DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP140^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300

% Computer : n009.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 08:55:52 AM UTC 2026

% Result   : Theorem 3.06s 1.75s
% Output   : Refutation 3.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   29 (  12 unt;   0 typ;   2 def)
%            Number of atoms       :  124 (  73 equ;   0 cnn)
%            Maximal formula atoms :   10 (   4 avg)
%            Number of connectives :  381 (  30   ~;  23   |;  12   &; 296   @)
%                                         (   2 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :   37 (  36 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  370 ( 367 usr;  26 con; 0-5 aty)
%            Number of variables   :   18 (   0   ^;  18   !;   0   ?;  18   :)

% 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_Pr2120184979lle_fm: $tType ).

thf(type_def_19,type,
    set_Pr560526279lle_tv: $tType ).

thf(type_def_20,type,
    set_Pr2061825550lle_tv: $tType ).

thf(type_def_21,type,
    set_Pr1357842111at_nat: $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,
    ord_le1007985907lle_fm: set_Pr2120184979lle_fm > set_Pr2120184979lle_fm > $o ).

thf(func_def_50,type,
    ord_le1784136743lle_tv: set_Pr560526279lle_tv > set_Pr560526279lle_tv > $o ).

thf(func_def_51,type,
    order_769474267at_nat: ( nat > nat ) > $o ).

thf(func_def_52,type,
    top_top_nat_o: nat > $o ).

thf(func_def_53,type,
    top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).

thf(func_def_54,type,
    top_to632227436_nat_o: product_prod_nat_nat > $o ).

thf(func_def_55,type,
    top_to1889334367e_tv_o: produc270694976lle_tv > $o ).

thf(func_def_56,type,
    top_to900819589_nat_o: produc194167194tv_nat > $o ).

thf(func_def_58,type,
    top_top_set_nat: set_nat ).

thf(func_def_59,type,
    top_to1057771083lle_tv: set_Pa1764573435lle_tv ).

thf(func_def_60,type,
    top_to138697918lle_tv: set_Pr2061825550lle_tv ).

thf(func_def_61,type,
    top_to775056195lle_fm: set_Pr2120184979lle_fm ).

thf(func_def_62,type,
    top_to1541413903at_nat: set_Pr1357842111at_nat ).

thf(func_def_63,type,
    top_to449985143lle_tv: set_Pr560526279lle_tv ).

thf(func_def_64,type,
    top_to1555900337at_nat: set_Pr1986765409at_nat ).

thf(func_def_65,type,
    top_to1411004326lle_tv: set_Pr13445366lle_tv ).

thf(func_def_66,type,
    top_to975729152tv_nat: set_Pr1725653840tv_nat ).

thf(func_def_67,type,
    top_to1871154984lle_tv: set_Pr2014382200lle_tv ).

thf(func_def_68,type,
    paraco761681009ge_int: ( nat > nat ) > ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ).

thf(func_def_69,type,
    paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).

thf(func_def_70,type,
    paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o ).

thf(func_def_71,type,
    paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).

thf(func_def_72,type,
    paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_73,type,
    paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_74,type,
    paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_75,type,
    paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_76,type,
    paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).

thf(func_def_77,type,
    paraco367965286_Truth: paraco1604210848lle_fm ).

thf(func_def_78,type,
    paraco1344940915le_Det: $o > paraco1605129243lle_tv ).

thf(func_def_79,type,
    paraco793048302_Indet: nat > paraco1605129243lle_tv ).

thf(func_def_80,type,
    paraco2051596139lle_tv: ( $o > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).

thf(func_def_81,type,
    paraco327635598_valid: paraco1604210848lle_fm > $o ).

thf(func_def_82,type,
    paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).

thf(func_def_83,type,
    produc1297923922lle_tv: ( list_char > paraco1605129243lle_tv ) > ( list_char > paraco1605129243lle_tv ) > produc1852595672lle_tv ).

thf(func_def_84,type,
    produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).

thf(func_def_85,type,
    produc780837143at_nat: ( nat > nat ) > ( nat > nat ) > produc1281043295at_nat ).

thf(func_def_86,type,
    produc1680557635lle_tv: ( nat > nat ) > paraco1605129243lle_tv > produc931990033lle_tv ).

thf(func_def_87,type,
    produc1943344577lle_tv: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc1443694919lle_tv ).

thf(func_def_88,type,
    produc1126104134lle_fm: paraco1604210848lle_fm > paraco1604210848lle_fm > produc450659916lle_fm ).

thf(func_def_89,type,
    produc1633679363at_nat: paraco1605129243lle_tv > ( nat > nat ) > produc596913417at_nat ).

thf(func_def_90,type,
    produc2058540732lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv ).

thf(func_def_91,type,
    produc407632608lle_fm: produc696645085lle_fm > produc696645085lle_fm > produc1250255278lle_fm ).

thf(func_def_92,type,
    produc2057188974lle_tv: produc931990033lle_tv > produc931990033lle_tv > produc1720769084lle_tv ).

thf(func_def_93,type,
    produc1942165868lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > produc696645085lle_fm > produc696645085lle_fm ).

thf(func_def_94,type,
    produc939316703lle_tv: ( ( nat > nat ) > nat > nat ) > produc931990033lle_tv > produc931990033lle_tv ).

thf(func_def_95,type,
    produc1807466521lle_tv: ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).

thf(func_def_96,type,
    produc109093078at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).

thf(func_def_97,type,
    produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv ).

thf(func_def_98,type,
    produc275353523e_fm_o: ( produc696645085lle_fm > $o ) > ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o ).

thf(func_def_99,type,
    produc752649287e_tv_o: ( produc931990033lle_tv > $o ) > ( nat > nat ) > paraco1605129243lle_tv > $o ).

thf(func_def_100,type,
    produc1900967599lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).

thf(func_def_101,type,
    produc1566550641lle_tv: ( ( list_char > paraco1605129243lle_tv ) > nat > nat ) > ( paraco1604210848lle_fm > paraco1605129243lle_tv ) > produc696645085lle_fm > produc931990033lle_tv ).

thf(func_def_102,type,
    produc951033137lle_fm: ( ( nat > nat ) > list_char > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1604210848lle_fm ) > produc931990033lle_tv > produc696645085lle_fm ).

thf(func_def_103,type,
    produc532909085lle_tv: ( ( nat > nat ) > nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).

thf(func_def_104,type,
    produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_105,type,
    produc313957681lle_tv: ( nat > nat ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc270694976lle_tv ).

thf(func_def_106,type,
    produc1685803475tv_nat: ( nat > nat ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > product_prod_nat_nat ).

thf(func_def_107,type,
    produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).

thf(func_def_108,type,
    produc1250721397at_nat: ( nat > paraco1605129243lle_tv ) > ( nat > nat ) > product_prod_nat_nat > produc194167194tv_nat ).

thf(func_def_109,type,
    produc210389789lle_tv: ( nat > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc1647334210lle_tv ).

thf(func_def_110,type,
    produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).

thf(func_def_111,type,
    produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).

thf(func_def_112,type,
    produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).

thf(func_def_113,type,
    produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).

thf(func_def_114,type,
    produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).

thf(func_def_115,type,
    produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).

thf(func_def_116,type,
    produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_117,type,
    produc1636169559lle_tv: produc931990033lle_tv > nat > nat ).

thf(func_def_118,type,
    produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm ).

thf(func_def_119,type,
    produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv ).

thf(func_def_120,type,
    produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm ).

thf(func_def_121,type,
    produc547496597lle_tv: produc931990033lle_tv > paraco1605129243lle_tv ).

thf(func_def_122,type,
    produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv ).

thf(func_def_123,type,
    produc500618325at_nat: produc596913417at_nat > nat > nat ).

thf(func_def_124,type,
    produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv ).

thf(func_def_125,type,
    produc225513635lle_tv: produc931990033lle_tv > produc596913417at_nat ).

thf(func_def_126,type,
    produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm ).

thf(func_def_127,type,
    produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv ).

thf(func_def_128,type,
    inv_image_nat_nat: set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).

thf(func_def_129,type,
    inv_im1292588663lle_tv: set_Pr1986765409at_nat > ( paraco1605129243lle_tv > nat ) > set_Pr2014382200lle_tv ).

thf(func_def_130,type,
    inv_im516950809tv_nat: set_Pr2014382200lle_tv > ( nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat ).

thf(func_def_131,type,
    inv_im719552961lle_tv: set_Pr2014382200lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pr2014382200lle_tv ).

thf(func_def_132,type,
    total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).

thf(func_def_133,type,
    total_1781621663lle_tv: set_Pa1764573435lle_tv > set_Pr2014382200lle_tv > $o ).

thf(func_def_134,type,
    total_1775715973at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).

thf(func_def_135,type,
    total_517371324lle_tv: set_Pr13445366lle_tv > set_Pr292927124lle_tv > $o ).

thf(func_def_136,type,
    total_440843542tv_nat: set_Pr1725653840tv_nat > set_Pr1943077434tv_nat > $o ).

thf(func_def_137,type,
    total_92239038lle_tv: set_Pr2014382200lle_tv > set_Pr2012908090lle_tv > $o ).

thf(func_def_138,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(func_def_139,type,
    collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).

thf(func_def_140,type,
    collec1102043437lle_tv: ( produc1852595672lle_tv > $o ) > set_Pr2061825550lle_tv ).

thf(func_def_141,type,
    collec835549234lle_fm: ( produc696645085lle_fm > $o ) > set_Pr2120184979lle_fm ).

thf(func_def_142,type,
    collec791369802at_nat: ( produc1281043295at_nat > $o ) > set_Pr1357842111at_nat ).

thf(func_def_143,type,
    collec1624074086lle_tv: ( produc931990033lle_tv > $o ) > set_Pr560526279lle_tv ).

thf(func_def_144,type,
    collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).

thf(func_def_145,type,
    collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).

thf(func_def_146,type,
    collec848462447tv_nat: ( produc194167194tv_nat > $o ) > set_Pr1725653840tv_nat ).

thf(func_def_147,type,
    image_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_148,type,
    image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).

thf(func_def_149,type,
    image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).

thf(func_def_150,type,
    image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).

thf(func_def_151,type,
    image_807538418lle_fm: ( produc696645085lle_fm > produc696645085lle_fm ) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm ).

thf(func_def_152,type,
    image_1154804148lle_tv: ( produc696645085lle_fm > produc931990033lle_tv ) > set_Pr2120184979lle_fm > set_Pr560526279lle_tv ).

thf(func_def_153,type,
    image_924970994lle_tv: ( produc696645085lle_fm > produc1443694919lle_tv ) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv ).

thf(func_def_154,type,
    image_1585092542lle_fm: ( produc931990033lle_tv > produc696645085lle_fm ) > set_Pr560526279lle_tv > set_Pr2120184979lle_fm ).

thf(func_def_155,type,
    image_1751508608lle_tv: ( produc931990033lle_tv > produc931990033lle_tv ) > set_Pr560526279lle_tv > set_Pr560526279lle_tv ).

thf(func_def_156,type,
    image_1724396928at_nat: ( produc931990033lle_tv > produc596913417at_nat ) > set_Pr560526279lle_tv > set_Pr840833727at_nat ).

thf(func_def_157,type,
    image_815163717at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).

thf(func_def_158,type,
    image_1674248956lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > set_Pr13445366lle_tv ).

thf(func_def_159,type,
    image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).

thf(func_def_160,type,
    image_1507992062lle_tv: ( product_prod_nat_nat > produc1647334210lle_tv ) > set_Pr1986765409at_nat > set_Pr2014382200lle_tv ).

thf(func_def_161,type,
    image_1787705850at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > set_Pr1986765409at_nat ).

thf(func_def_162,type,
    image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).

thf(func_def_163,type,
    image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).

thf(func_def_164,type,
    image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).

thf(func_def_165,type,
    image_326034184lle_fm: ( produc1443694919lle_tv > produc696645085lle_fm ) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm ).

thf(func_def_166,type,
    image_769496456lle_tv: ( produc596913417at_nat > produc931990033lle_tv ) > set_Pr840833727at_nat > set_Pr560526279lle_tv ).

thf(func_def_167,type,
    image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).

thf(func_def_168,type,
    image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).

thf(func_def_169,type,
    image_1221801032lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv ).

thf(func_def_170,type,
    accp_P2085826120lle_tv: ( produc931990033lle_tv > produc931990033lle_tv > $o ) > produc931990033lle_tv > $o ).

thf(func_def_171,type,
    lex_pr2001015487lle_fm: set_Pr2061825550lle_tv > set_Pr1019238018lle_fm > set_Pr1475944804lle_fm ).

thf(func_def_172,type,
    lex_pr1093414955lle_tv: set_Pr1357842111at_nat > set_Pr2014382200lle_tv > set_Pr698334450lle_tv ).

thf(func_def_173,type,
    lex_prod_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1490359111at_nat ).

thf(func_def_174,type,
    lex_pr413684186lle_tv: set_Pr1986765409at_nat > set_Pr2014382200lle_tv > set_Pr292927124lle_tv ).

thf(func_def_175,type,
    lex_pr1785529980tv_nat: set_Pr2014382200lle_tv > set_Pr1986765409at_nat > set_Pr1943077434tv_nat ).

thf(func_def_176,type,
    lex_pr567812260lle_tv: set_Pr2014382200lle_tv > set_Pr2014382200lle_tv > set_Pr2012908090lle_tv ).

thf(func_def_177,type,
    wf_nat: set_Pr1986765409at_nat > $o ).

thf(func_def_178,type,
    wf_Par1378404612lle_tv: set_Pr2014382200lle_tv > $o ).

thf(func_def_179,type,
    same_f1581085506lle_fm: ( ( list_char > paraco1605129243lle_tv ) > $o ) > ( ( list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm ) > set_Pr1475944804lle_fm ).

thf(func_def_180,type,
    same_f1138187694lle_tv: ( ( nat > nat ) > $o ) > ( ( nat > nat ) > set_Pr2014382200lle_tv ) > set_Pr698334450lle_tv ).

thf(func_def_181,type,
    member_nat: nat > set_nat > $o ).

thf(func_def_182,type,
    member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).

thf(func_def_183,type,
    member146333935lle_tv: produc1852595672lle_tv > set_Pr2061825550lle_tv > $o ).

thf(func_def_184,type,
    member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o ).

thf(func_def_185,type,
    member112824072at_nat: produc1281043295at_nat > set_Pr1357842111at_nat > $o ).

thf(func_def_186,type,
    member1569366824lle_tv: produc931990033lle_tv > set_Pr560526279lle_tv > $o ).

thf(func_def_187,type,
    member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).

thf(func_def_188,type,
    member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).

thf(func_def_189,type,
    member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o ).

thf(func_def_190,type,
    member334644067lle_fm: produc450659916lle_fm > set_Pr1019238018lle_fm > $o ).

thf(func_def_191,type,
    member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o ).

thf(func_def_192,type,
    member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).

thf(func_def_193,type,
    member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).

thf(func_def_194,type,
    member1592865093lle_fm: produc1250255278lle_fm > set_Pr1475944804lle_fm > $o ).

thf(func_def_195,type,
    member1339857875lle_tv: produc1720769084lle_tv > set_Pr698334450lle_tv > $o ).

thf(func_def_196,type,
    f: nat > nat ).

thf(func_def_197,type,
    i: list_char > paraco1605129243lle_tv ).

thf(func_def_198,type,
    p1: paraco1604210848lle_fm ).

thf(func_def_199,type,
    p2: paraco1604210848lle_fm ).

thf(func_def_211,type,
    sP0: ( paraco1604210848lle_fm > $o ) > $o ).

thf(func_def_212,type,
    sP1: ( paraco1604210848lle_fm > $o ) > $o ).

thf(func_def_213,type,
    sP2: ( paraco1604210848lle_fm > $o ) > $o ).

thf(func_def_214,type,
    sP3: ( paraco1604210848lle_fm > $o ) > $o ).

thf(func_def_215,type,
    sP4: paraco1605129243lle_tv > paraco1605129243lle_tv > ( nat > nat ) > $o ).

thf(func_def_216,type,
    sK5: set_Pr1986765409at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat ).

thf(func_def_217,type,
    sK6: paraco1605129243lle_tv > ( nat > paraco1605129243lle_tv ) > nat ).

thf(func_def_218,type,
    sK7: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_219,type,
    sK8: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_220,type,
    sK9: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_221,type,
    sK10: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_222,type,
    sK11: paraco1604210848lle_fm > list_char ).

thf(func_def_223,type,
    sK12: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_224,type,
    sK13: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_225,type,
    sK14: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_226,type,
    sK15: ( produc194167194tv_nat > produc194167194tv_nat ) > produc194167194tv_nat ).

thf(func_def_227,type,
    sK16: ( produc194167194tv_nat > produc194167194tv_nat ) > produc194167194tv_nat ).

thf(func_def_228,type,
    sK17: nat > ( nat > nat ) > nat ).

thf(func_def_229,type,
    sK18: ( nat > nat ) > nat ).

thf(func_def_230,type,
    sK19: ( paraco1605129243lle_tv > paraco1604210848lle_fm ) > produc696645085lle_fm > set_Pr560526279lle_tv > ( ( nat > nat ) > list_char > paraco1605129243lle_tv ) > nat > nat ).

thf(func_def_231,type,
    sK20: ( paraco1605129243lle_tv > paraco1604210848lle_fm ) > produc696645085lle_fm > set_Pr560526279lle_tv > ( ( nat > nat ) > list_char > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_232,type,
    sK21: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_233,type,
    sK22: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_234,type,
    sK23: set_Pr1986765409at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat ).

thf(func_def_235,type,
    sK24: set_Pr1986765409at_nat > ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat ).

thf(func_def_236,type,
    sK25: paraco1605129243lle_tv ).

thf(func_def_237,type,
    sK26: nat > ( nat > nat ) > nat ).

thf(func_def_238,type,
    sK27: produc931990033lle_tv > nat > nat ).

thf(func_def_239,type,
    sK28: produc931990033lle_tv > nat ).

thf(func_def_240,type,
    sK29: produc931990033lle_tv > nat > nat ).

thf(func_def_241,type,
    sK30: produc931990033lle_tv > $o ).

thf(func_def_242,type,
    sK31: set_Pr2014382200lle_tv > ( produc1647334210lle_tv > produc1647334210lle_tv ) > ( produc1647334210lle_tv > produc1647334210lle_tv ) > produc1647334210lle_tv ).

thf(func_def_243,type,
    sK32: ( produc931990033lle_tv > $o ) > nat > nat ).

thf(func_def_244,type,
    sK33: ( produc931990033lle_tv > $o ) > paraco1605129243lle_tv ).

thf(func_def_245,type,
    sK34: produc194167194tv_nat ).

thf(func_def_246,type,
    sK35: produc1281043295at_nat ).

thf(func_def_247,type,
    sK36: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_248,type,
    sK37: produc696645085lle_fm > paraco1604210848lle_fm ).

thf(func_def_249,type,
    sK38: ( nat > nat ) > ( nat > nat ) > set_nat > nat ).

thf(func_def_250,type,
    sK39: produc931990033lle_tv > ( ( list_char > paraco1605129243lle_tv ) > nat > nat ) > ( paraco1604210848lle_fm > paraco1605129243lle_tv ) > set_Pr2120184979lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_251,type,
    sK40: produc931990033lle_tv > ( ( list_char > paraco1605129243lle_tv ) > nat > nat ) > ( paraco1604210848lle_fm > paraco1605129243lle_tv ) > set_Pr2120184979lle_fm > paraco1604210848lle_fm ).

thf(func_def_252,type,
    sK41: nat > ( nat > nat ) > nat ).

thf(func_def_253,type,
    sK42: nat > nat > ( nat > nat ) > nat ).

thf(func_def_254,type,
    sK43: ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > nat ).

thf(func_def_255,type,
    sK44: produc696645085lle_fm ).

thf(func_def_256,type,
    sK45: produc931990033lle_tv > nat > nat ).

thf(func_def_257,type,
    sK46: produc931990033lle_tv > paraco1605129243lle_tv ).

thf(func_def_258,type,
    sK47: product_prod_nat_nat ).

thf(func_def_259,type,
    sK48: ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat ).

thf(func_def_260,type,
    sK49: ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat ).

thf(func_def_261,type,
    sK50: set_Pr560526279lle_tv > set_Pr560526279lle_tv > paraco1605129243lle_tv ).

thf(func_def_262,type,
    sK51: set_Pr560526279lle_tv > set_Pr560526279lle_tv > nat > nat ).

thf(func_def_263,type,
    sK52: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_264,type,
    sK53: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_265,type,
    sK54: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_266,type,
    sK55: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_267,type,
    sK56: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_268,type,
    sK57: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_269,type,
    sK58: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_270,type,
    sK59: ( paraco1604210848lle_fm > $o ) > list_char ).

thf(func_def_271,type,
    sK60: set_nat > ( nat > paraco1605129243lle_tv ) > nat ).

thf(func_def_272,type,
    sK61: set_nat > ( nat > paraco1605129243lle_tv ) > nat ).

thf(func_def_273,type,
    sK62: set_Pr1725653840tv_nat > ( produc194167194tv_nat > produc194167194tv_nat ) > produc194167194tv_nat ).

thf(func_def_274,type,
    sK63: set_Pr1725653840tv_nat > ( produc194167194tv_nat > produc194167194tv_nat ) > produc194167194tv_nat ).

thf(func_def_275,type,
    sK64: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > ( produc270694976lle_tv > produc270694976lle_tv ) > produc270694976lle_tv ).

thf(func_def_276,type,
    sK65: ( produc696645085lle_fm > $o ) > list_char > paraco1605129243lle_tv ).

thf(func_def_277,type,
    sK66: ( produc696645085lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_278,type,
    sK67: produc696645085lle_fm > ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > set_Pr2120184979lle_fm > ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > list_char > paraco1605129243lle_tv ).

thf(func_def_279,type,
    sK68: produc696645085lle_fm > ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > set_Pr2120184979lle_fm > ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > paraco1604210848lle_fm ).

thf(func_def_280,type,
    sK69: ( paraco1605129243lle_tv > nat ) > nat > paraco1605129243lle_tv ).

thf(func_def_281,type,
    sK70: ( produc194167194tv_nat > produc194167194tv_nat ) > produc194167194tv_nat ).

thf(func_def_282,type,
    sK71: ( produc194167194tv_nat > produc194167194tv_nat ) > produc194167194tv_nat ).

thf(func_def_283,type,
    sK72: produc696645085lle_fm > paraco1604210848lle_fm ).

thf(func_def_284,type,
    sK73: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_285,type,
    sK74: set_Pr1986765409at_nat > product_prod_nat_nat ).

thf(func_def_286,type,
    sK75: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_287,type,
    sK76: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_288,type,
    sK77: ( nat > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > set_nat > nat ).

thf(func_def_289,type,
    sK78: ( nat > nat ) > ( nat > nat ) > nat ).

thf(func_def_290,type,
    sK79: produc1852595672lle_tv ).

thf(func_def_291,type,
    sK80: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_292,type,
    sK81: ( nat > $o ) > ( nat > $o ) > nat ).

thf(func_def_293,type,
    sK82: ( nat > nat ) > set_nat > ( nat > nat ) > nat ).

thf(func_def_294,type,
    sK83: ( produc931990033lle_tv > $o ) > nat > nat ).

thf(func_def_295,type,
    sK84: ( produc931990033lle_tv > $o ) > paraco1605129243lle_tv ).

thf(func_def_296,type,
    sK85: produc931990033lle_tv > nat > nat ).

thf(func_def_297,type,
    sK86: produc931990033lle_tv > paraco1605129243lle_tv ).

thf(func_def_298,type,
    sK87: ( paraco1605129243lle_tv > $o ) > $o ).

thf(func_def_299,type,
    sK88: ( paraco1605129243lle_tv > $o ) > nat ).

thf(func_def_300,type,
    sK89: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > nat ).

thf(func_def_301,type,
    sK90: ( produc696645085lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_302,type,
    sK91: ( produc696645085lle_fm > $o ) > list_char > paraco1605129243lle_tv ).

thf(func_def_303,type,
    sK92: ( produc1647334210lle_tv > produc1647334210lle_tv ) > produc1647334210lle_tv ).

thf(func_def_304,type,
    sK93: ( produc1647334210lle_tv > produc1647334210lle_tv ) > produc1647334210lle_tv ).

thf(func_def_305,type,
    sK94: set_Pr2014382200lle_tv > ( produc1647334210lle_tv > produc1647334210lle_tv ) > produc1647334210lle_tv ).

thf(func_def_306,type,
    sK95: set_Pr2014382200lle_tv > ( produc1647334210lle_tv > produc1647334210lle_tv ) > produc1647334210lle_tv ).

thf(func_def_307,type,
    sK96: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > produc270694976lle_tv ).

thf(func_def_308,type,
    sK97: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > produc270694976lle_tv ).

thf(func_def_309,type,
    sK98: set_nat > nat ).

thf(func_def_310,type,
    sK99: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_311,type,
    sK100: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_312,type,
    sK101: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_313,type,
    sK102: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_314,type,
    sK103: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_315,type,
    sK104: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_316,type,
    sK105: ( paraco1604210848lle_fm > $o ) > paraco1604210848lle_fm ).

thf(func_def_317,type,
    sK106: ( paraco1604210848lle_fm > $o ) > list_char ).

thf(func_def_318,type,
    sK107: set_Pr2120184979lle_fm > produc696645085lle_fm ).

thf(func_def_319,type,
    sK108: set_Pr13445366lle_tv > produc270694976lle_tv ).

thf(func_def_320,type,
    sK109: paraco1604210848lle_fm > list_char ).

thf(func_def_321,type,
    sK110: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_322,type,
    sK111: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_323,type,
    sK112: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_324,type,
    sK113: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_325,type,
    sK114: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_326,type,
    sK115: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_327,type,
    sK116: paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(func_def_328,type,
    sK117: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).

thf(func_def_329,type,
    sK118: paraco1605129243lle_tv > nat ).

thf(func_def_330,type,
    sK119: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > ( produc194167194tv_nat > produc194167194tv_nat ) > produc194167194tv_nat ).

thf(func_def_331,type,
    sK120: ( paraco1605129243lle_tv > $o ) > nat ).

thf(func_def_332,type,
    sK121: paraco1605129243lle_tv > ( nat > paraco1605129243lle_tv ) > nat ).

thf(func_def_333,type,
    sK122: ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_334,type,
    sK123: paraco1604210848lle_fm > produc696645085lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_335,type,
    sK124: set_Pr560526279lle_tv > produc931990033lle_tv ).

thf(func_def_336,type,
    sK125: ( nat > nat ) > ( nat > nat ) > nat ).

thf(func_def_337,type,
    sK126: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_338,type,
    sK127: ( paraco1605129243lle_tv > nat ) > nat > paraco1605129243lle_tv ).

thf(func_def_339,type,
    sK128: set_Pr1725653840tv_nat > produc194167194tv_nat ).

thf(func_def_340,type,
    sK129: produc270694976lle_tv ).

thf(func_def_341,type,
    sK130: ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat ).

thf(func_def_342,type,
    sK131: ( product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat ).

thf(func_def_343,type,
    sK132: ( ( nat > nat ) > nat > nat ) > produc931990033lle_tv > set_Pr560526279lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_344,type,
    sK133: ( ( nat > nat ) > nat > nat ) > produc931990033lle_tv > set_Pr560526279lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > nat > nat ).

thf(func_def_345,type,
    sK134: ( nat > paraco1605129243lle_tv ) > nat ).

thf(func_def_346,type,
    sK135: ( nat > paraco1605129243lle_tv ) > nat ).

thf(func_def_347,type,
    sK136: ( nat > paraco1605129243lle_tv ) > nat ).

thf(func_def_348,type,
    sK137: ( nat > paraco1605129243lle_tv ) > nat ).

thf(func_def_349,type,
    sK138: paraco1605129243lle_tv > paraco1605129243lle_tv > $o ).

thf(func_def_350,type,
    sK139: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv > nat ).

thf(func_def_351,type,
    sK140: ( nat > nat ) > nat ).

thf(func_def_352,type,
    sK141: ( nat > nat ) > nat ).

thf(func_def_353,type,
    sK142: set_Pr2120184979lle_fm > set_Pr2120184979lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_354,type,
    sK143: set_Pr2120184979lle_fm > set_Pr2120184979lle_fm > paraco1604210848lle_fm ).

thf(func_def_355,type,
    sK144: set_Pr1357842111at_nat > produc1281043295at_nat ).

thf(func_def_356,type,
    sK145: produc931990033lle_tv ).

thf(func_def_357,type,
    sK146: paraco1605129243lle_tv > nat ).

thf(func_def_358,type,
    sK147: paraco1605129243lle_tv > $o ).

thf(func_def_359,type,
    sK148: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_360,type,
    sK149: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_361,type,
    sK150: paraco1605129243lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_362,type,
    sK151: ( nat > nat ) > nat ).

thf(func_def_363,type,
    sK152: ( nat > nat ) > nat ).

thf(func_def_364,type,
    sK153: set_Pr2061825550lle_tv > produc1852595672lle_tv ).

thf(func_def_365,type,
    sK154: ( produc1647334210lle_tv > produc1647334210lle_tv ) > produc1647334210lle_tv ).

thf(func_def_366,type,
    sK155: ( produc1647334210lle_tv > produc1647334210lle_tv ) > produc1647334210lle_tv ).

thf(func_def_367,type,
    sK156: ( paraco1605129243lle_tv > $o ) > ( paraco1605129243lle_tv > $o ) > paraco1605129243lle_tv ).

thf(func_def_368,type,
    sK157: paraco1605129243lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_369,type,
    sK158: paraco1605129243lle_tv > paraco1605129243lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_370,type,
    sK159: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).

thf(func_def_371,type,
    sK160: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > paraco1605129243lle_tv ).

thf(func_def_372,type,
    sK161: paraco1605129243lle_tv > produc931990033lle_tv > nat > nat ).

thf(func_def_373,type,
    sK162: nat ).

thf(func_def_374,type,
    sK163: set_nat > ( nat > nat ) > ( nat > nat ) > nat ).

thf(func_def_375,type,
    sK164: set_nat > ( nat > nat ) > ( nat > nat ) > nat ).

thf(func_def_376,type,
    sK165: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_377,type,
    sK166: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv ).

thf(func_def_378,type,
    sK167: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_379,type,
    sK168: produc696645085lle_fm > paraco1604210848lle_fm ).

thf(func_def_380,type,
    sK169: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_381,type,
    sK170: produc696645085lle_fm > paraco1604210848lle_fm ).

thf(func_def_382,type,
    sK171: produc696645085lle_fm > paraco1604210848lle_fm ).

thf(func_def_383,type,
    sK172: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_384,type,
    sK173: produc696645085lle_fm > list_char ).

thf(func_def_385,type,
    sK174: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_386,type,
    sK175: produc696645085lle_fm > paraco1604210848lle_fm ).

thf(func_def_387,type,
    sK176: produc696645085lle_fm > paraco1604210848lle_fm ).

thf(func_def_388,type,
    sK177: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_389,type,
    sK178: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).

thf(func_def_390,type,
    sK179: produc696645085lle_fm > paraco1604210848lle_fm ).

thf(func_def_391,type,
    sK180: produc696645085lle_fm > paraco1604210848lle_fm ).

thf(func_def_392,type,
    sK181: set_Pa1764573435lle_tv > paraco1605129243lle_tv ).

thf(func_def_393,type,
    sK182: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > paraco1605129243lle_tv ).

thf(func_def_394,type,
    sK183: ( produc270694976lle_tv > produc270694976lle_tv ) > produc270694976lle_tv ).

thf(func_def_395,type,
    sK184: ( produc270694976lle_tv > produc270694976lle_tv ) > produc270694976lle_tv ).

thf(func_def_396,type,
    sK185: ( paraco1605129243lle_tv > nat ) > nat ).

thf(func_def_397,type,
    sK186: nat > ( paraco1605129243lle_tv > nat ) > paraco1605129243lle_tv ).

thf(func_def_398,type,
    sK187: ( produc270694976lle_tv > produc270694976lle_tv ) > produc270694976lle_tv ).

thf(func_def_399,type,
    sK188: ( produc270694976lle_tv > produc270694976lle_tv ) > produc270694976lle_tv ).

thf(func_def_400,type,
    sK189: ( nat > nat ) > set_nat > nat ).

thf(func_def_401,type,
    sK190: ( nat > nat ) > set_nat > nat ).

thf(func_def_402,type,
    sK191: paraco1605129243lle_tv > paraco1605129243lle_tv > ( nat > nat ) > $o ).

thf(func_def_403,type,
    sK192: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv > nat ).

thf(func_def_404,type,
    sK193: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).

thf(func_def_405,type,
    sK194: produc931990033lle_tv > ( nat > nat ) > paraco1605129243lle_tv ).

thf(func_def_406,type,
    sK195: ( list_char > paraco1605129243lle_tv ) > produc696645085lle_fm > paraco1604210848lle_fm ).

thf(func_def_407,type,
    sK196: ( ( nat > nat ) > paraco1605129243lle_tv > $o ) > nat ).

thf(func_def_408,type,
    sK197: ( ( nat > nat ) > paraco1605129243lle_tv > $o ) > nat > nat ).

thf(func_def_409,type,
    sK198: ( ( nat > nat ) > paraco1605129243lle_tv > $o ) > $o ).

thf(func_def_410,type,
    sK199: ( ( nat > nat ) > paraco1605129243lle_tv > $o ) > nat > nat ).

thf(func_def_411,type,
    sK200: ( nat > nat ) > nat > nat ).

thf(func_def_413,type,
    ph202: 
      !>[X0: $tType] : X0 ).

thf(f2281,plain,
    $false,
    inference(avatar_sat_refutation,[status(thm)],[f2274,f2277,f2280]) ).

thf(f2280,plain,
    spl201_2,
    inference(avatar_contradiction_clause,[status(thm)],[f2279]) ).

thf(f2279,plain,
    ( $false
    | spl201_2 ),
    inference(trivial_inequality_removal,[status(thm)],[f2278]) ).

thf(f2278,plain,
    ( ( ( paraco1344940915le_Det @ $true )
     != ( paraco1344940915le_Det @ $true ) )
    | spl201_2 ),
    inference(superposition,[status(thm)],[f2266,f1835]) ).

thf(f1835,plain,
    ( ( paraco1325918602e_eval @ i @ p2 )
    = ( paraco1344940915le_Det @ $true ) ),
    inference(cnf_transformation,[status(thm)],[f632]) ).

thf(f632,plain,
    ( ( paraco1325918602e_eval @ i @ p2 )
    = ( paraco1344940915le_Det @ $true ) ),
    inference(fool_elimination,[status(thm)],[f2]) ).

thf(f2,axiom,
    ( ( paraco1325918602e_eval @ i @ p2 )
    = ( paraco1344940915le_Det @ $true ) ),
    file('/export/starexec/sandbox/tmp/tmp.J4RbD3yP62/DTF2THF_1342.p',fact_1_a) ).

thf(f2266,plain,
    ( ( ( paraco1325918602e_eval @ i @ p2 )
     != ( paraco1344940915le_Det @ $true ) )
    | spl201_2 ),
    inference(avatar_component_clause,[status(thm)],[f2265]) ).

thf(f2265,definition,
    ( spl201_2
  <=> ( ( paraco1325918602e_eval @ i @ p2 )
      = ( paraco1344940915le_Det @ $true ) ) ),
    introduced(definition,[new_symbols(naming,[spl201_2])],[avatar_definition]) ).

thf(f2277,plain,
    ( ~ spl201_2
    | spl201_1 ),
    inference(avatar_split_clause,[status(thm)],[f2276,f2261,f2265]) ).

thf(f2261,definition,
    ( spl201_1
  <=> ( ( paraco1325918602e_eval @ i @ p1 )
      = ( paraco1344940915le_Det @ $true ) ) ),
    introduced(definition,[new_symbols(naming,[spl201_1])],[avatar_definition]) ).

thf(f2276,plain,
    ( ( ( paraco1325918602e_eval @ i @ p2 )
     != ( paraco1344940915le_Det @ $true ) )
    | ( ( paraco1325918602e_eval @ i @ p1 )
      = ( paraco1344940915le_Det @ $true ) ) ),
    inference(duplicate_literal_removal,[status(thm)],[f2275]) ).

thf(f2275,plain,
    ( ( ( paraco1325918602e_eval @ i @ p2 )
     != ( paraco1344940915le_Det @ $true ) )
    | ( ( paraco1325918602e_eval @ i @ p1 )
      = ( paraco1344940915le_Det @ $true ) )
    | ( ( paraco1325918602e_eval @ i @ p1 )
      = ( paraco1344940915le_Det @ $true ) ) ),
    inference(forward_demodulation,[status(thm)],[f2256,f1835]) ).

thf(f2256,plain,
    ( ( ( paraco1325918602e_eval @ i @ p1 )
      = ( paraco1325918602e_eval @ i @ p2 ) )
    | ( ( paraco1325918602e_eval @ i @ p2 )
     != ( paraco1344940915le_Det @ $true ) )
    | ( ( paraco1325918602e_eval @ i @ p1 )
      = ( paraco1344940915le_Det @ $true ) ) ),
    inference(trivial_inequality_removal,[status(thm)],[f2253]) ).

thf(f2253,plain,
    ( ( ( paraco1325918602e_eval @ i @ p2 )
     != ( paraco1344940915le_Det @ $true ) )
    | ( ( paraco1325918602e_eval @ i @ p1 )
      = ( paraco1344940915le_Det @ $true ) )
    | ( ( paraco1325918602e_eval @ i @ p1 )
      = ( paraco1325918602e_eval @ i @ p2 ) )
    | ( ( paraco1325918602e_eval @ i @ p1 )
     != ( paraco1325918602e_eval @ i @ p1 ) ) ),
    inference(superposition,[status(thm)],[f1967,f1860]) ).

thf(f1860,plain,
    ! [X2: paraco1604210848lle_fm,X0: paraco1604210848lle_fm,X1: list_char > paraco1605129243lle_tv] :
      ( ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) )
        = ( paraco1325918602e_eval @ X1 @ X0 ) )
      | ( ( paraco1325918602e_eval @ X1 @ X2 )
       != ( paraco1344940915le_Det @ $true ) )
      | ( ( paraco1344940915le_Det @ $true )
        = ( paraco1325918602e_eval @ X1 @ X0 ) )
      | ( ( paraco1325918602e_eval @ X1 @ X2 )
        = ( paraco1325918602e_eval @ X1 @ X0 ) ) ),
    inference(cnf_transformation,[status(thm)],[f1151]) ).

thf(f1151,plain,
    ! [X0: paraco1604210848lle_fm,X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm] :
      ( ( ( ( ( ( paraco1325918602e_eval @ X1 @ X2 )
              = ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) ) )
            | ( ( paraco1344940915le_Det @ $true )
             != ( paraco1325918602e_eval @ X1 @ X0 ) ) )
          & ( ( ( paraco1344940915le_Det @ $true )
              = ( paraco1325918602e_eval @ X1 @ X0 ) )
            | ( ( ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) )
                  = ( paraco1325918602e_eval @ X1 @ X0 ) )
                | ( ( paraco1325918602e_eval @ X1 @ X2 )
                 != ( paraco1344940915le_Det @ $true ) ) )
              & ( ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) )
                  = ( paraco1344940915le_Det @ $false ) )
                | ( ( paraco1325918602e_eval @ X1 @ X2 )
                  = ( paraco1344940915le_Det @ $true ) ) ) ) ) )
        | ( ( paraco1325918602e_eval @ X1 @ X2 )
          = ( paraco1325918602e_eval @ X1 @ X0 ) ) )
      & ( ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) )
          = ( paraco1325918602e_eval @ X1 @ X0 ) )
        | ( ( paraco1325918602e_eval @ X1 @ X2 )
         != ( paraco1325918602e_eval @ X1 @ X0 ) ) ) ),
    inference(ennf_transformation,[status(thm)],[f462]) ).

thf(f462,plain,
    ! [X0: paraco1604210848lle_fm,X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm] :
      ( ( ( ( paraco1325918602e_eval @ X1 @ X2 )
         != ( paraco1325918602e_eval @ X1 @ X0 ) )
       => ( ( ( ( paraco1344940915le_Det @ $true )
              = ( paraco1325918602e_eval @ X1 @ X0 ) )
           => ( ( paraco1325918602e_eval @ X1 @ X2 )
              = ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) ) ) )
          & ( ( ( paraco1344940915le_Det @ $true )
             != ( paraco1325918602e_eval @ X1 @ X0 ) )
           => ( ( ( ( paraco1325918602e_eval @ X1 @ X2 )
                  = ( paraco1344940915le_Det @ $true ) )
               => ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) )
                  = ( paraco1325918602e_eval @ X1 @ X0 ) ) )
              & ( ( ( paraco1325918602e_eval @ X1 @ X2 )
                 != ( paraco1344940915le_Det @ $true ) )
               => ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) )
                  = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) )
      & ( ( ( paraco1325918602e_eval @ X1 @ X2 )
          = ( paraco1325918602e_eval @ X1 @ X0 ) )
       => ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) )
          = ( paraco1325918602e_eval @ X1 @ X0 ) ) ) ),
    inference(fool_elimination,[status(thm)],[f461]) ).

thf(f461,plain,
    ! [X0: paraco1604210848lle_fm,X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm] :
      ( ( ( ( paraco1325918602e_eval @ X1 @ X2 )
          = ( paraco1325918602e_eval @ X1 @ X0 ) )
       => ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) )
          = ( paraco1325918602e_eval @ X1 @ X0 ) ) )
      & ( ( ( paraco1325918602e_eval @ X1 @ X2 )
         != ( paraco1325918602e_eval @ X1 @ X0 ) )
       => ( ( ( ( paraco1325918602e_eval @ X1 @ X0 )
              = ( paraco1344940915le_Det @ $true ) )
           => ( ( paraco1325918602e_eval @ X1 @ X2 )
              = ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) ) ) )
          & ( ( ( paraco1325918602e_eval @ X1 @ X0 )
             != ( paraco1344940915le_Det @ $true ) )
           => ( ( ( ( paraco1344940915le_Det @ $true )
                 != ( paraco1325918602e_eval @ X1 @ X2 ) )
               => ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) )
                  = ( paraco1344940915le_Det @ $false ) ) )
              & ( ( ( paraco1344940915le_Det @ $true )
                  = ( paraco1325918602e_eval @ X1 @ X2 ) )
               => ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) )
                  = ( paraco1325918602e_eval @ X1 @ X0 ) ) ) ) ) ) ) ),
    inference(rectify,[status(thm)],[f6]) ).

thf(f6,axiom,
    ! [X5: paraco1604210848lle_fm,X4: list_char > paraco1605129243lle_tv,X6: paraco1604210848lle_fm] :
      ( ( ( ( paraco1325918602e_eval @ X4 @ X5 )
          = ( paraco1325918602e_eval @ X4 @ X6 ) )
       => ( ( paraco1325918602e_eval @ X4 @ X5 )
          = ( paraco1325918602e_eval @ X4 @ ( paraco69239110le_Con @ X5 @ X6 ) ) ) )
      & ( ( ( paraco1325918602e_eval @ X4 @ X5 )
         != ( paraco1325918602e_eval @ X4 @ X6 ) )
       => ( ( ( ( paraco1325918602e_eval @ X4 @ X5 )
              = ( paraco1344940915le_Det @ $true ) )
           => ( ( paraco1325918602e_eval @ X4 @ X6 )
              = ( paraco1325918602e_eval @ X4 @ ( paraco69239110le_Con @ X5 @ X6 ) ) ) )
          & ( ( ( paraco1325918602e_eval @ X4 @ X5 )
             != ( paraco1344940915le_Det @ $true ) )
           => ( ( ( ( paraco1344940915le_Det @ $true )
                 != ( paraco1325918602e_eval @ X4 @ X6 ) )
               => ( ( paraco1325918602e_eval @ X4 @ ( paraco69239110le_Con @ X5 @ X6 ) )
                  = ( paraco1344940915le_Det @ $false ) ) )
              & ( ( ( paraco1344940915le_Det @ $true )
                  = ( paraco1325918602e_eval @ X4 @ X6 ) )
               => ( ( paraco1325918602e_eval @ X4 @ X5 )
                  = ( paraco1325918602e_eval @ X4 @ ( paraco69239110le_Con @ X5 @ X6 ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.J4RbD3yP62/DTF2THF_1342.p',fact_5_eval_Osimps_I4_J) ).

thf(f1967,plain,
    ( ( paraco1325918602e_eval @ i @ p1 )
   != ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) ) ),
    inference(cnf_transformation,[status(thm)],[f961]) ).

thf(f961,plain,
    ( ( paraco1325918602e_eval @ i @ p1 )
   != ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) ) ),
    inference(flattening,[status(thm)],[f359]) ).

thf(f359,negated_conjecture,
    ( ( paraco1325918602e_eval @ i @ p1 )
   != ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) ) ),
    inference(negated_conjecture,[status(cth)],[f358]) ).

thf(f358,conjecture,
    ( ( paraco1325918602e_eval @ i @ p1 )
    = ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.J4RbD3yP62/DTF2THF_1342.p',conj_0) ).

thf(f2274,plain,
    ~ spl201_1,
    inference(avatar_split_clause,[status(thm)],[f2273,f2261]) ).

thf(f2273,plain,
    ( ( paraco1325918602e_eval @ i @ p1 )
   != ( paraco1344940915le_Det @ $true ) ),
    inference(forward_demodulation,[status(thm)],[f2257,f1835]) ).

thf(f2257,plain,
    ( ( paraco1325918602e_eval @ i @ p1 )
   != ( paraco1325918602e_eval @ i @ p2 ) ),
    inference(trivial_inequality_removal,[status(thm)],[f2254]) ).

thf(f2254,plain,
    ( ( ( paraco1325918602e_eval @ i @ p1 )
     != ( paraco1325918602e_eval @ i @ p2 ) )
    | ( ( paraco1325918602e_eval @ i @ p1 )
     != ( paraco1325918602e_eval @ i @ p1 ) ) ),
    inference(superposition,[status(thm)],[f1967,f1858]) ).

thf(f1858,plain,
    ! [X2: paraco1604210848lle_fm,X0: paraco1604210848lle_fm,X1: list_char > paraco1605129243lle_tv] :
      ( ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X0 @ X2 ) )
        = ( paraco1325918602e_eval @ X1 @ X0 ) )
      | ( ( paraco1325918602e_eval @ X1 @ X2 )
       != ( paraco1325918602e_eval @ X1 @ X0 ) ) ),
    inference(cnf_transformation,[status(thm)],[f1151]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP140^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13  % Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33  % Computer : n009.cluster.edu
% 0.16/0.33  % Model    : x86_64 x86_64
% 0.16/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33  % Memory   : 8042.1875MB
% 0.16/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33  % CPULimit : 300
% 0.16/0.33  % WCLimit  : 300
% 0.16/0.33  % DateTime : Tue Feb 24 08:27:25 EST 2026
% 0.16/0.34  % CPUTime  : 
% 0.16/0.34  Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45  ---- Original DTF file ---
% 0.30/0.46  thf(spec,logic,$$dhol).
% 0.30/0.46  %------------------------------------------------------------------------------
% 0.30/0.46  % File     : ITP140^1 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46  % Domain   : Interactive Theorem Proving
% 0.30/0.46  % Problem  : Sledgehammer Paraconsistency problem prob_947__3275214_1
% 0.30/0.46  % Version  : Especial.
% 0.30/0.46  % English  :
% 0.30/0.46  
% 0.30/0.46  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46  %          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46  % Source   : [Des21]
% 0.30/0.46  % Names    : Paraconsistency/prob_947__3275214_1 [Des21]
% 0.30/0.46  
% 0.30/0.46  % Status   : Theorem
% 0.30/0.46  % Rating   : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0
% 0.30/0.46  % Syntax   : Number of formulae    :  558 ( 169 unt; 200 typ;   0 def)
% 0.30/0.46  %            Number of atoms       : 1006 ( 555 equ;   0 cnn)
% 0.30/0.46  %            Maximal formula atoms :   16 (   2 avg)
% 0.30/0.46  %            Number of connectives : 2794 ( 113   ~;   4   |;  29   &;2180   @)
% 0.30/0.46  %                                         (   0 <=>; 468  =>;   0  <=;   0 <~>)
% 0.30/0.46  %            Maximal formula depth :   16 (   6 avg)
% 0.30/0.46  %            Number of types       :   37 (  36 usr)
% 0.30/0.46  %            Number of type conns  :  812 ( 812   >;   0   *;   0   +;   0  <<)
% 0.30/0.46  %            Number of symbols     :  167 ( 164 usr;  16 con; 0-3 aty)
% 0.30/0.46  %            Number of variables   : 1029 (  35   ^; 967   !;  27   ?;1029   :)
% 0.30/0.46  % SPC      : TH0_THM_EQU_NAR
% 0.30/0.46  
% 0.30/0.46  % Comments : This file was generated by Sledgehammer 2021-02-23 15:39:43.809
% 0.30/0.46  %------------------------------------------------------------------------------
% 0.30/0.46  % Could-be-implicit typings (36)
% 0.30/0.46  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,
% 0.30/0.46      set_Pr1475944804lle_fm: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1250255278lle_fm: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      set_Pr2012908090lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      set_Pr698334450lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1720769084lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      set_Pr2061825550lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      set_Pr1943077434tv_nat: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      set_Pr292927124lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1852595672lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      set_Pr1723822845lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      set_Pr2120184979lle_fm: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1443694919lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc696645085lle_fm: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      set_Pr1490359111at_nat: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.30/0.46      set_Pr2014382200lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 0.30/0.46      set_Pr1019238018lle_fm: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      set_Pr840833727at_nat: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      set_Pr560526279lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.46      produc1647334210lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 0.30/0.46      produc450659916lle_fm: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      set_Pr1357842111at_nat: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.30/0.46      produc596913417at_nat: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.46      produc931990033lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J,type,
% 0.30/0.46      set_Pr1725653840tv_nat: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.30/0.46      set_Pr13445366lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1281043295at_nat: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.30/0.46      produc194167194tv_nat: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.46      produc270694976lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.30/0.46      set_Pr1986765409at_nat: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.46      set_Pa1764573435lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.46      product_prod_nat_nat: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      paraco1605129243lle_tv: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 0.30/0.46      paraco1604210848lle_fm: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
% 0.30/0.46      list_char: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.46      set_nat: $tType ).
% 0.30/0.46  
% 0.30/0.46  thf(ty_n_t__Nat__Onat,type,
% 0.30/0.46      nat: $tType ).
% 0.30/0.46  
% 0.30/0.46  % Explicit typings (164)
% 0.30/0.46  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.46      inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.30/0.46      inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      inj_on26176689at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      inj_on1745913142lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      inj_on552895452tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Fun_Othe__inv__into_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.46      the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Fun_Othe__inv__into_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.46      ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.46      ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Orderings_Oord__class_Oless__eq_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,
% 0.30/0.46      ord_le1007985907lle_fm: set_Pr2120184979lle_fm > set_Pr2120184979lle_fm > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 0.30/0.46      ord_le1784136743lle_tv: set_Pr560526279lle_tv > set_Pr560526279lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.46      order_769474267at_nat: ( nat > nat ) > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.30/0.46      top_top_nat_o: nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_Eo_J,type,
% 0.30/0.46      top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.30/0.46      top_to632227436_nat_o: product_prod_nat_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      top_to1889334367e_tv_o: produc270694976lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      top_to900819589_nat_o: produc194167194tv_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Orderings_Otop__class_Otop_001_Eo,type,
% 0.30/0.46      top_top_o: $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.46      top_top_set_nat: set_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.46      top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      top_to138697918lle_tv: set_Pr2061825550lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      top_to775056195lle_fm: set_Pr2120184979lle_fm ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      top_to1541413903at_nat: set_Pr1357842111at_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      top_to449985143lle_tv: set_Pr560526279lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.30/0.46      top_to1555900337at_nat: set_Pr1986765409at_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      top_to1411004326lle_tv: set_Pr13445366lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      top_to975729152tv_nat: set_Pr1725653840tv_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      top_to1871154984lle_tv: set_Pr2014382200lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__int,type,
% 0.30/0.46      paraco761681009ge_int: ( nat > nat ) > ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv,type,
% 0.30/0.46      paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv__rel,type,
% 0.30/0.46      paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Oeval,type,
% 0.30/0.46      paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OCon_H,type,
% 0.30/0.46      paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql,type,
% 0.30/0.46      paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql_H,type,
% 0.30/0.46      paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_ONeg_H,type,
% 0.30/0.46      paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OPro,type,
% 0.30/0.46      paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OTruth,type,
% 0.30/0.46      paraco367965286_Truth: paraco1604210848lle_fm ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_ODet,type,
% 0.30/0.46      paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_OIndet,type,
% 0.30/0.46      paraco793048302_Indet: nat > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_Ocase__tv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      paraco2051596139lle_tv: ( $o > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid,type,
% 0.30/0.46      paraco327635598_valid: paraco1604210848lle_fm > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid__in,type,
% 0.30/0.46      paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1297923922lle_tv: ( list_char > paraco1605129243lle_tv ) > ( list_char > paraco1605129243lle_tv ) > produc1852595672lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc780837143at_nat: ( nat > nat ) > ( nat > nat ) > produc1281043295at_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      produc1680557635lle_tv: ( nat > nat ) > paraco1605129243lle_tv > produc931990033lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1943344577lle_tv: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc1443694919lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
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% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
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% 0.30/0.46  
% 0.30/0.46  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,
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% 0.30/0.46  
% 0.30/0.46  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,
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% 0.30/0.46  
% 0.30/0.46  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,
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% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc939316703lle_tv: ( ( nat > nat ) > nat > nat ) > produc931990033lle_tv > produc931990033lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
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% 0.30/0.46  
% 0.30/0.46  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,
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% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Obool_Ocase__bool_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
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% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Ocurry_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_Eo,type,
% 0.30/0.46      produc752649287e_tv_o: ( produc931990033lle_tv > $o ) > ( nat > nat ) > paraco1605129243lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1900967599lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1566550641lle_tv: ( ( list_char > paraco1605129243lle_tv ) > nat > nat ) > ( paraco1604210848lle_fm > paraco1605129243lle_tv ) > produc696645085lle_fm > produc931990033lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc951033137lle_fm: ( ( nat > nat ) > list_char > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1604210848lle_fm ) > produc931990033lle_tv > produc696645085lle_fm ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc532909085lle_tv: ( ( nat > nat ) > nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.46      produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      produc313957681lle_tv: ( nat > nat ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc270694976lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.30/0.46      produc1685803475tv_nat: ( nat > nat ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > product_prod_nat_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.46      produc1250721397at_nat: ( nat > paraco1605129243lle_tv ) > ( nat > nat ) > product_prod_nat_nat > produc194167194tv_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      produc210389789lle_tv: ( nat > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc1647334210lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.30/0.46      produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.46      produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.46      produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      produc1636169559lle_tv: produc931990033lle_tv > nat > nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Oprod_Ofst_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.46      produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      produc547496597lle_tv: produc931990033lle_tv > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Oprod_Osnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.46      produc500618325at_nat: produc596913417at_nat > nat > nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      produc225513635lle_tv: produc931990033lle_tv > produc596913417at_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Product__Type_Oprod_Oswap_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.46      produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.46      inv_image_nat_nat: set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      inv_im1292588663lle_tv: set_Pr1986765409at_nat > ( paraco1605129243lle_tv > nat ) > set_Pr2014382200lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Relation_Oinv__image_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.30/0.46      inv_im516950809tv_nat: set_Pr2014382200lle_tv > ( nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Relation_Oinv__image_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      inv_im719552961lle_tv: set_Pr2014382200lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pr2014382200lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Relation_Ototal__on_001t__Nat__Onat,type,
% 0.30/0.46      total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Relation_Ototal__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      total_1781621663lle_tv: set_Pa1764573435lle_tv > set_Pr2014382200lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.46      total_1775715973at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.46      total_517371324lle_tv: set_Pr13445366lle_tv > set_Pr292927124lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.30/0.46      total_440843542tv_nat: set_Pr1725653840tv_nat > set_Pr1943077434tv_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.46      total_92239038lle_tv: set_Pr2014382200lle_tv > set_Pr2012908090lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.30/0.46      collect_nat: ( nat > $o ) > set_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Set_OCollect_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      collec1102043437lle_tv: ( produc1852595672lle_tv > $o ) > set_Pr2061825550lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      collec835549234lle_fm: ( produc696645085lle_fm > $o ) > set_Pr2120184979lle_fm ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      collec791369802at_nat: ( produc1281043295at_nat > $o ) > set_Pr1357842111at_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      collec1624074086lle_tv: ( produc931990033lle_tv > $o ) > set_Pr560526279lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.46      collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.46      collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.30/0.46      collec848462447tv_nat: ( produc194167194tv_nat > $o ) > set_Pr1725653840tv_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.46      image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.30/0.46      image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_807538418lle_fm: ( produc696645085lle_fm > produc696645085lle_fm ) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_1154804148lle_tv: ( produc696645085lle_fm > produc931990033lle_tv ) > set_Pr2120184979lle_fm > set_Pr560526279lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_924970994lle_tv: ( produc696645085lle_fm > produc1443694919lle_tv ) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_1585092542lle_fm: ( produc931990033lle_tv > produc696645085lle_fm ) > set_Pr560526279lle_tv > set_Pr2120184979lle_fm ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_1751508608lle_tv: ( produc931990033lle_tv > produc931990033lle_tv ) > set_Pr560526279lle_tv > set_Pr560526279lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_1724396928at_nat: ( produc931990033lle_tv > produc596913417at_nat ) > set_Pr560526279lle_tv > set_Pr840833727at_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_815163717at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_1674248956lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > set_Pr13445366lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_1507992062lle_tv: ( product_prod_nat_nat > produc1647334210lle_tv ) > set_Pr1986765409at_nat > set_Pr2014382200lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_1787705850at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > set_Pr1986765409at_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_326034184lle_fm: ( produc1443694919lle_tv > produc696645085lle_fm ) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_769496456lle_tv: ( produc596913417at_nat > produc931990033lle_tv ) > set_Pr840833727at_nat > set_Pr560526279lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      image_1221801032lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      accp_P2085826120lle_tv: ( produc931990033lle_tv > produc931990033lle_tv > $o ) > produc931990033lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      lex_pr2001015487lle_fm: set_Pr2061825550lle_tv > set_Pr1019238018lle_fm > set_Pr1475944804lle_fm ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Wellfounded_Olex__prod_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      lex_pr1093414955lle_tv: set_Pr1357842111at_nat > set_Pr2014382200lle_tv > set_Pr698334450lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.46      lex_prod_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1490359111at_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      lex_pr413684186lle_tv: set_Pr1986765409at_nat > set_Pr2014382200lle_tv > set_Pr292927124lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Wellfounded_Olex__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 0.30/0.46      lex_pr1785529980tv_nat: set_Pr2014382200lle_tv > set_Pr1986765409at_nat > set_Pr1943077434tv_nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Wellfounded_Olex__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      lex_pr567812260lle_tv: set_Pr2014382200lle_tv > set_Pr2014382200lle_tv > set_Pr2012908090lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 0.30/0.46      wf_nat: set_Pr1986765409at_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Wellfounded_Owf_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      wf_Par1378404612lle_tv: set_Pr2014382200lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      same_f1581085506lle_fm: ( ( list_char > paraco1605129243lle_tv ) > $o ) > ( ( list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm ) > set_Pr1475944804lle_fm ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_Wfrec_Osame__fst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      same_f1138187694lle_tv: ( ( nat > nat ) > $o ) > ( ( nat > nat ) > set_Pr2014382200lle_tv ) > set_Pr698334450lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_member_001t__Nat__Onat,type,
% 0.30/0.46      member_nat: nat > set_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_member_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 0.30/0.46      member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      member146333935lle_tv: produc1852595672lle_tv > set_Pr2061825550lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      member112824072at_nat: produc1281043295at_nat > set_Pr1357842111at_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.46      member1569366824lle_tv: produc931990033lle_tv > set_Pr560526279lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.46      member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.46      member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 0.30/0.46      member334644067lle_fm: produc450659916lle_fm > set_Pr1019238018lle_fm > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.30/0.46      member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 0.30/0.46      member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 0.30/0.46      member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      member1592865093lle_fm: produc1250255278lle_fm > set_Pr1475944804lle_fm > $o ).
% 0.30/0.46  
% 0.30/0.46  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,
% 0.30/0.46      member1339857875lle_tv: produc1720769084lle_tv > set_Pr698334450lle_tv > $o ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_v_f,type,
% 0.30/0.46      f: nat > nat ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_v_i,type,
% 0.30/0.46      i: list_char > paraco1605129243lle_tv ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_v_p1____,type,
% 0.30/0.46      p1: paraco1604210848lle_fm ).
% 0.30/0.46  
% 0.30/0.46  thf(sy_v_p2____,type,
% 0.30/0.46      p2: paraco1604210848lle_fm ).
% 0.30/0.46  
% 0.30/0.46  % Relevant facts (354)
% 0.30/0.46  thf(fact_0_a_H_H,axiom,
% 0.30/0.46      ( ( paraco1325918602e_eval @ i @ p1 )
% 0.30/0.46     != ( paraco1344940915le_Det @ $true ) ) ).
% 0.30/0.46  
% 0.30/0.46  % a''
% 0.30/0.46  thf(fact_1_a,axiom,
% 0.30/0.46      ( ( paraco1325918602e_eval @ i @ p2 )
% 0.30/0.46      = ( paraco1344940915le_Det @ $true ) ) ).
% 0.30/0.46  
% 0.30/0.46  % a
% 0.30/0.46  thf(fact_2_a_H,axiom,
% 0.30/0.46      ( ( paraco1325918602e_eval @ i @ p1 )
% 0.30/0.46     != ( paraco1325918602e_eval @ i @ p2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % a'
% 0.30/0.46  thf(fact_3_fm_Oinject_I3_J,axiom,
% 0.30/0.46      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,Y41: paraco1604210848lle_fm,Y42: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.30/0.46          = ( paraco69239110le_Con @ Y41 @ Y42 ) )
% 0.30/0.46        = ( ( X41 = Y41 )
% 0.30/0.46          & ( X42 = Y42 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.inject(3)
% 0.30/0.46  thf(fact_4_b_H,axiom,
% 0.30/0.46      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 0.30/0.46     != ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % b'
% 0.30/0.46  thf(fact_5_eval_Osimps_I4_J,axiom,
% 0.30/0.46      ! [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46            = ( paraco1325918602e_eval @ I @ Q ) )
% 0.30/0.46         => ( ( paraco1325918602e_eval @ I @ ( paraco69239110le_Con @ P @ Q ) )
% 0.30/0.46            = ( paraco1325918602e_eval @ I @ P ) ) )
% 0.30/0.46        & ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46           != ( paraco1325918602e_eval @ I @ Q ) )
% 0.30/0.46         => ( ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46                = ( paraco1344940915le_Det @ $true ) )
% 0.30/0.46             => ( ( paraco1325918602e_eval @ I @ ( paraco69239110le_Con @ P @ Q ) )
% 0.30/0.46                = ( paraco1325918602e_eval @ I @ Q ) ) )
% 0.30/0.46            & ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46               != ( paraco1344940915le_Det @ $true ) )
% 0.30/0.46             => ( ( ( ( paraco1325918602e_eval @ I @ Q )
% 0.30/0.46                    = ( paraco1344940915le_Det @ $true ) )
% 0.30/0.46                 => ( ( paraco1325918602e_eval @ I @ ( paraco69239110le_Con @ P @ Q ) )
% 0.30/0.46                    = ( paraco1325918602e_eval @ I @ P ) ) )
% 0.30/0.46                & ( ( ( paraco1325918602e_eval @ I @ Q )
% 0.30/0.46                   != ( paraco1344940915le_Det @ $true ) )
% 0.30/0.46                 => ( ( paraco1325918602e_eval @ I @ ( paraco69239110le_Con @ P @ Q ) )
% 0.30/0.46                    = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % eval.simps(4)
% 0.30/0.46  thf(fact_6_ih2,axiom,
% 0.30/0.46      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
% 0.30/0.46      = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % ih2
% 0.30/0.46  thf(fact_7_ih1,axiom,
% 0.30/0.46      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 0.30/0.46      = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p1 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % ih1
% 0.30/0.46  thf(fact_8_b_H_H,axiom,
% 0.30/0.46      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 0.30/0.46     != ( paraco1344940915le_Det @ $true ) ) ).
% 0.30/0.46  
% 0.30/0.46  % b''
% 0.30/0.46  thf(fact_9_tv_Oinject_I1_J,axiom,
% 0.30/0.46      ! [X1: $o,Y1: $o] :
% 0.30/0.46        ( ( ( paraco1344940915le_Det @ X1 )
% 0.30/0.46          = ( paraco1344940915le_Det @ Y1 ) )
% 0.30/0.46        = ( X1 = Y1 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % tv.inject(1)
% 0.30/0.46  thf(fact_10_conjunction,axiom,
% 0.30/0.46      ! [P: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco327635598_valid @ ( paraco69239110le_Con @ P @ Q ) )
% 0.30/0.46        = ( ( paraco327635598_valid @ P )
% 0.30/0.46          & ( paraco327635598_valid @ Q ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % conjunction
% 0.30/0.46  thf(fact_11_conjunction__in,axiom,
% 0.30/0.46      ! [U: set_nat,P: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco55203475lid_in @ U @ ( paraco69239110le_Con @ P @ Q ) )
% 0.30/0.46        = ( ( paraco55203475lid_in @ U @ P )
% 0.30/0.46          & ( paraco55203475lid_in @ U @ Q ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % conjunction_in
% 0.30/0.46  thf(fact_12_fm_Odistinct_I13_J,axiom,
% 0.30/0.46      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.30/0.46        ( paraco367965286_Truth
% 0.30/0.46       != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(13)
% 0.30/0.46  thf(fact_13_fm_Odistinct_I25_J,axiom,
% 0.30/0.46      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.30/0.46       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(25)
% 0.30/0.46  thf(fact_14_fm_Oinject_I4_J,axiom,
% 0.30/0.46      ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,Y51: paraco1604210848lle_fm,Y52: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 0.30/0.46          = ( paraco1389086619le_Eql @ Y51 @ Y52 ) )
% 0.30/0.46        = ( ( X51 = Y51 )
% 0.30/0.46          & ( X52 = Y52 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.inject(4)
% 0.30/0.46  thf(fact_15_fm_Odistinct_I15_J,axiom,
% 0.30/0.46      ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.30/0.46        ( paraco367965286_Truth
% 0.30/0.46       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(15)
% 0.30/0.46  thf(fact_16_change__tv_Osimps_I1_J,axiom,
% 0.30/0.46      ! [F: nat > nat,B: $o] :
% 0.30/0.46        ( ( paraco1147068288nge_tv @ F @ ( paraco1344940915le_Det @ B ) )
% 0.30/0.46        = ( paraco1344940915le_Det @ B ) ) ).
% 0.30/0.46  
% 0.30/0.46  % change_tv.simps(1)
% 0.30/0.46  thf(fact_17_transfer,axiom,
% 0.30/0.46      ! [U: set_nat,P: paraco1604210848lle_fm] :
% 0.30/0.46        ( ~ ( paraco55203475lid_in @ U @ P )
% 0.30/0.46       => ~ ( paraco327635598_valid @ P ) ) ).
% 0.30/0.46  
% 0.30/0.46  % transfer
% 0.30/0.46  thf(fact_18_change__int__def,axiom,
% 0.30/0.46      ( paraco761681009ge_int
% 0.30/0.46      = ( ^ [F2: nat > nat,I2: list_char > paraco1605129243lle_tv,S: list_char] : ( paraco1147068288nge_tv @ F2 @ ( I2 @ S ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % change_int_def
% 0.30/0.46  thf(fact_19_valid__valid__in,axiom,
% 0.30/0.46      ! [P: paraco1604210848lle_fm,U: set_nat] :
% 0.30/0.46        ( ( paraco327635598_valid @ P )
% 0.30/0.46       => ( paraco55203475lid_in @ U @ P ) ) ).
% 0.30/0.46  
% 0.30/0.46  % valid_valid_in
% 0.30/0.46  thf(fact_20_eval__equality__simplify,axiom,
% 0.30/0.46      ! [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco1325918602e_eval @ I @ ( paraco1389086619le_Eql @ P @ Q ) )
% 0.30/0.46        = ( paraco1344940915le_Det
% 0.30/0.46          @ ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46            = ( paraco1325918602e_eval @ I @ Q ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % eval_equality_simplify
% 0.30/0.46  thf(fact_21_eval_Osimps_I5_J,axiom,
% 0.30/0.46      ! [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46            = ( paraco1325918602e_eval @ I @ Q ) )
% 0.30/0.46         => ( ( paraco1325918602e_eval @ I @ ( paraco1389086619le_Eql @ P @ Q ) )
% 0.30/0.46            = ( paraco1344940915le_Det @ $true ) ) )
% 0.30/0.46        & ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46           != ( paraco1325918602e_eval @ I @ Q ) )
% 0.30/0.46         => ( ( paraco1325918602e_eval @ I @ ( paraco1389086619le_Eql @ P @ Q ) )
% 0.30/0.46            = ( paraco1344940915le_Det @ $false ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % eval.simps(5)
% 0.30/0.46  thf(fact_22_eval_Osimps_I2_J,axiom,
% 0.30/0.46      ! [I: list_char > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( paraco1325918602e_eval @ I @ paraco367965286_Truth )
% 0.30/0.46        = ( paraco1344940915le_Det @ $true ) ) ).
% 0.30/0.46  
% 0.30/0.46  % eval.simps(2)
% 0.30/0.46  thf(fact_23_valid__def,axiom,
% 0.30/0.46      ( paraco327635598_valid
% 0.30/0.46      = ( ^ [P2: paraco1604210848lle_fm] :
% 0.30/0.46          ! [I2: list_char > paraco1605129243lle_tv] :
% 0.30/0.46            ( ( paraco1325918602e_eval @ I2 @ P2 )
% 0.30/0.46            = ( paraco1344940915le_Det @ $true ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % valid_def
% 0.30/0.46  thf(fact_24_change__tv_Oelims,axiom,
% 0.30/0.46      ! [X: nat > nat,Xa: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( ( paraco1147068288nge_tv @ X @ Xa )
% 0.30/0.46          = Y )
% 0.30/0.46       => ( ! [B2: $o] :
% 0.30/0.46              ( ( Xa
% 0.30/0.46                = ( paraco1344940915le_Det @ B2 ) )
% 0.30/0.46             => ( Y
% 0.30/0.46               != ( paraco1344940915le_Det @ B2 ) ) )
% 0.30/0.46         => ~ ! [N: nat] :
% 0.30/0.46                ( ( Xa
% 0.30/0.46                  = ( paraco793048302_Indet @ N ) )
% 0.30/0.46               => ( Y
% 0.30/0.46                 != ( paraco793048302_Indet @ ( X @ N ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % change_tv.elims
% 0.30/0.46  thf(fact_25_tv_Osimps_I5_J,axiom,
% 0.30/0.46      ! [F1: $o > paraco1605129243lle_tv,F22: nat > paraco1605129243lle_tv,X1: $o] :
% 0.30/0.46        ( ( paraco2051596139lle_tv @ F1 @ F22 @ ( paraco1344940915le_Det @ X1 ) )
% 0.30/0.46        = ( F1 @ X1 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % tv.simps(5)
% 0.30/0.46  thf(fact_26_eval__negation,axiom,
% 0.30/0.46      ! [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46            = ( paraco1344940915le_Det @ $false ) )
% 0.30/0.46         => ( ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ P ) )
% 0.30/0.46            = ( paraco1344940915le_Det @ $true ) ) )
% 0.30/0.46        & ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46           != ( paraco1344940915le_Det @ $false ) )
% 0.30/0.46         => ( ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46                = ( paraco1344940915le_Det @ $true ) )
% 0.30/0.46             => ( ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ P ) )
% 0.30/0.46                = ( paraco1344940915le_Det @ $false ) ) )
% 0.30/0.46            & ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46               != ( paraco1344940915le_Det @ $true ) )
% 0.30/0.46             => ( ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ P ) )
% 0.30/0.46                = ( paraco1325918602e_eval @ I @ P ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % eval_negation
% 0.30/0.46  thf(fact_27_assms,axiom,
% 0.30/0.46      inj_on_nat_nat @ f @ top_top_set_nat ).
% 0.30/0.46  
% 0.30/0.46  % assms
% 0.30/0.46  thf(fact_28_change__tv_Osimps_I2_J,axiom,
% 0.30/0.46      ! [F: nat > nat,N2: nat] :
% 0.30/0.46        ( ( paraco1147068288nge_tv @ F @ ( paraco793048302_Indet @ N2 ) )
% 0.30/0.46        = ( paraco793048302_Indet @ ( F @ N2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % change_tv.simps(2)
% 0.30/0.46  thf(fact_29_fm_Odistinct_I17_J,axiom,
% 0.30/0.46      ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.30/0.46        ( paraco367965286_Truth
% 0.30/0.46       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(17)
% 0.30/0.46  thf(fact_30_fm_Oinject_I2_J,axiom,
% 0.30/0.46      ! [X3: paraco1604210848lle_fm,Y3: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( ( paraco445776468le_Neg @ X3 )
% 0.30/0.46          = ( paraco445776468le_Neg @ Y3 ) )
% 0.30/0.46        = ( X3 = Y3 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.inject(2)
% 0.30/0.46  thf(fact_31_fm_Oinject_I5_J,axiom,
% 0.30/0.46      ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm,Y61: paraco1604210848lle_fm,Y62: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( ( paraco1745535428le_Eql @ X61 @ X62 )
% 0.30/0.46          = ( paraco1745535428le_Eql @ Y61 @ Y62 ) )
% 0.30/0.46        = ( ( X61 = Y61 )
% 0.30/0.46          & ( X62 = Y62 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.inject(5)
% 0.30/0.46  thf(fact_32_tv_Oinject_I2_J,axiom,
% 0.30/0.46      ! [X2: nat,Y2: nat] :
% 0.30/0.46        ( ( ( paraco793048302_Indet @ X2 )
% 0.30/0.46          = ( paraco793048302_Indet @ Y2 ) )
% 0.30/0.46        = ( X2 = Y2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % tv.inject(2)
% 0.30/0.46  thf(fact_33_fm_Odistinct_I23_J,axiom,
% 0.30/0.46      ! [X3: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco445776468le_Neg @ X3 )
% 0.30/0.46       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(23)
% 0.30/0.46  thf(fact_34_tv_Osimps_I6_J,axiom,
% 0.30/0.46      ! [F1: $o > paraco1605129243lle_tv,F22: nat > paraco1605129243lle_tv,X2: nat] :
% 0.30/0.46        ( ( paraco2051596139lle_tv @ F1 @ F22 @ ( paraco793048302_Indet @ X2 ) )
% 0.30/0.46        = ( F22 @ X2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % tv.simps(6)
% 0.30/0.46  thf(fact_35_mem__Collect__eq,axiom,
% 0.30/0.46      ! [A: produc696645085lle_fm,P3: produc696645085lle_fm > $o] :
% 0.30/0.46        ( ( member1474794996lle_fm @ A @ ( collec835549234lle_fm @ P3 ) )
% 0.30/0.46        = ( P3 @ A ) ) ).
% 0.30/0.46  
% 0.30/0.46  % mem_Collect_eq
% 0.30/0.46  thf(fact_36_mem__Collect__eq,axiom,
% 0.30/0.46      ! [A: produc1852595672lle_tv,P3: produc1852595672lle_tv > $o] :
% 0.30/0.46        ( ( member146333935lle_tv @ A @ ( collec1102043437lle_tv @ P3 ) )
% 0.30/0.46        = ( P3 @ A ) ) ).
% 0.30/0.46  
% 0.30/0.46  % mem_Collect_eq
% 0.30/0.46  thf(fact_37_mem__Collect__eq,axiom,
% 0.30/0.46      ! [A: produc931990033lle_tv,P3: produc931990033lle_tv > $o] :
% 0.30/0.46        ( ( member1569366824lle_tv @ A @ ( collec1624074086lle_tv @ P3 ) )
% 0.30/0.46        = ( P3 @ A ) ) ).
% 0.30/0.46  
% 0.30/0.46  % mem_Collect_eq
% 0.30/0.46  thf(fact_38_mem__Collect__eq,axiom,
% 0.30/0.46      ! [A: produc1281043295at_nat,P3: produc1281043295at_nat > $o] :
% 0.30/0.46        ( ( member112824072at_nat @ A @ ( collec791369802at_nat @ P3 ) )
% 0.30/0.46        = ( P3 @ A ) ) ).
% 0.30/0.46  
% 0.30/0.46  % mem_Collect_eq
% 0.30/0.46  thf(fact_39_mem__Collect__eq,axiom,
% 0.30/0.46      ! [A: paraco1605129243lle_tv,P3: paraco1605129243lle_tv > $o] :
% 0.30/0.46        ( ( member266900804lle_tv @ A @ ( collec1111687558lle_tv @ P3 ) )
% 0.30/0.46        = ( P3 @ A ) ) ).
% 0.30/0.46  
% 0.30/0.46  % mem_Collect_eq
% 0.30/0.46  thf(fact_40_mem__Collect__eq,axiom,
% 0.30/0.46      ! [A: nat,P3: nat > $o] :
% 0.30/0.46        ( ( member_nat @ A @ ( collect_nat @ P3 ) )
% 0.30/0.46        = ( P3 @ A ) ) ).
% 0.30/0.46  
% 0.30/0.46  % mem_Collect_eq
% 0.30/0.46  thf(fact_41_Collect__mem__eq,axiom,
% 0.30/0.46      ! [A2: set_Pr2120184979lle_fm] :
% 0.30/0.46        ( ( collec835549234lle_fm
% 0.30/0.46          @ ^ [X4: produc696645085lle_fm] : ( member1474794996lle_fm @ X4 @ A2 ) )
% 0.30/0.46        = A2 ) ).
% 0.30/0.46  
% 0.30/0.46  % Collect_mem_eq
% 0.30/0.46  thf(fact_42_Collect__mem__eq,axiom,
% 0.30/0.46      ! [A2: set_Pr2061825550lle_tv] :
% 0.30/0.46        ( ( collec1102043437lle_tv
% 0.30/0.46          @ ^ [X4: produc1852595672lle_tv] : ( member146333935lle_tv @ X4 @ A2 ) )
% 0.30/0.46        = A2 ) ).
% 0.30/0.46  
% 0.30/0.46  % Collect_mem_eq
% 0.30/0.46  thf(fact_43_Collect__mem__eq,axiom,
% 0.30/0.46      ! [A2: set_Pr560526279lle_tv] :
% 0.30/0.46        ( ( collec1624074086lle_tv
% 0.30/0.46          @ ^ [X4: produc931990033lle_tv] : ( member1569366824lle_tv @ X4 @ A2 ) )
% 0.30/0.46        = A2 ) ).
% 0.30/0.46  
% 0.30/0.46  % Collect_mem_eq
% 0.30/0.46  thf(fact_44_Collect__mem__eq,axiom,
% 0.30/0.46      ! [A2: set_Pr1357842111at_nat] :
% 0.30/0.46        ( ( collec791369802at_nat
% 0.30/0.46          @ ^ [X4: produc1281043295at_nat] : ( member112824072at_nat @ X4 @ A2 ) )
% 0.30/0.46        = A2 ) ).
% 0.30/0.46  
% 0.30/0.46  % Collect_mem_eq
% 0.30/0.46  thf(fact_45_Collect__mem__eq,axiom,
% 0.30/0.46      ! [A2: set_Pa1764573435lle_tv] :
% 0.30/0.46        ( ( collec1111687558lle_tv
% 0.30/0.46          @ ^ [X4: paraco1605129243lle_tv] : ( member266900804lle_tv @ X4 @ A2 ) )
% 0.30/0.46        = A2 ) ).
% 0.30/0.46  
% 0.30/0.46  % Collect_mem_eq
% 0.30/0.46  thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46      ! [A2: set_nat] :
% 0.30/0.46        ( ( collect_nat
% 0.30/0.46          @ ^ [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 0.30/0.46        = A2 ) ).
% 0.30/0.46  
% 0.30/0.46  % Collect_mem_eq
% 0.30/0.46  thf(fact_47_Collect__cong,axiom,
% 0.30/0.46      ! [P3: paraco1605129243lle_tv > $o,Q2: paraco1605129243lle_tv > $o] :
% 0.30/0.46        ( ! [X5: paraco1605129243lle_tv] :
% 0.30/0.46            ( ( P3 @ X5 )
% 0.30/0.46            = ( Q2 @ X5 ) )
% 0.30/0.46       => ( ( collec1111687558lle_tv @ P3 )
% 0.30/0.46          = ( collec1111687558lle_tv @ Q2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % Collect_cong
% 0.30/0.46  thf(fact_48_Collect__cong,axiom,
% 0.30/0.46      ! [P3: nat > $o,Q2: nat > $o] :
% 0.30/0.46        ( ! [X5: nat] :
% 0.30/0.46            ( ( P3 @ X5 )
% 0.30/0.46            = ( Q2 @ X5 ) )
% 0.30/0.46       => ( ( collect_nat @ P3 )
% 0.30/0.46          = ( collect_nat @ Q2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % Collect_cong
% 0.30/0.46  thf(fact_49_eval__equality,axiom,
% 0.30/0.46      ! [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46            = ( paraco1325918602e_eval @ I @ Q ) )
% 0.30/0.46         => ( ( paraco1325918602e_eval @ I @ ( paraco1745535428le_Eql @ P @ Q ) )
% 0.30/0.46            = ( paraco1344940915le_Det @ $true ) ) )
% 0.30/0.46        & ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46           != ( paraco1325918602e_eval @ I @ Q ) )
% 0.30/0.46         => ( ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46                = ( paraco1344940915le_Det @ $true ) )
% 0.30/0.46             => ( ( paraco1325918602e_eval @ I @ ( paraco1745535428le_Eql @ P @ Q ) )
% 0.30/0.46                = ( paraco1325918602e_eval @ I @ Q ) ) )
% 0.30/0.46            & ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46               != ( paraco1344940915le_Det @ $true ) )
% 0.30/0.46             => ( ( ( ( paraco1325918602e_eval @ I @ Q )
% 0.30/0.46                    = ( paraco1344940915le_Det @ $true ) )
% 0.30/0.46                 => ( ( paraco1325918602e_eval @ I @ ( paraco1745535428le_Eql @ P @ Q ) )
% 0.30/0.46                    = ( paraco1325918602e_eval @ I @ P ) ) )
% 0.30/0.46                & ( ( ( paraco1325918602e_eval @ I @ Q )
% 0.30/0.46                   != ( paraco1344940915le_Det @ $true ) )
% 0.30/0.46                 => ( ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46                        = ( paraco1344940915le_Det @ $false ) )
% 0.30/0.46                     => ( ( paraco1325918602e_eval @ I @ ( paraco1745535428le_Eql @ P @ Q ) )
% 0.30/0.46                        = ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ Q ) ) ) )
% 0.30/0.46                    & ( ( ( paraco1325918602e_eval @ I @ P )
% 0.30/0.46                       != ( paraco1344940915le_Det @ $false ) )
% 0.30/0.46                     => ( ( ( ( paraco1325918602e_eval @ I @ Q )
% 0.30/0.46                            = ( paraco1344940915le_Det @ $false ) )
% 0.30/0.46                         => ( ( paraco1325918602e_eval @ I @ ( paraco1745535428le_Eql @ P @ Q ) )
% 0.30/0.46                            = ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ P ) ) ) )
% 0.30/0.46                        & ( ( ( paraco1325918602e_eval @ I @ Q )
% 0.30/0.46                           != ( paraco1344940915le_Det @ $false ) )
% 0.30/0.46                         => ( ( paraco1325918602e_eval @ I @ ( paraco1745535428le_Eql @ P @ Q ) )
% 0.30/0.46                            = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % eval_equality
% 0.30/0.46  thf(fact_50_double__negation,axiom,
% 0.30/0.46      ( paraco1325918602e_eval
% 0.30/0.46      = ( ^ [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ P2 ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % double_negation
% 0.30/0.46  thf(fact_51_fm_Odistinct_I19_J,axiom,
% 0.30/0.46      ! [X3: paraco1604210848lle_fm,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco445776468le_Neg @ X3 )
% 0.30/0.46       != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(19)
% 0.30/0.46  thf(fact_52_string__tv_Oinduct,axiom,
% 0.30/0.46      ! [P3: paraco1605129243lle_tv > $o,A0: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( P3 @ ( paraco1344940915le_Det @ $true ) )
% 0.30/0.46       => ( ( P3 @ ( paraco1344940915le_Det @ $false ) )
% 0.30/0.46         => ( ! [N: nat] : ( P3 @ ( paraco793048302_Indet @ N ) )
% 0.30/0.46           => ( P3 @ A0 ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % string_tv.induct
% 0.30/0.46  thf(fact_53_change__tv_Oinduct,axiom,
% 0.30/0.46      ! [P3: ( nat > nat ) > paraco1605129243lle_tv > $o,A0: nat > nat,A1: paraco1605129243lle_tv] :
% 0.30/0.46        ( ! [F3: nat > nat,B2: $o] : ( P3 @ F3 @ ( paraco1344940915le_Det @ B2 ) )
% 0.30/0.46       => ( ! [F3: nat > nat,N: nat] : ( P3 @ F3 @ ( paraco793048302_Indet @ N ) )
% 0.30/0.46         => ( P3 @ A0 @ A1 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % change_tv.induct
% 0.30/0.46  thf(fact_54_string__tv_Ocases,axiom,
% 0.30/0.46      ! [X: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( X
% 0.30/0.46         != ( paraco1344940915le_Det @ $true ) )
% 0.30/0.46       => ( ( X
% 0.30/0.46           != ( paraco1344940915le_Det @ $false ) )
% 0.30/0.46         => ~ ! [N: nat] :
% 0.30/0.46                ( X
% 0.30/0.46               != ( paraco793048302_Indet @ N ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % string_tv.cases
% 0.30/0.46  thf(fact_55_tv_Oexhaust,axiom,
% 0.30/0.46      ! [Y: paraco1605129243lle_tv] :
% 0.30/0.46        ( ! [X12: $o] :
% 0.30/0.46            ( Y
% 0.30/0.46           != ( paraco1344940915le_Det @ X12 ) )
% 0.30/0.46       => ~ ! [X22: nat] :
% 0.30/0.46              ( Y
% 0.30/0.46             != ( paraco793048302_Indet @ X22 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % tv.exhaust
% 0.30/0.46  thf(fact_56_tv_Oinduct,axiom,
% 0.30/0.46      ! [P3: paraco1605129243lle_tv > $o,Tv: paraco1605129243lle_tv] :
% 0.30/0.46        ( ! [X5: $o] : ( P3 @ ( paraco1344940915le_Det @ X5 ) )
% 0.30/0.46       => ( ! [X5: nat] : ( P3 @ ( paraco793048302_Indet @ X5 ) )
% 0.30/0.46         => ( P3 @ Tv ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % tv.induct
% 0.30/0.46  thf(fact_57_tv_Odistinct_I1_J,axiom,
% 0.30/0.46      ! [X1: $o,X2: nat] :
% 0.30/0.46        ( ( paraco1344940915le_Det @ X1 )
% 0.30/0.46       != ( paraco793048302_Indet @ X2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % tv.distinct(1)
% 0.30/0.46  thf(fact_58_fm_Odistinct_I21_J,axiom,
% 0.30/0.46      ! [X3: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco445776468le_Neg @ X3 )
% 0.30/0.46       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(21)
% 0.30/0.46  thf(fact_59_fm_Odistinct_I11_J,axiom,
% 0.30/0.46      ! [X3: paraco1604210848lle_fm] :
% 0.30/0.46        ( paraco367965286_Truth
% 0.30/0.46       != ( paraco445776468le_Neg @ X3 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(11)
% 0.30/0.46  thf(fact_60_fm_Odistinct_I27_J,axiom,
% 0.30/0.46      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco69239110le_Con @ X41 @ X42 )
% 0.30/0.46       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(27)
% 0.30/0.46  thf(fact_61_fm_Odistinct_I29_J,axiom,
% 0.30/0.46      ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 0.30/0.46       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(29)
% 0.30/0.46  thf(fact_62_iso__tuple__UNIV__I,axiom,
% 0.30/0.46      ! [X: produc696645085lle_fm] : ( member1474794996lle_fm @ X @ top_to775056195lle_fm ) ).
% 0.30/0.46  
% 0.30/0.46  % iso_tuple_UNIV_I
% 0.30/0.46  thf(fact_63_iso__tuple__UNIV__I,axiom,
% 0.30/0.46      ! [X: produc1852595672lle_tv] : ( member146333935lle_tv @ X @ top_to138697918lle_tv ) ).
% 0.30/0.46  
% 0.30/0.46  % iso_tuple_UNIV_I
% 0.30/0.46  thf(fact_64_iso__tuple__UNIV__I,axiom,
% 0.30/0.46      ! [X: produc931990033lle_tv] : ( member1569366824lle_tv @ X @ top_to449985143lle_tv ) ).
% 0.30/0.46  
% 0.30/0.46  % iso_tuple_UNIV_I
% 0.30/0.46  thf(fact_65_iso__tuple__UNIV__I,axiom,
% 0.30/0.46      ! [X: produc1281043295at_nat] : ( member112824072at_nat @ X @ top_to1541413903at_nat ) ).
% 0.30/0.46  
% 0.30/0.46  % iso_tuple_UNIV_I
% 0.30/0.46  thf(fact_66_iso__tuple__UNIV__I,axiom,
% 0.30/0.46      ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 0.30/0.46  
% 0.30/0.46  % iso_tuple_UNIV_I
% 0.30/0.46  thf(fact_67_iso__tuple__UNIV__I,axiom,
% 0.30/0.46      ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 0.30/0.46  
% 0.30/0.46  % iso_tuple_UNIV_I
% 0.30/0.46  thf(fact_68_iso__tuple__UNIV__I,axiom,
% 0.30/0.46      ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 0.30/0.46  
% 0.30/0.46  % iso_tuple_UNIV_I
% 0.30/0.46  thf(fact_69_iso__tuple__UNIV__I,axiom,
% 0.30/0.46      ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.30/0.46  
% 0.30/0.46  % iso_tuple_UNIV_I
% 0.30/0.46  thf(fact_70_iso__tuple__UNIV__I,axiom,
% 0.30/0.46      ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 0.30/0.46  
% 0.30/0.46  % iso_tuple_UNIV_I
% 0.30/0.46  thf(fact_71_UNIV__I,axiom,
% 0.30/0.46      ! [X: produc696645085lle_fm] : ( member1474794996lle_fm @ X @ top_to775056195lle_fm ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_I
% 0.30/0.46  thf(fact_72_UNIV__I,axiom,
% 0.30/0.46      ! [X: produc1852595672lle_tv] : ( member146333935lle_tv @ X @ top_to138697918lle_tv ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_I
% 0.30/0.46  thf(fact_73_UNIV__I,axiom,
% 0.30/0.46      ! [X: produc931990033lle_tv] : ( member1569366824lle_tv @ X @ top_to449985143lle_tv ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_I
% 0.30/0.46  thf(fact_74_UNIV__I,axiom,
% 0.30/0.46      ! [X: produc1281043295at_nat] : ( member112824072at_nat @ X @ top_to1541413903at_nat ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_I
% 0.30/0.46  thf(fact_75_UNIV__I,axiom,
% 0.30/0.46      ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_I
% 0.30/0.46  thf(fact_76_UNIV__I,axiom,
% 0.30/0.46      ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_I
% 0.30/0.46  thf(fact_77_UNIV__I,axiom,
% 0.30/0.46      ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_I
% 0.30/0.46  thf(fact_78_UNIV__I,axiom,
% 0.30/0.46      ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_I
% 0.30/0.46  thf(fact_79_UNIV__I,axiom,
% 0.30/0.46      ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_I
% 0.30/0.46  thf(fact_80_top__apply,axiom,
% 0.30/0.46      ( top_to1299250770e_tv_o
% 0.30/0.46      = ( ^ [X4: paraco1605129243lle_tv] : top_top_o ) ) ).
% 0.30/0.46  
% 0.30/0.46  % top_apply
% 0.30/0.46  thf(fact_81_top__apply,axiom,
% 0.30/0.46      ( top_top_nat_o
% 0.30/0.46      = ( ^ [X4: nat] : top_top_o ) ) ).
% 0.30/0.46  
% 0.30/0.46  % top_apply
% 0.30/0.46  thf(fact_82_eval_Osimps_I3_J,axiom,
% 0.30/0.46      ! [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ P ) )
% 0.30/0.46        = ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1344940915le_Det @ $false ) @ ( paraco1344940915le_Det @ $true ) ) @ paraco793048302_Indet @ ( paraco1325918602e_eval @ I @ P ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % eval.simps(3)
% 0.30/0.46  thf(fact_83_inj__def,axiom,
% 0.30/0.46      ! [F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.30/0.46        ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 0.30/0.46        = ( ! [X4: produc1647334210lle_tv,Y4: produc1647334210lle_tv] :
% 0.30/0.46              ( ( ( F @ X4 )
% 0.30/0.46                = ( F @ Y4 ) )
% 0.30/0.46             => ( X4 = Y4 ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_def
% 0.30/0.46  thf(fact_84_inj__def,axiom,
% 0.30/0.46      ! [F: nat > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 0.30/0.46        = ( ! [X4: nat,Y4: nat] :
% 0.30/0.46              ( ( ( F @ X4 )
% 0.30/0.46                = ( F @ Y4 ) )
% 0.30/0.46             => ( X4 = Y4 ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_def
% 0.30/0.46  thf(fact_85_inj__def,axiom,
% 0.30/0.46      ! [F: produc194167194tv_nat > produc194167194tv_nat] :
% 0.30/0.46        ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 0.30/0.46        = ( ! [X4: produc194167194tv_nat,Y4: produc194167194tv_nat] :
% 0.30/0.46              ( ( ( F @ X4 )
% 0.30/0.46                = ( F @ Y4 ) )
% 0.30/0.46             => ( X4 = Y4 ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_def
% 0.30/0.46  thf(fact_86_inj__def,axiom,
% 0.30/0.46      ! [F: produc270694976lle_tv > produc270694976lle_tv] :
% 0.30/0.46        ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 0.30/0.46        = ( ! [X4: produc270694976lle_tv,Y4: produc270694976lle_tv] :
% 0.30/0.46              ( ( ( F @ X4 )
% 0.30/0.46                = ( F @ Y4 ) )
% 0.30/0.46             => ( X4 = Y4 ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_def
% 0.30/0.46  thf(fact_87_inj__def,axiom,
% 0.30/0.46      ! [F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.46        ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 0.30/0.46        = ( ! [X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 0.30/0.46              ( ( ( F @ X4 )
% 0.30/0.46                = ( F @ Y4 ) )
% 0.30/0.46             => ( X4 = Y4 ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_def
% 0.30/0.46  thf(fact_88_inj__def,axiom,
% 0.30/0.46      ! [F: nat > nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.46        = ( ! [X4: nat,Y4: nat] :
% 0.30/0.46              ( ( ( F @ X4 )
% 0.30/0.46                = ( F @ Y4 ) )
% 0.30/0.46             => ( X4 = Y4 ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_def
% 0.30/0.46  thf(fact_89_inj__def,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.46        = ( ! [X4: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
% 0.30/0.46              ( ( ( F @ X4 )
% 0.30/0.46                = ( F @ Y4 ) )
% 0.30/0.46             => ( X4 = Y4 ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_def
% 0.30/0.46  thf(fact_90_inj__eq,axiom,
% 0.30/0.46      ! [F: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.30/0.46        ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46          = ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_eq
% 0.30/0.46  thf(fact_91_inj__eq,axiom,
% 0.30/0.46      ! [F: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 0.30/0.46        ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46          = ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_eq
% 0.30/0.46  thf(fact_92_inj__eq,axiom,
% 0.30/0.46      ! [F: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.30/0.46        ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46          = ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_eq
% 0.30/0.46  thf(fact_93_inj__eq,axiom,
% 0.30/0.46      ! [F: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.30/0.46        ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46          = ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_eq
% 0.30/0.46  thf(fact_94_inj__eq,axiom,
% 0.30/0.46      ! [F: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.30/0.46        ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46          = ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_eq
% 0.30/0.46  thf(fact_95_inj__eq,axiom,
% 0.30/0.46      ! [F: nat > nat,X: nat,Y: nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46          = ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_eq
% 0.30/0.46  thf(fact_96_inj__eq,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46          = ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_eq
% 0.30/0.46  thf(fact_97_injI,axiom,
% 0.30/0.46      ! [F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.30/0.46        ( ! [X5: produc1647334210lle_tv,Y5: produc1647334210lle_tv] :
% 0.30/0.46            ( ( ( F @ X5 )
% 0.30/0.46              = ( F @ Y5 ) )
% 0.30/0.46           => ( X5 = Y5 ) )
% 0.30/0.46       => ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injI
% 0.30/0.46  thf(fact_98_injI,axiom,
% 0.30/0.46      ! [F: nat > paraco1605129243lle_tv] :
% 0.30/0.46        ( ! [X5: nat,Y5: nat] :
% 0.30/0.46            ( ( ( F @ X5 )
% 0.30/0.46              = ( F @ Y5 ) )
% 0.30/0.46           => ( X5 = Y5 ) )
% 0.30/0.46       => ( inj_on1955349912lle_tv @ F @ top_top_set_nat ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injI
% 0.30/0.46  thf(fact_99_injI,axiom,
% 0.30/0.46      ! [F: produc194167194tv_nat > produc194167194tv_nat] :
% 0.30/0.46        ( ! [X5: produc194167194tv_nat,Y5: produc194167194tv_nat] :
% 0.30/0.46            ( ( ( F @ X5 )
% 0.30/0.46              = ( F @ Y5 ) )
% 0.30/0.46           => ( X5 = Y5 ) )
% 0.30/0.46       => ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injI
% 0.30/0.46  thf(fact_100_injI,axiom,
% 0.30/0.46      ! [F: produc270694976lle_tv > produc270694976lle_tv] :
% 0.30/0.46        ( ! [X5: produc270694976lle_tv,Y5: produc270694976lle_tv] :
% 0.30/0.46            ( ( ( F @ X5 )
% 0.30/0.46              = ( F @ Y5 ) )
% 0.30/0.46           => ( X5 = Y5 ) )
% 0.30/0.46       => ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injI
% 0.30/0.46  thf(fact_101_injI,axiom,
% 0.30/0.46      ! [F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.46        ( ! [X5: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 0.30/0.46            ( ( ( F @ X5 )
% 0.30/0.46              = ( F @ Y5 ) )
% 0.30/0.46           => ( X5 = Y5 ) )
% 0.30/0.46       => ( inj_on26176689at_nat @ F @ top_to1555900337at_nat ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injI
% 0.30/0.46  thf(fact_102_injI,axiom,
% 0.30/0.46      ! [F: nat > nat] :
% 0.30/0.46        ( ! [X5: nat,Y5: nat] :
% 0.30/0.46            ( ( ( F @ X5 )
% 0.30/0.46              = ( F @ Y5 ) )
% 0.30/0.46           => ( X5 = Y5 ) )
% 0.30/0.46       => ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injI
% 0.30/0.46  thf(fact_103_injI,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.46        ( ! [X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] :
% 0.30/0.46            ( ( ( F @ X5 )
% 0.30/0.46              = ( F @ Y5 ) )
% 0.30/0.46           => ( X5 = Y5 ) )
% 0.30/0.46       => ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injI
% 0.30/0.46  thf(fact_104_injD,axiom,
% 0.30/0.46      ! [F: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.30/0.46        ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injD
% 0.30/0.46  thf(fact_105_injD,axiom,
% 0.30/0.46      ! [F: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 0.30/0.46        ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injD
% 0.30/0.46  thf(fact_106_injD,axiom,
% 0.30/0.46      ! [F: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.30/0.46        ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injD
% 0.30/0.46  thf(fact_107_injD,axiom,
% 0.30/0.46      ! [F: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.30/0.46        ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injD
% 0.30/0.46  thf(fact_108_injD,axiom,
% 0.30/0.46      ! [F: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.30/0.46        ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injD
% 0.30/0.46  thf(fact_109_injD,axiom,
% 0.30/0.46      ! [F: nat > nat,X: nat,Y: nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injD
% 0.30/0.46  thf(fact_110_injD,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( X = Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % injD
% 0.30/0.46  thf(fact_111_top__set__def,axiom,
% 0.30/0.46      ( top_to975729152tv_nat
% 0.30/0.46      = ( collec848462447tv_nat @ top_to900819589_nat_o ) ) ).
% 0.30/0.46  
% 0.30/0.46  % top_set_def
% 0.30/0.46  thf(fact_112_top__set__def,axiom,
% 0.30/0.46      ( top_to1411004326lle_tv
% 0.30/0.46      = ( collec924990229lle_tv @ top_to1889334367e_tv_o ) ) ).
% 0.30/0.46  
% 0.30/0.46  % top_set_def
% 0.30/0.46  thf(fact_113_top__set__def,axiom,
% 0.30/0.46      ( top_to1555900337at_nat
% 0.30/0.46      = ( collec7649004at_nat @ top_to632227436_nat_o ) ) ).
% 0.30/0.46  
% 0.30/0.46  % top_set_def
% 0.30/0.46  thf(fact_114_top__set__def,axiom,
% 0.30/0.46      ( top_top_set_nat
% 0.30/0.46      = ( collect_nat @ top_top_nat_o ) ) ).
% 0.30/0.46  
% 0.30/0.46  % top_set_def
% 0.30/0.46  thf(fact_115_top__set__def,axiom,
% 0.30/0.46      ( top_to1057771083lle_tv
% 0.30/0.46      = ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ) ).
% 0.30/0.46  
% 0.30/0.46  % top_set_def
% 0.30/0.46  thf(fact_116_change__tv__injection,axiom,
% 0.30/0.46      ! [F: nat > nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.46       => ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ F ) @ top_to1057771083lle_tv ) ) ).
% 0.30/0.46  
% 0.30/0.46  % change_tv_injection
% 0.30/0.46  thf(fact_117_UNIV__eq__I,axiom,
% 0.30/0.46      ! [A2: set_Pr2120184979lle_fm] :
% 0.30/0.46        ( ! [X5: produc696645085lle_fm] : ( member1474794996lle_fm @ X5 @ A2 )
% 0.30/0.46       => ( top_to775056195lle_fm = A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_eq_I
% 0.30/0.46  thf(fact_118_UNIV__eq__I,axiom,
% 0.30/0.46      ! [A2: set_Pr2061825550lle_tv] :
% 0.30/0.46        ( ! [X5: produc1852595672lle_tv] : ( member146333935lle_tv @ X5 @ A2 )
% 0.30/0.46       => ( top_to138697918lle_tv = A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_eq_I
% 0.30/0.46  thf(fact_119_UNIV__eq__I,axiom,
% 0.30/0.46      ! [A2: set_Pr560526279lle_tv] :
% 0.30/0.46        ( ! [X5: produc931990033lle_tv] : ( member1569366824lle_tv @ X5 @ A2 )
% 0.30/0.46       => ( top_to449985143lle_tv = A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_eq_I
% 0.30/0.46  thf(fact_120_UNIV__eq__I,axiom,
% 0.30/0.46      ! [A2: set_Pr1357842111at_nat] :
% 0.30/0.46        ( ! [X5: produc1281043295at_nat] : ( member112824072at_nat @ X5 @ A2 )
% 0.30/0.46       => ( top_to1541413903at_nat = A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_eq_I
% 0.30/0.46  thf(fact_121_UNIV__eq__I,axiom,
% 0.30/0.46      ! [A2: set_Pr1725653840tv_nat] :
% 0.30/0.46        ( ! [X5: produc194167194tv_nat] : ( member737151281tv_nat @ X5 @ A2 )
% 0.30/0.46       => ( top_to975729152tv_nat = A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_eq_I
% 0.30/0.46  thf(fact_122_UNIV__eq__I,axiom,
% 0.30/0.46      ! [A2: set_Pr13445366lle_tv] :
% 0.30/0.46        ( ! [X5: produc270694976lle_tv] : ( member813679063lle_tv @ X5 @ A2 )
% 0.30/0.46       => ( top_to1411004326lle_tv = A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_eq_I
% 0.30/0.46  thf(fact_123_UNIV__eq__I,axiom,
% 0.30/0.46      ! [A2: set_Pr1986765409at_nat] :
% 0.30/0.46        ( ! [X5: product_prod_nat_nat] : ( member701585322at_nat @ X5 @ A2 )
% 0.30/0.46       => ( top_to1555900337at_nat = A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_eq_I
% 0.30/0.46  thf(fact_124_UNIV__eq__I,axiom,
% 0.30/0.46      ! [A2: set_nat] :
% 0.30/0.46        ( ! [X5: nat] : ( member_nat @ X5 @ A2 )
% 0.30/0.46       => ( top_top_set_nat = A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_eq_I
% 0.30/0.46  thf(fact_125_UNIV__eq__I,axiom,
% 0.30/0.46      ! [A2: set_Pa1764573435lle_tv] :
% 0.30/0.46        ( ! [X5: paraco1605129243lle_tv] : ( member266900804lle_tv @ X5 @ A2 )
% 0.30/0.46       => ( top_to1057771083lle_tv = A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_eq_I
% 0.30/0.46  thf(fact_126_UNIV__witness,axiom,
% 0.30/0.46      ? [X5: produc696645085lle_fm] : ( member1474794996lle_fm @ X5 @ top_to775056195lle_fm ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_witness
% 0.30/0.46  thf(fact_127_UNIV__witness,axiom,
% 0.30/0.46      ? [X5: produc1852595672lle_tv] : ( member146333935lle_tv @ X5 @ top_to138697918lle_tv ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_witness
% 0.30/0.46  thf(fact_128_UNIV__witness,axiom,
% 0.30/0.46      ? [X5: produc931990033lle_tv] : ( member1569366824lle_tv @ X5 @ top_to449985143lle_tv ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_witness
% 0.30/0.46  thf(fact_129_UNIV__witness,axiom,
% 0.30/0.46      ? [X5: produc1281043295at_nat] : ( member112824072at_nat @ X5 @ top_to1541413903at_nat ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_witness
% 0.30/0.46  thf(fact_130_UNIV__witness,axiom,
% 0.30/0.46      ? [X5: produc194167194tv_nat] : ( member737151281tv_nat @ X5 @ top_to975729152tv_nat ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_witness
% 0.30/0.46  thf(fact_131_UNIV__witness,axiom,
% 0.30/0.46      ? [X5: produc270694976lle_tv] : ( member813679063lle_tv @ X5 @ top_to1411004326lle_tv ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_witness
% 0.30/0.46  thf(fact_132_UNIV__witness,axiom,
% 0.30/0.46      ? [X5: product_prod_nat_nat] : ( member701585322at_nat @ X5 @ top_to1555900337at_nat ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_witness
% 0.30/0.46  thf(fact_133_UNIV__witness,axiom,
% 0.30/0.46      ? [X5: nat] : ( member_nat @ X5 @ top_top_set_nat ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_witness
% 0.30/0.46  thf(fact_134_UNIV__witness,axiom,
% 0.30/0.46      ? [X5: paraco1605129243lle_tv] : ( member266900804lle_tv @ X5 @ top_to1057771083lle_tv ) ).
% 0.30/0.46  
% 0.30/0.46  % UNIV_witness
% 0.30/0.46  thf(fact_135_inj__onD,axiom,
% 0.30/0.46      ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.30/0.46        ( ( inj_on2112487900lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( ( member1531318361lle_tv @ X @ A2 )
% 0.30/0.46           => ( ( member1531318361lle_tv @ Y @ A2 )
% 0.30/0.46             => ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onD
% 0.30/0.46  thf(fact_136_inj__onD,axiom,
% 0.30/0.46      ! [F: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.30/0.46        ( ( inj_on552895452tv_nat @ F @ A2 )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( ( member737151281tv_nat @ X @ A2 )
% 0.30/0.46           => ( ( member737151281tv_nat @ Y @ A2 )
% 0.30/0.46             => ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onD
% 0.30/0.46  thf(fact_137_inj__onD,axiom,
% 0.30/0.46      ! [F: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.30/0.46        ( ( inj_on1745913142lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( ( member813679063lle_tv @ X @ A2 )
% 0.30/0.46           => ( ( member813679063lle_tv @ Y @ A2 )
% 0.30/0.46             => ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onD
% 0.30/0.46  thf(fact_138_inj__onD,axiom,
% 0.30/0.46      ! [F: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.30/0.46        ( ( inj_on26176689at_nat @ F @ A2 )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( ( member701585322at_nat @ X @ A2 )
% 0.30/0.46           => ( ( member701585322at_nat @ Y @ A2 )
% 0.30/0.46             => ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onD
% 0.30/0.46  thf(fact_139_inj__onD,axiom,
% 0.30/0.46      ! [F: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 0.30/0.46        ( ( inj_on1955349912lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( ( member_nat @ X @ A2 )
% 0.30/0.46           => ( ( member_nat @ Y @ A2 )
% 0.30/0.46             => ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onD
% 0.30/0.46  thf(fact_140_inj__onD,axiom,
% 0.30/0.46      ! [F: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F @ A2 )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( ( member_nat @ X @ A2 )
% 0.30/0.46           => ( ( member_nat @ Y @ A2 )
% 0.30/0.46             => ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onD
% 0.30/0.46  thf(fact_141_inj__onD,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = ( F @ Y ) )
% 0.30/0.46         => ( ( member266900804lle_tv @ X @ A2 )
% 0.30/0.46           => ( ( member266900804lle_tv @ Y @ A2 )
% 0.30/0.46             => ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onD
% 0.30/0.46  thf(fact_142_inj__onI,axiom,
% 0.30/0.46      ! [A2: set_Pr2014382200lle_tv,F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.30/0.46        ( ! [X5: produc1647334210lle_tv,Y5: produc1647334210lle_tv] :
% 0.30/0.46            ( ( member1531318361lle_tv @ X5 @ A2 )
% 0.30/0.46           => ( ( member1531318361lle_tv @ Y5 @ A2 )
% 0.30/0.46             => ( ( ( F @ X5 )
% 0.30/0.46                  = ( F @ Y5 ) )
% 0.30/0.46               => ( X5 = Y5 ) ) ) )
% 0.30/0.46       => ( inj_on2112487900lle_tv @ F @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onI
% 0.30/0.46  thf(fact_143_inj__onI,axiom,
% 0.30/0.46      ! [A2: set_Pr1725653840tv_nat,F: produc194167194tv_nat > produc194167194tv_nat] :
% 0.30/0.46        ( ! [X5: produc194167194tv_nat,Y5: produc194167194tv_nat] :
% 0.30/0.46            ( ( member737151281tv_nat @ X5 @ A2 )
% 0.30/0.46           => ( ( member737151281tv_nat @ Y5 @ A2 )
% 0.30/0.46             => ( ( ( F @ X5 )
% 0.30/0.46                  = ( F @ Y5 ) )
% 0.30/0.46               => ( X5 = Y5 ) ) ) )
% 0.30/0.46       => ( inj_on552895452tv_nat @ F @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onI
% 0.30/0.46  thf(fact_144_inj__onI,axiom,
% 0.30/0.46      ! [A2: set_Pr13445366lle_tv,F: produc270694976lle_tv > produc270694976lle_tv] :
% 0.30/0.46        ( ! [X5: produc270694976lle_tv,Y5: produc270694976lle_tv] :
% 0.30/0.46            ( ( member813679063lle_tv @ X5 @ A2 )
% 0.30/0.46           => ( ( member813679063lle_tv @ Y5 @ A2 )
% 0.30/0.46             => ( ( ( F @ X5 )
% 0.30/0.46                  = ( F @ Y5 ) )
% 0.30/0.46               => ( X5 = Y5 ) ) ) )
% 0.30/0.46       => ( inj_on1745913142lle_tv @ F @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onI
% 0.30/0.46  thf(fact_145_inj__onI,axiom,
% 0.30/0.46      ! [A2: set_Pr1986765409at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.46        ( ! [X5: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 0.30/0.46            ( ( member701585322at_nat @ X5 @ A2 )
% 0.30/0.46           => ( ( member701585322at_nat @ Y5 @ A2 )
% 0.30/0.46             => ( ( ( F @ X5 )
% 0.30/0.46                  = ( F @ Y5 ) )
% 0.30/0.46               => ( X5 = Y5 ) ) ) )
% 0.30/0.46       => ( inj_on26176689at_nat @ F @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onI
% 0.30/0.46  thf(fact_146_inj__onI,axiom,
% 0.30/0.46      ! [A2: set_nat,F: nat > paraco1605129243lle_tv] :
% 0.30/0.46        ( ! [X5: nat,Y5: nat] :
% 0.30/0.46            ( ( member_nat @ X5 @ A2 )
% 0.30/0.46           => ( ( member_nat @ Y5 @ A2 )
% 0.30/0.46             => ( ( ( F @ X5 )
% 0.30/0.46                  = ( F @ Y5 ) )
% 0.30/0.46               => ( X5 = Y5 ) ) ) )
% 0.30/0.46       => ( inj_on1955349912lle_tv @ F @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onI
% 0.30/0.46  thf(fact_147_inj__onI,axiom,
% 0.30/0.46      ! [A2: set_nat,F: nat > nat] :
% 0.30/0.46        ( ! [X5: nat,Y5: nat] :
% 0.30/0.46            ( ( member_nat @ X5 @ A2 )
% 0.30/0.46           => ( ( member_nat @ Y5 @ A2 )
% 0.30/0.46             => ( ( ( F @ X5 )
% 0.30/0.46                  = ( F @ Y5 ) )
% 0.30/0.46               => ( X5 = Y5 ) ) ) )
% 0.30/0.46       => ( inj_on_nat_nat @ F @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onI
% 0.30/0.46  thf(fact_148_inj__onI,axiom,
% 0.30/0.46      ! [A2: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.46        ( ! [X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] :
% 0.30/0.46            ( ( member266900804lle_tv @ X5 @ A2 )
% 0.30/0.46           => ( ( member266900804lle_tv @ Y5 @ A2 )
% 0.30/0.46             => ( ( ( F @ X5 )
% 0.30/0.46                  = ( F @ Y5 ) )
% 0.30/0.46               => ( X5 = Y5 ) ) ) )
% 0.30/0.46       => ( inj_on772319074lle_tv @ F @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_onI
% 0.30/0.46  thf(fact_149_inj__on__def,axiom,
% 0.30/0.46      ( inj_on2112487900lle_tv
% 0.30/0.46      = ( ^ [F2: produc1647334210lle_tv > produc1647334210lle_tv,A3: set_Pr2014382200lle_tv] :
% 0.30/0.46          ! [X4: produc1647334210lle_tv] :
% 0.30/0.46            ( ( member1531318361lle_tv @ X4 @ A3 )
% 0.30/0.46           => ! [Y4: produc1647334210lle_tv] :
% 0.30/0.46                ( ( member1531318361lle_tv @ Y4 @ A3 )
% 0.30/0.46               => ( ( ( F2 @ X4 )
% 0.30/0.46                    = ( F2 @ Y4 ) )
% 0.30/0.46                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_def
% 0.30/0.46  thf(fact_150_inj__on__def,axiom,
% 0.30/0.46      ( inj_on552895452tv_nat
% 0.30/0.46      = ( ^ [F2: produc194167194tv_nat > produc194167194tv_nat,A3: set_Pr1725653840tv_nat] :
% 0.30/0.46          ! [X4: produc194167194tv_nat] :
% 0.30/0.46            ( ( member737151281tv_nat @ X4 @ A3 )
% 0.30/0.46           => ! [Y4: produc194167194tv_nat] :
% 0.30/0.46                ( ( member737151281tv_nat @ Y4 @ A3 )
% 0.30/0.46               => ( ( ( F2 @ X4 )
% 0.30/0.46                    = ( F2 @ Y4 ) )
% 0.30/0.46                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_def
% 0.30/0.46  thf(fact_151_inj__on__def,axiom,
% 0.30/0.46      ( inj_on1745913142lle_tv
% 0.30/0.46      = ( ^ [F2: produc270694976lle_tv > produc270694976lle_tv,A3: set_Pr13445366lle_tv] :
% 0.30/0.46          ! [X4: produc270694976lle_tv] :
% 0.30/0.46            ( ( member813679063lle_tv @ X4 @ A3 )
% 0.30/0.46           => ! [Y4: produc270694976lle_tv] :
% 0.30/0.46                ( ( member813679063lle_tv @ Y4 @ A3 )
% 0.30/0.46               => ( ( ( F2 @ X4 )
% 0.30/0.46                    = ( F2 @ Y4 ) )
% 0.30/0.46                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_def
% 0.30/0.46  thf(fact_152_inj__on__def,axiom,
% 0.30/0.46      ( inj_on26176689at_nat
% 0.30/0.46      = ( ^ [F2: product_prod_nat_nat > product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 0.30/0.46          ! [X4: product_prod_nat_nat] :
% 0.30/0.46            ( ( member701585322at_nat @ X4 @ A3 )
% 0.30/0.46           => ! [Y4: product_prod_nat_nat] :
% 0.30/0.46                ( ( member701585322at_nat @ Y4 @ A3 )
% 0.30/0.46               => ( ( ( F2 @ X4 )
% 0.30/0.46                    = ( F2 @ Y4 ) )
% 0.30/0.46                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_def
% 0.30/0.46  thf(fact_153_inj__on__def,axiom,
% 0.30/0.46      ( inj_on1955349912lle_tv
% 0.30/0.46      = ( ^ [F2: nat > paraco1605129243lle_tv,A3: set_nat] :
% 0.30/0.46          ! [X4: nat] :
% 0.30/0.46            ( ( member_nat @ X4 @ A3 )
% 0.30/0.46           => ! [Y4: nat] :
% 0.30/0.46                ( ( member_nat @ Y4 @ A3 )
% 0.30/0.46               => ( ( ( F2 @ X4 )
% 0.30/0.46                    = ( F2 @ Y4 ) )
% 0.30/0.46                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_def
% 0.30/0.46  thf(fact_154_inj__on__def,axiom,
% 0.30/0.46      ( inj_on_nat_nat
% 0.30/0.46      = ( ^ [F2: nat > nat,A3: set_nat] :
% 0.30/0.46          ! [X4: nat] :
% 0.30/0.46            ( ( member_nat @ X4 @ A3 )
% 0.30/0.46           => ! [Y4: nat] :
% 0.30/0.46                ( ( member_nat @ Y4 @ A3 )
% 0.30/0.46               => ( ( ( F2 @ X4 )
% 0.30/0.46                    = ( F2 @ Y4 ) )
% 0.30/0.46                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_def
% 0.30/0.46  thf(fact_155_inj__on__def,axiom,
% 0.30/0.46      ( inj_on772319074lle_tv
% 0.30/0.46      = ( ^ [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A3: set_Pa1764573435lle_tv] :
% 0.30/0.46          ! [X4: paraco1605129243lle_tv] :
% 0.30/0.46            ( ( member266900804lle_tv @ X4 @ A3 )
% 0.30/0.46           => ! [Y4: paraco1605129243lle_tv] :
% 0.30/0.46                ( ( member266900804lle_tv @ Y4 @ A3 )
% 0.30/0.46               => ( ( ( F2 @ X4 )
% 0.30/0.46                    = ( F2 @ Y4 ) )
% 0.30/0.46                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_def
% 0.30/0.46  thf(fact_156_inj__on__cong,axiom,
% 0.30/0.46      ! [A2: set_Pr2014382200lle_tv,F: produc1647334210lle_tv > produc1647334210lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv] :
% 0.30/0.46        ( ! [A4: produc1647334210lle_tv] :
% 0.30/0.46            ( ( member1531318361lle_tv @ A4 @ A2 )
% 0.30/0.46           => ( ( F @ A4 )
% 0.30/0.46              = ( G @ A4 ) ) )
% 0.30/0.46       => ( ( inj_on2112487900lle_tv @ F @ A2 )
% 0.30/0.46          = ( inj_on2112487900lle_tv @ G @ A2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_cong
% 0.30/0.46  thf(fact_157_inj__on__cong,axiom,
% 0.30/0.46      ! [A2: set_Pr1725653840tv_nat,F: produc194167194tv_nat > produc194167194tv_nat,G: produc194167194tv_nat > produc194167194tv_nat] :
% 0.30/0.46        ( ! [A4: produc194167194tv_nat] :
% 0.30/0.46            ( ( member737151281tv_nat @ A4 @ A2 )
% 0.30/0.46           => ( ( F @ A4 )
% 0.30/0.46              = ( G @ A4 ) ) )
% 0.30/0.46       => ( ( inj_on552895452tv_nat @ F @ A2 )
% 0.30/0.46          = ( inj_on552895452tv_nat @ G @ A2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_cong
% 0.30/0.46  thf(fact_158_inj__on__cong,axiom,
% 0.30/0.46      ! [A2: set_Pr13445366lle_tv,F: produc270694976lle_tv > produc270694976lle_tv,G: produc270694976lle_tv > produc270694976lle_tv] :
% 0.30/0.46        ( ! [A4: produc270694976lle_tv] :
% 0.30/0.46            ( ( member813679063lle_tv @ A4 @ A2 )
% 0.30/0.46           => ( ( F @ A4 )
% 0.30/0.46              = ( G @ A4 ) ) )
% 0.30/0.46       => ( ( inj_on1745913142lle_tv @ F @ A2 )
% 0.30/0.46          = ( inj_on1745913142lle_tv @ G @ A2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_cong
% 0.30/0.46  thf(fact_159_inj__on__cong,axiom,
% 0.30/0.46      ! [A2: set_Pr1986765409at_nat,F: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.46        ( ! [A4: product_prod_nat_nat] :
% 0.30/0.46            ( ( member701585322at_nat @ A4 @ A2 )
% 0.30/0.46           => ( ( F @ A4 )
% 0.30/0.46              = ( G @ A4 ) ) )
% 0.30/0.46       => ( ( inj_on26176689at_nat @ F @ A2 )
% 0.30/0.46          = ( inj_on26176689at_nat @ G @ A2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_cong
% 0.30/0.46  thf(fact_160_inj__on__cong,axiom,
% 0.30/0.46      ! [A2: set_nat,F: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 0.30/0.46        ( ! [A4: nat] :
% 0.30/0.46            ( ( member_nat @ A4 @ A2 )
% 0.30/0.46           => ( ( F @ A4 )
% 0.30/0.46              = ( G @ A4 ) ) )
% 0.30/0.46       => ( ( inj_on1955349912lle_tv @ F @ A2 )
% 0.30/0.46          = ( inj_on1955349912lle_tv @ G @ A2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_cong
% 0.30/0.46  thf(fact_161_inj__on__cong,axiom,
% 0.30/0.46      ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 0.30/0.46        ( ! [A4: nat] :
% 0.30/0.46            ( ( member_nat @ A4 @ A2 )
% 0.30/0.46           => ( ( F @ A4 )
% 0.30/0.46              = ( G @ A4 ) ) )
% 0.30/0.46       => ( ( inj_on_nat_nat @ F @ A2 )
% 0.30/0.46          = ( inj_on_nat_nat @ G @ A2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_cong
% 0.30/0.46  thf(fact_162_inj__on__cong,axiom,
% 0.30/0.46      ! [A2: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.46        ( ! [A4: paraco1605129243lle_tv] :
% 0.30/0.46            ( ( member266900804lle_tv @ A4 @ A2 )
% 0.30/0.46           => ( ( F @ A4 )
% 0.30/0.46              = ( G @ A4 ) ) )
% 0.30/0.46       => ( ( inj_on772319074lle_tv @ F @ A2 )
% 0.30/0.46          = ( inj_on772319074lle_tv @ G @ A2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_cong
% 0.30/0.46  thf(fact_163_inj__on__eq__iff,axiom,
% 0.30/0.46      ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.30/0.46        ( ( inj_on2112487900lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( member1531318361lle_tv @ X @ A2 )
% 0.30/0.46         => ( ( member1531318361lle_tv @ Y @ A2 )
% 0.30/0.46           => ( ( ( F @ X )
% 0.30/0.46                = ( F @ Y ) )
% 0.30/0.46              = ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_eq_iff
% 0.30/0.46  thf(fact_164_inj__on__eq__iff,axiom,
% 0.30/0.46      ! [F: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.30/0.46        ( ( inj_on552895452tv_nat @ F @ A2 )
% 0.30/0.46       => ( ( member737151281tv_nat @ X @ A2 )
% 0.30/0.46         => ( ( member737151281tv_nat @ Y @ A2 )
% 0.30/0.46           => ( ( ( F @ X )
% 0.30/0.46                = ( F @ Y ) )
% 0.30/0.46              = ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_eq_iff
% 0.30/0.46  thf(fact_165_inj__on__eq__iff,axiom,
% 0.30/0.46      ! [F: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.30/0.46        ( ( inj_on1745913142lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( member813679063lle_tv @ X @ A2 )
% 0.30/0.46         => ( ( member813679063lle_tv @ Y @ A2 )
% 0.30/0.46           => ( ( ( F @ X )
% 0.30/0.46                = ( F @ Y ) )
% 0.30/0.46              = ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_eq_iff
% 0.30/0.46  thf(fact_166_inj__on__eq__iff,axiom,
% 0.30/0.46      ! [F: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.30/0.46        ( ( inj_on26176689at_nat @ F @ A2 )
% 0.30/0.46       => ( ( member701585322at_nat @ X @ A2 )
% 0.30/0.46         => ( ( member701585322at_nat @ Y @ A2 )
% 0.30/0.46           => ( ( ( F @ X )
% 0.30/0.46                = ( F @ Y ) )
% 0.30/0.46              = ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_eq_iff
% 0.30/0.46  thf(fact_167_inj__on__eq__iff,axiom,
% 0.30/0.46      ! [F: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 0.30/0.46        ( ( inj_on1955349912lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( member_nat @ X @ A2 )
% 0.30/0.46         => ( ( member_nat @ Y @ A2 )
% 0.30/0.46           => ( ( ( F @ X )
% 0.30/0.46                = ( F @ Y ) )
% 0.30/0.46              = ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_eq_iff
% 0.30/0.46  thf(fact_168_inj__on__eq__iff,axiom,
% 0.30/0.46      ! [F: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F @ A2 )
% 0.30/0.46       => ( ( member_nat @ X @ A2 )
% 0.30/0.46         => ( ( member_nat @ Y @ A2 )
% 0.30/0.46           => ( ( ( F @ X )
% 0.30/0.46                = ( F @ Y ) )
% 0.30/0.46              = ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_eq_iff
% 0.30/0.46  thf(fact_169_inj__on__eq__iff,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( member266900804lle_tv @ X @ A2 )
% 0.30/0.46         => ( ( member266900804lle_tv @ Y @ A2 )
% 0.30/0.46           => ( ( ( F @ X )
% 0.30/0.46                = ( F @ Y ) )
% 0.30/0.46              = ( X = Y ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_eq_iff
% 0.30/0.46  thf(fact_170_inj__on__contraD,axiom,
% 0.30/0.46      ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 0.30/0.46        ( ( inj_on2112487900lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( X != Y )
% 0.30/0.46         => ( ( member1531318361lle_tv @ X @ A2 )
% 0.30/0.46           => ( ( member1531318361lle_tv @ Y @ A2 )
% 0.30/0.46             => ( ( F @ X )
% 0.30/0.46               != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_contraD
% 0.30/0.46  thf(fact_171_inj__on__contraD,axiom,
% 0.30/0.46      ! [F: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 0.30/0.46        ( ( inj_on552895452tv_nat @ F @ A2 )
% 0.30/0.46       => ( ( X != Y )
% 0.30/0.46         => ( ( member737151281tv_nat @ X @ A2 )
% 0.30/0.46           => ( ( member737151281tv_nat @ Y @ A2 )
% 0.30/0.46             => ( ( F @ X )
% 0.30/0.46               != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_contraD
% 0.30/0.46  thf(fact_172_inj__on__contraD,axiom,
% 0.30/0.46      ! [F: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 0.30/0.46        ( ( inj_on1745913142lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( X != Y )
% 0.30/0.46         => ( ( member813679063lle_tv @ X @ A2 )
% 0.30/0.46           => ( ( member813679063lle_tv @ Y @ A2 )
% 0.30/0.46             => ( ( F @ X )
% 0.30/0.46               != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_contraD
% 0.30/0.46  thf(fact_173_inj__on__contraD,axiom,
% 0.30/0.46      ! [F: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.30/0.46        ( ( inj_on26176689at_nat @ F @ A2 )
% 0.30/0.46       => ( ( X != Y )
% 0.30/0.46         => ( ( member701585322at_nat @ X @ A2 )
% 0.30/0.46           => ( ( member701585322at_nat @ Y @ A2 )
% 0.30/0.46             => ( ( F @ X )
% 0.30/0.46               != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_contraD
% 0.30/0.46  thf(fact_174_inj__on__contraD,axiom,
% 0.30/0.46      ! [F: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 0.30/0.46        ( ( inj_on1955349912lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( X != Y )
% 0.30/0.46         => ( ( member_nat @ X @ A2 )
% 0.30/0.46           => ( ( member_nat @ Y @ A2 )
% 0.30/0.46             => ( ( F @ X )
% 0.30/0.46               != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_contraD
% 0.30/0.46  thf(fact_175_inj__on__contraD,axiom,
% 0.30/0.46      ! [F: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F @ A2 )
% 0.30/0.46       => ( ( X != Y )
% 0.30/0.46         => ( ( member_nat @ X @ A2 )
% 0.30/0.46           => ( ( member_nat @ Y @ A2 )
% 0.30/0.46             => ( ( F @ X )
% 0.30/0.46               != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_contraD
% 0.30/0.46  thf(fact_176_inj__on__contraD,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( X != Y )
% 0.30/0.46         => ( ( member266900804lle_tv @ X @ A2 )
% 0.30/0.46           => ( ( member266900804lle_tv @ Y @ A2 )
% 0.30/0.46             => ( ( F @ X )
% 0.30/0.46               != ( F @ Y ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_contraD
% 0.30/0.46  thf(fact_177_inj__on__inverseI,axiom,
% 0.30/0.46      ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 0.30/0.46        ( ! [X5: nat] :
% 0.30/0.46            ( ( member_nat @ X5 @ A2 )
% 0.30/0.46           => ( ( G @ ( F @ X5 ) )
% 0.30/0.46              = X5 ) )
% 0.30/0.46       => ( inj_on_nat_nat @ F @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_inverseI
% 0.30/0.46  thf(fact_178_inj__on__inverseI,axiom,
% 0.30/0.46      ! [A2: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.46        ( ! [X5: paraco1605129243lle_tv] :
% 0.30/0.46            ( ( member266900804lle_tv @ X5 @ A2 )
% 0.30/0.46           => ( ( G @ ( F @ X5 ) )
% 0.30/0.46              = X5 ) )
% 0.30/0.46       => ( inj_on772319074lle_tv @ F @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % inj_on_inverseI
% 0.30/0.46  thf(fact_179_fm_Oinduct,axiom,
% 0.30/0.46      ! [P3: paraco1604210848lle_fm > $o,Fm: paraco1604210848lle_fm] :
% 0.30/0.46        ( ! [X5: list_char] : ( P3 @ ( paraco1480028776le_Pro @ X5 ) )
% 0.30/0.46       => ( ( P3 @ paraco367965286_Truth )
% 0.30/0.46         => ( ! [X5: paraco1604210848lle_fm] :
% 0.30/0.46                ( ( P3 @ X5 )
% 0.30/0.46               => ( P3 @ ( paraco445776468le_Neg @ X5 ) ) )
% 0.30/0.46           => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.30/0.46                  ( ( P3 @ X1a )
% 0.30/0.46                 => ( ( P3 @ X22 )
% 0.30/0.46                   => ( P3 @ ( paraco69239110le_Con @ X1a @ X22 ) ) ) )
% 0.30/0.46             => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.30/0.46                    ( ( P3 @ X1a )
% 0.30/0.46                   => ( ( P3 @ X22 )
% 0.30/0.46                     => ( P3 @ ( paraco1389086619le_Eql @ X1a @ X22 ) ) ) )
% 0.30/0.46               => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 0.30/0.46                      ( ( P3 @ X1a )
% 0.30/0.46                     => ( ( P3 @ X22 )
% 0.30/0.46                       => ( P3 @ ( paraco1745535428le_Eql @ X1a @ X22 ) ) ) )
% 0.30/0.46                 => ( P3 @ Fm ) ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.induct
% 0.30/0.46  thf(fact_180_fm_Oexhaust,axiom,
% 0.30/0.46      ! [Y: paraco1604210848lle_fm] :
% 0.30/0.46        ( ! [X12: list_char] :
% 0.30/0.46            ( Y
% 0.30/0.46           != ( paraco1480028776le_Pro @ X12 ) )
% 0.30/0.46       => ( ( Y != paraco367965286_Truth )
% 0.30/0.46         => ( ! [X32: paraco1604210848lle_fm] :
% 0.30/0.46                ( Y
% 0.30/0.46               != ( paraco445776468le_Neg @ X32 ) )
% 0.30/0.46           => ( ! [X412: paraco1604210848lle_fm,X422: paraco1604210848lle_fm] :
% 0.30/0.46                  ( Y
% 0.30/0.46                 != ( paraco69239110le_Con @ X412 @ X422 ) )
% 0.30/0.46             => ( ! [X512: paraco1604210848lle_fm,X522: paraco1604210848lle_fm] :
% 0.30/0.46                    ( Y
% 0.30/0.46                   != ( paraco1389086619le_Eql @ X512 @ X522 ) )
% 0.30/0.46               => ~ ! [X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 0.30/0.46                      ( Y
% 0.30/0.46                     != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.exhaust
% 0.30/0.46  thf(fact_181_props_Ocases,axiom,
% 0.30/0.46      ! [X: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( X != paraco367965286_Truth )
% 0.30/0.46       => ( ! [S2: list_char] :
% 0.30/0.46              ( X
% 0.30/0.46             != ( paraco1480028776le_Pro @ S2 ) )
% 0.30/0.46         => ( ! [P4: paraco1604210848lle_fm] :
% 0.30/0.46                ( X
% 0.30/0.46               != ( paraco445776468le_Neg @ P4 ) )
% 0.30/0.46           => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.30/0.46                  ( X
% 0.30/0.46                 != ( paraco69239110le_Con @ P4 @ Q3 ) )
% 0.30/0.46             => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.30/0.46                    ( X
% 0.30/0.46                   != ( paraco1389086619le_Eql @ P4 @ Q3 ) )
% 0.30/0.46               => ~ ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.30/0.46                      ( X
% 0.30/0.46                     != ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % props.cases
% 0.30/0.46  thf(fact_182_props_Oinduct,axiom,
% 0.30/0.46      ! [P3: paraco1604210848lle_fm > $o,A0: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( P3 @ paraco367965286_Truth )
% 0.30/0.46       => ( ! [S2: list_char] : ( P3 @ ( paraco1480028776le_Pro @ S2 ) )
% 0.30/0.46         => ( ! [P4: paraco1604210848lle_fm] :
% 0.30/0.46                ( ( P3 @ P4 )
% 0.30/0.46               => ( P3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 0.30/0.46           => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.30/0.46                  ( ( P3 @ P4 )
% 0.30/0.46                 => ( ( P3 @ Q3 )
% 0.30/0.46                   => ( P3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) ) )
% 0.30/0.46             => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.30/0.46                    ( ( P3 @ P4 )
% 0.30/0.46                   => ( ( P3 @ Q3 )
% 0.30/0.46                     => ( P3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) ) )
% 0.30/0.46               => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.30/0.46                      ( ( P3 @ P4 )
% 0.30/0.46                     => ( ( P3 @ Q3 )
% 0.30/0.46                       => ( P3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) )
% 0.30/0.46                 => ( P3 @ A0 ) ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % props.induct
% 0.30/0.46  thf(fact_183_old_Obool_Osimps_I4_J,axiom,
% 0.30/0.46      ! [F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( produc234482697lle_tv @ F1 @ F22 @ $false )
% 0.30/0.46        = F22 ) ).
% 0.30/0.46  
% 0.30/0.46  % old.bool.simps(4)
% 0.30/0.46  thf(fact_184_old_Obool_Osimps_I3_J,axiom,
% 0.30/0.46      ! [F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( produc234482697lle_tv @ F1 @ F22 @ $true )
% 0.30/0.46        = F1 ) ).
% 0.30/0.46  
% 0.30/0.46  % old.bool.simps(3)
% 0.30/0.46  thf(fact_185_bool_Osplit__sel,axiom,
% 0.30/0.46      ! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool: $o] :
% 0.30/0.46        ( ( P3 @ ( produc234482697lle_tv @ F1 @ F22 @ Bool ) )
% 0.30/0.46        = ( ( Bool
% 0.30/0.46           => ( P3 @ F1 ) )
% 0.30/0.46          & ( ~ Bool
% 0.30/0.46           => ( P3 @ F22 ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % bool.split_sel
% 0.30/0.46  thf(fact_186_fm_Oinject_I1_J,axiom,
% 0.30/0.46      ! [X1: list_char,Y1: list_char] :
% 0.30/0.46        ( ( ( paraco1480028776le_Pro @ X1 )
% 0.30/0.46          = ( paraco1480028776le_Pro @ Y1 ) )
% 0.30/0.46        = ( X1 = Y1 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.inject(1)
% 0.30/0.46  thf(fact_187_eval_Osimps_I1_J,axiom,
% 0.30/0.46      ! [I: list_char > paraco1605129243lle_tv,S3: list_char] :
% 0.30/0.46        ( ( paraco1325918602e_eval @ I @ ( paraco1480028776le_Pro @ S3 ) )
% 0.30/0.46        = ( I @ S3 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % eval.simps(1)
% 0.30/0.46  thf(fact_188_fm_Odistinct_I3_J,axiom,
% 0.30/0.46      ! [X1: list_char,X3: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco1480028776le_Pro @ X1 )
% 0.30/0.46       != ( paraco445776468le_Neg @ X3 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(3)
% 0.30/0.46  thf(fact_189_fm_Odistinct_I5_J,axiom,
% 0.30/0.46      ! [X1: list_char,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco1480028776le_Pro @ X1 )
% 0.30/0.46       != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(5)
% 0.30/0.46  thf(fact_190_fm_Odistinct_I9_J,axiom,
% 0.30/0.46      ! [X1: list_char,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco1480028776le_Pro @ X1 )
% 0.30/0.46       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(9)
% 0.30/0.46  thf(fact_191_fm_Odistinct_I7_J,axiom,
% 0.30/0.46      ! [X1: list_char,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( paraco1480028776le_Pro @ X1 )
% 0.30/0.46       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(7)
% 0.30/0.46  thf(fact_192_fm_Odistinct_I1_J,axiom,
% 0.30/0.46      ! [X1: list_char] :
% 0.30/0.46        ( ( paraco1480028776le_Pro @ X1 )
% 0.30/0.46       != paraco367965286_Truth ) ).
% 0.30/0.46  
% 0.30/0.46  % fm.distinct(1)
% 0.30/0.46  thf(fact_193_bool_Osplit__sel__asm,axiom,
% 0.30/0.46      ! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool: $o] :
% 0.30/0.46        ( ( P3 @ ( produc234482697lle_tv @ F1 @ F22 @ Bool ) )
% 0.30/0.46        = ( ~ ( ( Bool
% 0.30/0.46                & ~ ( P3 @ F1 ) )
% 0.30/0.46              | ( ~ Bool
% 0.30/0.46                & ~ ( P3 @ F22 ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % bool.split_sel_asm
% 0.30/0.46  thf(fact_194_bool_Ocase__distrib,axiom,
% 0.30/0.46      ! [H: paraco1605129243lle_tv > paraco1605129243lle_tv,F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool: $o] :
% 0.30/0.46        ( ( H @ ( produc234482697lle_tv @ F1 @ F22 @ Bool ) )
% 0.30/0.46        = ( produc234482697lle_tv @ ( H @ F1 ) @ ( H @ F22 ) @ Bool ) ) ).
% 0.30/0.46  
% 0.30/0.46  % bool.case_distrib
% 0.30/0.46  thf(fact_195_bool_Ocase__eq__if,axiom,
% 0.30/0.46      ( produc234482697lle_tv
% 0.30/0.46      = ( ^ [F12: paraco1605129243lle_tv,F23: paraco1605129243lle_tv,Bool2: $o] : ( if_Par1134130401lle_tv @ Bool2 @ F12 @ F23 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % bool.case_eq_if
% 0.30/0.46  thf(fact_196_top__empty__eq,axiom,
% 0.30/0.46      ( top_top_nat_o
% 0.30/0.46      = ( ^ [X4: nat] : ( member_nat @ X4 @ top_top_set_nat ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % top_empty_eq
% 0.30/0.46  thf(fact_197_top__empty__eq,axiom,
% 0.30/0.46      ( top_to1299250770e_tv_o
% 0.30/0.46      = ( ^ [X4: paraco1605129243lle_tv] : ( member266900804lle_tv @ X4 @ top_to1057771083lle_tv ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % top_empty_eq
% 0.30/0.46  thf(fact_198_eval_Ocases,axiom,
% 0.30/0.46      ! [X: produc696645085lle_fm] :
% 0.30/0.46        ( ! [I3: list_char > paraco1605129243lle_tv,S2: list_char] :
% 0.30/0.46            ( X
% 0.30/0.46           != ( produc1710735575lle_fm @ I3 @ ( paraco1480028776le_Pro @ S2 ) ) )
% 0.30/0.46       => ( ! [I3: list_char > paraco1605129243lle_tv] :
% 0.30/0.46              ( X
% 0.30/0.46             != ( produc1710735575lle_fm @ I3 @ paraco367965286_Truth ) )
% 0.30/0.46         => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm] :
% 0.30/0.46                ( X
% 0.30/0.46               != ( produc1710735575lle_fm @ I3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 0.30/0.46           => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.30/0.46                  ( X
% 0.30/0.46                 != ( produc1710735575lle_fm @ I3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) )
% 0.30/0.46             => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.30/0.46                    ( X
% 0.30/0.46                   != ( produc1710735575lle_fm @ I3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) )
% 0.30/0.46               => ~ ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 0.30/0.46                      ( X
% 0.30/0.46                     != ( produc1710735575lle_fm @ I3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % eval.cases
% 0.30/0.46  thf(fact_199_old_Oprod_Oinject,axiom,
% 0.30/0.46      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( ( produc1710735575lle_fm @ A @ B )
% 0.30/0.46          = ( produc1710735575lle_fm @ A5 @ B3 ) )
% 0.30/0.46        = ( ( A = A5 )
% 0.30/0.46          & ( B = B3 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % old.prod.inject
% 0.30/0.46  thf(fact_200_old_Oprod_Oinject,axiom,
% 0.30/0.46      ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( ( produc1680557635lle_tv @ A @ B )
% 0.30/0.46          = ( produc1680557635lle_tv @ A5 @ B3 ) )
% 0.30/0.46        = ( ( A = A5 )
% 0.30/0.46          & ( B = B3 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % old.prod.inject
% 0.30/0.46  thf(fact_201_prod_Oinject,axiom,
% 0.30/0.46      ! [X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm,Y1: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( ( produc1710735575lle_fm @ X1 @ X2 )
% 0.30/0.46          = ( produc1710735575lle_fm @ Y1 @ Y2 ) )
% 0.30/0.46        = ( ( X1 = Y1 )
% 0.30/0.46          & ( X2 = Y2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % prod.inject
% 0.30/0.46  thf(fact_202_prod_Oinject,axiom,
% 0.30/0.46      ! [X1: nat > nat,X2: paraco1605129243lle_tv,Y1: nat > nat,Y2: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( ( produc1680557635lle_tv @ X1 @ X2 )
% 0.30/0.46          = ( produc1680557635lle_tv @ Y1 @ Y2 ) )
% 0.30/0.46        = ( ( X1 = Y1 )
% 0.30/0.46          & ( X2 = Y2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % prod.inject
% 0.30/0.46  thf(fact_203_apfst__conv,axiom,
% 0.30/0.46      ! [F: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( produc1942165868lle_fm @ F @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.30/0.46        = ( produc1710735575lle_fm @ ( F @ X ) @ Y ) ) ).
% 0.30/0.46  
% 0.30/0.46  % apfst_conv
% 0.30/0.46  thf(fact_204_apfst__conv,axiom,
% 0.30/0.46      ! [F: ( nat > nat ) > nat > nat,X: nat > nat,Y: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( produc939316703lle_tv @ F @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.30/0.46        = ( produc1680557635lle_tv @ ( F @ X ) @ Y ) ) ).
% 0.30/0.46  
% 0.30/0.46  % apfst_conv
% 0.30/0.46  thf(fact_205_apsnd__conv,axiom,
% 0.30/0.46      ! [F: paraco1604210848lle_fm > paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( produc1807466521lle_tv @ F @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.30/0.46        = ( produc1710735575lle_fm @ X @ ( F @ Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % apsnd_conv
% 0.30/0.46  thf(fact_206_apsnd__conv,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: nat > nat,Y: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( produc109093078at_nat @ F @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.30/0.46        = ( produc1680557635lle_tv @ X @ ( F @ Y ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % apsnd_conv
% 0.30/0.46  thf(fact_207_old_Oprod_Oinducts,axiom,
% 0.30/0.46      ! [P3: produc696645085lle_fm > $o,Prod: produc696645085lle_fm] :
% 0.30/0.46        ( ! [A4: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A4 @ B2 ) )
% 0.30/0.46       => ( P3 @ Prod ) ) ).
% 0.30/0.46  
% 0.30/0.46  % old.prod.inducts
% 0.30/0.46  thf(fact_208_old_Oprod_Oinducts,axiom,
% 0.30/0.46      ! [P3: produc931990033lle_tv > $o,Prod: produc931990033lle_tv] :
% 0.30/0.46        ( ! [A4: nat > nat,B2: paraco1605129243lle_tv] : ( P3 @ ( produc1680557635lle_tv @ A4 @ B2 ) )
% 0.30/0.46       => ( P3 @ Prod ) ) ).
% 0.30/0.46  
% 0.30/0.46  % old.prod.inducts
% 0.30/0.46  thf(fact_209_old_Oprod_Oexhaust,axiom,
% 0.30/0.46      ! [Y: produc696645085lle_fm] :
% 0.30/0.46        ~ ! [A4: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] :
% 0.30/0.46            ( Y
% 0.30/0.46           != ( produc1710735575lle_fm @ A4 @ B2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % old.prod.exhaust
% 0.30/0.46  thf(fact_210_old_Oprod_Oexhaust,axiom,
% 0.30/0.46      ! [Y: produc931990033lle_tv] :
% 0.30/0.46        ~ ! [A4: nat > nat,B2: paraco1605129243lle_tv] :
% 0.30/0.46            ( Y
% 0.30/0.46           != ( produc1680557635lle_tv @ A4 @ B2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % old.prod.exhaust
% 0.30/0.46  thf(fact_211_Pair__inject,axiom,
% 0.30/0.46      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( ( produc1710735575lle_fm @ A @ B )
% 0.30/0.46          = ( produc1710735575lle_fm @ A5 @ B3 ) )
% 0.30/0.46       => ~ ( ( A = A5 )
% 0.30/0.46           => ( B != B3 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % Pair_inject
% 0.30/0.46  thf(fact_212_Pair__inject,axiom,
% 0.30/0.46      ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( ( produc1680557635lle_tv @ A @ B )
% 0.30/0.46          = ( produc1680557635lle_tv @ A5 @ B3 ) )
% 0.30/0.46       => ~ ( ( A = A5 )
% 0.30/0.46           => ( B != B3 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % Pair_inject
% 0.30/0.46  thf(fact_213_prod__cases,axiom,
% 0.30/0.46      ! [P3: produc696645085lle_fm > $o,P: produc696645085lle_fm] :
% 0.30/0.46        ( ! [A4: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A4 @ B2 ) )
% 0.30/0.46       => ( P3 @ P ) ) ).
% 0.30/0.46  
% 0.30/0.46  % prod_cases
% 0.30/0.46  thf(fact_214_prod__cases,axiom,
% 0.30/0.46      ! [P3: produc931990033lle_tv > $o,P: produc931990033lle_tv] :
% 0.30/0.46        ( ! [A4: nat > nat,B2: paraco1605129243lle_tv] : ( P3 @ ( produc1680557635lle_tv @ A4 @ B2 ) )
% 0.30/0.46       => ( P3 @ P ) ) ).
% 0.30/0.46  
% 0.30/0.46  % prod_cases
% 0.30/0.46  thf(fact_215_surj__pair,axiom,
% 0.30/0.46      ! [P: produc696645085lle_fm] :
% 0.30/0.46      ? [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] :
% 0.30/0.46        ( P
% 0.30/0.46        = ( produc1710735575lle_fm @ X5 @ Y5 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % surj_pair
% 0.30/0.46  thf(fact_216_surj__pair,axiom,
% 0.30/0.46      ! [P: produc931990033lle_tv] :
% 0.30/0.46      ? [X5: nat > nat,Y5: paraco1605129243lle_tv] :
% 0.30/0.46        ( P
% 0.30/0.46        = ( produc1680557635lle_tv @ X5 @ Y5 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % surj_pair
% 0.30/0.46  thf(fact_217_prod_Oinj__map,axiom,
% 0.30/0.46      ! [F1: nat > nat,F22: nat > nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 0.30/0.46       => ( ( inj_on_nat_nat @ F22 @ top_top_set_nat )
% 0.30/0.46         => ( inj_on26176689at_nat @ ( produc505105722at_nat @ F1 @ F22 ) @ top_to1555900337at_nat ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % prod.inj_map
% 0.30/0.46  thf(fact_218_prod_Oinj__map,axiom,
% 0.30/0.46      ! [F1: nat > nat,F22: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 0.30/0.46       => ( ( inj_on772319074lle_tv @ F22 @ top_to1057771083lle_tv )
% 0.30/0.46         => ( inj_on1745913142lle_tv @ ( produc2101297531lle_tv @ F1 @ F22 ) @ top_to1411004326lle_tv ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % prod.inj_map
% 0.30/0.46  thf(fact_219_prod_Oinj__map,axiom,
% 0.30/0.46      ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F22: nat > nat] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 0.30/0.46       => ( ( inj_on_nat_nat @ F22 @ top_top_set_nat )
% 0.30/0.46         => ( inj_on552895452tv_nat @ ( produc42536895at_nat @ F1 @ F22 ) @ top_to975729152tv_nat ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % prod.inj_map
% 0.30/0.46  thf(fact_220_prod_Oinj__map,axiom,
% 0.30/0.46      ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F22: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 0.30/0.46       => ( ( inj_on772319074lle_tv @ F22 @ top_to1057771083lle_tv )
% 0.30/0.46         => ( inj_on2112487900lle_tv @ ( produc1345917071lle_tv @ F1 @ F22 ) @ top_to1871154984lle_tv ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % prod.inj_map
% 0.30/0.46  thf(fact_221_ssubst__Pair__rhs,axiom,
% 0.30/0.46      ! [R: list_char > paraco1605129243lle_tv,S3: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,S4: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S3 ) @ R2 )
% 0.30/0.46       => ( ( S4 = S3 )
% 0.30/0.46         => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S4 ) @ R2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % ssubst_Pair_rhs
% 0.30/0.46  thf(fact_222_ssubst__Pair__rhs,axiom,
% 0.30/0.46      ! [R: nat > nat,S3: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,S4: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ R @ S3 ) @ R2 )
% 0.30/0.46       => ( ( S4 = S3 )
% 0.30/0.46         => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ R @ S4 ) @ R2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % ssubst_Pair_rhs
% 0.30/0.46  thf(fact_223_curryI,axiom,
% 0.30/0.46      ! [F: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( F @ ( produc1710735575lle_fm @ A @ B ) )
% 0.30/0.46       => ( produc275353523e_fm_o @ F @ A @ B ) ) ).
% 0.30/0.46  
% 0.30/0.46  % curryI
% 0.30/0.46  thf(fact_224_curryI,axiom,
% 0.30/0.46      ! [F: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( F @ ( produc1680557635lle_tv @ A @ B ) )
% 0.30/0.46       => ( produc752649287e_tv_o @ F @ A @ B ) ) ).
% 0.30/0.46  
% 0.30/0.46  % curryI
% 0.30/0.46  thf(fact_225_map__prod__simp,axiom,
% 0.30/0.46      ! [F: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( produc1900967599lle_fm @ F @ G @ ( produc1710735575lle_fm @ A @ B ) )
% 0.30/0.46        = ( produc1710735575lle_fm @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_simp
% 0.30/0.46  thf(fact_226_map__prod__simp,axiom,
% 0.30/0.46      ! [F: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( produc1566550641lle_tv @ F @ G @ ( produc1710735575lle_fm @ A @ B ) )
% 0.30/0.46        = ( produc1680557635lle_tv @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_simp
% 0.30/0.46  thf(fact_227_map__prod__simp,axiom,
% 0.30/0.46      ! [F: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( produc951033137lle_fm @ F @ G @ ( produc1680557635lle_tv @ A @ B ) )
% 0.30/0.46        = ( produc1710735575lle_fm @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_simp
% 0.30/0.46  thf(fact_228_map__prod__simp,axiom,
% 0.30/0.46      ! [F: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( produc532909085lle_tv @ F @ G @ ( produc1680557635lle_tv @ A @ B ) )
% 0.30/0.46        = ( produc1680557635lle_tv @ ( F @ A ) @ ( G @ B ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_simp
% 0.30/0.46  thf(fact_229_curryD,axiom,
% 0.30/0.46      ! [F: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( produc275353523e_fm_o @ F @ A @ B )
% 0.30/0.46       => ( F @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % curryD
% 0.30/0.46  thf(fact_230_curryD,axiom,
% 0.30/0.46      ! [F: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( produc752649287e_tv_o @ F @ A @ B )
% 0.30/0.46       => ( F @ ( produc1680557635lle_tv @ A @ B ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % curryD
% 0.30/0.46  thf(fact_231_curryE,axiom,
% 0.30/0.46      ! [F: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( produc275353523e_fm_o @ F @ A @ B )
% 0.30/0.46       => ( F @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % curryE
% 0.30/0.46  thf(fact_232_curryE,axiom,
% 0.30/0.46      ! [F: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( produc752649287e_tv_o @ F @ A @ B )
% 0.30/0.46       => ( F @ ( produc1680557635lle_tv @ A @ B ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % curryE
% 0.30/0.46  thf(fact_233_change__tv_Ocases,axiom,
% 0.30/0.46      ! [X: produc931990033lle_tv] :
% 0.30/0.46        ( ! [F3: nat > nat,B2: $o] :
% 0.30/0.46            ( X
% 0.30/0.46           != ( produc1680557635lle_tv @ F3 @ ( paraco1344940915le_Det @ B2 ) ) )
% 0.30/0.46       => ~ ! [F3: nat > nat,N: nat] :
% 0.30/0.46              ( X
% 0.30/0.46             != ( produc1680557635lle_tv @ F3 @ ( paraco793048302_Indet @ N ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % change_tv.cases
% 0.30/0.46  thf(fact_234_the__inv__f__f,axiom,
% 0.30/0.46      ! [F: nat > nat,X: nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.46       => ( ( the_inv_into_nat_nat @ top_top_set_nat @ F @ ( F @ X ) )
% 0.30/0.46          = X ) ) ).
% 0.30/0.46  
% 0.30/0.46  % the_inv_f_f
% 0.30/0.46  thf(fact_235_the__inv__f__f,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.46       => ( ( the_in452116896lle_tv @ top_to1057771083lle_tv @ F @ ( F @ X ) )
% 0.30/0.46          = X ) ) ).
% 0.30/0.46  
% 0.30/0.46  % the_inv_f_f
% 0.30/0.46  thf(fact_236_change__tv_Opelims,axiom,
% 0.30/0.46      ! [X: nat > nat,Xa: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( ( paraco1147068288nge_tv @ X @ Xa )
% 0.30/0.46          = Y )
% 0.30/0.46       => ( ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ Xa ) )
% 0.30/0.46         => ( ! [B2: $o] :
% 0.30/0.46                ( ( Xa
% 0.30/0.46                  = ( paraco1344940915le_Det @ B2 ) )
% 0.30/0.46               => ( ( Y
% 0.30/0.46                    = ( paraco1344940915le_Det @ B2 ) )
% 0.30/0.46                 => ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ ( paraco1344940915le_Det @ B2 ) ) ) ) )
% 0.30/0.46           => ~ ! [N: nat] :
% 0.30/0.46                  ( ( Xa
% 0.30/0.46                    = ( paraco793048302_Indet @ N ) )
% 0.30/0.46                 => ( ( Y
% 0.30/0.46                      = ( paraco793048302_Indet @ ( X @ N ) ) )
% 0.30/0.46                   => ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ ( paraco793048302_Indet @ N ) ) ) ) ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % change_tv.pelims
% 0.30/0.46  thf(fact_237_the__inv__into__f__f,axiom,
% 0.30/0.46      ! [F: nat > nat,A2: set_nat,X: nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F @ A2 )
% 0.30/0.46       => ( ( member_nat @ X @ A2 )
% 0.30/0.46         => ( ( the_inv_into_nat_nat @ A2 @ F @ ( F @ X ) )
% 0.30/0.46            = X ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % the_inv_into_f_f
% 0.30/0.46  thf(fact_238_the__inv__into__f__f,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( member266900804lle_tv @ X @ A2 )
% 0.30/0.46         => ( ( the_in452116896lle_tv @ A2 @ F @ ( F @ X ) )
% 0.30/0.46            = X ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % the_inv_into_f_f
% 0.30/0.46  thf(fact_239_the__inv__into__f__eq,axiom,
% 0.30/0.46      ! [F: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F @ A2 )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = Y )
% 0.30/0.46         => ( ( member_nat @ X @ A2 )
% 0.30/0.46           => ( ( the_inv_into_nat_nat @ A2 @ F @ Y )
% 0.30/0.46              = X ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % the_inv_into_f_eq
% 0.30/0.46  thf(fact_240_the__inv__into__f__eq,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( ( F @ X )
% 0.30/0.46            = Y )
% 0.30/0.46         => ( ( member266900804lle_tv @ X @ A2 )
% 0.30/0.46           => ( ( the_in452116896lle_tv @ A2 @ F @ Y )
% 0.30/0.46              = X ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % the_inv_into_f_eq
% 0.30/0.46  thf(fact_241_total__inv__image,axiom,
% 0.30/0.46      ! [F: nat > nat,R: set_Pr1986765409at_nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.46       => ( ( total_on_nat @ top_top_set_nat @ R )
% 0.30/0.46         => ( total_on_nat @ top_top_set_nat @ ( inv_image_nat_nat @ R @ F ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % total_inv_image
% 0.30/0.46  thf(fact_242_total__inv__image,axiom,
% 0.30/0.46      ! [F: nat > paraco1605129243lle_tv,R: set_Pr2014382200lle_tv] :
% 0.30/0.46        ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 0.30/0.46       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 0.30/0.46         => ( total_on_nat @ top_top_set_nat @ ( inv_im516950809tv_nat @ R @ F ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % total_inv_image
% 0.30/0.46  thf(fact_243_total__inv__image,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > nat,R: set_Pr1986765409at_nat] :
% 0.30/0.46        ( ( inj_on1179712058tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.46       => ( ( total_on_nat @ top_top_set_nat @ R )
% 0.30/0.46         => ( total_1781621663lle_tv @ top_to1057771083lle_tv @ ( inv_im1292588663lle_tv @ R @ F ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % total_inv_image
% 0.30/0.46  thf(fact_244_total__inv__image,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,R: set_Pr2014382200lle_tv] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.46       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 0.30/0.46         => ( total_1781621663lle_tv @ top_to1057771083lle_tv @ ( inv_im719552961lle_tv @ R @ F ) ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % total_inv_image
% 0.30/0.46  thf(fact_245_the__inv__into__onto,axiom,
% 0.30/0.46      ! [F: nat > nat,A2: set_nat] :
% 0.30/0.46        ( ( inj_on_nat_nat @ F @ A2 )
% 0.30/0.46       => ( ( image_nat_nat @ ( the_inv_into_nat_nat @ A2 @ F ) @ ( image_nat_nat @ F @ A2 ) )
% 0.30/0.46          = A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % the_inv_into_onto
% 0.30/0.46  thf(fact_246_the__inv__into__onto,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.30/0.46        ( ( inj_on772319074lle_tv @ F @ A2 )
% 0.30/0.46       => ( ( image_335818702lle_tv @ ( the_in452116896lle_tv @ A2 @ F ) @ ( image_335818702lle_tv @ F @ A2 ) )
% 0.30/0.46          = A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % the_inv_into_onto
% 0.30/0.46  thf(fact_247_map__prod__imageI,axiom,
% 0.30/0.46      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm] :
% 0.30/0.46        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
% 0.30/0.46       => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F @ A ) @ ( G @ B ) ) @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F @ G ) @ R2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_imageI
% 0.30/0.46  thf(fact_248_map__prod__imageI,axiom,
% 0.30/0.46      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
% 0.30/0.46       => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ ( F @ A ) @ ( G @ B ) ) @ ( image_1154804148lle_tv @ ( produc1566550641lle_tv @ F @ G ) @ R2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_imageI
% 0.30/0.46  thf(fact_249_map__prod__imageI,axiom,
% 0.30/0.46      ! [A: nat > nat,B: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,F: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm] :
% 0.30/0.46        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ R2 )
% 0.30/0.46       => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F @ A ) @ ( G @ B ) ) @ ( image_1585092542lle_fm @ ( produc951033137lle_fm @ F @ G ) @ R2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_imageI
% 0.30/0.46  thf(fact_250_map__prod__imageI,axiom,
% 0.30/0.46      ! [A: nat > nat,B: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,F: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ R2 )
% 0.30/0.46       => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ ( F @ A ) @ ( G @ B ) ) @ ( image_1751508608lle_tv @ ( produc532909085lle_tv @ F @ G ) @ R2 ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_imageI
% 0.30/0.46  thf(fact_251_swap__simp,axiom,
% 0.30/0.46      ! [X: paraco1604210848lle_fm,Y: list_char > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( produc1232814113lle_tv @ ( produc1943344577lle_tv @ X @ Y ) )
% 0.30/0.46        = ( produc1710735575lle_fm @ Y @ X ) ) ).
% 0.30/0.46  
% 0.30/0.46  % swap_simp
% 0.30/0.46  thf(fact_252_swap__simp,axiom,
% 0.30/0.46      ! [X: paraco1605129243lle_tv,Y: nat > nat] :
% 0.30/0.46        ( ( produc178635363at_nat @ ( produc1633679363at_nat @ X @ Y ) )
% 0.30/0.46        = ( produc1680557635lle_tv @ Y @ X ) ) ).
% 0.30/0.46  
% 0.30/0.46  % swap_simp
% 0.30/0.46  thf(fact_253_swap__simp,axiom,
% 0.30/0.46      ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 0.30/0.46        ( ( produc1000205111lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.30/0.46        = ( produc1943344577lle_tv @ Y @ X ) ) ).
% 0.30/0.46  
% 0.30/0.46  % swap_simp
% 0.30/0.46  thf(fact_254_swap__simp,axiom,
% 0.30/0.46      ! [X: nat > nat,Y: paraco1605129243lle_tv] :
% 0.30/0.46        ( ( produc225513635lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.30/0.46        = ( produc1633679363at_nat @ Y @ X ) ) ).
% 0.30/0.46  
% 0.30/0.46  % swap_simp
% 0.30/0.46  thf(fact_255_pair__in__swap__image,axiom,
% 0.30/0.46      ! [Y: paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv,A2: set_Pr2120184979lle_fm] :
% 0.30/0.46        ( ( member74361182lle_tv @ ( produc1943344577lle_tv @ Y @ X ) @ ( image_924970994lle_tv @ produc1000205111lle_fm @ A2 ) )
% 0.30/0.46        = ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X @ Y ) @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % pair_in_swap_image
% 0.30/0.46  thf(fact_256_pair__in__swap__image,axiom,
% 0.30/0.46      ! [Y: paraco1605129243lle_tv,X: nat > nat,A2: set_Pr560526279lle_tv] :
% 0.30/0.46        ( ( member1234290208at_nat @ ( produc1633679363at_nat @ Y @ X ) @ ( image_1724396928at_nat @ produc225513635lle_tv @ A2 ) )
% 0.30/0.46        = ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X @ Y ) @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % pair_in_swap_image
% 0.30/0.46  thf(fact_257_pair__in__swap__image,axiom,
% 0.30/0.46      ! [Y: list_char > paraco1605129243lle_tv,X: paraco1604210848lle_fm,A2: set_Pr1723822845lle_tv] :
% 0.30/0.46        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ Y @ X ) @ ( image_326034184lle_fm @ produc1232814113lle_tv @ A2 ) )
% 0.30/0.46        = ( member74361182lle_tv @ ( produc1943344577lle_tv @ X @ Y ) @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % pair_in_swap_image
% 0.30/0.46  thf(fact_258_pair__in__swap__image,axiom,
% 0.30/0.46      ! [Y: nat > nat,X: paraco1605129243lle_tv,A2: set_Pr840833727at_nat] :
% 0.30/0.46        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ Y @ X ) @ ( image_769496456lle_tv @ produc178635363at_nat @ A2 ) )
% 0.30/0.46        = ( member1234290208at_nat @ ( produc1633679363at_nat @ X @ Y ) @ A2 ) ) ).
% 0.30/0.46  
% 0.30/0.46  % pair_in_swap_image
% 0.30/0.46  thf(fact_259_map__prod__surj,axiom,
% 0.30/0.46      ! [F: nat > nat,G: nat > nat] :
% 0.30/0.46        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.30/0.46          = top_top_set_nat )
% 0.30/0.46       => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.30/0.46            = top_top_set_nat )
% 0.30/0.46         => ( ( image_815163717at_nat @ ( produc505105722at_nat @ F @ G ) @ top_to1555900337at_nat )
% 0.30/0.46            = top_to1555900337at_nat ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_surj
% 0.30/0.46  thf(fact_260_map__prod__surj,axiom,
% 0.30/0.46      ! [F: nat > nat,G: nat > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.30/0.46          = top_top_set_nat )
% 0.30/0.46       => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.30/0.46            = top_to1057771083lle_tv )
% 0.30/0.46         => ( ( image_1674248956lle_tv @ ( produc313957681lle_tv @ F @ G ) @ top_to1555900337at_nat )
% 0.30/0.46            = top_to1411004326lle_tv ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_surj
% 0.30/0.46  thf(fact_261_map__prod__surj,axiom,
% 0.30/0.46      ! [F: nat > nat,G: paraco1605129243lle_tv > nat] :
% 0.30/0.46        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.30/0.46          = top_top_set_nat )
% 0.30/0.46       => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.30/0.46            = top_top_set_nat )
% 0.30/0.46         => ( ( image_1787705850at_nat @ ( produc1685803475tv_nat @ F @ G ) @ top_to1411004326lle_tv )
% 0.30/0.46            = top_to1555900337at_nat ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_surj
% 0.30/0.46  thf(fact_262_map__prod__surj,axiom,
% 0.30/0.46      ! [F: nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.30/0.46          = top_top_set_nat )
% 0.30/0.46       => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.30/0.46            = top_to1057771083lle_tv )
% 0.30/0.46         => ( ( image_149830562lle_tv @ ( produc2101297531lle_tv @ F @ G ) @ top_to1411004326lle_tv )
% 0.30/0.46            = top_to1411004326lle_tv ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_surj
% 0.30/0.46  thf(fact_263_map__prod__surj,axiom,
% 0.30/0.46      ! [F: nat > paraco1605129243lle_tv,G: nat > nat] :
% 0.30/0.46        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 0.30/0.46          = top_to1057771083lle_tv )
% 0.30/0.46       => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.30/0.46            = top_top_set_nat )
% 0.30/0.46         => ( ( image_1597721174tv_nat @ ( produc1250721397at_nat @ F @ G ) @ top_to1555900337at_nat )
% 0.30/0.46            = top_to975729152tv_nat ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_surj
% 0.30/0.46  thf(fact_264_map__prod__surj,axiom,
% 0.30/0.46      ! [F: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 0.30/0.46          = top_to1057771083lle_tv )
% 0.30/0.46       => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.30/0.46            = top_to1057771083lle_tv )
% 0.30/0.46         => ( ( image_1507992062lle_tv @ ( produc210389789lle_tv @ F @ G ) @ top_to1555900337at_nat )
% 0.30/0.46            = top_to1871154984lle_tv ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_surj
% 0.30/0.46  thf(fact_265_map__prod__surj,axiom,
% 0.30/0.46      ! [F: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > nat] :
% 0.30/0.46        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 0.30/0.46          = top_to1057771083lle_tv )
% 0.30/0.46       => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.30/0.46            = top_top_set_nat )
% 0.30/0.46         => ( ( image_53754658tv_nat @ ( produc189459613tv_nat @ F @ G ) @ top_to1411004326lle_tv )
% 0.30/0.46            = top_to975729152tv_nat ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_surj
% 0.30/0.46  thf(fact_266_map__prod__surj,axiom,
% 0.30/0.46      ! [F: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 0.30/0.46          = top_to1057771083lle_tv )
% 0.30/0.46       => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.30/0.46            = top_to1057771083lle_tv )
% 0.30/0.46         => ( ( image_988201162lle_tv @ ( produc1975500101lle_tv @ F @ G ) @ top_to1411004326lle_tv )
% 0.30/0.46            = top_to1871154984lle_tv ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_surj
% 0.30/0.46  thf(fact_267_map__prod__surj,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > nat,G: nat > nat] :
% 0.30/0.46        ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.46          = top_top_set_nat )
% 0.30/0.46       => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.30/0.46            = top_top_set_nat )
% 0.30/0.46         => ( ( image_1805124128at_nat @ ( produc386540311at_nat @ F @ G ) @ top_to975729152tv_nat )
% 0.30/0.46            = top_to1555900337at_nat ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_surj
% 0.30/0.46  thf(fact_268_map__prod__surj,axiom,
% 0.30/0.46      ! [F: paraco1605129243lle_tv > nat,G: nat > paraco1605129243lle_tv] :
% 0.30/0.46        ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.46          = top_top_set_nat )
% 0.30/0.46       => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.30/0.46            = top_to1057771083lle_tv )
% 0.30/0.46         => ( ( image_1200372424lle_tv @ ( produc72207551lle_tv @ F @ G ) @ top_to975729152tv_nat )
% 0.30/0.46            = top_to1411004326lle_tv ) ) ) ).
% 0.30/0.46  
% 0.30/0.46  % map_prod_surj
% 0.30/0.46  thf(fact_269_surj__def,axiom,
% 0.30/0.46      ! [F: nat > nat] :
% 0.30/0.46        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.30/0.47          = top_top_set_nat )
% 0.30/0.47        = ( ! [Y4: nat] :
% 0.30/0.47            ? [X4: nat] :
% 0.30/0.47              ( Y4
% 0.30/0.47              = ( F @ X4 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surj_def
% 0.30/0.47  thf(fact_270_surj__def,axiom,
% 0.30/0.47      ! [F: nat > paraco1605129243lle_tv] :
% 0.30/0.47        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 0.30/0.47          = top_to1057771083lle_tv )
% 0.30/0.47        = ( ! [Y4: paraco1605129243lle_tv] :
% 0.30/0.47            ? [X4: nat] :
% 0.30/0.47              ( Y4
% 0.30/0.47              = ( F @ X4 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surj_def
% 0.30/0.47  thf(fact_271_surj__def,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > nat] :
% 0.30/0.47        ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.47          = top_top_set_nat )
% 0.30/0.47        = ( ! [Y4: nat] :
% 0.30/0.47            ? [X4: paraco1605129243lle_tv] :
% 0.30/0.47              ( Y4
% 0.30/0.47              = ( F @ X4 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surj_def
% 0.30/0.47  thf(fact_272_surj__def,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.47        ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.47          = top_to1057771083lle_tv )
% 0.30/0.47        = ( ! [Y4: paraco1605129243lle_tv] :
% 0.30/0.47            ? [X4: paraco1605129243lle_tv] :
% 0.30/0.47              ( Y4
% 0.30/0.47              = ( F @ X4 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surj_def
% 0.30/0.47  thf(fact_273_surjI,axiom,
% 0.30/0.47      ! [G: nat > nat,F: nat > nat] :
% 0.30/0.47        ( ! [X5: nat] :
% 0.30/0.47            ( ( G @ ( F @ X5 ) )
% 0.30/0.47            = X5 )
% 0.30/0.47       => ( ( image_nat_nat @ G @ top_top_set_nat )
% 0.30/0.47          = top_top_set_nat ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjI
% 0.30/0.47  thf(fact_274_surjI,axiom,
% 0.30/0.47      ! [G: nat > paraco1605129243lle_tv,F: paraco1605129243lle_tv > nat] :
% 0.30/0.47        ( ! [X5: paraco1605129243lle_tv] :
% 0.30/0.47            ( ( G @ ( F @ X5 ) )
% 0.30/0.47            = X5 )
% 0.30/0.47       => ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 0.30/0.47          = top_to1057771083lle_tv ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjI
% 0.30/0.47  thf(fact_275_surjI,axiom,
% 0.30/0.47      ! [G: paraco1605129243lle_tv > nat,F: nat > paraco1605129243lle_tv] :
% 0.30/0.47        ( ! [X5: nat] :
% 0.30/0.47            ( ( G @ ( F @ X5 ) )
% 0.30/0.47            = X5 )
% 0.30/0.47       => ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 0.30/0.47          = top_top_set_nat ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjI
% 0.30/0.47  thf(fact_276_surjI,axiom,
% 0.30/0.47      ! [G: paraco1605129243lle_tv > paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.47        ( ! [X5: paraco1605129243lle_tv] :
% 0.30/0.47            ( ( G @ ( F @ X5 ) )
% 0.30/0.47            = X5 )
% 0.30/0.47       => ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 0.30/0.47          = top_to1057771083lle_tv ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjI
% 0.30/0.47  thf(fact_277_surjE,axiom,
% 0.30/0.47      ! [F: nat > nat,Y: nat] :
% 0.30/0.47        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.30/0.47          = top_top_set_nat )
% 0.30/0.47       => ~ ! [X5: nat] :
% 0.30/0.47              ( Y
% 0.30/0.47             != ( F @ X5 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjE
% 0.30/0.47  thf(fact_278_surjE,axiom,
% 0.30/0.47      ! [F: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 0.30/0.47          = top_to1057771083lle_tv )
% 0.30/0.47       => ~ ! [X5: nat] :
% 0.30/0.47              ( Y
% 0.30/0.47             != ( F @ X5 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjE
% 0.30/0.47  thf(fact_279_surjE,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > nat,Y: nat] :
% 0.30/0.47        ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.47          = top_top_set_nat )
% 0.30/0.47       => ~ ! [X5: paraco1605129243lle_tv] :
% 0.30/0.47              ( Y
% 0.30/0.47             != ( F @ X5 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjE
% 0.30/0.47  thf(fact_280_surjE,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.47          = top_to1057771083lle_tv )
% 0.30/0.47       => ~ ! [X5: paraco1605129243lle_tv] :
% 0.30/0.47              ( Y
% 0.30/0.47             != ( F @ X5 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjE
% 0.30/0.47  thf(fact_281_surjD,axiom,
% 0.30/0.47      ! [F: nat > nat,Y: nat] :
% 0.30/0.47        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.30/0.47          = top_top_set_nat )
% 0.30/0.47       => ? [X5: nat] :
% 0.30/0.47            ( Y
% 0.30/0.47            = ( F @ X5 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjD
% 0.30/0.47  thf(fact_282_surjD,axiom,
% 0.30/0.47      ! [F: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 0.30/0.47          = top_to1057771083lle_tv )
% 0.30/0.47       => ? [X5: nat] :
% 0.30/0.47            ( Y
% 0.30/0.47            = ( F @ X5 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjD
% 0.30/0.47  thf(fact_283_surjD,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > nat,Y: nat] :
% 0.30/0.47        ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 0.30/0.47          = top_top_set_nat )
% 0.30/0.47       => ? [X5: paraco1605129243lle_tv] :
% 0.30/0.47            ( Y
% 0.30/0.47            = ( F @ X5 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjD
% 0.30/0.47  thf(fact_284_surjD,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.47          = top_to1057771083lle_tv )
% 0.30/0.47       => ? [X5: paraco1605129243lle_tv] :
% 0.30/0.47            ( Y
% 0.30/0.47            = ( F @ X5 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjD
% 0.30/0.47  thf(fact_285_inj__on__image__iff,axiom,
% 0.30/0.47      ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 0.30/0.47        ( ! [X5: nat] :
% 0.30/0.47            ( ( member_nat @ X5 @ A2 )
% 0.30/0.47           => ! [Xa2: nat] :
% 0.30/0.47                ( ( member_nat @ Xa2 @ A2 )
% 0.30/0.47               => ( ( ( G @ ( F @ X5 ) )
% 0.30/0.47                    = ( G @ ( F @ Xa2 ) ) )
% 0.30/0.47                  = ( ( G @ X5 )
% 0.30/0.47                    = ( G @ Xa2 ) ) ) ) )
% 0.30/0.47       => ( ( inj_on_nat_nat @ F @ A2 )
% 0.30/0.47         => ( ( inj_on_nat_nat @ G @ ( image_nat_nat @ F @ A2 ) )
% 0.30/0.47            = ( inj_on_nat_nat @ G @ A2 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_on_image_iff
% 0.30/0.47  thf(fact_286_inj__on__image__iff,axiom,
% 0.30/0.47      ! [A2: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.47        ( ! [X5: paraco1605129243lle_tv] :
% 0.30/0.47            ( ( member266900804lle_tv @ X5 @ A2 )
% 0.30/0.47           => ! [Xa2: paraco1605129243lle_tv] :
% 0.30/0.47                ( ( member266900804lle_tv @ Xa2 @ A2 )
% 0.30/0.47               => ( ( ( G @ ( F @ X5 ) )
% 0.30/0.47                    = ( G @ ( F @ Xa2 ) ) )
% 0.30/0.47                  = ( ( G @ X5 )
% 0.30/0.47                    = ( G @ Xa2 ) ) ) ) )
% 0.30/0.47       => ( ( inj_on772319074lle_tv @ F @ A2 )
% 0.30/0.47         => ( ( inj_on772319074lle_tv @ G @ ( image_335818702lle_tv @ F @ A2 ) )
% 0.30/0.47            = ( inj_on772319074lle_tv @ G @ A2 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_on_image_iff
% 0.30/0.47  thf(fact_287_inj__image__mem__iff,axiom,
% 0.30/0.47      ! [F: nat > nat,A: nat,A2: set_nat] :
% 0.30/0.47        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.47       => ( ( member_nat @ ( F @ A ) @ ( image_nat_nat @ F @ A2 ) )
% 0.30/0.47          = ( member_nat @ A @ A2 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_image_mem_iff
% 0.30/0.47  thf(fact_288_inj__image__mem__iff,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.30/0.47        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.47       => ( ( member266900804lle_tv @ ( F @ A ) @ ( image_335818702lle_tv @ F @ A2 ) )
% 0.30/0.47          = ( member266900804lle_tv @ A @ A2 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_image_mem_iff
% 0.30/0.47  thf(fact_289_inj__image__eq__iff,axiom,
% 0.30/0.47      ! [F: nat > nat,A2: set_nat,B4: set_nat] :
% 0.30/0.47        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.47       => ( ( ( image_nat_nat @ F @ A2 )
% 0.30/0.47            = ( image_nat_nat @ F @ B4 ) )
% 0.30/0.47          = ( A2 = B4 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_image_eq_iff
% 0.30/0.47  thf(fact_290_inj__image__eq__iff,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.30/0.47        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.47       => ( ( ( image_335818702lle_tv @ F @ A2 )
% 0.30/0.47            = ( image_335818702lle_tv @ F @ B4 ) )
% 0.30/0.47          = ( A2 = B4 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_image_eq_iff
% 0.30/0.47  thf(fact_291_range__ex1__eq,axiom,
% 0.30/0.47      ! [F: nat > nat,B: nat] :
% 0.30/0.47        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.47       => ( ( member_nat @ B @ ( image_nat_nat @ F @ top_top_set_nat ) )
% 0.30/0.47          = ( ? [X4: nat] :
% 0.30/0.47                ( ( B
% 0.30/0.47                  = ( F @ X4 ) )
% 0.30/0.47                & ! [Y4: nat] :
% 0.30/0.47                    ( ( B
% 0.30/0.47                      = ( F @ Y4 ) )
% 0.30/0.47                   => ( Y4 = X4 ) ) ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % range_ex1_eq
% 0.30/0.47  thf(fact_292_range__ex1__eq,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.47       => ( ( member266900804lle_tv @ B @ ( image_335818702lle_tv @ F @ top_to1057771083lle_tv ) )
% 0.30/0.47          = ( ? [X4: paraco1605129243lle_tv] :
% 0.30/0.47                ( ( B
% 0.30/0.47                  = ( F @ X4 ) )
% 0.30/0.47                & ! [Y4: paraco1605129243lle_tv] :
% 0.30/0.47                    ( ( B
% 0.30/0.47                      = ( F @ Y4 ) )
% 0.30/0.47                   => ( Y4 = X4 ) ) ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % range_ex1_eq
% 0.30/0.47  thf(fact_293_prod__fun__imageE,axiom,
% 0.30/0.47      ! [C: produc696645085lle_fm,F: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm] :
% 0.30/0.47        ( ( member1474794996lle_fm @ C @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F @ G ) @ R2 ) )
% 0.30/0.47       => ~ ! [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] :
% 0.30/0.47              ( ( C
% 0.30/0.47                = ( produc1710735575lle_fm @ ( F @ X5 ) @ ( G @ Y5 ) ) )
% 0.30/0.47             => ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X5 @ Y5 ) @ R2 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % prod_fun_imageE
% 0.30/0.47  thf(fact_294_prod__fun__imageE,axiom,
% 0.30/0.47      ! [C: produc696645085lle_fm,F: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,R2: set_Pr560526279lle_tv] :
% 0.30/0.47        ( ( member1474794996lle_fm @ C @ ( image_1585092542lle_fm @ ( produc951033137lle_fm @ F @ G ) @ R2 ) )
% 0.30/0.47       => ~ ! [X5: nat > nat,Y5: paraco1605129243lle_tv] :
% 0.30/0.47              ( ( C
% 0.30/0.47                = ( produc1710735575lle_fm @ ( F @ X5 ) @ ( G @ Y5 ) ) )
% 0.30/0.47             => ~ ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X5 @ Y5 ) @ R2 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % prod_fun_imageE
% 0.30/0.47  thf(fact_295_prod__fun__imageE,axiom,
% 0.30/0.47      ! [C: produc931990033lle_tv,F: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv,R2: set_Pr2120184979lle_fm] :
% 0.30/0.47        ( ( member1569366824lle_tv @ C @ ( image_1154804148lle_tv @ ( produc1566550641lle_tv @ F @ G ) @ R2 ) )
% 0.30/0.47       => ~ ! [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] :
% 0.30/0.47              ( ( C
% 0.30/0.47                = ( produc1680557635lle_tv @ ( F @ X5 ) @ ( G @ Y5 ) ) )
% 0.30/0.47             => ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X5 @ Y5 ) @ R2 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % prod_fun_imageE
% 0.30/0.47  thf(fact_296_prod__fun__imageE,axiom,
% 0.30/0.47      ! [C: produc931990033lle_tv,F: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv,R2: set_Pr560526279lle_tv] :
% 0.30/0.47        ( ( member1569366824lle_tv @ C @ ( image_1751508608lle_tv @ ( produc532909085lle_tv @ F @ G ) @ R2 ) )
% 0.30/0.47       => ~ ! [X5: nat > nat,Y5: paraco1605129243lle_tv] :
% 0.30/0.47              ( ( C
% 0.30/0.47                = ( produc1680557635lle_tv @ ( F @ X5 ) @ ( G @ Y5 ) ) )
% 0.30/0.47             => ~ ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X5 @ Y5 ) @ R2 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % prod_fun_imageE
% 0.30/0.47  thf(fact_297_inj__on__the__inv__into,axiom,
% 0.30/0.47      ! [F: nat > nat,A2: set_nat] :
% 0.30/0.47        ( ( inj_on_nat_nat @ F @ A2 )
% 0.30/0.47       => ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ A2 @ F ) @ ( image_nat_nat @ F @ A2 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_on_the_inv_into
% 0.30/0.47  thf(fact_298_inj__on__the__inv__into,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.30/0.47        ( ( inj_on772319074lle_tv @ F @ A2 )
% 0.30/0.47       => ( inj_on772319074lle_tv @ ( the_in452116896lle_tv @ A2 @ F ) @ ( image_335818702lle_tv @ F @ A2 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_on_the_inv_into
% 0.30/0.47  thf(fact_299_f__the__inv__into__f,axiom,
% 0.30/0.47      ! [F: nat > nat,A2: set_nat,Y: nat] :
% 0.30/0.47        ( ( inj_on_nat_nat @ F @ A2 )
% 0.30/0.47       => ( ( member_nat @ Y @ ( image_nat_nat @ F @ A2 ) )
% 0.30/0.47         => ( ( F @ ( the_inv_into_nat_nat @ A2 @ F @ Y ) )
% 0.30/0.47            = Y ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % f_the_inv_into_f
% 0.30/0.47  thf(fact_300_f__the__inv__into__f,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( inj_on772319074lle_tv @ F @ A2 )
% 0.30/0.47       => ( ( member266900804lle_tv @ Y @ ( image_335818702lle_tv @ F @ A2 ) )
% 0.30/0.47         => ( ( F @ ( the_in452116896lle_tv @ A2 @ F @ Y ) )
% 0.30/0.47            = Y ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % f_the_inv_into_f
% 0.30/0.47  thf(fact_301_total__lex__prod,axiom,
% 0.30/0.47      ! [R: set_Pr1986765409at_nat,S3: set_Pr1986765409at_nat] :
% 0.30/0.47        ( ( total_on_nat @ top_top_set_nat @ R )
% 0.30/0.47       => ( ( total_on_nat @ top_top_set_nat @ S3 )
% 0.30/0.47         => ( total_1775715973at_nat @ top_to1555900337at_nat @ ( lex_prod_nat_nat @ R @ S3 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % total_lex_prod
% 0.30/0.47  thf(fact_302_total__lex__prod,axiom,
% 0.30/0.47      ! [R: set_Pr1986765409at_nat,S3: set_Pr2014382200lle_tv] :
% 0.30/0.47        ( ( total_on_nat @ top_top_set_nat @ R )
% 0.30/0.47       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ S3 )
% 0.30/0.47         => ( total_517371324lle_tv @ top_to1411004326lle_tv @ ( lex_pr413684186lle_tv @ R @ S3 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % total_lex_prod
% 0.30/0.47  thf(fact_303_total__lex__prod,axiom,
% 0.30/0.47      ! [R: set_Pr2014382200lle_tv,S3: set_Pr1986765409at_nat] :
% 0.30/0.47        ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 0.30/0.47       => ( ( total_on_nat @ top_top_set_nat @ S3 )
% 0.30/0.47         => ( total_440843542tv_nat @ top_to975729152tv_nat @ ( lex_pr1785529980tv_nat @ R @ S3 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % total_lex_prod
% 0.30/0.47  thf(fact_304_total__lex__prod,axiom,
% 0.30/0.47      ! [R: set_Pr2014382200lle_tv,S3: set_Pr2014382200lle_tv] :
% 0.30/0.47        ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 0.30/0.47       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ S3 )
% 0.30/0.47         => ( total_92239038lle_tv @ top_to1871154984lle_tv @ ( lex_pr567812260lle_tv @ R @ S3 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % total_lex_prod
% 0.30/0.47  thf(fact_305_in__lex__prod,axiom,
% 0.30/0.47      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm,R: set_Pr2061825550lle_tv,S3: set_Pr1019238018lle_fm] :
% 0.30/0.47        ( ( member1592865093lle_fm @ ( produc407632608lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ ( produc1710735575lle_fm @ A5 @ B3 ) ) @ ( lex_pr2001015487lle_fm @ R @ S3 ) )
% 0.30/0.47        = ( ( member146333935lle_tv @ ( produc1297923922lle_tv @ A @ A5 ) @ R )
% 0.30/0.47          | ( ( A = A5 )
% 0.30/0.47            & ( member334644067lle_fm @ ( produc1126104134lle_fm @ B @ B3 ) @ S3 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % in_lex_prod
% 0.30/0.47  thf(fact_306_in__lex__prod,axiom,
% 0.30/0.47      ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv,R: set_Pr1357842111at_nat,S3: set_Pr2014382200lle_tv] :
% 0.30/0.47        ( ( member1339857875lle_tv @ ( produc2057188974lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ ( produc1680557635lle_tv @ A5 @ B3 ) ) @ ( lex_pr1093414955lle_tv @ R @ S3 ) )
% 0.30/0.47        = ( ( member112824072at_nat @ ( produc780837143at_nat @ A @ A5 ) @ R )
% 0.30/0.47          | ( ( A = A5 )
% 0.30/0.47            & ( member1531318361lle_tv @ ( produc2058540732lle_tv @ B @ B3 ) @ S3 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % in_lex_prod
% 0.30/0.47  thf(fact_307_prod_Ocollapse,axiom,
% 0.30/0.47      ! [Prod: produc696645085lle_fm] :
% 0.30/0.47        ( ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) )
% 0.30/0.47        = Prod ) ).
% 0.30/0.47  
% 0.30/0.47  % prod.collapse
% 0.30/0.47  thf(fact_308_prod_Ocollapse,axiom,
% 0.30/0.47      ! [Prod: produc931990033lle_tv] :
% 0.30/0.47        ( ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ Prod ) @ ( produc547496597lle_tv @ Prod ) )
% 0.30/0.47        = Prod ) ).
% 0.30/0.47  
% 0.30/0.47  % prod.collapse
% 0.30/0.47  thf(fact_309_prod_Oswap__def,axiom,
% 0.30/0.47      ( produc1232814113lle_tv
% 0.30/0.47      = ( ^ [P2: produc1443694919lle_tv] : ( produc1710735575lle_fm @ ( produc381314067lle_tv @ P2 ) @ ( produc262413013lle_tv @ P2 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % prod.swap_def
% 0.30/0.47  thf(fact_310_prod_Oswap__def,axiom,
% 0.30/0.47      ( produc178635363at_nat
% 0.30/0.47      = ( ^ [P2: produc596913417at_nat] : ( produc1680557635lle_tv @ ( produc500618325at_nat @ P2 ) @ ( produc1589291287at_nat @ P2 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % prod.swap_def
% 0.30/0.47  thf(fact_311_fst__eqD,axiom,
% 0.30/0.47      ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv] :
% 0.30/0.47        ( ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.30/0.47          = A )
% 0.30/0.47       => ( X = A ) ) ).
% 0.30/0.47  
% 0.30/0.47  % fst_eqD
% 0.30/0.47  thf(fact_312_fst__eqD,axiom,
% 0.30/0.47      ! [X: nat > nat,Y: paraco1605129243lle_tv,A: nat > nat] :
% 0.30/0.47        ( ( ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.30/0.47          = A )
% 0.30/0.47       => ( X = A ) ) ).
% 0.30/0.47  
% 0.30/0.47  % fst_eqD
% 0.30/0.47  thf(fact_313_snd__eqD,axiom,
% 0.30/0.47      ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: paraco1604210848lle_fm] :
% 0.30/0.47        ( ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 0.30/0.47          = A )
% 0.30/0.47       => ( Y = A ) ) ).
% 0.30/0.47  
% 0.30/0.47  % snd_eqD
% 0.30/0.47  thf(fact_314_snd__eqD,axiom,
% 0.30/0.47      ! [X: nat > nat,Y: paraco1605129243lle_tv,A: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 0.30/0.47          = A )
% 0.30/0.47       => ( Y = A ) ) ).
% 0.30/0.47  
% 0.30/0.47  % snd_eqD
% 0.30/0.47  thf(fact_315_fst__conv,axiom,
% 0.30/0.47      ! [X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm] :
% 0.30/0.47        ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X1 @ X2 ) )
% 0.30/0.47        = X1 ) ).
% 0.30/0.47  
% 0.30/0.47  % fst_conv
% 0.30/0.47  thf(fact_316_fst__conv,axiom,
% 0.30/0.47      ! [X1: nat > nat,X2: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X1 @ X2 ) )
% 0.30/0.47        = X1 ) ).
% 0.30/0.47  
% 0.30/0.47  % fst_conv
% 0.30/0.47  thf(fact_317_snd__conv,axiom,
% 0.30/0.47      ! [X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm] :
% 0.30/0.47        ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X1 @ X2 ) )
% 0.30/0.47        = X2 ) ).
% 0.30/0.47  
% 0.30/0.47  % snd_conv
% 0.30/0.47  thf(fact_318_snd__conv,axiom,
% 0.30/0.47      ! [X1: nat > nat,X2: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X1 @ X2 ) )
% 0.30/0.47        = X2 ) ).
% 0.30/0.47  
% 0.30/0.47  % snd_conv
% 0.30/0.47  thf(fact_319_prod_Oexhaust__sel,axiom,
% 0.30/0.47      ! [Prod: produc696645085lle_fm] :
% 0.30/0.47        ( Prod
% 0.30/0.47        = ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % prod.exhaust_sel
% 0.30/0.47  thf(fact_320_prod_Oexhaust__sel,axiom,
% 0.30/0.47      ! [Prod: produc931990033lle_tv] :
% 0.30/0.47        ( Prod
% 0.30/0.47        = ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ Prod ) @ ( produc547496597lle_tv @ Prod ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % prod.exhaust_sel
% 0.30/0.47  thf(fact_321_surjective__pairing,axiom,
% 0.30/0.47      ! [T: produc696645085lle_fm] :
% 0.30/0.47        ( T
% 0.30/0.47        = ( produc1710735575lle_fm @ ( produc29804011lle_fm @ T ) @ ( produc148705065lle_fm @ T ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjective_pairing
% 0.30/0.47  thf(fact_322_surjective__pairing,axiom,
% 0.30/0.47      ! [T: produc931990033lle_tv] :
% 0.30/0.47        ( T
% 0.30/0.47        = ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ T ) @ ( produc547496597lle_tv @ T ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % surjective_pairing
% 0.30/0.47  thf(fact_323_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.30/0.47      ! [P3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: produc696645085lle_fm] :
% 0.30/0.47        ( ( P3 @ X @ Y )
% 0.30/0.47       => ( ( A
% 0.30/0.47            = ( produc1710735575lle_fm @ X @ Y ) )
% 0.30/0.47         => ( P3 @ ( produc29804011lle_fm @ A ) @ ( produc148705065lle_fm @ A ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % BNF_Greatest_Fixpoint.subst_Pair
% 0.30/0.47  thf(fact_324_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 0.30/0.47      ! [P3: ( nat > nat ) > paraco1605129243lle_tv > $o,X: nat > nat,Y: paraco1605129243lle_tv,A: produc931990033lle_tv] :
% 0.30/0.47        ( ( P3 @ X @ Y )
% 0.30/0.47       => ( ( A
% 0.30/0.47            = ( produc1680557635lle_tv @ X @ Y ) )
% 0.30/0.47         => ( P3 @ ( produc1636169559lle_tv @ A ) @ ( produc547496597lle_tv @ A ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % BNF_Greatest_Fixpoint.subst_Pair
% 0.30/0.47  thf(fact_325_conjI__realizer,axiom,
% 0.30/0.47      ! [P3: ( list_char > paraco1605129243lle_tv ) > $o,P: list_char > paraco1605129243lle_tv,Q2: paraco1604210848lle_fm > $o,Q: paraco1604210848lle_fm] :
% 0.30/0.47        ( ( P3 @ P )
% 0.30/0.47       => ( ( Q2 @ Q )
% 0.30/0.47         => ( ( P3 @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ P @ Q ) ) )
% 0.30/0.47            & ( Q2 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ P @ Q ) ) ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % conjI_realizer
% 0.30/0.47  thf(fact_326_conjI__realizer,axiom,
% 0.30/0.47      ! [P3: ( nat > nat ) > $o,P: nat > nat,Q2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( P3 @ P )
% 0.30/0.47       => ( ( Q2 @ Q )
% 0.30/0.47         => ( ( P3 @ ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ P @ Q ) ) )
% 0.30/0.47            & ( Q2 @ ( produc547496597lle_tv @ ( produc1680557635lle_tv @ P @ Q ) ) ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % conjI_realizer
% 0.30/0.47  thf(fact_327_exI__realizer,axiom,
% 0.30/0.47      ! [P3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > $o,Y: paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv] :
% 0.30/0.47        ( ( P3 @ Y @ X )
% 0.30/0.47       => ( P3 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X @ Y ) ) @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X @ Y ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % exI_realizer
% 0.30/0.47  thf(fact_328_exI__realizer,axiom,
% 0.30/0.47      ! [P3: paraco1605129243lle_tv > ( nat > nat ) > $o,Y: paraco1605129243lle_tv,X: nat > nat] :
% 0.30/0.47        ( ( P3 @ Y @ X )
% 0.30/0.47       => ( P3 @ ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X @ Y ) ) @ ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X @ Y ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % exI_realizer
% 0.30/0.47  thf(fact_329_sndI,axiom,
% 0.30/0.47      ! [X: produc696645085lle_fm,Y: list_char > paraco1605129243lle_tv,Z: paraco1604210848lle_fm] :
% 0.30/0.47        ( ( X
% 0.30/0.47          = ( produc1710735575lle_fm @ Y @ Z ) )
% 0.30/0.47       => ( ( produc148705065lle_fm @ X )
% 0.30/0.47          = Z ) ) ).
% 0.30/0.47  
% 0.30/0.47  % sndI
% 0.30/0.47  thf(fact_330_sndI,axiom,
% 0.30/0.47      ! [X: produc931990033lle_tv,Y: nat > nat,Z: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( X
% 0.30/0.47          = ( produc1680557635lle_tv @ Y @ Z ) )
% 0.30/0.47       => ( ( produc547496597lle_tv @ X )
% 0.30/0.47          = Z ) ) ).
% 0.30/0.47  
% 0.30/0.47  % sndI
% 0.30/0.47  thf(fact_331_eq__snd__iff,axiom,
% 0.30/0.47      ! [B: paraco1604210848lle_fm,P: produc696645085lle_fm] :
% 0.30/0.47        ( ( B
% 0.30/0.47          = ( produc148705065lle_fm @ P ) )
% 0.30/0.47        = ( ? [A6: list_char > paraco1605129243lle_tv] :
% 0.30/0.47              ( P
% 0.30/0.47              = ( produc1710735575lle_fm @ A6 @ B ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % eq_snd_iff
% 0.30/0.47  thf(fact_332_eq__snd__iff,axiom,
% 0.30/0.47      ! [B: paraco1605129243lle_tv,P: produc931990033lle_tv] :
% 0.30/0.47        ( ( B
% 0.30/0.47          = ( produc547496597lle_tv @ P ) )
% 0.30/0.47        = ( ? [A6: nat > nat] :
% 0.30/0.47              ( P
% 0.30/0.47              = ( produc1680557635lle_tv @ A6 @ B ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % eq_snd_iff
% 0.30/0.47  thf(fact_333_eq__fst__iff,axiom,
% 0.30/0.47      ! [A: list_char > paraco1605129243lle_tv,P: produc696645085lle_fm] :
% 0.30/0.47        ( ( A
% 0.30/0.47          = ( produc29804011lle_fm @ P ) )
% 0.30/0.47        = ( ? [B5: paraco1604210848lle_fm] :
% 0.30/0.47              ( P
% 0.30/0.47              = ( produc1710735575lle_fm @ A @ B5 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % eq_fst_iff
% 0.30/0.47  thf(fact_334_eq__fst__iff,axiom,
% 0.30/0.47      ! [A: nat > nat,P: produc931990033lle_tv] :
% 0.30/0.47        ( ( A
% 0.30/0.47          = ( produc1636169559lle_tv @ P ) )
% 0.30/0.47        = ( ? [B5: paraco1605129243lle_tv] :
% 0.30/0.47              ( P
% 0.30/0.47              = ( produc1680557635lle_tv @ A @ B5 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % eq_fst_iff
% 0.30/0.47  thf(fact_335_fstI,axiom,
% 0.30/0.47      ! [X: produc696645085lle_fm,Y: list_char > paraco1605129243lle_tv,Z: paraco1604210848lle_fm] :
% 0.30/0.47        ( ( X
% 0.30/0.47          = ( produc1710735575lle_fm @ Y @ Z ) )
% 0.30/0.47       => ( ( produc29804011lle_fm @ X )
% 0.30/0.47          = Y ) ) ).
% 0.30/0.47  
% 0.30/0.47  % fstI
% 0.30/0.47  thf(fact_336_fstI,axiom,
% 0.30/0.47      ! [X: produc931990033lle_tv,Y: nat > nat,Z: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( X
% 0.30/0.47          = ( produc1680557635lle_tv @ Y @ Z ) )
% 0.30/0.47       => ( ( produc1636169559lle_tv @ X )
% 0.30/0.47          = Y ) ) ).
% 0.30/0.47  
% 0.30/0.47  % fstI
% 0.30/0.47  thf(fact_337_same__fstI,axiom,
% 0.30/0.47      ! [P3: ( list_char > paraco1605129243lle_tv ) > $o,X: list_char > paraco1605129243lle_tv,Y6: paraco1604210848lle_fm,Y: paraco1604210848lle_fm,R2: ( list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm] :
% 0.30/0.47        ( ( P3 @ X )
% 0.30/0.47       => ( ( member334644067lle_fm @ ( produc1126104134lle_fm @ Y6 @ Y ) @ ( R2 @ X ) )
% 0.30/0.47         => ( member1592865093lle_fm @ ( produc407632608lle_fm @ ( produc1710735575lle_fm @ X @ Y6 ) @ ( produc1710735575lle_fm @ X @ Y ) ) @ ( same_f1581085506lle_fm @ P3 @ R2 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % same_fstI
% 0.30/0.47  thf(fact_338_same__fstI,axiom,
% 0.30/0.47      ! [P3: ( nat > nat ) > $o,X: nat > nat,Y6: paraco1605129243lle_tv,Y: paraco1605129243lle_tv,R2: ( nat > nat ) > set_Pr2014382200lle_tv] :
% 0.30/0.47        ( ( P3 @ X )
% 0.30/0.47       => ( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ Y6 @ Y ) @ ( R2 @ X ) )
% 0.30/0.47         => ( member1339857875lle_tv @ ( produc2057188974lle_tv @ ( produc1680557635lle_tv @ X @ Y6 ) @ ( produc1680557635lle_tv @ X @ Y ) ) @ ( same_f1138187694lle_tv @ P3 @ R2 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % same_fstI
% 0.30/0.47  thf(fact_339_wf__map__prod__image,axiom,
% 0.30/0.47      ! [R: set_Pr1986765409at_nat,F: nat > nat] :
% 0.30/0.47        ( ( wf_nat @ R )
% 0.30/0.47       => ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 0.30/0.47         => ( wf_nat @ ( image_815163717at_nat @ ( produc505105722at_nat @ F @ F ) @ R ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % wf_map_prod_image
% 0.30/0.47  thf(fact_340_wf__map__prod__image,axiom,
% 0.30/0.47      ! [R: set_Pr2014382200lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 0.30/0.47        ( ( wf_Par1378404612lle_tv @ R )
% 0.30/0.47       => ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 0.30/0.47         => ( wf_Par1378404612lle_tv @ ( image_1221801032lle_tv @ ( produc1345917071lle_tv @ F @ F ) @ R ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % wf_map_prod_image
% 0.30/0.47  thf(fact_341_the__inv__into__into,axiom,
% 0.30/0.47      ! [F: nat > nat,A2: set_nat,X: nat,B4: set_nat] :
% 0.30/0.47        ( ( inj_on_nat_nat @ F @ A2 )
% 0.30/0.47       => ( ( member_nat @ X @ ( image_nat_nat @ F @ A2 ) )
% 0.30/0.47         => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 0.30/0.47           => ( member_nat @ ( the_inv_into_nat_nat @ A2 @ F @ X ) @ B4 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % the_inv_into_into
% 0.30/0.47  thf(fact_342_the__inv__into__into,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.30/0.47        ( ( inj_on772319074lle_tv @ F @ A2 )
% 0.30/0.47       => ( ( member266900804lle_tv @ X @ ( image_335818702lle_tv @ F @ A2 ) )
% 0.30/0.47         => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 0.30/0.47           => ( member266900804lle_tv @ ( the_in452116896lle_tv @ A2 @ F @ X ) @ B4 ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % the_inv_into_into
% 0.30/0.47  thf(fact_343_strict__mono__inv,axiom,
% 0.30/0.47      ! [F: nat > nat,G: nat > nat] :
% 0.30/0.47        ( ( order_769474267at_nat @ F )
% 0.30/0.47       => ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 0.30/0.47            = top_top_set_nat )
% 0.30/0.47         => ( ! [X5: nat] :
% 0.30/0.47                ( ( G @ ( F @ X5 ) )
% 0.30/0.47                = X5 )
% 0.30/0.47           => ( order_769474267at_nat @ G ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % strict_mono_inv
% 0.30/0.47  thf(fact_344_subrelI,axiom,
% 0.30/0.47      ! [R: set_Pr2120184979lle_fm,S3: set_Pr2120184979lle_fm] :
% 0.30/0.47        ( ! [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] :
% 0.30/0.47            ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X5 @ Y5 ) @ R )
% 0.30/0.47           => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X5 @ Y5 ) @ S3 ) )
% 0.30/0.47       => ( ord_le1007985907lle_fm @ R @ S3 ) ) ).
% 0.30/0.47  
% 0.30/0.47  % subrelI
% 0.30/0.47  thf(fact_345_subrelI,axiom,
% 0.30/0.47      ! [R: set_Pr560526279lle_tv,S3: set_Pr560526279lle_tv] :
% 0.30/0.47        ( ! [X5: nat > nat,Y5: paraco1605129243lle_tv] :
% 0.30/0.47            ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X5 @ Y5 ) @ R )
% 0.30/0.47           => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X5 @ Y5 ) @ S3 ) )
% 0.30/0.47       => ( ord_le1784136743lle_tv @ R @ S3 ) ) ).
% 0.30/0.47  
% 0.30/0.47  % subrelI
% 0.30/0.47  thf(fact_346_inj__on__image__mem__iff,axiom,
% 0.30/0.47      ! [F: nat > nat,B4: set_nat,A: nat,A2: set_nat] :
% 0.30/0.47        ( ( inj_on_nat_nat @ F @ B4 )
% 0.30/0.47       => ( ( member_nat @ A @ B4 )
% 0.30/0.47         => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 0.30/0.47           => ( ( member_nat @ ( F @ A ) @ ( image_nat_nat @ F @ A2 ) )
% 0.30/0.47              = ( member_nat @ A @ A2 ) ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_on_image_mem_iff
% 0.30/0.47  thf(fact_347_inj__on__image__mem__iff,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv,A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.30/0.47        ( ( inj_on772319074lle_tv @ F @ B4 )
% 0.30/0.47       => ( ( member266900804lle_tv @ A @ B4 )
% 0.30/0.47         => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 0.30/0.47           => ( ( member266900804lle_tv @ ( F @ A ) @ ( image_335818702lle_tv @ F @ A2 ) )
% 0.30/0.47              = ( member266900804lle_tv @ A @ A2 ) ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_on_image_mem_iff
% 0.30/0.47  thf(fact_348_inj__on__image__eq__iff,axiom,
% 0.30/0.47      ! [F: nat > nat,C2: set_nat,A2: set_nat,B4: set_nat] :
% 0.30/0.47        ( ( inj_on_nat_nat @ F @ C2 )
% 0.30/0.47       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.47         => ( ( ord_less_eq_set_nat @ B4 @ C2 )
% 0.30/0.47           => ( ( ( image_nat_nat @ F @ A2 )
% 0.30/0.47                = ( image_nat_nat @ F @ B4 ) )
% 0.30/0.47              = ( A2 = B4 ) ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_on_image_eq_iff
% 0.30/0.47  thf(fact_349_inj__on__image__eq__iff,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,C2: set_Pa1764573435lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.30/0.47        ( ( inj_on772319074lle_tv @ F @ C2 )
% 0.30/0.47       => ( ( ord_le241064091lle_tv @ A2 @ C2 )
% 0.30/0.47         => ( ( ord_le241064091lle_tv @ B4 @ C2 )
% 0.30/0.47           => ( ( ( image_335818702lle_tv @ F @ A2 )
% 0.30/0.47                = ( image_335818702lle_tv @ F @ B4 ) )
% 0.30/0.47              = ( A2 = B4 ) ) ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_on_image_eq_iff
% 0.30/0.47  thf(fact_350_inj__on__subset,axiom,
% 0.30/0.47      ! [F: nat > nat,A2: set_nat,B4: set_nat] :
% 0.30/0.47        ( ( inj_on_nat_nat @ F @ A2 )
% 0.30/0.47       => ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 0.30/0.47         => ( inj_on_nat_nat @ F @ B4 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_on_subset
% 0.30/0.47  thf(fact_351_inj__on__subset,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 0.30/0.47        ( ( inj_on772319074lle_tv @ F @ A2 )
% 0.30/0.47       => ( ( ord_le241064091lle_tv @ B4 @ A2 )
% 0.30/0.47         => ( inj_on772319074lle_tv @ F @ B4 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % inj_on_subset
% 0.30/0.47  thf(fact_352_subset__inj__on,axiom,
% 0.30/0.47      ! [F: nat > nat,B4: set_nat,A2: set_nat] :
% 0.30/0.47        ( ( inj_on_nat_nat @ F @ B4 )
% 0.30/0.47       => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 0.30/0.47         => ( inj_on_nat_nat @ F @ A2 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % subset_inj_on
% 0.30/0.47  thf(fact_353_subset__inj__on,axiom,
% 0.30/0.47      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv,A2: set_Pa1764573435lle_tv] :
% 0.30/0.47        ( ( inj_on772319074lle_tv @ F @ B4 )
% 0.30/0.47       => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 0.30/0.47         => ( inj_on772319074lle_tv @ F @ A2 ) ) ) ).
% 0.30/0.47  
% 0.30/0.47  % subset_inj_on
% 0.30/0.47  
% 0.30/0.47  % Helper facts (3)
% 0.30/0.47  thf(help_If_3_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 0.30/0.47      ! [P3: $o] :
% 0.30/0.47        ( ( P3 = $true )
% 0.30/0.47        | ( P3 = $false ) ) ).
% 0.30/0.47  
% 0.30/0.47  thf(help_If_2_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 0.30/0.47      ! [X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( if_Par1134130401lle_tv @ $false @ X @ Y )
% 0.30/0.47        = Y ) ).
% 0.30/0.47  
% 0.30/0.47  thf(help_If_1_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 0.30/0.47      ! [X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 0.30/0.47        ( ( if_Par1134130401lle_tv @ $true @ X @ Y )
% 0.30/0.47        = X ) ).
% 0.30/0.47  
% 0.30/0.47  % Conjectures (1)
% 0.30/0.47  thf(conj_0,conjecture,
% 0.30/0.47      ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) )
% 0.30/0.47      = ( paraco1325918602e_eval @ i @ p1 ) ) ).
% 0.30/0.47  
% 0.30/0.47  %------------------------------------------------------------------------------
% 0.30/0.47  ------------------------
% 2.89/1.56  ---- Embedded in THF ---
% 2.89/1.56  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.89/1.56  %%% Generated on Tue Feb 24 08:27:26 EST 2026
% 2.89/1.56  %%% using '$$dhol' embedding, version 1.3.0.
% 2.89/1.56  %%% Logic specification used:
% 2.89/1.56  %%% thf(spec, logic, $$dhol).
% 2.89/1.56  
% 2.89/1.56  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.J4RbD3yP62/DTF2DTF1342.p
% See solution above
% 2.89/1.56  ------------------------
% 2.89/1.59  ---- Cleaned THF ---
% 2.89/1.59  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,
% 2.89/1.59      set_Pr1475944804lle_fm: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1250255278lle_fm: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      set_Pr2012908090lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      set_Pr698334450lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1720769084lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      set_Pr2061825550lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      set_Pr1943077434tv_nat: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      set_Pr292927124lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1852595672lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      set_Pr1723822845lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      set_Pr2120184979lle_fm: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1443694919lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc696645085lle_fm: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      set_Pr1490359111at_nat: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 2.89/1.59      set_Pr2014382200lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J_J,type,
% 2.89/1.59      set_Pr1019238018lle_fm: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      set_Pr840833727at_nat: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      set_Pr560526279lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.89/1.59      produc1647334210lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 2.89/1.59      produc450659916lle_fm: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      set_Pr1357842111at_nat: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.89/1.59      produc596913417at_nat: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.89/1.59      produc931990033lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J_J,type,
% 2.89/1.59      set_Pr1725653840tv_nat: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 2.89/1.59      set_Pr13445366lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1281043295at_nat: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 2.89/1.59      produc194167194tv_nat: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.89/1.59      produc270694976lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.89/1.59      set_Pr1986765409at_nat: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.89/1.59      set_Pa1764573435lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.89/1.59      product_prod_nat_nat: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      paraco1605129243lle_tv: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 2.89/1.59      paraco1604210848lle_fm: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__List__Olist_It__String__Ochar_J,type,
% 2.89/1.59      list_char: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 2.89/1.59      set_nat: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(ty_n_t__Nat__Onat,type,
% 2.89/1.59      nat: $tType ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.89/1.59      inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      inj_on1955349912lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 2.89/1.59      inj_on1179712058tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Fun_Oinj__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      inj_on772319074lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      inj_on26176689at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      inj_on1745913142lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      inj_on552895452tv_nat: ( produc194167194tv_nat > produc194167194tv_nat ) > set_Pr1725653840tv_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      inj_on2112487900lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Fun_Othe__inv__into_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.89/1.59      the_inv_into_nat_nat: set_nat > ( nat > nat ) > nat > nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Fun_Othe__inv__into_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      the_in452116896lle_tv: set_Pa1764573435lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.89/1.59      ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.89/1.59      ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Orderings_Oord__class_Oless__eq_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,
% 2.89/1.59      ord_le1007985907lle_fm: set_Pr2120184979lle_fm > set_Pr2120184979lle_fm > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J_J,type,
% 2.89/1.59      ord_le1784136743lle_tv: set_Pr560526279lle_tv > set_Pr560526279lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Orderings_Oorder__class_Ostrict__mono_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.89/1.59      order_769474267at_nat: ( nat > nat ) > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Nat__Onat_M_Eo_J,type,
% 2.89/1.59      top_top_nat_o: nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_Eo_J,type,
% 2.89/1.59      top_to1299250770e_tv_o: paraco1605129243lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Orderings_Otop__class_Otop_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 2.89/1.59      top_to632227436_nat_o: product_prod_nat_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      top_to1889334367e_tv_o: produc270694976lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      top_to900819589_nat_o: produc194167194tv_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Orderings_Otop__class_Otop_001_Eo,type,
% 2.89/1.59      top_top_o: $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 2.89/1.59      top_top_set_nat: set_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.89/1.59      top_to1057771083lle_tv: set_Pa1764573435lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      top_to138697918lle_tv: set_Pr2061825550lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      top_to775056195lle_fm: set_Pr2120184979lle_fm ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      top_to1541413903at_nat: set_Pr1357842111at_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      top_to449985143lle_tv: set_Pr560526279lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.89/1.59      top_to1555900337at_nat: set_Pr1986765409at_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      top_to1411004326lle_tv: set_Pr13445366lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      top_to975729152tv_nat: set_Pr1725653840tv_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      top_to1871154984lle_tv: set_Pr2014382200lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__int,type,
% 2.89/1.59      paraco761681009ge_int: ( nat > nat ) > ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv,type,
% 2.89/1.59      paraco1147068288nge_tv: ( nat > nat ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ochange__tv__rel,type,
% 2.89/1.59      paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Oeval,type,
% 2.89/1.59      paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OCon_H,type,
% 2.89/1.59      paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql,type,
% 2.89/1.59      paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OEql_H,type,
% 2.89/1.59      paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_ONeg_H,type,
% 2.89/1.59      paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OPro,type,
% 2.89/1.59      paraco1480028776le_Pro: list_char > paraco1604210848lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ofm_OTruth,type,
% 2.89/1.59      paraco367965286_Truth: paraco1604210848lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_ODet,type,
% 2.89/1.59      paraco1344940915le_Det: $o > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_OIndet,type,
% 2.89/1.59      paraco793048302_Indet: nat > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Otv_Ocase__tv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      paraco2051596139lle_tv: ( $o > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > paraco1605129243lle_tv > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid,type,
% 2.89/1.59      paraco327635598_valid: paraco1604210848lle_fm > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Paraconsistency__Mirabelle__qxuposogha_Ovalid__in,type,
% 2.89/1.59      paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1297923922lle_tv: ( list_char > paraco1605129243lle_tv ) > ( list_char > paraco1605129243lle_tv ) > produc1852595672lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1710735575lle_fm: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > produc696645085lle_fm ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc780837143at_nat: ( nat > nat ) > ( nat > nat ) > produc1281043295at_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      produc1680557635lle_tv: ( nat > nat ) > paraco1605129243lle_tv > produc931990033lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1943344577lle_tv: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > produc1443694919lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm_001t__Paraconsistency____Mirabelle____qxuposogha__Ofm,type,
% 2.89/1.59      produc1126104134lle_fm: paraco1604210848lle_fm > paraco1604210848lle_fm > produc450659916lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.89/1.59      produc1633679363at_nat: paraco1605129243lle_tv > ( nat > nat ) > produc596913417at_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_OPair_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      produc2058540732lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc407632608lle_fm: produc696645085lle_fm > produc696645085lle_fm > produc1250255278lle_fm ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc2057188974lle_tv: produc931990033lle_tv > produc931990033lle_tv > produc1720769084lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1942165868lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > produc696645085lle_fm > produc696645085lle_fm ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc939316703lle_tv: ( ( nat > nat ) > nat > nat ) > produc931990033lle_tv > produc931990033lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1807466521lle_tv: ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc109093078at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Obool_Ocase__bool_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc275353523e_fm_o: ( produc696645085lle_fm > $o ) > ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Ocurry_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_Eo,type,
% 2.89/1.59      produc752649287e_tv_o: ( produc931990033lle_tv > $o ) > ( nat > nat ) > paraco1605129243lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1900967599lle_fm: ( ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv ) > ( paraco1604210848lle_fm > paraco1604210848lle_fm ) > produc696645085lle_fm > produc696645085lle_fm ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1566550641lle_tv: ( ( list_char > paraco1605129243lle_tv ) > nat > nat ) > ( paraco1604210848lle_fm > paraco1605129243lle_tv ) > produc696645085lle_fm > produc931990033lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc951033137lle_fm: ( ( nat > nat ) > list_char > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1604210848lle_fm ) > produc931990033lle_tv > produc696645085lle_fm ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc532909085lle_tv: ( ( nat > nat ) > nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc931990033lle_tv > produc931990033lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.89/1.59      produc505105722at_nat: ( nat > nat ) > ( nat > nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      produc313957681lle_tv: ( nat > nat ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc270694976lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 2.89/1.59      produc1685803475tv_nat: ( nat > nat ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > product_prod_nat_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      produc2101297531lle_tv: ( nat > nat ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc270694976lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.89/1.59      produc1250721397at_nat: ( nat > paraco1605129243lle_tv ) > ( nat > nat ) > product_prod_nat_nat > produc194167194tv_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      produc210389789lle_tv: ( nat > paraco1605129243lle_tv ) > ( nat > paraco1605129243lle_tv ) > product_prod_nat_nat > produc1647334210lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Omap__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 2.89/1.59      produc189459613tv_nat: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > nat ) > produc270694976lle_tv > produc194167194tv_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1975500101lle_tv: ( nat > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc270694976lle_tv > produc1647334210lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.89/1.59      produc386540311at_nat: ( paraco1605129243lle_tv > nat ) > ( nat > nat ) > produc194167194tv_nat > product_prod_nat_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      produc72207551lle_tv: ( paraco1605129243lle_tv > nat ) > ( nat > paraco1605129243lle_tv ) > produc194167194tv_nat > produc270694976lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Omap__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.89/1.59      produc42536895at_nat: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( nat > nat ) > produc194167194tv_nat > produc194167194tv_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1345917071lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > produc1647334210lle_tv > produc1647334210lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Oprod_Ofst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      produc1636169559lle_tv: produc931990033lle_tv > nat > nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Oprod_Ofst_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.89/1.59      produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Oprod_Osnd_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      produc547496597lle_tv: produc931990033lle_tv > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Oprod_Osnd_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.89/1.59      produc500618325at_nat: produc596913417at_nat > nat > nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Oprod_Oswap_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      produc225513635lle_tv: produc931990033lle_tv > produc596913417at_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Product__Type_Oprod_Oswap_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.89/1.59      produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.89/1.59      inv_image_nat_nat: set_Pr1986765409at_nat > ( nat > nat ) > set_Pr1986765409at_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Relation_Oinv__image_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      inv_im1292588663lle_tv: set_Pr1986765409at_nat > ( paraco1605129243lle_tv > nat ) > set_Pr2014382200lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Relation_Oinv__image_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 2.89/1.59      inv_im516950809tv_nat: set_Pr2014382200lle_tv > ( nat > paraco1605129243lle_tv ) > set_Pr1986765409at_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Relation_Oinv__image_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      inv_im719552961lle_tv: set_Pr2014382200lle_tv > ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pr2014382200lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Relation_Ototal__on_001t__Nat__Onat,type,
% 2.89/1.59      total_on_nat: set_nat > set_Pr1986765409at_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Relation_Ototal__on_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      total_1781621663lle_tv: set_Pa1764573435lle_tv > set_Pr2014382200lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.89/1.59      total_1775715973at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.89/1.59      total_517371324lle_tv: set_Pr13445366lle_tv > set_Pr292927124lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 2.89/1.59      total_440843542tv_nat: set_Pr1725653840tv_nat > set_Pr1943077434tv_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Relation_Ototal__on_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.89/1.59      total_92239038lle_tv: set_Pr2014382200lle_tv > set_Pr2012908090lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 2.89/1.59      collect_nat: ( nat > $o ) > set_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Set_OCollect_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      collec1111687558lle_tv: ( paraco1605129243lle_tv > $o ) > set_Pa1764573435lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      collec1102043437lle_tv: ( produc1852595672lle_tv > $o ) > set_Pr2061825550lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      collec835549234lle_fm: ( produc696645085lle_fm > $o ) > set_Pr2120184979lle_fm ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      collec791369802at_nat: ( produc1281043295at_nat > $o ) > set_Pr1357842111at_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      collec1624074086lle_tv: ( produc931990033lle_tv > $o ) > set_Pr560526279lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.89/1.59      collec7649004at_nat: ( product_prod_nat_nat > $o ) > set_Pr1986765409at_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.89/1.59      collec924990229lle_tv: ( produc270694976lle_tv > $o ) > set_Pr13445366lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 2.89/1.59      collec848462447tv_nat: ( produc194167194tv_nat > $o ) > set_Pr1725653840tv_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.89/1.59      image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      image_1151963140lle_tv: ( nat > paraco1605129243lle_tv ) > set_nat > set_Pa1764573435lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 2.89/1.59      image_376325286tv_nat: ( paraco1605129243lle_tv > nat ) > set_Pa1764573435lle_tv > set_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Set_Oimage_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      image_335818702lle_tv: ( paraco1605129243lle_tv > paraco1605129243lle_tv ) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_807538418lle_fm: ( produc696645085lle_fm > produc696645085lle_fm ) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_1154804148lle_tv: ( produc696645085lle_fm > produc931990033lle_tv ) > set_Pr2120184979lle_fm > set_Pr560526279lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_924970994lle_tv: ( produc696645085lle_fm > produc1443694919lle_tv ) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_1585092542lle_fm: ( produc931990033lle_tv > produc696645085lle_fm ) > set_Pr560526279lle_tv > set_Pr2120184979lle_fm ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_1751508608lle_tv: ( produc931990033lle_tv > produc931990033lle_tv ) > set_Pr560526279lle_tv > set_Pr560526279lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_1724396928at_nat: ( produc931990033lle_tv > produc596913417at_nat ) > set_Pr560526279lle_tv > set_Pr840833727at_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_815163717at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1986765409at_nat > set_Pr1986765409at_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_1674248956lle_tv: ( product_prod_nat_nat > produc270694976lle_tv ) > set_Pr1986765409at_nat > set_Pr13445366lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_1597721174tv_nat: ( product_prod_nat_nat > produc194167194tv_nat ) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_1507992062lle_tv: ( product_prod_nat_nat > produc1647334210lle_tv ) > set_Pr1986765409at_nat > set_Pr2014382200lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_1787705850at_nat: ( produc270694976lle_tv > product_prod_nat_nat ) > set_Pr13445366lle_tv > set_Pr1986765409at_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_149830562lle_tv: ( produc270694976lle_tv > produc270694976lle_tv ) > set_Pr13445366lle_tv > set_Pr13445366lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_53754658tv_nat: ( produc270694976lle_tv > produc194167194tv_nat ) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_988201162lle_tv: ( produc270694976lle_tv > produc1647334210lle_tv ) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_326034184lle_fm: ( produc1443694919lle_tv > produc696645085lle_fm ) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_769496456lle_tv: ( produc596913417at_nat > produc931990033lle_tv ) > set_Pr840833727at_nat > set_Pr560526279lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_1805124128at_nat: ( produc194167194tv_nat > product_prod_nat_nat ) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_1200372424lle_tv: ( produc194167194tv_nat > produc270694976lle_tv ) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      image_1221801032lle_tv: ( produc1647334210lle_tv > produc1647334210lle_tv ) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      accp_P2085826120lle_tv: ( produc931990033lle_tv > produc931990033lle_tv > $o ) > produc931990033lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      lex_pr2001015487lle_fm: set_Pr2061825550lle_tv > set_Pr1019238018lle_fm > set_Pr1475944804lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Wellfounded_Olex__prod_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      lex_pr1093414955lle_tv: set_Pr1357842111at_nat > set_Pr2014382200lle_tv > set_Pr698334450lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Nat__Onat,type,
% 2.89/1.59      lex_prod_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1490359111at_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Wellfounded_Olex__prod_001t__Nat__Onat_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      lex_pr413684186lle_tv: set_Pr1986765409at_nat > set_Pr2014382200lle_tv > set_Pr292927124lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Wellfounded_Olex__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Nat__Onat,type,
% 2.89/1.59      lex_pr1785529980tv_nat: set_Pr2014382200lle_tv > set_Pr1986765409at_nat > set_Pr1943077434tv_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Wellfounded_Olex__prod_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      lex_pr567812260lle_tv: set_Pr2014382200lle_tv > set_Pr2014382200lle_tv > set_Pr2012908090lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 2.89/1.59      wf_nat: set_Pr1986765409at_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Wellfounded_Owf_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      wf_Par1378404612lle_tv: set_Pr2014382200lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      same_f1581085506lle_fm: ( ( list_char > paraco1605129243lle_tv ) > $o ) > ( ( list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm ) > set_Pr1475944804lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_Wfrec_Osame__fst_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      same_f1138187694lle_tv: ( ( nat > nat ) > $o ) > ( ( nat > nat ) > set_Pr2014382200lle_tv ) > set_Pr698334450lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_member_001t__Nat__Onat,type,
% 2.89/1.59      member_nat: nat > set_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_member_001t__Paraconsistency____Mirabelle____qxuposogha__Otv,type,
% 2.89/1.59      member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      member146333935lle_tv: produc1852595672lle_tv > set_Pr2061825550lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      member112824072at_nat: produc1281043295at_nat > set_Pr1357842111at_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.89/1.59      member1569366824lle_tv: produc931990033lle_tv > set_Pr560526279lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 2.89/1.59      member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.89/1.59      member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Ofm_Mt__Paraconsistency____Mirabelle____qxuposogha__Ofm_J,type,
% 2.89/1.59      member334644067lle_fm: produc450659916lle_fm > set_Pr1019238018lle_fm > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 2.89/1.59      member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Nat__Onat_J,type,
% 2.89/1.59      member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_c_member_001t__Product____Type__Oprod_It__Paraconsistency____Mirabelle____qxuposogha__Otv_Mt__Paraconsistency____Mirabelle____qxuposogha__Otv_J,type,
% 2.89/1.59      member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      member1592865093lle_fm: produc1250255278lle_fm > set_Pr1475944804lle_fm > $o ).
% 2.89/1.59  
% 2.89/1.59  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,
% 2.89/1.59      member1339857875lle_tv: produc1720769084lle_tv > set_Pr698334450lle_tv > $o ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_v_f,type,
% 2.89/1.59      f: nat > nat ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_v_i,type,
% 2.89/1.59      i: list_char > paraco1605129243lle_tv ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_v_p1____,type,
% 2.89/1.59      p1: paraco1604210848lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(sy_v_p2____,type,
% 2.89/1.59      p2: paraco1604210848lle_fm ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_0_a_H_H,axiom,
% 2.89/1.59      ( ( paraco1325918602e_eval @ i @ p1 )
% 2.89/1.59     != ( paraco1344940915le_Det @ $true ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_1_a,axiom,
% 2.89/1.59      ( ( paraco1325918602e_eval @ i @ p2 )
% 2.89/1.59      = ( paraco1344940915le_Det @ $true ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_2_a_H,axiom,
% 2.89/1.59      ( ( paraco1325918602e_eval @ i @ p1 )
% 2.89/1.59     != ( paraco1325918602e_eval @ i @ p2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_3_fm_Oinject_I3_J,axiom,
% 2.89/1.59      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,Y41: paraco1604210848lle_fm,Y42: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( ( paraco69239110le_Con @ X41 @ X42 )
% 2.89/1.59          = ( paraco69239110le_Con @ Y41 @ Y42 ) )
% 2.89/1.59        = ( ( X41 = Y41 )
% 2.89/1.59          & ( X42 = Y42 ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_4_b_H,axiom,
% 2.89/1.59      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 2.89/1.59     != ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_5_eval_Osimps_I4_J,axiom,
% 2.89/1.59      ! [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59            = ( paraco1325918602e_eval @ I @ Q ) )
% 2.89/1.59         => ( ( paraco1325918602e_eval @ I @ ( paraco69239110le_Con @ P @ Q ) )
% 2.89/1.59            = ( paraco1325918602e_eval @ I @ P ) ) )
% 2.89/1.59        & ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59           != ( paraco1325918602e_eval @ I @ Q ) )
% 2.89/1.59         => ( ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59                = ( paraco1344940915le_Det @ $true ) )
% 2.89/1.59             => ( ( paraco1325918602e_eval @ I @ ( paraco69239110le_Con @ P @ Q ) )
% 2.89/1.59                = ( paraco1325918602e_eval @ I @ Q ) ) )
% 2.89/1.59            & ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59               != ( paraco1344940915le_Det @ $true ) )
% 2.89/1.59             => ( ( ( ( paraco1325918602e_eval @ I @ Q )
% 2.89/1.59                    = ( paraco1344940915le_Det @ $true ) )
% 2.89/1.59                 => ( ( paraco1325918602e_eval @ I @ ( paraco69239110le_Con @ P @ Q ) )
% 2.89/1.59                    = ( paraco1325918602e_eval @ I @ P ) ) )
% 2.89/1.59                & ( ( ( paraco1325918602e_eval @ I @ Q )
% 2.89/1.59                   != ( paraco1344940915le_Det @ $true ) )
% 2.89/1.59                 => ( ( paraco1325918602e_eval @ I @ ( paraco69239110le_Con @ P @ Q ) )
% 2.89/1.59                    = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_6_ih2,axiom,
% 2.89/1.59      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p2 )
% 2.89/1.59      = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p2 ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_7_ih1,axiom,
% 2.89/1.59      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 2.89/1.59      = ( paraco1147068288nge_tv @ f @ ( paraco1325918602e_eval @ i @ p1 ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_8_b_H_H,axiom,
% 2.89/1.59      ( ( paraco1325918602e_eval @ ( paraco761681009ge_int @ f @ i ) @ p1 )
% 2.89/1.59     != ( paraco1344940915le_Det @ $true ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_9_tv_Oinject_I1_J,axiom,
% 2.89/1.59      ! [X1: $o,Y1: $o] :
% 2.89/1.59        ( ( ( paraco1344940915le_Det @ X1 )
% 2.89/1.59          = ( paraco1344940915le_Det @ Y1 ) )
% 2.89/1.59        = ( X1 = Y1 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_10_conjunction,axiom,
% 2.89/1.59      ! [P: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( paraco327635598_valid @ ( paraco69239110le_Con @ P @ Q ) )
% 2.89/1.59        = ( ( paraco327635598_valid @ P )
% 2.89/1.59          & ( paraco327635598_valid @ Q ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_11_conjunction__in,axiom,
% 2.89/1.59      ! [U: set_nat,P: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( paraco55203475lid_in @ U @ ( paraco69239110le_Con @ P @ Q ) )
% 2.89/1.59        = ( ( paraco55203475lid_in @ U @ P )
% 2.89/1.59          & ( paraco55203475lid_in @ U @ Q ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_12_fm_Odistinct_I13_J,axiom,
% 2.89/1.59      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 2.89/1.59        ( paraco367965286_Truth
% 2.89/1.59       != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_13_fm_Odistinct_I25_J,axiom,
% 2.89/1.59      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( paraco69239110le_Con @ X41 @ X42 )
% 2.89/1.59       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_14_fm_Oinject_I4_J,axiom,
% 2.89/1.59      ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,Y51: paraco1604210848lle_fm,Y52: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 2.89/1.59          = ( paraco1389086619le_Eql @ Y51 @ Y52 ) )
% 2.89/1.59        = ( ( X51 = Y51 )
% 2.89/1.59          & ( X52 = Y52 ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_15_fm_Odistinct_I15_J,axiom,
% 2.89/1.59      ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 2.89/1.59        ( paraco367965286_Truth
% 2.89/1.59       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_16_change__tv_Osimps_I1_J,axiom,
% 2.89/1.59      ! [F: nat > nat,B: $o] :
% 2.89/1.59        ( ( paraco1147068288nge_tv @ F @ ( paraco1344940915le_Det @ B ) )
% 2.89/1.59        = ( paraco1344940915le_Det @ B ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_17_transfer,axiom,
% 2.89/1.59      ! [U: set_nat,P: paraco1604210848lle_fm] :
% 2.89/1.59        ( ~ ( paraco55203475lid_in @ U @ P )
% 2.89/1.59       => ~ ( paraco327635598_valid @ P ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_18_change__int__def,axiom,
% 2.89/1.59      ( paraco761681009ge_int
% 2.89/1.59      = ( ^ [F2: nat > nat,I2: list_char > paraco1605129243lle_tv,S: list_char] : ( paraco1147068288nge_tv @ F2 @ ( I2 @ S ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_19_valid__valid__in,axiom,
% 2.89/1.59      ! [P: paraco1604210848lle_fm,U: set_nat] :
% 2.89/1.59        ( ( paraco327635598_valid @ P )
% 2.89/1.59       => ( paraco55203475lid_in @ U @ P ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_20_eval__equality__simplify,axiom,
% 2.89/1.59      ! [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( paraco1325918602e_eval @ I @ ( paraco1389086619le_Eql @ P @ Q ) )
% 2.89/1.59        = ( paraco1344940915le_Det
% 2.89/1.59          @ ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59            = ( paraco1325918602e_eval @ I @ Q ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_21_eval_Osimps_I5_J,axiom,
% 2.89/1.59      ! [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59            = ( paraco1325918602e_eval @ I @ Q ) )
% 2.89/1.59         => ( ( paraco1325918602e_eval @ I @ ( paraco1389086619le_Eql @ P @ Q ) )
% 2.89/1.59            = ( paraco1344940915le_Det @ $true ) ) )
% 2.89/1.59        & ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59           != ( paraco1325918602e_eval @ I @ Q ) )
% 2.89/1.59         => ( ( paraco1325918602e_eval @ I @ ( paraco1389086619le_Eql @ P @ Q ) )
% 2.89/1.59            = ( paraco1344940915le_Det @ $false ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_22_eval_Osimps_I2_J,axiom,
% 2.89/1.59      ! [I: list_char > paraco1605129243lle_tv] :
% 2.89/1.59        ( ( paraco1325918602e_eval @ I @ paraco367965286_Truth )
% 2.89/1.59        = ( paraco1344940915le_Det @ $true ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_23_valid__def,axiom,
% 2.89/1.59      ( paraco327635598_valid
% 2.89/1.59      = ( ^ [P2: paraco1604210848lle_fm] :
% 2.89/1.59          ! [I2: list_char > paraco1605129243lle_tv] :
% 2.89/1.59            ( ( paraco1325918602e_eval @ I2 @ P2 )
% 2.89/1.59            = ( paraco1344940915le_Det @ $true ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_24_change__tv_Oelims,axiom,
% 2.89/1.59      ! [X: nat > nat,Xa: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 2.89/1.59        ( ( ( paraco1147068288nge_tv @ X @ Xa )
% 2.89/1.59          = Y )
% 2.89/1.59       => ( ! [B2: $o] :
% 2.89/1.59              ( ( Xa
% 2.89/1.59                = ( paraco1344940915le_Det @ B2 ) )
% 2.89/1.59             => ( Y
% 2.89/1.59               != ( paraco1344940915le_Det @ B2 ) ) )
% 2.89/1.59         => ~ ! [N: nat] :
% 2.89/1.59                ( ( Xa
% 2.89/1.59                  = ( paraco793048302_Indet @ N ) )
% 2.89/1.59               => ( Y
% 2.89/1.59                 != ( paraco793048302_Indet @ ( X @ N ) ) ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_25_tv_Osimps_I5_J,axiom,
% 2.89/1.59      ! [F1: $o > paraco1605129243lle_tv,F22: nat > paraco1605129243lle_tv,X1: $o] :
% 2.89/1.59        ( ( paraco2051596139lle_tv @ F1 @ F22 @ ( paraco1344940915le_Det @ X1 ) )
% 2.89/1.59        = ( F1 @ X1 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_26_eval__negation,axiom,
% 2.89/1.59      ! [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59            = ( paraco1344940915le_Det @ $false ) )
% 2.89/1.59         => ( ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ P ) )
% 2.89/1.59            = ( paraco1344940915le_Det @ $true ) ) )
% 2.89/1.59        & ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59           != ( paraco1344940915le_Det @ $false ) )
% 2.89/1.59         => ( ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59                = ( paraco1344940915le_Det @ $true ) )
% 2.89/1.59             => ( ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ P ) )
% 2.89/1.59                = ( paraco1344940915le_Det @ $false ) ) )
% 2.89/1.59            & ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59               != ( paraco1344940915le_Det @ $true ) )
% 2.89/1.59             => ( ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ P ) )
% 2.89/1.59                = ( paraco1325918602e_eval @ I @ P ) ) ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_27_assms,axiom,
% 2.89/1.59      inj_on_nat_nat @ f @ top_top_set_nat ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_28_change__tv_Osimps_I2_J,axiom,
% 2.89/1.59      ! [F: nat > nat,N2: nat] :
% 2.89/1.59        ( ( paraco1147068288nge_tv @ F @ ( paraco793048302_Indet @ N2 ) )
% 2.89/1.59        = ( paraco793048302_Indet @ ( F @ N2 ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_29_fm_Odistinct_I17_J,axiom,
% 2.89/1.59      ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 2.89/1.59        ( paraco367965286_Truth
% 2.89/1.59       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_30_fm_Oinject_I2_J,axiom,
% 2.89/1.59      ! [X3: paraco1604210848lle_fm,Y3: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( ( paraco445776468le_Neg @ X3 )
% 2.89/1.59          = ( paraco445776468le_Neg @ Y3 ) )
% 2.89/1.59        = ( X3 = Y3 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_31_fm_Oinject_I5_J,axiom,
% 2.89/1.59      ! [X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm,Y61: paraco1604210848lle_fm,Y62: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( ( paraco1745535428le_Eql @ X61 @ X62 )
% 2.89/1.59          = ( paraco1745535428le_Eql @ Y61 @ Y62 ) )
% 2.89/1.59        = ( ( X61 = Y61 )
% 2.89/1.59          & ( X62 = Y62 ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_32_tv_Oinject_I2_J,axiom,
% 2.89/1.59      ! [X2: nat,Y2: nat] :
% 2.89/1.59        ( ( ( paraco793048302_Indet @ X2 )
% 2.89/1.59          = ( paraco793048302_Indet @ Y2 ) )
% 2.89/1.59        = ( X2 = Y2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_33_fm_Odistinct_I23_J,axiom,
% 2.89/1.59      ! [X3: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( paraco445776468le_Neg @ X3 )
% 2.89/1.59       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_34_tv_Osimps_I6_J,axiom,
% 2.89/1.59      ! [F1: $o > paraco1605129243lle_tv,F22: nat > paraco1605129243lle_tv,X2: nat] :
% 2.89/1.59        ( ( paraco2051596139lle_tv @ F1 @ F22 @ ( paraco793048302_Indet @ X2 ) )
% 2.89/1.59        = ( F22 @ X2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_35_mem__Collect__eq,axiom,
% 2.89/1.59      ! [A: produc696645085lle_fm,P3: produc696645085lle_fm > $o] :
% 2.89/1.59        ( ( member1474794996lle_fm @ A @ ( collec835549234lle_fm @ P3 ) )
% 2.89/1.59        = ( P3 @ A ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_36_mem__Collect__eq,axiom,
% 2.89/1.59      ! [A: produc1852595672lle_tv,P3: produc1852595672lle_tv > $o] :
% 2.89/1.59        ( ( member146333935lle_tv @ A @ ( collec1102043437lle_tv @ P3 ) )
% 2.89/1.59        = ( P3 @ A ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_37_mem__Collect__eq,axiom,
% 2.89/1.59      ! [A: produc931990033lle_tv,P3: produc931990033lle_tv > $o] :
% 2.89/1.59        ( ( member1569366824lle_tv @ A @ ( collec1624074086lle_tv @ P3 ) )
% 2.89/1.59        = ( P3 @ A ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_38_mem__Collect__eq,axiom,
% 2.89/1.59      ! [A: produc1281043295at_nat,P3: produc1281043295at_nat > $o] :
% 2.89/1.59        ( ( member112824072at_nat @ A @ ( collec791369802at_nat @ P3 ) )
% 2.89/1.59        = ( P3 @ A ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_39_mem__Collect__eq,axiom,
% 2.89/1.59      ! [A: paraco1605129243lle_tv,P3: paraco1605129243lle_tv > $o] :
% 2.89/1.59        ( ( member266900804lle_tv @ A @ ( collec1111687558lle_tv @ P3 ) )
% 2.89/1.59        = ( P3 @ A ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_40_mem__Collect__eq,axiom,
% 2.89/1.59      ! [A: nat,P3: nat > $o] :
% 2.89/1.59        ( ( member_nat @ A @ ( collect_nat @ P3 ) )
% 2.89/1.59        = ( P3 @ A ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_41_Collect__mem__eq,axiom,
% 2.89/1.59      ! [A2: set_Pr2120184979lle_fm] :
% 2.89/1.59        ( ( collec835549234lle_fm
% 2.89/1.59          @ ^ [X4: produc696645085lle_fm] : ( member1474794996lle_fm @ X4 @ A2 ) )
% 2.89/1.59        = A2 ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_42_Collect__mem__eq,axiom,
% 2.89/1.59      ! [A2: set_Pr2061825550lle_tv] :
% 2.89/1.59        ( ( collec1102043437lle_tv
% 2.89/1.59          @ ^ [X4: produc1852595672lle_tv] : ( member146333935lle_tv @ X4 @ A2 ) )
% 2.89/1.59        = A2 ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_43_Collect__mem__eq,axiom,
% 2.89/1.59      ! [A2: set_Pr560526279lle_tv] :
% 2.89/1.59        ( ( collec1624074086lle_tv
% 2.89/1.59          @ ^ [X4: produc931990033lle_tv] : ( member1569366824lle_tv @ X4 @ A2 ) )
% 2.89/1.59        = A2 ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_44_Collect__mem__eq,axiom,
% 2.89/1.59      ! [A2: set_Pr1357842111at_nat] :
% 2.89/1.59        ( ( collec791369802at_nat
% 2.89/1.59          @ ^ [X4: produc1281043295at_nat] : ( member112824072at_nat @ X4 @ A2 ) )
% 2.89/1.59        = A2 ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_45_Collect__mem__eq,axiom,
% 2.89/1.59      ! [A2: set_Pa1764573435lle_tv] :
% 2.89/1.59        ( ( collec1111687558lle_tv
% 2.89/1.59          @ ^ [X4: paraco1605129243lle_tv] : ( member266900804lle_tv @ X4 @ A2 ) )
% 2.89/1.59        = A2 ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_46_Collect__mem__eq,axiom,
% 2.89/1.59      ! [A2: set_nat] :
% 2.89/1.59        ( ( collect_nat
% 2.89/1.59          @ ^ [X4: nat] : ( member_nat @ X4 @ A2 ) )
% 2.89/1.59        = A2 ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_47_Collect__cong,axiom,
% 2.89/1.59      ! [P3: paraco1605129243lle_tv > $o,Q2: paraco1605129243lle_tv > $o] :
% 2.89/1.59        ( ! [X5: paraco1605129243lle_tv] :
% 2.89/1.59            ( ( P3 @ X5 )
% 2.89/1.59            = ( Q2 @ X5 ) )
% 2.89/1.59       => ( ( collec1111687558lle_tv @ P3 )
% 2.89/1.59          = ( collec1111687558lle_tv @ Q2 ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_48_Collect__cong,axiom,
% 2.89/1.59      ! [P3: nat > $o,Q2: nat > $o] :
% 2.89/1.59        ( ! [X5: nat] :
% 2.89/1.59            ( ( P3 @ X5 )
% 2.89/1.59            = ( Q2 @ X5 ) )
% 2.89/1.59       => ( ( collect_nat @ P3 )
% 2.89/1.59          = ( collect_nat @ Q2 ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_49_eval__equality,axiom,
% 2.89/1.59      ! [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm,Q: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59            = ( paraco1325918602e_eval @ I @ Q ) )
% 2.89/1.59         => ( ( paraco1325918602e_eval @ I @ ( paraco1745535428le_Eql @ P @ Q ) )
% 2.89/1.59            = ( paraco1344940915le_Det @ $true ) ) )
% 2.89/1.59        & ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59           != ( paraco1325918602e_eval @ I @ Q ) )
% 2.89/1.59         => ( ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59                = ( paraco1344940915le_Det @ $true ) )
% 2.89/1.59             => ( ( paraco1325918602e_eval @ I @ ( paraco1745535428le_Eql @ P @ Q ) )
% 2.89/1.59                = ( paraco1325918602e_eval @ I @ Q ) ) )
% 2.89/1.59            & ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59               != ( paraco1344940915le_Det @ $true ) )
% 2.89/1.59             => ( ( ( ( paraco1325918602e_eval @ I @ Q )
% 2.89/1.59                    = ( paraco1344940915le_Det @ $true ) )
% 2.89/1.59                 => ( ( paraco1325918602e_eval @ I @ ( paraco1745535428le_Eql @ P @ Q ) )
% 2.89/1.59                    = ( paraco1325918602e_eval @ I @ P ) ) )
% 2.89/1.59                & ( ( ( paraco1325918602e_eval @ I @ Q )
% 2.89/1.59                   != ( paraco1344940915le_Det @ $true ) )
% 2.89/1.59                 => ( ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59                        = ( paraco1344940915le_Det @ $false ) )
% 2.89/1.59                     => ( ( paraco1325918602e_eval @ I @ ( paraco1745535428le_Eql @ P @ Q ) )
% 2.89/1.59                        = ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ Q ) ) ) )
% 2.89/1.59                    & ( ( ( paraco1325918602e_eval @ I @ P )
% 2.89/1.59                       != ( paraco1344940915le_Det @ $false ) )
% 2.89/1.59                     => ( ( ( ( paraco1325918602e_eval @ I @ Q )
% 2.89/1.59                            = ( paraco1344940915le_Det @ $false ) )
% 2.89/1.59                         => ( ( paraco1325918602e_eval @ I @ ( paraco1745535428le_Eql @ P @ Q ) )
% 2.89/1.59                            = ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ P ) ) ) )
% 2.89/1.59                        & ( ( ( paraco1325918602e_eval @ I @ Q )
% 2.89/1.59                           != ( paraco1344940915le_Det @ $false ) )
% 2.89/1.59                         => ( ( paraco1325918602e_eval @ I @ ( paraco1745535428le_Eql @ P @ Q ) )
% 2.89/1.59                            = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_50_double__negation,axiom,
% 2.89/1.59      ( paraco1325918602e_eval
% 2.89/1.59      = ( ^ [I2: list_char > paraco1605129243lle_tv,P2: paraco1604210848lle_fm] : ( paraco1325918602e_eval @ I2 @ ( paraco445776468le_Neg @ ( paraco445776468le_Neg @ P2 ) ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_51_fm_Odistinct_I19_J,axiom,
% 2.89/1.59      ! [X3: paraco1604210848lle_fm,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( paraco445776468le_Neg @ X3 )
% 2.89/1.59       != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_52_string__tv_Oinduct,axiom,
% 2.89/1.59      ! [P3: paraco1605129243lle_tv > $o,A0: paraco1605129243lle_tv] :
% 2.89/1.59        ( ( P3 @ ( paraco1344940915le_Det @ $true ) )
% 2.89/1.59       => ( ( P3 @ ( paraco1344940915le_Det @ $false ) )
% 2.89/1.59         => ( ! [N: nat] : ( P3 @ ( paraco793048302_Indet @ N ) )
% 2.89/1.59           => ( P3 @ A0 ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_53_change__tv_Oinduct,axiom,
% 2.89/1.59      ! [P3: ( nat > nat ) > paraco1605129243lle_tv > $o,A0: nat > nat,A1: paraco1605129243lle_tv] :
% 2.89/1.59        ( ! [F3: nat > nat,B2: $o] : ( P3 @ F3 @ ( paraco1344940915le_Det @ B2 ) )
% 2.89/1.59       => ( ! [F3: nat > nat,N: nat] : ( P3 @ F3 @ ( paraco793048302_Indet @ N ) )
% 2.89/1.59         => ( P3 @ A0 @ A1 ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_54_string__tv_Ocases,axiom,
% 2.89/1.59      ! [X: paraco1605129243lle_tv] :
% 2.89/1.59        ( ( X
% 2.89/1.59         != ( paraco1344940915le_Det @ $true ) )
% 2.89/1.59       => ( ( X
% 2.89/1.59           != ( paraco1344940915le_Det @ $false ) )
% 2.89/1.59         => ~ ! [N: nat] :
% 2.89/1.59                ( X
% 2.89/1.59               != ( paraco793048302_Indet @ N ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_55_tv_Oexhaust,axiom,
% 2.89/1.59      ! [Y: paraco1605129243lle_tv] :
% 2.89/1.59        ( ! [X12: $o] :
% 2.89/1.59            ( Y
% 2.89/1.59           != ( paraco1344940915le_Det @ X12 ) )
% 2.89/1.59       => ~ ! [X22: nat] :
% 2.89/1.59              ( Y
% 2.89/1.59             != ( paraco793048302_Indet @ X22 ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_56_tv_Oinduct,axiom,
% 2.89/1.59      ! [P3: paraco1605129243lle_tv > $o,Tv: paraco1605129243lle_tv] :
% 2.89/1.59        ( ! [X5: $o] : ( P3 @ ( paraco1344940915le_Det @ X5 ) )
% 2.89/1.59       => ( ! [X5: nat] : ( P3 @ ( paraco793048302_Indet @ X5 ) )
% 2.89/1.59         => ( P3 @ Tv ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_57_tv_Odistinct_I1_J,axiom,
% 2.89/1.59      ! [X1: $o,X2: nat] :
% 2.89/1.59        ( ( paraco1344940915le_Det @ X1 )
% 2.89/1.59       != ( paraco793048302_Indet @ X2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_58_fm_Odistinct_I21_J,axiom,
% 2.89/1.59      ! [X3: paraco1604210848lle_fm,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( paraco445776468le_Neg @ X3 )
% 2.89/1.59       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_59_fm_Odistinct_I11_J,axiom,
% 2.89/1.59      ! [X3: paraco1604210848lle_fm] :
% 2.89/1.59        ( paraco367965286_Truth
% 2.89/1.59       != ( paraco445776468le_Neg @ X3 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_60_fm_Odistinct_I27_J,axiom,
% 2.89/1.59      ! [X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( paraco69239110le_Con @ X41 @ X42 )
% 2.89/1.59       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_61_fm_Odistinct_I29_J,axiom,
% 2.89/1.59      ! [X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( paraco1389086619le_Eql @ X51 @ X52 )
% 2.89/1.59       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_62_iso__tuple__UNIV__I,axiom,
% 2.89/1.59      ! [X: produc696645085lle_fm] : ( member1474794996lle_fm @ X @ top_to775056195lle_fm ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_63_iso__tuple__UNIV__I,axiom,
% 2.89/1.59      ! [X: produc1852595672lle_tv] : ( member146333935lle_tv @ X @ top_to138697918lle_tv ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_64_iso__tuple__UNIV__I,axiom,
% 2.89/1.59      ! [X: produc931990033lle_tv] : ( member1569366824lle_tv @ X @ top_to449985143lle_tv ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_65_iso__tuple__UNIV__I,axiom,
% 2.89/1.59      ! [X: produc1281043295at_nat] : ( member112824072at_nat @ X @ top_to1541413903at_nat ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_66_iso__tuple__UNIV__I,axiom,
% 2.89/1.59      ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_67_iso__tuple__UNIV__I,axiom,
% 2.89/1.59      ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_68_iso__tuple__UNIV__I,axiom,
% 2.89/1.59      ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_69_iso__tuple__UNIV__I,axiom,
% 2.89/1.59      ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_70_iso__tuple__UNIV__I,axiom,
% 2.89/1.59      ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_71_UNIV__I,axiom,
% 2.89/1.59      ! [X: produc696645085lle_fm] : ( member1474794996lle_fm @ X @ top_to775056195lle_fm ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_72_UNIV__I,axiom,
% 2.89/1.59      ! [X: produc1852595672lle_tv] : ( member146333935lle_tv @ X @ top_to138697918lle_tv ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_73_UNIV__I,axiom,
% 2.89/1.59      ! [X: produc931990033lle_tv] : ( member1569366824lle_tv @ X @ top_to449985143lle_tv ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_74_UNIV__I,axiom,
% 2.89/1.59      ! [X: produc1281043295at_nat] : ( member112824072at_nat @ X @ top_to1541413903at_nat ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_75_UNIV__I,axiom,
% 2.89/1.59      ! [X: produc194167194tv_nat] : ( member737151281tv_nat @ X @ top_to975729152tv_nat ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_76_UNIV__I,axiom,
% 2.89/1.59      ! [X: produc270694976lle_tv] : ( member813679063lle_tv @ X @ top_to1411004326lle_tv ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_77_UNIV__I,axiom,
% 2.89/1.59      ! [X: product_prod_nat_nat] : ( member701585322at_nat @ X @ top_to1555900337at_nat ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_78_UNIV__I,axiom,
% 2.89/1.59      ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_79_UNIV__I,axiom,
% 2.89/1.59      ! [X: paraco1605129243lle_tv] : ( member266900804lle_tv @ X @ top_to1057771083lle_tv ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_80_top__apply,axiom,
% 2.89/1.59      ( top_to1299250770e_tv_o
% 2.89/1.59      = ( ^ [X4: paraco1605129243lle_tv] : top_top_o ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_81_top__apply,axiom,
% 2.89/1.59      ( top_top_nat_o
% 2.89/1.59      = ( ^ [X4: nat] : top_top_o ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_82_eval_Osimps_I3_J,axiom,
% 2.89/1.59      ! [I: list_char > paraco1605129243lle_tv,P: paraco1604210848lle_fm] :
% 2.89/1.59        ( ( paraco1325918602e_eval @ I @ ( paraco445776468le_Neg @ P ) )
% 2.89/1.59        = ( paraco2051596139lle_tv @ ( produc234482697lle_tv @ ( paraco1344940915le_Det @ $false ) @ ( paraco1344940915le_Det @ $true ) ) @ paraco793048302_Indet @ ( paraco1325918602e_eval @ I @ P ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_83_inj__def,axiom,
% 2.89/1.59      ! [F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 2.89/1.59        ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 2.89/1.59        = ( ! [X4: produc1647334210lle_tv,Y4: produc1647334210lle_tv] :
% 2.89/1.59              ( ( ( F @ X4 )
% 2.89/1.59                = ( F @ Y4 ) )
% 2.89/1.59             => ( X4 = Y4 ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_84_inj__def,axiom,
% 2.89/1.59      ! [F: nat > paraco1605129243lle_tv] :
% 2.89/1.59        ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 2.89/1.59        = ( ! [X4: nat,Y4: nat] :
% 2.89/1.59              ( ( ( F @ X4 )
% 2.89/1.59                = ( F @ Y4 ) )
% 2.89/1.59             => ( X4 = Y4 ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_85_inj__def,axiom,
% 2.89/1.59      ! [F: produc194167194tv_nat > produc194167194tv_nat] :
% 2.89/1.59        ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 2.89/1.59        = ( ! [X4: produc194167194tv_nat,Y4: produc194167194tv_nat] :
% 2.89/1.59              ( ( ( F @ X4 )
% 2.89/1.59                = ( F @ Y4 ) )
% 2.89/1.59             => ( X4 = Y4 ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_86_inj__def,axiom,
% 2.89/1.59      ! [F: produc270694976lle_tv > produc270694976lle_tv] :
% 2.89/1.59        ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 2.89/1.59        = ( ! [X4: produc270694976lle_tv,Y4: produc270694976lle_tv] :
% 2.89/1.59              ( ( ( F @ X4 )
% 2.89/1.59                = ( F @ Y4 ) )
% 2.89/1.59             => ( X4 = Y4 ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_87_inj__def,axiom,
% 2.89/1.59      ! [F: product_prod_nat_nat > product_prod_nat_nat] :
% 2.89/1.59        ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 2.89/1.59        = ( ! [X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 2.89/1.59              ( ( ( F @ X4 )
% 2.89/1.59                = ( F @ Y4 ) )
% 2.89/1.59             => ( X4 = Y4 ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_88_inj__def,axiom,
% 2.89/1.59      ! [F: nat > nat] :
% 2.89/1.59        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 2.89/1.59        = ( ! [X4: nat,Y4: nat] :
% 2.89/1.59              ( ( ( F @ X4 )
% 2.89/1.59                = ( F @ Y4 ) )
% 2.89/1.59             => ( X4 = Y4 ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_89_inj__def,axiom,
% 2.89/1.59      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.89/1.59        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 2.89/1.59        = ( ! [X4: paraco1605129243lle_tv,Y4: paraco1605129243lle_tv] :
% 2.89/1.59              ( ( ( F @ X4 )
% 2.89/1.59                = ( F @ Y4 ) )
% 2.89/1.59             => ( X4 = Y4 ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_90_inj__eq,axiom,
% 2.89/1.59      ! [F: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 2.89/1.59        ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59          = ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_91_inj__eq,axiom,
% 2.89/1.59      ! [F: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 2.89/1.59        ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59          = ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_92_inj__eq,axiom,
% 2.89/1.59      ! [F: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 2.89/1.59        ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59          = ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_93_inj__eq,axiom,
% 2.89/1.59      ! [F: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 2.89/1.59        ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59          = ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_94_inj__eq,axiom,
% 2.89/1.59      ! [F: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.89/1.59        ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59          = ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_95_inj__eq,axiom,
% 2.89/1.59      ! [F: nat > nat,X: nat,Y: nat] :
% 2.89/1.59        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59          = ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_96_inj__eq,axiom,
% 2.89/1.59      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 2.89/1.59        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59          = ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_97_injI,axiom,
% 2.89/1.59      ! [F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 2.89/1.59        ( ! [X5: produc1647334210lle_tv,Y5: produc1647334210lle_tv] :
% 2.89/1.59            ( ( ( F @ X5 )
% 2.89/1.59              = ( F @ Y5 ) )
% 2.89/1.59           => ( X5 = Y5 ) )
% 2.89/1.59       => ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_98_injI,axiom,
% 2.89/1.59      ! [F: nat > paraco1605129243lle_tv] :
% 2.89/1.59        ( ! [X5: nat,Y5: nat] :
% 2.89/1.59            ( ( ( F @ X5 )
% 2.89/1.59              = ( F @ Y5 ) )
% 2.89/1.59           => ( X5 = Y5 ) )
% 2.89/1.59       => ( inj_on1955349912lle_tv @ F @ top_top_set_nat ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_99_injI,axiom,
% 2.89/1.59      ! [F: produc194167194tv_nat > produc194167194tv_nat] :
% 2.89/1.59        ( ! [X5: produc194167194tv_nat,Y5: produc194167194tv_nat] :
% 2.89/1.59            ( ( ( F @ X5 )
% 2.89/1.59              = ( F @ Y5 ) )
% 2.89/1.59           => ( X5 = Y5 ) )
% 2.89/1.59       => ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_100_injI,axiom,
% 2.89/1.59      ! [F: produc270694976lle_tv > produc270694976lle_tv] :
% 2.89/1.59        ( ! [X5: produc270694976lle_tv,Y5: produc270694976lle_tv] :
% 2.89/1.59            ( ( ( F @ X5 )
% 2.89/1.59              = ( F @ Y5 ) )
% 2.89/1.59           => ( X5 = Y5 ) )
% 2.89/1.59       => ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_101_injI,axiom,
% 2.89/1.59      ! [F: product_prod_nat_nat > product_prod_nat_nat] :
% 2.89/1.59        ( ! [X5: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 2.89/1.59            ( ( ( F @ X5 )
% 2.89/1.59              = ( F @ Y5 ) )
% 2.89/1.59           => ( X5 = Y5 ) )
% 2.89/1.59       => ( inj_on26176689at_nat @ F @ top_to1555900337at_nat ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_102_injI,axiom,
% 2.89/1.59      ! [F: nat > nat] :
% 2.89/1.59        ( ! [X5: nat,Y5: nat] :
% 2.89/1.59            ( ( ( F @ X5 )
% 2.89/1.59              = ( F @ Y5 ) )
% 2.89/1.59           => ( X5 = Y5 ) )
% 2.89/1.59       => ( inj_on_nat_nat @ F @ top_top_set_nat ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_103_injI,axiom,
% 2.89/1.59      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.89/1.59        ( ! [X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] :
% 2.89/1.59            ( ( ( F @ X5 )
% 2.89/1.59              = ( F @ Y5 ) )
% 2.89/1.59           => ( X5 = Y5 ) )
% 2.89/1.59       => ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_104_injD,axiom,
% 2.89/1.59      ! [F: produc1647334210lle_tv > produc1647334210lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 2.89/1.59        ( ( inj_on2112487900lle_tv @ F @ top_to1871154984lle_tv )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59         => ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_105_injD,axiom,
% 2.89/1.59      ! [F: nat > paraco1605129243lle_tv,X: nat,Y: nat] :
% 2.89/1.59        ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59         => ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_106_injD,axiom,
% 2.89/1.59      ! [F: produc194167194tv_nat > produc194167194tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 2.89/1.59        ( ( inj_on552895452tv_nat @ F @ top_to975729152tv_nat )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59         => ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_107_injD,axiom,
% 2.89/1.59      ! [F: produc270694976lle_tv > produc270694976lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 2.89/1.59        ( ( inj_on1745913142lle_tv @ F @ top_to1411004326lle_tv )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59         => ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_108_injD,axiom,
% 2.89/1.59      ! [F: product_prod_nat_nat > product_prod_nat_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.89/1.59        ( ( inj_on26176689at_nat @ F @ top_to1555900337at_nat )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59         => ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_109_injD,axiom,
% 2.89/1.59      ! [F: nat > nat,X: nat,Y: nat] :
% 2.89/1.59        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59         => ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_110_injD,axiom,
% 2.89/1.59      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 2.89/1.59        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59         => ( X = Y ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_111_top__set__def,axiom,
% 2.89/1.59      ( top_to975729152tv_nat
% 2.89/1.59      = ( collec848462447tv_nat @ top_to900819589_nat_o ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_112_top__set__def,axiom,
% 2.89/1.59      ( top_to1411004326lle_tv
% 2.89/1.59      = ( collec924990229lle_tv @ top_to1889334367e_tv_o ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_113_top__set__def,axiom,
% 2.89/1.59      ( top_to1555900337at_nat
% 2.89/1.59      = ( collec7649004at_nat @ top_to632227436_nat_o ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_114_top__set__def,axiom,
% 2.89/1.59      ( top_top_set_nat
% 2.89/1.59      = ( collect_nat @ top_top_nat_o ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_115_top__set__def,axiom,
% 2.89/1.59      ( top_to1057771083lle_tv
% 2.89/1.59      = ( collec1111687558lle_tv @ top_to1299250770e_tv_o ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_116_change__tv__injection,axiom,
% 2.89/1.59      ! [F: nat > nat] :
% 2.89/1.59        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 2.89/1.59       => ( inj_on772319074lle_tv @ ( paraco1147068288nge_tv @ F ) @ top_to1057771083lle_tv ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_117_UNIV__eq__I,axiom,
% 2.89/1.59      ! [A2: set_Pr2120184979lle_fm] :
% 2.89/1.59        ( ! [X5: produc696645085lle_fm] : ( member1474794996lle_fm @ X5 @ A2 )
% 2.89/1.59       => ( top_to775056195lle_fm = A2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_118_UNIV__eq__I,axiom,
% 2.89/1.59      ! [A2: set_Pr2061825550lle_tv] :
% 2.89/1.59        ( ! [X5: produc1852595672lle_tv] : ( member146333935lle_tv @ X5 @ A2 )
% 2.89/1.59       => ( top_to138697918lle_tv = A2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_119_UNIV__eq__I,axiom,
% 2.89/1.59      ! [A2: set_Pr560526279lle_tv] :
% 2.89/1.59        ( ! [X5: produc931990033lle_tv] : ( member1569366824lle_tv @ X5 @ A2 )
% 2.89/1.59       => ( top_to449985143lle_tv = A2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_120_UNIV__eq__I,axiom,
% 2.89/1.59      ! [A2: set_Pr1357842111at_nat] :
% 2.89/1.59        ( ! [X5: produc1281043295at_nat] : ( member112824072at_nat @ X5 @ A2 )
% 2.89/1.59       => ( top_to1541413903at_nat = A2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_121_UNIV__eq__I,axiom,
% 2.89/1.59      ! [A2: set_Pr1725653840tv_nat] :
% 2.89/1.59        ( ! [X5: produc194167194tv_nat] : ( member737151281tv_nat @ X5 @ A2 )
% 2.89/1.59       => ( top_to975729152tv_nat = A2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_122_UNIV__eq__I,axiom,
% 2.89/1.59      ! [A2: set_Pr13445366lle_tv] :
% 2.89/1.59        ( ! [X5: produc270694976lle_tv] : ( member813679063lle_tv @ X5 @ A2 )
% 2.89/1.59       => ( top_to1411004326lle_tv = A2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_123_UNIV__eq__I,axiom,
% 2.89/1.59      ! [A2: set_Pr1986765409at_nat] :
% 2.89/1.59        ( ! [X5: product_prod_nat_nat] : ( member701585322at_nat @ X5 @ A2 )
% 2.89/1.59       => ( top_to1555900337at_nat = A2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_124_UNIV__eq__I,axiom,
% 2.89/1.59      ! [A2: set_nat] :
% 2.89/1.59        ( ! [X5: nat] : ( member_nat @ X5 @ A2 )
% 2.89/1.59       => ( top_top_set_nat = A2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_125_UNIV__eq__I,axiom,
% 2.89/1.59      ! [A2: set_Pa1764573435lle_tv] :
% 2.89/1.59        ( ! [X5: paraco1605129243lle_tv] : ( member266900804lle_tv @ X5 @ A2 )
% 2.89/1.59       => ( top_to1057771083lle_tv = A2 ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_126_UNIV__witness,axiom,
% 2.89/1.59      ? [X5: produc696645085lle_fm] : ( member1474794996lle_fm @ X5 @ top_to775056195lle_fm ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_127_UNIV__witness,axiom,
% 2.89/1.59      ? [X5: produc1852595672lle_tv] : ( member146333935lle_tv @ X5 @ top_to138697918lle_tv ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_128_UNIV__witness,axiom,
% 2.89/1.59      ? [X5: produc931990033lle_tv] : ( member1569366824lle_tv @ X5 @ top_to449985143lle_tv ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_129_UNIV__witness,axiom,
% 2.89/1.59      ? [X5: produc1281043295at_nat] : ( member112824072at_nat @ X5 @ top_to1541413903at_nat ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_130_UNIV__witness,axiom,
% 2.89/1.59      ? [X5: produc194167194tv_nat] : ( member737151281tv_nat @ X5 @ top_to975729152tv_nat ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_131_UNIV__witness,axiom,
% 2.89/1.59      ? [X5: produc270694976lle_tv] : ( member813679063lle_tv @ X5 @ top_to1411004326lle_tv ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_132_UNIV__witness,axiom,
% 2.89/1.59      ? [X5: product_prod_nat_nat] : ( member701585322at_nat @ X5 @ top_to1555900337at_nat ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_133_UNIV__witness,axiom,
% 2.89/1.59      ? [X5: nat] : ( member_nat @ X5 @ top_top_set_nat ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_134_UNIV__witness,axiom,
% 2.89/1.59      ? [X5: paraco1605129243lle_tv] : ( member266900804lle_tv @ X5 @ top_to1057771083lle_tv ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_135_inj__onD,axiom,
% 2.89/1.59      ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 2.89/1.59        ( ( inj_on2112487900lle_tv @ F @ A2 )
% 2.89/1.59       => ( ( ( F @ X )
% 2.89/1.59            = ( F @ Y ) )
% 2.89/1.59         => ( ( member1531318361lle_tv @ X @ A2 )
% 2.89/1.59           => ( ( member1531318361lle_tv @ Y @ A2 )
% 2.89/1.59             => ( X = Y ) ) ) ) ) ).
% 2.89/1.59  
% 2.89/1.59  thf(fact_136_inj__onD,axiom,
% 2.89/1.59      ! [F: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 2.89/1.60        ( ( inj_on552895452tv_nat @ F @ A2 )
% 2.89/1.60       => ( ( ( F @ X )
% 2.89/1.60            = ( F @ Y ) )
% 2.89/1.60         => ( ( member737151281tv_nat @ X @ A2 )
% 2.89/1.60           => ( ( member737151281tv_nat @ Y @ A2 )
% 2.89/1.60             => ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_137_inj__onD,axiom,
% 2.89/1.60      ! [F: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 2.89/1.60        ( ( inj_on1745913142lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( ( F @ X )
% 2.89/1.60            = ( F @ Y ) )
% 2.89/1.60         => ( ( member813679063lle_tv @ X @ A2 )
% 2.89/1.60           => ( ( member813679063lle_tv @ Y @ A2 )
% 2.89/1.60             => ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_138_inj__onD,axiom,
% 2.89/1.60      ! [F: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.89/1.60        ( ( inj_on26176689at_nat @ F @ A2 )
% 2.89/1.60       => ( ( ( F @ X )
% 2.89/1.60            = ( F @ Y ) )
% 2.89/1.60         => ( ( member701585322at_nat @ X @ A2 )
% 2.89/1.60           => ( ( member701585322at_nat @ Y @ A2 )
% 2.89/1.60             => ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_139_inj__onD,axiom,
% 2.89/1.60      ! [F: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 2.89/1.60        ( ( inj_on1955349912lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( ( F @ X )
% 2.89/1.60            = ( F @ Y ) )
% 2.89/1.60         => ( ( member_nat @ X @ A2 )
% 2.89/1.60           => ( ( member_nat @ Y @ A2 )
% 2.89/1.60             => ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_140_inj__onD,axiom,
% 2.89/1.60      ! [F: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 2.89/1.60        ( ( inj_on_nat_nat @ F @ A2 )
% 2.89/1.60       => ( ( ( F @ X )
% 2.89/1.60            = ( F @ Y ) )
% 2.89/1.60         => ( ( member_nat @ X @ A2 )
% 2.89/1.60           => ( ( member_nat @ Y @ A2 )
% 2.89/1.60             => ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_141_inj__onD,axiom,
% 2.89/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( inj_on772319074lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( ( F @ X )
% 2.89/1.60            = ( F @ Y ) )
% 2.89/1.60         => ( ( member266900804lle_tv @ X @ A2 )
% 2.89/1.60           => ( ( member266900804lle_tv @ Y @ A2 )
% 2.89/1.60             => ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_142_inj__onI,axiom,
% 2.89/1.60      ! [A2: set_Pr2014382200lle_tv,F: produc1647334210lle_tv > produc1647334210lle_tv] :
% 2.89/1.60        ( ! [X5: produc1647334210lle_tv,Y5: produc1647334210lle_tv] :
% 2.89/1.60            ( ( member1531318361lle_tv @ X5 @ A2 )
% 2.89/1.60           => ( ( member1531318361lle_tv @ Y5 @ A2 )
% 2.89/1.60             => ( ( ( F @ X5 )
% 2.89/1.60                  = ( F @ Y5 ) )
% 2.89/1.60               => ( X5 = Y5 ) ) ) )
% 2.89/1.60       => ( inj_on2112487900lle_tv @ F @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_143_inj__onI,axiom,
% 2.89/1.60      ! [A2: set_Pr1725653840tv_nat,F: produc194167194tv_nat > produc194167194tv_nat] :
% 2.89/1.60        ( ! [X5: produc194167194tv_nat,Y5: produc194167194tv_nat] :
% 2.89/1.60            ( ( member737151281tv_nat @ X5 @ A2 )
% 2.89/1.60           => ( ( member737151281tv_nat @ Y5 @ A2 )
% 2.89/1.60             => ( ( ( F @ X5 )
% 2.89/1.60                  = ( F @ Y5 ) )
% 2.89/1.60               => ( X5 = Y5 ) ) ) )
% 2.89/1.60       => ( inj_on552895452tv_nat @ F @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_144_inj__onI,axiom,
% 2.89/1.60      ! [A2: set_Pr13445366lle_tv,F: produc270694976lle_tv > produc270694976lle_tv] :
% 2.89/1.60        ( ! [X5: produc270694976lle_tv,Y5: produc270694976lle_tv] :
% 2.89/1.60            ( ( member813679063lle_tv @ X5 @ A2 )
% 2.89/1.60           => ( ( member813679063lle_tv @ Y5 @ A2 )
% 2.89/1.60             => ( ( ( F @ X5 )
% 2.89/1.60                  = ( F @ Y5 ) )
% 2.89/1.60               => ( X5 = Y5 ) ) ) )
% 2.89/1.60       => ( inj_on1745913142lle_tv @ F @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_145_inj__onI,axiom,
% 2.89/1.60      ! [A2: set_Pr1986765409at_nat,F: product_prod_nat_nat > product_prod_nat_nat] :
% 2.89/1.60        ( ! [X5: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 2.89/1.60            ( ( member701585322at_nat @ X5 @ A2 )
% 2.89/1.60           => ( ( member701585322at_nat @ Y5 @ A2 )
% 2.89/1.60             => ( ( ( F @ X5 )
% 2.89/1.60                  = ( F @ Y5 ) )
% 2.89/1.60               => ( X5 = Y5 ) ) ) )
% 2.89/1.60       => ( inj_on26176689at_nat @ F @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_146_inj__onI,axiom,
% 2.89/1.60      ! [A2: set_nat,F: nat > paraco1605129243lle_tv] :
% 2.89/1.60        ( ! [X5: nat,Y5: nat] :
% 2.89/1.60            ( ( member_nat @ X5 @ A2 )
% 2.89/1.60           => ( ( member_nat @ Y5 @ A2 )
% 2.89/1.60             => ( ( ( F @ X5 )
% 2.89/1.60                  = ( F @ Y5 ) )
% 2.89/1.60               => ( X5 = Y5 ) ) ) )
% 2.89/1.60       => ( inj_on1955349912lle_tv @ F @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_147_inj__onI,axiom,
% 2.89/1.60      ! [A2: set_nat,F: nat > nat] :
% 2.89/1.60        ( ! [X5: nat,Y5: nat] :
% 2.89/1.60            ( ( member_nat @ X5 @ A2 )
% 2.89/1.60           => ( ( member_nat @ Y5 @ A2 )
% 2.89/1.60             => ( ( ( F @ X5 )
% 2.89/1.60                  = ( F @ Y5 ) )
% 2.89/1.60               => ( X5 = Y5 ) ) ) )
% 2.89/1.60       => ( inj_on_nat_nat @ F @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_148_inj__onI,axiom,
% 2.89/1.60      ! [A2: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.89/1.60        ( ! [X5: paraco1605129243lle_tv,Y5: paraco1605129243lle_tv] :
% 2.89/1.60            ( ( member266900804lle_tv @ X5 @ A2 )
% 2.89/1.60           => ( ( member266900804lle_tv @ Y5 @ A2 )
% 2.89/1.60             => ( ( ( F @ X5 )
% 2.89/1.60                  = ( F @ Y5 ) )
% 2.89/1.60               => ( X5 = Y5 ) ) ) )
% 2.89/1.60       => ( inj_on772319074lle_tv @ F @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_149_inj__on__def,axiom,
% 2.89/1.60      ( inj_on2112487900lle_tv
% 2.89/1.60      = ( ^ [F2: produc1647334210lle_tv > produc1647334210lle_tv,A3: set_Pr2014382200lle_tv] :
% 2.89/1.60          ! [X4: produc1647334210lle_tv] :
% 2.89/1.60            ( ( member1531318361lle_tv @ X4 @ A3 )
% 2.89/1.60           => ! [Y4: produc1647334210lle_tv] :
% 2.89/1.60                ( ( member1531318361lle_tv @ Y4 @ A3 )
% 2.89/1.60               => ( ( ( F2 @ X4 )
% 2.89/1.60                    = ( F2 @ Y4 ) )
% 2.89/1.60                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_150_inj__on__def,axiom,
% 2.89/1.60      ( inj_on552895452tv_nat
% 2.89/1.60      = ( ^ [F2: produc194167194tv_nat > produc194167194tv_nat,A3: set_Pr1725653840tv_nat] :
% 2.89/1.60          ! [X4: produc194167194tv_nat] :
% 2.89/1.60            ( ( member737151281tv_nat @ X4 @ A3 )
% 2.89/1.60           => ! [Y4: produc194167194tv_nat] :
% 2.89/1.60                ( ( member737151281tv_nat @ Y4 @ A3 )
% 2.89/1.60               => ( ( ( F2 @ X4 )
% 2.89/1.60                    = ( F2 @ Y4 ) )
% 2.89/1.60                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_151_inj__on__def,axiom,
% 2.89/1.60      ( inj_on1745913142lle_tv
% 2.89/1.60      = ( ^ [F2: produc270694976lle_tv > produc270694976lle_tv,A3: set_Pr13445366lle_tv] :
% 2.89/1.60          ! [X4: produc270694976lle_tv] :
% 2.89/1.60            ( ( member813679063lle_tv @ X4 @ A3 )
% 2.89/1.60           => ! [Y4: produc270694976lle_tv] :
% 2.89/1.60                ( ( member813679063lle_tv @ Y4 @ A3 )
% 2.89/1.60               => ( ( ( F2 @ X4 )
% 2.89/1.60                    = ( F2 @ Y4 ) )
% 2.89/1.60                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_152_inj__on__def,axiom,
% 2.89/1.60      ( inj_on26176689at_nat
% 2.89/1.60      = ( ^ [F2: product_prod_nat_nat > product_prod_nat_nat,A3: set_Pr1986765409at_nat] :
% 2.89/1.60          ! [X4: product_prod_nat_nat] :
% 2.89/1.60            ( ( member701585322at_nat @ X4 @ A3 )
% 2.89/1.60           => ! [Y4: product_prod_nat_nat] :
% 2.89/1.60                ( ( member701585322at_nat @ Y4 @ A3 )
% 2.89/1.60               => ( ( ( F2 @ X4 )
% 2.89/1.60                    = ( F2 @ Y4 ) )
% 2.89/1.60                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_153_inj__on__def,axiom,
% 2.89/1.60      ( inj_on1955349912lle_tv
% 2.89/1.60      = ( ^ [F2: nat > paraco1605129243lle_tv,A3: set_nat] :
% 2.89/1.60          ! [X4: nat] :
% 2.89/1.60            ( ( member_nat @ X4 @ A3 )
% 2.89/1.60           => ! [Y4: nat] :
% 2.89/1.60                ( ( member_nat @ Y4 @ A3 )
% 2.89/1.60               => ( ( ( F2 @ X4 )
% 2.89/1.60                    = ( F2 @ Y4 ) )
% 2.89/1.60                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_154_inj__on__def,axiom,
% 2.89/1.60      ( inj_on_nat_nat
% 2.89/1.60      = ( ^ [F2: nat > nat,A3: set_nat] :
% 2.89/1.60          ! [X4: nat] :
% 2.89/1.60            ( ( member_nat @ X4 @ A3 )
% 2.89/1.60           => ! [Y4: nat] :
% 2.89/1.60                ( ( member_nat @ Y4 @ A3 )
% 2.89/1.60               => ( ( ( F2 @ X4 )
% 2.89/1.60                    = ( F2 @ Y4 ) )
% 2.89/1.60                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_155_inj__on__def,axiom,
% 2.89/1.60      ( inj_on772319074lle_tv
% 2.89/1.60      = ( ^ [F2: paraco1605129243lle_tv > paraco1605129243lle_tv,A3: set_Pa1764573435lle_tv] :
% 2.89/1.60          ! [X4: paraco1605129243lle_tv] :
% 2.89/1.60            ( ( member266900804lle_tv @ X4 @ A3 )
% 2.89/1.60           => ! [Y4: paraco1605129243lle_tv] :
% 2.89/1.60                ( ( member266900804lle_tv @ Y4 @ A3 )
% 2.89/1.60               => ( ( ( F2 @ X4 )
% 2.89/1.60                    = ( F2 @ Y4 ) )
% 2.89/1.60                 => ( X4 = Y4 ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_156_inj__on__cong,axiom,
% 2.89/1.60      ! [A2: set_Pr2014382200lle_tv,F: produc1647334210lle_tv > produc1647334210lle_tv,G: produc1647334210lle_tv > produc1647334210lle_tv] :
% 2.89/1.60        ( ! [A4: produc1647334210lle_tv] :
% 2.89/1.60            ( ( member1531318361lle_tv @ A4 @ A2 )
% 2.89/1.60           => ( ( F @ A4 )
% 2.89/1.60              = ( G @ A4 ) ) )
% 2.89/1.60       => ( ( inj_on2112487900lle_tv @ F @ A2 )
% 2.89/1.60          = ( inj_on2112487900lle_tv @ G @ A2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_157_inj__on__cong,axiom,
% 2.89/1.60      ! [A2: set_Pr1725653840tv_nat,F: produc194167194tv_nat > produc194167194tv_nat,G: produc194167194tv_nat > produc194167194tv_nat] :
% 2.89/1.60        ( ! [A4: produc194167194tv_nat] :
% 2.89/1.60            ( ( member737151281tv_nat @ A4 @ A2 )
% 2.89/1.60           => ( ( F @ A4 )
% 2.89/1.60              = ( G @ A4 ) ) )
% 2.89/1.60       => ( ( inj_on552895452tv_nat @ F @ A2 )
% 2.89/1.60          = ( inj_on552895452tv_nat @ G @ A2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_158_inj__on__cong,axiom,
% 2.89/1.60      ! [A2: set_Pr13445366lle_tv,F: produc270694976lle_tv > produc270694976lle_tv,G: produc270694976lle_tv > produc270694976lle_tv] :
% 2.89/1.60        ( ! [A4: produc270694976lle_tv] :
% 2.89/1.60            ( ( member813679063lle_tv @ A4 @ A2 )
% 2.89/1.60           => ( ( F @ A4 )
% 2.89/1.60              = ( G @ A4 ) ) )
% 2.89/1.60       => ( ( inj_on1745913142lle_tv @ F @ A2 )
% 2.89/1.60          = ( inj_on1745913142lle_tv @ G @ A2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_159_inj__on__cong,axiom,
% 2.89/1.60      ! [A2: set_Pr1986765409at_nat,F: product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat] :
% 2.89/1.60        ( ! [A4: product_prod_nat_nat] :
% 2.89/1.60            ( ( member701585322at_nat @ A4 @ A2 )
% 2.89/1.60           => ( ( F @ A4 )
% 2.89/1.60              = ( G @ A4 ) ) )
% 2.89/1.60       => ( ( inj_on26176689at_nat @ F @ A2 )
% 2.89/1.60          = ( inj_on26176689at_nat @ G @ A2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_160_inj__on__cong,axiom,
% 2.89/1.60      ! [A2: set_nat,F: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 2.89/1.60        ( ! [A4: nat] :
% 2.89/1.60            ( ( member_nat @ A4 @ A2 )
% 2.89/1.60           => ( ( F @ A4 )
% 2.89/1.60              = ( G @ A4 ) ) )
% 2.89/1.60       => ( ( inj_on1955349912lle_tv @ F @ A2 )
% 2.89/1.60          = ( inj_on1955349912lle_tv @ G @ A2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_161_inj__on__cong,axiom,
% 2.89/1.60      ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 2.89/1.60        ( ! [A4: nat] :
% 2.89/1.60            ( ( member_nat @ A4 @ A2 )
% 2.89/1.60           => ( ( F @ A4 )
% 2.89/1.60              = ( G @ A4 ) ) )
% 2.89/1.60       => ( ( inj_on_nat_nat @ F @ A2 )
% 2.89/1.60          = ( inj_on_nat_nat @ G @ A2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_162_inj__on__cong,axiom,
% 2.89/1.60      ! [A2: set_Pa1764573435lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.89/1.60        ( ! [A4: paraco1605129243lle_tv] :
% 2.89/1.60            ( ( member266900804lle_tv @ A4 @ A2 )
% 2.89/1.60           => ( ( F @ A4 )
% 2.89/1.60              = ( G @ A4 ) ) )
% 2.89/1.60       => ( ( inj_on772319074lle_tv @ F @ A2 )
% 2.89/1.60          = ( inj_on772319074lle_tv @ G @ A2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_163_inj__on__eq__iff,axiom,
% 2.89/1.60      ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 2.89/1.60        ( ( inj_on2112487900lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( member1531318361lle_tv @ X @ A2 )
% 2.89/1.60         => ( ( member1531318361lle_tv @ Y @ A2 )
% 2.89/1.60           => ( ( ( F @ X )
% 2.89/1.60                = ( F @ Y ) )
% 2.89/1.60              = ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_164_inj__on__eq__iff,axiom,
% 2.89/1.60      ! [F: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 2.89/1.60        ( ( inj_on552895452tv_nat @ F @ A2 )
% 2.89/1.60       => ( ( member737151281tv_nat @ X @ A2 )
% 2.89/1.60         => ( ( member737151281tv_nat @ Y @ A2 )
% 2.89/1.60           => ( ( ( F @ X )
% 2.89/1.60                = ( F @ Y ) )
% 2.89/1.60              = ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_165_inj__on__eq__iff,axiom,
% 2.89/1.60      ! [F: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 2.89/1.60        ( ( inj_on1745913142lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( member813679063lle_tv @ X @ A2 )
% 2.89/1.60         => ( ( member813679063lle_tv @ Y @ A2 )
% 2.89/1.60           => ( ( ( F @ X )
% 2.89/1.60                = ( F @ Y ) )
% 2.89/1.60              = ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_166_inj__on__eq__iff,axiom,
% 2.89/1.60      ! [F: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.89/1.60        ( ( inj_on26176689at_nat @ F @ A2 )
% 2.89/1.60       => ( ( member701585322at_nat @ X @ A2 )
% 2.89/1.60         => ( ( member701585322at_nat @ Y @ A2 )
% 2.89/1.60           => ( ( ( F @ X )
% 2.89/1.60                = ( F @ Y ) )
% 2.89/1.60              = ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_167_inj__on__eq__iff,axiom,
% 2.89/1.60      ! [F: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 2.89/1.60        ( ( inj_on1955349912lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( member_nat @ X @ A2 )
% 2.89/1.60         => ( ( member_nat @ Y @ A2 )
% 2.89/1.60           => ( ( ( F @ X )
% 2.89/1.60                = ( F @ Y ) )
% 2.89/1.60              = ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_168_inj__on__eq__iff,axiom,
% 2.89/1.60      ! [F: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 2.89/1.60        ( ( inj_on_nat_nat @ F @ A2 )
% 2.89/1.60       => ( ( member_nat @ X @ A2 )
% 2.89/1.60         => ( ( member_nat @ Y @ A2 )
% 2.89/1.60           => ( ( ( F @ X )
% 2.89/1.60                = ( F @ Y ) )
% 2.89/1.60              = ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_169_inj__on__eq__iff,axiom,
% 2.89/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( inj_on772319074lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( member266900804lle_tv @ X @ A2 )
% 2.89/1.60         => ( ( member266900804lle_tv @ Y @ A2 )
% 2.89/1.60           => ( ( ( F @ X )
% 2.89/1.60                = ( F @ Y ) )
% 2.89/1.60              = ( X = Y ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_170_inj__on__contraD,axiom,
% 2.89/1.60      ! [F: produc1647334210lle_tv > produc1647334210lle_tv,A2: set_Pr2014382200lle_tv,X: produc1647334210lle_tv,Y: produc1647334210lle_tv] :
% 2.89/1.60        ( ( inj_on2112487900lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( X != Y )
% 2.89/1.60         => ( ( member1531318361lle_tv @ X @ A2 )
% 2.89/1.60           => ( ( member1531318361lle_tv @ Y @ A2 )
% 2.89/1.60             => ( ( F @ X )
% 2.89/1.60               != ( F @ Y ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_171_inj__on__contraD,axiom,
% 2.89/1.60      ! [F: produc194167194tv_nat > produc194167194tv_nat,A2: set_Pr1725653840tv_nat,X: produc194167194tv_nat,Y: produc194167194tv_nat] :
% 2.89/1.60        ( ( inj_on552895452tv_nat @ F @ A2 )
% 2.89/1.60       => ( ( X != Y )
% 2.89/1.60         => ( ( member737151281tv_nat @ X @ A2 )
% 2.89/1.60           => ( ( member737151281tv_nat @ Y @ A2 )
% 2.89/1.60             => ( ( F @ X )
% 2.89/1.60               != ( F @ Y ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_172_inj__on__contraD,axiom,
% 2.89/1.60      ! [F: produc270694976lle_tv > produc270694976lle_tv,A2: set_Pr13445366lle_tv,X: produc270694976lle_tv,Y: produc270694976lle_tv] :
% 2.89/1.60        ( ( inj_on1745913142lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( X != Y )
% 2.89/1.60         => ( ( member813679063lle_tv @ X @ A2 )
% 2.89/1.60           => ( ( member813679063lle_tv @ Y @ A2 )
% 2.89/1.60             => ( ( F @ X )
% 2.89/1.60               != ( F @ Y ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_173_inj__on__contraD,axiom,
% 2.89/1.60      ! [F: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1986765409at_nat,X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 2.89/1.60        ( ( inj_on26176689at_nat @ F @ A2 )
% 2.89/1.60       => ( ( X != Y )
% 2.89/1.60         => ( ( member701585322at_nat @ X @ A2 )
% 2.89/1.60           => ( ( member701585322at_nat @ Y @ A2 )
% 2.89/1.60             => ( ( F @ X )
% 2.89/1.60               != ( F @ Y ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_174_inj__on__contraD,axiom,
% 2.89/1.60      ! [F: nat > paraco1605129243lle_tv,A2: set_nat,X: nat,Y: nat] :
% 2.89/1.60        ( ( inj_on1955349912lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( X != Y )
% 2.89/1.60         => ( ( member_nat @ X @ A2 )
% 2.89/1.60           => ( ( member_nat @ Y @ A2 )
% 2.89/1.60             => ( ( F @ X )
% 2.89/1.60               != ( F @ Y ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_175_inj__on__contraD,axiom,
% 2.89/1.60      ! [F: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 2.89/1.60        ( ( inj_on_nat_nat @ F @ A2 )
% 2.89/1.60       => ( ( X != Y )
% 2.89/1.60         => ( ( member_nat @ X @ A2 )
% 2.89/1.60           => ( ( member_nat @ Y @ A2 )
% 2.89/1.60             => ( ( F @ X )
% 2.89/1.60               != ( F @ Y ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_176_inj__on__contraD,axiom,
% 2.89/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( inj_on772319074lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( X != Y )
% 2.89/1.60         => ( ( member266900804lle_tv @ X @ A2 )
% 2.89/1.60           => ( ( member266900804lle_tv @ Y @ A2 )
% 2.89/1.60             => ( ( F @ X )
% 2.89/1.60               != ( F @ Y ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_177_inj__on__inverseI,axiom,
% 2.89/1.60      ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 2.89/1.60        ( ! [X5: nat] :
% 2.89/1.60            ( ( member_nat @ X5 @ A2 )
% 2.89/1.60           => ( ( G @ ( F @ X5 ) )
% 2.89/1.60              = X5 ) )
% 2.89/1.60       => ( inj_on_nat_nat @ F @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_178_inj__on__inverseI,axiom,
% 2.89/1.60      ! [A2: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.89/1.60        ( ! [X5: paraco1605129243lle_tv] :
% 2.89/1.60            ( ( member266900804lle_tv @ X5 @ A2 )
% 2.89/1.60           => ( ( G @ ( F @ X5 ) )
% 2.89/1.60              = X5 ) )
% 2.89/1.60       => ( inj_on772319074lle_tv @ F @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_179_fm_Oinduct,axiom,
% 2.89/1.60      ! [P3: paraco1604210848lle_fm > $o,Fm: paraco1604210848lle_fm] :
% 2.89/1.60        ( ! [X5: list_char] : ( P3 @ ( paraco1480028776le_Pro @ X5 ) )
% 2.89/1.60       => ( ( P3 @ paraco367965286_Truth )
% 2.89/1.60         => ( ! [X5: paraco1604210848lle_fm] :
% 2.89/1.60                ( ( P3 @ X5 )
% 2.89/1.60               => ( P3 @ ( paraco445776468le_Neg @ X5 ) ) )
% 2.89/1.60           => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 2.89/1.60                  ( ( P3 @ X1a )
% 2.89/1.60                 => ( ( P3 @ X22 )
% 2.89/1.60                   => ( P3 @ ( paraco69239110le_Con @ X1a @ X22 ) ) ) )
% 2.89/1.60             => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 2.89/1.60                    ( ( P3 @ X1a )
% 2.89/1.60                   => ( ( P3 @ X22 )
% 2.89/1.60                     => ( P3 @ ( paraco1389086619le_Eql @ X1a @ X22 ) ) ) )
% 2.89/1.60               => ( ! [X1a: paraco1604210848lle_fm,X22: paraco1604210848lle_fm] :
% 2.89/1.60                      ( ( P3 @ X1a )
% 2.89/1.60                     => ( ( P3 @ X22 )
% 2.89/1.60                       => ( P3 @ ( paraco1745535428le_Eql @ X1a @ X22 ) ) ) )
% 2.89/1.60                 => ( P3 @ Fm ) ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_180_fm_Oexhaust,axiom,
% 2.89/1.60      ! [Y: paraco1604210848lle_fm] :
% 2.89/1.60        ( ! [X12: list_char] :
% 2.89/1.60            ( Y
% 2.89/1.60           != ( paraco1480028776le_Pro @ X12 ) )
% 2.89/1.60       => ( ( Y != paraco367965286_Truth )
% 2.89/1.60         => ( ! [X32: paraco1604210848lle_fm] :
% 2.89/1.60                ( Y
% 2.89/1.60               != ( paraco445776468le_Neg @ X32 ) )
% 2.89/1.60           => ( ! [X412: paraco1604210848lle_fm,X422: paraco1604210848lle_fm] :
% 2.89/1.60                  ( Y
% 2.89/1.60                 != ( paraco69239110le_Con @ X412 @ X422 ) )
% 2.89/1.60             => ( ! [X512: paraco1604210848lle_fm,X522: paraco1604210848lle_fm] :
% 2.89/1.60                    ( Y
% 2.89/1.60                   != ( paraco1389086619le_Eql @ X512 @ X522 ) )
% 2.89/1.60               => ~ ! [X612: paraco1604210848lle_fm,X622: paraco1604210848lle_fm] :
% 2.89/1.60                      ( Y
% 2.89/1.60                     != ( paraco1745535428le_Eql @ X612 @ X622 ) ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_181_props_Ocases,axiom,
% 2.89/1.60      ! [X: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( X != paraco367965286_Truth )
% 2.89/1.60       => ( ! [S2: list_char] :
% 2.89/1.60              ( X
% 2.89/1.60             != ( paraco1480028776le_Pro @ S2 ) )
% 2.89/1.60         => ( ! [P4: paraco1604210848lle_fm] :
% 2.89/1.60                ( X
% 2.89/1.60               != ( paraco445776468le_Neg @ P4 ) )
% 2.89/1.60           => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 2.89/1.60                  ( X
% 2.89/1.60                 != ( paraco69239110le_Con @ P4 @ Q3 ) )
% 2.89/1.60             => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 2.89/1.60                    ( X
% 2.89/1.60                   != ( paraco1389086619le_Eql @ P4 @ Q3 ) )
% 2.89/1.60               => ~ ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 2.89/1.60                      ( X
% 2.89/1.60                     != ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_182_props_Oinduct,axiom,
% 2.89/1.60      ! [P3: paraco1604210848lle_fm > $o,A0: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( P3 @ paraco367965286_Truth )
% 2.89/1.60       => ( ! [S2: list_char] : ( P3 @ ( paraco1480028776le_Pro @ S2 ) )
% 2.89/1.60         => ( ! [P4: paraco1604210848lle_fm] :
% 2.89/1.60                ( ( P3 @ P4 )
% 2.89/1.60               => ( P3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 2.89/1.60           => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 2.89/1.60                  ( ( P3 @ P4 )
% 2.89/1.60                 => ( ( P3 @ Q3 )
% 2.89/1.60                   => ( P3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) ) )
% 2.89/1.60             => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 2.89/1.60                    ( ( P3 @ P4 )
% 2.89/1.60                   => ( ( P3 @ Q3 )
% 2.89/1.60                     => ( P3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) ) )
% 2.89/1.60               => ( ! [P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 2.89/1.60                      ( ( P3 @ P4 )
% 2.89/1.60                     => ( ( P3 @ Q3 )
% 2.89/1.60                       => ( P3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) )
% 2.89/1.60                 => ( P3 @ A0 ) ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_183_old_Obool_Osimps_I4_J,axiom,
% 2.89/1.60      ! [F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( produc234482697lle_tv @ F1 @ F22 @ $false )
% 2.89/1.60        = F22 ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_184_old_Obool_Osimps_I3_J,axiom,
% 2.89/1.60      ! [F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( produc234482697lle_tv @ F1 @ F22 @ $true )
% 2.89/1.60        = F1 ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_185_bool_Osplit__sel,axiom,
% 2.89/1.60      ! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool: $o] :
% 2.89/1.60        ( ( P3 @ ( produc234482697lle_tv @ F1 @ F22 @ Bool ) )
% 2.89/1.60        = ( ( Bool
% 2.89/1.60           => ( P3 @ F1 ) )
% 2.89/1.60          & ( ~ Bool
% 2.89/1.60           => ( P3 @ F22 ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_186_fm_Oinject_I1_J,axiom,
% 2.89/1.60      ! [X1: list_char,Y1: list_char] :
% 2.89/1.60        ( ( ( paraco1480028776le_Pro @ X1 )
% 2.89/1.60          = ( paraco1480028776le_Pro @ Y1 ) )
% 2.89/1.60        = ( X1 = Y1 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_187_eval_Osimps_I1_J,axiom,
% 2.89/1.60      ! [I: list_char > paraco1605129243lle_tv,S3: list_char] :
% 2.89/1.60        ( ( paraco1325918602e_eval @ I @ ( paraco1480028776le_Pro @ S3 ) )
% 2.89/1.60        = ( I @ S3 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_188_fm_Odistinct_I3_J,axiom,
% 2.89/1.60      ! [X1: list_char,X3: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( paraco1480028776le_Pro @ X1 )
% 2.89/1.60       != ( paraco445776468le_Neg @ X3 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_189_fm_Odistinct_I5_J,axiom,
% 2.89/1.60      ! [X1: list_char,X41: paraco1604210848lle_fm,X42: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( paraco1480028776le_Pro @ X1 )
% 2.89/1.60       != ( paraco69239110le_Con @ X41 @ X42 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_190_fm_Odistinct_I9_J,axiom,
% 2.89/1.60      ! [X1: list_char,X61: paraco1604210848lle_fm,X62: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( paraco1480028776le_Pro @ X1 )
% 2.89/1.60       != ( paraco1745535428le_Eql @ X61 @ X62 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_191_fm_Odistinct_I7_J,axiom,
% 2.89/1.60      ! [X1: list_char,X51: paraco1604210848lle_fm,X52: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( paraco1480028776le_Pro @ X1 )
% 2.89/1.60       != ( paraco1389086619le_Eql @ X51 @ X52 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_192_fm_Odistinct_I1_J,axiom,
% 2.89/1.60      ! [X1: list_char] :
% 2.89/1.60        ( ( paraco1480028776le_Pro @ X1 )
% 2.89/1.60       != paraco367965286_Truth ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_193_bool_Osplit__sel__asm,axiom,
% 2.89/1.60      ! [P3: paraco1605129243lle_tv > $o,F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool: $o] :
% 2.89/1.60        ( ( P3 @ ( produc234482697lle_tv @ F1 @ F22 @ Bool ) )
% 2.89/1.60        = ( ~ ( ( Bool
% 2.89/1.60                & ~ ( P3 @ F1 ) )
% 2.89/1.60              | ( ~ Bool
% 2.89/1.60                & ~ ( P3 @ F22 ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_194_bool_Ocase__distrib,axiom,
% 2.89/1.60      ! [H: paraco1605129243lle_tv > paraco1605129243lle_tv,F1: paraco1605129243lle_tv,F22: paraco1605129243lle_tv,Bool: $o] :
% 2.89/1.60        ( ( H @ ( produc234482697lle_tv @ F1 @ F22 @ Bool ) )
% 2.89/1.60        = ( produc234482697lle_tv @ ( H @ F1 ) @ ( H @ F22 ) @ Bool ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_195_bool_Ocase__eq__if,axiom,
% 2.89/1.60      ( produc234482697lle_tv
% 2.89/1.60      = ( ^ [F12: paraco1605129243lle_tv,F23: paraco1605129243lle_tv,Bool2: $o] : ( if_Par1134130401lle_tv @ Bool2 @ F12 @ F23 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_196_top__empty__eq,axiom,
% 2.89/1.60      ( top_top_nat_o
% 2.89/1.60      = ( ^ [X4: nat] : ( member_nat @ X4 @ top_top_set_nat ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_197_top__empty__eq,axiom,
% 2.89/1.60      ( top_to1299250770e_tv_o
% 2.89/1.60      = ( ^ [X4: paraco1605129243lle_tv] : ( member266900804lle_tv @ X4 @ top_to1057771083lle_tv ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_198_eval_Ocases,axiom,
% 2.89/1.60      ! [X: produc696645085lle_fm] :
% 2.89/1.60        ( ! [I3: list_char > paraco1605129243lle_tv,S2: list_char] :
% 2.89/1.60            ( X
% 2.89/1.60           != ( produc1710735575lle_fm @ I3 @ ( paraco1480028776le_Pro @ S2 ) ) )
% 2.89/1.60       => ( ! [I3: list_char > paraco1605129243lle_tv] :
% 2.89/1.60              ( X
% 2.89/1.60             != ( produc1710735575lle_fm @ I3 @ paraco367965286_Truth ) )
% 2.89/1.60         => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm] :
% 2.89/1.60                ( X
% 2.89/1.60               != ( produc1710735575lle_fm @ I3 @ ( paraco445776468le_Neg @ P4 ) ) )
% 2.89/1.60           => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 2.89/1.60                  ( X
% 2.89/1.60                 != ( produc1710735575lle_fm @ I3 @ ( paraco69239110le_Con @ P4 @ Q3 ) ) )
% 2.89/1.60             => ( ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 2.89/1.60                    ( X
% 2.89/1.60                   != ( produc1710735575lle_fm @ I3 @ ( paraco1389086619le_Eql @ P4 @ Q3 ) ) )
% 2.89/1.60               => ~ ! [I3: list_char > paraco1605129243lle_tv,P4: paraco1604210848lle_fm,Q3: paraco1604210848lle_fm] :
% 2.89/1.60                      ( X
% 2.89/1.60                     != ( produc1710735575lle_fm @ I3 @ ( paraco1745535428le_Eql @ P4 @ Q3 ) ) ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_199_old_Oprod_Oinject,axiom,
% 2.89/1.60      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( ( produc1710735575lle_fm @ A @ B )
% 2.89/1.60          = ( produc1710735575lle_fm @ A5 @ B3 ) )
% 2.89/1.60        = ( ( A = A5 )
% 2.89/1.60          & ( B = B3 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_200_old_Oprod_Oinject,axiom,
% 2.89/1.60      ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( ( produc1680557635lle_tv @ A @ B )
% 2.89/1.60          = ( produc1680557635lle_tv @ A5 @ B3 ) )
% 2.89/1.60        = ( ( A = A5 )
% 2.89/1.60          & ( B = B3 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_201_prod_Oinject,axiom,
% 2.89/1.60      ! [X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm,Y1: list_char > paraco1605129243lle_tv,Y2: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( ( produc1710735575lle_fm @ X1 @ X2 )
% 2.89/1.60          = ( produc1710735575lle_fm @ Y1 @ Y2 ) )
% 2.89/1.60        = ( ( X1 = Y1 )
% 2.89/1.60          & ( X2 = Y2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_202_prod_Oinject,axiom,
% 2.89/1.60      ! [X1: nat > nat,X2: paraco1605129243lle_tv,Y1: nat > nat,Y2: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( ( produc1680557635lle_tv @ X1 @ X2 )
% 2.89/1.60          = ( produc1680557635lle_tv @ Y1 @ Y2 ) )
% 2.89/1.60        = ( ( X1 = Y1 )
% 2.89/1.60          & ( X2 = Y2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_203_apfst__conv,axiom,
% 2.89/1.60      ! [F: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( produc1942165868lle_fm @ F @ ( produc1710735575lle_fm @ X @ Y ) )
% 2.89/1.60        = ( produc1710735575lle_fm @ ( F @ X ) @ Y ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_204_apfst__conv,axiom,
% 2.89/1.60      ! [F: ( nat > nat ) > nat > nat,X: nat > nat,Y: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( produc939316703lle_tv @ F @ ( produc1680557635lle_tv @ X @ Y ) )
% 2.89/1.60        = ( produc1680557635lle_tv @ ( F @ X ) @ Y ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_205_apsnd__conv,axiom,
% 2.89/1.60      ! [F: paraco1604210848lle_fm > paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( produc1807466521lle_tv @ F @ ( produc1710735575lle_fm @ X @ Y ) )
% 2.89/1.60        = ( produc1710735575lle_fm @ X @ ( F @ Y ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_206_apsnd__conv,axiom,
% 2.89/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: nat > nat,Y: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( produc109093078at_nat @ F @ ( produc1680557635lle_tv @ X @ Y ) )
% 2.89/1.60        = ( produc1680557635lle_tv @ X @ ( F @ Y ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_207_old_Oprod_Oinducts,axiom,
% 2.89/1.60      ! [P3: produc696645085lle_fm > $o,Prod: produc696645085lle_fm] :
% 2.89/1.60        ( ! [A4: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A4 @ B2 ) )
% 2.89/1.60       => ( P3 @ Prod ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_208_old_Oprod_Oinducts,axiom,
% 2.89/1.60      ! [P3: produc931990033lle_tv > $o,Prod: produc931990033lle_tv] :
% 2.89/1.60        ( ! [A4: nat > nat,B2: paraco1605129243lle_tv] : ( P3 @ ( produc1680557635lle_tv @ A4 @ B2 ) )
% 2.89/1.60       => ( P3 @ Prod ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_209_old_Oprod_Oexhaust,axiom,
% 2.89/1.60      ! [Y: produc696645085lle_fm] :
% 2.89/1.60        ~ ! [A4: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] :
% 2.89/1.60            ( Y
% 2.89/1.60           != ( produc1710735575lle_fm @ A4 @ B2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_210_old_Oprod_Oexhaust,axiom,
% 2.89/1.60      ! [Y: produc931990033lle_tv] :
% 2.89/1.60        ~ ! [A4: nat > nat,B2: paraco1605129243lle_tv] :
% 2.89/1.60            ( Y
% 2.89/1.60           != ( produc1680557635lle_tv @ A4 @ B2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_211_Pair__inject,axiom,
% 2.89/1.60      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( ( produc1710735575lle_fm @ A @ B )
% 2.89/1.60          = ( produc1710735575lle_fm @ A5 @ B3 ) )
% 2.89/1.60       => ~ ( ( A = A5 )
% 2.89/1.60           => ( B != B3 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_212_Pair__inject,axiom,
% 2.89/1.60      ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( ( produc1680557635lle_tv @ A @ B )
% 2.89/1.60          = ( produc1680557635lle_tv @ A5 @ B3 ) )
% 2.89/1.60       => ~ ( ( A = A5 )
% 2.89/1.60           => ( B != B3 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_213_prod__cases,axiom,
% 2.89/1.60      ! [P3: produc696645085lle_fm > $o,P: produc696645085lle_fm] :
% 2.89/1.60        ( ! [A4: list_char > paraco1605129243lle_tv,B2: paraco1604210848lle_fm] : ( P3 @ ( produc1710735575lle_fm @ A4 @ B2 ) )
% 2.89/1.60       => ( P3 @ P ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_214_prod__cases,axiom,
% 2.89/1.60      ! [P3: produc931990033lle_tv > $o,P: produc931990033lle_tv] :
% 2.89/1.60        ( ! [A4: nat > nat,B2: paraco1605129243lle_tv] : ( P3 @ ( produc1680557635lle_tv @ A4 @ B2 ) )
% 2.89/1.60       => ( P3 @ P ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_215_surj__pair,axiom,
% 2.89/1.60      ! [P: produc696645085lle_fm] :
% 2.89/1.60      ? [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] :
% 2.89/1.60        ( P
% 2.89/1.60        = ( produc1710735575lle_fm @ X5 @ Y5 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_216_surj__pair,axiom,
% 2.89/1.60      ! [P: produc931990033lle_tv] :
% 2.89/1.60      ? [X5: nat > nat,Y5: paraco1605129243lle_tv] :
% 2.89/1.60        ( P
% 2.89/1.60        = ( produc1680557635lle_tv @ X5 @ Y5 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_217_prod_Oinj__map,axiom,
% 2.89/1.60      ! [F1: nat > nat,F22: nat > nat] :
% 2.89/1.60        ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 2.89/1.60       => ( ( inj_on_nat_nat @ F22 @ top_top_set_nat )
% 2.89/1.60         => ( inj_on26176689at_nat @ ( produc505105722at_nat @ F1 @ F22 ) @ top_to1555900337at_nat ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_218_prod_Oinj__map,axiom,
% 2.89/1.60      ! [F1: nat > nat,F22: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.89/1.60        ( ( inj_on_nat_nat @ F1 @ top_top_set_nat )
% 2.89/1.60       => ( ( inj_on772319074lle_tv @ F22 @ top_to1057771083lle_tv )
% 2.89/1.60         => ( inj_on1745913142lle_tv @ ( produc2101297531lle_tv @ F1 @ F22 ) @ top_to1411004326lle_tv ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_219_prod_Oinj__map,axiom,
% 2.89/1.60      ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F22: nat > nat] :
% 2.89/1.60        ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 2.89/1.60       => ( ( inj_on_nat_nat @ F22 @ top_top_set_nat )
% 2.89/1.60         => ( inj_on552895452tv_nat @ ( produc42536895at_nat @ F1 @ F22 ) @ top_to975729152tv_nat ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_220_prod_Oinj__map,axiom,
% 2.89/1.60      ! [F1: paraco1605129243lle_tv > paraco1605129243lle_tv,F22: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.89/1.60        ( ( inj_on772319074lle_tv @ F1 @ top_to1057771083lle_tv )
% 2.89/1.60       => ( ( inj_on772319074lle_tv @ F22 @ top_to1057771083lle_tv )
% 2.89/1.60         => ( inj_on2112487900lle_tv @ ( produc1345917071lle_tv @ F1 @ F22 ) @ top_to1871154984lle_tv ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_221_ssubst__Pair__rhs,axiom,
% 2.89/1.60      ! [R: list_char > paraco1605129243lle_tv,S3: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,S4: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S3 ) @ R2 )
% 2.89/1.60       => ( ( S4 = S3 )
% 2.89/1.60         => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ R @ S4 ) @ R2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_222_ssubst__Pair__rhs,axiom,
% 2.89/1.60      ! [R: nat > nat,S3: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,S4: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ R @ S3 ) @ R2 )
% 2.89/1.60       => ( ( S4 = S3 )
% 2.89/1.60         => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ R @ S4 ) @ R2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_223_curryI,axiom,
% 2.89/1.60      ! [F: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( F @ ( produc1710735575lle_fm @ A @ B ) )
% 2.89/1.60       => ( produc275353523e_fm_o @ F @ A @ B ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_224_curryI,axiom,
% 2.89/1.60      ! [F: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( F @ ( produc1680557635lle_tv @ A @ B ) )
% 2.89/1.60       => ( produc752649287e_tv_o @ F @ A @ B ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_225_map__prod__simp,axiom,
% 2.89/1.60      ! [F: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( produc1900967599lle_fm @ F @ G @ ( produc1710735575lle_fm @ A @ B ) )
% 2.89/1.60        = ( produc1710735575lle_fm @ ( F @ A ) @ ( G @ B ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_226_map__prod__simp,axiom,
% 2.89/1.60      ! [F: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( produc1566550641lle_tv @ F @ G @ ( produc1710735575lle_fm @ A @ B ) )
% 2.89/1.60        = ( produc1680557635lle_tv @ ( F @ A ) @ ( G @ B ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_227_map__prod__simp,axiom,
% 2.89/1.60      ! [F: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,A: nat > nat,B: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( produc951033137lle_fm @ F @ G @ ( produc1680557635lle_tv @ A @ B ) )
% 2.89/1.60        = ( produc1710735575lle_fm @ ( F @ A ) @ ( G @ B ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_228_map__prod__simp,axiom,
% 2.89/1.60      ! [F: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv,A: nat > nat,B: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( produc532909085lle_tv @ F @ G @ ( produc1680557635lle_tv @ A @ B ) )
% 2.89/1.60        = ( produc1680557635lle_tv @ ( F @ A ) @ ( G @ B ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_229_curryD,axiom,
% 2.89/1.60      ! [F: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( produc275353523e_fm_o @ F @ A @ B )
% 2.89/1.60       => ( F @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_230_curryD,axiom,
% 2.89/1.60      ! [F: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( produc752649287e_tv_o @ F @ A @ B )
% 2.89/1.60       => ( F @ ( produc1680557635lle_tv @ A @ B ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_231_curryE,axiom,
% 2.89/1.60      ! [F: produc696645085lle_fm > $o,A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( produc275353523e_fm_o @ F @ A @ B )
% 2.89/1.60       => ( F @ ( produc1710735575lle_fm @ A @ B ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_232_curryE,axiom,
% 2.89/1.60      ! [F: produc931990033lle_tv > $o,A: nat > nat,B: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( produc752649287e_tv_o @ F @ A @ B )
% 2.89/1.60       => ( F @ ( produc1680557635lle_tv @ A @ B ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_233_change__tv_Ocases,axiom,
% 2.89/1.60      ! [X: produc931990033lle_tv] :
% 2.89/1.60        ( ! [F3: nat > nat,B2: $o] :
% 2.89/1.60            ( X
% 2.89/1.60           != ( produc1680557635lle_tv @ F3 @ ( paraco1344940915le_Det @ B2 ) ) )
% 2.89/1.60       => ~ ! [F3: nat > nat,N: nat] :
% 2.89/1.60              ( X
% 2.89/1.60             != ( produc1680557635lle_tv @ F3 @ ( paraco793048302_Indet @ N ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_234_the__inv__f__f,axiom,
% 2.89/1.60      ! [F: nat > nat,X: nat] :
% 2.89/1.60        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 2.89/1.60       => ( ( the_inv_into_nat_nat @ top_top_set_nat @ F @ ( F @ X ) )
% 2.89/1.60          = X ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_235_the__inv__f__f,axiom,
% 2.89/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,X: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 2.89/1.60       => ( ( the_in452116896lle_tv @ top_to1057771083lle_tv @ F @ ( F @ X ) )
% 2.89/1.60          = X ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_236_change__tv_Opelims,axiom,
% 2.89/1.60      ! [X: nat > nat,Xa: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( ( paraco1147068288nge_tv @ X @ Xa )
% 2.89/1.60          = Y )
% 2.89/1.60       => ( ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ Xa ) )
% 2.89/1.60         => ( ! [B2: $o] :
% 2.89/1.60                ( ( Xa
% 2.89/1.60                  = ( paraco1344940915le_Det @ B2 ) )
% 2.89/1.60               => ( ( Y
% 2.89/1.60                    = ( paraco1344940915le_Det @ B2 ) )
% 2.89/1.60                 => ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ ( paraco1344940915le_Det @ B2 ) ) ) ) )
% 2.89/1.60           => ~ ! [N: nat] :
% 2.89/1.60                  ( ( Xa
% 2.89/1.60                    = ( paraco793048302_Indet @ N ) )
% 2.89/1.60                 => ( ( Y
% 2.89/1.60                      = ( paraco793048302_Indet @ ( X @ N ) ) )
% 2.89/1.60                   => ~ ( accp_P2085826120lle_tv @ paraco1632582009tv_rel @ ( produc1680557635lle_tv @ X @ ( paraco793048302_Indet @ N ) ) ) ) ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_237_the__inv__into__f__f,axiom,
% 2.89/1.60      ! [F: nat > nat,A2: set_nat,X: nat] :
% 2.89/1.60        ( ( inj_on_nat_nat @ F @ A2 )
% 2.89/1.60       => ( ( member_nat @ X @ A2 )
% 2.89/1.60         => ( ( the_inv_into_nat_nat @ A2 @ F @ ( F @ X ) )
% 2.89/1.60            = X ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_238_the__inv__into__f__f,axiom,
% 2.89/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( inj_on772319074lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( member266900804lle_tv @ X @ A2 )
% 2.89/1.60         => ( ( the_in452116896lle_tv @ A2 @ F @ ( F @ X ) )
% 2.89/1.60            = X ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_239_the__inv__into__f__eq,axiom,
% 2.89/1.60      ! [F: nat > nat,A2: set_nat,X: nat,Y: nat] :
% 2.89/1.60        ( ( inj_on_nat_nat @ F @ A2 )
% 2.89/1.60       => ( ( ( F @ X )
% 2.89/1.60            = Y )
% 2.89/1.60         => ( ( member_nat @ X @ A2 )
% 2.89/1.60           => ( ( the_inv_into_nat_nat @ A2 @ F @ Y )
% 2.89/1.60              = X ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_240_the__inv__into__f__eq,axiom,
% 2.89/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( inj_on772319074lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( ( F @ X )
% 2.89/1.60            = Y )
% 2.89/1.60         => ( ( member266900804lle_tv @ X @ A2 )
% 2.89/1.60           => ( ( the_in452116896lle_tv @ A2 @ F @ Y )
% 2.89/1.60              = X ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_241_total__inv__image,axiom,
% 2.89/1.60      ! [F: nat > nat,R: set_Pr1986765409at_nat] :
% 2.89/1.60        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 2.89/1.60       => ( ( total_on_nat @ top_top_set_nat @ R )
% 2.89/1.60         => ( total_on_nat @ top_top_set_nat @ ( inv_image_nat_nat @ R @ F ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_242_total__inv__image,axiom,
% 2.89/1.60      ! [F: nat > paraco1605129243lle_tv,R: set_Pr2014382200lle_tv] :
% 2.89/1.60        ( ( inj_on1955349912lle_tv @ F @ top_top_set_nat )
% 2.89/1.60       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 2.89/1.60         => ( total_on_nat @ top_top_set_nat @ ( inv_im516950809tv_nat @ R @ F ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_243_total__inv__image,axiom,
% 2.89/1.60      ! [F: paraco1605129243lle_tv > nat,R: set_Pr1986765409at_nat] :
% 2.89/1.60        ( ( inj_on1179712058tv_nat @ F @ top_to1057771083lle_tv )
% 2.89/1.60       => ( ( total_on_nat @ top_top_set_nat @ R )
% 2.89/1.60         => ( total_1781621663lle_tv @ top_to1057771083lle_tv @ ( inv_im1292588663lle_tv @ R @ F ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_244_total__inv__image,axiom,
% 2.89/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,R: set_Pr2014382200lle_tv] :
% 2.89/1.60        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 2.89/1.60       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 2.89/1.60         => ( total_1781621663lle_tv @ top_to1057771083lle_tv @ ( inv_im719552961lle_tv @ R @ F ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_245_the__inv__into__onto,axiom,
% 2.89/1.60      ! [F: nat > nat,A2: set_nat] :
% 2.89/1.60        ( ( inj_on_nat_nat @ F @ A2 )
% 2.89/1.60       => ( ( image_nat_nat @ ( the_inv_into_nat_nat @ A2 @ F ) @ ( image_nat_nat @ F @ A2 ) )
% 2.89/1.60          = A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_246_the__inv__into__onto,axiom,
% 2.89/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 2.89/1.60        ( ( inj_on772319074lle_tv @ F @ A2 )
% 2.89/1.60       => ( ( image_335818702lle_tv @ ( the_in452116896lle_tv @ A2 @ F ) @ ( image_335818702lle_tv @ F @ A2 ) )
% 2.89/1.60          = A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_247_map__prod__imageI,axiom,
% 2.89/1.60      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm] :
% 2.89/1.60        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
% 2.89/1.60       => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F @ A ) @ ( G @ B ) ) @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F @ G ) @ R2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_248_map__prod__imageI,axiom,
% 2.89/1.60      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm,F: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv] :
% 2.89/1.60        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ R2 )
% 2.89/1.60       => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ ( F @ A ) @ ( G @ B ) ) @ ( image_1154804148lle_tv @ ( produc1566550641lle_tv @ F @ G ) @ R2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_249_map__prod__imageI,axiom,
% 2.89/1.60      ! [A: nat > nat,B: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,F: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm] :
% 2.89/1.60        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ R2 )
% 2.89/1.60       => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ ( F @ A ) @ ( G @ B ) ) @ ( image_1585092542lle_fm @ ( produc951033137lle_fm @ F @ G ) @ R2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_250_map__prod__imageI,axiom,
% 2.89/1.60      ! [A: nat > nat,B: paraco1605129243lle_tv,R2: set_Pr560526279lle_tv,F: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.89/1.60        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ R2 )
% 2.89/1.60       => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ ( F @ A ) @ ( G @ B ) ) @ ( image_1751508608lle_tv @ ( produc532909085lle_tv @ F @ G ) @ R2 ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_251_swap__simp,axiom,
% 2.89/1.60      ! [X: paraco1604210848lle_fm,Y: list_char > paraco1605129243lle_tv] :
% 2.89/1.60        ( ( produc1232814113lle_tv @ ( produc1943344577lle_tv @ X @ Y ) )
% 2.89/1.60        = ( produc1710735575lle_fm @ Y @ X ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_252_swap__simp,axiom,
% 2.89/1.60      ! [X: paraco1605129243lle_tv,Y: nat > nat] :
% 2.89/1.60        ( ( produc178635363at_nat @ ( produc1633679363at_nat @ X @ Y ) )
% 2.89/1.60        = ( produc1680557635lle_tv @ Y @ X ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_253_swap__simp,axiom,
% 2.89/1.60      ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm] :
% 2.89/1.60        ( ( produc1000205111lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 2.89/1.60        = ( produc1943344577lle_tv @ Y @ X ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_254_swap__simp,axiom,
% 2.89/1.60      ! [X: nat > nat,Y: paraco1605129243lle_tv] :
% 2.89/1.60        ( ( produc225513635lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 2.89/1.60        = ( produc1633679363at_nat @ Y @ X ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_255_pair__in__swap__image,axiom,
% 2.89/1.60      ! [Y: paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv,A2: set_Pr2120184979lle_fm] :
% 2.89/1.60        ( ( member74361182lle_tv @ ( produc1943344577lle_tv @ Y @ X ) @ ( image_924970994lle_tv @ produc1000205111lle_fm @ A2 ) )
% 2.89/1.60        = ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X @ Y ) @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_256_pair__in__swap__image,axiom,
% 2.89/1.60      ! [Y: paraco1605129243lle_tv,X: nat > nat,A2: set_Pr560526279lle_tv] :
% 2.89/1.60        ( ( member1234290208at_nat @ ( produc1633679363at_nat @ Y @ X ) @ ( image_1724396928at_nat @ produc225513635lle_tv @ A2 ) )
% 2.89/1.60        = ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X @ Y ) @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_257_pair__in__swap__image,axiom,
% 2.89/1.60      ! [Y: list_char > paraco1605129243lle_tv,X: paraco1604210848lle_fm,A2: set_Pr1723822845lle_tv] :
% 2.89/1.60        ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ Y @ X ) @ ( image_326034184lle_fm @ produc1232814113lle_tv @ A2 ) )
% 2.89/1.60        = ( member74361182lle_tv @ ( produc1943344577lle_tv @ X @ Y ) @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_258_pair__in__swap__image,axiom,
% 2.89/1.60      ! [Y: nat > nat,X: paraco1605129243lle_tv,A2: set_Pr840833727at_nat] :
% 2.89/1.60        ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ Y @ X ) @ ( image_769496456lle_tv @ produc178635363at_nat @ A2 ) )
% 2.89/1.60        = ( member1234290208at_nat @ ( produc1633679363at_nat @ X @ Y ) @ A2 ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_259_map__prod__surj,axiom,
% 2.89/1.60      ! [F: nat > nat,G: nat > nat] :
% 2.89/1.60        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 2.89/1.60          = top_top_set_nat )
% 2.89/1.60       => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 2.89/1.60            = top_top_set_nat )
% 2.89/1.60         => ( ( image_815163717at_nat @ ( produc505105722at_nat @ F @ G ) @ top_to1555900337at_nat )
% 2.89/1.60            = top_to1555900337at_nat ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_260_map__prod__surj,axiom,
% 2.89/1.60      ! [F: nat > nat,G: nat > paraco1605129243lle_tv] :
% 2.89/1.60        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 2.89/1.60          = top_top_set_nat )
% 2.89/1.60       => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 2.89/1.60            = top_to1057771083lle_tv )
% 2.89/1.60         => ( ( image_1674248956lle_tv @ ( produc313957681lle_tv @ F @ G ) @ top_to1555900337at_nat )
% 2.89/1.60            = top_to1411004326lle_tv ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_261_map__prod__surj,axiom,
% 2.89/1.60      ! [F: nat > nat,G: paraco1605129243lle_tv > nat] :
% 2.89/1.60        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 2.89/1.60          = top_top_set_nat )
% 2.89/1.60       => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 2.89/1.60            = top_top_set_nat )
% 2.89/1.60         => ( ( image_1787705850at_nat @ ( produc1685803475tv_nat @ F @ G ) @ top_to1411004326lle_tv )
% 2.89/1.60            = top_to1555900337at_nat ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_262_map__prod__surj,axiom,
% 2.89/1.60      ! [F: nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.89/1.60        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 2.89/1.60          = top_top_set_nat )
% 2.89/1.60       => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 2.89/1.60            = top_to1057771083lle_tv )
% 2.89/1.60         => ( ( image_149830562lle_tv @ ( produc2101297531lle_tv @ F @ G ) @ top_to1411004326lle_tv )
% 2.89/1.60            = top_to1411004326lle_tv ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_263_map__prod__surj,axiom,
% 2.89/1.60      ! [F: nat > paraco1605129243lle_tv,G: nat > nat] :
% 2.89/1.60        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 2.89/1.60          = top_to1057771083lle_tv )
% 2.89/1.60       => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 2.89/1.60            = top_top_set_nat )
% 2.89/1.60         => ( ( image_1597721174tv_nat @ ( produc1250721397at_nat @ F @ G ) @ top_to1555900337at_nat )
% 2.89/1.60            = top_to975729152tv_nat ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_264_map__prod__surj,axiom,
% 2.89/1.60      ! [F: nat > paraco1605129243lle_tv,G: nat > paraco1605129243lle_tv] :
% 2.89/1.60        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 2.89/1.60          = top_to1057771083lle_tv )
% 2.89/1.60       => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 2.89/1.60            = top_to1057771083lle_tv )
% 2.89/1.60         => ( ( image_1507992062lle_tv @ ( produc210389789lle_tv @ F @ G ) @ top_to1555900337at_nat )
% 2.89/1.60            = top_to1871154984lle_tv ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_265_map__prod__surj,axiom,
% 2.89/1.60      ! [F: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > nat] :
% 2.89/1.60        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 2.89/1.60          = top_to1057771083lle_tv )
% 2.89/1.60       => ( ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 2.89/1.60            = top_top_set_nat )
% 2.89/1.60         => ( ( image_53754658tv_nat @ ( produc189459613tv_nat @ F @ G ) @ top_to1411004326lle_tv )
% 2.89/1.60            = top_to975729152tv_nat ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_266_map__prod__surj,axiom,
% 2.89/1.60      ! [F: nat > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 2.89/1.60        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 2.89/1.60          = top_to1057771083lle_tv )
% 2.89/1.60       => ( ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 2.89/1.60            = top_to1057771083lle_tv )
% 2.89/1.60         => ( ( image_988201162lle_tv @ ( produc1975500101lle_tv @ F @ G ) @ top_to1411004326lle_tv )
% 2.89/1.60            = top_to1871154984lle_tv ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_267_map__prod__surj,axiom,
% 2.89/1.60      ! [F: paraco1605129243lle_tv > nat,G: nat > nat] :
% 2.89/1.60        ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 2.89/1.60          = top_top_set_nat )
% 2.89/1.60       => ( ( ( image_nat_nat @ G @ top_top_set_nat )
% 2.89/1.60            = top_top_set_nat )
% 2.89/1.60         => ( ( image_1805124128at_nat @ ( produc386540311at_nat @ F @ G ) @ top_to975729152tv_nat )
% 2.89/1.60            = top_to1555900337at_nat ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_268_map__prod__surj,axiom,
% 2.89/1.60      ! [F: paraco1605129243lle_tv > nat,G: nat > paraco1605129243lle_tv] :
% 2.89/1.60        ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 2.89/1.60          = top_top_set_nat )
% 2.89/1.60       => ( ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 2.89/1.60            = top_to1057771083lle_tv )
% 2.89/1.60         => ( ( image_1200372424lle_tv @ ( produc72207551lle_tv @ F @ G ) @ top_to975729152tv_nat )
% 2.89/1.60            = top_to1411004326lle_tv ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_269_surj__def,axiom,
% 2.89/1.60      ! [F: nat > nat] :
% 2.89/1.60        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 2.89/1.60          = top_top_set_nat )
% 2.89/1.60        = ( ! [Y4: nat] :
% 2.89/1.60            ? [X4: nat] :
% 2.89/1.60              ( Y4
% 2.89/1.60              = ( F @ X4 ) ) ) ) ).
% 2.89/1.60  
% 2.89/1.60  thf(fact_270_surj__def,axiom,
% 2.89/1.60      ! [F: nat > paraco1605129243lle_tv] :
% 2.89/1.60        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 3.06/1.60          = top_to1057771083lle_tv )
% 3.06/1.60        = ( ! [Y4: paraco1605129243lle_tv] :
% 3.06/1.60            ? [X4: nat] :
% 3.06/1.60              ( Y4
% 3.06/1.60              = ( F @ X4 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_271_surj__def,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > nat] :
% 3.06/1.60        ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 3.06/1.60          = top_top_set_nat )
% 3.06/1.60        = ( ! [Y4: nat] :
% 3.06/1.60            ? [X4: paraco1605129243lle_tv] :
% 3.06/1.60              ( Y4
% 3.06/1.60              = ( F @ X4 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_272_surj__def,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.60        ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 3.06/1.60          = top_to1057771083lle_tv )
% 3.06/1.60        = ( ! [Y4: paraco1605129243lle_tv] :
% 3.06/1.60            ? [X4: paraco1605129243lle_tv] :
% 3.06/1.60              ( Y4
% 3.06/1.60              = ( F @ X4 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_273_surjI,axiom,
% 3.06/1.60      ! [G: nat > nat,F: nat > nat] :
% 3.06/1.60        ( ! [X5: nat] :
% 3.06/1.60            ( ( G @ ( F @ X5 ) )
% 3.06/1.60            = X5 )
% 3.06/1.60       => ( ( image_nat_nat @ G @ top_top_set_nat )
% 3.06/1.60          = top_top_set_nat ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_274_surjI,axiom,
% 3.06/1.60      ! [G: nat > paraco1605129243lle_tv,F: paraco1605129243lle_tv > nat] :
% 3.06/1.60        ( ! [X5: paraco1605129243lle_tv] :
% 3.06/1.60            ( ( G @ ( F @ X5 ) )
% 3.06/1.60            = X5 )
% 3.06/1.60       => ( ( image_1151963140lle_tv @ G @ top_top_set_nat )
% 3.06/1.60          = top_to1057771083lle_tv ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_275_surjI,axiom,
% 3.06/1.60      ! [G: paraco1605129243lle_tv > nat,F: nat > paraco1605129243lle_tv] :
% 3.06/1.60        ( ! [X5: nat] :
% 3.06/1.60            ( ( G @ ( F @ X5 ) )
% 3.06/1.60            = X5 )
% 3.06/1.60       => ( ( image_376325286tv_nat @ G @ top_to1057771083lle_tv )
% 3.06/1.60          = top_top_set_nat ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_276_surjI,axiom,
% 3.06/1.60      ! [G: paraco1605129243lle_tv > paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.60        ( ! [X5: paraco1605129243lle_tv] :
% 3.06/1.60            ( ( G @ ( F @ X5 ) )
% 3.06/1.60            = X5 )
% 3.06/1.60       => ( ( image_335818702lle_tv @ G @ top_to1057771083lle_tv )
% 3.06/1.60          = top_to1057771083lle_tv ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_277_surjE,axiom,
% 3.06/1.60      ! [F: nat > nat,Y: nat] :
% 3.06/1.60        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 3.06/1.60          = top_top_set_nat )
% 3.06/1.60       => ~ ! [X5: nat] :
% 3.06/1.60              ( Y
% 3.06/1.60             != ( F @ X5 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_278_surjE,axiom,
% 3.06/1.60      ! [F: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 3.06/1.60          = top_to1057771083lle_tv )
% 3.06/1.60       => ~ ! [X5: nat] :
% 3.06/1.60              ( Y
% 3.06/1.60             != ( F @ X5 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_279_surjE,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > nat,Y: nat] :
% 3.06/1.60        ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 3.06/1.60          = top_top_set_nat )
% 3.06/1.60       => ~ ! [X5: paraco1605129243lle_tv] :
% 3.06/1.60              ( Y
% 3.06/1.60             != ( F @ X5 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_280_surjE,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 3.06/1.60          = top_to1057771083lle_tv )
% 3.06/1.60       => ~ ! [X5: paraco1605129243lle_tv] :
% 3.06/1.60              ( Y
% 3.06/1.60             != ( F @ X5 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_281_surjD,axiom,
% 3.06/1.60      ! [F: nat > nat,Y: nat] :
% 3.06/1.60        ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 3.06/1.60          = top_top_set_nat )
% 3.06/1.60       => ? [X5: nat] :
% 3.06/1.60            ( Y
% 3.06/1.60            = ( F @ X5 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_282_surjD,axiom,
% 3.06/1.60      ! [F: nat > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( ( image_1151963140lle_tv @ F @ top_top_set_nat )
% 3.06/1.60          = top_to1057771083lle_tv )
% 3.06/1.60       => ? [X5: nat] :
% 3.06/1.60            ( Y
% 3.06/1.60            = ( F @ X5 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_283_surjD,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > nat,Y: nat] :
% 3.06/1.60        ( ( ( image_376325286tv_nat @ F @ top_to1057771083lle_tv )
% 3.06/1.60          = top_top_set_nat )
% 3.06/1.60       => ? [X5: paraco1605129243lle_tv] :
% 3.06/1.60            ( Y
% 3.06/1.60            = ( F @ X5 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_284_surjD,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( ( image_335818702lle_tv @ F @ top_to1057771083lle_tv )
% 3.06/1.60          = top_to1057771083lle_tv )
% 3.06/1.60       => ? [X5: paraco1605129243lle_tv] :
% 3.06/1.60            ( Y
% 3.06/1.60            = ( F @ X5 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_285_inj__on__image__iff,axiom,
% 3.06/1.60      ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 3.06/1.60        ( ! [X5: nat] :
% 3.06/1.60            ( ( member_nat @ X5 @ A2 )
% 3.06/1.60           => ! [Xa2: nat] :
% 3.06/1.60                ( ( member_nat @ Xa2 @ A2 )
% 3.06/1.60               => ( ( ( G @ ( F @ X5 ) )
% 3.06/1.60                    = ( G @ ( F @ Xa2 ) ) )
% 3.06/1.60                  = ( ( G @ X5 )
% 3.06/1.60                    = ( G @ Xa2 ) ) ) ) )
% 3.06/1.60       => ( ( inj_on_nat_nat @ F @ A2 )
% 3.06/1.60         => ( ( inj_on_nat_nat @ G @ ( image_nat_nat @ F @ A2 ) )
% 3.06/1.60            = ( inj_on_nat_nat @ G @ A2 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_286_inj__on__image__iff,axiom,
% 3.06/1.60      ! [A2: set_Pa1764573435lle_tv,G: paraco1605129243lle_tv > paraco1605129243lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.60        ( ! [X5: paraco1605129243lle_tv] :
% 3.06/1.60            ( ( member266900804lle_tv @ X5 @ A2 )
% 3.06/1.60           => ! [Xa2: paraco1605129243lle_tv] :
% 3.06/1.60                ( ( member266900804lle_tv @ Xa2 @ A2 )
% 3.06/1.60               => ( ( ( G @ ( F @ X5 ) )
% 3.06/1.60                    = ( G @ ( F @ Xa2 ) ) )
% 3.06/1.60                  = ( ( G @ X5 )
% 3.06/1.60                    = ( G @ Xa2 ) ) ) ) )
% 3.06/1.60       => ( ( inj_on772319074lle_tv @ F @ A2 )
% 3.06/1.60         => ( ( inj_on772319074lle_tv @ G @ ( image_335818702lle_tv @ F @ A2 ) )
% 3.06/1.60            = ( inj_on772319074lle_tv @ G @ A2 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_287_inj__image__mem__iff,axiom,
% 3.06/1.60      ! [F: nat > nat,A: nat,A2: set_nat] :
% 3.06/1.60        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 3.06/1.60       => ( ( member_nat @ ( F @ A ) @ ( image_nat_nat @ F @ A2 ) )
% 3.06/1.60          = ( member_nat @ A @ A2 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_288_inj__image__mem__iff,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 3.06/1.60        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 3.06/1.60       => ( ( member266900804lle_tv @ ( F @ A ) @ ( image_335818702lle_tv @ F @ A2 ) )
% 3.06/1.60          = ( member266900804lle_tv @ A @ A2 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_289_inj__image__eq__iff,axiom,
% 3.06/1.60      ! [F: nat > nat,A2: set_nat,B4: set_nat] :
% 3.06/1.60        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 3.06/1.60       => ( ( ( image_nat_nat @ F @ A2 )
% 3.06/1.60            = ( image_nat_nat @ F @ B4 ) )
% 3.06/1.60          = ( A2 = B4 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_290_inj__image__eq__iff,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 3.06/1.60        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 3.06/1.60       => ( ( ( image_335818702lle_tv @ F @ A2 )
% 3.06/1.60            = ( image_335818702lle_tv @ F @ B4 ) )
% 3.06/1.60          = ( A2 = B4 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_291_range__ex1__eq,axiom,
% 3.06/1.60      ! [F: nat > nat,B: nat] :
% 3.06/1.60        ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 3.06/1.60       => ( ( member_nat @ B @ ( image_nat_nat @ F @ top_top_set_nat ) )
% 3.06/1.60          = ( ? [X4: nat] :
% 3.06/1.60                ( ( B
% 3.06/1.60                  = ( F @ X4 ) )
% 3.06/1.60                & ! [Y4: nat] :
% 3.06/1.60                    ( ( B
% 3.06/1.60                      = ( F @ Y4 ) )
% 3.06/1.60                   => ( Y4 = X4 ) ) ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_292_range__ex1__eq,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 3.06/1.60       => ( ( member266900804lle_tv @ B @ ( image_335818702lle_tv @ F @ top_to1057771083lle_tv ) )
% 3.06/1.60          = ( ? [X4: paraco1605129243lle_tv] :
% 3.06/1.60                ( ( B
% 3.06/1.60                  = ( F @ X4 ) )
% 3.06/1.60                & ! [Y4: paraco1605129243lle_tv] :
% 3.06/1.60                    ( ( B
% 3.06/1.60                      = ( F @ Y4 ) )
% 3.06/1.60                   => ( Y4 = X4 ) ) ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_293_prod__fun__imageE,axiom,
% 3.06/1.60      ! [C: produc696645085lle_fm,F: ( list_char > paraco1605129243lle_tv ) > list_char > paraco1605129243lle_tv,G: paraco1604210848lle_fm > paraco1604210848lle_fm,R2: set_Pr2120184979lle_fm] :
% 3.06/1.60        ( ( member1474794996lle_fm @ C @ ( image_807538418lle_fm @ ( produc1900967599lle_fm @ F @ G ) @ R2 ) )
% 3.06/1.60       => ~ ! [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] :
% 3.06/1.60              ( ( C
% 3.06/1.60                = ( produc1710735575lle_fm @ ( F @ X5 ) @ ( G @ Y5 ) ) )
% 3.06/1.60             => ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X5 @ Y5 ) @ R2 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_294_prod__fun__imageE,axiom,
% 3.06/1.60      ! [C: produc696645085lle_fm,F: ( nat > nat ) > list_char > paraco1605129243lle_tv,G: paraco1605129243lle_tv > paraco1604210848lle_fm,R2: set_Pr560526279lle_tv] :
% 3.06/1.60        ( ( member1474794996lle_fm @ C @ ( image_1585092542lle_fm @ ( produc951033137lle_fm @ F @ G ) @ R2 ) )
% 3.06/1.60       => ~ ! [X5: nat > nat,Y5: paraco1605129243lle_tv] :
% 3.06/1.60              ( ( C
% 3.06/1.60                = ( produc1710735575lle_fm @ ( F @ X5 ) @ ( G @ Y5 ) ) )
% 3.06/1.60             => ~ ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X5 @ Y5 ) @ R2 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_295_prod__fun__imageE,axiom,
% 3.06/1.60      ! [C: produc931990033lle_tv,F: ( list_char > paraco1605129243lle_tv ) > nat > nat,G: paraco1604210848lle_fm > paraco1605129243lle_tv,R2: set_Pr2120184979lle_fm] :
% 3.06/1.60        ( ( member1569366824lle_tv @ C @ ( image_1154804148lle_tv @ ( produc1566550641lle_tv @ F @ G ) @ R2 ) )
% 3.06/1.60       => ~ ! [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] :
% 3.06/1.60              ( ( C
% 3.06/1.60                = ( produc1680557635lle_tv @ ( F @ X5 ) @ ( G @ Y5 ) ) )
% 3.06/1.60             => ~ ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X5 @ Y5 ) @ R2 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_296_prod__fun__imageE,axiom,
% 3.06/1.60      ! [C: produc931990033lle_tv,F: ( nat > nat ) > nat > nat,G: paraco1605129243lle_tv > paraco1605129243lle_tv,R2: set_Pr560526279lle_tv] :
% 3.06/1.60        ( ( member1569366824lle_tv @ C @ ( image_1751508608lle_tv @ ( produc532909085lle_tv @ F @ G ) @ R2 ) )
% 3.06/1.60       => ~ ! [X5: nat > nat,Y5: paraco1605129243lle_tv] :
% 3.06/1.60              ( ( C
% 3.06/1.60                = ( produc1680557635lle_tv @ ( F @ X5 ) @ ( G @ Y5 ) ) )
% 3.06/1.60             => ~ ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X5 @ Y5 ) @ R2 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_297_inj__on__the__inv__into,axiom,
% 3.06/1.60      ! [F: nat > nat,A2: set_nat] :
% 3.06/1.60        ( ( inj_on_nat_nat @ F @ A2 )
% 3.06/1.60       => ( inj_on_nat_nat @ ( the_inv_into_nat_nat @ A2 @ F ) @ ( image_nat_nat @ F @ A2 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_298_inj__on__the__inv__into,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 3.06/1.60        ( ( inj_on772319074lle_tv @ F @ A2 )
% 3.06/1.60       => ( inj_on772319074lle_tv @ ( the_in452116896lle_tv @ A2 @ F ) @ ( image_335818702lle_tv @ F @ A2 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_299_f__the__inv__into__f,axiom,
% 3.06/1.60      ! [F: nat > nat,A2: set_nat,Y: nat] :
% 3.06/1.60        ( ( inj_on_nat_nat @ F @ A2 )
% 3.06/1.60       => ( ( member_nat @ Y @ ( image_nat_nat @ F @ A2 ) )
% 3.06/1.60         => ( ( F @ ( the_inv_into_nat_nat @ A2 @ F @ Y ) )
% 3.06/1.60            = Y ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_300_f__the__inv__into__f,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( inj_on772319074lle_tv @ F @ A2 )
% 3.06/1.60       => ( ( member266900804lle_tv @ Y @ ( image_335818702lle_tv @ F @ A2 ) )
% 3.06/1.60         => ( ( F @ ( the_in452116896lle_tv @ A2 @ F @ Y ) )
% 3.06/1.60            = Y ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_301_total__lex__prod,axiom,
% 3.06/1.60      ! [R: set_Pr1986765409at_nat,S3: set_Pr1986765409at_nat] :
% 3.06/1.60        ( ( total_on_nat @ top_top_set_nat @ R )
% 3.06/1.60       => ( ( total_on_nat @ top_top_set_nat @ S3 )
% 3.06/1.60         => ( total_1775715973at_nat @ top_to1555900337at_nat @ ( lex_prod_nat_nat @ R @ S3 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_302_total__lex__prod,axiom,
% 3.06/1.60      ! [R: set_Pr1986765409at_nat,S3: set_Pr2014382200lle_tv] :
% 3.06/1.60        ( ( total_on_nat @ top_top_set_nat @ R )
% 3.06/1.60       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ S3 )
% 3.06/1.60         => ( total_517371324lle_tv @ top_to1411004326lle_tv @ ( lex_pr413684186lle_tv @ R @ S3 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_303_total__lex__prod,axiom,
% 3.06/1.60      ! [R: set_Pr2014382200lle_tv,S3: set_Pr1986765409at_nat] :
% 3.06/1.60        ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 3.06/1.60       => ( ( total_on_nat @ top_top_set_nat @ S3 )
% 3.06/1.60         => ( total_440843542tv_nat @ top_to975729152tv_nat @ ( lex_pr1785529980tv_nat @ R @ S3 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_304_total__lex__prod,axiom,
% 3.06/1.60      ! [R: set_Pr2014382200lle_tv,S3: set_Pr2014382200lle_tv] :
% 3.06/1.60        ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ R )
% 3.06/1.60       => ( ( total_1781621663lle_tv @ top_to1057771083lle_tv @ S3 )
% 3.06/1.60         => ( total_92239038lle_tv @ top_to1871154984lle_tv @ ( lex_pr567812260lle_tv @ R @ S3 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_305_in__lex__prod,axiom,
% 3.06/1.60      ! [A: list_char > paraco1605129243lle_tv,B: paraco1604210848lle_fm,A5: list_char > paraco1605129243lle_tv,B3: paraco1604210848lle_fm,R: set_Pr2061825550lle_tv,S3: set_Pr1019238018lle_fm] :
% 3.06/1.60        ( ( member1592865093lle_fm @ ( produc407632608lle_fm @ ( produc1710735575lle_fm @ A @ B ) @ ( produc1710735575lle_fm @ A5 @ B3 ) ) @ ( lex_pr2001015487lle_fm @ R @ S3 ) )
% 3.06/1.60        = ( ( member146333935lle_tv @ ( produc1297923922lle_tv @ A @ A5 ) @ R )
% 3.06/1.60          | ( ( A = A5 )
% 3.06/1.60            & ( member334644067lle_fm @ ( produc1126104134lle_fm @ B @ B3 ) @ S3 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_306_in__lex__prod,axiom,
% 3.06/1.60      ! [A: nat > nat,B: paraco1605129243lle_tv,A5: nat > nat,B3: paraco1605129243lle_tv,R: set_Pr1357842111at_nat,S3: set_Pr2014382200lle_tv] :
% 3.06/1.60        ( ( member1339857875lle_tv @ ( produc2057188974lle_tv @ ( produc1680557635lle_tv @ A @ B ) @ ( produc1680557635lle_tv @ A5 @ B3 ) ) @ ( lex_pr1093414955lle_tv @ R @ S3 ) )
% 3.06/1.60        = ( ( member112824072at_nat @ ( produc780837143at_nat @ A @ A5 ) @ R )
% 3.06/1.60          | ( ( A = A5 )
% 3.06/1.60            & ( member1531318361lle_tv @ ( produc2058540732lle_tv @ B @ B3 ) @ S3 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_307_prod_Ocollapse,axiom,
% 3.06/1.60      ! [Prod: produc696645085lle_fm] :
% 3.06/1.60        ( ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) )
% 3.06/1.60        = Prod ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_308_prod_Ocollapse,axiom,
% 3.06/1.60      ! [Prod: produc931990033lle_tv] :
% 3.06/1.60        ( ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ Prod ) @ ( produc547496597lle_tv @ Prod ) )
% 3.06/1.60        = Prod ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_309_prod_Oswap__def,axiom,
% 3.06/1.60      ( produc1232814113lle_tv
% 3.06/1.60      = ( ^ [P2: produc1443694919lle_tv] : ( produc1710735575lle_fm @ ( produc381314067lle_tv @ P2 ) @ ( produc262413013lle_tv @ P2 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_310_prod_Oswap__def,axiom,
% 3.06/1.60      ( produc178635363at_nat
% 3.06/1.60      = ( ^ [P2: produc596913417at_nat] : ( produc1680557635lle_tv @ ( produc500618325at_nat @ P2 ) @ ( produc1589291287at_nat @ P2 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_311_fst__eqD,axiom,
% 3.06/1.60      ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: list_char > paraco1605129243lle_tv] :
% 3.06/1.60        ( ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 3.06/1.60          = A )
% 3.06/1.60       => ( X = A ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_312_fst__eqD,axiom,
% 3.06/1.60      ! [X: nat > nat,Y: paraco1605129243lle_tv,A: nat > nat] :
% 3.06/1.60        ( ( ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 3.06/1.60          = A )
% 3.06/1.60       => ( X = A ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_313_snd__eqD,axiom,
% 3.06/1.60      ! [X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: paraco1604210848lle_fm] :
% 3.06/1.60        ( ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X @ Y ) )
% 3.06/1.60          = A )
% 3.06/1.60       => ( Y = A ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_314_snd__eqD,axiom,
% 3.06/1.60      ! [X: nat > nat,Y: paraco1605129243lle_tv,A: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X @ Y ) )
% 3.06/1.60          = A )
% 3.06/1.60       => ( Y = A ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_315_fst__conv,axiom,
% 3.06/1.60      ! [X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm] :
% 3.06/1.60        ( ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X1 @ X2 ) )
% 3.06/1.60        = X1 ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_316_fst__conv,axiom,
% 3.06/1.60      ! [X1: nat > nat,X2: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X1 @ X2 ) )
% 3.06/1.60        = X1 ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_317_snd__conv,axiom,
% 3.06/1.60      ! [X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm] :
% 3.06/1.60        ( ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X1 @ X2 ) )
% 3.06/1.60        = X2 ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_318_snd__conv,axiom,
% 3.06/1.60      ! [X1: nat > nat,X2: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X1 @ X2 ) )
% 3.06/1.60        = X2 ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_319_prod_Oexhaust__sel,axiom,
% 3.06/1.60      ! [Prod: produc696645085lle_fm] :
% 3.06/1.60        ( Prod
% 3.06/1.60        = ( produc1710735575lle_fm @ ( produc29804011lle_fm @ Prod ) @ ( produc148705065lle_fm @ Prod ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_320_prod_Oexhaust__sel,axiom,
% 3.06/1.60      ! [Prod: produc931990033lle_tv] :
% 3.06/1.60        ( Prod
% 3.06/1.60        = ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ Prod ) @ ( produc547496597lle_tv @ Prod ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_321_surjective__pairing,axiom,
% 3.06/1.60      ! [T: produc696645085lle_fm] :
% 3.06/1.60        ( T
% 3.06/1.60        = ( produc1710735575lle_fm @ ( produc29804011lle_fm @ T ) @ ( produc148705065lle_fm @ T ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_322_surjective__pairing,axiom,
% 3.06/1.60      ! [T: produc931990033lle_tv] :
% 3.06/1.60        ( T
% 3.06/1.60        = ( produc1680557635lle_tv @ ( produc1636169559lle_tv @ T ) @ ( produc547496597lle_tv @ T ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_323_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.06/1.60      ! [P3: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > $o,X: list_char > paraco1605129243lle_tv,Y: paraco1604210848lle_fm,A: produc696645085lle_fm] :
% 3.06/1.60        ( ( P3 @ X @ Y )
% 3.06/1.60       => ( ( A
% 3.06/1.60            = ( produc1710735575lle_fm @ X @ Y ) )
% 3.06/1.60         => ( P3 @ ( produc29804011lle_fm @ A ) @ ( produc148705065lle_fm @ A ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_324_BNF__Greatest__Fixpoint_Osubst__Pair,axiom,
% 3.06/1.60      ! [P3: ( nat > nat ) > paraco1605129243lle_tv > $o,X: nat > nat,Y: paraco1605129243lle_tv,A: produc931990033lle_tv] :
% 3.06/1.60        ( ( P3 @ X @ Y )
% 3.06/1.60       => ( ( A
% 3.06/1.60            = ( produc1680557635lle_tv @ X @ Y ) )
% 3.06/1.60         => ( P3 @ ( produc1636169559lle_tv @ A ) @ ( produc547496597lle_tv @ A ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_325_conjI__realizer,axiom,
% 3.06/1.60      ! [P3: ( list_char > paraco1605129243lle_tv ) > $o,P: list_char > paraco1605129243lle_tv,Q2: paraco1604210848lle_fm > $o,Q: paraco1604210848lle_fm] :
% 3.06/1.60        ( ( P3 @ P )
% 3.06/1.60       => ( ( Q2 @ Q )
% 3.06/1.60         => ( ( P3 @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ P @ Q ) ) )
% 3.06/1.60            & ( Q2 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ P @ Q ) ) ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_326_conjI__realizer,axiom,
% 3.06/1.60      ! [P3: ( nat > nat ) > $o,P: nat > nat,Q2: paraco1605129243lle_tv > $o,Q: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( P3 @ P )
% 3.06/1.60       => ( ( Q2 @ Q )
% 3.06/1.60         => ( ( P3 @ ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ P @ Q ) ) )
% 3.06/1.60            & ( Q2 @ ( produc547496597lle_tv @ ( produc1680557635lle_tv @ P @ Q ) ) ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_327_exI__realizer,axiom,
% 3.06/1.60      ! [P3: paraco1604210848lle_fm > ( list_char > paraco1605129243lle_tv ) > $o,Y: paraco1604210848lle_fm,X: list_char > paraco1605129243lle_tv] :
% 3.06/1.60        ( ( P3 @ Y @ X )
% 3.06/1.60       => ( P3 @ ( produc148705065lle_fm @ ( produc1710735575lle_fm @ X @ Y ) ) @ ( produc29804011lle_fm @ ( produc1710735575lle_fm @ X @ Y ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_328_exI__realizer,axiom,
% 3.06/1.60      ! [P3: paraco1605129243lle_tv > ( nat > nat ) > $o,Y: paraco1605129243lle_tv,X: nat > nat] :
% 3.06/1.60        ( ( P3 @ Y @ X )
% 3.06/1.60       => ( P3 @ ( produc547496597lle_tv @ ( produc1680557635lle_tv @ X @ Y ) ) @ ( produc1636169559lle_tv @ ( produc1680557635lle_tv @ X @ Y ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_329_sndI,axiom,
% 3.06/1.60      ! [X: produc696645085lle_fm,Y: list_char > paraco1605129243lle_tv,Z: paraco1604210848lle_fm] :
% 3.06/1.60        ( ( X
% 3.06/1.60          = ( produc1710735575lle_fm @ Y @ Z ) )
% 3.06/1.60       => ( ( produc148705065lle_fm @ X )
% 3.06/1.60          = Z ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_330_sndI,axiom,
% 3.06/1.60      ! [X: produc931990033lle_tv,Y: nat > nat,Z: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( X
% 3.06/1.60          = ( produc1680557635lle_tv @ Y @ Z ) )
% 3.06/1.60       => ( ( produc547496597lle_tv @ X )
% 3.06/1.60          = Z ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_331_eq__snd__iff,axiom,
% 3.06/1.60      ! [B: paraco1604210848lle_fm,P: produc696645085lle_fm] :
% 3.06/1.60        ( ( B
% 3.06/1.60          = ( produc148705065lle_fm @ P ) )
% 3.06/1.60        = ( ? [A6: list_char > paraco1605129243lle_tv] :
% 3.06/1.60              ( P
% 3.06/1.60              = ( produc1710735575lle_fm @ A6 @ B ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_332_eq__snd__iff,axiom,
% 3.06/1.60      ! [B: paraco1605129243lle_tv,P: produc931990033lle_tv] :
% 3.06/1.60        ( ( B
% 3.06/1.60          = ( produc547496597lle_tv @ P ) )
% 3.06/1.60        = ( ? [A6: nat > nat] :
% 3.06/1.60              ( P
% 3.06/1.60              = ( produc1680557635lle_tv @ A6 @ B ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_333_eq__fst__iff,axiom,
% 3.06/1.60      ! [A: list_char > paraco1605129243lle_tv,P: produc696645085lle_fm] :
% 3.06/1.60        ( ( A
% 3.06/1.60          = ( produc29804011lle_fm @ P ) )
% 3.06/1.60        = ( ? [B5: paraco1604210848lle_fm] :
% 3.06/1.60              ( P
% 3.06/1.60              = ( produc1710735575lle_fm @ A @ B5 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_334_eq__fst__iff,axiom,
% 3.06/1.60      ! [A: nat > nat,P: produc931990033lle_tv] :
% 3.06/1.60        ( ( A
% 3.06/1.60          = ( produc1636169559lle_tv @ P ) )
% 3.06/1.60        = ( ? [B5: paraco1605129243lle_tv] :
% 3.06/1.60              ( P
% 3.06/1.60              = ( produc1680557635lle_tv @ A @ B5 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_335_fstI,axiom,
% 3.06/1.60      ! [X: produc696645085lle_fm,Y: list_char > paraco1605129243lle_tv,Z: paraco1604210848lle_fm] :
% 3.06/1.60        ( ( X
% 3.06/1.60          = ( produc1710735575lle_fm @ Y @ Z ) )
% 3.06/1.60       => ( ( produc29804011lle_fm @ X )
% 3.06/1.60          = Y ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_336_fstI,axiom,
% 3.06/1.60      ! [X: produc931990033lle_tv,Y: nat > nat,Z: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( X
% 3.06/1.60          = ( produc1680557635lle_tv @ Y @ Z ) )
% 3.06/1.60       => ( ( produc1636169559lle_tv @ X )
% 3.06/1.60          = Y ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_337_same__fstI,axiom,
% 3.06/1.60      ! [P3: ( list_char > paraco1605129243lle_tv ) > $o,X: list_char > paraco1605129243lle_tv,Y6: paraco1604210848lle_fm,Y: paraco1604210848lle_fm,R2: ( list_char > paraco1605129243lle_tv ) > set_Pr1019238018lle_fm] :
% 3.06/1.60        ( ( P3 @ X )
% 3.06/1.60       => ( ( member334644067lle_fm @ ( produc1126104134lle_fm @ Y6 @ Y ) @ ( R2 @ X ) )
% 3.06/1.60         => ( member1592865093lle_fm @ ( produc407632608lle_fm @ ( produc1710735575lle_fm @ X @ Y6 ) @ ( produc1710735575lle_fm @ X @ Y ) ) @ ( same_f1581085506lle_fm @ P3 @ R2 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_338_same__fstI,axiom,
% 3.06/1.60      ! [P3: ( nat > nat ) > $o,X: nat > nat,Y6: paraco1605129243lle_tv,Y: paraco1605129243lle_tv,R2: ( nat > nat ) > set_Pr2014382200lle_tv] :
% 3.06/1.60        ( ( P3 @ X )
% 3.06/1.60       => ( ( member1531318361lle_tv @ ( produc2058540732lle_tv @ Y6 @ Y ) @ ( R2 @ X ) )
% 3.06/1.60         => ( member1339857875lle_tv @ ( produc2057188974lle_tv @ ( produc1680557635lle_tv @ X @ Y6 ) @ ( produc1680557635lle_tv @ X @ Y ) ) @ ( same_f1138187694lle_tv @ P3 @ R2 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_339_wf__map__prod__image,axiom,
% 3.06/1.60      ! [R: set_Pr1986765409at_nat,F: nat > nat] :
% 3.06/1.60        ( ( wf_nat @ R )
% 3.06/1.60       => ( ( inj_on_nat_nat @ F @ top_top_set_nat )
% 3.06/1.60         => ( wf_nat @ ( image_815163717at_nat @ ( produc505105722at_nat @ F @ F ) @ R ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_340_wf__map__prod__image,axiom,
% 3.06/1.60      ! [R: set_Pr2014382200lle_tv,F: paraco1605129243lle_tv > paraco1605129243lle_tv] :
% 3.06/1.60        ( ( wf_Par1378404612lle_tv @ R )
% 3.06/1.60       => ( ( inj_on772319074lle_tv @ F @ top_to1057771083lle_tv )
% 3.06/1.60         => ( wf_Par1378404612lle_tv @ ( image_1221801032lle_tv @ ( produc1345917071lle_tv @ F @ F ) @ R ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_341_the__inv__into__into,axiom,
% 3.06/1.60      ! [F: nat > nat,A2: set_nat,X: nat,B4: set_nat] :
% 3.06/1.60        ( ( inj_on_nat_nat @ F @ A2 )
% 3.06/1.60       => ( ( member_nat @ X @ ( image_nat_nat @ F @ A2 ) )
% 3.06/1.60         => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 3.06/1.60           => ( member_nat @ ( the_inv_into_nat_nat @ A2 @ F @ X ) @ B4 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_342_the__inv__into__into,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,X: paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv] :
% 3.06/1.60        ( ( inj_on772319074lle_tv @ F @ A2 )
% 3.06/1.60       => ( ( member266900804lle_tv @ X @ ( image_335818702lle_tv @ F @ A2 ) )
% 3.06/1.60         => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 3.06/1.60           => ( member266900804lle_tv @ ( the_in452116896lle_tv @ A2 @ F @ X ) @ B4 ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_343_strict__mono__inv,axiom,
% 3.06/1.60      ! [F: nat > nat,G: nat > nat] :
% 3.06/1.60        ( ( order_769474267at_nat @ F )
% 3.06/1.60       => ( ( ( image_nat_nat @ F @ top_top_set_nat )
% 3.06/1.60            = top_top_set_nat )
% 3.06/1.60         => ( ! [X5: nat] :
% 3.06/1.60                ( ( G @ ( F @ X5 ) )
% 3.06/1.60                = X5 )
% 3.06/1.60           => ( order_769474267at_nat @ G ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_344_subrelI,axiom,
% 3.06/1.60      ! [R: set_Pr2120184979lle_fm,S3: set_Pr2120184979lle_fm] :
% 3.06/1.60        ( ! [X5: list_char > paraco1605129243lle_tv,Y5: paraco1604210848lle_fm] :
% 3.06/1.60            ( ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X5 @ Y5 ) @ R )
% 3.06/1.60           => ( member1474794996lle_fm @ ( produc1710735575lle_fm @ X5 @ Y5 ) @ S3 ) )
% 3.06/1.60       => ( ord_le1007985907lle_fm @ R @ S3 ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_345_subrelI,axiom,
% 3.06/1.60      ! [R: set_Pr560526279lle_tv,S3: set_Pr560526279lle_tv] :
% 3.06/1.60        ( ! [X5: nat > nat,Y5: paraco1605129243lle_tv] :
% 3.06/1.60            ( ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X5 @ Y5 ) @ R )
% 3.06/1.60           => ( member1569366824lle_tv @ ( produc1680557635lle_tv @ X5 @ Y5 ) @ S3 ) )
% 3.06/1.60       => ( ord_le1784136743lle_tv @ R @ S3 ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_346_inj__on__image__mem__iff,axiom,
% 3.06/1.60      ! [F: nat > nat,B4: set_nat,A: nat,A2: set_nat] :
% 3.06/1.60        ( ( inj_on_nat_nat @ F @ B4 )
% 3.06/1.60       => ( ( member_nat @ A @ B4 )
% 3.06/1.60         => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 3.06/1.60           => ( ( member_nat @ ( F @ A ) @ ( image_nat_nat @ F @ A2 ) )
% 3.06/1.60              = ( member_nat @ A @ A2 ) ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_347_inj__on__image__mem__iff,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv,A: paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv] :
% 3.06/1.60        ( ( inj_on772319074lle_tv @ F @ B4 )
% 3.06/1.60       => ( ( member266900804lle_tv @ A @ B4 )
% 3.06/1.60         => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 3.06/1.60           => ( ( member266900804lle_tv @ ( F @ A ) @ ( image_335818702lle_tv @ F @ A2 ) )
% 3.06/1.60              = ( member266900804lle_tv @ A @ A2 ) ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_348_inj__on__image__eq__iff,axiom,
% 3.06/1.60      ! [F: nat > nat,C2: set_nat,A2: set_nat,B4: set_nat] :
% 3.06/1.60        ( ( inj_on_nat_nat @ F @ C2 )
% 3.06/1.60       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 3.06/1.60         => ( ( ord_less_eq_set_nat @ B4 @ C2 )
% 3.06/1.60           => ( ( ( image_nat_nat @ F @ A2 )
% 3.06/1.60                = ( image_nat_nat @ F @ B4 ) )
% 3.06/1.60              = ( A2 = B4 ) ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_349_inj__on__image__eq__iff,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,C2: set_Pa1764573435lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 3.06/1.60        ( ( inj_on772319074lle_tv @ F @ C2 )
% 3.06/1.60       => ( ( ord_le241064091lle_tv @ A2 @ C2 )
% 3.06/1.60         => ( ( ord_le241064091lle_tv @ B4 @ C2 )
% 3.06/1.60           => ( ( ( image_335818702lle_tv @ F @ A2 )
% 3.06/1.60                = ( image_335818702lle_tv @ F @ B4 ) )
% 3.06/1.60              = ( A2 = B4 ) ) ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_350_inj__on__subset,axiom,
% 3.06/1.60      ! [F: nat > nat,A2: set_nat,B4: set_nat] :
% 3.06/1.60        ( ( inj_on_nat_nat @ F @ A2 )
% 3.06/1.60       => ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 3.06/1.60         => ( inj_on_nat_nat @ F @ B4 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_351_inj__on__subset,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,A2: set_Pa1764573435lle_tv,B4: set_Pa1764573435lle_tv] :
% 3.06/1.60        ( ( inj_on772319074lle_tv @ F @ A2 )
% 3.06/1.60       => ( ( ord_le241064091lle_tv @ B4 @ A2 )
% 3.06/1.60         => ( inj_on772319074lle_tv @ F @ B4 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_352_subset__inj__on,axiom,
% 3.06/1.60      ! [F: nat > nat,B4: set_nat,A2: set_nat] :
% 3.06/1.60        ( ( inj_on_nat_nat @ F @ B4 )
% 3.06/1.60       => ( ( ord_less_eq_set_nat @ A2 @ B4 )
% 3.06/1.60         => ( inj_on_nat_nat @ F @ A2 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(fact_353_subset__inj__on,axiom,
% 3.06/1.60      ! [F: paraco1605129243lle_tv > paraco1605129243lle_tv,B4: set_Pa1764573435lle_tv,A2: set_Pa1764573435lle_tv] :
% 3.06/1.60        ( ( inj_on772319074lle_tv @ F @ B4 )
% 3.06/1.60       => ( ( ord_le241064091lle_tv @ A2 @ B4 )
% 3.06/1.60         => ( inj_on772319074lle_tv @ F @ A2 ) ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(help_If_3_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 3.06/1.60      ! [P3: $o] :
% 3.06/1.60        ( ( P3 = $true )
% 3.06/1.60        | ( P3 = $false ) ) ).
% 3.06/1.60  
% 3.06/1.60  thf(help_If_2_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 3.06/1.60      ! [X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( if_Par1134130401lle_tv @ $false @ X @ Y )
% 3.06/1.60        = Y ) ).
% 3.06/1.60  
% 3.06/1.60  thf(help_If_1_1_If_001t__Paraconsistency____Mirabelle____qxuposogha__Otv_T,axiom,
% 3.06/1.60      ! [X: paraco1605129243lle_tv,Y: paraco1605129243lle_tv] :
% 3.06/1.60        ( ( if_Par1134130401lle_tv @ $true @ X @ Y )
% 3.06/1.60        = X ) ).
% 3.06/1.60  
% 3.06/1.60  thf(conj_0,conjecture,
% 3.06/1.60      ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) )
% 3.06/1.60      = ( paraco1325918602e_eval @ i @ p1 ) ) ).
% 3.06/1.60  ------------------------
% 3.06/1.64  % (1443)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/183Mi)
% 3.06/1.64  % (1444)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_1342 for (2999ds/4Mi)
% 3.06/1.64  % (1444)Instruction limit reached!
% 3.06/1.64  % (1444)------------------------------
% 3.06/1.64  % (1444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.64  % (1444)Termination reason: Unknown
% 3.06/1.64  % (1444)Termination phase: shuffling
% 3.06/1.64  
% 3.06/1.64  % (1444)Memory used [KB]: 1663
% 3.06/1.64  % (1444)Time elapsed: 0.003 s
% 3.06/1.64  % (1444)Instructions burned: 5 (million)
% 3.06/1.64  % (1444)------------------------------
% 3.06/1.64  % (1444)------------------------------
% 3.06/1.64  % (1445)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_1342 for (2999ds/27Mi)
% 3.06/1.64  % (1446)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/2Mi)
% 3.06/1.64  % (1447)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_1342 for (2999ds/2Mi)
% 3.06/1.65  % (1448)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_1342 for (2999ds/275Mi)
% 3.06/1.65  % (1449)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/18Mi)
% 3.06/1.65  % (1446)Instruction limit reached!
% 3.06/1.65  % (1446)------------------------------
% 3.06/1.65  % (1446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.65  % (1446)Termination reason: Unknown
% 3.06/1.65  % (1446)Termination phase: shuffling
% 3.06/1.65  
% 3.06/1.65  % (1446)Memory used [KB]: 1535
% 3.06/1.65  % (1446)Time elapsed: 0.004 s
% 3.06/1.65  % (1446)Instructions burned: 2 (million)
% 3.06/1.65  % (1446)------------------------------
% 3.06/1.65  % (1446)------------------------------
% 3.06/1.65  % (1447)Instruction limit reached!
% 3.06/1.65  % (1447)------------------------------
% 3.06/1.65  % (1447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.65  % (1447)Termination reason: Unknown
% 3.06/1.65  % (1447)Termination phase: shuffling
% 3.06/1.65  
% 3.06/1.65  % (1447)Memory used [KB]: 1535
% 3.06/1.65  % (1447)Time elapsed: 0.004 s
% 3.06/1.65  % (1447)Instructions burned: 3 (million)
% 3.06/1.65  % (1447)------------------------------
% 3.06/1.65  % (1447)------------------------------
% 3.06/1.65  % (1450)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/3Mi)
% 3.06/1.65  % (1450)Instruction limit reached!
% 3.06/1.65  % (1450)------------------------------
% 3.06/1.65  % (1450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.65  % (1450)Termination reason: Unknown
% 3.06/1.65  % (1450)Termination phase: shuffling
% 3.06/1.65  
% 3.06/1.65  % (1450)Memory used [KB]: 1663
% 3.06/1.65  % (1450)Time elapsed: 0.003 s
% 3.06/1.65  % (1450)Instructions burned: 5 (million)
% 3.06/1.65  % (1450)------------------------------
% 3.06/1.65  % (1450)------------------------------
% 3.06/1.66  % (1449)Instruction limit reached!
% 3.06/1.66  % (1449)------------------------------
% 3.06/1.66  % (1449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.66  % (1449)Termination reason: Unknown
% 3.06/1.66  % (1449)Termination phase: shuffling
% 3.06/1.66  
% 3.06/1.66  % (1449)Memory used [KB]: 2046
% 3.06/1.66  % (1449)Time elapsed: 0.014 s
% 3.06/1.66  % (1449)Instructions burned: 19 (million)
% 3.06/1.66  % (1449)------------------------------
% 3.06/1.66  % (1449)------------------------------
% 3.06/1.66  % (1453)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_1342 for (2999ds/3Mi)
% 3.06/1.66  % (1453)Instruction limit reached!
% 3.06/1.66  % (1453)------------------------------
% 3.06/1.66  % (1453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.66  % (1453)Termination reason: Unknown
% 3.06/1.66  % (1453)Termination phase: shuffling
% 3.06/1.66  
% 3.06/1.66  % (1453)Memory used [KB]: 1535
% 3.06/1.66  % (1453)Time elapsed: 0.002 s
% 3.06/1.66  % (1453)Instructions burned: 3 (million)
% 3.06/1.66  % (1453)------------------------------
% 3.06/1.66  % (1453)------------------------------
% 3.06/1.66  % (1445)Instruction limit reached!
% 3.06/1.66  % (1445)------------------------------
% 3.06/1.66  % (1445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.66  % (1445)Termination reason: Unknown
% 3.06/1.66  % (1445)Termination phase: Property scanning
% 3.06/1.66  
% 3.06/1.66  % (1445)Memory used [KB]: 2046
% 3.06/1.66  % (1445)Time elapsed: 0.019 s
% 3.06/1.66  % (1445)Instructions burned: 28 (million)
% 3.06/1.66  % (1445)------------------------------
% 3.06/1.66  % (1445)------------------------------
% 3.06/1.66  % (1451)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_1342 for (2999ds/37Mi)
% 3.06/1.66  % (1452)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_1342 for (2999ds/15Mi)
% 3.06/1.67  % (1455)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/7Mi)
% 3.06/1.67  % (1452)Instruction limit reached!
% 3.06/1.67  % (1452)------------------------------
% 3.06/1.67  % (1452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.67  % (1452)Termination reason: Unknown
% 3.06/1.67  % (1452)Termination phase: shuffling
% 3.06/1.67  
% 3.06/1.67  % (1452)Memory used [KB]: 1918
% 3.06/1.67  % (1452)Time elapsed: 0.010 s
% 3.06/1.67  % (1452)Instructions burned: 15 (million)
% 3.06/1.67  % (1452)------------------------------
% 3.06/1.67  % (1452)------------------------------
% 3.06/1.67  % (1455)Instruction limit reached!
% 3.06/1.67  % (1455)------------------------------
% 3.06/1.67  % (1455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.67  % (1455)Termination reason: Unknown
% 3.06/1.67  % (1455)Termination phase: shuffling
% 3.06/1.67  
% 3.06/1.67  % (1455)Memory used [KB]: 1791
% 3.06/1.67  % (1455)Time elapsed: 0.004 s
% 3.06/1.67  % (1455)Instructions burned: 9 (million)
% 3.06/1.67  % (1455)------------------------------
% 3.06/1.67  % (1455)------------------------------
% 3.06/1.67  % (1448)Refutation not found, incomplete strategy
% 3.06/1.67  % (1448)------------------------------
% 3.06/1.67  % (1448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.67  % (1448)Termination reason: Refutation not found, incomplete strategy
% 3.06/1.67  
% 3.06/1.67  
% 3.06/1.67  % (1448)Memory used [KB]: 6652
% 3.06/1.67  % (1448)Time elapsed: 0.030 s
% 3.06/1.67  % (1448)Instructions burned: 46 (million)
% 3.06/1.67  % (1448)------------------------------
% 3.06/1.67  % (1448)------------------------------
% 3.06/1.67  % (1454)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/1041Mi)
% 3.06/1.68  % (1456)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/16Mi)
% 3.06/1.68  % (1458)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/3Mi)
% 3.06/1.68  % (1451)Instruction limit reached!
% 3.06/1.68  % (1451)------------------------------
% 3.06/1.68  % (1451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.68  % (1451)Termination reason: Unknown
% 3.06/1.68  % (1451)Termination phase: shuffling
% 3.06/1.68  
% 3.06/1.68  % (1451)Memory used [KB]: 2302
% 3.06/1.68  % (1451)Time elapsed: 0.021 s
% 3.06/1.68  % (1451)Instructions burned: 37 (million)
% 3.06/1.68  % (1451)------------------------------
% 3.06/1.68  % (1451)------------------------------
% 3.06/1.68  % (1458)Instruction limit reached!
% 3.06/1.68  % (1458)------------------------------
% 3.06/1.68  % (1458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.68  % (1458)Termination reason: Unknown
% 3.06/1.68  % (1458)Termination phase: shuffling
% 3.06/1.68  
% 3.06/1.68  % (1458)Memory used [KB]: 1663
% 3.06/1.68  % (1458)Time elapsed: 0.003 s
% 3.06/1.68  % (1458)Instructions burned: 5 (million)
% 3.06/1.68  % (1458)------------------------------
% 3.06/1.68  % (1458)------------------------------
% 3.06/1.69  % (1443)Instruction limit reached!
% 3.06/1.69  % (1443)------------------------------
% 3.06/1.69  % (1443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.69  % (1443)Termination reason: Unknown
% 3.06/1.69  % (1443)Termination phase: Saturation
% 3.06/1.69  
% 3.06/1.69  % (1443)Memory used [KB]: 7547
% 3.06/1.69  % (1443)Time elapsed: 0.053 s
% 3.06/1.69  % (1443)Instructions burned: 185 (million)
% 3.06/1.69  % (1443)------------------------------
% 3.06/1.69  % (1443)------------------------------
% 3.06/1.69  % (1456)Instruction limit reached!
% 3.06/1.69  % (1456)------------------------------
% 3.06/1.69  % (1456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.69  % (1456)Termination reason: Unknown
% 3.06/1.69  % (1456)Termination phase: shuffling
% 3.06/1.69  
% 3.06/1.69  % (1456)Memory used [KB]: 1918
% 3.06/1.69  % (1456)Time elapsed: 0.012 s
% 3.06/1.69  % (1456)Instructions burned: 16 (million)
% 3.06/1.69  % (1456)------------------------------
% 3.06/1.69  % (1456)------------------------------
% 3.06/1.69  % (1457)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/3Mi)
% 3.06/1.69  % (1459)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/7Mi)
% 3.06/1.69  % (1457)Instruction limit reached!
% 3.06/1.69  % (1457)------------------------------
% 3.06/1.69  % (1457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.69  % (1457)Termination reason: Unknown
% 3.06/1.69  % (1457)Termination phase: shuffling
% 3.06/1.69  
% 3.06/1.69  % (1457)Memory used [KB]: 1535
% 3.06/1.69  % (1457)Time elapsed: 0.005 s
% 3.06/1.69  % (1457)Instructions burned: 4 (million)
% 3.06/1.69  % (1457)------------------------------
% 3.06/1.69  % (1457)------------------------------
% 3.06/1.69  % (1461)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/4Mi)
% 3.06/1.70  % (1461)Instruction limit reached!
% 3.06/1.70  % (1461)------------------------------
% 3.06/1.70  % (1461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.70  % (1461)Termination reason: Unknown
% 3.06/1.70  % (1461)Termination phase: shuffling
% 3.06/1.70  
% 3.06/1.70  % (1461)Memory used [KB]: 1663
% 3.06/1.70  % (1461)Time elapsed: 0.003 s
% 3.06/1.70  % (1461)Instructions burned: 6 (million)
% 3.06/1.70  % (1461)------------------------------
% 3.06/1.70  % (1461)------------------------------
% 3.06/1.70  % (1459)Instruction limit reached!
% 3.06/1.70  % (1459)------------------------------
% 3.06/1.70  % (1459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.70  % (1459)Termination reason: Unknown
% 3.06/1.70  % (1459)Termination phase: shuffling
% 3.06/1.70  
% 3.06/1.70  % (1459)Memory used [KB]: 1791
% 3.06/1.70  % (1459)Time elapsed: 0.007 s
% 3.06/1.70  % (1459)Instructions burned: 8 (million)
% 3.06/1.70  % (1459)------------------------------
% 3.06/1.70  % (1459)------------------------------
% 3.06/1.70  % (1462)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/18Mi)
% 3.06/1.70  % (1460)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/3Mi)
% 3.06/1.70  % (1460)Instruction limit reached!
% 3.06/1.70  % (1460)------------------------------
% 3.06/1.70  % (1460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.70  % (1460)Termination reason: Unknown
% 3.06/1.70  % (1460)Termination phase: shuffling
% 3.06/1.70  
% 3.06/1.70  % (1460)Memory used [KB]: 1535
% 3.06/1.70  % (1460)Time elapsed: 0.003 s
% 3.06/1.70  % (1460)Instructions burned: 4 (million)
% 3.06/1.70  % (1460)------------------------------
% 3.06/1.70  % (1460)------------------------------
% 3.06/1.70  % (1462)Instruction limit reached!
% 3.06/1.70  % (1462)------------------------------
% 3.06/1.70  % (1462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.70  % (1462)Termination reason: Unknown
% 3.06/1.70  % (1462)Termination phase: shuffling
% 3.06/1.70  
% 3.06/1.70  % (1462)Memory used [KB]: 1918
% 3.06/1.70  % (1462)Time elapsed: 0.007 s
% 3.06/1.70  % (1462)Instructions burned: 18 (million)
% 3.06/1.70  % (1462)------------------------------
% 3.06/1.70  % (1462)------------------------------
% 3.06/1.70  % (1465)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/902Mi)
% 3.06/1.71  % (1463)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/710Mi)
% 3.06/1.71  % (1464)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/6Mi)
% 3.06/1.71  % (1467)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/5Mi)
% 3.06/1.71  % (1467)Instruction limit reached!
% 3.06/1.71  % (1467)------------------------------
% 3.06/1.71  % (1467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.71  % (1467)Termination reason: Unknown
% 3.06/1.71  % (1467)Termination phase: shuffling
% 3.06/1.71  
% 3.06/1.71  % (1467)Memory used [KB]: 1663
% 3.06/1.71  % (1467)Time elapsed: 0.003 s
% 3.06/1.71  % (1467)Instructions burned: 7 (million)
% 3.06/1.71  % (1467)------------------------------
% 3.06/1.71  % (1467)------------------------------
% 3.06/1.71  % (1468)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/6Mi)
% 3.06/1.71  % (1466)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_1342 for (2999ds/21Mi)
% 3.06/1.71  % (1464)Instruction limit reached!
% 3.06/1.71  % (1464)------------------------------
% 3.06/1.71  % (1464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.71  % (1464)Termination reason: Unknown
% 3.06/1.71  % (1464)Termination phase: shuffling
% 3.06/1.71  
% 3.06/1.71  % (1464)Memory used [KB]: 1663
% 3.06/1.71  % (1464)Time elapsed: 0.006 s
% 3.06/1.71  % (1464)Instructions burned: 6 (million)
% 3.06/1.71  % (1464)------------------------------
% 3.06/1.71  % (1464)------------------------------
% 3.06/1.72  % (1468)Instruction limit reached!
% 3.06/1.72  % (1468)------------------------------
% 3.06/1.72  % (1468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.72  % (1468)Termination reason: Unknown
% 3.06/1.72  % (1468)Termination phase: shuffling
% 3.06/1.72  
% 3.06/1.72  % (1468)Memory used [KB]: 1791
% 3.06/1.72  % (1468)Time elapsed: 0.004 s
% 3.06/1.72  % (1468)Instructions burned: 9 (million)
% 3.06/1.72  % (1468)------------------------------
% 3.06/1.72  % (1468)------------------------------
% 3.06/1.72  % (1469)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_1342 for (2998ds/377Mi)
% 3.06/1.73  % (1471)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_1342 for (2998ds/19Mi)
% 3.06/1.73  % (1466)Instruction limit reached!
% 3.06/1.73  % (1466)------------------------------
% 3.06/1.73  % (1466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.73  % (1466)Termination reason: Unknown
% 3.06/1.73  % (1466)Termination phase: shuffling
% 3.06/1.73  
% 3.06/1.73  % (1466)Memory used [KB]: 1918
% 3.06/1.73  % (1466)Time elapsed: 0.015 s
% 3.06/1.73  % (1466)Instructions burned: 21 (million)
% 3.06/1.73  % (1466)------------------------------
% 3.06/1.73  % (1466)------------------------------
% 3.06/1.73  % (1471)Instruction limit reached!
% 3.06/1.73  % (1471)------------------------------
% 3.06/1.73  % (1471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.73  % (1471)Termination reason: Unknown
% 3.06/1.73  % (1471)Termination phase: shuffling
% 3.06/1.73  
% 3.06/1.73  % (1471)Memory used [KB]: 2046
% 3.06/1.73  % (1471)Time elapsed: 0.007 s
% 3.06/1.73  % (1471)Instructions burned: 22 (million)
% 3.06/1.73  % (1471)------------------------------
% 3.06/1.73  % (1471)------------------------------
% 3.06/1.73  % (1470)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_1342 for (2998ds/779Mi)
% 3.06/1.73  % (1463)Refutation not found, incomplete strategy
% 3.06/1.73  % (1463)------------------------------
% 3.06/1.73  % (1463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.73  % (1463)Termination reason: Refutation not found, incomplete strategy
% 3.06/1.73  
% 3.06/1.73  
% 3.06/1.73  % (1463)Memory used [KB]: 6652
% 3.06/1.73  % (1463)Time elapsed: 0.030 s
% 3.06/1.73  % (1463)Instructions burned: 46 (million)
% 3.06/1.73  % (1463)------------------------------
% 3.06/1.73  % (1463)------------------------------
% 3.06/1.74  % (1473)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_1342 for (2998ds/17Mi)
% 3.06/1.74  % (1472)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_1342 for (2998ds/879Mi)
% 3.06/1.74  % (1465)First to succeed.
% 3.06/1.75  % (1473)Instruction limit reached!
% 3.06/1.75  % (1473)------------------------------
% 3.06/1.75  % (1473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.75  % (1473)Termination reason: Unknown
% 3.06/1.75  % (1473)Termination phase: shuffling
% 3.06/1.75  
% 3.06/1.75  % (1473)Memory used [KB]: 1918
% 3.06/1.75  % (1473)Time elapsed: 0.007 s
% 3.06/1.75  % (1473)Instructions burned: 18 (million)
% 3.06/1.75  % (1473)------------------------------
% 3.06/1.75  % (1473)------------------------------
% 3.06/1.75  % (1465)Refutation found. Thanks to Tanya!
% 3.06/1.75  % SZS status Theorem for DTF2THF_1342
% 3.06/1.75  % SZS output start Proof for DTF2THF_1342
% 3.06/1.75  thf(type_def_5, type, nat: $tType).
% 3.06/1.75  thf(type_def_7, type, set_nat: $tType).
% 3.06/1.75  thf(type_def_8, type, paraco1605129243lle_tv: $tType).
% 3.06/1.75  thf(type_def_9, type, set_Pa1764573435lle_tv: $tType).
% 3.06/1.75  thf(type_def_10, type, product_prod_nat_nat: $tType).
% 3.06/1.75  thf(type_def_11, type, set_Pr1986765409at_nat: $tType).
% 3.06/1.75  thf(type_def_12, type, produc270694976lle_tv: $tType).
% 3.06/1.75  thf(type_def_13, type, set_Pr13445366lle_tv: $tType).
% 3.06/1.75  thf(type_def_14, type, produc194167194tv_nat: $tType).
% 3.06/1.75  thf(type_def_15, type, set_Pr1725653840tv_nat: $tType).
% 3.06/1.75  thf(type_def_16, type, produc1647334210lle_tv: $tType).
% 3.06/1.75  thf(type_def_17, type, set_Pr2014382200lle_tv: $tType).
% 3.06/1.75  thf(type_def_18, type, set_Pr2120184979lle_fm: $tType).
% 3.06/1.75  thf(type_def_19, type, set_Pr560526279lle_tv: $tType).
% 3.06/1.75  thf(type_def_20, type, set_Pr2061825550lle_tv: $tType).
% 3.06/1.75  thf(type_def_21, type, set_Pr1357842111at_nat: $tType).
% 3.06/1.75  thf(type_def_22, type, list_char: $tType).
% 3.06/1.75  thf(type_def_23, type, produc931990033lle_tv: $tType).
% 3.06/1.75  thf(type_def_24, type, paraco1604210848lle_fm: $tType).
% 3.06/1.75  thf(type_def_25, type, produc1852595672lle_tv: $tType).
% 3.06/1.75  thf(type_def_26, type, produc696645085lle_fm: $tType).
% 3.06/1.75  thf(type_def_27, type, produc1281043295at_nat: $tType).
% 3.06/1.75  thf(type_def_28, type, produc1443694919lle_tv: $tType).
% 3.06/1.75  thf(type_def_29, type, produc450659916lle_fm: $tType).
% 3.06/1.75  thf(type_def_30, type, produc596913417at_nat: $tType).
% 3.06/1.75  thf(type_def_31, type, produc1250255278lle_fm: $tType).
% 3.06/1.75  thf(type_def_32, type, produc1720769084lle_tv: $tType).
% 3.06/1.75  thf(type_def_33, type, set_Pr1490359111at_nat: $tType).
% 3.06/1.75  thf(type_def_34, type, set_Pr292927124lle_tv: $tType).
% 3.06/1.75  thf(type_def_35, type, set_Pr1943077434tv_nat: $tType).
% 3.06/1.75  thf(type_def_36, type, set_Pr2012908090lle_tv: $tType).
% 3.06/1.75  thf(type_def_37, type, set_Pr1723822845lle_tv: $tType).
% 3.06/1.75  thf(type_def_38, type, set_Pr840833727at_nat: $tType).
% 3.06/1.75  thf(type_def_39, type, set_Pr1019238018lle_fm: $tType).
% 3.06/1.75  thf(type_def_40, type, set_Pr1475944804lle_fm: $tType).
% 3.06/1.75  thf(type_def_41, type, set_Pr698334450lle_tv: $tType).
% 3.06/1.75  thf(func_def_0, type, set_Pr1475944804lle_fm: $tType).
% 3.06/1.75  thf(func_def_1, type, produc1250255278lle_fm: $tType).
% 3.06/1.75  thf(func_def_2, type, set_Pr2012908090lle_tv: $tType).
% 3.06/1.75  thf(func_def_3, type, set_Pr698334450lle_tv: $tType).
% 3.06/1.75  thf(func_def_4, type, produc1720769084lle_tv: $tType).
% 3.06/1.75  thf(func_def_5, type, set_Pr2061825550lle_tv: $tType).
% 3.06/1.75  thf(func_def_6, type, set_Pr1943077434tv_nat: $tType).
% 3.06/1.75  thf(func_def_7, type, set_Pr292927124lle_tv: $tType).
% 3.06/1.75  thf(func_def_8, type, produc1852595672lle_tv: $tType).
% 3.06/1.75  thf(func_def_9, type, set_Pr1723822845lle_tv: $tType).
% 3.06/1.75  thf(func_def_10, type, set_Pr2120184979lle_fm: $tType).
% 3.06/1.75  thf(func_def_11, type, produc1443694919lle_tv: $tType).
% 3.06/1.75  thf(func_def_12, type, produc696645085lle_fm: $tType).
% 3.06/1.75  thf(func_def_13, type, set_Pr1490359111at_nat: $tType).
% 3.06/1.75  thf(func_def_14, type, set_Pr2014382200lle_tv: $tType).
% 3.06/1.75  thf(func_def_15, type, set_Pr1019238018lle_fm: $tType).
% 3.06/1.75  thf(func_def_16, type, set_Pr840833727at_nat: $tType).
% 3.06/1.75  thf(func_def_17, type, set_Pr560526279lle_tv: $tType).
% 3.06/1.75  thf(func_def_18, type, produc1647334210lle_tv: $tType).
% 3.06/1.75  thf(func_def_19, type, produc450659916lle_fm: $tType).
% 3.06/1.75  thf(func_def_20, type, set_Pr1357842111at_nat: $tType).
% 3.06/1.75  thf(func_def_21, type, produc596913417at_nat: $tType).
% 3.06/1.75  thf(func_def_22, type, produc931990033lle_tv: $tType).
% 3.06/1.75  thf(func_def_23, type, set_Pr1725653840tv_nat: $tType).
% 3.06/1.75  thf(func_def_24, type, set_Pr13445366lle_tv: $tType).
% 3.06/1.75  thf(func_def_25, type, produc1281043295at_nat: $tType).
% 3.06/1.75  thf(func_def_26, type, produc194167194tv_nat: $tType).
% 3.06/1.75  thf(func_def_27, type, produc270694976lle_tv: $tType).
% 3.06/1.75  thf(func_def_28, type, set_Pr1986765409at_nat: $tType).
% 3.06/1.75  thf(func_def_29, type, set_Pa1764573435lle_tv: $tType).
% 3.06/1.75  thf(func_def_30, type, product_prod_nat_nat: $tType).
% 3.06/1.75  thf(func_def_31, type, paraco1605129243lle_tv: $tType).
% 3.06/1.75  thf(func_def_32, type, paraco1604210848lle_fm: $tType).
% 3.06/1.75  thf(func_def_33, type, list_char: $tType).
% 3.06/1.75  thf(func_def_34, type, set_nat: $tType).
% 3.06/1.75  thf(func_def_35, type, nat: $tType).
% 3.06/1.75  thf(func_def_36, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 3.06/1.75  thf(func_def_37, type, inj_on1955349912lle_tv: (nat > paraco1605129243lle_tv) > set_nat > $o).
% 3.06/1.75  thf(func_def_38, type, inj_on1179712058tv_nat: (paraco1605129243lle_tv > nat) > set_Pa1764573435lle_tv > $o).
% 3.06/1.75  thf(func_def_39, type, inj_on772319074lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > $o).
% 3.06/1.75  thf(func_def_40, type, inj_on26176689at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1986765409at_nat > $o).
% 3.06/1.75  thf(func_def_41, type, inj_on1745913142lle_tv: (produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > $o).
% 3.06/1.75  thf(func_def_42, type, inj_on552895452tv_nat: (produc194167194tv_nat > produc194167194tv_nat) > set_Pr1725653840tv_nat > $o).
% 3.06/1.75  thf(func_def_43, type, inj_on2112487900lle_tv: (produc1647334210lle_tv > produc1647334210lle_tv) > set_Pr2014382200lle_tv > $o).
% 3.06/1.75  thf(func_def_44, type, the_inv_into_nat_nat: set_nat > (nat > nat) > nat > nat).
% 3.06/1.75  thf(func_def_45, type, the_in452116896lle_tv: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_46, type, if_Par1134130401lle_tv: $o > paraco1605129243lle_tv > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_47, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 3.06/1.75  thf(func_def_48, type, ord_le241064091lle_tv: set_Pa1764573435lle_tv > set_Pa1764573435lle_tv > $o).
% 3.06/1.75  thf(func_def_49, type, ord_le1007985907lle_fm: set_Pr2120184979lle_fm > set_Pr2120184979lle_fm > $o).
% 3.06/1.75  thf(func_def_50, type, ord_le1784136743lle_tv: set_Pr560526279lle_tv > set_Pr560526279lle_tv > $o).
% 3.06/1.75  thf(func_def_51, type, order_769474267at_nat: (nat > nat) > $o).
% 3.06/1.75  thf(func_def_52, type, top_top_nat_o: nat > $o).
% 3.06/1.75  thf(func_def_53, type, top_to1299250770e_tv_o: paraco1605129243lle_tv > $o).
% 3.06/1.75  thf(func_def_54, type, top_to632227436_nat_o: product_prod_nat_nat > $o).
% 3.06/1.75  thf(func_def_55, type, top_to1889334367e_tv_o: produc270694976lle_tv > $o).
% 3.06/1.75  thf(func_def_56, type, top_to900819589_nat_o: produc194167194tv_nat > $o).
% 3.06/1.75  thf(func_def_58, type, top_top_set_nat: set_nat).
% 3.06/1.75  thf(func_def_59, type, top_to1057771083lle_tv: set_Pa1764573435lle_tv).
% 3.06/1.75  thf(func_def_60, type, top_to138697918lle_tv: set_Pr2061825550lle_tv).
% 3.06/1.75  thf(func_def_61, type, top_to775056195lle_fm: set_Pr2120184979lle_fm).
% 3.06/1.75  thf(func_def_62, type, top_to1541413903at_nat: set_Pr1357842111at_nat).
% 3.06/1.75  thf(func_def_63, type, top_to449985143lle_tv: set_Pr560526279lle_tv).
% 3.06/1.75  thf(func_def_64, type, top_to1555900337at_nat: set_Pr1986765409at_nat).
% 3.06/1.75  thf(func_def_65, type, top_to1411004326lle_tv: set_Pr13445366lle_tv).
% 3.06/1.75  thf(func_def_66, type, top_to975729152tv_nat: set_Pr1725653840tv_nat).
% 3.06/1.75  thf(func_def_67, type, top_to1871154984lle_tv: set_Pr2014382200lle_tv).
% 3.06/1.75  thf(func_def_68, type, paraco761681009ge_int: (nat > nat) > (list_char > paraco1605129243lle_tv) > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_69, type, paraco1147068288nge_tv: (nat > nat) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_70, type, paraco1632582009tv_rel: produc931990033lle_tv > produc931990033lle_tv > $o).
% 3.06/1.75  thf(func_def_71, type, paraco1325918602e_eval: (list_char > paraco1605129243lle_tv) > paraco1604210848lle_fm > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_72, type, paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_73, type, paraco1389086619le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_74, type, paraco1745535428le_Eql: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_75, type, paraco445776468le_Neg: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_76, type, paraco1480028776le_Pro: list_char > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_77, type, paraco367965286_Truth: paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_78, type, paraco1344940915le_Det: $o > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_79, type, paraco793048302_Indet: nat > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_80, type, paraco2051596139lle_tv: ($o > paraco1605129243lle_tv) > (nat > paraco1605129243lle_tv) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_81, type, paraco327635598_valid: paraco1604210848lle_fm > $o).
% 3.06/1.75  thf(func_def_82, type, paraco55203475lid_in: set_nat > paraco1604210848lle_fm > $o).
% 3.06/1.75  thf(func_def_83, type, produc1297923922lle_tv: (list_char > paraco1605129243lle_tv) > (list_char > paraco1605129243lle_tv) > produc1852595672lle_tv).
% 3.06/1.75  thf(func_def_84, type, produc1710735575lle_fm: (list_char > paraco1605129243lle_tv) > paraco1604210848lle_fm > produc696645085lle_fm).
% 3.06/1.75  thf(func_def_85, type, produc780837143at_nat: (nat > nat) > (nat > nat) > produc1281043295at_nat).
% 3.06/1.75  thf(func_def_86, type, produc1680557635lle_tv: (nat > nat) > paraco1605129243lle_tv > produc931990033lle_tv).
% 3.06/1.75  thf(func_def_87, type, produc1943344577lle_tv: paraco1604210848lle_fm > (list_char > paraco1605129243lle_tv) > produc1443694919lle_tv).
% 3.06/1.75  thf(func_def_88, type, produc1126104134lle_fm: paraco1604210848lle_fm > paraco1604210848lle_fm > produc450659916lle_fm).
% 3.06/1.75  thf(func_def_89, type, produc1633679363at_nat: paraco1605129243lle_tv > (nat > nat) > produc596913417at_nat).
% 3.06/1.75  thf(func_def_90, type, produc2058540732lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > produc1647334210lle_tv).
% 3.06/1.75  thf(func_def_91, type, produc407632608lle_fm: produc696645085lle_fm > produc696645085lle_fm > produc1250255278lle_fm).
% 3.06/1.75  thf(func_def_92, type, produc2057188974lle_tv: produc931990033lle_tv > produc931990033lle_tv > produc1720769084lle_tv).
% 3.06/1.75  thf(func_def_93, type, produc1942165868lle_fm: ((list_char > paraco1605129243lle_tv) > list_char > paraco1605129243lle_tv) > produc696645085lle_fm > produc696645085lle_fm).
% 3.06/1.75  thf(func_def_94, type, produc939316703lle_tv: ((nat > nat) > nat > nat) > produc931990033lle_tv > produc931990033lle_tv).
% 3.06/1.75  thf(func_def_95, type, produc1807466521lle_tv: (paraco1604210848lle_fm > paraco1604210848lle_fm) > produc696645085lle_fm > produc696645085lle_fm).
% 3.06/1.75  thf(func_def_96, type, produc109093078at_nat: (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc931990033lle_tv > produc931990033lle_tv).
% 3.06/1.75  thf(func_def_97, type, produc234482697lle_tv: paraco1605129243lle_tv > paraco1605129243lle_tv > $o > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_98, type, produc275353523e_fm_o: (produc696645085lle_fm > $o) > (list_char > paraco1605129243lle_tv) > paraco1604210848lle_fm > $o).
% 3.06/1.75  thf(func_def_99, type, produc752649287e_tv_o: (produc931990033lle_tv > $o) > (nat > nat) > paraco1605129243lle_tv > $o).
% 3.06/1.75  thf(func_def_100, type, produc1900967599lle_fm: ((list_char > paraco1605129243lle_tv) > list_char > paraco1605129243lle_tv) > (paraco1604210848lle_fm > paraco1604210848lle_fm) > produc696645085lle_fm > produc696645085lle_fm).
% 3.06/1.75  thf(func_def_101, type, produc1566550641lle_tv: ((list_char > paraco1605129243lle_tv) > nat > nat) > (paraco1604210848lle_fm > paraco1605129243lle_tv) > produc696645085lle_fm > produc931990033lle_tv).
% 3.06/1.75  thf(func_def_102, type, produc951033137lle_fm: ((nat > nat) > list_char > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1604210848lle_fm) > produc931990033lle_tv > produc696645085lle_fm).
% 3.06/1.75  thf(func_def_103, type, produc532909085lle_tv: ((nat > nat) > nat > nat) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc931990033lle_tv > produc931990033lle_tv).
% 3.06/1.75  thf(func_def_104, type, produc505105722at_nat: (nat > nat) > (nat > nat) > product_prod_nat_nat > product_prod_nat_nat).
% 3.06/1.75  thf(func_def_105, type, produc313957681lle_tv: (nat > nat) > (nat > paraco1605129243lle_tv) > product_prod_nat_nat > produc270694976lle_tv).
% 3.06/1.75  thf(func_def_106, type, produc1685803475tv_nat: (nat > nat) > (paraco1605129243lle_tv > nat) > produc270694976lle_tv > product_prod_nat_nat).
% 3.06/1.75  thf(func_def_107, type, produc2101297531lle_tv: (nat > nat) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc270694976lle_tv > produc270694976lle_tv).
% 3.06/1.75  thf(func_def_108, type, produc1250721397at_nat: (nat > paraco1605129243lle_tv) > (nat > nat) > product_prod_nat_nat > produc194167194tv_nat).
% 3.06/1.75  thf(func_def_109, type, produc210389789lle_tv: (nat > paraco1605129243lle_tv) > (nat > paraco1605129243lle_tv) > product_prod_nat_nat > produc1647334210lle_tv).
% 3.06/1.75  thf(func_def_110, type, produc189459613tv_nat: (nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > nat) > produc270694976lle_tv > produc194167194tv_nat).
% 3.06/1.75  thf(func_def_111, type, produc1975500101lle_tv: (nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc270694976lle_tv > produc1647334210lle_tv).
% 3.06/1.75  thf(func_def_112, type, produc386540311at_nat: (paraco1605129243lle_tv > nat) > (nat > nat) > produc194167194tv_nat > product_prod_nat_nat).
% 3.06/1.75  thf(func_def_113, type, produc72207551lle_tv: (paraco1605129243lle_tv > nat) > (nat > paraco1605129243lle_tv) > produc194167194tv_nat > produc270694976lle_tv).
% 3.06/1.75  thf(func_def_114, type, produc42536895at_nat: (paraco1605129243lle_tv > paraco1605129243lle_tv) > (nat > nat) > produc194167194tv_nat > produc194167194tv_nat).
% 3.06/1.75  thf(func_def_115, type, produc1345917071lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > produc1647334210lle_tv > produc1647334210lle_tv).
% 3.06/1.75  thf(func_def_116, type, produc29804011lle_fm: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_117, type, produc1636169559lle_tv: produc931990033lle_tv > nat > nat).
% 3.06/1.75  thf(func_def_118, type, produc262413013lle_tv: produc1443694919lle_tv > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_119, type, produc1589291287at_nat: produc596913417at_nat > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_120, type, produc148705065lle_fm: produc696645085lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_121, type, produc547496597lle_tv: produc931990033lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_122, type, produc381314067lle_tv: produc1443694919lle_tv > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_123, type, produc500618325at_nat: produc596913417at_nat > nat > nat).
% 3.06/1.75  thf(func_def_124, type, produc1000205111lle_fm: produc696645085lle_fm > produc1443694919lle_tv).
% 3.06/1.75  thf(func_def_125, type, produc225513635lle_tv: produc931990033lle_tv > produc596913417at_nat).
% 3.06/1.75  thf(func_def_126, type, produc1232814113lle_tv: produc1443694919lle_tv > produc696645085lle_fm).
% 3.06/1.75  thf(func_def_127, type, produc178635363at_nat: produc596913417at_nat > produc931990033lle_tv).
% 3.06/1.75  thf(func_def_128, type, inv_image_nat_nat: set_Pr1986765409at_nat > (nat > nat) > set_Pr1986765409at_nat).
% 3.06/1.75  thf(func_def_129, type, inv_im1292588663lle_tv: set_Pr1986765409at_nat > (paraco1605129243lle_tv > nat) > set_Pr2014382200lle_tv).
% 3.06/1.75  thf(func_def_130, type, inv_im516950809tv_nat: set_Pr2014382200lle_tv > (nat > paraco1605129243lle_tv) > set_Pr1986765409at_nat).
% 3.06/1.75  thf(func_def_131, type, inv_im719552961lle_tv: set_Pr2014382200lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pr2014382200lle_tv).
% 3.06/1.75  thf(func_def_132, type, total_on_nat: set_nat > set_Pr1986765409at_nat > $o).
% 3.06/1.75  thf(func_def_133, type, total_1781621663lle_tv: set_Pa1764573435lle_tv > set_Pr2014382200lle_tv > $o).
% 3.06/1.75  thf(func_def_134, type, total_1775715973at_nat: set_Pr1986765409at_nat > set_Pr1490359111at_nat > $o).
% 3.06/1.75  thf(func_def_135, type, total_517371324lle_tv: set_Pr13445366lle_tv > set_Pr292927124lle_tv > $o).
% 3.06/1.75  thf(func_def_136, type, total_440843542tv_nat: set_Pr1725653840tv_nat > set_Pr1943077434tv_nat > $o).
% 3.06/1.75  thf(func_def_137, type, total_92239038lle_tv: set_Pr2014382200lle_tv > set_Pr2012908090lle_tv > $o).
% 3.06/1.75  thf(func_def_138, type, collect_nat: (nat > $o) > set_nat).
% 3.06/1.75  thf(func_def_139, type, collec1111687558lle_tv: (paraco1605129243lle_tv > $o) > set_Pa1764573435lle_tv).
% 3.06/1.75  thf(func_def_140, type, collec1102043437lle_tv: (produc1852595672lle_tv > $o) > set_Pr2061825550lle_tv).
% 3.06/1.75  thf(func_def_141, type, collec835549234lle_fm: (produc696645085lle_fm > $o) > set_Pr2120184979lle_fm).
% 3.06/1.75  thf(func_def_142, type, collec791369802at_nat: (produc1281043295at_nat > $o) > set_Pr1357842111at_nat).
% 3.06/1.75  thf(func_def_143, type, collec1624074086lle_tv: (produc931990033lle_tv > $o) > set_Pr560526279lle_tv).
% 3.06/1.75  thf(func_def_144, type, collec7649004at_nat: (product_prod_nat_nat > $o) > set_Pr1986765409at_nat).
% 3.06/1.75  thf(func_def_145, type, collec924990229lle_tv: (produc270694976lle_tv > $o) > set_Pr13445366lle_tv).
% 3.06/1.75  thf(func_def_146, type, collec848462447tv_nat: (produc194167194tv_nat > $o) > set_Pr1725653840tv_nat).
% 3.06/1.75  thf(func_def_147, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 3.06/1.75  thf(func_def_148, type, image_1151963140lle_tv: (nat > paraco1605129243lle_tv) > set_nat > set_Pa1764573435lle_tv).
% 3.06/1.75  thf(func_def_149, type, image_376325286tv_nat: (paraco1605129243lle_tv > nat) > set_Pa1764573435lle_tv > set_nat).
% 3.06/1.75  thf(func_def_150, type, image_335818702lle_tv: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > set_Pa1764573435lle_tv).
% 3.06/1.75  thf(func_def_151, type, image_807538418lle_fm: (produc696645085lle_fm > produc696645085lle_fm) > set_Pr2120184979lle_fm > set_Pr2120184979lle_fm).
% 3.06/1.75  thf(func_def_152, type, image_1154804148lle_tv: (produc696645085lle_fm > produc931990033lle_tv) > set_Pr2120184979lle_fm > set_Pr560526279lle_tv).
% 3.06/1.75  thf(func_def_153, type, image_924970994lle_tv: (produc696645085lle_fm > produc1443694919lle_tv) > set_Pr2120184979lle_fm > set_Pr1723822845lle_tv).
% 3.06/1.75  thf(func_def_154, type, image_1585092542lle_fm: (produc931990033lle_tv > produc696645085lle_fm) > set_Pr560526279lle_tv > set_Pr2120184979lle_fm).
% 3.06/1.75  thf(func_def_155, type, image_1751508608lle_tv: (produc931990033lle_tv > produc931990033lle_tv) > set_Pr560526279lle_tv > set_Pr560526279lle_tv).
% 3.06/1.75  thf(func_def_156, type, image_1724396928at_nat: (produc931990033lle_tv > produc596913417at_nat) > set_Pr560526279lle_tv > set_Pr840833727at_nat).
% 3.06/1.75  thf(func_def_157, type, image_815163717at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1986765409at_nat > set_Pr1986765409at_nat).
% 3.06/1.75  thf(func_def_158, type, image_1674248956lle_tv: (product_prod_nat_nat > produc270694976lle_tv) > set_Pr1986765409at_nat > set_Pr13445366lle_tv).
% 3.06/1.75  thf(func_def_159, type, image_1597721174tv_nat: (product_prod_nat_nat > produc194167194tv_nat) > set_Pr1986765409at_nat > set_Pr1725653840tv_nat).
% 3.06/1.75  thf(func_def_160, type, image_1507992062lle_tv: (product_prod_nat_nat > produc1647334210lle_tv) > set_Pr1986765409at_nat > set_Pr2014382200lle_tv).
% 3.06/1.75  thf(func_def_161, type, image_1787705850at_nat: (produc270694976lle_tv > product_prod_nat_nat) > set_Pr13445366lle_tv > set_Pr1986765409at_nat).
% 3.06/1.75  thf(func_def_162, type, image_149830562lle_tv: (produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > set_Pr13445366lle_tv).
% 3.06/1.75  thf(func_def_163, type, image_53754658tv_nat: (produc270694976lle_tv > produc194167194tv_nat) > set_Pr13445366lle_tv > set_Pr1725653840tv_nat).
% 3.06/1.75  thf(func_def_164, type, image_988201162lle_tv: (produc270694976lle_tv > produc1647334210lle_tv) > set_Pr13445366lle_tv > set_Pr2014382200lle_tv).
% 3.06/1.75  thf(func_def_165, type, image_326034184lle_fm: (produc1443694919lle_tv > produc696645085lle_fm) > set_Pr1723822845lle_tv > set_Pr2120184979lle_fm).
% 3.06/1.75  thf(func_def_166, type, image_769496456lle_tv: (produc596913417at_nat > produc931990033lle_tv) > set_Pr840833727at_nat > set_Pr560526279lle_tv).
% 3.06/1.75  thf(func_def_167, type, image_1805124128at_nat: (produc194167194tv_nat > product_prod_nat_nat) > set_Pr1725653840tv_nat > set_Pr1986765409at_nat).
% 3.06/1.75  thf(func_def_168, type, image_1200372424lle_tv: (produc194167194tv_nat > produc270694976lle_tv) > set_Pr1725653840tv_nat > set_Pr13445366lle_tv).
% 3.06/1.75  thf(func_def_169, type, image_1221801032lle_tv: (produc1647334210lle_tv > produc1647334210lle_tv) > set_Pr2014382200lle_tv > set_Pr2014382200lle_tv).
% 3.06/1.75  thf(func_def_170, type, accp_P2085826120lle_tv: (produc931990033lle_tv > produc931990033lle_tv > $o) > produc931990033lle_tv > $o).
% 3.06/1.75  thf(func_def_171, type, lex_pr2001015487lle_fm: set_Pr2061825550lle_tv > set_Pr1019238018lle_fm > set_Pr1475944804lle_fm).
% 3.06/1.75  thf(func_def_172, type, lex_pr1093414955lle_tv: set_Pr1357842111at_nat > set_Pr2014382200lle_tv > set_Pr698334450lle_tv).
% 3.06/1.75  thf(func_def_173, type, lex_prod_nat_nat: set_Pr1986765409at_nat > set_Pr1986765409at_nat > set_Pr1490359111at_nat).
% 3.06/1.75  thf(func_def_174, type, lex_pr413684186lle_tv: set_Pr1986765409at_nat > set_Pr2014382200lle_tv > set_Pr292927124lle_tv).
% 3.06/1.75  thf(func_def_175, type, lex_pr1785529980tv_nat: set_Pr2014382200lle_tv > set_Pr1986765409at_nat > set_Pr1943077434tv_nat).
% 3.06/1.75  thf(func_def_176, type, lex_pr567812260lle_tv: set_Pr2014382200lle_tv > set_Pr2014382200lle_tv > set_Pr2012908090lle_tv).
% 3.06/1.75  thf(func_def_177, type, wf_nat: set_Pr1986765409at_nat > $o).
% 3.06/1.75  thf(func_def_178, type, wf_Par1378404612lle_tv: set_Pr2014382200lle_tv > $o).
% 3.06/1.75  thf(func_def_179, type, same_f1581085506lle_fm: ((list_char > paraco1605129243lle_tv) > $o) > ((list_char > paraco1605129243lle_tv) > set_Pr1019238018lle_fm) > set_Pr1475944804lle_fm).
% 3.06/1.75  thf(func_def_180, type, same_f1138187694lle_tv: ((nat > nat) > $o) > ((nat > nat) > set_Pr2014382200lle_tv) > set_Pr698334450lle_tv).
% 3.06/1.75  thf(func_def_181, type, member_nat: nat > set_nat > $o).
% 3.06/1.75  thf(func_def_182, type, member266900804lle_tv: paraco1605129243lle_tv > set_Pa1764573435lle_tv > $o).
% 3.06/1.75  thf(func_def_183, type, member146333935lle_tv: produc1852595672lle_tv > set_Pr2061825550lle_tv > $o).
% 3.06/1.75  thf(func_def_184, type, member1474794996lle_fm: produc696645085lle_fm > set_Pr2120184979lle_fm > $o).
% 3.06/1.75  thf(func_def_185, type, member112824072at_nat: produc1281043295at_nat > set_Pr1357842111at_nat > $o).
% 3.06/1.75  thf(func_def_186, type, member1569366824lle_tv: produc931990033lle_tv > set_Pr560526279lle_tv > $o).
% 3.06/1.75  thf(func_def_187, type, member701585322at_nat: product_prod_nat_nat > set_Pr1986765409at_nat > $o).
% 3.06/1.75  thf(func_def_188, type, member813679063lle_tv: produc270694976lle_tv > set_Pr13445366lle_tv > $o).
% 3.06/1.75  thf(func_def_189, type, member74361182lle_tv: produc1443694919lle_tv > set_Pr1723822845lle_tv > $o).
% 3.06/1.75  thf(func_def_190, type, member334644067lle_fm: produc450659916lle_fm > set_Pr1019238018lle_fm > $o).
% 3.06/1.75  thf(func_def_191, type, member1234290208at_nat: produc596913417at_nat > set_Pr840833727at_nat > $o).
% 3.06/1.75  thf(func_def_192, type, member737151281tv_nat: produc194167194tv_nat > set_Pr1725653840tv_nat > $o).
% 3.06/1.75  thf(func_def_193, type, member1531318361lle_tv: produc1647334210lle_tv > set_Pr2014382200lle_tv > $o).
% 3.06/1.75  thf(func_def_194, type, member1592865093lle_fm: produc1250255278lle_fm > set_Pr1475944804lle_fm > $o).
% 3.06/1.75  thf(func_def_195, type, member1339857875lle_tv: produc1720769084lle_tv > set_Pr698334450lle_tv > $o).
% 3.06/1.75  thf(func_def_196, type, f: nat > nat).
% 3.06/1.75  thf(func_def_197, type, i: list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_198, type, p1: paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_199, type, p2: paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_211, type, sP0: (paraco1604210848lle_fm > $o) > $o).
% 3.06/1.75  thf(func_def_212, type, sP1: (paraco1604210848lle_fm > $o) > $o).
% 3.06/1.75  thf(func_def_213, type, sP2: (paraco1604210848lle_fm > $o) > $o).
% 3.06/1.75  thf(func_def_214, type, sP3: (paraco1604210848lle_fm > $o) > $o).
% 3.06/1.75  thf(func_def_215, type, sP4: paraco1605129243lle_tv > paraco1605129243lle_tv > (nat > nat) > $o).
% 3.06/1.75  thf(func_def_216, type, sK5: set_Pr1986765409at_nat > (product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat).
% 3.06/1.75  thf(func_def_217, type, sK6: paraco1605129243lle_tv > (nat > paraco1605129243lle_tv) > nat).
% 3.06/1.75  thf(func_def_218, type, sK7: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_219, type, sK8: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_220, type, sK9: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_221, type, sK10: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_222, type, sK11: paraco1604210848lle_fm > list_char).
% 3.06/1.75  thf(func_def_223, type, sK12: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_224, type, sK13: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_225, type, sK14: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_226, type, sK15: (produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat).
% 3.06/1.75  thf(func_def_227, type, sK16: (produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat).
% 3.06/1.75  thf(func_def_228, type, sK17: nat > (nat > nat) > nat).
% 3.06/1.75  thf(func_def_229, type, sK18: (nat > nat) > nat).
% 3.06/1.75  thf(func_def_230, type, sK19: (paraco1605129243lle_tv > paraco1604210848lle_fm) > produc696645085lle_fm > set_Pr560526279lle_tv > ((nat > nat) > list_char > paraco1605129243lle_tv) > nat > nat).
% 3.06/1.75  thf(func_def_231, type, sK20: (paraco1605129243lle_tv > paraco1604210848lle_fm) > produc696645085lle_fm > set_Pr560526279lle_tv > ((nat > nat) > list_char > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_232, type, sK21: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_233, type, sK22: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_234, type, sK23: set_Pr1986765409at_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat).
% 3.06/1.75  thf(func_def_235, type, sK24: set_Pr1986765409at_nat > (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat).
% 3.06/1.75  thf(func_def_236, type, sK25: paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_237, type, sK26: nat > (nat > nat) > nat).
% 3.06/1.75  thf(func_def_238, type, sK27: produc931990033lle_tv > nat > nat).
% 3.06/1.75  thf(func_def_239, type, sK28: produc931990033lle_tv > nat).
% 3.06/1.75  thf(func_def_240, type, sK29: produc931990033lle_tv > nat > nat).
% 3.06/1.75  thf(func_def_241, type, sK30: produc931990033lle_tv > $o).
% 3.06/1.75  thf(func_def_242, type, sK31: set_Pr2014382200lle_tv > (produc1647334210lle_tv > produc1647334210lle_tv) > (produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv).
% 3.06/1.75  thf(func_def_243, type, sK32: (produc931990033lle_tv > $o) > nat > nat).
% 3.06/1.75  thf(func_def_244, type, sK33: (produc931990033lle_tv > $o) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_245, type, sK34: produc194167194tv_nat).
% 3.06/1.75  thf(func_def_246, type, sK35: produc1281043295at_nat).
% 3.06/1.75  thf(func_def_247, type, sK36: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_248, type, sK37: produc696645085lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_249, type, sK38: (nat > nat) > (nat > nat) > set_nat > nat).
% 3.06/1.75  thf(func_def_250, type, sK39: produc931990033lle_tv > ((list_char > paraco1605129243lle_tv) > nat > nat) > (paraco1604210848lle_fm > paraco1605129243lle_tv) > set_Pr2120184979lle_fm > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_251, type, sK40: produc931990033lle_tv > ((list_char > paraco1605129243lle_tv) > nat > nat) > (paraco1604210848lle_fm > paraco1605129243lle_tv) > set_Pr2120184979lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_252, type, sK41: nat > (nat > nat) > nat).
% 3.06/1.75  thf(func_def_253, type, sK42: nat > nat > (nat > nat) > nat).
% 3.06/1.75  thf(func_def_254, type, sK43: (nat > paraco1605129243lle_tv) > paraco1605129243lle_tv > nat).
% 3.06/1.75  thf(func_def_255, type, sK44: produc696645085lle_fm).
% 3.06/1.75  thf(func_def_256, type, sK45: produc931990033lle_tv > nat > nat).
% 3.06/1.75  thf(func_def_257, type, sK46: produc931990033lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_258, type, sK47: product_prod_nat_nat).
% 3.06/1.75  thf(func_def_259, type, sK48: (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat).
% 3.06/1.75  thf(func_def_260, type, sK49: (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat).
% 3.06/1.75  thf(func_def_261, type, sK50: set_Pr560526279lle_tv > set_Pr560526279lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_262, type, sK51: set_Pr560526279lle_tv > set_Pr560526279lle_tv > nat > nat).
% 3.06/1.75  thf(func_def_263, type, sK52: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_264, type, sK53: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_265, type, sK54: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_266, type, sK55: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_267, type, sK56: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_268, type, sK57: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_269, type, sK58: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_270, type, sK59: (paraco1604210848lle_fm > $o) > list_char).
% 3.06/1.75  thf(func_def_271, type, sK60: set_nat > (nat > paraco1605129243lle_tv) > nat).
% 3.06/1.75  thf(func_def_272, type, sK61: set_nat > (nat > paraco1605129243lle_tv) > nat).
% 3.06/1.75  thf(func_def_273, type, sK62: set_Pr1725653840tv_nat > (produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat).
% 3.06/1.75  thf(func_def_274, type, sK63: set_Pr1725653840tv_nat > (produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat).
% 3.06/1.75  thf(func_def_275, type, sK64: (produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > (produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv).
% 3.06/1.75  thf(func_def_276, type, sK65: (produc696645085lle_fm > $o) > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_277, type, sK66: (produc696645085lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_278, type, sK67: produc696645085lle_fm > ((list_char > paraco1605129243lle_tv) > list_char > paraco1605129243lle_tv) > set_Pr2120184979lle_fm > (paraco1604210848lle_fm > paraco1604210848lle_fm) > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_279, type, sK68: produc696645085lle_fm > ((list_char > paraco1605129243lle_tv) > list_char > paraco1605129243lle_tv) > set_Pr2120184979lle_fm > (paraco1604210848lle_fm > paraco1604210848lle_fm) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_280, type, sK69: (paraco1605129243lle_tv > nat) > nat > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_281, type, sK70: (produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat).
% 3.06/1.75  thf(func_def_282, type, sK71: (produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat).
% 3.06/1.75  thf(func_def_283, type, sK72: produc696645085lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_284, type, sK73: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_285, type, sK74: set_Pr1986765409at_nat > product_prod_nat_nat).
% 3.06/1.75  thf(func_def_286, type, sK75: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_287, type, sK76: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_288, type, sK77: (nat > paraco1605129243lle_tv) > (nat > paraco1605129243lle_tv) > set_nat > nat).
% 3.06/1.75  thf(func_def_289, type, sK78: (nat > nat) > (nat > nat) > nat).
% 3.06/1.75  thf(func_def_290, type, sK79: produc1852595672lle_tv).
% 3.06/1.75  thf(func_def_291, type, sK80: set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_292, type, sK81: (nat > $o) > (nat > $o) > nat).
% 3.06/1.75  thf(func_def_293, type, sK82: (nat > nat) > set_nat > (nat > nat) > nat).
% 3.06/1.75  thf(func_def_294, type, sK83: (produc931990033lle_tv > $o) > nat > nat).
% 3.06/1.75  thf(func_def_295, type, sK84: (produc931990033lle_tv > $o) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_296, type, sK85: produc931990033lle_tv > nat > nat).
% 3.06/1.75  thf(func_def_297, type, sK86: produc931990033lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_298, type, sK87: (paraco1605129243lle_tv > $o) > $o).
% 3.06/1.75  thf(func_def_299, type, sK88: (paraco1605129243lle_tv > $o) > nat).
% 3.06/1.75  thf(func_def_300, type, sK89: (nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > nat) > nat).
% 3.06/1.75  thf(func_def_301, type, sK90: (produc696645085lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_302, type, sK91: (produc696645085lle_fm > $o) > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_303, type, sK92: (produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv).
% 3.06/1.75  thf(func_def_304, type, sK93: (produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv).
% 3.06/1.75  thf(func_def_305, type, sK94: set_Pr2014382200lle_tv > (produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv).
% 3.06/1.75  thf(func_def_306, type, sK95: set_Pr2014382200lle_tv > (produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv).
% 3.06/1.75  thf(func_def_307, type, sK96: (produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > produc270694976lle_tv).
% 3.06/1.75  thf(func_def_308, type, sK97: (produc270694976lle_tv > produc270694976lle_tv) > set_Pr13445366lle_tv > produc270694976lle_tv).
% 3.06/1.75  thf(func_def_309, type, sK98: set_nat > nat).
% 3.06/1.75  thf(func_def_310, type, sK99: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_311, type, sK100: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_312, type, sK101: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_313, type, sK102: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_314, type, sK103: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_315, type, sK104: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_316, type, sK105: (paraco1604210848lle_fm > $o) > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_317, type, sK106: (paraco1604210848lle_fm > $o) > list_char).
% 3.06/1.75  thf(func_def_318, type, sK107: set_Pr2120184979lle_fm > produc696645085lle_fm).
% 3.06/1.75  thf(func_def_319, type, sK108: set_Pr13445366lle_tv > produc270694976lle_tv).
% 3.06/1.75  thf(func_def_320, type, sK109: paraco1604210848lle_fm > list_char).
% 3.06/1.75  thf(func_def_321, type, sK110: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_322, type, sK111: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_323, type, sK112: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_324, type, sK113: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_325, type, sK114: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_326, type, sK115: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_327, type, sK116: paraco1604210848lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_328, type, sK117: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_329, type, sK118: paraco1605129243lle_tv > nat).
% 3.06/1.75  thf(func_def_330, type, sK119: (produc194167194tv_nat > produc194167194tv_nat) > set_Pr1725653840tv_nat > (produc194167194tv_nat > produc194167194tv_nat) > produc194167194tv_nat).
% 3.06/1.75  thf(func_def_331, type, sK120: (paraco1605129243lle_tv > $o) > nat).
% 3.06/1.75  thf(func_def_332, type, sK121: paraco1605129243lle_tv > (nat > paraco1605129243lle_tv) > nat).
% 3.06/1.75  thf(func_def_333, type, sK122: (nat > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_334, type, sK123: paraco1604210848lle_fm > produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_335, type, sK124: set_Pr560526279lle_tv > produc931990033lle_tv).
% 3.06/1.75  thf(func_def_336, type, sK125: (nat > nat) > (nat > nat) > nat).
% 3.06/1.75  thf(func_def_337, type, sK126: (paraco1605129243lle_tv > paraco1605129243lle_tv) > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_338, type, sK127: (paraco1605129243lle_tv > nat) > nat > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_339, type, sK128: set_Pr1725653840tv_nat > produc194167194tv_nat).
% 3.06/1.75  thf(func_def_340, type, sK129: produc270694976lle_tv).
% 3.06/1.75  thf(func_def_341, type, sK130: (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat).
% 3.06/1.75  thf(func_def_342, type, sK131: (product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat).
% 3.06/1.75  thf(func_def_343, type, sK132: ((nat > nat) > nat > nat) > produc931990033lle_tv > set_Pr560526279lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_344, type, sK133: ((nat > nat) > nat > nat) > produc931990033lle_tv > set_Pr560526279lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > nat > nat).
% 3.06/1.75  thf(func_def_345, type, sK134: (nat > paraco1605129243lle_tv) > nat).
% 3.06/1.75  thf(func_def_346, type, sK135: (nat > paraco1605129243lle_tv) > nat).
% 3.06/1.75  thf(func_def_347, type, sK136: (nat > paraco1605129243lle_tv) > nat).
% 3.06/1.75  thf(func_def_348, type, sK137: (nat > paraco1605129243lle_tv) > nat).
% 3.06/1.75  thf(func_def_349, type, sK138: paraco1605129243lle_tv > paraco1605129243lle_tv > $o).
% 3.06/1.75  thf(func_def_350, type, sK139: (nat > nat) > paraco1605129243lle_tv > paraco1605129243lle_tv > nat).
% 3.06/1.75  thf(func_def_351, type, sK140: (nat > nat) > nat).
% 3.06/1.75  thf(func_def_352, type, sK141: (nat > nat) > nat).
% 3.06/1.75  thf(func_def_353, type, sK142: set_Pr2120184979lle_fm > set_Pr2120184979lle_fm > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_354, type, sK143: set_Pr2120184979lle_fm > set_Pr2120184979lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_355, type, sK144: set_Pr1357842111at_nat > produc1281043295at_nat).
% 3.06/1.75  thf(func_def_356, type, sK145: produc931990033lle_tv).
% 3.06/1.75  thf(func_def_357, type, sK146: paraco1605129243lle_tv > nat).
% 3.06/1.75  thf(func_def_358, type, sK147: paraco1605129243lle_tv > $o).
% 3.06/1.75  thf(func_def_359, type, sK148: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_360, type, sK149: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_361, type, sK150: paraco1605129243lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_362, type, sK151: (nat > nat) > nat).
% 3.06/1.75  thf(func_def_363, type, sK152: (nat > nat) > nat).
% 3.06/1.75  thf(func_def_364, type, sK153: set_Pr2061825550lle_tv > produc1852595672lle_tv).
% 3.06/1.75  thf(func_def_365, type, sK154: (produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv).
% 3.06/1.75  thf(func_def_366, type, sK155: (produc1647334210lle_tv > produc1647334210lle_tv) > produc1647334210lle_tv).
% 3.06/1.75  thf(func_def_367, type, sK156: (paraco1605129243lle_tv > $o) > (paraco1605129243lle_tv > $o) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_368, type, sK157: paraco1605129243lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_369, type, sK158: paraco1605129243lle_tv > paraco1605129243lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_370, type, sK159: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_371, type, sK160: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_372, type, sK161: paraco1605129243lle_tv > produc931990033lle_tv > nat > nat).
% 3.06/1.75  thf(func_def_373, type, sK162: nat).
% 3.06/1.75  thf(func_def_374, type, sK163: set_nat > (nat > nat) > (nat > nat) > nat).
% 3.06/1.75  thf(func_def_375, type, sK164: set_nat > (nat > nat) > (nat > nat) > nat).
% 3.06/1.75  thf(func_def_376, type, sK165: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_377, type, sK166: (paraco1605129243lle_tv > paraco1605129243lle_tv) > set_Pa1764573435lle_tv > (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_378, type, sK167: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_379, type, sK168: produc696645085lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_380, type, sK169: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_381, type, sK170: produc696645085lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_382, type, sK171: produc696645085lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_383, type, sK172: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_384, type, sK173: produc696645085lle_fm > list_char).
% 3.06/1.75  thf(func_def_385, type, sK174: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_386, type, sK175: produc696645085lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_387, type, sK176: produc696645085lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_388, type, sK177: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_389, type, sK178: produc696645085lle_fm > list_char > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_390, type, sK179: produc696645085lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_391, type, sK180: produc696645085lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_392, type, sK181: set_Pa1764573435lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_393, type, sK182: (nat > paraco1605129243lle_tv) > (paraco1605129243lle_tv > nat) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_394, type, sK183: (produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv).
% 3.06/1.75  thf(func_def_395, type, sK184: (produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv).
% 3.06/1.75  thf(func_def_396, type, sK185: (paraco1605129243lle_tv > nat) > nat).
% 3.06/1.75  thf(func_def_397, type, sK186: nat > (paraco1605129243lle_tv > nat) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_398, type, sK187: (produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv).
% 3.06/1.75  thf(func_def_399, type, sK188: (produc270694976lle_tv > produc270694976lle_tv) > produc270694976lle_tv).
% 3.06/1.75  thf(func_def_400, type, sK189: (nat > nat) > set_nat > nat).
% 3.06/1.75  thf(func_def_401, type, sK190: (nat > nat) > set_nat > nat).
% 3.06/1.75  thf(func_def_402, type, sK191: paraco1605129243lle_tv > paraco1605129243lle_tv > (nat > nat) > $o).
% 3.06/1.75  thf(func_def_403, type, sK192: (nat > nat) > paraco1605129243lle_tv > paraco1605129243lle_tv > nat).
% 3.06/1.75  thf(func_def_404, type, sK193: (paraco1605129243lle_tv > paraco1605129243lle_tv) > paraco1605129243lle_tv > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_405, type, sK194: produc931990033lle_tv > (nat > nat) > paraco1605129243lle_tv).
% 3.06/1.75  thf(func_def_406, type, sK195: (list_char > paraco1605129243lle_tv) > produc696645085lle_fm > paraco1604210848lle_fm).
% 3.06/1.75  thf(func_def_407, type, sK196: ((nat > nat) > paraco1605129243lle_tv > $o) > nat).
% 3.06/1.75  thf(func_def_408, type, sK197: ((nat > nat) > paraco1605129243lle_tv > $o) > nat > nat).
% 3.06/1.75  thf(func_def_409, type, sK198: ((nat > nat) > paraco1605129243lle_tv > $o) > $o).
% 3.06/1.75  thf(func_def_410, type, sK199: ((nat > nat) > paraco1605129243lle_tv > $o) > nat > nat).
% 3.06/1.75  thf(func_def_411, type, sK200: (nat > nat) > nat > nat).
% 3.06/1.75  thf(func_def_413, type, ph202: !>[X0: $tType]:(X0)).
% 3.06/1.75  thf(f2281,plain,(
% 3.06/1.75    $false),
% 3.06/1.75    inference(avatar_sat_refutation,[status(thm)],[f2274,f2277,f2280])).
% 3.06/1.75  thf(f2280,plain,(
% 3.06/1.75    spl201_2),
% 3.06/1.75    inference(avatar_contradiction_clause,[status(thm)],[f2279])).
% 3.06/1.75  thf(f2279,plain,(
% 3.06/1.75    $false | spl201_2),
% 3.06/1.75    inference(trivial_inequality_removal,[status(thm)],[f2278])).
% 3.06/1.75  thf(f2278,plain,(
% 3.06/1.75    ((paraco1344940915le_Det @ $true) != (paraco1344940915le_Det @ $true)) | spl201_2),
% 3.06/1.75    inference(superposition,[status(thm)],[f2266,f1835])).
% 3.06/1.75  thf(f1835,plain,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p2) = (paraco1344940915le_Det @ $true))),
% 3.06/1.75    inference(cnf_transformation,[status(thm)],[f632])).
% 3.06/1.75  thf(f632,plain,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p2) = (paraco1344940915le_Det @ $true))),
% 3.06/1.75    inference(fool_elimination,[status(thm)],[f2])).
% 3.06/1.75  thf(f2,axiom,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p2) = (paraco1344940915le_Det @ $true))),
% 3.06/1.75    file('/export/starexec/sandbox/tmp/tmp.J4RbD3yP62/DTF2THF_1342.p',fact_1_a)).
% 3.06/1.75  thf(f2266,plain,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p2) != (paraco1344940915le_Det @ $true)) | spl201_2),
% 3.06/1.75    inference(avatar_component_clause,[status(thm)],[f2265])).
% 3.06/1.75  thf(f2265,definition,(
% 3.06/1.75    spl201_2 <=> ((paraco1325918602e_eval @ i @ p2) = (paraco1344940915le_Det @ $true))),
% 3.06/1.75    introduced(definition,[new_symbols(naming,[spl201_2])],[avatar_definition])).
% 3.06/1.75  thf(f2277,plain,(
% 3.06/1.75    ~spl201_2 | spl201_1),
% 3.06/1.75    inference(avatar_split_clause,[status(thm)],[f2276,f2261,f2265])).
% 3.06/1.75  thf(f2261,definition,(
% 3.06/1.75    spl201_1 <=> ((paraco1325918602e_eval @ i @ p1) = (paraco1344940915le_Det @ $true))),
% 3.06/1.75    introduced(definition,[new_symbols(naming,[spl201_1])],[avatar_definition])).
% 3.06/1.75  thf(f2276,plain,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p2) != (paraco1344940915le_Det @ $true)) | ((paraco1325918602e_eval @ i @ p1) = (paraco1344940915le_Det @ $true))),
% 3.06/1.75    inference(duplicate_literal_removal,[status(thm)],[f2275])).
% 3.06/1.75  thf(f2275,plain,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p2) != (paraco1344940915le_Det @ $true)) | ((paraco1325918602e_eval @ i @ p1) = (paraco1344940915le_Det @ $true)) | ((paraco1325918602e_eval @ i @ p1) = (paraco1344940915le_Det @ $true))),
% 3.06/1.75    inference(forward_demodulation,[status(thm)],[f2256,f1835])).
% 3.06/1.75  thf(f2256,plain,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p1) = (paraco1325918602e_eval @ i @ p2)) | ((paraco1325918602e_eval @ i @ p2) != (paraco1344940915le_Det @ $true)) | ((paraco1325918602e_eval @ i @ p1) = (paraco1344940915le_Det @ $true))),
% 3.06/1.75    inference(trivial_inequality_removal,[status(thm)],[f2253])).
% 3.06/1.75  thf(f2253,plain,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p2) != (paraco1344940915le_Det @ $true)) | ((paraco1325918602e_eval @ i @ p1) = (paraco1344940915le_Det @ $true)) | ((paraco1325918602e_eval @ i @ p1) = (paraco1325918602e_eval @ i @ p2)) | ((paraco1325918602e_eval @ i @ p1) != (paraco1325918602e_eval @ i @ p1))),
% 3.06/1.75    inference(superposition,[status(thm)],[f1967,f1860])).
% 3.06/1.75  thf(f1860,plain,(
% 3.06/1.75    ( ! [X2 : paraco1604210848lle_fm,X0 : paraco1604210848lle_fm,X1 : list_char > paraco1605129243lle_tv] : (((paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)) = (paraco1325918602e_eval @ X1 @ X0)) | ((paraco1325918602e_eval @ X1 @ X2) != (paraco1344940915le_Det @ $true)) | ((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X1 @ X0)) | ((paraco1325918602e_eval @ X1 @ X2) = (paraco1325918602e_eval @ X1 @ X0))) )),
% 3.06/1.75    inference(cnf_transformation,[status(thm)],[f1151])).
% 3.06/1.75  thf(f1151,plain,(
% 3.06/1.75    ! [X0 : paraco1604210848lle_fm,X1 : list_char > paraco1605129243lle_tv,X2 : paraco1604210848lle_fm] : ((((((paraco1325918602e_eval @ X1 @ X2) = (paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2))) | ((paraco1344940915le_Det @ $true) != (paraco1325918602e_eval @ X1 @ X0))) & (((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X1 @ X0)) | ((((paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)) = (paraco1325918602e_eval @ X1 @ X0)) | ((paraco1325918602e_eval @ X1 @ X2) != (paraco1344940915le_Det @ $true))) & (((paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)) = (paraco1344940915le_Det @ $false)) | ((paraco1325918602e_eval @ X1 @ X2) = (paraco1344940915le_Det @ $true)))))) | ((paraco1325918602e_eval @ X1 @ X2) = (paraco1325918602e_eval @ X1 @ X0))) & (((paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)) = (paraco1325918602e_eval @ X1 @ X0)) | ((paraco1325918602e_eval @ X1 @ X2) != (paraco1325918602e_eval @ X1 @ X0))))),
% 3.06/1.75    inference(ennf_transformation,[status(thm)],[f462])).
% 3.06/1.75  thf(f462,plain,(
% 3.06/1.75    ! [X0 : paraco1604210848lle_fm,X1 : list_char > paraco1605129243lle_tv,X2 : paraco1604210848lle_fm] : ((((paraco1325918602e_eval @ X1 @ X2) != (paraco1325918602e_eval @ X1 @ X0)) => ((((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X1 @ X0)) => ((paraco1325918602e_eval @ X1 @ X2) = (paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)))) & (((paraco1344940915le_Det @ $true) != (paraco1325918602e_eval @ X1 @ X0)) => ((((paraco1325918602e_eval @ X1 @ X2) = (paraco1344940915le_Det @ $true)) => ((paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)) = (paraco1325918602e_eval @ X1 @ X0))) & (((paraco1325918602e_eval @ X1 @ X2) != (paraco1344940915le_Det @ $true)) => ((paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)) = (paraco1344940915le_Det @ $false))))))) & (((paraco1325918602e_eval @ X1 @ X2) = (paraco1325918602e_eval @ X1 @ X0)) => ((paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)) = (paraco1325918602e_eval @ X1 @ X0))))),
% 3.06/1.75    inference(fool_elimination,[status(thm)],[f461])).
% 3.06/1.75  thf(f461,plain,(
% 3.06/1.75    ! [X0 : paraco1604210848lle_fm,X1 : list_char > paraco1605129243lle_tv,X2 : paraco1604210848lle_fm] : ((((paraco1325918602e_eval @ X1 @ X2) = (paraco1325918602e_eval @ X1 @ X0)) => ((paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)) = (paraco1325918602e_eval @ X1 @ X0))) & (((paraco1325918602e_eval @ X1 @ X2) != (paraco1325918602e_eval @ X1 @ X0)) => ((((paraco1325918602e_eval @ X1 @ X0) = (paraco1344940915le_Det @ $true)) => ((paraco1325918602e_eval @ X1 @ X2) = (paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)))) & (((paraco1325918602e_eval @ X1 @ X0) != (paraco1344940915le_Det @ $true)) => ((((paraco1344940915le_Det @ $true) != (paraco1325918602e_eval @ X1 @ X2)) => ((paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)) = (paraco1344940915le_Det @ $false))) & (((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X1 @ X2)) => ((paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)) = (paraco1325918602e_eval @ X1 @ X0))))))))),
% 3.06/1.75    inference(rectify,[status(thm)],[f6])).
% 3.06/1.75  thf(f6,axiom,(
% 3.06/1.75    ! [X5 : paraco1604210848lle_fm,X4 : list_char > paraco1605129243lle_tv,X6 : paraco1604210848lle_fm] : ((((paraco1325918602e_eval @ X4 @ X5) = (paraco1325918602e_eval @ X4 @ X6)) => ((paraco1325918602e_eval @ X4 @ X5) = (paraco1325918602e_eval @ X4 @ (paraco69239110le_Con @ X5 @ X6)))) & (((paraco1325918602e_eval @ X4 @ X5) != (paraco1325918602e_eval @ X4 @ X6)) => ((((paraco1325918602e_eval @ X4 @ X5) = (paraco1344940915le_Det @ $true)) => ((paraco1325918602e_eval @ X4 @ X6) = (paraco1325918602e_eval @ X4 @ (paraco69239110le_Con @ X5 @ X6)))) & (((paraco1325918602e_eval @ X4 @ X5) != (paraco1344940915le_Det @ $true)) => ((((paraco1344940915le_Det @ $true) != (paraco1325918602e_eval @ X4 @ X6)) => ((paraco1325918602e_eval @ X4 @ (paraco69239110le_Con @ X5 @ X6)) = (paraco1344940915le_Det @ $false))) & (((paraco1344940915le_Det @ $true) = (paraco1325918602e_eval @ X4 @ X6)) => ((paraco1325918602e_eval @ X4 @ X5) = (paraco1325918602e_eval @ X4 @ (paraco69239110le_Con @ X5 @ X6)))))))))),
% 3.06/1.75    file('/export/starexec/sandbox/tmp/tmp.J4RbD3yP62/DTF2THF_1342.p',fact_5_eval_Osimps_I4_J)).
% 3.06/1.75  thf(f1967,plain,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p1) != (paraco1325918602e_eval @ i @ (paraco69239110le_Con @ p1 @ p2)))),
% 3.06/1.75    inference(cnf_transformation,[status(thm)],[f961])).
% 3.06/1.75  thf(f961,plain,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p1) != (paraco1325918602e_eval @ i @ (paraco69239110le_Con @ p1 @ p2)))),
% 3.06/1.75    inference(flattening,[status(thm)],[f359])).
% 3.06/1.75  thf(f359,negated_conjecture,(
% 3.06/1.75    ~((paraco1325918602e_eval @ i @ p1) = (paraco1325918602e_eval @ i @ (paraco69239110le_Con @ p1 @ p2)))),
% 3.06/1.75    inference(negated_conjecture,[status(cth)],[f358])).
% 3.06/1.75  thf(f358,conjecture,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p1) = (paraco1325918602e_eval @ i @ (paraco69239110le_Con @ p1 @ p2)))),
% 3.06/1.75    file('/export/starexec/sandbox/tmp/tmp.J4RbD3yP62/DTF2THF_1342.p',conj_0)).
% 3.06/1.75  thf(f2274,plain,(
% 3.06/1.75    ~spl201_1),
% 3.06/1.75    inference(avatar_split_clause,[status(thm)],[f2273,f2261])).
% 3.06/1.75  thf(f2273,plain,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p1) != (paraco1344940915le_Det @ $true))),
% 3.06/1.75    inference(forward_demodulation,[status(thm)],[f2257,f1835])).
% 3.06/1.75  thf(f2257,plain,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p1) != (paraco1325918602e_eval @ i @ p2))),
% 3.06/1.75    inference(trivial_inequality_removal,[status(thm)],[f2254])).
% 3.06/1.75  thf(f2254,plain,(
% 3.06/1.75    ((paraco1325918602e_eval @ i @ p1) != (paraco1325918602e_eval @ i @ p2)) | ((paraco1325918602e_eval @ i @ p1) != (paraco1325918602e_eval @ i @ p1))),
% 3.06/1.75    inference(superposition,[status(thm)],[f1967,f1858])).
% 3.06/1.75  thf(f1858,plain,(
% 3.06/1.75    ( ! [X2 : paraco1604210848lle_fm,X0 : paraco1604210848lle_fm,X1 : list_char > paraco1605129243lle_tv] : (((paraco1325918602e_eval @ X1 @ (paraco69239110le_Con @ X0 @ X2)) = (paraco1325918602e_eval @ X1 @ X0)) | ((paraco1325918602e_eval @ X1 @ X2) != (paraco1325918602e_eval @ X1 @ X0))) )),
% 3.06/1.75    inference(cnf_transformation,[status(thm)],[f1151])).
% 3.06/1.75  % SZS output end Proof for DTF2THF_1342
% 3.06/1.75  % (1465)------------------------------
% 3.06/1.75  % (1465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.06/1.75  % (1465)Termination reason: Refutation
% 3.06/1.75  
% 3.06/1.75  % (1465)Memory used [KB]: 7803
% 3.06/1.75  % (1465)Time elapsed: 0.042 s
% 3.06/1.75  % (1465)Instructions burned: 132 (million)
% 3.06/1.75  % (1465)------------------------------
% 3.06/1.75  % (1465)------------------------------
% 3.06/1.75  % (1442)Success in time 0.135 s
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