produc450659916lle_fm > set_Pr1019238018lle_fm > $o).
% 3.14/1.64  thf(func_def_188, type, member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o).
% 3.14/1.64  thf(func_def_189, type, member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o).
% 3.14/1.64  thf(func_def_190, type, member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o).
% 3.14/1.64  thf(func_def_191, type, member1592865093lle_fm: produc1250255278lle_fm > set_Pr1475944804lle_fm > $o).
% 3.14/1.64  thf(func_def_192, type, member1339857875lle_tv: produc1720769084lle_tv > set_Pr698334450lle_tv > $o).
% 3.14/1.64  thf(func_def_193, type, f: nat > nat).
% 3.14/1.64  thf(func_def_194, type, i: list_char > paraco1605129243lle_tv).
% 3.14/1.64  thf(func_def_195, type, p1: paraco1604210848lle_fm).
% 3.14/1.64  thf(func_def_196, type, p2: paraco1604210848lle_fm).
% 3.14/1.64  thf(func_def_208, type, sK0: (nat > nat) > nat).
% 3.14/1.64  thf(func_def_209, type, sK1: (nat > nat) > nat).
% 3.14/1.64  thf(func_def_210, type, sK2: (nat > nat) > nat).
% 3.14/1.64  thf(func_def_211, type, sK3: (nat > nat) > nat).
% 3.14/1.64  thf(func_def_212, type, sK4: paraco1605129243lle_tv > paraco1605129243lle_tv > $o).
% 3.14/1.64  thf(func_def_213, type, sK5: paraco1605129243lle_tv > (nat > nat) > paraco1605129243lle_tv > nat).
% 3.14/1.64  thf(func_def_215, type, ph7: !>[X0: $tType]:(X0)).
% 3.14/1.64  thf(f931,plain,(
% 3.14/1.64    $false),
% 3.14/1.64    inference(trivial_inequality_removal,[status(thm)],[f930])).
% 3.14/1.64  thf(f930,plain,(
% 3.14/1.64    ($false = $true)),
% 3.14/1.64    inference(equality_resolution,[status(thm)],[f927])).
% 3.14/1.64  thf(f927,plain,(
% 3.14/1.64    ( ! [X0 : $o] : (((paraco1344940915le_Det @ X0) != (paraco1344940915le_Det @ $false)) | ($true = X0)) )),
% 3.14/1.64    inference(superposition,[status(thm)],[f894,f924])).
% 3.14/1.64  thf(f924,plain,(
% 3.14/1.64    ((paraco1344940915le_Det @ $true) = (paraco1344940915le_Det @ $false))),
% 3.14/1.64    inference(forward_demodulation,[status(thm)],[f895,f892])).
% 3.14/1.64  thf(f892,plain,(
% 3.14/1.64    ((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) = (paraco1344940915le_Det @ $false))),
% 3.14/1.64    inference(cnf_transformation,[status(thm)],[f714])).
% 3.14/1.64  thf(f714,plain,(
% 3.14/1.64    ((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) = (paraco1344940915le_Det @ $false))),
% 3.14/1.64    inference(fool_elimination,[status(thm)],[f7])).
% 3.14/1.64  thf(f7,axiom,(
% 3.14/1.64    ((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) = (paraco1344940915le_Det @ $false))),
% 3.14/1.64    file('/export/starexec/sandbox2/tmp/tmp.b6Vcvump8L/DTF2THF_12469.p',fact_6_b)).
% 3.14/1.64  thf(f895,plain,(
% 3.14/1.64    ((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) = (paraco1344940915le_Det @ $true))),
% 3.14/1.64    inference(cnf_transformation,[status(thm)],[f851])).
% 3.14/1.64  thf(f851,plain,(
% 3.14/1.64    ((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) = (paraco1344940915le_Det @ $true))),
% 3.14/1.64    inference(flattening,[status(thm)],[f387])).
% 3.14/1.64  thf(f387,plain,(
% 3.14/1.64    ~((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) != (paraco1344940915le_Det @ $true))),
% 3.14/1.64    inference(fool_elimination,[status(thm)],[f359])).
% 3.14/1.64  thf(f359,negated_conjecture,(
% 3.14/1.64    ~((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) != (paraco1344940915le_Det @ $true))),
% 3.14/1.64    inference(negated_conjecture,[status(cth)],[f358])).
% 3.14/1.64  thf(f358,conjecture,(
% 3.14/1.64    ((paraco1325918602e_eval @ (paraco761681009ge_int @ f @ i) @ p2) != (paraco1344940915le_Det @ $true))),
% 3.14/1.64    file('/export/starexec/sandbox2/tmp/tmp.b6Vcvump8L/DTF2THF_12469.p',conj_0)).
% 3.14/1.64  thf(f894,plain,(
% 3.14/1.64    ( ! [X0 : $o,X1 : $o] : (((paraco1344940915le_Det @ X0) != (paraco1344940915le_Det @ X1)) | (X0 = X1)) )),
% 3.14/1.64    inference(cnf_transformation,[status(thm)],[f868])).
% 3.14/1.64  thf(f868,plain,(
% 3.14/1.64    ! [X0 : $o,X1 : $o] : (((X0 = X1) | ((paraco1344940915le_Det @ X0) != (paraco1344940915le_Det @ X1))) & (((paraco1344940915le_Det @ X0) = (paraco1344940915le_Det @ X1)) | (X0 != X1)))),
% 3.14/1.64    inference(nnf_transformation,[status(thm)],[f407])).
% 3.14/1.64  thf(f407,plain,(
% 3.14/1.64    ! [X0 : $o,X1 : $o] : ((X0 = X1) <=> ((paraco1344940915le_Det @ X0) = (paraco1344940915le_Det @ X1)))),
% 3.14/1.64    inference(fool_elimination,[status(thm)],[f9])).
% 3.14/1.64  thf(f9,axiom,(
% 3.14/1.64    ! [X0 : $o,X1 : $o] : (((paraco1344940915le_Det @ X0) = (paraco1344940915le_Det @ X1)) = (X0 = X1))),
% 3.14/1.64    file('/export/starexec/sandbox2/tmp/tmp.b6Vcvump8L/DTF2THF_12469.p',fact_8_tv_Oinject_I1_J)).
% 3.14/1.64  % SZS output end Proof for DTF2THF_12469
% 3.14/1.64  % (12576)------------------------------
% 3.14/1.64  % (12576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.14/1.64  % (12576)Termination reason: Refutation
% 3.14/1.64  
% 3.14/1.64  % (12576)Memory used [KB]: 6652
% 3.14/1.64  % (12576)Time elapsed: 0.026 s
% 3.14/1.64  % (12576)Instructions burned: 47 (million)
% 3.14/1.64  % (12576)------------------------------
% 3.14/1.64  % (12576)------------------------------
% 3.14/1.64  % (12570)Success in time 0.052 s
%------------------------------------------------------------------------------