DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP193^1 : 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 : n010.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Feb 25 08:56:18 AM UTC 2026

% Result   : Theorem 6.54s 2.17s
% Output   : Refutation 6.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   20 (   8 unt;   0 typ;   0 def)
%            Number of atoms       :   97 (  33 equ;   0 cnn)
%            Maximal formula atoms :    4 (   4 avg)
%            Number of connectives :  166 (  14   ~;   7   |;  20   &; 122   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :   16 (  15 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  175 ( 172 usr;  16 con; 0-4 aty)
%            Number of variables   :   29 (  19   ^;  10   !;   0   ?;  29   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_15,type,
    finite_finite_int: set_int > $o ).

thf(func_def_16,type,
    finite385822667ly_int: set_poly_int > $o ).

thf(func_def_17,type,
    finite1328464339y_real: set_poly_poly_real > $o ).

thf(func_def_18,type,
    finite1810960971y_real: set_poly_real > $o ).

thf(func_def_19,type,
    finite_finite_real: set_real > $o ).

thf(func_def_20,type,
    finite26677625et_int: set_set_int > $o ).

thf(func_def_21,type,
    finite475462905t_real: set_set_real > $o ).

thf(func_def_22,type,
    one_one_int: int ).

thf(func_def_23,type,
    one_one_poly_real: poly_real ).

thf(func_def_24,type,
    zero_zero_int: int ).

thf(func_def_25,type,
    zero_zero_poly_int: poly_int ).

thf(func_def_26,type,
    zero_z1549157189ly_int: poly_poly_int ).

thf(func_def_27,type,
    zero_z935034829y_real: poly_poly_poly_real ).

thf(func_def_28,type,
    zero_z1423781445y_real: poly_poly_real ).

thf(func_def_29,type,
    zero_zero_poly_real: poly_real ).

thf(func_def_30,type,
    zero_zero_real: real ).

thf(func_def_31,type,
    groups2051521940al_int: ( real > int ) > set_real > int ).

thf(func_def_32,type,
    ord_less_int: int > int > $o ).

thf(func_def_33,type,
    ord_less_poly_int: poly_int > poly_int > $o ).

thf(func_def_34,type,
    ord_le38482960y_real: poly_poly_real > poly_poly_real > $o ).

thf(func_def_35,type,
    ord_less_poly_real: poly_real > poly_real > $o ).

thf(func_def_36,type,
    ord_less_real: real > real > $o ).

thf(func_def_37,type,
    ord_less_set_int: set_int > set_int > $o ).

thf(func_def_38,type,
    ord_less_set_real: set_real > set_real > $o ).

thf(func_def_39,type,
    ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_40,type,
    ord_less_eq_int: int > int > $o ).

thf(func_def_41,type,
    ord_less_eq_poly_int: poly_int > poly_int > $o ).

thf(func_def_42,type,
    ord_le893774876y_real: poly_poly_real > poly_poly_real > $o ).

thf(func_def_43,type,
    ord_le1180086932y_real: poly_real > poly_real > $o ).

thf(func_def_44,type,
    ord_less_eq_real: real > real > $o ).

thf(func_def_45,type,
    ord_less_eq_set_int: set_int > set_int > $o ).

thf(func_def_46,type,
    ord_less_eq_set_real: set_real > set_real > $o ).

thf(func_def_47,type,
    is_zero_int: poly_int > $o ).

thf(func_def_48,type,
    is_zero_poly_real: poly_poly_real > $o ).

thf(func_def_49,type,
    is_zero_real: poly_real > $o ).

thf(func_def_50,type,
    poly_int2: poly_int > int > int ).

thf(func_def_51,type,
    poly_poly_int2: poly_poly_int > poly_int > poly_int ).

thf(func_def_52,type,
    poly_poly_poly_real2: poly_poly_poly_real > poly_poly_real > poly_poly_real ).

thf(func_def_53,type,
    poly_poly_real2: poly_poly_real > poly_real > poly_real ).

thf(func_def_54,type,
    poly_real2: poly_real > real > real ).

thf(func_def_55,type,
    poly_cutoff_int: nat > poly_int > poly_int ).

thf(func_def_56,type,
    poly_c1404107022y_real: nat > poly_poly_real > poly_poly_real ).

thf(func_def_57,type,
    poly_cutoff_real: nat > poly_real > poly_real ).

thf(func_def_58,type,
    collect_int: ( int > $o ) > set_int ).

thf(func_def_59,type,
    collect_poly_int: ( poly_int > $o ) > set_poly_int ).

thf(func_def_60,type,
    collec927113489y_real: ( poly_poly_real > $o ) > set_poly_poly_real ).

thf(func_def_61,type,
    collect_poly_real: ( poly_real > $o ) > set_poly_real ).

thf(func_def_62,type,
    collect_real: ( real > $o ) > set_real ).

thf(func_def_63,type,
    collect_set_int: ( set_int > $o ) > set_set_int ).

thf(func_def_64,type,
    collect_set_real: ( set_real > $o ) > set_set_real ).

thf(func_def_65,type,
    sturm_308542325x_poly: real > real > poly_real > poly_real > int ).

thf(func_def_66,type,
    sturm_1953858694_cross: poly_real > real > real > int ).

thf(func_def_67,type,
    sturm_276991412p_poly: poly_real > poly_real > real > int ).

thf(func_def_68,type,
    member_int: int > set_int > $o ).

thf(func_def_69,type,
    member_real: real > set_real > $o ).

thf(func_def_70,type,
    a: real ).

thf(func_def_71,type,
    a2: real ).

thf(func_def_72,type,
    b: real ).

thf(func_def_73,type,
    b2: real ).

thf(func_def_74,type,
    p: poly_real ).

thf(func_def_90,type,
    diff: 
      !>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X0 > X1 ) > X0 ) ).

thf(func_def_91,type,
    sP0: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_92,type,
    sP1: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_93,type,
    sP2: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_94,type,
    sP3: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > $o ).

thf(func_def_95,type,
    sK4: ( real > int ) > real ).

thf(func_def_96,type,
    sK5: ( real > int ) > real ).

thf(func_def_97,type,
    sK6: real > real ).

thf(func_def_98,type,
    sK7: real > real > real > real ).

thf(func_def_99,type,
    sK8: real > real ).

thf(func_def_100,type,
    sK9: real > real ).

thf(func_def_101,type,
    sK10: real > set_real > real ).

thf(func_def_102,type,
    sK11: set_real > real ).

thf(func_def_103,type,
    sK12: real > set_real > real ).

thf(func_def_104,type,
    sK13: real > real ).

thf(func_def_105,type,
    sK14: set_real > real > real ).

thf(func_def_106,type,
    sK15: ( int > real ) > int ).

thf(func_def_107,type,
    sK16: ( int > real ) > int ).

thf(func_def_108,type,
    sK17: ( int > real ) > int ).

thf(func_def_109,type,
    sK18: ( int > real ) > int ).

thf(func_def_110,type,
    sK19: ( int > real ) > int ).

thf(func_def_111,type,
    sK20: ( int > real ) > int ).

thf(func_def_112,type,
    sK21: ( int > real ) > int ).

thf(func_def_113,type,
    sK22: ( int > real ) > int ).

thf(func_def_114,type,
    sK23: set_real > real > real ).

thf(func_def_115,type,
    sK24: ( real > int ) > real ).

thf(func_def_116,type,
    sK25: ( real > int ) > real ).

thf(func_def_117,type,
    sK26: real > real ).

thf(func_def_118,type,
    sK27: real > real > real ).

thf(func_def_119,type,
    sK28: real > real ).

thf(func_def_120,type,
    sK29: real > real ).

thf(func_def_121,type,
    sK30: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_122,type,
    sK31: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_123,type,
    sK32: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_124,type,
    sK33: real > real ).

thf(func_def_125,type,
    sK34: ( real > real ) > real ).

thf(func_def_126,type,
    sK35: ( real > real ) > real ).

thf(func_def_127,type,
    sK36: poly_real > real > real > real ).

thf(func_def_128,type,
    sK37: ( real > int ) > real ).

thf(func_def_129,type,
    sK38: ( real > int ) > real ).

thf(func_def_130,type,
    sK39: ( real > real > $o ) > real ).

thf(func_def_131,type,
    sK40: ( real > real > $o ) > real ).

thf(func_def_132,type,
    sK41: ( real > real > $o ) > real ).

thf(func_def_133,type,
    sK42: ( real > real > $o ) > real ).

thf(func_def_134,type,
    sK43: ( real > real > $o ) > real ).

thf(func_def_135,type,
    sK44: ( real > real ) > real ).

thf(func_def_136,type,
    sK45: ( real > real ) > real ).

thf(func_def_137,type,
    sK46: ( real > real ) > real ).

thf(func_def_138,type,
    sK47: ( real > real ) > real ).

thf(func_def_139,type,
    sK48: poly_real > real ).

thf(func_def_140,type,
    sK49: real > real ).

thf(func_def_141,type,
    sK50: ( real > int ) > real ).

thf(func_def_142,type,
    sK51: ( real > int ) > real ).

thf(func_def_143,type,
    sK52: set_int > ( int > real > $o ) > set_real > real ).

thf(func_def_144,type,
    sK53: set_int > ( int > real > $o ) > set_real > int ).

thf(func_def_145,type,
    sK54: ( real > int > $o ) > set_real > set_int > int ).

thf(func_def_146,type,
    sK55: ( real > int > $o ) > set_real > set_int > real ).

thf(func_def_147,type,
    sK56: ( real > $o ) > real ).

thf(func_def_148,type,
    sK57: poly_real > real > real ).

thf(func_def_149,type,
    sK58: real > poly_real > real > real ).

thf(func_def_150,type,
    sK59: real > poly_real > real > real ).

thf(func_def_151,type,
    sK60: real > poly_real > real > real ).

thf(func_def_152,type,
    sK61: poly_real > real > real > real ).

thf(func_def_153,type,
    sK62: poly_real > real > real > real ).

thf(func_def_154,type,
    sK63: poly_real > real > real > real ).

thf(func_def_155,type,
    sK64: ( int > real ) > int ).

thf(func_def_156,type,
    sK65: ( int > real ) > int ).

thf(func_def_157,type,
    sK66: real > real ).

thf(func_def_158,type,
    sK67: ( real > int ) > real ).

thf(func_def_159,type,
    sK68: ( real > int ) > real ).

thf(func_def_160,type,
    sK69: ( real > $o ) > ( real > $o ) > real ).

thf(func_def_161,type,
    sK70: poly_real > real > real > real ).

thf(func_def_162,type,
    sK71: ( real > int ) > real ).

thf(func_def_163,type,
    sK72: ( real > int ) > real ).

thf(func_def_164,type,
    sK73: ( real > $o ) > real > real > real ).

thf(func_def_165,type,
    sK74: real > ( real > $o ) > real > real ).

thf(func_def_166,type,
    sK75: ( real > real > $o ) > set_real > set_real > real ).

thf(func_def_167,type,
    sK76: ( real > real > $o ) > set_real > set_real > real ).

thf(func_def_168,type,
    sK77: real > real ).

thf(func_def_169,type,
    sK78: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_170,type,
    sK79: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_171,type,
    sK80: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_172,type,
    sK81: ( int > real ) > int ).

thf(func_def_173,type,
    sK82: ( int > real ) > int ).

thf(func_def_174,type,
    sK83: ( int > real ) > int ).

thf(func_def_175,type,
    sK84: ( int > real ) > int ).

thf(func_def_176,type,
    sK85: ( int > real ) > int ).

thf(func_def_177,type,
    sK86: ( int > real ) > int ).

thf(func_def_178,type,
    sK87: ( real > real ) > real ).

thf(func_def_179,type,
    sK88: ( real > real ) > real ).

thf(func_def_180,type,
    sK89: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_181,type,
    sK90: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_182,type,
    sK91: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_183,type,
    sK92: real > real > real ).

thf(func_def_184,type,
    sK93: ( real > $o ) > ( real > $o ) > real ).

thf(func_def_185,type,
    sK94: ( real > real ) > real ).

thf(func_def_186,type,
    sK95: ( real > real ) > real ).

thf(func_def_187,type,
    sK96: ( real > real ) > real ).

thf(func_def_188,type,
    sK97: ( real > real ) > real ).

thf(func_def_189,type,
    sK98: real > poly_real > real ).

thf(func_def_190,type,
    sK99: ( real > $o ) > ( real > $o ) > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_191,type,
    sK100: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_192,type,
    sK101: real > ( real > $o ) > ( real > $o ) > real ).

thf(func_def_193,type,
    sK102: ( real > real ) > real ).

thf(func_def_194,type,
    sK103: ( real > real ) > real ).

thf(func_def_195,type,
    sK104: ( real > real ) > real ).

thf(func_def_196,type,
    sK105: ( real > real ) > real ).

thf(func_def_197,type,
    sK106: real > real > real > real ).

thf(func_def_198,type,
    sK107: ( real > $o ) > ( real > $o ) > real ).

thf(func_def_199,type,
    sK108: real > real > real ).

thf(func_def_200,type,
    sK109: real > real > real ).

thf(func_def_202,type,
    ph111: 
      !>[X0: $tType] : X0 ).

thf(f1781,plain,
    $false,
    inference(subsumption_resolution,[status(thm)],[f1770,f1492]) ).

thf(f1492,plain,
    ( ( finite_finite_real
      @ ( collect_real
        @ ^ [Y0: real] :
            ( ( poly_real2 @ p @ Y0 )
            = zero_zero_real ) ) )
    = $true ),
    inference(cnf_transformation,[status(thm)],[f637]) ).

thf(f637,plain,
    ( ( finite_finite_real
      @ ( collect_real
        @ ^ [Y0: real] :
            ( ( poly_real2 @ p @ Y0 )
            = zero_zero_real ) ) )
    = $true ),
    inference(fool_elimination,[status(thm)],[f636]) ).

thf(f636,plain,
    ( finite_finite_real
    @ ( collect_real
      @ ^ [X0: real] :
          ( ( poly_real2 @ p @ X0 )
          = zero_zero_real ) ) ),
    inference(rectify,[status(thm)],[f1]) ).

thf(f1,axiom,
    ( finite_finite_real
    @ ( collect_real
      @ ^ [X0: real] :
          ( ( poly_real2 @ p @ X0 )
          = zero_zero_real ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.JM2D9zVyZJ/DTF2THF_31682.p',fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062) ).

thf(f1770,plain,
    ( ( finite_finite_real
      @ ( collect_real
        @ ^ [Y0: real] :
            ( ( poly_real2 @ p @ Y0 )
            = zero_zero_real ) ) )
   != $true ),
    inference(trivial_inequality_removal,[status(thm)],[f1761]) ).

thf(f1761,plain,
    ( ( ( finite_finite_real
        @ ( collect_real
          @ ^ [Y0: real] :
              ( ( poly_real2 @ p @ Y0 )
              = zero_zero_real ) ) )
     != $true )
    | ( $true != $true ) ),
    inference(superposition,[status(thm)],[f1727,f1468]) ).

thf(f1468,plain,
    ! [X0: real > $o,X1: real > $o] :
      ( ( ( finite_finite_real
          @ ( collect_real
            @ ^ [Y0: real] :
                ( ( X1 @ Y0 )
                & ( X0 @ Y0 ) ) ) )
        = $true )
      | ( ( finite_finite_real @ ( collect_real @ X1 ) )
       != $true ) ),
    inference(cnf_transformation,[status(thm)],[f1114]) ).

thf(f1114,plain,
    ! [X0: real > $o,X1: real > $o] :
      ( ( ( ( finite_finite_real @ ( collect_real @ X1 ) )
         != $true )
        & ( ( finite_finite_real @ ( collect_real @ X0 ) )
         != $true ) )
      | ( ( finite_finite_real
          @ ( collect_real
            @ ^ [Y0: real] :
                ( ( X1 @ Y0 )
                & ( X0 @ Y0 ) ) ) )
        = $true ) ),
    inference(ennf_transformation,[status(thm)],[f903]) ).

thf(f903,plain,
    ! [X0: real > $o,X1: real > $o] :
      ( ( ( ( finite_finite_real @ ( collect_real @ X0 ) )
          = $true )
        | ( ( finite_finite_real @ ( collect_real @ X1 ) )
          = $true ) )
     => ( ( finite_finite_real
          @ ( collect_real
            @ ^ [Y0: real] :
                ( ( X1 @ Y0 )
                & ( X0 @ Y0 ) ) ) )
        = $true ) ),
    inference(fool_elimination,[status(thm)],[f902]) ).

thf(f902,plain,
    ! [X0: real > $o,X1: real > $o] :
      ( ( ( finite_finite_real @ ( collect_real @ X0 ) )
        | ( finite_finite_real @ ( collect_real @ X1 ) ) )
     => ( finite_finite_real
        @ ( collect_real
          @ ^ [X2: real] :
              ( ( X0 @ X2 )
              & ( X1 @ X2 ) ) ) ) ),
    inference(rectify,[status(thm)],[f12]) ).

thf(f12,axiom,
    ! [X3: real > $o,X4: real > $o] :
      ( ( ( finite_finite_real @ ( collect_real @ X3 ) )
        | ( finite_finite_real @ ( collect_real @ X4 ) ) )
     => ( finite_finite_real
        @ ( collect_real
          @ ^ [X0: real] :
              ( ( X3 @ X0 )
              & ( X4 @ X0 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.JM2D9zVyZJ/DTF2THF_31682.p',fact_11_finite__Collect__conjI) ).

thf(f1727,plain,
    ( ( finite_finite_real
      @ ( collect_real
        @ ^ [Y0: real] :
            ( ( ( poly_real2 @ p @ Y0 )
              = zero_zero_real )
            & ( ord_less_real @ a @ Y0 ) ) ) )
   != $true ),
    inference(trivial_inequality_removal,[status(thm)],[f1725]) ).

thf(f1725,plain,
    ( ( ( finite_finite_real
        @ ( collect_real
          @ ^ [Y0: real] :
              ( ( ( poly_real2 @ p @ Y0 )
                = zero_zero_real )
              & ( ord_less_real @ a @ Y0 ) ) ) )
     != $true )
    | ( $true != $true ) ),
    inference(superposition,[status(thm)],[f1677,f1468]) ).

thf(f1677,plain,
    ( ( finite_finite_real
      @ ( collect_real
        @ ^ [Y0: real] :
            ( ( ( poly_real2 @ p @ Y0 )
              = zero_zero_real )
            & ( ord_less_real @ a @ Y0 )
            & ( ord_less_real @ Y0 @ b ) ) ) )
   != $true ),
    inference(cnf_transformation,[status(thm)],[f1017]) ).

thf(f1017,plain,
    ( ( finite_finite_real
      @ ( collect_real
        @ ^ [Y0: real] :
            ( ( ( poly_real2 @ p @ Y0 )
              = zero_zero_real )
            & ( ord_less_real @ a @ Y0 )
            & ( ord_less_real @ Y0 @ b ) ) ) )
   != $true ),
    inference(flattening,[status(thm)],[f745]) ).

thf(f745,plain,
    ( ( finite_finite_real
      @ ( collect_real
        @ ^ [Y0: real] :
            ( ( ( poly_real2 @ p @ Y0 )
              = zero_zero_real )
            & ( ord_less_real @ a @ Y0 )
            & ( ord_less_real @ Y0 @ b ) ) ) )
   != $true ),
    inference(fool_elimination,[status(thm)],[f744]) ).

thf(f744,plain,
    ~ ( finite_finite_real
      @ ( collect_real
        @ ^ [X0: real] :
            ( ( ord_less_real @ X0 @ b )
            & ( ord_less_real @ a @ X0 )
            & ( ( poly_real2 @ p @ X0 )
              = zero_zero_real ) ) ) ),
    inference(rectify,[status(thm)],[f352]) ).

thf(f352,negated_conjecture,
    ~ ( finite_finite_real
      @ ( collect_real
        @ ^ [X0: real] :
            ( ( ord_less_real @ X0 @ b )
            & ( ord_less_real @ a @ X0 )
            & ( ( poly_real2 @ p @ X0 )
              = zero_zero_real ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f351]) ).

thf(f351,conjecture,
    ( finite_finite_real
    @ ( collect_real
      @ ^ [X0: real] :
          ( ( ord_less_real @ X0 @ b )
          & ( ord_less_real @ a @ X0 )
          & ( ( poly_real2 @ p @ X0 )
            = zero_zero_real ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.JM2D9zVyZJ/DTF2THF_31682.p',conj_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP193^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13  % Command  : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33  % Computer : n010.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
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Tue Feb 24 08:29:18 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
% 0.28/0.45  ---- Original DTF file ---
% 0.28/0.45  thf(spec,logic,$$dhol).
% 0.28/0.45  %------------------------------------------------------------------------------
% 0.28/0.45  % File     : ITP193^1 : TPTP v9.2.1. Released v7.5.0.
% 0.28/0.45  % Domain   : Interactive Theorem Proving
% 0.28/0.45  % Problem  : Sledgehammer Sturm_Tarski problem prob_1192__5884460_1
% 0.28/0.45  % Version  : Especial.
% 0.28/0.45  % English  :
% 0.28/0.45  
% 0.28/0.45  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.45  %          : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.45  % Source   : [Des21]
% 0.28/0.45  % Names    : Sturm_Tarski/prob_1192__5884460_1 [Des21]
% 0.28/0.45  
% 0.28/0.45  % Status   : Theorem
% 0.28/0.45  % 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
% 0.28/0.45  % Syntax   : Number of formulae    :  426 ( 113 unt;  75 typ;   0 def)
% 0.28/0.45  %            Number of atoms       : 1144 ( 273 equ;   0 cnn)
% 0.28/0.45  %            Maximal formula atoms :   12 (   3 avg)
% 0.28/0.45  %            Number of connectives : 3014 ( 146   ~;  43   |;  87   &;2157   @)
% 0.28/0.45  %                                         (   0 <=>; 581  =>;   0  <=;   0 <~>)
% 0.28/0.45  %            Maximal formula depth :   18 (   7 avg)
% 0.28/0.45  %            Number of types       :   16 (  15 usr)
% 0.28/0.45  %            Number of type conns  :  215 ( 215   >;   0   *;   0   +;   0  <<)
% 0.28/0.45  %            Number of symbols     :   61 (  60 usr;  14 con; 0-4 aty)
% 0.28/0.45  %            Number of variables   : 1091 (  95   ^; 927   !;  69   ?;1091   :)
% 0.28/0.45  % SPC      : TH0_THM_EQU_NAR
% 0.28/0.45  
% 0.28/0.45  % Comments : This file was generated by Sledgehammer 2021-02-23 15:44:34.506
% 0.28/0.45  %------------------------------------------------------------------------------
% 0.28/0.45  % Could-be-implicit typings (15)
% 0.28/0.45  thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.28/0.45      poly_poly_poly_real: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.28/0.45      set_poly_poly_real: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.28/0.45      poly_poly_real: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Int__Oint_J_J,type,
% 0.28/0.45      poly_poly_int: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.28/0.45      set_poly_real: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Int__Oint_J_J,type,
% 0.28/0.45      set_poly_int: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Real__Oreal_J_J,type,
% 0.28/0.45      set_set_real: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 0.28/0.45      set_set_int: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.28/0.45      poly_real: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.28/0.45      poly_int: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.45      set_real: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.45      set_int: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Real__Oreal,type,
% 0.28/0.45      real: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Nat__Onat,type,
% 0.28/0.45      nat: $tType ).
% 0.28/0.45  
% 0.28/0.45  thf(ty_n_t__Int__Oint,type,
% 0.28/0.45      int: $tType ).
% 0.28/0.45  
% 0.28/0.45  % Explicit typings (60)
% 0.28/0.45  thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 0.28/0.45      finite_finite_int: set_int > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Finite__Set_Ofinite_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.28/0.45      finite385822667ly_int: set_poly_int > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Finite__Set_Ofinite_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.28/0.45      finite1328464339y_real: set_poly_poly_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Finite__Set_Ofinite_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.28/0.45      finite1810960971y_real: set_poly_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 0.28/0.45      finite_finite_real: set_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.45      finite26677625et_int: set_set_int > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.45      finite475462905t_real: set_set_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 0.28/0.45      one_one_int: int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.28/0.45      one_one_poly_real: poly_real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 0.28/0.45      zero_zero_int: int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.28/0.45      zero_zero_poly_int: poly_int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Int__Oint_J_J,type,
% 0.28/0.45      zero_z1549157189ly_int: poly_poly_int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 0.28/0.45      zero_z935034829y_real: poly_poly_poly_real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.28/0.45      zero_z1423781445y_real: poly_poly_real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.28/0.45      zero_zero_poly_real: poly_real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 0.28/0.45      zero_zero_real: real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Int__Oint,type,
% 0.28/0.45      groups2051521940al_int: ( real > int ) > set_real > int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 0.28/0.45      ord_less_int: int > int > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.28/0.45      ord_less_poly_int: poly_int > poly_int > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.28/0.45      ord_le38482960y_real: poly_poly_real > poly_poly_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.28/0.45      ord_less_poly_real: poly_real > poly_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 0.28/0.45      ord_less_real: real > real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.45      ord_less_set_int: set_int > set_int > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.45      ord_less_set_real: set_real > set_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Real__Oreal_M_Eo_J,type,
% 0.28/0.45      ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 0.28/0.45      ord_less_eq_int: int > int > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.28/0.45      ord_less_eq_poly_int: poly_int > poly_int > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.28/0.45      ord_le893774876y_real: poly_poly_real > poly_poly_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.28/0.45      ord_le1180086932y_real: poly_real > poly_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 0.28/0.45      ord_less_eq_real: real > real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.45      ord_less_eq_set_int: set_int > set_int > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.45      ord_less_eq_set_real: set_real > set_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Polynomial_Ois__zero_001t__Int__Oint,type,
% 0.28/0.45      is_zero_int: poly_int > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.28/0.45      is_zero_poly_real: poly_poly_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Polynomial_Ois__zero_001t__Real__Oreal,type,
% 0.28/0.45      is_zero_real: poly_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Polynomial_Opoly_001t__Int__Oint,type,
% 0.28/0.45      poly_int2: poly_int > int > int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.28/0.45      poly_poly_int2: poly_poly_int > poly_int > poly_int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.28/0.45      poly_poly_poly_real2: poly_poly_poly_real > poly_poly_real > poly_poly_real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.28/0.45      poly_poly_real2: poly_poly_real > poly_real > poly_real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Polynomial_Opoly_001t__Real__Oreal,type,
% 0.28/0.45      poly_real2: poly_real > real > real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Polynomial_Opoly__cutoff_001t__Int__Oint,type,
% 0.28/0.45      poly_cutoff_int: nat > poly_int > poly_int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Polynomial_Opoly__cutoff_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.28/0.45      poly_c1404107022y_real: nat > poly_poly_real > poly_poly_real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Polynomial_Opoly__cutoff_001t__Real__Oreal,type,
% 0.28/0.45      poly_cutoff_real: nat > poly_real > poly_real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 0.28/0.45      collect_int: ( int > $o ) > set_int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Set_OCollect_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 0.28/0.45      collect_poly_int: ( poly_int > $o ) > set_poly_int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Set_OCollect_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 0.28/0.45      collec927113489y_real: ( poly_poly_real > $o ) > set_poly_poly_real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Set_OCollect_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 0.28/0.45      collect_poly_real: ( poly_real > $o ) > set_poly_real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 0.28/0.45      collect_real: ( real > $o ) > set_real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Int__Oint_J,type,
% 0.28/0.45      collect_set_int: ( set_int > $o ) > set_set_int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Real__Oreal_J,type,
% 0.28/0.45      collect_set_real: ( set_real > $o ) > set_set_real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Sturm__Tarski__Mirabelle__skihomvtkj_Ocindex__poly,type,
% 0.28/0.45      sturm_308542325x_poly: real > real > poly_real > poly_real > int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Sturm__Tarski__Mirabelle__skihomvtkj_Ocross,type,
% 0.28/0.45      sturm_1953858694_cross: poly_real > real > real > int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_Sturm__Tarski__Mirabelle__skihomvtkj_Ojump__poly,type,
% 0.28/0.45      sturm_276991412p_poly: poly_real > poly_real > real > int ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_member_001t__Int__Oint,type,
% 0.28/0.45      member_int: int > set_int > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_c_member_001t__Real__Oreal,type,
% 0.28/0.45      member_real: real > set_real > $o ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_v_a,type,
% 0.28/0.45      a: real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_v_a_H,type,
% 0.28/0.45      a2: real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_v_b,type,
% 0.28/0.45      b: real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_v_b_H,type,
% 0.28/0.45      b2: real ).
% 0.28/0.45  
% 0.28/0.45  thf(sy_v_p,type,
% 0.28/0.45      p: poly_real ).
% 0.28/0.45  
% 0.28/0.45  % Relevant facts (350)
% 0.28/0.45  thf(fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062,axiom,
% 0.28/0.45      ( finite_finite_real
% 0.28/0.45      @ ( collect_real
% 0.28/0.45        @ ^ [X: real] :
% 0.28/0.45            ( ( poly_real2 @ p @ X )
% 0.28/0.45            = zero_zero_real ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % \<open>finite {x. poly p x = 0}\<close>
% 0.28/0.45  thf(fact_1_assms_I2_J,axiom,
% 0.28/0.45      ord_less_real @ a2 @ b2 ).
% 0.28/0.45  
% 0.28/0.45  % assms(2)
% 0.28/0.45  thf(fact_2_assms_I3_J,axiom,
% 0.28/0.45      ord_less_real @ b2 @ b ).
% 0.28/0.45  
% 0.28/0.45  % assms(3)
% 0.28/0.45  thf(fact_3_assms_I1_J,axiom,
% 0.28/0.45      ord_less_real @ a @ a2 ).
% 0.28/0.45  
% 0.28/0.45  % assms(1)
% 0.28/0.45  thf(fact_4_False,axiom,
% 0.28/0.45      p != zero_zero_poly_real ).
% 0.28/0.45  
% 0.28/0.45  % False
% 0.28/0.45  thf(fact_5_poly__0,axiom,
% 0.28/0.45      ! [X2: poly_int] :
% 0.28/0.45        ( ( poly_poly_int2 @ zero_z1549157189ly_int @ X2 )
% 0.28/0.45        = zero_zero_poly_int ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_0
% 0.28/0.45  thf(fact_6_poly__0,axiom,
% 0.28/0.45      ! [X2: poly_poly_real] :
% 0.28/0.45        ( ( poly_poly_poly_real2 @ zero_z935034829y_real @ X2 )
% 0.28/0.45        = zero_z1423781445y_real ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_0
% 0.28/0.45  thf(fact_7_poly__0,axiom,
% 0.28/0.45      ! [X2: poly_real] :
% 0.28/0.45        ( ( poly_poly_real2 @ zero_z1423781445y_real @ X2 )
% 0.28/0.45        = zero_zero_poly_real ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_0
% 0.28/0.45  thf(fact_8_poly__0,axiom,
% 0.28/0.45      ! [X2: int] :
% 0.28/0.45        ( ( poly_int2 @ zero_zero_poly_int @ X2 )
% 0.28/0.45        = zero_zero_int ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_0
% 0.28/0.45  thf(fact_9_poly__0,axiom,
% 0.28/0.45      ! [X2: real] :
% 0.28/0.45        ( ( poly_real2 @ zero_zero_poly_real @ X2 )
% 0.28/0.45        = zero_zero_real ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_0
% 0.28/0.45  thf(fact_10_assms_I4_J,axiom,
% 0.28/0.45      ! [X3: real] :
% 0.28/0.45        ( ( ( ( ord_less_real @ a @ X3 )
% 0.28/0.45            & ( ord_less_eq_real @ X3 @ a2 ) )
% 0.28/0.45          | ( ( ord_less_eq_real @ b2 @ X3 )
% 0.28/0.45            & ( ord_less_real @ X3 @ b ) ) )
% 0.28/0.45       => ( ( poly_real2 @ p @ X3 )
% 0.28/0.45         != zero_zero_real ) ) ).
% 0.28/0.45  
% 0.28/0.45  % assms(4)
% 0.28/0.45  thf(fact_11_finite__Collect__conjI,axiom,
% 0.28/0.45      ! [P: real > $o,Q: real > $o] :
% 0.28/0.45        ( ( ( finite_finite_real @ ( collect_real @ P ) )
% 0.28/0.45          | ( finite_finite_real @ ( collect_real @ Q ) ) )
% 0.28/0.45       => ( finite_finite_real
% 0.28/0.45          @ ( collect_real
% 0.28/0.45            @ ^ [X: real] :
% 0.28/0.45                ( ( P @ X )
% 0.28/0.45                & ( Q @ X ) ) ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % finite_Collect_conjI
% 0.28/0.45  thf(fact_12_finite__Collect__conjI,axiom,
% 0.28/0.45      ! [P: int > $o,Q: int > $o] :
% 0.28/0.45        ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 0.28/0.45          | ( finite_finite_int @ ( collect_int @ Q ) ) )
% 0.28/0.45       => ( finite_finite_int
% 0.28/0.45          @ ( collect_int
% 0.28/0.45            @ ^ [X: int] :
% 0.28/0.45                ( ( P @ X )
% 0.28/0.45                & ( Q @ X ) ) ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % finite_Collect_conjI
% 0.28/0.45  thf(fact_13_finite__Collect__disjI,axiom,
% 0.28/0.45      ! [P: real > $o,Q: real > $o] :
% 0.28/0.45        ( ( finite_finite_real
% 0.28/0.45          @ ( collect_real
% 0.28/0.45            @ ^ [X: real] :
% 0.28/0.45                ( ( P @ X )
% 0.28/0.45                | ( Q @ X ) ) ) )
% 0.28/0.45        = ( ( finite_finite_real @ ( collect_real @ P ) )
% 0.28/0.45          & ( finite_finite_real @ ( collect_real @ Q ) ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % finite_Collect_disjI
% 0.28/0.45  thf(fact_14_finite__Collect__disjI,axiom,
% 0.28/0.45      ! [P: int > $o,Q: int > $o] :
% 0.28/0.45        ( ( finite_finite_int
% 0.28/0.45          @ ( collect_int
% 0.28/0.45            @ ^ [X: int] :
% 0.28/0.45                ( ( P @ X )
% 0.28/0.45                | ( Q @ X ) ) ) )
% 0.28/0.45        = ( ( finite_finite_int @ ( collect_int @ P ) )
% 0.28/0.45          & ( finite_finite_int @ ( collect_int @ Q ) ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % finite_Collect_disjI
% 0.28/0.45  thf(fact_15_poly__roots__finite,axiom,
% 0.28/0.45      ! [P2: poly_poly_int] :
% 0.28/0.45        ( ( P2 != zero_z1549157189ly_int )
% 0.28/0.45       => ( finite385822667ly_int
% 0.28/0.45          @ ( collect_poly_int
% 0.28/0.45            @ ^ [X: poly_int] :
% 0.28/0.45                ( ( poly_poly_int2 @ P2 @ X )
% 0.28/0.45                = zero_zero_poly_int ) ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_roots_finite
% 0.28/0.45  thf(fact_16_poly__roots__finite,axiom,
% 0.28/0.45      ! [P2: poly_poly_poly_real] :
% 0.28/0.45        ( ( P2 != zero_z935034829y_real )
% 0.28/0.45       => ( finite1328464339y_real
% 0.28/0.45          @ ( collec927113489y_real
% 0.28/0.45            @ ^ [X: poly_poly_real] :
% 0.28/0.45                ( ( poly_poly_poly_real2 @ P2 @ X )
% 0.28/0.45                = zero_z1423781445y_real ) ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_roots_finite
% 0.28/0.45  thf(fact_17_poly__roots__finite,axiom,
% 0.28/0.45      ! [P2: poly_real] :
% 0.28/0.45        ( ( P2 != zero_zero_poly_real )
% 0.28/0.45       => ( finite_finite_real
% 0.28/0.45          @ ( collect_real
% 0.28/0.45            @ ^ [X: real] :
% 0.28/0.45                ( ( poly_real2 @ P2 @ X )
% 0.28/0.45                = zero_zero_real ) ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_roots_finite
% 0.28/0.45  thf(fact_18_poly__roots__finite,axiom,
% 0.28/0.45      ! [P2: poly_int] :
% 0.28/0.45        ( ( P2 != zero_zero_poly_int )
% 0.28/0.45       => ( finite_finite_int
% 0.28/0.45          @ ( collect_int
% 0.28/0.45            @ ^ [X: int] :
% 0.28/0.45                ( ( poly_int2 @ P2 @ X )
% 0.28/0.45                = zero_zero_int ) ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_roots_finite
% 0.28/0.45  thf(fact_19_poly__roots__finite,axiom,
% 0.28/0.45      ! [P2: poly_poly_real] :
% 0.28/0.45        ( ( P2 != zero_z1423781445y_real )
% 0.28/0.45       => ( finite1810960971y_real
% 0.28/0.45          @ ( collect_poly_real
% 0.28/0.45            @ ^ [X: poly_real] :
% 0.28/0.45                ( ( poly_poly_real2 @ P2 @ X )
% 0.28/0.45                = zero_zero_poly_real ) ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_roots_finite
% 0.28/0.45  thf(fact_20_poly__IVT__neg,axiom,
% 0.28/0.45      ! [A: real,B: real,P2: poly_real] :
% 0.28/0.45        ( ( ord_less_real @ A @ B )
% 0.28/0.45       => ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P2 @ A ) )
% 0.28/0.45         => ( ( ord_less_real @ ( poly_real2 @ P2 @ B ) @ zero_zero_real )
% 0.28/0.45           => ? [X4: real] :
% 0.28/0.45                ( ( ord_less_real @ A @ X4 )
% 0.28/0.45                & ( ord_less_real @ X4 @ B )
% 0.28/0.45                & ( ( poly_real2 @ P2 @ X4 )
% 0.28/0.45                  = zero_zero_real ) ) ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_IVT_neg
% 0.28/0.45  thf(fact_21_poly__IVT__pos,axiom,
% 0.28/0.45      ! [A: real,B: real,P2: poly_real] :
% 0.28/0.45        ( ( ord_less_real @ A @ B )
% 0.28/0.45       => ( ( ord_less_real @ ( poly_real2 @ P2 @ A ) @ zero_zero_real )
% 0.28/0.45         => ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P2 @ B ) )
% 0.28/0.45           => ? [X4: real] :
% 0.28/0.45                ( ( ord_less_real @ A @ X4 )
% 0.28/0.45                & ( ord_less_real @ X4 @ B )
% 0.28/0.45                & ( ( poly_real2 @ P2 @ X4 )
% 0.28/0.45                  = zero_zero_real ) ) ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_IVT_pos
% 0.28/0.45  thf(fact_22_poly__all__0__iff__0,axiom,
% 0.28/0.45      ! [P2: poly_real] :
% 0.28/0.45        ( ( ! [X: real] :
% 0.28/0.45              ( ( poly_real2 @ P2 @ X )
% 0.28/0.45              = zero_zero_real ) )
% 0.28/0.45        = ( P2 = zero_zero_poly_real ) ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_all_0_iff_0
% 0.28/0.45  thf(fact_23_poly__all__0__iff__0,axiom,
% 0.28/0.45      ! [P2: poly_poly_real] :
% 0.28/0.45        ( ( ! [X: poly_real] :
% 0.28/0.45              ( ( poly_poly_real2 @ P2 @ X )
% 0.28/0.45              = zero_zero_poly_real ) )
% 0.28/0.45        = ( P2 = zero_z1423781445y_real ) ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_all_0_iff_0
% 0.28/0.45  thf(fact_24_poly__all__0__iff__0,axiom,
% 0.28/0.45      ! [P2: poly_int] :
% 0.28/0.45        ( ( ! [X: int] :
% 0.28/0.45              ( ( poly_int2 @ P2 @ X )
% 0.28/0.45              = zero_zero_int ) )
% 0.28/0.45        = ( P2 = zero_zero_poly_int ) ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_all_0_iff_0
% 0.28/0.45  thf(fact_25_poly__all__0__iff__0,axiom,
% 0.28/0.45      ! [P2: poly_poly_int] :
% 0.28/0.45        ( ( ! [X: poly_int] :
% 0.28/0.45              ( ( poly_poly_int2 @ P2 @ X )
% 0.28/0.45              = zero_zero_poly_int ) )
% 0.28/0.45        = ( P2 = zero_z1549157189ly_int ) ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_all_0_iff_0
% 0.28/0.45  thf(fact_26_poly__all__0__iff__0,axiom,
% 0.28/0.45      ! [P2: poly_poly_poly_real] :
% 0.28/0.45        ( ( ! [X: poly_poly_real] :
% 0.28/0.45              ( ( poly_poly_poly_real2 @ P2 @ X )
% 0.28/0.45              = zero_z1423781445y_real ) )
% 0.28/0.45        = ( P2 = zero_z935034829y_real ) ) ).
% 0.28/0.45  
% 0.28/0.45  % poly_all_0_iff_0
% 0.28/0.45  thf(fact_27_less__numeral__extra_I3_J,axiom,
% 0.28/0.45      ~ ( ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real ) ).
% 0.28/0.45  
% 0.28/0.45  % less_numeral_extra(3)
% 0.28/0.45  thf(fact_28_less__numeral__extra_I3_J,axiom,
% 0.28/0.45      ~ ( ord_less_poly_int @ zero_zero_poly_int @ zero_zero_poly_int ) ).
% 0.28/0.45  
% 0.28/0.45  % less_numeral_extra(3)
% 0.28/0.45  thf(fact_29_less__numeral__extra_I3_J,axiom,
% 0.28/0.45      ~ ( ord_le38482960y_real @ zero_z1423781445y_real @ zero_z1423781445y_real ) ).
% 0.28/0.45  
% 0.28/0.45  % less_numeral_extra(3)
% 0.28/0.45  thf(fact_30_less__numeral__extra_I3_J,axiom,
% 0.28/0.45      ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 0.28/0.45  
% 0.28/0.45  % less_numeral_extra(3)
% 0.28/0.45  thf(fact_31_less__numeral__extra_I3_J,axiom,
% 0.28/0.45      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.28/0.45  
% 0.28/0.45  % less_numeral_extra(3)
% 0.28/0.45  thf(fact_32_le__numeral__extra_I3_J,axiom,
% 0.28/0.45      ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real ).
% 0.28/0.45  
% 0.28/0.45  % le_numeral_extra(3)
% 0.28/0.45  thf(fact_33_le__numeral__extra_I3_J,axiom,
% 0.28/0.45      ord_less_eq_poly_int @ zero_zero_poly_int @ zero_zero_poly_int ).
% 0.28/0.45  
% 0.28/0.45  % le_numeral_extra(3)
% 0.28/0.45  thf(fact_34_le__numeral__extra_I3_J,axiom,
% 0.28/0.45      ord_le893774876y_real @ zero_z1423781445y_real @ zero_z1423781445y_real ).
% 0.28/0.45  
% 0.28/0.45  % le_numeral_extra(3)
% 0.28/0.45  thf(fact_35_le__numeral__extra_I3_J,axiom,
% 0.28/0.45      ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 0.28/0.45  
% 0.28/0.45  % le_numeral_extra(3)
% 0.28/0.45  thf(fact_36_le__numeral__extra_I3_J,axiom,
% 0.28/0.45      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.28/0.45  
% 0.28/0.45  % le_numeral_extra(3)
% 0.28/0.45  thf(fact_37_finite__psubset__induct,axiom,
% 0.28/0.45      ! [A2: set_real,P: set_real > $o] :
% 0.28/0.45        ( ( finite_finite_real @ A2 )
% 0.28/0.45       => ( ! [A3: set_real] :
% 0.28/0.45              ( ( finite_finite_real @ A3 )
% 0.28/0.45             => ( ! [B2: set_real] :
% 0.28/0.45                    ( ( ord_less_set_real @ B2 @ A3 )
% 0.28/0.45                   => ( P @ B2 ) )
% 0.28/0.45               => ( P @ A3 ) ) )
% 0.28/0.45         => ( P @ A2 ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % finite_psubset_induct
% 0.28/0.45  thf(fact_38_finite__psubset__induct,axiom,
% 0.28/0.45      ! [A2: set_int,P: set_int > $o] :
% 0.28/0.45        ( ( finite_finite_int @ A2 )
% 0.28/0.45       => ( ! [A3: set_int] :
% 0.28/0.45              ( ( finite_finite_int @ A3 )
% 0.28/0.45             => ( ! [B2: set_int] :
% 0.28/0.45                    ( ( ord_less_set_int @ B2 @ A3 )
% 0.28/0.45                   => ( P @ B2 ) )
% 0.28/0.45               => ( P @ A3 ) ) )
% 0.28/0.45         => ( P @ A2 ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % finite_psubset_induct
% 0.28/0.45  thf(fact_39_finite__has__minimal2,axiom,
% 0.28/0.45      ! [A2: set_real,A: real] :
% 0.28/0.45        ( ( finite_finite_real @ A2 )
% 0.28/0.45       => ( ( member_real @ A @ A2 )
% 0.28/0.45         => ? [X4: real] :
% 0.28/0.45              ( ( member_real @ X4 @ A2 )
% 0.28/0.45              & ( ord_less_eq_real @ X4 @ A )
% 0.28/0.45              & ! [Xa: real] :
% 0.28/0.45                  ( ( member_real @ Xa @ A2 )
% 0.28/0.45                 => ( ( ord_less_eq_real @ Xa @ X4 )
% 0.28/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.28/0.45  
% 0.28/0.45  % finite_has_minimal2
% 0.28/0.45  thf(fact_40_finite__has__minimal2,axiom,
% 0.28/0.45      ! [A2: set_int,A: int] :
% 0.28/0.45        ( ( finite_finite_int @ A2 )
% 0.28/0.45       => ( ( member_int @ A @ A2 )
% 0.28/0.45         => ? [X4: int] :
% 0.28/0.45              ( ( member_int @ X4 @ A2 )
% 0.28/0.45              & ( ord_less_eq_int @ X4 @ A )
% 0.28/0.45              & ! [Xa: int] :
% 0.28/0.45                  ( ( member_int @ Xa @ A2 )
% 0.28/0.45                 => ( ( ord_less_eq_int @ Xa @ X4 )
% 0.28/0.45                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % finite_has_minimal2
% 0.28/0.46  thf(fact_41_finite__has__maximal2,axiom,
% 0.28/0.46      ! [A2: set_real,A: real] :
% 0.28/0.46        ( ( finite_finite_real @ A2 )
% 0.28/0.46       => ( ( member_real @ A @ A2 )
% 0.28/0.46         => ? [X4: real] :
% 0.28/0.46              ( ( member_real @ X4 @ A2 )
% 0.28/0.46              & ( ord_less_eq_real @ A @ X4 )
% 0.28/0.46              & ! [Xa: real] :
% 0.28/0.46                  ( ( member_real @ Xa @ A2 )
% 0.28/0.46                 => ( ( ord_less_eq_real @ X4 @ Xa )
% 0.28/0.46                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % finite_has_maximal2
% 0.28/0.46  thf(fact_42_finite__has__maximal2,axiom,
% 0.28/0.46      ! [A2: set_int,A: int] :
% 0.28/0.46        ( ( finite_finite_int @ A2 )
% 0.28/0.46       => ( ( member_int @ A @ A2 )
% 0.28/0.46         => ? [X4: int] :
% 0.28/0.46              ( ( member_int @ X4 @ A2 )
% 0.28/0.46              & ( ord_less_eq_int @ A @ X4 )
% 0.28/0.46              & ! [Xa: int] :
% 0.28/0.46                  ( ( member_int @ Xa @ A2 )
% 0.28/0.46                 => ( ( ord_less_eq_int @ X4 @ Xa )
% 0.28/0.46                   => ( X4 = Xa ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % finite_has_maximal2
% 0.28/0.46  thf(fact_43_next__non__root__interval,axiom,
% 0.28/0.46      ! [P2: poly_real,Lb: real] :
% 0.28/0.46        ( ( P2 != zero_zero_poly_real )
% 0.28/0.46       => ~ ! [Ub: real] :
% 0.28/0.46              ( ( ord_less_real @ Lb @ Ub )
% 0.28/0.46             => ~ ! [Z: real] :
% 0.28/0.46                    ( ( ( ord_less_real @ Lb @ Z )
% 0.28/0.46                      & ( ord_less_eq_real @ Z @ Ub ) )
% 0.28/0.46                   => ( ( poly_real2 @ P2 @ Z )
% 0.28/0.46                     != zero_zero_real ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % next_non_root_interval
% 0.28/0.46  thf(fact_44_last__non__root__interval,axiom,
% 0.28/0.46      ! [P2: poly_real,Ub2: real] :
% 0.28/0.46        ( ( P2 != zero_zero_poly_real )
% 0.28/0.46       => ~ ! [Lb2: real] :
% 0.28/0.46              ( ( ord_less_real @ Lb2 @ Ub2 )
% 0.28/0.46             => ~ ! [Z: real] :
% 0.28/0.46                    ( ( ( ord_less_eq_real @ Lb2 @ Z )
% 0.28/0.46                      & ( ord_less_real @ Z @ Ub2 ) )
% 0.28/0.46                   => ( ( poly_real2 @ P2 @ Z )
% 0.28/0.46                     != zero_zero_real ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % last_non_root_interval
% 0.28/0.46  thf(fact_45_zero__reorient,axiom,
% 0.28/0.46      ! [X2: real] :
% 0.28/0.46        ( ( zero_zero_real = X2 )
% 0.28/0.46        = ( X2 = zero_zero_real ) ) ).
% 0.28/0.46  
% 0.28/0.46  % zero_reorient
% 0.28/0.46  thf(fact_46_zero__reorient,axiom,
% 0.28/0.46      ! [X2: poly_real] :
% 0.28/0.46        ( ( zero_zero_poly_real = X2 )
% 0.28/0.46        = ( X2 = zero_zero_poly_real ) ) ).
% 0.28/0.46  
% 0.28/0.46  % zero_reorient
% 0.28/0.46  thf(fact_47_zero__reorient,axiom,
% 0.28/0.46      ! [X2: int] :
% 0.28/0.46        ( ( zero_zero_int = X2 )
% 0.28/0.46        = ( X2 = zero_zero_int ) ) ).
% 0.28/0.46  
% 0.28/0.46  % zero_reorient
% 0.28/0.46  thf(fact_48_zero__reorient,axiom,
% 0.28/0.46      ! [X2: poly_int] :
% 0.28/0.46        ( ( zero_zero_poly_int = X2 )
% 0.28/0.46        = ( X2 = zero_zero_poly_int ) ) ).
% 0.28/0.46  
% 0.28/0.46  % zero_reorient
% 0.28/0.46  thf(fact_49_zero__reorient,axiom,
% 0.28/0.46      ! [X2: poly_poly_real] :
% 0.28/0.46        ( ( zero_z1423781445y_real = X2 )
% 0.28/0.46        = ( X2 = zero_z1423781445y_real ) ) ).
% 0.28/0.46  
% 0.28/0.46  % zero_reorient
% 0.28/0.46  thf(fact_50_not__eq__pos__or__neg__iff__2,axiom,
% 0.28/0.46      ! [Lb: real,Ub2: real,P2: poly_real] :
% 0.28/0.46        ( ( ! [Z2: real] :
% 0.28/0.46              ( ( ( ord_less_eq_real @ Lb @ Z2 )
% 0.28/0.46                & ( ord_less_real @ Z2 @ Ub2 ) )
% 0.28/0.46             => ( ( poly_real2 @ P2 @ Z2 )
% 0.28/0.46               != zero_zero_real ) ) )
% 0.28/0.46        = ( ! [Z2: real] :
% 0.28/0.46              ( ( ( ord_less_eq_real @ Lb @ Z2 )
% 0.28/0.46                & ( ord_less_real @ Z2 @ Ub2 ) )
% 0.28/0.46             => ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P2 @ Z2 ) ) )
% 0.28/0.46          | ! [Z2: real] :
% 0.28/0.46              ( ( ( ord_less_eq_real @ Lb @ Z2 )
% 0.28/0.46                & ( ord_less_real @ Z2 @ Ub2 ) )
% 0.28/0.46             => ( ord_less_real @ ( poly_real2 @ P2 @ Z2 ) @ zero_zero_real ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % not_eq_pos_or_neg_iff_2
% 0.28/0.46  thf(fact_51_not__eq__pos__or__neg__iff__1,axiom,
% 0.28/0.46      ! [Lb: real,Ub2: real,P2: poly_real] :
% 0.28/0.46        ( ( ! [Z2: real] :
% 0.28/0.46              ( ( ( ord_less_real @ Lb @ Z2 )
% 0.28/0.46                & ( ord_less_eq_real @ Z2 @ Ub2 ) )
% 0.28/0.46             => ( ( poly_real2 @ P2 @ Z2 )
% 0.28/0.46               != zero_zero_real ) ) )
% 0.28/0.46        = ( ! [Z2: real] :
% 0.28/0.46              ( ( ( ord_less_real @ Lb @ Z2 )
% 0.28/0.46                & ( ord_less_eq_real @ Z2 @ Ub2 ) )
% 0.28/0.46             => ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P2 @ Z2 ) ) )
% 0.28/0.46          | ! [Z2: real] :
% 0.28/0.46              ( ( ( ord_less_real @ Lb @ Z2 )
% 0.28/0.46                & ( ord_less_eq_real @ Z2 @ Ub2 ) )
% 0.28/0.46             => ( ord_less_real @ ( poly_real2 @ P2 @ Z2 ) @ zero_zero_real ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % not_eq_pos_or_neg_iff_1
% 0.28/0.46  thf(fact_52_poly__eq__poly__eq__iff,axiom,
% 0.28/0.46      ! [P2: poly_real,Q2: poly_real] :
% 0.28/0.46        ( ( ( poly_real2 @ P2 )
% 0.28/0.46          = ( poly_real2 @ Q2 ) )
% 0.28/0.46        = ( P2 = Q2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % poly_eq_poly_eq_iff
% 0.28/0.46  thf(fact_53_poly__eq__poly__eq__iff,axiom,
% 0.28/0.46      ! [P2: poly_int,Q2: poly_int] :
% 0.28/0.46        ( ( ( poly_int2 @ P2 )
% 0.28/0.46          = ( poly_int2 @ Q2 ) )
% 0.28/0.46        = ( P2 = Q2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % poly_eq_poly_eq_iff
% 0.28/0.46  thf(fact_54_poly__eq__poly__eq__iff,axiom,
% 0.28/0.46      ! [P2: poly_poly_real,Q2: poly_poly_real] :
% 0.28/0.46        ( ( ( poly_poly_real2 @ P2 )
% 0.28/0.46          = ( poly_poly_real2 @ Q2 ) )
% 0.28/0.46        = ( P2 = Q2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % poly_eq_poly_eq_iff
% 0.28/0.46  thf(fact_55_pigeonhole__infinite__rel,axiom,
% 0.28/0.46      ! [A2: set_real,B3: set_real,R: real > real > $o] :
% 0.28/0.46        ( ~ ( finite_finite_real @ A2 )
% 0.28/0.46       => ( ( finite_finite_real @ B3 )
% 0.28/0.46         => ( ! [X4: real] :
% 0.28/0.46                ( ( member_real @ X4 @ A2 )
% 0.28/0.46               => ? [Xa: real] :
% 0.28/0.46                    ( ( member_real @ Xa @ B3 )
% 0.28/0.46                    & ( R @ X4 @ Xa ) ) )
% 0.28/0.46           => ? [X4: real] :
% 0.28/0.46                ( ( member_real @ X4 @ B3 )
% 0.28/0.46                & ~ ( finite_finite_real
% 0.28/0.46                    @ ( collect_real
% 0.28/0.46                      @ ^ [A4: real] :
% 0.28/0.46                          ( ( member_real @ A4 @ A2 )
% 0.28/0.46                          & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pigeonhole_infinite_rel
% 0.28/0.46  thf(fact_56_pigeonhole__infinite__rel,axiom,
% 0.28/0.46      ! [A2: set_real,B3: set_int,R: real > int > $o] :
% 0.28/0.46        ( ~ ( finite_finite_real @ A2 )
% 0.28/0.46       => ( ( finite_finite_int @ B3 )
% 0.28/0.46         => ( ! [X4: real] :
% 0.28/0.46                ( ( member_real @ X4 @ A2 )
% 0.28/0.46               => ? [Xa: int] :
% 0.28/0.46                    ( ( member_int @ Xa @ B3 )
% 0.28/0.46                    & ( R @ X4 @ Xa ) ) )
% 0.28/0.46           => ? [X4: int] :
% 0.28/0.46                ( ( member_int @ X4 @ B3 )
% 0.28/0.46                & ~ ( finite_finite_real
% 0.28/0.46                    @ ( collect_real
% 0.28/0.46                      @ ^ [A4: real] :
% 0.28/0.46                          ( ( member_real @ A4 @ A2 )
% 0.28/0.46                          & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pigeonhole_infinite_rel
% 0.28/0.46  thf(fact_57_pigeonhole__infinite__rel,axiom,
% 0.28/0.46      ! [A2: set_int,B3: set_real,R: int > real > $o] :
% 0.28/0.46        ( ~ ( finite_finite_int @ A2 )
% 0.28/0.46       => ( ( finite_finite_real @ B3 )
% 0.28/0.46         => ( ! [X4: int] :
% 0.28/0.46                ( ( member_int @ X4 @ A2 )
% 0.28/0.46               => ? [Xa: real] :
% 0.28/0.46                    ( ( member_real @ Xa @ B3 )
% 0.28/0.46                    & ( R @ X4 @ Xa ) ) )
% 0.28/0.46           => ? [X4: real] :
% 0.28/0.46                ( ( member_real @ X4 @ B3 )
% 0.28/0.46                & ~ ( finite_finite_int
% 0.28/0.46                    @ ( collect_int
% 0.28/0.46                      @ ^ [A4: int] :
% 0.28/0.46                          ( ( member_int @ A4 @ A2 )
% 0.28/0.46                          & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pigeonhole_infinite_rel
% 0.28/0.46  thf(fact_58_pigeonhole__infinite__rel,axiom,
% 0.28/0.46      ! [A2: set_int,B3: set_int,R: int > int > $o] :
% 0.28/0.46        ( ~ ( finite_finite_int @ A2 )
% 0.28/0.46       => ( ( finite_finite_int @ B3 )
% 0.28/0.46         => ( ! [X4: int] :
% 0.28/0.46                ( ( member_int @ X4 @ A2 )
% 0.28/0.46               => ? [Xa: int] :
% 0.28/0.46                    ( ( member_int @ Xa @ B3 )
% 0.28/0.46                    & ( R @ X4 @ Xa ) ) )
% 0.28/0.46           => ? [X4: int] :
% 0.28/0.46                ( ( member_int @ X4 @ B3 )
% 0.28/0.46                & ~ ( finite_finite_int
% 0.28/0.46                    @ ( collect_int
% 0.28/0.46                      @ ^ [A4: int] :
% 0.28/0.46                          ( ( member_int @ A4 @ A2 )
% 0.28/0.46                          & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pigeonhole_infinite_rel
% 0.28/0.46  thf(fact_59_not__finite__existsD,axiom,
% 0.28/0.46      ! [P: real > $o] :
% 0.28/0.46        ( ~ ( finite_finite_real @ ( collect_real @ P ) )
% 0.28/0.46       => ? [X_1: real] : ( P @ X_1 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % not_finite_existsD
% 0.28/0.46  thf(fact_60_not__finite__existsD,axiom,
% 0.28/0.46      ! [P: int > $o] :
% 0.28/0.46        ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 0.28/0.46       => ? [X_1: int] : ( P @ X_1 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % not_finite_existsD
% 0.28/0.46  thf(fact_61_order__refl,axiom,
% 0.28/0.46      ! [X2: real] : ( ord_less_eq_real @ X2 @ X2 ) ).
% 0.28/0.46  
% 0.28/0.46  % order_refl
% 0.28/0.46  thf(fact_62_order__refl,axiom,
% 0.28/0.46      ! [X2: int] : ( ord_less_eq_int @ X2 @ X2 ) ).
% 0.28/0.46  
% 0.28/0.46  % order_refl
% 0.28/0.46  thf(fact_63_cross__no__root,axiom,
% 0.28/0.46      ! [A: real,B: real,P2: poly_real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ! [X4: real] :
% 0.28/0.46              ( ( ( ord_less_real @ A @ X4 )
% 0.28/0.46                & ( ord_less_real @ X4 @ B ) )
% 0.28/0.46             => ( ( poly_real2 @ P2 @ X4 )
% 0.28/0.46               != zero_zero_real ) )
% 0.28/0.46         => ( ( sturm_1953858694_cross @ P2 @ A @ B )
% 0.28/0.46            = zero_zero_int ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % cross_no_root
% 0.28/0.46  thf(fact_64_less__eq__real__def,axiom,
% 0.28/0.46      ( ord_less_eq_real
% 0.28/0.46      = ( ^ [X: real,Y: real] :
% 0.28/0.46            ( ( ord_less_real @ X @ Y )
% 0.28/0.46            | ( X = Y ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_eq_real_def
% 0.28/0.46  thf(fact_65_complete__interval,axiom,
% 0.28/0.46      ! [A: real,B: real,P: real > $o] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ( P @ A )
% 0.28/0.46         => ( ~ ( P @ B )
% 0.28/0.46           => ? [C: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ A @ C )
% 0.28/0.46                & ( ord_less_eq_real @ C @ B )
% 0.28/0.46                & ! [X3: real] :
% 0.28/0.46                    ( ( ( ord_less_eq_real @ A @ X3 )
% 0.28/0.46                      & ( ord_less_real @ X3 @ C ) )
% 0.28/0.46                   => ( P @ X3 ) )
% 0.28/0.46                & ! [D: real] :
% 0.28/0.46                    ( ! [X4: real] :
% 0.28/0.46                        ( ( ( ord_less_eq_real @ A @ X4 )
% 0.28/0.46                          & ( ord_less_real @ X4 @ D ) )
% 0.28/0.46                       => ( P @ X4 ) )
% 0.28/0.46                   => ( ord_less_eq_real @ D @ C ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % complete_interval
% 0.28/0.46  thf(fact_66_complete__interval,axiom,
% 0.28/0.46      ! [A: int,B: int,P: int > $o] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ( ( P @ A )
% 0.28/0.46         => ( ~ ( P @ B )
% 0.28/0.46           => ? [C: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ A @ C )
% 0.28/0.46                & ( ord_less_eq_int @ C @ B )
% 0.28/0.46                & ! [X3: int] :
% 0.28/0.46                    ( ( ( ord_less_eq_int @ A @ X3 )
% 0.28/0.46                      & ( ord_less_int @ X3 @ C ) )
% 0.28/0.46                   => ( P @ X3 ) )
% 0.28/0.46                & ! [D: int] :
% 0.28/0.46                    ( ! [X4: int] :
% 0.28/0.46                        ( ( ( ord_less_eq_int @ A @ X4 )
% 0.28/0.46                          & ( ord_less_int @ X4 @ D ) )
% 0.28/0.46                       => ( P @ X4 ) )
% 0.28/0.46                   => ( ord_less_eq_int @ D @ C ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % complete_interval
% 0.28/0.46  thf(fact_67_order_Onot__eq__order__implies__strict,axiom,
% 0.28/0.46      ! [A: real,B: real] :
% 0.28/0.46        ( ( A != B )
% 0.28/0.46       => ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46         => ( ord_less_real @ A @ B ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.not_eq_order_implies_strict
% 0.28/0.46  thf(fact_68_order_Onot__eq__order__implies__strict,axiom,
% 0.28/0.46      ! [A: int,B: int] :
% 0.28/0.46        ( ( A != B )
% 0.28/0.46       => ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46         => ( ord_less_int @ A @ B ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.not_eq_order_implies_strict
% 0.28/0.46  thf(fact_69_dual__order_Ostrict__implies__order,axiom,
% 0.28/0.46      ! [B: real,A: real] :
% 0.28/0.46        ( ( ord_less_real @ B @ A )
% 0.28/0.46       => ( ord_less_eq_real @ B @ A ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.strict_implies_order
% 0.28/0.46  thf(fact_70_dual__order_Ostrict__implies__order,axiom,
% 0.28/0.46      ! [B: int,A: int] :
% 0.28/0.46        ( ( ord_less_int @ B @ A )
% 0.28/0.46       => ( ord_less_eq_int @ B @ A ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.strict_implies_order
% 0.28/0.46  thf(fact_71_dual__order_Ostrict__iff__order,axiom,
% 0.28/0.46      ( ord_less_real
% 0.28/0.46      = ( ^ [B4: real,A4: real] :
% 0.28/0.46            ( ( ord_less_eq_real @ B4 @ A4 )
% 0.28/0.46            & ( A4 != B4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.strict_iff_order
% 0.28/0.46  thf(fact_72_dual__order_Ostrict__iff__order,axiom,
% 0.28/0.46      ( ord_less_int
% 0.28/0.46      = ( ^ [B4: int,A4: int] :
% 0.28/0.46            ( ( ord_less_eq_int @ B4 @ A4 )
% 0.28/0.46            & ( A4 != B4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.strict_iff_order
% 0.28/0.46  thf(fact_73_dual__order_Oorder__iff__strict,axiom,
% 0.28/0.46      ( ord_less_eq_real
% 0.28/0.46      = ( ^ [B4: real,A4: real] :
% 0.28/0.46            ( ( ord_less_real @ B4 @ A4 )
% 0.28/0.46            | ( A4 = B4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.order_iff_strict
% 0.28/0.46  thf(fact_74_dual__order_Oorder__iff__strict,axiom,
% 0.28/0.46      ( ord_less_eq_int
% 0.28/0.46      = ( ^ [B4: int,A4: int] :
% 0.28/0.46            ( ( ord_less_int @ B4 @ A4 )
% 0.28/0.46            | ( A4 = B4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.order_iff_strict
% 0.28/0.46  thf(fact_75_mem__Collect__eq,axiom,
% 0.28/0.46      ! [A: real,P: real > $o] :
% 0.28/0.46        ( ( member_real @ A @ ( collect_real @ P ) )
% 0.28/0.46        = ( P @ A ) ) ).
% 0.28/0.46  
% 0.28/0.46  % mem_Collect_eq
% 0.28/0.46  thf(fact_76_mem__Collect__eq,axiom,
% 0.28/0.46      ! [A: int,P: int > $o] :
% 0.28/0.46        ( ( member_int @ A @ ( collect_int @ P ) )
% 0.28/0.46        = ( P @ A ) ) ).
% 0.28/0.46  
% 0.28/0.46  % mem_Collect_eq
% 0.28/0.46  thf(fact_77_Collect__mem__eq,axiom,
% 0.28/0.46      ! [A2: set_real] :
% 0.28/0.46        ( ( collect_real
% 0.28/0.46          @ ^ [X: real] : ( member_real @ X @ A2 ) )
% 0.28/0.46        = A2 ) ).
% 0.28/0.46  
% 0.28/0.46  % Collect_mem_eq
% 0.28/0.46  thf(fact_78_Collect__mem__eq,axiom,
% 0.28/0.46      ! [A2: set_int] :
% 0.28/0.46        ( ( collect_int
% 0.28/0.46          @ ^ [X: int] : ( member_int @ X @ A2 ) )
% 0.28/0.46        = A2 ) ).
% 0.28/0.46  
% 0.28/0.46  % Collect_mem_eq
% 0.28/0.46  thf(fact_79_Collect__cong,axiom,
% 0.28/0.46      ! [P: real > $o,Q: real > $o] :
% 0.28/0.46        ( ! [X4: real] :
% 0.28/0.46            ( ( P @ X4 )
% 0.28/0.46            = ( Q @ X4 ) )
% 0.28/0.46       => ( ( collect_real @ P )
% 0.28/0.46          = ( collect_real @ Q ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % Collect_cong
% 0.28/0.46  thf(fact_80_Collect__cong,axiom,
% 0.28/0.46      ! [P: int > $o,Q: int > $o] :
% 0.28/0.46        ( ! [X4: int] :
% 0.28/0.46            ( ( P @ X4 )
% 0.28/0.46            = ( Q @ X4 ) )
% 0.28/0.46       => ( ( collect_int @ P )
% 0.28/0.46          = ( collect_int @ Q ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % Collect_cong
% 0.28/0.46  thf(fact_81_order_Ostrict__implies__order,axiom,
% 0.28/0.46      ! [A: real,B: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ord_less_eq_real @ A @ B ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.strict_implies_order
% 0.28/0.46  thf(fact_82_order_Ostrict__implies__order,axiom,
% 0.28/0.46      ! [A: int,B: int] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.strict_implies_order
% 0.28/0.46  thf(fact_83_dense__le__bounded,axiom,
% 0.28/0.46      ! [X2: real,Y2: real,Z3: real] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ( ! [W: real] :
% 0.28/0.46              ( ( ord_less_real @ X2 @ W )
% 0.28/0.46             => ( ( ord_less_real @ W @ Y2 )
% 0.28/0.46               => ( ord_less_eq_real @ W @ Z3 ) ) )
% 0.28/0.46         => ( ord_less_eq_real @ Y2 @ Z3 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dense_le_bounded
% 0.28/0.46  thf(fact_84_finite__Collect__subsets,axiom,
% 0.28/0.46      ! [A2: set_real] :
% 0.28/0.46        ( ( finite_finite_real @ A2 )
% 0.28/0.46       => ( finite475462905t_real
% 0.28/0.46          @ ( collect_set_real
% 0.28/0.46            @ ^ [B5: set_real] : ( ord_less_eq_set_real @ B5 @ A2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % finite_Collect_subsets
% 0.28/0.46  thf(fact_85_finite__Collect__subsets,axiom,
% 0.28/0.46      ! [A2: set_int] :
% 0.28/0.46        ( ( finite_finite_int @ A2 )
% 0.28/0.46       => ( finite26677625et_int
% 0.28/0.46          @ ( collect_set_int
% 0.28/0.46            @ ^ [B5: set_int] : ( ord_less_eq_set_int @ B5 @ A2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % finite_Collect_subsets
% 0.28/0.46  thf(fact_86_cross__0,axiom,
% 0.28/0.46      ! [A: real,B: real] :
% 0.28/0.46        ( ( sturm_1953858694_cross @ zero_zero_poly_real @ A @ B )
% 0.28/0.46        = zero_zero_int ) ).
% 0.28/0.46  
% 0.28/0.46  % cross_0
% 0.28/0.46  thf(fact_87_finite__subset,axiom,
% 0.28/0.46      ! [A2: set_real,B3: set_real] :
% 0.28/0.46        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.28/0.46       => ( ( finite_finite_real @ B3 )
% 0.28/0.46         => ( finite_finite_real @ A2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % finite_subset
% 0.28/0.46  thf(fact_88_finite__subset,axiom,
% 0.28/0.46      ! [A2: set_int,B3: set_int] :
% 0.28/0.46        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.28/0.46       => ( ( finite_finite_int @ B3 )
% 0.28/0.46         => ( finite_finite_int @ A2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % finite_subset
% 0.28/0.46  thf(fact_89_infinite__super,axiom,
% 0.28/0.46      ! [S: set_real,T: set_real] :
% 0.28/0.46        ( ( ord_less_eq_set_real @ S @ T )
% 0.28/0.46       => ( ~ ( finite_finite_real @ S )
% 0.28/0.46         => ~ ( finite_finite_real @ T ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % infinite_super
% 0.28/0.46  thf(fact_90_infinite__super,axiom,
% 0.28/0.46      ! [S: set_int,T: set_int] :
% 0.28/0.46        ( ( ord_less_eq_set_int @ S @ T )
% 0.28/0.46       => ( ~ ( finite_finite_int @ S )
% 0.28/0.46         => ~ ( finite_finite_int @ T ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % infinite_super
% 0.28/0.46  thf(fact_91_rev__finite__subset,axiom,
% 0.28/0.46      ! [B3: set_real,A2: set_real] :
% 0.28/0.46        ( ( finite_finite_real @ B3 )
% 0.28/0.46       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.28/0.46         => ( finite_finite_real @ A2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % rev_finite_subset
% 0.28/0.46  thf(fact_92_rev__finite__subset,axiom,
% 0.28/0.46      ! [B3: set_int,A2: set_int] :
% 0.28/0.46        ( ( finite_finite_int @ B3 )
% 0.28/0.46       => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 0.28/0.46         => ( finite_finite_int @ A2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % rev_finite_subset
% 0.28/0.46  thf(fact_93_dual__order_Oantisym,axiom,
% 0.28/0.46      ! [B: real,A: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ B @ A )
% 0.28/0.46       => ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46         => ( A = B ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.antisym
% 0.28/0.46  thf(fact_94_dual__order_Oantisym,axiom,
% 0.28/0.46      ! [B: int,A: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ B @ A )
% 0.28/0.46       => ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46         => ( A = B ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.antisym
% 0.28/0.46  thf(fact_95_dual__order_Oeq__iff,axiom,
% 0.28/0.46      ( ( ^ [Y3: real,Z4: real] : ( Y3 = Z4 ) )
% 0.28/0.46      = ( ^ [A4: real,B4: real] :
% 0.28/0.46            ( ( ord_less_eq_real @ B4 @ A4 )
% 0.28/0.46            & ( ord_less_eq_real @ A4 @ B4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.eq_iff
% 0.28/0.46  thf(fact_96_dual__order_Oeq__iff,axiom,
% 0.28/0.46      ( ( ^ [Y3: int,Z4: int] : ( Y3 = Z4 ) )
% 0.28/0.46      = ( ^ [A4: int,B4: int] :
% 0.28/0.46            ( ( ord_less_eq_int @ B4 @ A4 )
% 0.28/0.46            & ( ord_less_eq_int @ A4 @ B4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.eq_iff
% 0.28/0.46  thf(fact_97_dual__order_Otrans,axiom,
% 0.28/0.46      ! [B: real,A: real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ B @ A )
% 0.28/0.46       => ( ( ord_less_eq_real @ C2 @ B )
% 0.28/0.46         => ( ord_less_eq_real @ C2 @ A ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.trans
% 0.28/0.46  thf(fact_98_dual__order_Otrans,axiom,
% 0.28/0.46      ! [B: int,A: int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ B @ A )
% 0.28/0.46       => ( ( ord_less_eq_int @ C2 @ B )
% 0.28/0.46         => ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.trans
% 0.28/0.46  thf(fact_99_linorder__wlog,axiom,
% 0.28/0.46      ! [P: real > real > $o,A: real,B: real] :
% 0.28/0.46        ( ! [A5: real,B6: real] :
% 0.28/0.46            ( ( ord_less_eq_real @ A5 @ B6 )
% 0.28/0.46           => ( P @ A5 @ B6 ) )
% 0.28/0.46       => ( ! [A5: real,B6: real] :
% 0.28/0.46              ( ( P @ B6 @ A5 )
% 0.28/0.46             => ( P @ A5 @ B6 ) )
% 0.28/0.46         => ( P @ A @ B ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % linorder_wlog
% 0.28/0.46  thf(fact_100_linorder__wlog,axiom,
% 0.28/0.46      ! [P: int > int > $o,A: int,B: int] :
% 0.28/0.46        ( ! [A5: int,B6: int] :
% 0.28/0.46            ( ( ord_less_eq_int @ A5 @ B6 )
% 0.28/0.46           => ( P @ A5 @ B6 ) )
% 0.28/0.46       => ( ! [A5: int,B6: int] :
% 0.28/0.46              ( ( P @ B6 @ A5 )
% 0.28/0.46             => ( P @ A5 @ B6 ) )
% 0.28/0.46         => ( P @ A @ B ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % linorder_wlog
% 0.28/0.46  thf(fact_101_dual__order_Orefl,axiom,
% 0.28/0.46      ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.refl
% 0.28/0.46  thf(fact_102_dual__order_Orefl,axiom,
% 0.28/0.46      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.refl
% 0.28/0.46  thf(fact_103_order__trans,axiom,
% 0.28/0.46      ! [X2: real,Y2: real,Z3: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_eq_real @ Y2 @ Z3 )
% 0.28/0.46         => ( ord_less_eq_real @ X2 @ Z3 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_trans
% 0.28/0.46  thf(fact_104_order__trans,axiom,
% 0.28/0.46      ! [X2: int,Y2: int,Z3: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_eq_int @ Y2 @ Z3 )
% 0.28/0.46         => ( ord_less_eq_int @ X2 @ Z3 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_trans
% 0.28/0.46  thf(fact_105_order__class_Oorder_Oantisym,axiom,
% 0.28/0.46      ! [A: real,B: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_real @ B @ A )
% 0.28/0.46         => ( A = B ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_class.order.antisym
% 0.28/0.46  thf(fact_106_order__class_Oorder_Oantisym,axiom,
% 0.28/0.46      ! [A: int,B: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_int @ B @ A )
% 0.28/0.46         => ( A = B ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_class.order.antisym
% 0.28/0.46  thf(fact_107_ord__le__eq__trans,axiom,
% 0.28/0.46      ! [A: real,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46       => ( ( B = C2 )
% 0.28/0.46         => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_le_eq_trans
% 0.28/0.46  thf(fact_108_ord__le__eq__trans,axiom,
% 0.28/0.46      ! [A: int,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46       => ( ( B = C2 )
% 0.28/0.46         => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_le_eq_trans
% 0.28/0.46  thf(fact_109_ord__eq__le__trans,axiom,
% 0.28/0.46      ! [A: real,B: real,C2: real] :
% 0.28/0.46        ( ( A = B )
% 0.28/0.46       => ( ( ord_less_eq_real @ B @ C2 )
% 0.28/0.46         => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_eq_le_trans
% 0.28/0.46  thf(fact_110_ord__eq__le__trans,axiom,
% 0.28/0.46      ! [A: int,B: int,C2: int] :
% 0.28/0.46        ( ( A = B )
% 0.28/0.46       => ( ( ord_less_eq_int @ B @ C2 )
% 0.28/0.46         => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_eq_le_trans
% 0.28/0.46  thf(fact_111_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.46      ( ( ^ [Y3: real,Z4: real] : ( Y3 = Z4 ) )
% 0.28/0.46      = ( ^ [A4: real,B4: real] :
% 0.28/0.46            ( ( ord_less_eq_real @ A4 @ B4 )
% 0.28/0.46            & ( ord_less_eq_real @ B4 @ A4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_class.order.eq_iff
% 0.28/0.46  thf(fact_112_order__class_Oorder_Oeq__iff,axiom,
% 0.28/0.46      ( ( ^ [Y3: int,Z4: int] : ( Y3 = Z4 ) )
% 0.28/0.46      = ( ^ [A4: int,B4: int] :
% 0.28/0.46            ( ( ord_less_eq_int @ A4 @ B4 )
% 0.28/0.46            & ( ord_less_eq_int @ B4 @ A4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_class.order.eq_iff
% 0.28/0.46  thf(fact_113_antisym__conv,axiom,
% 0.28/0.46      ! [Y2: real,X2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ Y2 @ X2 )
% 0.28/0.46       => ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.28/0.46          = ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % antisym_conv
% 0.28/0.46  thf(fact_114_antisym__conv,axiom,
% 0.28/0.46      ! [Y2: int,X2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ Y2 @ X2 )
% 0.28/0.46       => ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.28/0.46          = ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % antisym_conv
% 0.28/0.46  thf(fact_115_le__cases3,axiom,
% 0.28/0.46      ! [X2: real,Y2: real,Z3: real] :
% 0.28/0.46        ( ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.28/0.46         => ~ ( ord_less_eq_real @ Y2 @ Z3 ) )
% 0.28/0.46       => ( ( ( ord_less_eq_real @ Y2 @ X2 )
% 0.28/0.46           => ~ ( ord_less_eq_real @ X2 @ Z3 ) )
% 0.28/0.46         => ( ( ( ord_less_eq_real @ X2 @ Z3 )
% 0.28/0.46             => ~ ( ord_less_eq_real @ Z3 @ Y2 ) )
% 0.28/0.46           => ( ( ( ord_less_eq_real @ Z3 @ Y2 )
% 0.28/0.46               => ~ ( ord_less_eq_real @ Y2 @ X2 ) )
% 0.28/0.46             => ( ( ( ord_less_eq_real @ Y2 @ Z3 )
% 0.28/0.46                 => ~ ( ord_less_eq_real @ Z3 @ X2 ) )
% 0.28/0.46               => ~ ( ( ord_less_eq_real @ Z3 @ X2 )
% 0.28/0.46                   => ~ ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_cases3
% 0.28/0.46  thf(fact_116_le__cases3,axiom,
% 0.28/0.46      ! [X2: int,Y2: int,Z3: int] :
% 0.28/0.46        ( ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.28/0.46         => ~ ( ord_less_eq_int @ Y2 @ Z3 ) )
% 0.28/0.46       => ( ( ( ord_less_eq_int @ Y2 @ X2 )
% 0.28/0.46           => ~ ( ord_less_eq_int @ X2 @ Z3 ) )
% 0.28/0.46         => ( ( ( ord_less_eq_int @ X2 @ Z3 )
% 0.28/0.46             => ~ ( ord_less_eq_int @ Z3 @ Y2 ) )
% 0.28/0.46           => ( ( ( ord_less_eq_int @ Z3 @ Y2 )
% 0.28/0.46               => ~ ( ord_less_eq_int @ Y2 @ X2 ) )
% 0.28/0.46             => ( ( ( ord_less_eq_int @ Y2 @ Z3 )
% 0.28/0.46                 => ~ ( ord_less_eq_int @ Z3 @ X2 ) )
% 0.28/0.46               => ~ ( ( ord_less_eq_int @ Z3 @ X2 )
% 0.28/0.46                   => ~ ( ord_less_eq_int @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_cases3
% 0.28/0.46  thf(fact_117_order_Otrans,axiom,
% 0.28/0.46      ! [A: real,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_real @ B @ C2 )
% 0.28/0.46         => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.trans
% 0.28/0.46  thf(fact_118_order_Otrans,axiom,
% 0.28/0.46      ! [A: int,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_int @ B @ C2 )
% 0.28/0.46         => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.trans
% 0.28/0.46  thf(fact_119_le__cases,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ~ ( ord_less_eq_real @ X2 @ Y2 )
% 0.28/0.46       => ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_cases
% 0.28/0.46  thf(fact_120_le__cases,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ~ ( ord_less_eq_int @ X2 @ Y2 )
% 0.28/0.46       => ( ord_less_eq_int @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_cases
% 0.28/0.46  thf(fact_121_eq__refl,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( X2 = Y2 )
% 0.28/0.46       => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % eq_refl
% 0.28/0.46  thf(fact_122_eq__refl,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( X2 = Y2 )
% 0.28/0.46       => ( ord_less_eq_int @ X2 @ Y2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % eq_refl
% 0.28/0.46  thf(fact_123_linear,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.28/0.46        | ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % linear
% 0.28/0.46  thf(fact_124_linear,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.28/0.46        | ( ord_less_eq_int @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % linear
% 0.28/0.46  thf(fact_125_antisym,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_eq_real @ Y2 @ X2 )
% 0.28/0.46         => ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % antisym
% 0.28/0.46  thf(fact_126_antisym,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_eq_int @ Y2 @ X2 )
% 0.28/0.46         => ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % antisym
% 0.28/0.46  thf(fact_127_eq__iff,axiom,
% 0.28/0.46      ( ( ^ [Y3: real,Z4: real] : ( Y3 = Z4 ) )
% 0.28/0.46      = ( ^ [X: real,Y: real] :
% 0.28/0.46            ( ( ord_less_eq_real @ X @ Y )
% 0.28/0.46            & ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % eq_iff
% 0.28/0.46  thf(fact_128_eq__iff,axiom,
% 0.28/0.46      ( ( ^ [Y3: int,Z4: int] : ( Y3 = Z4 ) )
% 0.28/0.46      = ( ^ [X: int,Y: int] :
% 0.28/0.46            ( ( ord_less_eq_int @ X @ Y )
% 0.28/0.46            & ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % eq_iff
% 0.28/0.46  thf(fact_129_ord__le__eq__subst,axiom,
% 0.28/0.46      ! [A: real,B: real,F: real > real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46       => ( ( ( F @ B )
% 0.28/0.46            = C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_le_eq_subst
% 0.28/0.46  thf(fact_130_ord__le__eq__subst,axiom,
% 0.28/0.46      ! [A: real,B: real,F: real > int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46       => ( ( ( F @ B )
% 0.28/0.46            = C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_le_eq_subst
% 0.28/0.46  thf(fact_131_ord__le__eq__subst,axiom,
% 0.28/0.46      ! [A: int,B: int,F: int > real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46       => ( ( ( F @ B )
% 0.28/0.46            = C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_le_eq_subst
% 0.28/0.46  thf(fact_132_ord__le__eq__subst,axiom,
% 0.28/0.46      ! [A: int,B: int,F: int > int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46       => ( ( ( F @ B )
% 0.28/0.46            = C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_le_eq_subst
% 0.28/0.46  thf(fact_133_ord__eq__le__subst,axiom,
% 0.28/0.46      ! [A: real,F: real > real,B: real,C2: real] :
% 0.28/0.46        ( ( A
% 0.28/0.46          = ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_eq_real @ B @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_eq_le_subst
% 0.28/0.46  thf(fact_134_ord__eq__le__subst,axiom,
% 0.28/0.46      ! [A: int,F: real > int,B: real,C2: real] :
% 0.28/0.46        ( ( A
% 0.28/0.46          = ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_eq_real @ B @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_eq_le_subst
% 0.28/0.46  thf(fact_135_ord__eq__le__subst,axiom,
% 0.28/0.46      ! [A: real,F: int > real,B: int,C2: int] :
% 0.28/0.46        ( ( A
% 0.28/0.46          = ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_eq_int @ B @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_eq_le_subst
% 0.28/0.46  thf(fact_136_ord__eq__le__subst,axiom,
% 0.28/0.46      ! [A: int,F: int > int,B: int,C2: int] :
% 0.28/0.46        ( ( A
% 0.28/0.46          = ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_eq_int @ B @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_eq_le_subst
% 0.28/0.46  thf(fact_137_order__subst2,axiom,
% 0.28/0.46      ! [A: real,B: real,F: real > real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_subst2
% 0.28/0.46  thf(fact_138_order__subst2,axiom,
% 0.28/0.46      ! [A: real,B: real,F: real > int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_subst2
% 0.28/0.46  thf(fact_139_order__subst2,axiom,
% 0.28/0.46      ! [A: int,B: int,F: int > real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_subst2
% 0.28/0.46  thf(fact_140_order__subst2,axiom,
% 0.28/0.46      ! [A: int,B: int,F: int > int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_subst2
% 0.28/0.46  thf(fact_141_order__subst1,axiom,
% 0.28/0.46      ! [A: real,F: real > real,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_eq_real @ B @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_subst1
% 0.28/0.46  thf(fact_142_order__subst1,axiom,
% 0.28/0.46      ! [A: real,F: int > real,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_eq_int @ B @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_subst1
% 0.28/0.46  thf(fact_143_order__subst1,axiom,
% 0.28/0.46      ! [A: int,F: real > int,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_eq_real @ B @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_subst1
% 0.28/0.46  thf(fact_144_order__subst1,axiom,
% 0.28/0.46      ! [A: int,F: int > int,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_eq_int @ B @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_subst1
% 0.28/0.46  thf(fact_145_ord__eq__less__subst,axiom,
% 0.28/0.46      ! [A: real,F: real > real,B: real,C2: real] :
% 0.28/0.46        ( ( A
% 0.28/0.46          = ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_real @ B @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_eq_less_subst
% 0.28/0.46  thf(fact_146_ord__eq__less__subst,axiom,
% 0.28/0.46      ! [A: int,F: real > int,B: real,C2: real] :
% 0.28/0.46        ( ( A
% 0.28/0.46          = ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_real @ B @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_eq_less_subst
% 0.28/0.46  thf(fact_147_ord__eq__less__subst,axiom,
% 0.28/0.46      ! [A: real,F: int > real,B: int,C2: int] :
% 0.28/0.46        ( ( A
% 0.28/0.46          = ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_int @ B @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_eq_less_subst
% 0.28/0.46  thf(fact_148_ord__eq__less__subst,axiom,
% 0.28/0.46      ! [A: int,F: int > int,B: int,C2: int] :
% 0.28/0.46        ( ( A
% 0.28/0.46          = ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_int @ B @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_eq_less_subst
% 0.28/0.46  thf(fact_149_ord__less__eq__subst,axiom,
% 0.28/0.46      ! [A: real,B: real,F: real > real,C2: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ( ( F @ B )
% 0.28/0.46            = C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_less_eq_subst
% 0.28/0.46  thf(fact_150_ord__less__eq__subst,axiom,
% 0.28/0.46      ! [A: real,B: real,F: real > int,C2: int] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ( ( F @ B )
% 0.28/0.46            = C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_less_eq_subst
% 0.28/0.46  thf(fact_151_ord__less__eq__subst,axiom,
% 0.28/0.46      ! [A: int,B: int,F: int > real,C2: real] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ( ( ( F @ B )
% 0.28/0.46            = C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_less_eq_subst
% 0.28/0.46  thf(fact_152_ord__less__eq__subst,axiom,
% 0.28/0.46      ! [A: int,B: int,F: int > int,C2: int] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ( ( ( F @ B )
% 0.28/0.46            = C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_less_eq_subst
% 0.28/0.46  thf(fact_153_order__less__subst1,axiom,
% 0.28/0.46      ! [A: real,F: real > real,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_real @ B @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_subst1
% 0.28/0.46  thf(fact_154_order__less__subst1,axiom,
% 0.28/0.46      ! [A: real,F: int > real,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_int @ B @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_subst1
% 0.28/0.46  thf(fact_155_order__less__subst1,axiom,
% 0.28/0.46      ! [A: int,F: real > int,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_real @ B @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_subst1
% 0.28/0.46  thf(fact_156_order__less__subst1,axiom,
% 0.28/0.46      ! [A: int,F: int > int,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_int @ B @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_subst1
% 0.28/0.46  thf(fact_157_order__less__subst2,axiom,
% 0.28/0.46      ! [A: real,B: real,F: real > real,C2: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_subst2
% 0.28/0.46  thf(fact_158_order__less__subst2,axiom,
% 0.28/0.46      ! [A: real,B: real,F: real > int,C2: int] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_subst2
% 0.28/0.46  thf(fact_159_order__less__subst2,axiom,
% 0.28/0.46      ! [A: int,B: int,F: int > real,C2: real] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_subst2
% 0.28/0.46  thf(fact_160_order__less__subst2,axiom,
% 0.28/0.46      ! [A: int,B: int,F: int > int,C2: int] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_subst2
% 0.28/0.46  thf(fact_161_lt__ex,axiom,
% 0.28/0.46      ! [X2: real] :
% 0.28/0.46      ? [Y4: real] : ( ord_less_real @ Y4 @ X2 ) ).
% 0.28/0.46  
% 0.28/0.46  % lt_ex
% 0.28/0.46  thf(fact_162_lt__ex,axiom,
% 0.28/0.46      ! [X2: int] :
% 0.28/0.46      ? [Y4: int] : ( ord_less_int @ Y4 @ X2 ) ).
% 0.28/0.46  
% 0.28/0.46  % lt_ex
% 0.28/0.46  thf(fact_163_gt__ex,axiom,
% 0.28/0.46      ! [X2: real] :
% 0.28/0.46      ? [X_1: real] : ( ord_less_real @ X2 @ X_1 ) ).
% 0.28/0.46  
% 0.28/0.46  % gt_ex
% 0.28/0.46  thf(fact_164_gt__ex,axiom,
% 0.28/0.46      ! [X2: int] :
% 0.28/0.46      ? [X_1: int] : ( ord_less_int @ X2 @ X_1 ) ).
% 0.28/0.46  
% 0.28/0.46  % gt_ex
% 0.28/0.46  thf(fact_165_neqE,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( X2 != Y2 )
% 0.28/0.46       => ( ~ ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46         => ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % neqE
% 0.28/0.46  thf(fact_166_neqE,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( X2 != Y2 )
% 0.28/0.46       => ( ~ ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46         => ( ord_less_int @ Y2 @ X2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % neqE
% 0.28/0.46  thf(fact_167_neq__iff,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( X2 != Y2 )
% 0.28/0.46        = ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46          | ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % neq_iff
% 0.28/0.46  thf(fact_168_neq__iff,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( X2 != Y2 )
% 0.28/0.46        = ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46          | ( ord_less_int @ Y2 @ X2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % neq_iff
% 0.28/0.46  thf(fact_169_order_Oasym,axiom,
% 0.28/0.46      ! [A: real,B: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ~ ( ord_less_real @ B @ A ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.asym
% 0.28/0.46  thf(fact_170_order_Oasym,axiom,
% 0.28/0.46      ! [A: int,B: int] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.asym
% 0.28/0.46  thf(fact_171_dense,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ? [Z5: real] :
% 0.28/0.46            ( ( ord_less_real @ X2 @ Z5 )
% 0.28/0.46            & ( ord_less_real @ Z5 @ Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dense
% 0.28/0.46  thf(fact_172_less__imp__neq,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ( X2 != Y2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_imp_neq
% 0.28/0.46  thf(fact_173_less__imp__neq,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ( X2 != Y2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_imp_neq
% 0.28/0.46  thf(fact_174_less__asym,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ~ ( ord_less_real @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_asym
% 0.28/0.46  thf(fact_175_less__asym,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ~ ( ord_less_int @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_asym
% 0.28/0.46  thf(fact_176_less__asym_H,axiom,
% 0.28/0.46      ! [A: real,B: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ~ ( ord_less_real @ B @ A ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_asym'
% 0.28/0.46  thf(fact_177_less__asym_H,axiom,
% 0.28/0.46      ! [A: int,B: int] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_asym'
% 0.28/0.46  thf(fact_178_less__trans,axiom,
% 0.28/0.46      ! [X2: real,Y2: real,Z3: real] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_real @ Y2 @ Z3 )
% 0.28/0.46         => ( ord_less_real @ X2 @ Z3 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_trans
% 0.28/0.46  thf(fact_179_less__trans,axiom,
% 0.28/0.46      ! [X2: int,Y2: int,Z3: int] :
% 0.28/0.46        ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_int @ Y2 @ Z3 )
% 0.28/0.46         => ( ord_less_int @ X2 @ Z3 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_trans
% 0.28/0.46  thf(fact_180_less__linear,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46        | ( X2 = Y2 )
% 0.28/0.46        | ( ord_less_real @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_linear
% 0.28/0.46  thf(fact_181_less__linear,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46        | ( X2 = Y2 )
% 0.28/0.46        | ( ord_less_int @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_linear
% 0.28/0.46  thf(fact_182_less__irrefl,axiom,
% 0.28/0.46      ! [X2: real] :
% 0.28/0.46        ~ ( ord_less_real @ X2 @ X2 ) ).
% 0.28/0.46  
% 0.28/0.46  % less_irrefl
% 0.28/0.46  thf(fact_183_less__irrefl,axiom,
% 0.28/0.46      ! [X2: int] :
% 0.28/0.46        ~ ( ord_less_int @ X2 @ X2 ) ).
% 0.28/0.46  
% 0.28/0.46  % less_irrefl
% 0.28/0.46  thf(fact_184_ord__eq__less__trans,axiom,
% 0.28/0.46      ! [A: real,B: real,C2: real] :
% 0.28/0.46        ( ( A = B )
% 0.28/0.46       => ( ( ord_less_real @ B @ C2 )
% 0.28/0.46         => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_eq_less_trans
% 0.28/0.46  thf(fact_185_ord__eq__less__trans,axiom,
% 0.28/0.46      ! [A: int,B: int,C2: int] :
% 0.28/0.46        ( ( A = B )
% 0.28/0.46       => ( ( ord_less_int @ B @ C2 )
% 0.28/0.46         => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_eq_less_trans
% 0.28/0.46  thf(fact_186_ord__less__eq__trans,axiom,
% 0.28/0.46      ! [A: real,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ( B = C2 )
% 0.28/0.46         => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_less_eq_trans
% 0.28/0.46  thf(fact_187_ord__less__eq__trans,axiom,
% 0.28/0.46      ! [A: int,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ( ( B = C2 )
% 0.28/0.46         => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ord_less_eq_trans
% 0.28/0.46  thf(fact_188_dual__order_Oasym,axiom,
% 0.28/0.46      ! [B: real,A: real] :
% 0.28/0.46        ( ( ord_less_real @ B @ A )
% 0.28/0.46       => ~ ( ord_less_real @ A @ B ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.asym
% 0.28/0.46  thf(fact_189_dual__order_Oasym,axiom,
% 0.28/0.46      ! [B: int,A: int] :
% 0.28/0.46        ( ( ord_less_int @ B @ A )
% 0.28/0.46       => ~ ( ord_less_int @ A @ B ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.asym
% 0.28/0.46  thf(fact_190_less__imp__not__eq,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ( X2 != Y2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_imp_not_eq
% 0.28/0.46  thf(fact_191_less__imp__not__eq,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ( X2 != Y2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_imp_not_eq
% 0.28/0.46  thf(fact_192_less__not__sym,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ~ ( ord_less_real @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_not_sym
% 0.28/0.46  thf(fact_193_less__not__sym,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ~ ( ord_less_int @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_not_sym
% 0.28/0.46  thf(fact_194_antisym__conv3,axiom,
% 0.28/0.46      ! [Y2: real,X2: real] :
% 0.28/0.46        ( ~ ( ord_less_real @ Y2 @ X2 )
% 0.28/0.46       => ( ( ~ ( ord_less_real @ X2 @ Y2 ) )
% 0.28/0.46          = ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % antisym_conv3
% 0.28/0.46  thf(fact_195_antisym__conv3,axiom,
% 0.28/0.46      ! [Y2: int,X2: int] :
% 0.28/0.46        ( ~ ( ord_less_int @ Y2 @ X2 )
% 0.28/0.46       => ( ( ~ ( ord_less_int @ X2 @ Y2 ) )
% 0.28/0.46          = ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % antisym_conv3
% 0.28/0.46  thf(fact_196_less__imp__not__eq2,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ( Y2 != X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_imp_not_eq2
% 0.28/0.46  thf(fact_197_less__imp__not__eq2,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ( Y2 != X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_imp_not_eq2
% 0.28/0.46  thf(fact_198_less__imp__triv,axiom,
% 0.28/0.46      ! [X2: real,Y2: real,P: $o] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_real @ Y2 @ X2 )
% 0.28/0.46         => P ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_imp_triv
% 0.28/0.46  thf(fact_199_less__imp__triv,axiom,
% 0.28/0.46      ! [X2: int,Y2: int,P: $o] :
% 0.28/0.46        ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_int @ Y2 @ X2 )
% 0.28/0.46         => P ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_imp_triv
% 0.28/0.46  thf(fact_200_linorder__cases,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ~ ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ( ( X2 != Y2 )
% 0.28/0.46         => ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % linorder_cases
% 0.28/0.46  thf(fact_201_linorder__cases,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ~ ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ( ( X2 != Y2 )
% 0.28/0.46         => ( ord_less_int @ Y2 @ X2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % linorder_cases
% 0.28/0.46  thf(fact_202_dual__order_Oirrefl,axiom,
% 0.28/0.46      ! [A: real] :
% 0.28/0.46        ~ ( ord_less_real @ A @ A ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.irrefl
% 0.28/0.46  thf(fact_203_dual__order_Oirrefl,axiom,
% 0.28/0.46      ! [A: int] :
% 0.28/0.46        ~ ( ord_less_int @ A @ A ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.irrefl
% 0.28/0.46  thf(fact_204_order_Ostrict__trans,axiom,
% 0.28/0.46      ! [A: real,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_real @ B @ C2 )
% 0.28/0.46         => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.strict_trans
% 0.28/0.46  thf(fact_205_order_Ostrict__trans,axiom,
% 0.28/0.46      ! [A: int,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_int @ B @ C2 )
% 0.28/0.46         => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.strict_trans
% 0.28/0.46  thf(fact_206_less__imp__not__less,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ~ ( ord_less_real @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_imp_not_less
% 0.28/0.46  thf(fact_207_less__imp__not__less,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ~ ( ord_less_int @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_imp_not_less
% 0.28/0.46  thf(fact_208_linorder__less__wlog,axiom,
% 0.28/0.46      ! [P: real > real > $o,A: real,B: real] :
% 0.28/0.46        ( ! [A5: real,B6: real] :
% 0.28/0.46            ( ( ord_less_real @ A5 @ B6 )
% 0.28/0.46           => ( P @ A5 @ B6 ) )
% 0.28/0.46       => ( ! [A5: real] : ( P @ A5 @ A5 )
% 0.28/0.46         => ( ! [A5: real,B6: real] :
% 0.28/0.46                ( ( P @ B6 @ A5 )
% 0.28/0.46               => ( P @ A5 @ B6 ) )
% 0.28/0.46           => ( P @ A @ B ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % linorder_less_wlog
% 0.28/0.46  thf(fact_209_linorder__less__wlog,axiom,
% 0.28/0.46      ! [P: int > int > $o,A: int,B: int] :
% 0.28/0.46        ( ! [A5: int,B6: int] :
% 0.28/0.46            ( ( ord_less_int @ A5 @ B6 )
% 0.28/0.46           => ( P @ A5 @ B6 ) )
% 0.28/0.46       => ( ! [A5: int] : ( P @ A5 @ A5 )
% 0.28/0.46         => ( ! [A5: int,B6: int] :
% 0.28/0.46                ( ( P @ B6 @ A5 )
% 0.28/0.46               => ( P @ A5 @ B6 ) )
% 0.28/0.46           => ( P @ A @ B ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % linorder_less_wlog
% 0.28/0.46  thf(fact_210_dual__order_Ostrict__trans,axiom,
% 0.28/0.46      ! [B: real,A: real,C2: real] :
% 0.28/0.46        ( ( ord_less_real @ B @ A )
% 0.28/0.46       => ( ( ord_less_real @ C2 @ B )
% 0.28/0.46         => ( ord_less_real @ C2 @ A ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.strict_trans
% 0.28/0.46  thf(fact_211_dual__order_Ostrict__trans,axiom,
% 0.28/0.46      ! [B: int,A: int,C2: int] :
% 0.28/0.46        ( ( ord_less_int @ B @ A )
% 0.28/0.46       => ( ( ord_less_int @ C2 @ B )
% 0.28/0.46         => ( ord_less_int @ C2 @ A ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.strict_trans
% 0.28/0.46  thf(fact_212_not__less__iff__gr__or__eq,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ~ ( ord_less_real @ X2 @ Y2 ) )
% 0.28/0.46        = ( ( ord_less_real @ Y2 @ X2 )
% 0.28/0.46          | ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % not_less_iff_gr_or_eq
% 0.28/0.46  thf(fact_213_not__less__iff__gr__or__eq,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ~ ( ord_less_int @ X2 @ Y2 ) )
% 0.28/0.46        = ( ( ord_less_int @ Y2 @ X2 )
% 0.28/0.46          | ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % not_less_iff_gr_or_eq
% 0.28/0.46  thf(fact_214_order_Ostrict__implies__not__eq,axiom,
% 0.28/0.46      ! [A: real,B: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( A != B ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.strict_implies_not_eq
% 0.28/0.46  thf(fact_215_order_Ostrict__implies__not__eq,axiom,
% 0.28/0.46      ! [A: int,B: int] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ( A != B ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.strict_implies_not_eq
% 0.28/0.46  thf(fact_216_dual__order_Ostrict__implies__not__eq,axiom,
% 0.28/0.46      ! [B: real,A: real] :
% 0.28/0.46        ( ( ord_less_real @ B @ A )
% 0.28/0.46       => ( A != B ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.strict_implies_not_eq
% 0.28/0.46  thf(fact_217_dual__order_Ostrict__implies__not__eq,axiom,
% 0.28/0.46      ! [B: int,A: int] :
% 0.28/0.46        ( ( ord_less_int @ B @ A )
% 0.28/0.46       => ( A != B ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.strict_implies_not_eq
% 0.28/0.46  thf(fact_218_ex__gt__or__lt,axiom,
% 0.28/0.46      ! [A: real] :
% 0.28/0.46      ? [B6: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B6 )
% 0.28/0.46        | ( ord_less_real @ B6 @ A ) ) ).
% 0.28/0.46  
% 0.28/0.46  % ex_gt_or_lt
% 0.28/0.46  thf(fact_219_complete__real,axiom,
% 0.28/0.46      ! [S: set_real] :
% 0.28/0.46        ( ? [X3: real] : ( member_real @ X3 @ S )
% 0.28/0.46       => ( ? [Z: real] :
% 0.28/0.46            ! [X4: real] :
% 0.28/0.46              ( ( member_real @ X4 @ S )
% 0.28/0.46             => ( ord_less_eq_real @ X4 @ Z ) )
% 0.28/0.46         => ? [Y4: real] :
% 0.28/0.46              ( ! [X3: real] :
% 0.28/0.46                  ( ( member_real @ X3 @ S )
% 0.28/0.46                 => ( ord_less_eq_real @ X3 @ Y4 ) )
% 0.28/0.46              & ! [Z: real] :
% 0.28/0.46                  ( ! [X4: real] :
% 0.28/0.46                      ( ( member_real @ X4 @ S )
% 0.28/0.46                     => ( ord_less_eq_real @ X4 @ Z ) )
% 0.28/0.46                 => ( ord_less_eq_real @ Y4 @ Z ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % complete_real
% 0.28/0.46  thf(fact_220_field__lbound__gt__zero,axiom,
% 0.28/0.46      ! [D1: real,D2: real] :
% 0.28/0.46        ( ( ord_less_real @ zero_zero_real @ D1 )
% 0.28/0.46       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 0.28/0.46         => ? [E: real] :
% 0.28/0.46              ( ( ord_less_real @ zero_zero_real @ E )
% 0.28/0.46              & ( ord_less_real @ E @ D1 )
% 0.28/0.46              & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % field_lbound_gt_zero
% 0.28/0.46  thf(fact_221_leD,axiom,
% 0.28/0.46      ! [Y2: real,X2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ Y2 @ X2 )
% 0.28/0.46       => ~ ( ord_less_real @ X2 @ Y2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % leD
% 0.28/0.46  thf(fact_222_leD,axiom,
% 0.28/0.46      ! [Y2: int,X2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ Y2 @ X2 )
% 0.28/0.46       => ~ ( ord_less_int @ X2 @ Y2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % leD
% 0.28/0.46  thf(fact_223_leI,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ~ ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % leI
% 0.28/0.46  thf(fact_224_leI,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ~ ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ( ord_less_eq_int @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % leI
% 0.28/0.46  thf(fact_225_le__less,axiom,
% 0.28/0.46      ( ord_less_eq_real
% 0.28/0.46      = ( ^ [X: real,Y: real] :
% 0.28/0.46            ( ( ord_less_real @ X @ Y )
% 0.28/0.46            | ( X = Y ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_less
% 0.28/0.46  thf(fact_226_le__less,axiom,
% 0.28/0.46      ( ord_less_eq_int
% 0.28/0.46      = ( ^ [X: int,Y: int] :
% 0.28/0.46            ( ( ord_less_int @ X @ Y )
% 0.28/0.46            | ( X = Y ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_less
% 0.28/0.46  thf(fact_227_less__le,axiom,
% 0.28/0.46      ( ord_less_real
% 0.28/0.46      = ( ^ [X: real,Y: real] :
% 0.28/0.46            ( ( ord_less_eq_real @ X @ Y )
% 0.28/0.46            & ( X != Y ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_le
% 0.28/0.46  thf(fact_228_less__le,axiom,
% 0.28/0.46      ( ord_less_int
% 0.28/0.46      = ( ^ [X: int,Y: int] :
% 0.28/0.46            ( ( ord_less_eq_int @ X @ Y )
% 0.28/0.46            & ( X != Y ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_le
% 0.28/0.46  thf(fact_229_order__le__less__subst1,axiom,
% 0.28/0.46      ! [A: real,F: real > real,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_real @ B @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_le_less_subst1
% 0.28/0.46  thf(fact_230_order__le__less__subst1,axiom,
% 0.28/0.46      ! [A: real,F: int > real,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_int @ B @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_le_less_subst1
% 0.28/0.46  thf(fact_231_order__le__less__subst1,axiom,
% 0.28/0.46      ! [A: int,F: real > int,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_real @ B @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_le_less_subst1
% 0.28/0.46  thf(fact_232_order__le__less__subst1,axiom,
% 0.28/0.46      ! [A: int,F: int > int,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_int @ B @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_le_less_subst1
% 0.28/0.46  thf(fact_233_order__le__less__subst2,axiom,
% 0.28/0.46      ! [A: real,B: real,F: real > real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_le_less_subst2
% 0.28/0.46  thf(fact_234_order__le__less__subst2,axiom,
% 0.28/0.46      ! [A: real,B: real,F: real > int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_le_less_subst2
% 0.28/0.46  thf(fact_235_order__le__less__subst2,axiom,
% 0.28/0.46      ! [A: int,B: int,F: int > real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_le_less_subst2
% 0.28/0.46  thf(fact_236_order__le__less__subst2,axiom,
% 0.28/0.46      ! [A: int,B: int,F: int > int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_le_less_subst2
% 0.28/0.46  thf(fact_237_order__less__le__subst1,axiom,
% 0.28/0.46      ! [A: real,F: real > real,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_eq_real @ B @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_le_subst1
% 0.28/0.46  thf(fact_238_order__less__le__subst1,axiom,
% 0.28/0.46      ! [A: int,F: real > int,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_eq_real @ B @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_le_subst1
% 0.28/0.46  thf(fact_239_order__less__le__subst1,axiom,
% 0.28/0.46      ! [A: real,F: int > real,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_real @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_eq_int @ B @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_le_subst1
% 0.28/0.46  thf(fact_240_order__less__le__subst1,axiom,
% 0.28/0.46      ! [A: int,F: int > int,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_int @ A @ ( F @ B ) )
% 0.28/0.46       => ( ( ord_less_eq_int @ B @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_le_subst1
% 0.28/0.46  thf(fact_241_order__less__le__subst2,axiom,
% 0.28/0.46      ! [A: real,B: real,F: real > real,C2: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_le_subst2
% 0.28/0.46  thf(fact_242_order__less__le__subst2,axiom,
% 0.28/0.46      ! [A: int,B: int,F: int > real,C2: real] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_le_subst2
% 0.28/0.46  thf(fact_243_order__less__le__subst2,axiom,
% 0.28/0.46      ! [A: real,B: real,F: real > int,C2: int] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: real,Y4: real] :
% 0.28/0.46                ( ( ord_less_real @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_le_subst2
% 0.28/0.46  thf(fact_244_order__less__le__subst2,axiom,
% 0.28/0.46      ! [A: int,B: int,F: int > int,C2: int] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 0.28/0.46         => ( ! [X4: int,Y4: int] :
% 0.28/0.46                ( ( ord_less_int @ X4 @ Y4 )
% 0.28/0.46               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.28/0.46           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order_less_le_subst2
% 0.28/0.46  thf(fact_245_not__le,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ~ ( ord_less_eq_real @ X2 @ Y2 ) )
% 0.28/0.46        = ( ord_less_real @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % not_le
% 0.28/0.46  thf(fact_246_not__le,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ~ ( ord_less_eq_int @ X2 @ Y2 ) )
% 0.28/0.46        = ( ord_less_int @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % not_le
% 0.28/0.46  thf(fact_247_not__less,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ~ ( ord_less_real @ X2 @ Y2 ) )
% 0.28/0.46        = ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % not_less
% 0.28/0.46  thf(fact_248_not__less,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ~ ( ord_less_int @ X2 @ Y2 ) )
% 0.28/0.46        = ( ord_less_eq_int @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % not_less
% 0.28/0.46  thf(fact_249_le__neq__trans,axiom,
% 0.28/0.46      ! [A: real,B: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46       => ( ( A != B )
% 0.28/0.46         => ( ord_less_real @ A @ B ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_neq_trans
% 0.28/0.46  thf(fact_250_le__neq__trans,axiom,
% 0.28/0.46      ! [A: int,B: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46       => ( ( A != B )
% 0.28/0.46         => ( ord_less_int @ A @ B ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_neq_trans
% 0.28/0.46  thf(fact_251_antisym__conv1,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ~ ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.28/0.46          = ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % antisym_conv1
% 0.28/0.46  thf(fact_252_antisym__conv1,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ~ ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.28/0.46          = ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % antisym_conv1
% 0.28/0.46  thf(fact_253_antisym__conv2,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.28/0.46       => ( ( ~ ( ord_less_real @ X2 @ Y2 ) )
% 0.28/0.46          = ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % antisym_conv2
% 0.28/0.46  thf(fact_254_antisym__conv2,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.28/0.46       => ( ( ~ ( ord_less_int @ X2 @ Y2 ) )
% 0.28/0.46          = ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % antisym_conv2
% 0.28/0.46  thf(fact_255_less__imp__le,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_imp_le
% 0.28/0.46  thf(fact_256_less__imp__le,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ( ord_less_eq_int @ X2 @ Y2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_imp_le
% 0.28/0.46  thf(fact_257_le__less__trans,axiom,
% 0.28/0.46      ! [X2: real,Y2: real,Z3: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_real @ Y2 @ Z3 )
% 0.28/0.46         => ( ord_less_real @ X2 @ Z3 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_less_trans
% 0.28/0.46  thf(fact_258_le__less__trans,axiom,
% 0.28/0.46      ! [X2: int,Y2: int,Z3: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_int @ Y2 @ Z3 )
% 0.28/0.46         => ( ord_less_int @ X2 @ Z3 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_less_trans
% 0.28/0.46  thf(fact_259_less__le__trans,axiom,
% 0.28/0.46      ! [X2: real,Y2: real,Z3: real] :
% 0.28/0.46        ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_eq_real @ Y2 @ Z3 )
% 0.28/0.46         => ( ord_less_real @ X2 @ Z3 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_le_trans
% 0.28/0.46  thf(fact_260_less__le__trans,axiom,
% 0.28/0.46      ! [X2: int,Y2: int,Z3: int] :
% 0.28/0.46        ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_eq_int @ Y2 @ Z3 )
% 0.28/0.46         => ( ord_less_int @ X2 @ Z3 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_le_trans
% 0.28/0.46  thf(fact_261_dense__ge,axiom,
% 0.28/0.46      ! [Z3: real,Y2: real] :
% 0.28/0.46        ( ! [X4: real] :
% 0.28/0.46            ( ( ord_less_real @ Z3 @ X4 )
% 0.28/0.46           => ( ord_less_eq_real @ Y2 @ X4 ) )
% 0.28/0.46       => ( ord_less_eq_real @ Y2 @ Z3 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dense_ge
% 0.28/0.46  thf(fact_262_dense__le,axiom,
% 0.28/0.46      ! [Y2: real,Z3: real] :
% 0.28/0.46        ( ! [X4: real] :
% 0.28/0.46            ( ( ord_less_real @ X4 @ Y2 )
% 0.28/0.46           => ( ord_less_eq_real @ X4 @ Z3 ) )
% 0.28/0.46       => ( ord_less_eq_real @ Y2 @ Z3 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dense_le
% 0.28/0.46  thf(fact_263_le__less__linear,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.28/0.46        | ( ord_less_real @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_less_linear
% 0.28/0.46  thf(fact_264_le__less__linear,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.28/0.46        | ( ord_less_int @ Y2 @ X2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_less_linear
% 0.28/0.46  thf(fact_265_le__imp__less__or__eq,axiom,
% 0.28/0.46      ! [X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_real @ X2 @ Y2 )
% 0.28/0.46          | ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_imp_less_or_eq
% 0.28/0.46  thf(fact_266_le__imp__less__or__eq,axiom,
% 0.28/0.46      ! [X2: int,Y2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.28/0.46       => ( ( ord_less_int @ X2 @ Y2 )
% 0.28/0.46          | ( X2 = Y2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % le_imp_less_or_eq
% 0.28/0.46  thf(fact_267_less__le__not__le,axiom,
% 0.28/0.46      ( ord_less_real
% 0.28/0.46      = ( ^ [X: real,Y: real] :
% 0.28/0.46            ( ( ord_less_eq_real @ X @ Y )
% 0.28/0.46            & ~ ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_le_not_le
% 0.28/0.46  thf(fact_268_less__le__not__le,axiom,
% 0.28/0.46      ( ord_less_int
% 0.28/0.46      = ( ^ [X: int,Y: int] :
% 0.28/0.46            ( ( ord_less_eq_int @ X @ Y )
% 0.28/0.46            & ~ ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_le_not_le
% 0.28/0.46  thf(fact_269_not__le__imp__less,axiom,
% 0.28/0.46      ! [Y2: real,X2: real] :
% 0.28/0.46        ( ~ ( ord_less_eq_real @ Y2 @ X2 )
% 0.28/0.46       => ( ord_less_real @ X2 @ Y2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % not_le_imp_less
% 0.28/0.46  thf(fact_270_not__le__imp__less,axiom,
% 0.28/0.46      ! [Y2: int,X2: int] :
% 0.28/0.46        ( ~ ( ord_less_eq_int @ Y2 @ X2 )
% 0.28/0.46       => ( ord_less_int @ X2 @ Y2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % not_le_imp_less
% 0.28/0.46  thf(fact_271_order_Ostrict__trans1,axiom,
% 0.28/0.46      ! [A: real,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_real @ B @ C2 )
% 0.28/0.46         => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.strict_trans1
% 0.28/0.46  thf(fact_272_order_Ostrict__trans1,axiom,
% 0.28/0.46      ! [A: int,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_int @ B @ C2 )
% 0.28/0.46         => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.strict_trans1
% 0.28/0.46  thf(fact_273_order_Ostrict__trans2,axiom,
% 0.28/0.46      ! [A: real,B: real,C2: real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_real @ B @ C2 )
% 0.28/0.46         => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.strict_trans2
% 0.28/0.46  thf(fact_274_order_Ostrict__trans2,axiom,
% 0.28/0.46      ! [A: int,B: int,C2: int] :
% 0.28/0.46        ( ( ord_less_int @ A @ B )
% 0.28/0.46       => ( ( ord_less_eq_int @ B @ C2 )
% 0.28/0.46         => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.strict_trans2
% 0.28/0.46  thf(fact_275_order_Oorder__iff__strict,axiom,
% 0.28/0.46      ( ord_less_eq_real
% 0.28/0.46      = ( ^ [A4: real,B4: real] :
% 0.28/0.46            ( ( ord_less_real @ A4 @ B4 )
% 0.28/0.46            | ( A4 = B4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.order_iff_strict
% 0.28/0.46  thf(fact_276_order_Oorder__iff__strict,axiom,
% 0.28/0.46      ( ord_less_eq_int
% 0.28/0.46      = ( ^ [A4: int,B4: int] :
% 0.28/0.46            ( ( ord_less_int @ A4 @ B4 )
% 0.28/0.46            | ( A4 = B4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.order_iff_strict
% 0.28/0.46  thf(fact_277_order_Ostrict__iff__order,axiom,
% 0.28/0.46      ( ord_less_real
% 0.28/0.46      = ( ^ [A4: real,B4: real] :
% 0.28/0.46            ( ( ord_less_eq_real @ A4 @ B4 )
% 0.28/0.46            & ( A4 != B4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.strict_iff_order
% 0.28/0.46  thf(fact_278_order_Ostrict__iff__order,axiom,
% 0.28/0.46      ( ord_less_int
% 0.28/0.46      = ( ^ [A4: int,B4: int] :
% 0.28/0.46            ( ( ord_less_eq_int @ A4 @ B4 )
% 0.28/0.46            & ( A4 != B4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % order.strict_iff_order
% 0.28/0.46  thf(fact_279_dual__order_Ostrict__trans1,axiom,
% 0.28/0.46      ! [B: real,A: real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_real @ B @ A )
% 0.28/0.46       => ( ( ord_less_real @ C2 @ B )
% 0.28/0.46         => ( ord_less_real @ C2 @ A ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.strict_trans1
% 0.28/0.46  thf(fact_280_dual__order_Ostrict__trans1,axiom,
% 0.28/0.46      ! [B: int,A: int,C2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ B @ A )
% 0.28/0.46       => ( ( ord_less_int @ C2 @ B )
% 0.28/0.46         => ( ord_less_int @ C2 @ A ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.strict_trans1
% 0.28/0.46  thf(fact_281_dual__order_Ostrict__trans2,axiom,
% 0.28/0.46      ! [B: real,A: real,C2: real] :
% 0.28/0.46        ( ( ord_less_real @ B @ A )
% 0.28/0.46       => ( ( ord_less_eq_real @ C2 @ B )
% 0.28/0.46         => ( ord_less_real @ C2 @ A ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.strict_trans2
% 0.28/0.46  thf(fact_282_dual__order_Ostrict__trans2,axiom,
% 0.28/0.46      ! [B: int,A: int,C2: int] :
% 0.28/0.46        ( ( ord_less_int @ B @ A )
% 0.28/0.46       => ( ( ord_less_eq_int @ C2 @ B )
% 0.28/0.46         => ( ord_less_int @ C2 @ A ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dual_order.strict_trans2
% 0.28/0.46  thf(fact_283_dense__ge__bounded,axiom,
% 0.28/0.46      ! [Z3: real,X2: real,Y2: real] :
% 0.28/0.46        ( ( ord_less_real @ Z3 @ X2 )
% 0.28/0.46       => ( ! [W: real] :
% 0.28/0.46              ( ( ord_less_real @ Z3 @ W )
% 0.28/0.46             => ( ( ord_less_real @ W @ X2 )
% 0.28/0.46               => ( ord_less_eq_real @ Y2 @ W ) ) )
% 0.28/0.46         => ( ord_less_eq_real @ Y2 @ Z3 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % dense_ge_bounded
% 0.28/0.46  thf(fact_284_minf_I8_J,axiom,
% 0.28/0.46      ! [T2: real] :
% 0.28/0.46      ? [Z5: real] :
% 0.28/0.46      ! [X3: real] :
% 0.28/0.46        ( ( ord_less_real @ X3 @ Z5 )
% 0.28/0.46       => ~ ( ord_less_eq_real @ T2 @ X3 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % minf(8)
% 0.28/0.46  thf(fact_285_minf_I8_J,axiom,
% 0.28/0.46      ! [T2: int] :
% 0.28/0.46      ? [Z5: int] :
% 0.28/0.46      ! [X3: int] :
% 0.28/0.46        ( ( ord_less_int @ X3 @ Z5 )
% 0.28/0.46       => ~ ( ord_less_eq_int @ T2 @ X3 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % minf(8)
% 0.28/0.46  thf(fact_286_minf_I6_J,axiom,
% 0.28/0.46      ! [T2: real] :
% 0.28/0.46      ? [Z5: real] :
% 0.28/0.46      ! [X3: real] :
% 0.28/0.46        ( ( ord_less_real @ X3 @ Z5 )
% 0.28/0.46       => ( ord_less_eq_real @ X3 @ T2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % minf(6)
% 0.28/0.46  thf(fact_287_minf_I6_J,axiom,
% 0.28/0.46      ! [T2: int] :
% 0.28/0.46      ? [Z5: int] :
% 0.28/0.46      ! [X3: int] :
% 0.28/0.46        ( ( ord_less_int @ X3 @ Z5 )
% 0.28/0.46       => ( ord_less_eq_int @ X3 @ T2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % minf(6)
% 0.28/0.46  thf(fact_288_pinf_I8_J,axiom,
% 0.28/0.46      ! [T2: real] :
% 0.28/0.46      ? [Z5: real] :
% 0.28/0.46      ! [X3: real] :
% 0.28/0.46        ( ( ord_less_real @ Z5 @ X3 )
% 0.28/0.46       => ( ord_less_eq_real @ T2 @ X3 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(8)
% 0.28/0.46  thf(fact_289_pinf_I8_J,axiom,
% 0.28/0.46      ! [T2: int] :
% 0.28/0.46      ? [Z5: int] :
% 0.28/0.46      ! [X3: int] :
% 0.28/0.46        ( ( ord_less_int @ Z5 @ X3 )
% 0.28/0.46       => ( ord_less_eq_int @ T2 @ X3 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(8)
% 0.28/0.46  thf(fact_290_pinf_I6_J,axiom,
% 0.28/0.46      ! [T2: real] :
% 0.28/0.46      ? [Z5: real] :
% 0.28/0.46      ! [X3: real] :
% 0.28/0.46        ( ( ord_less_real @ Z5 @ X3 )
% 0.28/0.46       => ~ ( ord_less_eq_real @ X3 @ T2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(6)
% 0.28/0.46  thf(fact_291_pinf_I6_J,axiom,
% 0.28/0.46      ! [T2: int] :
% 0.28/0.46      ? [Z5: int] :
% 0.28/0.46      ! [X3: int] :
% 0.28/0.46        ( ( ord_less_int @ Z5 @ X3 )
% 0.28/0.46       => ~ ( ord_less_eq_int @ X3 @ T2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(6)
% 0.28/0.46  thf(fact_292_verit__comp__simplify1_I3_J,axiom,
% 0.28/0.46      ! [B7: real,A6: real] :
% 0.28/0.46        ( ( ~ ( ord_less_eq_real @ B7 @ A6 ) )
% 0.28/0.46        = ( ord_less_real @ A6 @ B7 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % verit_comp_simplify1(3)
% 0.28/0.46  thf(fact_293_verit__comp__simplify1_I3_J,axiom,
% 0.28/0.46      ! [B7: int,A6: int] :
% 0.28/0.46        ( ( ~ ( ord_less_eq_int @ B7 @ A6 ) )
% 0.28/0.46        = ( ord_less_int @ A6 @ B7 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % verit_comp_simplify1(3)
% 0.28/0.46  thf(fact_294_is__zero__null,axiom,
% 0.28/0.46      ( is_zero_real
% 0.28/0.46      = ( ^ [P3: poly_real] : ( P3 = zero_zero_poly_real ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % is_zero_null
% 0.28/0.46  thf(fact_295_is__zero__null,axiom,
% 0.28/0.46      ( is_zero_int
% 0.28/0.46      = ( ^ [P3: poly_int] : ( P3 = zero_zero_poly_int ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % is_zero_null
% 0.28/0.46  thf(fact_296_is__zero__null,axiom,
% 0.28/0.46      ( is_zero_poly_real
% 0.28/0.46      = ( ^ [P3: poly_poly_real] : ( P3 = zero_z1423781445y_real ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % is_zero_null
% 0.28/0.46  thf(fact_297_poly__cutoff__0,axiom,
% 0.28/0.46      ! [N: nat] :
% 0.28/0.46        ( ( poly_cutoff_real @ N @ zero_zero_poly_real )
% 0.28/0.46        = zero_zero_poly_real ) ).
% 0.28/0.46  
% 0.28/0.46  % poly_cutoff_0
% 0.28/0.46  thf(fact_298_poly__cutoff__0,axiom,
% 0.28/0.46      ! [N: nat] :
% 0.28/0.46        ( ( poly_cutoff_int @ N @ zero_zero_poly_int )
% 0.28/0.46        = zero_zero_poly_int ) ).
% 0.28/0.46  
% 0.28/0.46  % poly_cutoff_0
% 0.28/0.46  thf(fact_299_poly__cutoff__0,axiom,
% 0.28/0.46      ! [N: nat] :
% 0.28/0.46        ( ( poly_c1404107022y_real @ N @ zero_z1423781445y_real )
% 0.28/0.46        = zero_z1423781445y_real ) ).
% 0.28/0.46  
% 0.28/0.46  % poly_cutoff_0
% 0.28/0.46  thf(fact_300_subsetI,axiom,
% 0.28/0.46      ! [A2: set_real,B3: set_real] :
% 0.28/0.46        ( ! [X4: real] :
% 0.28/0.46            ( ( member_real @ X4 @ A2 )
% 0.28/0.46           => ( member_real @ X4 @ B3 ) )
% 0.28/0.46       => ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % subsetI
% 0.28/0.46  thf(fact_301_in__mono,axiom,
% 0.28/0.46      ! [A2: set_real,B3: set_real,X2: real] :
% 0.28/0.46        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.28/0.46       => ( ( member_real @ X2 @ A2 )
% 0.28/0.46         => ( member_real @ X2 @ B3 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % in_mono
% 0.28/0.46  thf(fact_302_subsetD,axiom,
% 0.28/0.46      ! [A2: set_real,B3: set_real,C2: real] :
% 0.28/0.46        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 0.28/0.46       => ( ( member_real @ C2 @ A2 )
% 0.28/0.46         => ( member_real @ C2 @ B3 ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % subsetD
% 0.28/0.46  thf(fact_303_subset__eq,axiom,
% 0.28/0.46      ( ord_less_eq_set_real
% 0.28/0.46      = ( ^ [A7: set_real,B5: set_real] :
% 0.28/0.46          ! [X: real] :
% 0.28/0.46            ( ( member_real @ X @ A7 )
% 0.28/0.46           => ( member_real @ X @ B5 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % subset_eq
% 0.28/0.46  thf(fact_304_subset__iff,axiom,
% 0.28/0.46      ( ord_less_eq_set_real
% 0.28/0.46      = ( ^ [A7: set_real,B5: set_real] :
% 0.28/0.46          ! [T3: real] :
% 0.28/0.46            ( ( member_real @ T3 @ A7 )
% 0.28/0.46           => ( member_real @ T3 @ B5 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % subset_iff
% 0.28/0.46  thf(fact_305_Collect__mono,axiom,
% 0.28/0.46      ! [P: real > $o,Q: real > $o] :
% 0.28/0.46        ( ! [X4: real] :
% 0.28/0.46            ( ( P @ X4 )
% 0.28/0.46           => ( Q @ X4 ) )
% 0.28/0.46       => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % Collect_mono
% 0.28/0.46  thf(fact_306_Collect__mono,axiom,
% 0.28/0.46      ! [P: int > $o,Q: int > $o] :
% 0.28/0.46        ( ! [X4: int] :
% 0.28/0.46            ( ( P @ X4 )
% 0.28/0.46           => ( Q @ X4 ) )
% 0.28/0.46       => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % Collect_mono
% 0.28/0.46  thf(fact_307_Collect__subset,axiom,
% 0.28/0.46      ! [A2: set_real,P: real > $o] :
% 0.28/0.46        ( ord_less_eq_set_real
% 0.28/0.46        @ ( collect_real
% 0.28/0.46          @ ^ [X: real] :
% 0.28/0.46              ( ( member_real @ X @ A2 )
% 0.28/0.46              & ( P @ X ) ) )
% 0.28/0.46        @ A2 ) ).
% 0.28/0.46  
% 0.28/0.46  % Collect_subset
% 0.28/0.46  thf(fact_308_Collect__subset,axiom,
% 0.28/0.46      ! [A2: set_int,P: int > $o] :
% 0.28/0.46        ( ord_less_eq_set_int
% 0.28/0.46        @ ( collect_int
% 0.28/0.46          @ ^ [X: int] :
% 0.28/0.46              ( ( member_int @ X @ A2 )
% 0.28/0.46              & ( P @ X ) ) )
% 0.28/0.46        @ A2 ) ).
% 0.28/0.46  
% 0.28/0.46  % Collect_subset
% 0.28/0.46  thf(fact_309_less__eq__set__def,axiom,
% 0.28/0.46      ( ord_less_eq_set_real
% 0.28/0.46      = ( ^ [A7: set_real,B5: set_real] :
% 0.28/0.46            ( ord_less_eq_real_o
% 0.28/0.46            @ ^ [X: real] : ( member_real @ X @ A7 )
% 0.28/0.46            @ ^ [X: real] : ( member_real @ X @ B5 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % less_eq_set_def
% 0.28/0.46  thf(fact_310_Collect__mono__iff,axiom,
% 0.28/0.46      ! [P: real > $o,Q: real > $o] :
% 0.28/0.46        ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 0.28/0.46        = ( ! [X: real] :
% 0.28/0.46              ( ( P @ X )
% 0.28/0.46             => ( Q @ X ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % Collect_mono_iff
% 0.28/0.46  thf(fact_311_Collect__mono__iff,axiom,
% 0.28/0.46      ! [P: int > $o,Q: int > $o] :
% 0.28/0.46        ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 0.28/0.46        = ( ! [X: int] :
% 0.28/0.46              ( ( P @ X )
% 0.28/0.46             => ( Q @ X ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % Collect_mono_iff
% 0.28/0.46  thf(fact_312_verit__la__disequality,axiom,
% 0.28/0.46      ! [A: real,B: real] :
% 0.28/0.46        ( ( A = B )
% 0.28/0.46        | ~ ( ord_less_eq_real @ A @ B )
% 0.28/0.46        | ~ ( ord_less_eq_real @ B @ A ) ) ).
% 0.28/0.46  
% 0.28/0.46  % verit_la_disequality
% 0.28/0.46  thf(fact_313_verit__la__disequality,axiom,
% 0.28/0.46      ! [A: int,B: int] :
% 0.28/0.46        ( ( A = B )
% 0.28/0.46        | ~ ( ord_less_eq_int @ A @ B )
% 0.28/0.46        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 0.28/0.46  
% 0.28/0.46  % verit_la_disequality
% 0.28/0.46  thf(fact_314_verit__comp__simplify1_I1_J,axiom,
% 0.28/0.46      ! [A: real] :
% 0.28/0.46        ~ ( ord_less_real @ A @ A ) ).
% 0.28/0.46  
% 0.28/0.46  % verit_comp_simplify1(1)
% 0.28/0.46  thf(fact_315_verit__comp__simplify1_I1_J,axiom,
% 0.28/0.46      ! [A: int] :
% 0.28/0.46        ~ ( ord_less_int @ A @ A ) ).
% 0.28/0.46  
% 0.28/0.46  % verit_comp_simplify1(1)
% 0.28/0.46  thf(fact_316_pinf_I1_J,axiom,
% 0.28/0.46      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 0.28/0.46        ( ? [Z: real] :
% 0.28/0.46          ! [X4: real] :
% 0.28/0.46            ( ( ord_less_real @ Z @ X4 )
% 0.28/0.46           => ( ( P @ X4 )
% 0.28/0.46              = ( P4 @ X4 ) ) )
% 0.28/0.46       => ( ? [Z: real] :
% 0.28/0.46            ! [X4: real] :
% 0.28/0.46              ( ( ord_less_real @ Z @ X4 )
% 0.28/0.46             => ( ( Q @ X4 )
% 0.28/0.46                = ( Q3 @ X4 ) ) )
% 0.28/0.46         => ? [Z5: real] :
% 0.28/0.46            ! [X3: real] :
% 0.28/0.46              ( ( ord_less_real @ Z5 @ X3 )
% 0.28/0.46             => ( ( ( P @ X3 )
% 0.28/0.46                  & ( Q @ X3 ) )
% 0.28/0.46                = ( ( P4 @ X3 )
% 0.28/0.46                  & ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(1)
% 0.28/0.46  thf(fact_317_pinf_I1_J,axiom,
% 0.28/0.46      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 0.28/0.46        ( ? [Z: int] :
% 0.28/0.46          ! [X4: int] :
% 0.28/0.46            ( ( ord_less_int @ Z @ X4 )
% 0.28/0.46           => ( ( P @ X4 )
% 0.28/0.46              = ( P4 @ X4 ) ) )
% 0.28/0.46       => ( ? [Z: int] :
% 0.28/0.46            ! [X4: int] :
% 0.28/0.46              ( ( ord_less_int @ Z @ X4 )
% 0.28/0.46             => ( ( Q @ X4 )
% 0.28/0.46                = ( Q3 @ X4 ) ) )
% 0.28/0.46         => ? [Z5: int] :
% 0.28/0.46            ! [X3: int] :
% 0.28/0.46              ( ( ord_less_int @ Z5 @ X3 )
% 0.28/0.46             => ( ( ( P @ X3 )
% 0.28/0.46                  & ( Q @ X3 ) )
% 0.28/0.46                = ( ( P4 @ X3 )
% 0.28/0.46                  & ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(1)
% 0.28/0.46  thf(fact_318_pinf_I2_J,axiom,
% 0.28/0.46      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 0.28/0.46        ( ? [Z: real] :
% 0.28/0.46          ! [X4: real] :
% 0.28/0.46            ( ( ord_less_real @ Z @ X4 )
% 0.28/0.46           => ( ( P @ X4 )
% 0.28/0.46              = ( P4 @ X4 ) ) )
% 0.28/0.46       => ( ? [Z: real] :
% 0.28/0.46            ! [X4: real] :
% 0.28/0.46              ( ( ord_less_real @ Z @ X4 )
% 0.28/0.46             => ( ( Q @ X4 )
% 0.28/0.46                = ( Q3 @ X4 ) ) )
% 0.28/0.46         => ? [Z5: real] :
% 0.28/0.46            ! [X3: real] :
% 0.28/0.46              ( ( ord_less_real @ Z5 @ X3 )
% 0.28/0.46             => ( ( ( P @ X3 )
% 0.28/0.46                  | ( Q @ X3 ) )
% 0.28/0.46                = ( ( P4 @ X3 )
% 0.28/0.46                  | ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(2)
% 0.28/0.46  thf(fact_319_pinf_I2_J,axiom,
% 0.28/0.46      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 0.28/0.46        ( ? [Z: int] :
% 0.28/0.46          ! [X4: int] :
% 0.28/0.46            ( ( ord_less_int @ Z @ X4 )
% 0.28/0.46           => ( ( P @ X4 )
% 0.28/0.46              = ( P4 @ X4 ) ) )
% 0.28/0.46       => ( ? [Z: int] :
% 0.28/0.46            ! [X4: int] :
% 0.28/0.46              ( ( ord_less_int @ Z @ X4 )
% 0.28/0.46             => ( ( Q @ X4 )
% 0.28/0.46                = ( Q3 @ X4 ) ) )
% 0.28/0.46         => ? [Z5: int] :
% 0.28/0.46            ! [X3: int] :
% 0.28/0.46              ( ( ord_less_int @ Z5 @ X3 )
% 0.28/0.46             => ( ( ( P @ X3 )
% 0.28/0.46                  | ( Q @ X3 ) )
% 0.28/0.46                = ( ( P4 @ X3 )
% 0.28/0.46                  | ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(2)
% 0.28/0.46  thf(fact_320_pinf_I3_J,axiom,
% 0.28/0.46      ! [T2: real] :
% 0.28/0.46      ? [Z5: real] :
% 0.28/0.46      ! [X3: real] :
% 0.28/0.46        ( ( ord_less_real @ Z5 @ X3 )
% 0.28/0.46       => ( X3 != T2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(3)
% 0.28/0.46  thf(fact_321_pinf_I3_J,axiom,
% 0.28/0.46      ! [T2: int] :
% 0.28/0.46      ? [Z5: int] :
% 0.28/0.46      ! [X3: int] :
% 0.28/0.46        ( ( ord_less_int @ Z5 @ X3 )
% 0.28/0.46       => ( X3 != T2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(3)
% 0.28/0.46  thf(fact_322_pinf_I4_J,axiom,
% 0.28/0.46      ! [T2: real] :
% 0.28/0.46      ? [Z5: real] :
% 0.28/0.46      ! [X3: real] :
% 0.28/0.46        ( ( ord_less_real @ Z5 @ X3 )
% 0.28/0.46       => ( X3 != T2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(4)
% 0.28/0.46  thf(fact_323_pinf_I4_J,axiom,
% 0.28/0.46      ! [T2: int] :
% 0.28/0.46      ? [Z5: int] :
% 0.28/0.46      ! [X3: int] :
% 0.28/0.46        ( ( ord_less_int @ Z5 @ X3 )
% 0.28/0.46       => ( X3 != T2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(4)
% 0.28/0.46  thf(fact_324_pinf_I5_J,axiom,
% 0.28/0.46      ! [T2: real] :
% 0.28/0.46      ? [Z5: real] :
% 0.28/0.46      ! [X3: real] :
% 0.28/0.46        ( ( ord_less_real @ Z5 @ X3 )
% 0.28/0.46       => ~ ( ord_less_real @ X3 @ T2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(5)
% 0.28/0.46  thf(fact_325_pinf_I5_J,axiom,
% 0.28/0.46      ! [T2: int] :
% 0.28/0.46      ? [Z5: int] :
% 0.28/0.46      ! [X3: int] :
% 0.28/0.46        ( ( ord_less_int @ Z5 @ X3 )
% 0.28/0.46       => ~ ( ord_less_int @ X3 @ T2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(5)
% 0.28/0.46  thf(fact_326_pinf_I7_J,axiom,
% 0.28/0.46      ! [T2: real] :
% 0.28/0.46      ? [Z5: real] :
% 0.28/0.46      ! [X3: real] :
% 0.28/0.46        ( ( ord_less_real @ Z5 @ X3 )
% 0.28/0.46       => ( ord_less_real @ T2 @ X3 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(7)
% 0.28/0.46  thf(fact_327_pinf_I7_J,axiom,
% 0.28/0.46      ! [T2: int] :
% 0.28/0.46      ? [Z5: int] :
% 0.28/0.46      ! [X3: int] :
% 0.28/0.46        ( ( ord_less_int @ Z5 @ X3 )
% 0.28/0.46       => ( ord_less_int @ T2 @ X3 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % pinf(7)
% 0.28/0.46  thf(fact_328_minf_I1_J,axiom,
% 0.28/0.46      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 0.28/0.46        ( ? [Z: real] :
% 0.28/0.46          ! [X4: real] :
% 0.28/0.46            ( ( ord_less_real @ X4 @ Z )
% 0.28/0.46           => ( ( P @ X4 )
% 0.28/0.46              = ( P4 @ X4 ) ) )
% 0.28/0.46       => ( ? [Z: real] :
% 0.28/0.46            ! [X4: real] :
% 0.28/0.46              ( ( ord_less_real @ X4 @ Z )
% 0.28/0.46             => ( ( Q @ X4 )
% 0.28/0.46                = ( Q3 @ X4 ) ) )
% 0.28/0.46         => ? [Z5: real] :
% 0.28/0.46            ! [X3: real] :
% 0.28/0.46              ( ( ord_less_real @ X3 @ Z5 )
% 0.28/0.46             => ( ( ( P @ X3 )
% 0.28/0.46                  & ( Q @ X3 ) )
% 0.28/0.46                = ( ( P4 @ X3 )
% 0.28/0.46                  & ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % minf(1)
% 0.28/0.46  thf(fact_329_minf_I1_J,axiom,
% 0.28/0.46      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 0.28/0.46        ( ? [Z: int] :
% 0.28/0.46          ! [X4: int] :
% 0.28/0.46            ( ( ord_less_int @ X4 @ Z )
% 0.28/0.46           => ( ( P @ X4 )
% 0.28/0.46              = ( P4 @ X4 ) ) )
% 0.28/0.46       => ( ? [Z: int] :
% 0.28/0.46            ! [X4: int] :
% 0.28/0.46              ( ( ord_less_int @ X4 @ Z )
% 0.28/0.46             => ( ( Q @ X4 )
% 0.28/0.46                = ( Q3 @ X4 ) ) )
% 0.28/0.46         => ? [Z5: int] :
% 0.28/0.46            ! [X3: int] :
% 0.28/0.46              ( ( ord_less_int @ X3 @ Z5 )
% 0.28/0.46             => ( ( ( P @ X3 )
% 0.28/0.46                  & ( Q @ X3 ) )
% 0.28/0.46                = ( ( P4 @ X3 )
% 0.28/0.46                  & ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % minf(1)
% 0.28/0.46  thf(fact_330_minf_I2_J,axiom,
% 0.28/0.46      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 0.28/0.46        ( ? [Z: real] :
% 0.28/0.46          ! [X4: real] :
% 0.28/0.46            ( ( ord_less_real @ X4 @ Z )
% 0.28/0.46           => ( ( P @ X4 )
% 0.28/0.46              = ( P4 @ X4 ) ) )
% 0.28/0.46       => ( ? [Z: real] :
% 0.28/0.46            ! [X4: real] :
% 0.28/0.46              ( ( ord_less_real @ X4 @ Z )
% 0.28/0.46             => ( ( Q @ X4 )
% 0.28/0.46                = ( Q3 @ X4 ) ) )
% 0.28/0.46         => ? [Z5: real] :
% 0.28/0.46            ! [X3: real] :
% 0.28/0.46              ( ( ord_less_real @ X3 @ Z5 )
% 0.28/0.46             => ( ( ( P @ X3 )
% 0.28/0.46                  | ( Q @ X3 ) )
% 0.28/0.46                = ( ( P4 @ X3 )
% 0.28/0.46                  | ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % minf(2)
% 0.28/0.46  thf(fact_331_minf_I2_J,axiom,
% 0.28/0.46      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 0.28/0.46        ( ? [Z: int] :
% 0.28/0.46          ! [X4: int] :
% 0.28/0.46            ( ( ord_less_int @ X4 @ Z )
% 0.28/0.46           => ( ( P @ X4 )
% 0.28/0.46              = ( P4 @ X4 ) ) )
% 0.28/0.46       => ( ? [Z: int] :
% 0.28/0.46            ! [X4: int] :
% 0.28/0.46              ( ( ord_less_int @ X4 @ Z )
% 0.28/0.46             => ( ( Q @ X4 )
% 0.28/0.46                = ( Q3 @ X4 ) ) )
% 0.28/0.46         => ? [Z5: int] :
% 0.28/0.46            ! [X3: int] :
% 0.28/0.46              ( ( ord_less_int @ X3 @ Z5 )
% 0.28/0.46             => ( ( ( P @ X3 )
% 0.28/0.46                  | ( Q @ X3 ) )
% 0.28/0.46                = ( ( P4 @ X3 )
% 0.28/0.46                  | ( Q3 @ X3 ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % minf(2)
% 0.28/0.46  thf(fact_332_minf_I3_J,axiom,
% 0.28/0.46      ! [T2: int] :
% 0.28/0.46      ? [Z5: int] :
% 0.28/0.46      ! [X3: int] :
% 0.28/0.46        ( ( ord_less_int @ X3 @ Z5 )
% 0.28/0.46       => ( X3 != T2 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % minf(3)
% 0.28/0.46  thf(fact_333_conj__le__cong,axiom,
% 0.28/0.46      ! [X2: int,X5: int,P: $o,P4: $o] :
% 0.28/0.46        ( ( X2 = X5 )
% 0.28/0.46       => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.28/0.46           => ( P = P4 ) )
% 0.28/0.46         => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.28/0.46              & P )
% 0.28/0.46            = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.28/0.46              & P4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % conj_le_cong
% 0.28/0.46  thf(fact_334_imp__le__cong,axiom,
% 0.28/0.46      ! [X2: int,X5: int,P: $o,P4: $o] :
% 0.28/0.46        ( ( X2 = X5 )
% 0.28/0.46       => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.28/0.46           => ( P = P4 ) )
% 0.28/0.46         => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 0.28/0.46             => P )
% 0.28/0.46            = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 0.28/0.46             => P4 ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % imp_le_cong
% 0.28/0.46  thf(fact_335_jump__poly__not__root,axiom,
% 0.28/0.46      ! [P2: poly_real,X2: real,Q2: poly_real] :
% 0.28/0.46        ( ( ( poly_real2 @ P2 @ X2 )
% 0.28/0.46         != zero_zero_real )
% 0.28/0.46       => ( ( sturm_276991412p_poly @ Q2 @ P2 @ X2 )
% 0.28/0.46          = zero_zero_int ) ) ).
% 0.28/0.46  
% 0.28/0.46  % jump_poly_not_root
% 0.28/0.46  thf(fact_336_jump__poly0_I2_J,axiom,
% 0.28/0.46      ! [Q2: poly_real,X2: real] :
% 0.28/0.46        ( ( sturm_276991412p_poly @ Q2 @ zero_zero_poly_real @ X2 )
% 0.28/0.46        = zero_zero_int ) ).
% 0.28/0.46  
% 0.28/0.46  % jump_poly0(2)
% 0.28/0.46  thf(fact_337_jump__poly0_I1_J,axiom,
% 0.28/0.46      ! [P2: poly_real,X2: real] :
% 0.28/0.46        ( ( sturm_276991412p_poly @ zero_zero_poly_real @ P2 @ X2 )
% 0.28/0.46        = zero_zero_int ) ).
% 0.28/0.46  
% 0.28/0.46  % jump_poly0(1)
% 0.28/0.46  thf(fact_338_verit__la__generic,axiom,
% 0.28/0.46      ! [A: int,X2: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ A @ X2 )
% 0.28/0.46        | ( A = X2 )
% 0.28/0.46        | ( ord_less_eq_int @ X2 @ A ) ) ).
% 0.28/0.46  
% 0.28/0.46  % verit_la_generic
% 0.28/0.46  thf(fact_339_finite__interval__int1,axiom,
% 0.28/0.46      ! [A: int,B: int] :
% 0.28/0.46        ( finite_finite_int
% 0.28/0.46        @ ( collect_int
% 0.28/0.46          @ ^ [I: int] :
% 0.28/0.46              ( ( ord_less_eq_int @ A @ I )
% 0.28/0.46              & ( ord_less_eq_int @ I @ B ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % finite_interval_int1
% 0.28/0.46  thf(fact_340_finite__interval__int2,axiom,
% 0.28/0.46      ! [A: int,B: int] :
% 0.28/0.46        ( finite_finite_int
% 0.28/0.46        @ ( collect_int
% 0.28/0.46          @ ^ [I: int] :
% 0.28/0.46              ( ( ord_less_eq_int @ A @ I )
% 0.28/0.46              & ( ord_less_int @ I @ B ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % finite_interval_int2
% 0.28/0.46  thf(fact_341_finite__interval__int4,axiom,
% 0.28/0.46      ! [A: int,B: int] :
% 0.28/0.46        ( finite_finite_int
% 0.28/0.46        @ ( collect_int
% 0.28/0.46          @ ^ [I: int] :
% 0.28/0.46              ( ( ord_less_int @ A @ I )
% 0.28/0.46              & ( ord_less_int @ I @ B ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % finite_interval_int4
% 0.28/0.46  thf(fact_342_finite__interval__int3,axiom,
% 0.28/0.46      ! [A: int,B: int] :
% 0.28/0.46        ( finite_finite_int
% 0.28/0.46        @ ( collect_int
% 0.28/0.46          @ ^ [I: int] :
% 0.28/0.46              ( ( ord_less_int @ A @ I )
% 0.28/0.46              & ( ord_less_eq_int @ I @ B ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % finite_interval_int3
% 0.28/0.46  thf(fact_343_less__int__code_I1_J,axiom,
% 0.28/0.46      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.28/0.46  
% 0.28/0.46  % less_int_code(1)
% 0.28/0.46  thf(fact_344_less__eq__int__code_I1_J,axiom,
% 0.28/0.46      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.28/0.46  
% 0.28/0.46  % less_eq_int_code(1)
% 0.28/0.46  thf(fact_345_cindex__poly__0_I2_J,axiom,
% 0.28/0.46      ! [A: real,B: real,Q2: poly_real] :
% 0.28/0.46        ( ( sturm_308542325x_poly @ A @ B @ Q2 @ zero_zero_poly_real )
% 0.28/0.46        = zero_zero_int ) ).
% 0.28/0.46  
% 0.28/0.46  % cindex_poly_0(2)
% 0.28/0.46  thf(fact_346_cindex__poly__0_I1_J,axiom,
% 0.28/0.46      ! [A: real,B: real,P2: poly_real] :
% 0.28/0.46        ( ( sturm_308542325x_poly @ A @ B @ zero_zero_poly_real @ P2 )
% 0.28/0.46        = zero_zero_int ) ).
% 0.28/0.46  
% 0.28/0.46  % cindex_poly_0(1)
% 0.28/0.46  thf(fact_347_cindex__poly__cross,axiom,
% 0.28/0.46      ! [A: real,B: real,P2: poly_real] :
% 0.28/0.46        ( ( ord_less_real @ A @ B )
% 0.28/0.46       => ( ( ( poly_real2 @ P2 @ A )
% 0.28/0.46           != zero_zero_real )
% 0.28/0.46         => ( ( ( poly_real2 @ P2 @ B )
% 0.28/0.46             != zero_zero_real )
% 0.28/0.46           => ( ( sturm_308542325x_poly @ A @ B @ one_one_poly_real @ P2 )
% 0.28/0.46              = ( sturm_1953858694_cross @ P2 @ A @ B ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % cindex_poly_cross
% 0.28/0.46  thf(fact_348_cindex__poly__def,axiom,
% 0.28/0.46      ( sturm_308542325x_poly
% 0.28/0.46      = ( ^ [A4: real,B4: real,Q4: poly_real,P3: poly_real] :
% 0.28/0.46            ( groups2051521940al_int @ ( sturm_276991412p_poly @ Q4 @ P3 )
% 0.28/0.46            @ ( collect_real
% 0.28/0.46              @ ^ [X: real] :
% 0.28/0.46                  ( ( ( poly_real2 @ P3 @ X )
% 0.28/0.46                    = zero_zero_real )
% 0.28/0.46                  & ( ord_less_real @ A4 @ X )
% 0.28/0.46                  & ( ord_less_real @ X @ B4 ) ) ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  % cindex_poly_def
% 0.28/0.46  thf(fact_349_int__one__le__iff__zero__less,axiom,
% 0.28/0.46      ! [Z3: int] :
% 0.28/0.46        ( ( ord_less_eq_int @ one_one_int @ Z3 )
% 0.28/0.46        = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 0.28/0.46  
% 0.28/0.46  % int_one_le_iff_zero_less
% 0.28/0.46  
% 0.28/0.46  % Conjectures (1)
% 0.28/0.46  thf(conj_0,conjecture,
% 0.28/0.46      ( finite_finite_real
% 0.28/0.46      @ ( collect_real
% 0.28/0.46        @ ^ [X: real] :
% 0.28/0.46            ( ( ( poly_real2 @ p @ X )
% 0.28/0.46              = zero_zero_real )
% 0.28/0.46            & ( ord_less_real @ a @ X )
% 0.28/0.46            & ( ord_less_real @ X @ b ) ) ) ) ).
% 0.28/0.46  
% 0.28/0.46  %------------------------------------------------------------------------------
% 0.28/0.46  ------------------------
% 3.05/1.55  ---- Embedded in THF ---
% 3.05/1.55  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.05/1.55  %%% Generated on Tue Feb 24 08:29:19 EST 2026
% 3.05/1.55  %%% using '$$dhol' embedding, version 1.3.0.
% 3.05/1.55  %%% Logic specification used:
% 3.05/1.55  %%% thf(spec, logic, $$dhol).
% 3.05/1.55  
% 3.05/1.55  % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.JM2D9zVyZJ/DTF2DTF31682.p
% See solution above
% 3.05/1.55  ------------------------
% 3.05/1.58  ---- Cleaned THF ---
% 3.05/1.58  thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 3.05/1.58      poly_poly_poly_real: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 3.05/1.58      set_poly_poly_real: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.05/1.58      poly_poly_real: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Int__Oint_J_J,type,
% 3.05/1.58      poly_poly_int: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.05/1.58      set_poly_real: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Int__Oint_J_J,type,
% 3.05/1.58      set_poly_int: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Real__Oreal_J_J,type,
% 3.05/1.58      set_set_real: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 3.05/1.58      set_set_int: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.05/1.58      poly_real: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Polynomial__Opoly_It__Int__Oint_J,type,
% 3.05/1.58      poly_int: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Set__Oset_It__Real__Oreal_J,type,
% 3.05/1.58      set_real: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
% 3.05/1.58      set_int: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Real__Oreal,type,
% 3.05/1.58      real: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Nat__Onat,type,
% 3.05/1.58      nat: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(ty_n_t__Int__Oint,type,
% 3.05/1.58      int: $tType ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 3.05/1.58      finite_finite_int: set_int > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Finite__Set_Ofinite_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 3.05/1.58      finite385822667ly_int: set_poly_int > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Finite__Set_Ofinite_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.05/1.58      finite1328464339y_real: set_poly_poly_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Finite__Set_Ofinite_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.05/1.58      finite1810960971y_real: set_poly_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 3.05/1.58      finite_finite_real: set_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Int__Oint_J,type,
% 3.05/1.58      finite26677625et_int: set_set_int > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Real__Oreal_J,type,
% 3.05/1.58      finite475462905t_real: set_set_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 3.05/1.58      one_one_int: int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.05/1.58      one_one_poly_real: poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 3.05/1.58      zero_zero_int: int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 3.05/1.58      zero_zero_poly_int: poly_int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Int__Oint_J_J,type,
% 3.05/1.58      zero_z1549157189ly_int: poly_poly_int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J_J,type,
% 3.05/1.58      zero_z935034829y_real: poly_poly_poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.05/1.58      zero_z1423781445y_real: poly_poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.05/1.58      zero_zero_poly_real: poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 3.05/1.58      zero_zero_real: real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Real__Oreal_001t__Int__Oint,type,
% 3.05/1.58      groups2051521940al_int: ( real > int ) > set_real > int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 3.05/1.58      ord_less_int: int > int > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 3.05/1.58      ord_less_poly_int: poly_int > poly_int > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.05/1.58      ord_le38482960y_real: poly_poly_real > poly_poly_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.05/1.58      ord_less_poly_real: poly_real > poly_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 3.05/1.58      ord_less_real: real > real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
% 3.05/1.58      ord_less_set_int: set_int > set_int > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Real__Oreal_J,type,
% 3.05/1.58      ord_less_set_real: set_real > set_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Real__Oreal_M_Eo_J,type,
% 3.05/1.58      ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 3.05/1.58      ord_less_eq_int: int > int > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 3.05/1.58      ord_less_eq_poly_int: poly_int > poly_int > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.05/1.58      ord_le893774876y_real: poly_poly_real > poly_poly_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.05/1.58      ord_le1180086932y_real: poly_real > poly_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 3.05/1.58      ord_less_eq_real: real > real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
% 3.05/1.58      ord_less_eq_set_int: set_int > set_int > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
% 3.05/1.58      ord_less_eq_set_real: set_real > set_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Polynomial_Ois__zero_001t__Int__Oint,type,
% 3.05/1.58      is_zero_int: poly_int > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.05/1.58      is_zero_poly_real: poly_poly_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Polynomial_Ois__zero_001t__Real__Oreal,type,
% 3.05/1.58      is_zero_real: poly_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Polynomial_Opoly_001t__Int__Oint,type,
% 3.05/1.58      poly_int2: poly_int > int > int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 3.05/1.58      poly_poly_int2: poly_poly_int > poly_int > poly_int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.05/1.58      poly_poly_poly_real2: poly_poly_poly_real > poly_poly_real > poly_poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.05/1.58      poly_poly_real2: poly_poly_real > poly_real > poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Polynomial_Opoly_001t__Real__Oreal,type,
% 3.05/1.58      poly_real2: poly_real > real > real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Polynomial_Opoly__cutoff_001t__Int__Oint,type,
% 3.05/1.58      poly_cutoff_int: nat > poly_int > poly_int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Polynomial_Opoly__cutoff_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.05/1.58      poly_c1404107022y_real: nat > poly_poly_real > poly_poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Polynomial_Opoly__cutoff_001t__Real__Oreal,type,
% 3.05/1.58      poly_cutoff_real: nat > poly_real > poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Set_OCollect_001t__Int__Oint,type,
% 3.05/1.58      collect_int: ( int > $o ) > set_int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Set_OCollect_001t__Polynomial__Opoly_It__Int__Oint_J,type,
% 3.05/1.58      collect_poly_int: ( poly_int > $o ) > set_poly_int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Set_OCollect_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J,type,
% 3.05/1.58      collec927113489y_real: ( poly_poly_real > $o ) > set_poly_poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Set_OCollect_001t__Polynomial__Opoly_It__Real__Oreal_J,type,
% 3.05/1.58      collect_poly_real: ( poly_real > $o ) > set_poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 3.05/1.58      collect_real: ( real > $o ) > set_real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Int__Oint_J,type,
% 3.05/1.58      collect_set_int: ( set_int > $o ) > set_set_int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Set_OCollect_001t__Set__Oset_It__Real__Oreal_J,type,
% 3.05/1.58      collect_set_real: ( set_real > $o ) > set_set_real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Sturm__Tarski__Mirabelle__skihomvtkj_Ocindex__poly,type,
% 3.05/1.58      sturm_308542325x_poly: real > real > poly_real > poly_real > int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Sturm__Tarski__Mirabelle__skihomvtkj_Ocross,type,
% 3.05/1.58      sturm_1953858694_cross: poly_real > real > real > int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_Sturm__Tarski__Mirabelle__skihomvtkj_Ojump__poly,type,
% 3.05/1.58      sturm_276991412p_poly: poly_real > poly_real > real > int ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_member_001t__Int__Oint,type,
% 3.05/1.58      member_int: int > set_int > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_c_member_001t__Real__Oreal,type,
% 3.05/1.58      member_real: real > set_real > $o ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_v_a,type,
% 3.05/1.58      a: real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_v_a_H,type,
% 3.05/1.58      a2: real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_v_b,type,
% 3.05/1.58      b: real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_v_b_H,type,
% 3.05/1.58      b2: real ).
% 3.05/1.58  
% 3.05/1.58  thf(sy_v_p,type,
% 3.05/1.58      p: poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062,axiom,
% 3.05/1.58      ( finite_finite_real
% 3.05/1.58      @ ( collect_real
% 3.05/1.58        @ ^ [X: real] :
% 3.05/1.58            ( ( poly_real2 @ p @ X )
% 3.05/1.58            = zero_zero_real ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_1_assms_I2_J,axiom,
% 3.05/1.58      ord_less_real @ a2 @ b2 ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_2_assms_I3_J,axiom,
% 3.05/1.58      ord_less_real @ b2 @ b ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_3_assms_I1_J,axiom,
% 3.05/1.58      ord_less_real @ a @ a2 ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_4_False,axiom,
% 3.05/1.58      p != zero_zero_poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_5_poly__0,axiom,
% 3.05/1.58      ! [X2: poly_int] :
% 3.05/1.58        ( ( poly_poly_int2 @ zero_z1549157189ly_int @ X2 )
% 3.05/1.58        = zero_zero_poly_int ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_6_poly__0,axiom,
% 3.05/1.58      ! [X2: poly_poly_real] :
% 3.05/1.58        ( ( poly_poly_poly_real2 @ zero_z935034829y_real @ X2 )
% 3.05/1.58        = zero_z1423781445y_real ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_7_poly__0,axiom,
% 3.05/1.58      ! [X2: poly_real] :
% 3.05/1.58        ( ( poly_poly_real2 @ zero_z1423781445y_real @ X2 )
% 3.05/1.58        = zero_zero_poly_real ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_8_poly__0,axiom,
% 3.05/1.58      ! [X2: int] :
% 3.05/1.58        ( ( poly_int2 @ zero_zero_poly_int @ X2 )
% 3.05/1.58        = zero_zero_int ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_9_poly__0,axiom,
% 3.05/1.58      ! [X2: real] :
% 3.05/1.58        ( ( poly_real2 @ zero_zero_poly_real @ X2 )
% 3.05/1.58        = zero_zero_real ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_10_assms_I4_J,axiom,
% 3.05/1.58      ! [X3: real] :
% 3.05/1.58        ( ( ( ( ord_less_real @ a @ X3 )
% 3.05/1.58            & ( ord_less_eq_real @ X3 @ a2 ) )
% 3.05/1.58          | ( ( ord_less_eq_real @ b2 @ X3 )
% 3.05/1.58            & ( ord_less_real @ X3 @ b ) ) )
% 3.05/1.58       => ( ( poly_real2 @ p @ X3 )
% 3.05/1.58         != zero_zero_real ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_11_finite__Collect__conjI,axiom,
% 3.05/1.58      ! [P: real > $o,Q: real > $o] :
% 3.05/1.58        ( ( ( finite_finite_real @ ( collect_real @ P ) )
% 3.05/1.58          | ( finite_finite_real @ ( collect_real @ Q ) ) )
% 3.05/1.58       => ( finite_finite_real
% 3.05/1.58          @ ( collect_real
% 3.05/1.58            @ ^ [X: real] :
% 3.05/1.58                ( ( P @ X )
% 3.05/1.58                & ( Q @ X ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_12_finite__Collect__conjI,axiom,
% 3.05/1.58      ! [P: int > $o,Q: int > $o] :
% 3.05/1.58        ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 3.05/1.58          | ( finite_finite_int @ ( collect_int @ Q ) ) )
% 3.05/1.58       => ( finite_finite_int
% 3.05/1.58          @ ( collect_int
% 3.05/1.58            @ ^ [X: int] :
% 3.05/1.58                ( ( P @ X )
% 3.05/1.58                & ( Q @ X ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_13_finite__Collect__disjI,axiom,
% 3.05/1.58      ! [P: real > $o,Q: real > $o] :
% 3.05/1.58        ( ( finite_finite_real
% 3.05/1.58          @ ( collect_real
% 3.05/1.58            @ ^ [X: real] :
% 3.05/1.58                ( ( P @ X )
% 3.05/1.58                | ( Q @ X ) ) ) )
% 3.05/1.58        = ( ( finite_finite_real @ ( collect_real @ P ) )
% 3.05/1.58          & ( finite_finite_real @ ( collect_real @ Q ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_14_finite__Collect__disjI,axiom,
% 3.05/1.58      ! [P: int > $o,Q: int > $o] :
% 3.05/1.58        ( ( finite_finite_int
% 3.05/1.58          @ ( collect_int
% 3.05/1.58            @ ^ [X: int] :
% 3.05/1.58                ( ( P @ X )
% 3.05/1.58                | ( Q @ X ) ) ) )
% 3.05/1.58        = ( ( finite_finite_int @ ( collect_int @ P ) )
% 3.05/1.58          & ( finite_finite_int @ ( collect_int @ Q ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_15_poly__roots__finite,axiom,
% 3.05/1.58      ! [P2: poly_poly_int] :
% 3.05/1.58        ( ( P2 != zero_z1549157189ly_int )
% 3.05/1.58       => ( finite385822667ly_int
% 3.05/1.58          @ ( collect_poly_int
% 3.05/1.58            @ ^ [X: poly_int] :
% 3.05/1.58                ( ( poly_poly_int2 @ P2 @ X )
% 3.05/1.58                = zero_zero_poly_int ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_16_poly__roots__finite,axiom,
% 3.05/1.58      ! [P2: poly_poly_poly_real] :
% 3.05/1.58        ( ( P2 != zero_z935034829y_real )
% 3.05/1.58       => ( finite1328464339y_real
% 3.05/1.58          @ ( collec927113489y_real
% 3.05/1.58            @ ^ [X: poly_poly_real] :
% 3.05/1.58                ( ( poly_poly_poly_real2 @ P2 @ X )
% 3.05/1.58                = zero_z1423781445y_real ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_17_poly__roots__finite,axiom,
% 3.05/1.58      ! [P2: poly_real] :
% 3.05/1.58        ( ( P2 != zero_zero_poly_real )
% 3.05/1.58       => ( finite_finite_real
% 3.05/1.58          @ ( collect_real
% 3.05/1.58            @ ^ [X: real] :
% 3.05/1.58                ( ( poly_real2 @ P2 @ X )
% 3.05/1.58                = zero_zero_real ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_18_poly__roots__finite,axiom,
% 3.05/1.58      ! [P2: poly_int] :
% 3.05/1.58        ( ( P2 != zero_zero_poly_int )
% 3.05/1.58       => ( finite_finite_int
% 3.05/1.58          @ ( collect_int
% 3.05/1.58            @ ^ [X: int] :
% 3.05/1.58                ( ( poly_int2 @ P2 @ X )
% 3.05/1.58                = zero_zero_int ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_19_poly__roots__finite,axiom,
% 3.05/1.58      ! [P2: poly_poly_real] :
% 3.05/1.58        ( ( P2 != zero_z1423781445y_real )
% 3.05/1.58       => ( finite1810960971y_real
% 3.05/1.58          @ ( collect_poly_real
% 3.05/1.58            @ ^ [X: poly_real] :
% 3.05/1.58                ( ( poly_poly_real2 @ P2 @ X )
% 3.05/1.58                = zero_zero_poly_real ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_20_poly__IVT__neg,axiom,
% 3.05/1.58      ! [A: real,B: real,P2: poly_real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P2 @ A ) )
% 3.05/1.58         => ( ( ord_less_real @ ( poly_real2 @ P2 @ B ) @ zero_zero_real )
% 3.05/1.58           => ? [X4: real] :
% 3.05/1.58                ( ( ord_less_real @ A @ X4 )
% 3.05/1.58                & ( ord_less_real @ X4 @ B )
% 3.05/1.58                & ( ( poly_real2 @ P2 @ X4 )
% 3.05/1.58                  = zero_zero_real ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_21_poly__IVT__pos,axiom,
% 3.05/1.58      ! [A: real,B: real,P2: poly_real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_real @ ( poly_real2 @ P2 @ A ) @ zero_zero_real )
% 3.05/1.58         => ( ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P2 @ B ) )
% 3.05/1.58           => ? [X4: real] :
% 3.05/1.58                ( ( ord_less_real @ A @ X4 )
% 3.05/1.58                & ( ord_less_real @ X4 @ B )
% 3.05/1.58                & ( ( poly_real2 @ P2 @ X4 )
% 3.05/1.58                  = zero_zero_real ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_22_poly__all__0__iff__0,axiom,
% 3.05/1.58      ! [P2: poly_real] :
% 3.05/1.58        ( ( ! [X: real] :
% 3.05/1.58              ( ( poly_real2 @ P2 @ X )
% 3.05/1.58              = zero_zero_real ) )
% 3.05/1.58        = ( P2 = zero_zero_poly_real ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_23_poly__all__0__iff__0,axiom,
% 3.05/1.58      ! [P2: poly_poly_real] :
% 3.05/1.58        ( ( ! [X: poly_real] :
% 3.05/1.58              ( ( poly_poly_real2 @ P2 @ X )
% 3.05/1.58              = zero_zero_poly_real ) )
% 3.05/1.58        = ( P2 = zero_z1423781445y_real ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_24_poly__all__0__iff__0,axiom,
% 3.05/1.58      ! [P2: poly_int] :
% 3.05/1.58        ( ( ! [X: int] :
% 3.05/1.58              ( ( poly_int2 @ P2 @ X )
% 3.05/1.58              = zero_zero_int ) )
% 3.05/1.58        = ( P2 = zero_zero_poly_int ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_25_poly__all__0__iff__0,axiom,
% 3.05/1.58      ! [P2: poly_poly_int] :
% 3.05/1.58        ( ( ! [X: poly_int] :
% 3.05/1.58              ( ( poly_poly_int2 @ P2 @ X )
% 3.05/1.58              = zero_zero_poly_int ) )
% 3.05/1.58        = ( P2 = zero_z1549157189ly_int ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_26_poly__all__0__iff__0,axiom,
% 3.05/1.58      ! [P2: poly_poly_poly_real] :
% 3.05/1.58        ( ( ! [X: poly_poly_real] :
% 3.05/1.58              ( ( poly_poly_poly_real2 @ P2 @ X )
% 3.05/1.58              = zero_z1423781445y_real ) )
% 3.05/1.58        = ( P2 = zero_z935034829y_real ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_27_less__numeral__extra_I3_J,axiom,
% 3.05/1.58      ~ ( ord_less_poly_real @ zero_zero_poly_real @ zero_zero_poly_real ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_28_less__numeral__extra_I3_J,axiom,
% 3.05/1.58      ~ ( ord_less_poly_int @ zero_zero_poly_int @ zero_zero_poly_int ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_29_less__numeral__extra_I3_J,axiom,
% 3.05/1.58      ~ ( ord_le38482960y_real @ zero_z1423781445y_real @ zero_z1423781445y_real ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_30_less__numeral__extra_I3_J,axiom,
% 3.05/1.58      ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_31_less__numeral__extra_I3_J,axiom,
% 3.05/1.58      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_32_le__numeral__extra_I3_J,axiom,
% 3.05/1.58      ord_le1180086932y_real @ zero_zero_poly_real @ zero_zero_poly_real ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_33_le__numeral__extra_I3_J,axiom,
% 3.05/1.58      ord_less_eq_poly_int @ zero_zero_poly_int @ zero_zero_poly_int ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_34_le__numeral__extra_I3_J,axiom,
% 3.05/1.58      ord_le893774876y_real @ zero_z1423781445y_real @ zero_z1423781445y_real ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_35_le__numeral__extra_I3_J,axiom,
% 3.05/1.58      ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_36_le__numeral__extra_I3_J,axiom,
% 3.05/1.58      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_37_finite__psubset__induct,axiom,
% 3.05/1.58      ! [A2: set_real,P: set_real > $o] :
% 3.05/1.58        ( ( finite_finite_real @ A2 )
% 3.05/1.58       => ( ! [A3: set_real] :
% 3.05/1.58              ( ( finite_finite_real @ A3 )
% 3.05/1.58             => ( ! [B2: set_real] :
% 3.05/1.58                    ( ( ord_less_set_real @ B2 @ A3 )
% 3.05/1.58                   => ( P @ B2 ) )
% 3.05/1.58               => ( P @ A3 ) ) )
% 3.05/1.58         => ( P @ A2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_38_finite__psubset__induct,axiom,
% 3.05/1.58      ! [A2: set_int,P: set_int > $o] :
% 3.05/1.58        ( ( finite_finite_int @ A2 )
% 3.05/1.58       => ( ! [A3: set_int] :
% 3.05/1.58              ( ( finite_finite_int @ A3 )
% 3.05/1.58             => ( ! [B2: set_int] :
% 3.05/1.58                    ( ( ord_less_set_int @ B2 @ A3 )
% 3.05/1.58                   => ( P @ B2 ) )
% 3.05/1.58               => ( P @ A3 ) ) )
% 3.05/1.58         => ( P @ A2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_39_finite__has__minimal2,axiom,
% 3.05/1.58      ! [A2: set_real,A: real] :
% 3.05/1.58        ( ( finite_finite_real @ A2 )
% 3.05/1.58       => ( ( member_real @ A @ A2 )
% 3.05/1.58         => ? [X4: real] :
% 3.05/1.58              ( ( member_real @ X4 @ A2 )
% 3.05/1.58              & ( ord_less_eq_real @ X4 @ A )
% 3.05/1.58              & ! [Xa: real] :
% 3.05/1.58                  ( ( member_real @ Xa @ A2 )
% 3.05/1.58                 => ( ( ord_less_eq_real @ Xa @ X4 )
% 3.05/1.58                   => ( X4 = Xa ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_40_finite__has__minimal2,axiom,
% 3.05/1.58      ! [A2: set_int,A: int] :
% 3.05/1.58        ( ( finite_finite_int @ A2 )
% 3.05/1.58       => ( ( member_int @ A @ A2 )
% 3.05/1.58         => ? [X4: int] :
% 3.05/1.58              ( ( member_int @ X4 @ A2 )
% 3.05/1.58              & ( ord_less_eq_int @ X4 @ A )
% 3.05/1.58              & ! [Xa: int] :
% 3.05/1.58                  ( ( member_int @ Xa @ A2 )
% 3.05/1.58                 => ( ( ord_less_eq_int @ Xa @ X4 )
% 3.05/1.58                   => ( X4 = Xa ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_41_finite__has__maximal2,axiom,
% 3.05/1.58      ! [A2: set_real,A: real] :
% 3.05/1.58        ( ( finite_finite_real @ A2 )
% 3.05/1.58       => ( ( member_real @ A @ A2 )
% 3.05/1.58         => ? [X4: real] :
% 3.05/1.58              ( ( member_real @ X4 @ A2 )
% 3.05/1.58              & ( ord_less_eq_real @ A @ X4 )
% 3.05/1.58              & ! [Xa: real] :
% 3.05/1.58                  ( ( member_real @ Xa @ A2 )
% 3.05/1.58                 => ( ( ord_less_eq_real @ X4 @ Xa )
% 3.05/1.58                   => ( X4 = Xa ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_42_finite__has__maximal2,axiom,
% 3.05/1.58      ! [A2: set_int,A: int] :
% 3.05/1.58        ( ( finite_finite_int @ A2 )
% 3.05/1.58       => ( ( member_int @ A @ A2 )
% 3.05/1.58         => ? [X4: int] :
% 3.05/1.58              ( ( member_int @ X4 @ A2 )
% 3.05/1.58              & ( ord_less_eq_int @ A @ X4 )
% 3.05/1.58              & ! [Xa: int] :
% 3.05/1.58                  ( ( member_int @ Xa @ A2 )
% 3.05/1.58                 => ( ( ord_less_eq_int @ X4 @ Xa )
% 3.05/1.58                   => ( X4 = Xa ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_43_next__non__root__interval,axiom,
% 3.05/1.58      ! [P2: poly_real,Lb: real] :
% 3.05/1.58        ( ( P2 != zero_zero_poly_real )
% 3.05/1.58       => ~ ! [Ub: real] :
% 3.05/1.58              ( ( ord_less_real @ Lb @ Ub )
% 3.05/1.58             => ~ ! [Z: real] :
% 3.05/1.58                    ( ( ( ord_less_real @ Lb @ Z )
% 3.05/1.58                      & ( ord_less_eq_real @ Z @ Ub ) )
% 3.05/1.58                   => ( ( poly_real2 @ P2 @ Z )
% 3.05/1.58                     != zero_zero_real ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_44_last__non__root__interval,axiom,
% 3.05/1.58      ! [P2: poly_real,Ub2: real] :
% 3.05/1.58        ( ( P2 != zero_zero_poly_real )
% 3.05/1.58       => ~ ! [Lb2: real] :
% 3.05/1.58              ( ( ord_less_real @ Lb2 @ Ub2 )
% 3.05/1.58             => ~ ! [Z: real] :
% 3.05/1.58                    ( ( ( ord_less_eq_real @ Lb2 @ Z )
% 3.05/1.58                      & ( ord_less_real @ Z @ Ub2 ) )
% 3.05/1.58                   => ( ( poly_real2 @ P2 @ Z )
% 3.05/1.58                     != zero_zero_real ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_45_zero__reorient,axiom,
% 3.05/1.58      ! [X2: real] :
% 3.05/1.58        ( ( zero_zero_real = X2 )
% 3.05/1.58        = ( X2 = zero_zero_real ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_46_zero__reorient,axiom,
% 3.05/1.58      ! [X2: poly_real] :
% 3.05/1.58        ( ( zero_zero_poly_real = X2 )
% 3.05/1.58        = ( X2 = zero_zero_poly_real ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_47_zero__reorient,axiom,
% 3.05/1.58      ! [X2: int] :
% 3.05/1.58        ( ( zero_zero_int = X2 )
% 3.05/1.58        = ( X2 = zero_zero_int ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_48_zero__reorient,axiom,
% 3.05/1.58      ! [X2: poly_int] :
% 3.05/1.58        ( ( zero_zero_poly_int = X2 )
% 3.05/1.58        = ( X2 = zero_zero_poly_int ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_49_zero__reorient,axiom,
% 3.05/1.58      ! [X2: poly_poly_real] :
% 3.05/1.58        ( ( zero_z1423781445y_real = X2 )
% 3.05/1.58        = ( X2 = zero_z1423781445y_real ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_50_not__eq__pos__or__neg__iff__2,axiom,
% 3.05/1.58      ! [Lb: real,Ub2: real,P2: poly_real] :
% 3.05/1.58        ( ( ! [Z2: real] :
% 3.05/1.58              ( ( ( ord_less_eq_real @ Lb @ Z2 )
% 3.05/1.58                & ( ord_less_real @ Z2 @ Ub2 ) )
% 3.05/1.58             => ( ( poly_real2 @ P2 @ Z2 )
% 3.05/1.58               != zero_zero_real ) ) )
% 3.05/1.58        = ( ! [Z2: real] :
% 3.05/1.58              ( ( ( ord_less_eq_real @ Lb @ Z2 )
% 3.05/1.58                & ( ord_less_real @ Z2 @ Ub2 ) )
% 3.05/1.58             => ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P2 @ Z2 ) ) )
% 3.05/1.58          | ! [Z2: real] :
% 3.05/1.58              ( ( ( ord_less_eq_real @ Lb @ Z2 )
% 3.05/1.58                & ( ord_less_real @ Z2 @ Ub2 ) )
% 3.05/1.58             => ( ord_less_real @ ( poly_real2 @ P2 @ Z2 ) @ zero_zero_real ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_51_not__eq__pos__or__neg__iff__1,axiom,
% 3.05/1.58      ! [Lb: real,Ub2: real,P2: poly_real] :
% 3.05/1.58        ( ( ! [Z2: real] :
% 3.05/1.58              ( ( ( ord_less_real @ Lb @ Z2 )
% 3.05/1.58                & ( ord_less_eq_real @ Z2 @ Ub2 ) )
% 3.05/1.58             => ( ( poly_real2 @ P2 @ Z2 )
% 3.05/1.58               != zero_zero_real ) ) )
% 3.05/1.58        = ( ! [Z2: real] :
% 3.05/1.58              ( ( ( ord_less_real @ Lb @ Z2 )
% 3.05/1.58                & ( ord_less_eq_real @ Z2 @ Ub2 ) )
% 3.05/1.58             => ( ord_less_real @ zero_zero_real @ ( poly_real2 @ P2 @ Z2 ) ) )
% 3.05/1.58          | ! [Z2: real] :
% 3.05/1.58              ( ( ( ord_less_real @ Lb @ Z2 )
% 3.05/1.58                & ( ord_less_eq_real @ Z2 @ Ub2 ) )
% 3.05/1.58             => ( ord_less_real @ ( poly_real2 @ P2 @ Z2 ) @ zero_zero_real ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_52_poly__eq__poly__eq__iff,axiom,
% 3.05/1.58      ! [P2: poly_real,Q2: poly_real] :
% 3.05/1.58        ( ( ( poly_real2 @ P2 )
% 3.05/1.58          = ( poly_real2 @ Q2 ) )
% 3.05/1.58        = ( P2 = Q2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_53_poly__eq__poly__eq__iff,axiom,
% 3.05/1.58      ! [P2: poly_int,Q2: poly_int] :
% 3.05/1.58        ( ( ( poly_int2 @ P2 )
% 3.05/1.58          = ( poly_int2 @ Q2 ) )
% 3.05/1.58        = ( P2 = Q2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_54_poly__eq__poly__eq__iff,axiom,
% 3.05/1.58      ! [P2: poly_poly_real,Q2: poly_poly_real] :
% 3.05/1.58        ( ( ( poly_poly_real2 @ P2 )
% 3.05/1.58          = ( poly_poly_real2 @ Q2 ) )
% 3.05/1.58        = ( P2 = Q2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_55_pigeonhole__infinite__rel,axiom,
% 3.05/1.58      ! [A2: set_real,B3: set_real,R: real > real > $o] :
% 3.05/1.58        ( ~ ( finite_finite_real @ A2 )
% 3.05/1.58       => ( ( finite_finite_real @ B3 )
% 3.05/1.58         => ( ! [X4: real] :
% 3.05/1.58                ( ( member_real @ X4 @ A2 )
% 3.05/1.58               => ? [Xa: real] :
% 3.05/1.58                    ( ( member_real @ Xa @ B3 )
% 3.05/1.58                    & ( R @ X4 @ Xa ) ) )
% 3.05/1.58           => ? [X4: real] :
% 3.05/1.58                ( ( member_real @ X4 @ B3 )
% 3.05/1.58                & ~ ( finite_finite_real
% 3.05/1.58                    @ ( collect_real
% 3.05/1.58                      @ ^ [A4: real] :
% 3.05/1.58                          ( ( member_real @ A4 @ A2 )
% 3.05/1.58                          & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_56_pigeonhole__infinite__rel,axiom,
% 3.05/1.58      ! [A2: set_real,B3: set_int,R: real > int > $o] :
% 3.05/1.58        ( ~ ( finite_finite_real @ A2 )
% 3.05/1.58       => ( ( finite_finite_int @ B3 )
% 3.05/1.58         => ( ! [X4: real] :
% 3.05/1.58                ( ( member_real @ X4 @ A2 )
% 3.05/1.58               => ? [Xa: int] :
% 3.05/1.58                    ( ( member_int @ Xa @ B3 )
% 3.05/1.58                    & ( R @ X4 @ Xa ) ) )
% 3.05/1.58           => ? [X4: int] :
% 3.05/1.58                ( ( member_int @ X4 @ B3 )
% 3.05/1.58                & ~ ( finite_finite_real
% 3.05/1.58                    @ ( collect_real
% 3.05/1.58                      @ ^ [A4: real] :
% 3.05/1.58                          ( ( member_real @ A4 @ A2 )
% 3.05/1.58                          & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_57_pigeonhole__infinite__rel,axiom,
% 3.05/1.58      ! [A2: set_int,B3: set_real,R: int > real > $o] :
% 3.05/1.58        ( ~ ( finite_finite_int @ A2 )
% 3.05/1.58       => ( ( finite_finite_real @ B3 )
% 3.05/1.58         => ( ! [X4: int] :
% 3.05/1.58                ( ( member_int @ X4 @ A2 )
% 3.05/1.58               => ? [Xa: real] :
% 3.05/1.58                    ( ( member_real @ Xa @ B3 )
% 3.05/1.58                    & ( R @ X4 @ Xa ) ) )
% 3.05/1.58           => ? [X4: real] :
% 3.05/1.58                ( ( member_real @ X4 @ B3 )
% 3.05/1.58                & ~ ( finite_finite_int
% 3.05/1.58                    @ ( collect_int
% 3.05/1.58                      @ ^ [A4: int] :
% 3.05/1.58                          ( ( member_int @ A4 @ A2 )
% 3.05/1.58                          & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_58_pigeonhole__infinite__rel,axiom,
% 3.05/1.58      ! [A2: set_int,B3: set_int,R: int > int > $o] :
% 3.05/1.58        ( ~ ( finite_finite_int @ A2 )
% 3.05/1.58       => ( ( finite_finite_int @ B3 )
% 3.05/1.58         => ( ! [X4: int] :
% 3.05/1.58                ( ( member_int @ X4 @ A2 )
% 3.05/1.58               => ? [Xa: int] :
% 3.05/1.58                    ( ( member_int @ Xa @ B3 )
% 3.05/1.58                    & ( R @ X4 @ Xa ) ) )
% 3.05/1.58           => ? [X4: int] :
% 3.05/1.58                ( ( member_int @ X4 @ B3 )
% 3.05/1.58                & ~ ( finite_finite_int
% 3.05/1.58                    @ ( collect_int
% 3.05/1.58                      @ ^ [A4: int] :
% 3.05/1.58                          ( ( member_int @ A4 @ A2 )
% 3.05/1.58                          & ( R @ A4 @ X4 ) ) ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_59_not__finite__existsD,axiom,
% 3.05/1.58      ! [P: real > $o] :
% 3.05/1.58        ( ~ ( finite_finite_real @ ( collect_real @ P ) )
% 3.05/1.58       => ? [X_1: real] : ( P @ X_1 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_60_not__finite__existsD,axiom,
% 3.05/1.58      ! [P: int > $o] :
% 3.05/1.58        ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 3.05/1.58       => ? [X_1: int] : ( P @ X_1 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_61_order__refl,axiom,
% 3.05/1.58      ! [X2: real] : ( ord_less_eq_real @ X2 @ X2 ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_62_order__refl,axiom,
% 3.05/1.58      ! [X2: int] : ( ord_less_eq_int @ X2 @ X2 ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_63_cross__no__root,axiom,
% 3.05/1.58      ! [A: real,B: real,P2: poly_real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ! [X4: real] :
% 3.05/1.58              ( ( ( ord_less_real @ A @ X4 )
% 3.05/1.58                & ( ord_less_real @ X4 @ B ) )
% 3.05/1.58             => ( ( poly_real2 @ P2 @ X4 )
% 3.05/1.58               != zero_zero_real ) )
% 3.05/1.58         => ( ( sturm_1953858694_cross @ P2 @ A @ B )
% 3.05/1.58            = zero_zero_int ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_64_less__eq__real__def,axiom,
% 3.05/1.58      ( ord_less_eq_real
% 3.05/1.58      = ( ^ [X: real,Y: real] :
% 3.05/1.58            ( ( ord_less_real @ X @ Y )
% 3.05/1.58            | ( X = Y ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_65_complete__interval,axiom,
% 3.05/1.58      ! [A: real,B: real,P: real > $o] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( P @ A )
% 3.05/1.58         => ( ~ ( P @ B )
% 3.05/1.58           => ? [C: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ A @ C )
% 3.05/1.58                & ( ord_less_eq_real @ C @ B )
% 3.05/1.58                & ! [X3: real] :
% 3.05/1.58                    ( ( ( ord_less_eq_real @ A @ X3 )
% 3.05/1.58                      & ( ord_less_real @ X3 @ C ) )
% 3.05/1.58                   => ( P @ X3 ) )
% 3.05/1.58                & ! [D: real] :
% 3.05/1.58                    ( ! [X4: real] :
% 3.05/1.58                        ( ( ( ord_less_eq_real @ A @ X4 )
% 3.05/1.58                          & ( ord_less_real @ X4 @ D ) )
% 3.05/1.58                       => ( P @ X4 ) )
% 3.05/1.58                   => ( ord_less_eq_real @ D @ C ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_66_complete__interval,axiom,
% 3.05/1.58      ! [A: int,B: int,P: int > $o] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ( ( P @ A )
% 3.05/1.58         => ( ~ ( P @ B )
% 3.05/1.58           => ? [C: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ A @ C )
% 3.05/1.58                & ( ord_less_eq_int @ C @ B )
% 3.05/1.58                & ! [X3: int] :
% 3.05/1.58                    ( ( ( ord_less_eq_int @ A @ X3 )
% 3.05/1.58                      & ( ord_less_int @ X3 @ C ) )
% 3.05/1.58                   => ( P @ X3 ) )
% 3.05/1.58                & ! [D: int] :
% 3.05/1.58                    ( ! [X4: int] :
% 3.05/1.58                        ( ( ( ord_less_eq_int @ A @ X4 )
% 3.05/1.58                          & ( ord_less_int @ X4 @ D ) )
% 3.05/1.58                       => ( P @ X4 ) )
% 3.05/1.58                   => ( ord_less_eq_int @ D @ C ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_67_order_Onot__eq__order__implies__strict,axiom,
% 3.05/1.58      ! [A: real,B: real] :
% 3.05/1.58        ( ( A != B )
% 3.05/1.58       => ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58         => ( ord_less_real @ A @ B ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_68_order_Onot__eq__order__implies__strict,axiom,
% 3.05/1.58      ! [A: int,B: int] :
% 3.05/1.58        ( ( A != B )
% 3.05/1.58       => ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58         => ( ord_less_int @ A @ B ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_69_dual__order_Ostrict__implies__order,axiom,
% 3.05/1.58      ! [B: real,A: real] :
% 3.05/1.58        ( ( ord_less_real @ B @ A )
% 3.05/1.58       => ( ord_less_eq_real @ B @ A ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_70_dual__order_Ostrict__implies__order,axiom,
% 3.05/1.58      ! [B: int,A: int] :
% 3.05/1.58        ( ( ord_less_int @ B @ A )
% 3.05/1.58       => ( ord_less_eq_int @ B @ A ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_71_dual__order_Ostrict__iff__order,axiom,
% 3.05/1.58      ( ord_less_real
% 3.05/1.58      = ( ^ [B4: real,A4: real] :
% 3.05/1.58            ( ( ord_less_eq_real @ B4 @ A4 )
% 3.05/1.58            & ( A4 != B4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_72_dual__order_Ostrict__iff__order,axiom,
% 3.05/1.58      ( ord_less_int
% 3.05/1.58      = ( ^ [B4: int,A4: int] :
% 3.05/1.58            ( ( ord_less_eq_int @ B4 @ A4 )
% 3.05/1.58            & ( A4 != B4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_73_dual__order_Oorder__iff__strict,axiom,
% 3.05/1.58      ( ord_less_eq_real
% 3.05/1.58      = ( ^ [B4: real,A4: real] :
% 3.05/1.58            ( ( ord_less_real @ B4 @ A4 )
% 3.05/1.58            | ( A4 = B4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_74_dual__order_Oorder__iff__strict,axiom,
% 3.05/1.58      ( ord_less_eq_int
% 3.05/1.58      = ( ^ [B4: int,A4: int] :
% 3.05/1.58            ( ( ord_less_int @ B4 @ A4 )
% 3.05/1.58            | ( A4 = B4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_75_mem__Collect__eq,axiom,
% 3.05/1.58      ! [A: real,P: real > $o] :
% 3.05/1.58        ( ( member_real @ A @ ( collect_real @ P ) )
% 3.05/1.58        = ( P @ A ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_76_mem__Collect__eq,axiom,
% 3.05/1.58      ! [A: int,P: int > $o] :
% 3.05/1.58        ( ( member_int @ A @ ( collect_int @ P ) )
% 3.05/1.58        = ( P @ A ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_77_Collect__mem__eq,axiom,
% 3.05/1.58      ! [A2: set_real] :
% 3.05/1.58        ( ( collect_real
% 3.05/1.58          @ ^ [X: real] : ( member_real @ X @ A2 ) )
% 3.05/1.58        = A2 ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_78_Collect__mem__eq,axiom,
% 3.05/1.58      ! [A2: set_int] :
% 3.05/1.58        ( ( collect_int
% 3.05/1.58          @ ^ [X: int] : ( member_int @ X @ A2 ) )
% 3.05/1.58        = A2 ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_79_Collect__cong,axiom,
% 3.05/1.58      ! [P: real > $o,Q: real > $o] :
% 3.05/1.58        ( ! [X4: real] :
% 3.05/1.58            ( ( P @ X4 )
% 3.05/1.58            = ( Q @ X4 ) )
% 3.05/1.58       => ( ( collect_real @ P )
% 3.05/1.58          = ( collect_real @ Q ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_80_Collect__cong,axiom,
% 3.05/1.58      ! [P: int > $o,Q: int > $o] :
% 3.05/1.58        ( ! [X4: int] :
% 3.05/1.58            ( ( P @ X4 )
% 3.05/1.58            = ( Q @ X4 ) )
% 3.05/1.58       => ( ( collect_int @ P )
% 3.05/1.58          = ( collect_int @ Q ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_81_order_Ostrict__implies__order,axiom,
% 3.05/1.58      ! [A: real,B: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ord_less_eq_real @ A @ B ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_82_order_Ostrict__implies__order,axiom,
% 3.05/1.58      ! [A: int,B: int] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ( ord_less_eq_int @ A @ B ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_83_dense__le__bounded,axiom,
% 3.05/1.58      ! [X2: real,Y2: real,Z3: real] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ( ! [W: real] :
% 3.05/1.58              ( ( ord_less_real @ X2 @ W )
% 3.05/1.58             => ( ( ord_less_real @ W @ Y2 )
% 3.05/1.58               => ( ord_less_eq_real @ W @ Z3 ) ) )
% 3.05/1.58         => ( ord_less_eq_real @ Y2 @ Z3 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_84_finite__Collect__subsets,axiom,
% 3.05/1.58      ! [A2: set_real] :
% 3.05/1.58        ( ( finite_finite_real @ A2 )
% 3.05/1.58       => ( finite475462905t_real
% 3.05/1.58          @ ( collect_set_real
% 3.05/1.58            @ ^ [B5: set_real] : ( ord_less_eq_set_real @ B5 @ A2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_85_finite__Collect__subsets,axiom,
% 3.05/1.58      ! [A2: set_int] :
% 3.05/1.58        ( ( finite_finite_int @ A2 )
% 3.05/1.58       => ( finite26677625et_int
% 3.05/1.58          @ ( collect_set_int
% 3.05/1.58            @ ^ [B5: set_int] : ( ord_less_eq_set_int @ B5 @ A2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_86_cross__0,axiom,
% 3.05/1.58      ! [A: real,B: real] :
% 3.05/1.58        ( ( sturm_1953858694_cross @ zero_zero_poly_real @ A @ B )
% 3.05/1.58        = zero_zero_int ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_87_finite__subset,axiom,
% 3.05/1.58      ! [A2: set_real,B3: set_real] :
% 3.05/1.58        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 3.05/1.58       => ( ( finite_finite_real @ B3 )
% 3.05/1.58         => ( finite_finite_real @ A2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_88_finite__subset,axiom,
% 3.05/1.58      ! [A2: set_int,B3: set_int] :
% 3.05/1.58        ( ( ord_less_eq_set_int @ A2 @ B3 )
% 3.05/1.58       => ( ( finite_finite_int @ B3 )
% 3.05/1.58         => ( finite_finite_int @ A2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_89_infinite__super,axiom,
% 3.05/1.58      ! [S: set_real,T: set_real] :
% 3.05/1.58        ( ( ord_less_eq_set_real @ S @ T )
% 3.05/1.58       => ( ~ ( finite_finite_real @ S )
% 3.05/1.58         => ~ ( finite_finite_real @ T ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_90_infinite__super,axiom,
% 3.05/1.58      ! [S: set_int,T: set_int] :
% 3.05/1.58        ( ( ord_less_eq_set_int @ S @ T )
% 3.05/1.58       => ( ~ ( finite_finite_int @ S )
% 3.05/1.58         => ~ ( finite_finite_int @ T ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_91_rev__finite__subset,axiom,
% 3.05/1.58      ! [B3: set_real,A2: set_real] :
% 3.05/1.58        ( ( finite_finite_real @ B3 )
% 3.05/1.58       => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 3.05/1.58         => ( finite_finite_real @ A2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_92_rev__finite__subset,axiom,
% 3.05/1.58      ! [B3: set_int,A2: set_int] :
% 3.05/1.58        ( ( finite_finite_int @ B3 )
% 3.05/1.58       => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 3.05/1.58         => ( finite_finite_int @ A2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_93_dual__order_Oantisym,axiom,
% 3.05/1.58      ! [B: real,A: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ B @ A )
% 3.05/1.58       => ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58         => ( A = B ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_94_dual__order_Oantisym,axiom,
% 3.05/1.58      ! [B: int,A: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ B @ A )
% 3.05/1.58       => ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58         => ( A = B ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_95_dual__order_Oeq__iff,axiom,
% 3.05/1.58      ( ( ^ [Y3: real,Z4: real] : ( Y3 = Z4 ) )
% 3.05/1.58      = ( ^ [A4: real,B4: real] :
% 3.05/1.58            ( ( ord_less_eq_real @ B4 @ A4 )
% 3.05/1.58            & ( ord_less_eq_real @ A4 @ B4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_96_dual__order_Oeq__iff,axiom,
% 3.05/1.58      ( ( ^ [Y3: int,Z4: int] : ( Y3 = Z4 ) )
% 3.05/1.58      = ( ^ [A4: int,B4: int] :
% 3.05/1.58            ( ( ord_less_eq_int @ B4 @ A4 )
% 3.05/1.58            & ( ord_less_eq_int @ A4 @ B4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_97_dual__order_Otrans,axiom,
% 3.05/1.58      ! [B: real,A: real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ B @ A )
% 3.05/1.58       => ( ( ord_less_eq_real @ C2 @ B )
% 3.05/1.58         => ( ord_less_eq_real @ C2 @ A ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_98_dual__order_Otrans,axiom,
% 3.05/1.58      ! [B: int,A: int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ B @ A )
% 3.05/1.58       => ( ( ord_less_eq_int @ C2 @ B )
% 3.05/1.58         => ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_99_linorder__wlog,axiom,
% 3.05/1.58      ! [P: real > real > $o,A: real,B: real] :
% 3.05/1.58        ( ! [A5: real,B6: real] :
% 3.05/1.58            ( ( ord_less_eq_real @ A5 @ B6 )
% 3.05/1.58           => ( P @ A5 @ B6 ) )
% 3.05/1.58       => ( ! [A5: real,B6: real] :
% 3.05/1.58              ( ( P @ B6 @ A5 )
% 3.05/1.58             => ( P @ A5 @ B6 ) )
% 3.05/1.58         => ( P @ A @ B ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_100_linorder__wlog,axiom,
% 3.05/1.58      ! [P: int > int > $o,A: int,B: int] :
% 3.05/1.58        ( ! [A5: int,B6: int] :
% 3.05/1.58            ( ( ord_less_eq_int @ A5 @ B6 )
% 3.05/1.58           => ( P @ A5 @ B6 ) )
% 3.05/1.58       => ( ! [A5: int,B6: int] :
% 3.05/1.58              ( ( P @ B6 @ A5 )
% 3.05/1.58             => ( P @ A5 @ B6 ) )
% 3.05/1.58         => ( P @ A @ B ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_101_dual__order_Orefl,axiom,
% 3.05/1.58      ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_102_dual__order_Orefl,axiom,
% 3.05/1.58      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_103_order__trans,axiom,
% 3.05/1.58      ! [X2: real,Y2: real,Z3: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_eq_real @ Y2 @ Z3 )
% 3.05/1.58         => ( ord_less_eq_real @ X2 @ Z3 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_104_order__trans,axiom,
% 3.05/1.58      ! [X2: int,Y2: int,Z3: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_eq_int @ Y2 @ Z3 )
% 3.05/1.58         => ( ord_less_eq_int @ X2 @ Z3 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_105_order__class_Oorder_Oantisym,axiom,
% 3.05/1.58      ! [A: real,B: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_real @ B @ A )
% 3.05/1.58         => ( A = B ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_106_order__class_Oorder_Oantisym,axiom,
% 3.05/1.58      ! [A: int,B: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_int @ B @ A )
% 3.05/1.58         => ( A = B ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_107_ord__le__eq__trans,axiom,
% 3.05/1.58      ! [A: real,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58       => ( ( B = C2 )
% 3.05/1.58         => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_108_ord__le__eq__trans,axiom,
% 3.05/1.58      ! [A: int,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58       => ( ( B = C2 )
% 3.05/1.58         => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_109_ord__eq__le__trans,axiom,
% 3.05/1.58      ! [A: real,B: real,C2: real] :
% 3.05/1.58        ( ( A = B )
% 3.05/1.58       => ( ( ord_less_eq_real @ B @ C2 )
% 3.05/1.58         => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_110_ord__eq__le__trans,axiom,
% 3.05/1.58      ! [A: int,B: int,C2: int] :
% 3.05/1.58        ( ( A = B )
% 3.05/1.58       => ( ( ord_less_eq_int @ B @ C2 )
% 3.05/1.58         => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_111_order__class_Oorder_Oeq__iff,axiom,
% 3.05/1.58      ( ( ^ [Y3: real,Z4: real] : ( Y3 = Z4 ) )
% 3.05/1.58      = ( ^ [A4: real,B4: real] :
% 3.05/1.58            ( ( ord_less_eq_real @ A4 @ B4 )
% 3.05/1.58            & ( ord_less_eq_real @ B4 @ A4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_112_order__class_Oorder_Oeq__iff,axiom,
% 3.05/1.58      ( ( ^ [Y3: int,Z4: int] : ( Y3 = Z4 ) )
% 3.05/1.58      = ( ^ [A4: int,B4: int] :
% 3.05/1.58            ( ( ord_less_eq_int @ A4 @ B4 )
% 3.05/1.58            & ( ord_less_eq_int @ B4 @ A4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_113_antisym__conv,axiom,
% 3.05/1.58      ! [Y2: real,X2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ Y2 @ X2 )
% 3.05/1.58       => ( ( ord_less_eq_real @ X2 @ Y2 )
% 3.05/1.58          = ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_114_antisym__conv,axiom,
% 3.05/1.58      ! [Y2: int,X2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ Y2 @ X2 )
% 3.05/1.58       => ( ( ord_less_eq_int @ X2 @ Y2 )
% 3.05/1.58          = ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_115_le__cases3,axiom,
% 3.05/1.58      ! [X2: real,Y2: real,Z3: real] :
% 3.05/1.58        ( ( ( ord_less_eq_real @ X2 @ Y2 )
% 3.05/1.58         => ~ ( ord_less_eq_real @ Y2 @ Z3 ) )
% 3.05/1.58       => ( ( ( ord_less_eq_real @ Y2 @ X2 )
% 3.05/1.58           => ~ ( ord_less_eq_real @ X2 @ Z3 ) )
% 3.05/1.58         => ( ( ( ord_less_eq_real @ X2 @ Z3 )
% 3.05/1.58             => ~ ( ord_less_eq_real @ Z3 @ Y2 ) )
% 3.05/1.58           => ( ( ( ord_less_eq_real @ Z3 @ Y2 )
% 3.05/1.58               => ~ ( ord_less_eq_real @ Y2 @ X2 ) )
% 3.05/1.58             => ( ( ( ord_less_eq_real @ Y2 @ Z3 )
% 3.05/1.58                 => ~ ( ord_less_eq_real @ Z3 @ X2 ) )
% 3.05/1.58               => ~ ( ( ord_less_eq_real @ Z3 @ X2 )
% 3.05/1.58                   => ~ ( ord_less_eq_real @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_116_le__cases3,axiom,
% 3.05/1.58      ! [X2: int,Y2: int,Z3: int] :
% 3.05/1.58        ( ( ( ord_less_eq_int @ X2 @ Y2 )
% 3.05/1.58         => ~ ( ord_less_eq_int @ Y2 @ Z3 ) )
% 3.05/1.58       => ( ( ( ord_less_eq_int @ Y2 @ X2 )
% 3.05/1.58           => ~ ( ord_less_eq_int @ X2 @ Z3 ) )
% 3.05/1.58         => ( ( ( ord_less_eq_int @ X2 @ Z3 )
% 3.05/1.58             => ~ ( ord_less_eq_int @ Z3 @ Y2 ) )
% 3.05/1.58           => ( ( ( ord_less_eq_int @ Z3 @ Y2 )
% 3.05/1.58               => ~ ( ord_less_eq_int @ Y2 @ X2 ) )
% 3.05/1.58             => ( ( ( ord_less_eq_int @ Y2 @ Z3 )
% 3.05/1.58                 => ~ ( ord_less_eq_int @ Z3 @ X2 ) )
% 3.05/1.58               => ~ ( ( ord_less_eq_int @ Z3 @ X2 )
% 3.05/1.58                   => ~ ( ord_less_eq_int @ X2 @ Y2 ) ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_117_order_Otrans,axiom,
% 3.05/1.58      ! [A: real,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_real @ B @ C2 )
% 3.05/1.58         => ( ord_less_eq_real @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_118_order_Otrans,axiom,
% 3.05/1.58      ! [A: int,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_int @ B @ C2 )
% 3.05/1.58         => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_119_le__cases,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ~ ( ord_less_eq_real @ X2 @ Y2 )
% 3.05/1.58       => ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_120_le__cases,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ~ ( ord_less_eq_int @ X2 @ Y2 )
% 3.05/1.58       => ( ord_less_eq_int @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_121_eq__refl,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( X2 = Y2 )
% 3.05/1.58       => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_122_eq__refl,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( X2 = Y2 )
% 3.05/1.58       => ( ord_less_eq_int @ X2 @ Y2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_123_linear,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ X2 @ Y2 )
% 3.05/1.58        | ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_124_linear,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ X2 @ Y2 )
% 3.05/1.58        | ( ord_less_eq_int @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_125_antisym,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_eq_real @ Y2 @ X2 )
% 3.05/1.58         => ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_126_antisym,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_eq_int @ Y2 @ X2 )
% 3.05/1.58         => ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_127_eq__iff,axiom,
% 3.05/1.58      ( ( ^ [Y3: real,Z4: real] : ( Y3 = Z4 ) )
% 3.05/1.58      = ( ^ [X: real,Y: real] :
% 3.05/1.58            ( ( ord_less_eq_real @ X @ Y )
% 3.05/1.58            & ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_128_eq__iff,axiom,
% 3.05/1.58      ( ( ^ [Y3: int,Z4: int] : ( Y3 = Z4 ) )
% 3.05/1.58      = ( ^ [X: int,Y: int] :
% 3.05/1.58            ( ( ord_less_eq_int @ X @ Y )
% 3.05/1.58            & ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_129_ord__le__eq__subst,axiom,
% 3.05/1.58      ! [A: real,B: real,F: real > real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58       => ( ( ( F @ B )
% 3.05/1.58            = C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_130_ord__le__eq__subst,axiom,
% 3.05/1.58      ! [A: real,B: real,F: real > int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58       => ( ( ( F @ B )
% 3.05/1.58            = C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_131_ord__le__eq__subst,axiom,
% 3.05/1.58      ! [A: int,B: int,F: int > real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58       => ( ( ( F @ B )
% 3.05/1.58            = C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_132_ord__le__eq__subst,axiom,
% 3.05/1.58      ! [A: int,B: int,F: int > int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58       => ( ( ( F @ B )
% 3.05/1.58            = C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_133_ord__eq__le__subst,axiom,
% 3.05/1.58      ! [A: real,F: real > real,B: real,C2: real] :
% 3.05/1.58        ( ( A
% 3.05/1.58          = ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_eq_real @ B @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_134_ord__eq__le__subst,axiom,
% 3.05/1.58      ! [A: int,F: real > int,B: real,C2: real] :
% 3.05/1.58        ( ( A
% 3.05/1.58          = ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_eq_real @ B @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_135_ord__eq__le__subst,axiom,
% 3.05/1.58      ! [A: real,F: int > real,B: int,C2: int] :
% 3.05/1.58        ( ( A
% 3.05/1.58          = ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_eq_int @ B @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_136_ord__eq__le__subst,axiom,
% 3.05/1.58      ! [A: int,F: int > int,B: int,C2: int] :
% 3.05/1.58        ( ( A
% 3.05/1.58          = ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_eq_int @ B @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_137_order__subst2,axiom,
% 3.05/1.58      ! [A: real,B: real,F: real > real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_138_order__subst2,axiom,
% 3.05/1.58      ! [A: real,B: real,F: real > int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_139_order__subst2,axiom,
% 3.05/1.58      ! [A: int,B: int,F: int > real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_140_order__subst2,axiom,
% 3.05/1.58      ! [A: int,B: int,F: int > int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_141_order__subst1,axiom,
% 3.05/1.58      ! [A: real,F: real > real,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_eq_real @ B @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_142_order__subst1,axiom,
% 3.05/1.58      ! [A: real,F: int > real,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_eq_int @ B @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_143_order__subst1,axiom,
% 3.05/1.58      ! [A: int,F: real > int,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_eq_real @ B @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_144_order__subst1,axiom,
% 3.05/1.58      ! [A: int,F: int > int,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_eq_int @ B @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_eq_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_145_ord__eq__less__subst,axiom,
% 3.05/1.58      ! [A: real,F: real > real,B: real,C2: real] :
% 3.05/1.58        ( ( A
% 3.05/1.58          = ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_real @ B @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_146_ord__eq__less__subst,axiom,
% 3.05/1.58      ! [A: int,F: real > int,B: real,C2: real] :
% 3.05/1.58        ( ( A
% 3.05/1.58          = ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_real @ B @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_147_ord__eq__less__subst,axiom,
% 3.05/1.58      ! [A: real,F: int > real,B: int,C2: int] :
% 3.05/1.58        ( ( A
% 3.05/1.58          = ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_int @ B @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_148_ord__eq__less__subst,axiom,
% 3.05/1.58      ! [A: int,F: int > int,B: int,C2: int] :
% 3.05/1.58        ( ( A
% 3.05/1.58          = ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_int @ B @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_149_ord__less__eq__subst,axiom,
% 3.05/1.58      ! [A: real,B: real,F: real > real,C2: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( ( F @ B )
% 3.05/1.58            = C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_150_ord__less__eq__subst,axiom,
% 3.05/1.58      ! [A: real,B: real,F: real > int,C2: int] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( ( F @ B )
% 3.05/1.58            = C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_151_ord__less__eq__subst,axiom,
% 3.05/1.58      ! [A: int,B: int,F: int > real,C2: real] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ( ( ( F @ B )
% 3.05/1.58            = C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_152_ord__less__eq__subst,axiom,
% 3.05/1.58      ! [A: int,B: int,F: int > int,C2: int] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ( ( ( F @ B )
% 3.05/1.58            = C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_153_order__less__subst1,axiom,
% 3.05/1.58      ! [A: real,F: real > real,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_real @ B @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_154_order__less__subst1,axiom,
% 3.05/1.58      ! [A: real,F: int > real,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_real @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_int @ B @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_155_order__less__subst1,axiom,
% 3.05/1.58      ! [A: int,F: real > int,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_int @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_real @ B @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_156_order__less__subst1,axiom,
% 3.05/1.58      ! [A: int,F: int > int,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_int @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_int @ B @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_157_order__less__subst2,axiom,
% 3.05/1.58      ! [A: real,B: real,F: real > real,C2: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_158_order__less__subst2,axiom,
% 3.05/1.58      ! [A: real,B: real,F: real > int,C2: int] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_159_order__less__subst2,axiom,
% 3.05/1.58      ! [A: int,B: int,F: int > real,C2: real] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_160_order__less__subst2,axiom,
% 3.05/1.58      ! [A: int,B: int,F: int > int,C2: int] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_161_lt__ex,axiom,
% 3.05/1.58      ! [X2: real] :
% 3.05/1.58      ? [Y4: real] : ( ord_less_real @ Y4 @ X2 ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_162_lt__ex,axiom,
% 3.05/1.58      ! [X2: int] :
% 3.05/1.58      ? [Y4: int] : ( ord_less_int @ Y4 @ X2 ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_163_gt__ex,axiom,
% 3.05/1.58      ! [X2: real] :
% 3.05/1.58      ? [X_1: real] : ( ord_less_real @ X2 @ X_1 ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_164_gt__ex,axiom,
% 3.05/1.58      ! [X2: int] :
% 3.05/1.58      ? [X_1: int] : ( ord_less_int @ X2 @ X_1 ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_165_neqE,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( X2 != Y2 )
% 3.05/1.58       => ( ~ ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58         => ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_166_neqE,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( X2 != Y2 )
% 3.05/1.58       => ( ~ ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58         => ( ord_less_int @ Y2 @ X2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_167_neq__iff,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( X2 != Y2 )
% 3.05/1.58        = ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58          | ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_168_neq__iff,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( X2 != Y2 )
% 3.05/1.58        = ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58          | ( ord_less_int @ Y2 @ X2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_169_order_Oasym,axiom,
% 3.05/1.58      ! [A: real,B: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ~ ( ord_less_real @ B @ A ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_170_order_Oasym,axiom,
% 3.05/1.58      ! [A: int,B: int] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ~ ( ord_less_int @ B @ A ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_171_dense,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ? [Z5: real] :
% 3.05/1.58            ( ( ord_less_real @ X2 @ Z5 )
% 3.05/1.58            & ( ord_less_real @ Z5 @ Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_172_less__imp__neq,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ( X2 != Y2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_173_less__imp__neq,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ( X2 != Y2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_174_less__asym,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ~ ( ord_less_real @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_175_less__asym,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ~ ( ord_less_int @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_176_less__asym_H,axiom,
% 3.05/1.58      ! [A: real,B: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ~ ( ord_less_real @ B @ A ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_177_less__asym_H,axiom,
% 3.05/1.58      ! [A: int,B: int] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ~ ( ord_less_int @ B @ A ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_178_less__trans,axiom,
% 3.05/1.58      ! [X2: real,Y2: real,Z3: real] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_real @ Y2 @ Z3 )
% 3.05/1.58         => ( ord_less_real @ X2 @ Z3 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_179_less__trans,axiom,
% 3.05/1.58      ! [X2: int,Y2: int,Z3: int] :
% 3.05/1.58        ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_int @ Y2 @ Z3 )
% 3.05/1.58         => ( ord_less_int @ X2 @ Z3 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_180_less__linear,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58        | ( X2 = Y2 )
% 3.05/1.58        | ( ord_less_real @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_181_less__linear,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58        | ( X2 = Y2 )
% 3.05/1.58        | ( ord_less_int @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_182_less__irrefl,axiom,
% 3.05/1.58      ! [X2: real] :
% 3.05/1.58        ~ ( ord_less_real @ X2 @ X2 ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_183_less__irrefl,axiom,
% 3.05/1.58      ! [X2: int] :
% 3.05/1.58        ~ ( ord_less_int @ X2 @ X2 ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_184_ord__eq__less__trans,axiom,
% 3.05/1.58      ! [A: real,B: real,C2: real] :
% 3.05/1.58        ( ( A = B )
% 3.05/1.58       => ( ( ord_less_real @ B @ C2 )
% 3.05/1.58         => ( ord_less_real @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_185_ord__eq__less__trans,axiom,
% 3.05/1.58      ! [A: int,B: int,C2: int] :
% 3.05/1.58        ( ( A = B )
% 3.05/1.58       => ( ( ord_less_int @ B @ C2 )
% 3.05/1.58         => ( ord_less_int @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_186_ord__less__eq__trans,axiom,
% 3.05/1.58      ! [A: real,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( B = C2 )
% 3.05/1.58         => ( ord_less_real @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_187_ord__less__eq__trans,axiom,
% 3.05/1.58      ! [A: int,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ( ( B = C2 )
% 3.05/1.58         => ( ord_less_int @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_188_dual__order_Oasym,axiom,
% 3.05/1.58      ! [B: real,A: real] :
% 3.05/1.58        ( ( ord_less_real @ B @ A )
% 3.05/1.58       => ~ ( ord_less_real @ A @ B ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_189_dual__order_Oasym,axiom,
% 3.05/1.58      ! [B: int,A: int] :
% 3.05/1.58        ( ( ord_less_int @ B @ A )
% 3.05/1.58       => ~ ( ord_less_int @ A @ B ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_190_less__imp__not__eq,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ( X2 != Y2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_191_less__imp__not__eq,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ( X2 != Y2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_192_less__not__sym,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ~ ( ord_less_real @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_193_less__not__sym,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ~ ( ord_less_int @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_194_antisym__conv3,axiom,
% 3.05/1.58      ! [Y2: real,X2: real] :
% 3.05/1.58        ( ~ ( ord_less_real @ Y2 @ X2 )
% 3.05/1.58       => ( ( ~ ( ord_less_real @ X2 @ Y2 ) )
% 3.05/1.58          = ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_195_antisym__conv3,axiom,
% 3.05/1.58      ! [Y2: int,X2: int] :
% 3.05/1.58        ( ~ ( ord_less_int @ Y2 @ X2 )
% 3.05/1.58       => ( ( ~ ( ord_less_int @ X2 @ Y2 ) )
% 3.05/1.58          = ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_196_less__imp__not__eq2,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ( Y2 != X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_197_less__imp__not__eq2,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ( Y2 != X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_198_less__imp__triv,axiom,
% 3.05/1.58      ! [X2: real,Y2: real,P: $o] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_real @ Y2 @ X2 )
% 3.05/1.58         => P ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_199_less__imp__triv,axiom,
% 3.05/1.58      ! [X2: int,Y2: int,P: $o] :
% 3.05/1.58        ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_int @ Y2 @ X2 )
% 3.05/1.58         => P ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_200_linorder__cases,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ~ ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ( ( X2 != Y2 )
% 3.05/1.58         => ( ord_less_real @ Y2 @ X2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_201_linorder__cases,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ~ ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ( ( X2 != Y2 )
% 3.05/1.58         => ( ord_less_int @ Y2 @ X2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_202_dual__order_Oirrefl,axiom,
% 3.05/1.58      ! [A: real] :
% 3.05/1.58        ~ ( ord_less_real @ A @ A ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_203_dual__order_Oirrefl,axiom,
% 3.05/1.58      ! [A: int] :
% 3.05/1.58        ~ ( ord_less_int @ A @ A ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_204_order_Ostrict__trans,axiom,
% 3.05/1.58      ! [A: real,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_real @ B @ C2 )
% 3.05/1.58         => ( ord_less_real @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_205_order_Ostrict__trans,axiom,
% 3.05/1.58      ! [A: int,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_int @ B @ C2 )
% 3.05/1.58         => ( ord_less_int @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_206_less__imp__not__less,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ~ ( ord_less_real @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_207_less__imp__not__less,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ~ ( ord_less_int @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_208_linorder__less__wlog,axiom,
% 3.05/1.58      ! [P: real > real > $o,A: real,B: real] :
% 3.05/1.58        ( ! [A5: real,B6: real] :
% 3.05/1.58            ( ( ord_less_real @ A5 @ B6 )
% 3.05/1.58           => ( P @ A5 @ B6 ) )
% 3.05/1.58       => ( ! [A5: real] : ( P @ A5 @ A5 )
% 3.05/1.58         => ( ! [A5: real,B6: real] :
% 3.05/1.58                ( ( P @ B6 @ A5 )
% 3.05/1.58               => ( P @ A5 @ B6 ) )
% 3.05/1.58           => ( P @ A @ B ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_209_linorder__less__wlog,axiom,
% 3.05/1.58      ! [P: int > int > $o,A: int,B: int] :
% 3.05/1.58        ( ! [A5: int,B6: int] :
% 3.05/1.58            ( ( ord_less_int @ A5 @ B6 )
% 3.05/1.58           => ( P @ A5 @ B6 ) )
% 3.05/1.58       => ( ! [A5: int] : ( P @ A5 @ A5 )
% 3.05/1.58         => ( ! [A5: int,B6: int] :
% 3.05/1.58                ( ( P @ B6 @ A5 )
% 3.05/1.58               => ( P @ A5 @ B6 ) )
% 3.05/1.58           => ( P @ A @ B ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_210_dual__order_Ostrict__trans,axiom,
% 3.05/1.58      ! [B: real,A: real,C2: real] :
% 3.05/1.58        ( ( ord_less_real @ B @ A )
% 3.05/1.58       => ( ( ord_less_real @ C2 @ B )
% 3.05/1.58         => ( ord_less_real @ C2 @ A ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_211_dual__order_Ostrict__trans,axiom,
% 3.05/1.58      ! [B: int,A: int,C2: int] :
% 3.05/1.58        ( ( ord_less_int @ B @ A )
% 3.05/1.58       => ( ( ord_less_int @ C2 @ B )
% 3.05/1.58         => ( ord_less_int @ C2 @ A ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_212_not__less__iff__gr__or__eq,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ~ ( ord_less_real @ X2 @ Y2 ) )
% 3.05/1.58        = ( ( ord_less_real @ Y2 @ X2 )
% 3.05/1.58          | ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_213_not__less__iff__gr__or__eq,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ~ ( ord_less_int @ X2 @ Y2 ) )
% 3.05/1.58        = ( ( ord_less_int @ Y2 @ X2 )
% 3.05/1.58          | ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_214_order_Ostrict__implies__not__eq,axiom,
% 3.05/1.58      ! [A: real,B: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( A != B ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_215_order_Ostrict__implies__not__eq,axiom,
% 3.05/1.58      ! [A: int,B: int] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ( A != B ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_216_dual__order_Ostrict__implies__not__eq,axiom,
% 3.05/1.58      ! [B: real,A: real] :
% 3.05/1.58        ( ( ord_less_real @ B @ A )
% 3.05/1.58       => ( A != B ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_217_dual__order_Ostrict__implies__not__eq,axiom,
% 3.05/1.58      ! [B: int,A: int] :
% 3.05/1.58        ( ( ord_less_int @ B @ A )
% 3.05/1.58       => ( A != B ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_218_ex__gt__or__lt,axiom,
% 3.05/1.58      ! [A: real] :
% 3.05/1.58      ? [B6: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B6 )
% 3.05/1.58        | ( ord_less_real @ B6 @ A ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_219_complete__real,axiom,
% 3.05/1.58      ! [S: set_real] :
% 3.05/1.58        ( ? [X3: real] : ( member_real @ X3 @ S )
% 3.05/1.58       => ( ? [Z: real] :
% 3.05/1.58            ! [X4: real] :
% 3.05/1.58              ( ( member_real @ X4 @ S )
% 3.05/1.58             => ( ord_less_eq_real @ X4 @ Z ) )
% 3.05/1.58         => ? [Y4: real] :
% 3.05/1.58              ( ! [X3: real] :
% 3.05/1.58                  ( ( member_real @ X3 @ S )
% 3.05/1.58                 => ( ord_less_eq_real @ X3 @ Y4 ) )
% 3.05/1.58              & ! [Z: real] :
% 3.05/1.58                  ( ! [X4: real] :
% 3.05/1.58                      ( ( member_real @ X4 @ S )
% 3.05/1.58                     => ( ord_less_eq_real @ X4 @ Z ) )
% 3.05/1.58                 => ( ord_less_eq_real @ Y4 @ Z ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_220_field__lbound__gt__zero,axiom,
% 3.05/1.58      ! [D1: real,D2: real] :
% 3.05/1.58        ( ( ord_less_real @ zero_zero_real @ D1 )
% 3.05/1.58       => ( ( ord_less_real @ zero_zero_real @ D2 )
% 3.05/1.58         => ? [E: real] :
% 3.05/1.58              ( ( ord_less_real @ zero_zero_real @ E )
% 3.05/1.58              & ( ord_less_real @ E @ D1 )
% 3.05/1.58              & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_221_leD,axiom,
% 3.05/1.58      ! [Y2: real,X2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ Y2 @ X2 )
% 3.05/1.58       => ~ ( ord_less_real @ X2 @ Y2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_222_leD,axiom,
% 3.05/1.58      ! [Y2: int,X2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ Y2 @ X2 )
% 3.05/1.58       => ~ ( ord_less_int @ X2 @ Y2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_223_leI,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ~ ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_224_leI,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ~ ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ( ord_less_eq_int @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_225_le__less,axiom,
% 3.05/1.58      ( ord_less_eq_real
% 3.05/1.58      = ( ^ [X: real,Y: real] :
% 3.05/1.58            ( ( ord_less_real @ X @ Y )
% 3.05/1.58            | ( X = Y ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_226_le__less,axiom,
% 3.05/1.58      ( ord_less_eq_int
% 3.05/1.58      = ( ^ [X: int,Y: int] :
% 3.05/1.58            ( ( ord_less_int @ X @ Y )
% 3.05/1.58            | ( X = Y ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_227_less__le,axiom,
% 3.05/1.58      ( ord_less_real
% 3.05/1.58      = ( ^ [X: real,Y: real] :
% 3.05/1.58            ( ( ord_less_eq_real @ X @ Y )
% 3.05/1.58            & ( X != Y ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_228_less__le,axiom,
% 3.05/1.58      ( ord_less_int
% 3.05/1.58      = ( ^ [X: int,Y: int] :
% 3.05/1.58            ( ( ord_less_eq_int @ X @ Y )
% 3.05/1.58            & ( X != Y ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_229_order__le__less__subst1,axiom,
% 3.05/1.58      ! [A: real,F: real > real,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_real @ B @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_230_order__le__less__subst1,axiom,
% 3.05/1.58      ! [A: real,F: int > real,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_int @ B @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_231_order__le__less__subst1,axiom,
% 3.05/1.58      ! [A: int,F: real > int,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_real @ B @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_232_order__le__less__subst1,axiom,
% 3.05/1.58      ! [A: int,F: int > int,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_int @ B @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_233_order__le__less__subst2,axiom,
% 3.05/1.58      ! [A: real,B: real,F: real > real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_234_order__le__less__subst2,axiom,
% 3.05/1.58      ! [A: real,B: real,F: real > int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_235_order__le__less__subst2,axiom,
% 3.05/1.58      ! [A: int,B: int,F: int > real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_real @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_236_order__le__less__subst2,axiom,
% 3.05/1.58      ! [A: int,B: int,F: int > int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_int @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_237_order__less__le__subst1,axiom,
% 3.05/1.58      ! [A: real,F: real > real,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_eq_real @ B @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_238_order__less__le__subst1,axiom,
% 3.05/1.58      ! [A: int,F: real > int,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_int @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_eq_real @ B @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_eq_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_239_order__less__le__subst1,axiom,
% 3.05/1.58      ! [A: real,F: int > real,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_real @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_eq_int @ B @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_240_order__less__le__subst1,axiom,
% 3.05/1.58      ! [A: int,F: int > int,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_int @ A @ ( F @ B ) )
% 3.05/1.58       => ( ( ord_less_eq_int @ B @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_eq_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ A @ ( F @ C2 ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_241_order__less__le__subst2,axiom,
% 3.05/1.58      ! [A: real,B: real,F: real > real,C2: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_242_order__less__le__subst2,axiom,
% 3.05/1.58      ! [A: int,B: int,F: int > real,C2: real] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_real @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_real @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_243_order__less__le__subst2,axiom,
% 3.05/1.58      ! [A: real,B: real,F: real > int,C2: int] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: real,Y4: real] :
% 3.05/1.58                ( ( ord_less_real @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_244_order__less__le__subst2,axiom,
% 3.05/1.58      ! [A: int,B: int,F: int > int,C2: int] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_int @ ( F @ B ) @ C2 )
% 3.05/1.58         => ( ! [X4: int,Y4: int] :
% 3.05/1.58                ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.58               => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.58           => ( ord_less_int @ ( F @ A ) @ C2 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_245_not__le,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ~ ( ord_less_eq_real @ X2 @ Y2 ) )
% 3.05/1.58        = ( ord_less_real @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_246_not__le,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ~ ( ord_less_eq_int @ X2 @ Y2 ) )
% 3.05/1.58        = ( ord_less_int @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_247_not__less,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ~ ( ord_less_real @ X2 @ Y2 ) )
% 3.05/1.58        = ( ord_less_eq_real @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_248_not__less,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ~ ( ord_less_int @ X2 @ Y2 ) )
% 3.05/1.58        = ( ord_less_eq_int @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_249_le__neq__trans,axiom,
% 3.05/1.58      ! [A: real,B: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58       => ( ( A != B )
% 3.05/1.58         => ( ord_less_real @ A @ B ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_250_le__neq__trans,axiom,
% 3.05/1.58      ! [A: int,B: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58       => ( ( A != B )
% 3.05/1.58         => ( ord_less_int @ A @ B ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_251_antisym__conv1,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ~ ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_eq_real @ X2 @ Y2 )
% 3.05/1.58          = ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_252_antisym__conv1,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ~ ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_eq_int @ X2 @ Y2 )
% 3.05/1.58          = ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_253_antisym__conv2,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ X2 @ Y2 )
% 3.05/1.58       => ( ( ~ ( ord_less_real @ X2 @ Y2 ) )
% 3.05/1.58          = ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_254_antisym__conv2,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ X2 @ Y2 )
% 3.05/1.58       => ( ( ~ ( ord_less_int @ X2 @ Y2 ) )
% 3.05/1.58          = ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_255_less__imp__le,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ( ord_less_eq_real @ X2 @ Y2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_256_less__imp__le,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ( ord_less_eq_int @ X2 @ Y2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_257_le__less__trans,axiom,
% 3.05/1.58      ! [X2: real,Y2: real,Z3: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_real @ Y2 @ Z3 )
% 3.05/1.58         => ( ord_less_real @ X2 @ Z3 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_258_le__less__trans,axiom,
% 3.05/1.58      ! [X2: int,Y2: int,Z3: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_int @ Y2 @ Z3 )
% 3.05/1.58         => ( ord_less_int @ X2 @ Z3 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_259_less__le__trans,axiom,
% 3.05/1.58      ! [X2: real,Y2: real,Z3: real] :
% 3.05/1.58        ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_eq_real @ Y2 @ Z3 )
% 3.05/1.58         => ( ord_less_real @ X2 @ Z3 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_260_less__le__trans,axiom,
% 3.05/1.58      ! [X2: int,Y2: int,Z3: int] :
% 3.05/1.58        ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_eq_int @ Y2 @ Z3 )
% 3.05/1.58         => ( ord_less_int @ X2 @ Z3 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_261_dense__ge,axiom,
% 3.05/1.58      ! [Z3: real,Y2: real] :
% 3.05/1.58        ( ! [X4: real] :
% 3.05/1.58            ( ( ord_less_real @ Z3 @ X4 )
% 3.05/1.58           => ( ord_less_eq_real @ Y2 @ X4 ) )
% 3.05/1.58       => ( ord_less_eq_real @ Y2 @ Z3 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_262_dense__le,axiom,
% 3.05/1.58      ! [Y2: real,Z3: real] :
% 3.05/1.58        ( ! [X4: real] :
% 3.05/1.58            ( ( ord_less_real @ X4 @ Y2 )
% 3.05/1.58           => ( ord_less_eq_real @ X4 @ Z3 ) )
% 3.05/1.58       => ( ord_less_eq_real @ Y2 @ Z3 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_263_le__less__linear,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ X2 @ Y2 )
% 3.05/1.58        | ( ord_less_real @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_264_le__less__linear,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ X2 @ Y2 )
% 3.05/1.58        | ( ord_less_int @ Y2 @ X2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_265_le__imp__less__or__eq,axiom,
% 3.05/1.58      ! [X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_real @ X2 @ Y2 )
% 3.05/1.58          | ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_266_le__imp__less__or__eq,axiom,
% 3.05/1.58      ! [X2: int,Y2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ X2 @ Y2 )
% 3.05/1.58       => ( ( ord_less_int @ X2 @ Y2 )
% 3.05/1.58          | ( X2 = Y2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_267_less__le__not__le,axiom,
% 3.05/1.58      ( ord_less_real
% 3.05/1.58      = ( ^ [X: real,Y: real] :
% 3.05/1.58            ( ( ord_less_eq_real @ X @ Y )
% 3.05/1.58            & ~ ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_268_less__le__not__le,axiom,
% 3.05/1.58      ( ord_less_int
% 3.05/1.58      = ( ^ [X: int,Y: int] :
% 3.05/1.58            ( ( ord_less_eq_int @ X @ Y )
% 3.05/1.58            & ~ ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_269_not__le__imp__less,axiom,
% 3.05/1.58      ! [Y2: real,X2: real] :
% 3.05/1.58        ( ~ ( ord_less_eq_real @ Y2 @ X2 )
% 3.05/1.58       => ( ord_less_real @ X2 @ Y2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_270_not__le__imp__less,axiom,
% 3.05/1.58      ! [Y2: int,X2: int] :
% 3.05/1.58        ( ~ ( ord_less_eq_int @ Y2 @ X2 )
% 3.05/1.58       => ( ord_less_int @ X2 @ Y2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_271_order_Ostrict__trans1,axiom,
% 3.05/1.58      ! [A: real,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_real @ B @ C2 )
% 3.05/1.58         => ( ord_less_real @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_272_order_Ostrict__trans1,axiom,
% 3.05/1.58      ! [A: int,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_int @ B @ C2 )
% 3.05/1.58         => ( ord_less_int @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_273_order_Ostrict__trans2,axiom,
% 3.05/1.58      ! [A: real,B: real,C2: real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_real @ B @ C2 )
% 3.05/1.58         => ( ord_less_real @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_274_order_Ostrict__trans2,axiom,
% 3.05/1.58      ! [A: int,B: int,C2: int] :
% 3.05/1.58        ( ( ord_less_int @ A @ B )
% 3.05/1.58       => ( ( ord_less_eq_int @ B @ C2 )
% 3.05/1.58         => ( ord_less_int @ A @ C2 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_275_order_Oorder__iff__strict,axiom,
% 3.05/1.58      ( ord_less_eq_real
% 3.05/1.58      = ( ^ [A4: real,B4: real] :
% 3.05/1.58            ( ( ord_less_real @ A4 @ B4 )
% 3.05/1.58            | ( A4 = B4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_276_order_Oorder__iff__strict,axiom,
% 3.05/1.58      ( ord_less_eq_int
% 3.05/1.58      = ( ^ [A4: int,B4: int] :
% 3.05/1.58            ( ( ord_less_int @ A4 @ B4 )
% 3.05/1.58            | ( A4 = B4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_277_order_Ostrict__iff__order,axiom,
% 3.05/1.58      ( ord_less_real
% 3.05/1.58      = ( ^ [A4: real,B4: real] :
% 3.05/1.58            ( ( ord_less_eq_real @ A4 @ B4 )
% 3.05/1.58            & ( A4 != B4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_278_order_Ostrict__iff__order,axiom,
% 3.05/1.58      ( ord_less_int
% 3.05/1.58      = ( ^ [A4: int,B4: int] :
% 3.05/1.58            ( ( ord_less_eq_int @ A4 @ B4 )
% 3.05/1.58            & ( A4 != B4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_279_dual__order_Ostrict__trans1,axiom,
% 3.05/1.58      ! [B: real,A: real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_real @ B @ A )
% 3.05/1.58       => ( ( ord_less_real @ C2 @ B )
% 3.05/1.58         => ( ord_less_real @ C2 @ A ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_280_dual__order_Ostrict__trans1,axiom,
% 3.05/1.58      ! [B: int,A: int,C2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ B @ A )
% 3.05/1.58       => ( ( ord_less_int @ C2 @ B )
% 3.05/1.58         => ( ord_less_int @ C2 @ A ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_281_dual__order_Ostrict__trans2,axiom,
% 3.05/1.58      ! [B: real,A: real,C2: real] :
% 3.05/1.58        ( ( ord_less_real @ B @ A )
% 3.05/1.58       => ( ( ord_less_eq_real @ C2 @ B )
% 3.05/1.58         => ( ord_less_real @ C2 @ A ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_282_dual__order_Ostrict__trans2,axiom,
% 3.05/1.58      ! [B: int,A: int,C2: int] :
% 3.05/1.58        ( ( ord_less_int @ B @ A )
% 3.05/1.58       => ( ( ord_less_eq_int @ C2 @ B )
% 3.05/1.58         => ( ord_less_int @ C2 @ A ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_283_dense__ge__bounded,axiom,
% 3.05/1.58      ! [Z3: real,X2: real,Y2: real] :
% 3.05/1.58        ( ( ord_less_real @ Z3 @ X2 )
% 3.05/1.58       => ( ! [W: real] :
% 3.05/1.58              ( ( ord_less_real @ Z3 @ W )
% 3.05/1.58             => ( ( ord_less_real @ W @ X2 )
% 3.05/1.58               => ( ord_less_eq_real @ Y2 @ W ) ) )
% 3.05/1.58         => ( ord_less_eq_real @ Y2 @ Z3 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_284_minf_I8_J,axiom,
% 3.05/1.58      ! [T2: real] :
% 3.05/1.58      ? [Z5: real] :
% 3.05/1.58      ! [X3: real] :
% 3.05/1.58        ( ( ord_less_real @ X3 @ Z5 )
% 3.05/1.58       => ~ ( ord_less_eq_real @ T2 @ X3 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_285_minf_I8_J,axiom,
% 3.05/1.58      ! [T2: int] :
% 3.05/1.58      ? [Z5: int] :
% 3.05/1.58      ! [X3: int] :
% 3.05/1.58        ( ( ord_less_int @ X3 @ Z5 )
% 3.05/1.58       => ~ ( ord_less_eq_int @ T2 @ X3 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_286_minf_I6_J,axiom,
% 3.05/1.58      ! [T2: real] :
% 3.05/1.58      ? [Z5: real] :
% 3.05/1.58      ! [X3: real] :
% 3.05/1.58        ( ( ord_less_real @ X3 @ Z5 )
% 3.05/1.58       => ( ord_less_eq_real @ X3 @ T2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_287_minf_I6_J,axiom,
% 3.05/1.58      ! [T2: int] :
% 3.05/1.58      ? [Z5: int] :
% 3.05/1.58      ! [X3: int] :
% 3.05/1.58        ( ( ord_less_int @ X3 @ Z5 )
% 3.05/1.58       => ( ord_less_eq_int @ X3 @ T2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_288_pinf_I8_J,axiom,
% 3.05/1.58      ! [T2: real] :
% 3.05/1.58      ? [Z5: real] :
% 3.05/1.58      ! [X3: real] :
% 3.05/1.58        ( ( ord_less_real @ Z5 @ X3 )
% 3.05/1.58       => ( ord_less_eq_real @ T2 @ X3 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_289_pinf_I8_J,axiom,
% 3.05/1.58      ! [T2: int] :
% 3.05/1.58      ? [Z5: int] :
% 3.05/1.58      ! [X3: int] :
% 3.05/1.58        ( ( ord_less_int @ Z5 @ X3 )
% 3.05/1.58       => ( ord_less_eq_int @ T2 @ X3 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_290_pinf_I6_J,axiom,
% 3.05/1.58      ! [T2: real] :
% 3.05/1.58      ? [Z5: real] :
% 3.05/1.58      ! [X3: real] :
% 3.05/1.58        ( ( ord_less_real @ Z5 @ X3 )
% 3.05/1.58       => ~ ( ord_less_eq_real @ X3 @ T2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_291_pinf_I6_J,axiom,
% 3.05/1.58      ! [T2: int] :
% 3.05/1.58      ? [Z5: int] :
% 3.05/1.58      ! [X3: int] :
% 3.05/1.58        ( ( ord_less_int @ Z5 @ X3 )
% 3.05/1.58       => ~ ( ord_less_eq_int @ X3 @ T2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_292_verit__comp__simplify1_I3_J,axiom,
% 3.05/1.58      ! [B7: real,A6: real] :
% 3.05/1.58        ( ( ~ ( ord_less_eq_real @ B7 @ A6 ) )
% 3.05/1.58        = ( ord_less_real @ A6 @ B7 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_293_verit__comp__simplify1_I3_J,axiom,
% 3.05/1.58      ! [B7: int,A6: int] :
% 3.05/1.58        ( ( ~ ( ord_less_eq_int @ B7 @ A6 ) )
% 3.05/1.58        = ( ord_less_int @ A6 @ B7 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_294_is__zero__null,axiom,
% 3.05/1.58      ( is_zero_real
% 3.05/1.58      = ( ^ [P3: poly_real] : ( P3 = zero_zero_poly_real ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_295_is__zero__null,axiom,
% 3.05/1.58      ( is_zero_int
% 3.05/1.58      = ( ^ [P3: poly_int] : ( P3 = zero_zero_poly_int ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_296_is__zero__null,axiom,
% 3.05/1.58      ( is_zero_poly_real
% 3.05/1.58      = ( ^ [P3: poly_poly_real] : ( P3 = zero_z1423781445y_real ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_297_poly__cutoff__0,axiom,
% 3.05/1.58      ! [N: nat] :
% 3.05/1.58        ( ( poly_cutoff_real @ N @ zero_zero_poly_real )
% 3.05/1.58        = zero_zero_poly_real ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_298_poly__cutoff__0,axiom,
% 3.05/1.58      ! [N: nat] :
% 3.05/1.58        ( ( poly_cutoff_int @ N @ zero_zero_poly_int )
% 3.05/1.58        = zero_zero_poly_int ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_299_poly__cutoff__0,axiom,
% 3.05/1.58      ! [N: nat] :
% 3.05/1.58        ( ( poly_c1404107022y_real @ N @ zero_z1423781445y_real )
% 3.05/1.58        = zero_z1423781445y_real ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_300_subsetI,axiom,
% 3.05/1.58      ! [A2: set_real,B3: set_real] :
% 3.05/1.58        ( ! [X4: real] :
% 3.05/1.58            ( ( member_real @ X4 @ A2 )
% 3.05/1.58           => ( member_real @ X4 @ B3 ) )
% 3.05/1.58       => ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_301_in__mono,axiom,
% 3.05/1.58      ! [A2: set_real,B3: set_real,X2: real] :
% 3.05/1.58        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 3.05/1.58       => ( ( member_real @ X2 @ A2 )
% 3.05/1.58         => ( member_real @ X2 @ B3 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_302_subsetD,axiom,
% 3.05/1.58      ! [A2: set_real,B3: set_real,C2: real] :
% 3.05/1.58        ( ( ord_less_eq_set_real @ A2 @ B3 )
% 3.05/1.58       => ( ( member_real @ C2 @ A2 )
% 3.05/1.58         => ( member_real @ C2 @ B3 ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_303_subset__eq,axiom,
% 3.05/1.58      ( ord_less_eq_set_real
% 3.05/1.58      = ( ^ [A7: set_real,B5: set_real] :
% 3.05/1.58          ! [X: real] :
% 3.05/1.58            ( ( member_real @ X @ A7 )
% 3.05/1.58           => ( member_real @ X @ B5 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_304_subset__iff,axiom,
% 3.05/1.58      ( ord_less_eq_set_real
% 3.05/1.58      = ( ^ [A7: set_real,B5: set_real] :
% 3.05/1.58          ! [T3: real] :
% 3.05/1.58            ( ( member_real @ T3 @ A7 )
% 3.05/1.58           => ( member_real @ T3 @ B5 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_305_Collect__mono,axiom,
% 3.05/1.58      ! [P: real > $o,Q: real > $o] :
% 3.05/1.58        ( ! [X4: real] :
% 3.05/1.58            ( ( P @ X4 )
% 3.05/1.58           => ( Q @ X4 ) )
% 3.05/1.58       => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_306_Collect__mono,axiom,
% 3.05/1.58      ! [P: int > $o,Q: int > $o] :
% 3.05/1.58        ( ! [X4: int] :
% 3.05/1.58            ( ( P @ X4 )
% 3.05/1.58           => ( Q @ X4 ) )
% 3.05/1.58       => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_307_Collect__subset,axiom,
% 3.05/1.58      ! [A2: set_real,P: real > $o] :
% 3.05/1.58        ( ord_less_eq_set_real
% 3.05/1.58        @ ( collect_real
% 3.05/1.58          @ ^ [X: real] :
% 3.05/1.58              ( ( member_real @ X @ A2 )
% 3.05/1.58              & ( P @ X ) ) )
% 3.05/1.58        @ A2 ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_308_Collect__subset,axiom,
% 3.05/1.58      ! [A2: set_int,P: int > $o] :
% 3.05/1.58        ( ord_less_eq_set_int
% 3.05/1.58        @ ( collect_int
% 3.05/1.58          @ ^ [X: int] :
% 3.05/1.58              ( ( member_int @ X @ A2 )
% 3.05/1.58              & ( P @ X ) ) )
% 3.05/1.58        @ A2 ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_309_less__eq__set__def,axiom,
% 3.05/1.58      ( ord_less_eq_set_real
% 3.05/1.58      = ( ^ [A7: set_real,B5: set_real] :
% 3.05/1.58            ( ord_less_eq_real_o
% 3.05/1.58            @ ^ [X: real] : ( member_real @ X @ A7 )
% 3.05/1.58            @ ^ [X: real] : ( member_real @ X @ B5 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_310_Collect__mono__iff,axiom,
% 3.05/1.58      ! [P: real > $o,Q: real > $o] :
% 3.05/1.58        ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 3.05/1.58        = ( ! [X: real] :
% 3.05/1.58              ( ( P @ X )
% 3.05/1.58             => ( Q @ X ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_311_Collect__mono__iff,axiom,
% 3.05/1.58      ! [P: int > $o,Q: int > $o] :
% 3.05/1.58        ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 3.05/1.58        = ( ! [X: int] :
% 3.05/1.58              ( ( P @ X )
% 3.05/1.58             => ( Q @ X ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_312_verit__la__disequality,axiom,
% 3.05/1.58      ! [A: real,B: real] :
% 3.05/1.58        ( ( A = B )
% 3.05/1.58        | ~ ( ord_less_eq_real @ A @ B )
% 3.05/1.58        | ~ ( ord_less_eq_real @ B @ A ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_313_verit__la__disequality,axiom,
% 3.05/1.58      ! [A: int,B: int] :
% 3.05/1.58        ( ( A = B )
% 3.05/1.58        | ~ ( ord_less_eq_int @ A @ B )
% 3.05/1.58        | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_314_verit__comp__simplify1_I1_J,axiom,
% 3.05/1.58      ! [A: real] :
% 3.05/1.58        ~ ( ord_less_real @ A @ A ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_315_verit__comp__simplify1_I1_J,axiom,
% 3.05/1.58      ! [A: int] :
% 3.05/1.58        ~ ( ord_less_int @ A @ A ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_316_pinf_I1_J,axiom,
% 3.05/1.58      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 3.05/1.58        ( ? [Z: real] :
% 3.05/1.58          ! [X4: real] :
% 3.05/1.58            ( ( ord_less_real @ Z @ X4 )
% 3.05/1.58           => ( ( P @ X4 )
% 3.05/1.58              = ( P4 @ X4 ) ) )
% 3.05/1.58       => ( ? [Z: real] :
% 3.05/1.58            ! [X4: real] :
% 3.05/1.58              ( ( ord_less_real @ Z @ X4 )
% 3.05/1.58             => ( ( Q @ X4 )
% 3.05/1.58                = ( Q3 @ X4 ) ) )
% 3.05/1.58         => ? [Z5: real] :
% 3.05/1.58            ! [X3: real] :
% 3.05/1.58              ( ( ord_less_real @ Z5 @ X3 )
% 3.05/1.58             => ( ( ( P @ X3 )
% 3.05/1.58                  & ( Q @ X3 ) )
% 3.05/1.58                = ( ( P4 @ X3 )
% 3.05/1.58                  & ( Q3 @ X3 ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_317_pinf_I1_J,axiom,
% 3.05/1.58      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 3.05/1.58        ( ? [Z: int] :
% 3.05/1.58          ! [X4: int] :
% 3.05/1.58            ( ( ord_less_int @ Z @ X4 )
% 3.05/1.58           => ( ( P @ X4 )
% 3.05/1.58              = ( P4 @ X4 ) ) )
% 3.05/1.58       => ( ? [Z: int] :
% 3.05/1.58            ! [X4: int] :
% 3.05/1.58              ( ( ord_less_int @ Z @ X4 )
% 3.05/1.58             => ( ( Q @ X4 )
% 3.05/1.58                = ( Q3 @ X4 ) ) )
% 3.05/1.58         => ? [Z5: int] :
% 3.05/1.58            ! [X3: int] :
% 3.05/1.58              ( ( ord_less_int @ Z5 @ X3 )
% 3.05/1.58             => ( ( ( P @ X3 )
% 3.05/1.58                  & ( Q @ X3 ) )
% 3.05/1.58                = ( ( P4 @ X3 )
% 3.05/1.58                  & ( Q3 @ X3 ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_318_pinf_I2_J,axiom,
% 3.05/1.58      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 3.05/1.58        ( ? [Z: real] :
% 3.05/1.58          ! [X4: real] :
% 3.05/1.58            ( ( ord_less_real @ Z @ X4 )
% 3.05/1.58           => ( ( P @ X4 )
% 3.05/1.58              = ( P4 @ X4 ) ) )
% 3.05/1.58       => ( ? [Z: real] :
% 3.05/1.58            ! [X4: real] :
% 3.05/1.58              ( ( ord_less_real @ Z @ X4 )
% 3.05/1.58             => ( ( Q @ X4 )
% 3.05/1.58                = ( Q3 @ X4 ) ) )
% 3.05/1.58         => ? [Z5: real] :
% 3.05/1.58            ! [X3: real] :
% 3.05/1.58              ( ( ord_less_real @ Z5 @ X3 )
% 3.05/1.58             => ( ( ( P @ X3 )
% 3.05/1.58                  | ( Q @ X3 ) )
% 3.05/1.58                = ( ( P4 @ X3 )
% 3.05/1.58                  | ( Q3 @ X3 ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_319_pinf_I2_J,axiom,
% 3.05/1.58      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 3.05/1.58        ( ? [Z: int] :
% 3.05/1.58          ! [X4: int] :
% 3.05/1.58            ( ( ord_less_int @ Z @ X4 )
% 3.05/1.58           => ( ( P @ X4 )
% 3.05/1.58              = ( P4 @ X4 ) ) )
% 3.05/1.58       => ( ? [Z: int] :
% 3.05/1.58            ! [X4: int] :
% 3.05/1.58              ( ( ord_less_int @ Z @ X4 )
% 3.05/1.58             => ( ( Q @ X4 )
% 3.05/1.58                = ( Q3 @ X4 ) ) )
% 3.05/1.58         => ? [Z5: int] :
% 3.05/1.58            ! [X3: int] :
% 3.05/1.58              ( ( ord_less_int @ Z5 @ X3 )
% 3.05/1.58             => ( ( ( P @ X3 )
% 3.05/1.58                  | ( Q @ X3 ) )
% 3.05/1.58                = ( ( P4 @ X3 )
% 3.05/1.58                  | ( Q3 @ X3 ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_320_pinf_I3_J,axiom,
% 3.05/1.58      ! [T2: real] :
% 3.05/1.58      ? [Z5: real] :
% 3.05/1.58      ! [X3: real] :
% 3.05/1.58        ( ( ord_less_real @ Z5 @ X3 )
% 3.05/1.58       => ( X3 != T2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_321_pinf_I3_J,axiom,
% 3.05/1.58      ! [T2: int] :
% 3.05/1.58      ? [Z5: int] :
% 3.05/1.58      ! [X3: int] :
% 3.05/1.58        ( ( ord_less_int @ Z5 @ X3 )
% 3.05/1.58       => ( X3 != T2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_322_pinf_I4_J,axiom,
% 3.05/1.58      ! [T2: real] :
% 3.05/1.58      ? [Z5: real] :
% 3.05/1.58      ! [X3: real] :
% 3.05/1.58        ( ( ord_less_real @ Z5 @ X3 )
% 3.05/1.58       => ( X3 != T2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_323_pinf_I4_J,axiom,
% 3.05/1.58      ! [T2: int] :
% 3.05/1.58      ? [Z5: int] :
% 3.05/1.58      ! [X3: int] :
% 3.05/1.58        ( ( ord_less_int @ Z5 @ X3 )
% 3.05/1.58       => ( X3 != T2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_324_pinf_I5_J,axiom,
% 3.05/1.58      ! [T2: real] :
% 3.05/1.58      ? [Z5: real] :
% 3.05/1.58      ! [X3: real] :
% 3.05/1.58        ( ( ord_less_real @ Z5 @ X3 )
% 3.05/1.58       => ~ ( ord_less_real @ X3 @ T2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_325_pinf_I5_J,axiom,
% 3.05/1.58      ! [T2: int] :
% 3.05/1.58      ? [Z5: int] :
% 3.05/1.58      ! [X3: int] :
% 3.05/1.58        ( ( ord_less_int @ Z5 @ X3 )
% 3.05/1.58       => ~ ( ord_less_int @ X3 @ T2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_326_pinf_I7_J,axiom,
% 3.05/1.58      ! [T2: real] :
% 3.05/1.58      ? [Z5: real] :
% 3.05/1.58      ! [X3: real] :
% 3.05/1.58        ( ( ord_less_real @ Z5 @ X3 )
% 3.05/1.58       => ( ord_less_real @ T2 @ X3 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_327_pinf_I7_J,axiom,
% 3.05/1.58      ! [T2: int] :
% 3.05/1.58      ? [Z5: int] :
% 3.05/1.58      ! [X3: int] :
% 3.05/1.58        ( ( ord_less_int @ Z5 @ X3 )
% 3.05/1.58       => ( ord_less_int @ T2 @ X3 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_328_minf_I1_J,axiom,
% 3.05/1.58      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 3.05/1.58        ( ? [Z: real] :
% 3.05/1.58          ! [X4: real] :
% 3.05/1.58            ( ( ord_less_real @ X4 @ Z )
% 3.05/1.58           => ( ( P @ X4 )
% 3.05/1.58              = ( P4 @ X4 ) ) )
% 3.05/1.58       => ( ? [Z: real] :
% 3.05/1.58            ! [X4: real] :
% 3.05/1.58              ( ( ord_less_real @ X4 @ Z )
% 3.05/1.58             => ( ( Q @ X4 )
% 3.05/1.58                = ( Q3 @ X4 ) ) )
% 3.05/1.58         => ? [Z5: real] :
% 3.05/1.58            ! [X3: real] :
% 3.05/1.58              ( ( ord_less_real @ X3 @ Z5 )
% 3.05/1.58             => ( ( ( P @ X3 )
% 3.05/1.58                  & ( Q @ X3 ) )
% 3.05/1.58                = ( ( P4 @ X3 )
% 3.05/1.58                  & ( Q3 @ X3 ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_329_minf_I1_J,axiom,
% 3.05/1.58      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 3.05/1.58        ( ? [Z: int] :
% 3.05/1.58          ! [X4: int] :
% 3.05/1.58            ( ( ord_less_int @ X4 @ Z )
% 3.05/1.58           => ( ( P @ X4 )
% 3.05/1.58              = ( P4 @ X4 ) ) )
% 3.05/1.58       => ( ? [Z: int] :
% 3.05/1.58            ! [X4: int] :
% 3.05/1.58              ( ( ord_less_int @ X4 @ Z )
% 3.05/1.58             => ( ( Q @ X4 )
% 3.05/1.58                = ( Q3 @ X4 ) ) )
% 3.05/1.58         => ? [Z5: int] :
% 3.05/1.58            ! [X3: int] :
% 3.05/1.58              ( ( ord_less_int @ X3 @ Z5 )
% 3.05/1.58             => ( ( ( P @ X3 )
% 3.05/1.58                  & ( Q @ X3 ) )
% 3.05/1.58                = ( ( P4 @ X3 )
% 3.05/1.58                  & ( Q3 @ X3 ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_330_minf_I2_J,axiom,
% 3.05/1.58      ! [P: real > $o,P4: real > $o,Q: real > $o,Q3: real > $o] :
% 3.05/1.58        ( ? [Z: real] :
% 3.05/1.58          ! [X4: real] :
% 3.05/1.58            ( ( ord_less_real @ X4 @ Z )
% 3.05/1.58           => ( ( P @ X4 )
% 3.05/1.58              = ( P4 @ X4 ) ) )
% 3.05/1.58       => ( ? [Z: real] :
% 3.05/1.58            ! [X4: real] :
% 3.05/1.58              ( ( ord_less_real @ X4 @ Z )
% 3.05/1.58             => ( ( Q @ X4 )
% 3.05/1.58                = ( Q3 @ X4 ) ) )
% 3.05/1.58         => ? [Z5: real] :
% 3.05/1.58            ! [X3: real] :
% 3.05/1.58              ( ( ord_less_real @ X3 @ Z5 )
% 3.05/1.58             => ( ( ( P @ X3 )
% 3.05/1.58                  | ( Q @ X3 ) )
% 3.05/1.58                = ( ( P4 @ X3 )
% 3.05/1.58                  | ( Q3 @ X3 ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_331_minf_I2_J,axiom,
% 3.05/1.58      ! [P: int > $o,P4: int > $o,Q: int > $o,Q3: int > $o] :
% 3.05/1.58        ( ? [Z: int] :
% 3.05/1.58          ! [X4: int] :
% 3.05/1.58            ( ( ord_less_int @ X4 @ Z )
% 3.05/1.58           => ( ( P @ X4 )
% 3.05/1.58              = ( P4 @ X4 ) ) )
% 3.05/1.58       => ( ? [Z: int] :
% 3.05/1.58            ! [X4: int] :
% 3.05/1.58              ( ( ord_less_int @ X4 @ Z )
% 3.05/1.58             => ( ( Q @ X4 )
% 3.05/1.58                = ( Q3 @ X4 ) ) )
% 3.05/1.58         => ? [Z5: int] :
% 3.05/1.58            ! [X3: int] :
% 3.05/1.58              ( ( ord_less_int @ X3 @ Z5 )
% 3.05/1.58             => ( ( ( P @ X3 )
% 3.05/1.58                  | ( Q @ X3 ) )
% 3.05/1.58                = ( ( P4 @ X3 )
% 3.05/1.58                  | ( Q3 @ X3 ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_332_minf_I3_J,axiom,
% 3.05/1.58      ! [T2: int] :
% 3.05/1.58      ? [Z5: int] :
% 3.05/1.58      ! [X3: int] :
% 3.05/1.58        ( ( ord_less_int @ X3 @ Z5 )
% 3.05/1.58       => ( X3 != T2 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_333_conj__le__cong,axiom,
% 3.05/1.58      ! [X2: int,X5: int,P: $o,P4: $o] :
% 3.05/1.58        ( ( X2 = X5 )
% 3.05/1.58       => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 3.05/1.58           => ( P = P4 ) )
% 3.05/1.58         => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 3.05/1.58              & P )
% 3.05/1.58            = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 3.05/1.58              & P4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_334_imp__le__cong,axiom,
% 3.05/1.58      ! [X2: int,X5: int,P: $o,P4: $o] :
% 3.05/1.58        ( ( X2 = X5 )
% 3.05/1.58       => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 3.05/1.58           => ( P = P4 ) )
% 3.05/1.58         => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 3.05/1.58             => P )
% 3.05/1.58            = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 3.05/1.58             => P4 ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_335_jump__poly__not__root,axiom,
% 3.05/1.58      ! [P2: poly_real,X2: real,Q2: poly_real] :
% 3.05/1.58        ( ( ( poly_real2 @ P2 @ X2 )
% 3.05/1.58         != zero_zero_real )
% 3.05/1.58       => ( ( sturm_276991412p_poly @ Q2 @ P2 @ X2 )
% 3.05/1.58          = zero_zero_int ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_336_jump__poly0_I2_J,axiom,
% 3.05/1.58      ! [Q2: poly_real,X2: real] :
% 3.05/1.58        ( ( sturm_276991412p_poly @ Q2 @ zero_zero_poly_real @ X2 )
% 3.05/1.58        = zero_zero_int ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_337_jump__poly0_I1_J,axiom,
% 3.05/1.58      ! [P2: poly_real,X2: real] :
% 3.05/1.58        ( ( sturm_276991412p_poly @ zero_zero_poly_real @ P2 @ X2 )
% 3.05/1.58        = zero_zero_int ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_338_verit__la__generic,axiom,
% 3.05/1.58      ! [A: int,X2: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ A @ X2 )
% 3.05/1.58        | ( A = X2 )
% 3.05/1.58        | ( ord_less_eq_int @ X2 @ A ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_339_finite__interval__int1,axiom,
% 3.05/1.58      ! [A: int,B: int] :
% 3.05/1.58        ( finite_finite_int
% 3.05/1.58        @ ( collect_int
% 3.05/1.58          @ ^ [I: int] :
% 3.05/1.58              ( ( ord_less_eq_int @ A @ I )
% 3.05/1.58              & ( ord_less_eq_int @ I @ B ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_340_finite__interval__int2,axiom,
% 3.05/1.58      ! [A: int,B: int] :
% 3.05/1.58        ( finite_finite_int
% 3.05/1.58        @ ( collect_int
% 3.05/1.58          @ ^ [I: int] :
% 3.05/1.58              ( ( ord_less_eq_int @ A @ I )
% 3.05/1.58              & ( ord_less_int @ I @ B ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_341_finite__interval__int4,axiom,
% 3.05/1.58      ! [A: int,B: int] :
% 3.05/1.58        ( finite_finite_int
% 3.05/1.58        @ ( collect_int
% 3.05/1.58          @ ^ [I: int] :
% 3.05/1.58              ( ( ord_less_int @ A @ I )
% 3.05/1.58              & ( ord_less_int @ I @ B ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_342_finite__interval__int3,axiom,
% 3.05/1.58      ! [A: int,B: int] :
% 3.05/1.58        ( finite_finite_int
% 3.05/1.58        @ ( collect_int
% 3.05/1.58          @ ^ [I: int] :
% 3.05/1.58              ( ( ord_less_int @ A @ I )
% 3.05/1.58              & ( ord_less_eq_int @ I @ B ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_343_less__int__code_I1_J,axiom,
% 3.05/1.58      ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_344_less__eq__int__code_I1_J,axiom,
% 3.05/1.58      ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_345_cindex__poly__0_I2_J,axiom,
% 3.05/1.58      ! [A: real,B: real,Q2: poly_real] :
% 3.05/1.58        ( ( sturm_308542325x_poly @ A @ B @ Q2 @ zero_zero_poly_real )
% 3.05/1.58        = zero_zero_int ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_346_cindex__poly__0_I1_J,axiom,
% 3.05/1.58      ! [A: real,B: real,P2: poly_real] :
% 3.05/1.58        ( ( sturm_308542325x_poly @ A @ B @ zero_zero_poly_real @ P2 )
% 3.05/1.58        = zero_zero_int ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_347_cindex__poly__cross,axiom,
% 3.05/1.58      ! [A: real,B: real,P2: poly_real] :
% 3.05/1.58        ( ( ord_less_real @ A @ B )
% 3.05/1.58       => ( ( ( poly_real2 @ P2 @ A )
% 3.05/1.58           != zero_zero_real )
% 3.05/1.58         => ( ( ( poly_real2 @ P2 @ B )
% 3.05/1.58             != zero_zero_real )
% 3.05/1.58           => ( ( sturm_308542325x_poly @ A @ B @ one_one_poly_real @ P2 )
% 3.05/1.58              = ( sturm_1953858694_cross @ P2 @ A @ B ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_348_cindex__poly__def,axiom,
% 3.05/1.58      ( sturm_308542325x_poly
% 3.05/1.58      = ( ^ [A4: real,B4: real,Q4: poly_real,P3: poly_real] :
% 3.05/1.58            ( groups2051521940al_int @ ( sturm_276991412p_poly @ Q4 @ P3 )
% 3.05/1.58            @ ( collect_real
% 3.05/1.58              @ ^ [X: real] :
% 3.05/1.58                  ( ( ( poly_real2 @ P3 @ X )
% 3.05/1.58                    = zero_zero_real )
% 3.05/1.58                  & ( ord_less_real @ A4 @ X )
% 3.05/1.58                  & ( ord_less_real @ X @ B4 ) ) ) ) ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(fact_349_int__one__le__iff__zero__less,axiom,
% 3.05/1.58      ! [Z3: int] :
% 3.05/1.58        ( ( ord_less_eq_int @ one_one_int @ Z3 )
% 3.05/1.58        = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 3.05/1.58  
% 3.05/1.58  thf(conj_0,conjecture,
% 3.05/1.58      ( finite_finite_real
% 3.05/1.58      @ ( collect_real
% 3.05/1.58        @ ^ [X: real] :
% 3.05/1.58            ( ( ( poly_real2 @ p @ X )
% 3.05/1.58              = zero_zero_real )
% 3.05/1.58            & ( ord_less_real @ a @ X )
% 3.05/1.58            & ( ord_less_real @ X @ b ) ) ) ) ).
% 3.05/1.58  ------------------------
% 3.18/1.61  % (31882)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_31682 for (2999ds/275Mi)
% 3.18/1.61  % (31879)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/2Mi)
% 3.18/1.61  % (31881)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_31682 for (2999ds/2Mi)
% 3.18/1.61  % (31877)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_31682 for (2999ds/4Mi)
% 3.18/1.61  % (31876)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/183Mi)
% 3.18/1.61  % (31878)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_31682 for (2999ds/27Mi)
% 3.18/1.61  % (31877)Instruction limit reached!
% 3.18/1.61  % (31877)------------------------------
% 3.18/1.61  % (31877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.61  % (31877)Termination reason: Unknown
% 3.18/1.61  % (31877)Termination phase: shuffling
% 3.18/1.61  
% 3.18/1.61  % (31877)Memory used [KB]: 1407
% 3.18/1.61  % (31877)Time elapsed: 0.003 s
% 3.18/1.61  % (31877)Instructions burned: 4 (million)
% 3.18/1.61  % (31877)------------------------------
% 3.18/1.61  % (31877)------------------------------
% 3.18/1.61  % (31879)Instruction limit reached!
% 3.18/1.61  % (31879)------------------------------
% 3.18/1.61  % (31879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.61  % (31879)Termination reason: Unknown
% 3.18/1.61  % (31879)Termination phase: shuffling
% 3.18/1.61  
% 3.18/1.61  % (31879)Memory used [KB]: 1535
% 3.18/1.61  % (31879)Time elapsed: 0.003 s
% 3.18/1.61  % (31879)Instructions burned: 4 (million)
% 3.18/1.61  % (31879)------------------------------
% 3.18/1.61  % (31879)------------------------------
% 3.18/1.61  % (31881)Instruction limit reached!
% 3.18/1.61  % (31881)------------------------------
% 3.18/1.61  % (31881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.61  % (31881)Termination reason: Unknown
% 3.18/1.61  % (31881)Termination phase: shuffling
% 3.18/1.61  
% 3.18/1.61  % (31881)Memory used [KB]: 1535
% 3.18/1.61  % (31881)Time elapsed: 0.003 s
% 3.18/1.61  % (31881)Instructions burned: 4 (million)
% 3.18/1.61  % (31881)------------------------------
% 3.18/1.61  % (31881)------------------------------
% 3.18/1.62  % (31883)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/18Mi)
% 3.18/1.62  % (31886)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/3Mi)
% 3.18/1.62  % (31887)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_31682 for (2999ds/37Mi)
% 3.18/1.62  % (31888)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_31682 for (2999ds/15Mi)
% 3.18/1.62  % (31886)Instruction limit reached!
% 3.18/1.62  % (31886)------------------------------
% 3.18/1.62  % (31886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.62  % (31886)Termination reason: Unknown
% 3.18/1.62  % (31886)Termination phase: shuffling
% 3.18/1.62  
% 3.18/1.62  % (31886)Memory used [KB]: 1407
% 3.18/1.62  % (31886)Time elapsed: 0.002 s
% 3.18/1.62  % (31886)Instructions burned: 3 (million)
% 3.18/1.62  % (31886)------------------------------
% 3.18/1.62  % (31886)------------------------------
% 3.18/1.62  % (31878)Instruction limit reached!
% 3.18/1.62  % (31878)------------------------------
% 3.18/1.62  % (31878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.62  % (31878)Termination reason: Unknown
% 3.18/1.62  % (31878)Termination phase: Property scanning
% 3.18/1.62  
% 3.18/1.62  % (31878)Memory used [KB]: 2046
% 3.18/1.62  % (31878)Time elapsed: 0.013 s
% 3.18/1.62  % (31878)Instructions burned: 30 (million)
% 3.18/1.62  % (31878)------------------------------
% 3.18/1.62  % (31878)------------------------------
% 3.18/1.62  % (31883)Instruction limit reached!
% 3.18/1.62  % (31883)------------------------------
% 3.18/1.62  % (31883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.62  % (31883)Termination reason: Unknown
% 3.18/1.62  % (31883)Termination phase: shuffling
% 3.18/1.62  
% 3.18/1.62  % (31883)Memory used [KB]: 1791
% 3.18/1.62  % (31883)Time elapsed: 0.011 s
% 3.18/1.62  % (31883)Instructions burned: 18 (million)
% 3.18/1.62  % (31883)------------------------------
% 3.18/1.62  % (31883)------------------------------
% 3.18/1.63  % (31888)Instruction limit reached!
% 3.18/1.63  % (31888)------------------------------
% 3.18/1.63  % (31888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.63  % (31888)Termination reason: Unknown
% 3.18/1.63  % (31888)Termination phase: shuffling
% 3.18/1.63  
% 3.18/1.63  % (31888)Memory used [KB]: 1791
% 3.18/1.63  % (31888)Time elapsed: 0.006 s
% 3.18/1.63  % (31888)Instructions burned: 15 (million)
% 3.18/1.63  % (31888)------------------------------
% 3.18/1.63  % (31888)------------------------------
% 3.18/1.63  % (31889)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_31682 for (2999ds/3Mi)
% 3.18/1.63  % (31887)Instruction limit reached!
% 3.18/1.63  % (31887)------------------------------
% 3.18/1.63  % (31887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.63  % (31887)Termination reason: Unknown
% 3.18/1.63  % (31887)Termination phase: shuffling
% 3.18/1.63  
% 3.18/1.63  % (31887)Memory used [KB]: 2302
% 3.18/1.63  % (31887)Time elapsed: 0.012 s
% 3.18/1.63  % (31887)Instructions burned: 40 (million)
% 3.18/1.63  % (31887)------------------------------
% 3.18/1.63  % (31887)------------------------------
% 3.18/1.63  % (31889)Instruction limit reached!
% 3.18/1.63  % (31889)------------------------------
% 3.18/1.63  % (31889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.63  % (31889)Termination reason: Unknown
% 3.18/1.63  % (31889)Termination phase: shuffling
% 3.18/1.63  
% 3.18/1.63  % (31889)Memory used [KB]: 1407
% 3.18/1.63  % (31889)Time elapsed: 0.002 s
% 3.18/1.63  % (31889)Instructions burned: 3 (million)
% 3.18/1.63  % (31889)------------------------------
% 3.18/1.63  % (31889)------------------------------
% 3.18/1.63  % (31890)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_31682 for (2999ds/1041Mi)
% 3.18/1.63  % (31891)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/7Mi)
% 3.18/1.64  % (31891)Instruction limit reached!
% 3.18/1.64  % (31891)------------------------------
% 3.18/1.64  % (31891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.64  % (31891)Termination reason: Unknown
% 3.18/1.64  % (31891)Termination phase: shuffling
% 3.18/1.64  
% 3.18/1.64  % (31891)Memory used [KB]: 1535
% 3.18/1.64  % (31891)Time elapsed: 0.004 s
% 3.18/1.64  % (31891)Instructions burned: 7 (million)
% 3.18/1.64  % (31891)------------------------------
% 3.18/1.64  % (31891)------------------------------
% 3.18/1.64  % (31893)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_31682 for (2999ds/3Mi)
% 3.18/1.64  % (31894)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_31682 for (2999ds/3Mi)
% 3.18/1.64  % (31892)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/16Mi)
% 3.18/1.64  % (31893)Instruction limit reached!
% 3.18/1.64  % (31893)------------------------------
% 3.18/1.64  % (31893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.64  % (31893)Termination reason: Unknown
% 3.18/1.64  % (31893)Termination phase: shuffling
% 3.18/1.64  
% 3.18/1.64  % (31893)Memory used [KB]: 1535
% 3.18/1.64  % (31893)Time elapsed: 0.003 s
% 3.18/1.64  % (31893)Instructions burned: 5 (million)
% 3.18/1.64  % (31893)------------------------------
% 3.18/1.64  % (31893)------------------------------
% 3.18/1.64  % (31894)Instruction limit reached!
% 3.18/1.64  % (31894)------------------------------
% 3.18/1.64  % (31894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.64  % (31894)Termination reason: Unknown
% 3.18/1.64  % (31894)Termination phase: shuffling
% 3.18/1.64  
% 3.18/1.64  % (31894)Memory used [KB]: 1535
% 3.18/1.64  % (31894)Time elapsed: 0.003 s
% 3.18/1.64  % (31894)Instructions burned: 5 (million)
% 3.18/1.64  % (31894)------------------------------
% 3.18/1.64  % (31894)------------------------------
% 3.18/1.65  % (31895)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/7Mi)
% 3.18/1.65  % (31892)Instruction limit reached!
% 3.18/1.65  % (31892)------------------------------
% 3.18/1.65  % (31892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.65  % (31892)Termination reason: Unknown
% 3.18/1.65  % (31892)Termination phase: shuffling
% 3.18/1.65  
% 3.18/1.65  % (31892)Memory used [KB]: 1791
% 3.18/1.65  % (31892)Time elapsed: 0.007 s
% 3.18/1.65  % (31892)Instructions burned: 18 (million)
% 3.18/1.65  % (31892)------------------------------
% 3.18/1.65  % (31892)------------------------------
% 3.18/1.65  % (31895)Instruction limit reached!
% 3.18/1.65  % (31895)------------------------------
% 3.18/1.65  % (31895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.65  % (31895)Termination reason: Unknown
% 3.18/1.65  % (31895)Termination phase: shuffling
% 3.18/1.65  
% 3.18/1.65  % (31895)Memory used [KB]: 1663
% 3.18/1.65  % (31895)Time elapsed: 0.004 s
% 3.18/1.65  % (31895)Instructions burned: 9 (million)
% 3.18/1.65  % (31895)------------------------------
% 3.18/1.65  % (31895)------------------------------
% 3.18/1.65  % (31898)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/3Mi)
% 3.18/1.65  % (31899)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/4Mi)
% 3.18/1.65  % (31898)Instruction limit reached!
% 3.18/1.65  % (31898)------------------------------
% 3.18/1.65  % (31898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.65  % (31898)Termination reason: Unknown
% 3.18/1.65  % (31898)Termination phase: shuffling
% 3.18/1.65  
% 3.18/1.65  % (31898)Memory used [KB]: 1535
% 3.18/1.65  % (31898)Time elapsed: 0.002 s
% 3.18/1.65  % (31898)Instructions burned: 4 (million)
% 3.18/1.65  % (31898)------------------------------
% 3.18/1.65  % (31898)------------------------------
% 3.18/1.65  % (31899)Instruction limit reached!
% 3.18/1.65  % (31899)------------------------------
% 3.18/1.65  % (31899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.65  % (31899)Termination reason: Unknown
% 3.18/1.65  % (31899)Termination phase: shuffling
% 3.18/1.65  
% 3.18/1.65  % (31899)Memory used [KB]: 1407
% 3.18/1.65  % (31899)Time elapsed: 0.002 s
% 3.18/1.65  % (31899)Instructions burned: 4 (million)
% 3.18/1.65  % (31899)------------------------------
% 3.18/1.65  % (31899)------------------------------
% 3.18/1.66  % (31900)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/18Mi)
% 3.18/1.66  % (31901)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/710Mi)
% 3.18/1.67  % (31900)Instruction limit reached!
% 3.18/1.67  % (31900)------------------------------
% 3.18/1.67  % (31900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.67  % (31900)Termination reason: Unknown
% 3.18/1.67  % (31900)Termination phase: shuffling
% 3.18/1.67  
% 3.18/1.67  % (31900)Memory used [KB]: 1791
% 3.18/1.67  % (31900)Time elapsed: 0.011 s
% 3.18/1.67  % (31900)Instructions burned: 19 (million)
% 3.18/1.67  % (31900)------------------------------
% 3.18/1.67  % (31900)------------------------------
% 3.18/1.67  % (31902)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/6Mi)
% 3.18/1.67  % (31903)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_31682 for (2999ds/902Mi)
% 3.18/1.67  % (31876)Instruction limit reached!
% 3.18/1.67  % (31876)------------------------------
% 3.18/1.67  % (31876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.67  % (31876)Termination reason: Unknown
% 3.18/1.67  % (31876)Termination phase: Saturation
% 3.18/1.67  
% 3.18/1.67  % (31876)Memory used [KB]: 7547
% 3.18/1.67  % (31876)Time elapsed: 0.060 s
% 3.18/1.67  % (31876)Instructions burned: 183 (million)
% 3.18/1.67  % (31876)------------------------------
% 3.18/1.67  % (31876)------------------------------
% 3.18/1.67  % (31902)Instruction limit reached!
% 3.18/1.67  % (31902)------------------------------
% 3.18/1.67  % (31902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.67  % (31902)Termination reason: Unknown
% 3.18/1.67  % (31902)Termination phase: shuffling
% 3.18/1.67  
% 3.18/1.67  % (31902)Memory used [KB]: 1535
% 3.18/1.67  % (31902)Time elapsed: 0.005 s
% 3.18/1.67  % (31902)Instructions burned: 6 (million)
% 3.18/1.67  % (31902)------------------------------
% 3.18/1.67  % (31902)------------------------------
% 3.18/1.68  % (31911)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_31682 for (2999ds/21Mi)
% 3.18/1.68  % (31911)Instruction limit reached!
% 3.18/1.68  % (31911)------------------------------
% 3.18/1.68  % (31911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.68  % (31911)Termination reason: Unknown
% 3.18/1.68  % (31911)Termination phase: shuffling
% 3.18/1.68  
% 3.18/1.68  % (31911)Memory used [KB]: 1918
% 3.18/1.68  % (31911)Time elapsed: 0.009 s
% 3.18/1.68  % (31911)Instructions burned: 22 (million)
% 3.18/1.68  % (31911)------------------------------
% 3.18/1.68  % (31911)------------------------------
% 3.18/1.69  % (31912)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/5Mi)
% 3.18/1.69  % (31914)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_31682 for (2999ds/6Mi)
% 3.18/1.69  % (31914)Instruction limit reached!
% 3.18/1.69  % (31914)------------------------------
% 3.18/1.69  % (31914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.69  % (31914)Termination reason: Unknown
% 3.18/1.69  % (31914)Termination phase: shuffling
% 3.18/1.69  
% 3.18/1.69  % (31914)Memory used [KB]: 1535
% 3.18/1.69  % (31914)Time elapsed: 0.003 s
% 3.18/1.69  % (31914)Instructions burned: 7 (million)
% 3.18/1.69  % (31914)------------------------------
% 3.18/1.69  % (31914)------------------------------
% 3.18/1.69  % (31912)Instruction limit reached!
% 3.18/1.69  % (31912)------------------------------
% 3.18/1.69  % (31912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.69  % (31912)Termination reason: Unknown
% 3.18/1.69  % (31912)Termination phase: shuffling
% 3.18/1.69  
% 3.18/1.69  % (31912)Memory used [KB]: 1535
% 3.18/1.69  % (31912)Time elapsed: 0.004 s
% 3.18/1.69  % (31912)Instructions burned: 6 (million)
% 3.18/1.69  % (31912)------------------------------
% 3.18/1.69  % (31912)------------------------------
% 3.18/1.70  % (31919)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_31682 for (2999ds/377Mi)
% 3.18/1.70  % (31920)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_31682 for (2999ds/779Mi)
% 3.18/1.70  % (31882)Instruction limit reached!
% 3.18/1.70  % (31882)------------------------------
% 3.18/1.70  % (31882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.70  % (31882)Termination reason: Unknown
% 3.18/1.70  % (31882)Termination phase: Saturation
% 3.18/1.70  
% 3.18/1.70  % (31882)Memory used [KB]: 7164
% 3.18/1.70  % (31882)Time elapsed: 0.094 s
% 3.18/1.70  % (31882)Instructions burned: 276 (million)
% 3.18/1.70  % (31882)------------------------------
% 3.18/1.70  % (31882)------------------------------
% 3.18/1.71  % (31921)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_31682 for (2999ds/19Mi)
% 3.18/1.71  % (31921)Instruction limit reached!
% 3.18/1.71  % (31921)------------------------------
% 3.18/1.71  % (31921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.71  % (31921)Termination reason: Unknown
% 3.18/1.71  % (31921)Termination phase: shuffling
% 3.18/1.71  
% 3.18/1.71  % (31921)Memory used [KB]: 1791
% 3.18/1.71  % (31921)Time elapsed: 0.008 s
% 3.18/1.71  % (31921)Instructions burned: 20 (million)
% 3.18/1.71  % (31921)------------------------------
% 3.18/1.71  % (31921)------------------------------
% 3.18/1.71  % (31924)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_31682 for (2998ds/879Mi)
% 3.18/1.72  % (31928)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_31682 for (2998ds/17Mi)
% 3.18/1.73  % (31928)Instruction limit reached!
% 3.18/1.73  % (31928)------------------------------
% 3.18/1.73  % (31928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.73  % (31928)Termination reason: Unknown
% 3.18/1.73  % (31928)Termination phase: shuffling
% 3.18/1.73  
% 3.18/1.73  % (31928)Memory used [KB]: 1791
% 3.18/1.73  % (31928)Time elapsed: 0.007 s
% 3.18/1.73  % (31928)Instructions burned: 19 (million)
% 3.18/1.73  % (31928)------------------------------
% 3.18/1.73  % (31928)------------------------------
% 3.18/1.74  % (31929)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_31682 for (2998ds/3Mi)
% 3.18/1.74  % (31929)Instruction limit reached!
% 3.18/1.74  % (31929)------------------------------
% 3.18/1.74  % (31929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.74  % (31929)Termination reason: Unknown
% 3.18/1.74  % (31929)Termination phase: shuffling
% 3.18/1.74  
% 3.18/1.74  % (31929)Memory used [KB]: 1535
% 3.18/1.74  % (31929)Time elapsed: 0.003 s
% 3.18/1.74  % (31929)Instructions burned: 5 (million)
% 3.18/1.74  % (31929)------------------------------
% 3.18/1.74  % (31929)------------------------------
% 3.18/1.75  % (31930)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_31682 for (2998ds/30Mi)
% 3.18/1.76  % (31930)Instruction limit reached!
% 3.18/1.76  % (31930)------------------------------
% 3.18/1.76  % (31930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.76  % (31930)Termination reason: Unknown
% 3.18/1.76  % (31930)Termination phase: Property scanning
% 3.18/1.76  
% 3.18/1.76  % (31930)Memory used [KB]: 2046
% 3.18/1.76  % (31930)Time elapsed: 0.011 s
% 3.18/1.76  % (31930)Instructions burned: 31 (million)
% 3.18/1.76  % (31930)------------------------------
% 3.18/1.76  % (31930)------------------------------
% 3.18/1.77  % (31931)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_31682 for (2998ds/127Mi)
% 3.18/1.80  % (31931)Instruction limit reached!
% 3.18/1.80  % (31931)------------------------------
% 3.18/1.80  % (31931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.80  % (31931)Termination reason: Unknown
% 3.18/1.80  % (31931)Termination phase: Property scanning
% 3.18/1.80  
% 3.18/1.80  % (31931)Memory used [KB]: 2814
% 3.18/1.80  % (31931)Time elapsed: 0.036 s
% 3.18/1.80  % (31931)Instructions burned: 130 (million)
% 3.18/1.80  % (31931)------------------------------
% 3.18/1.80  % (31931)------------------------------
% 3.18/1.81  % (31919)Instruction limit reached!
% 3.18/1.81  % (31919)------------------------------
% 3.18/1.81  % (31919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.81  % (31919)Termination reason: Unknown
% 3.18/1.81  % (31919)Termination phase: Saturation
% 3.18/1.81  
% 3.18/1.81  % (31919)Memory used [KB]: 8315
% 3.18/1.81  % (31919)Time elapsed: 0.112 s
% 3.18/1.81  % (31919)Instructions burned: 378 (million)
% 3.18/1.81  % (31919)------------------------------
% 3.18/1.81  % (31919)------------------------------
% 3.18/1.81  % (31932)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_31682 for (2997ds/100Mi)
% 3.18/1.82  % (31933)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_31682 for (2997ds/3Mi)
% 3.18/1.82  % (31933)Instruction limit reached!
% 3.18/1.82  % (31933)------------------------------
% 3.18/1.82  % (31933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.82  % (31933)Termination reason: Unknown
% 3.18/1.82  % (31933)Termination phase: shuffling
% 3.18/1.82  
% 3.18/1.82  % (31933)Memory used [KB]: 1535
% 3.18/1.82  % (31933)Time elapsed: 0.003 s
% 3.18/1.82  % (31933)Instructions burned: 6 (million)
% 3.18/1.82  % (31933)------------------------------
% 3.18/1.82  % (31933)------------------------------
% 3.18/1.83  % (31934)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_31682 for (2997ds/20Mi)
% 3.18/1.84  % (31934)Instruction limit reached!
% 3.18/1.84  % (31934)------------------------------
% 3.18/1.84  % (31934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.84  % (31934)Termination reason: Unknown
% 3.18/1.84  % (31934)Termination phase: shuffling
% 3.18/1.84  
% 3.18/1.84  % (31934)Memory used [KB]: 1918
% 3.18/1.84  % (31934)Time elapsed: 0.008 s
% 3.18/1.84  % (31934)Instructions burned: 21 (million)
% 3.18/1.84  % (31934)------------------------------
% 3.18/1.84  % (31934)------------------------------
% 3.18/1.84  % (31932)Instruction limit reached!
% 3.18/1.84  % (31932)------------------------------
% 3.18/1.84  % (31932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.84  % (31932)Termination reason: Unknown
% 3.18/1.84  % (31932)Termination phase: Property scanning
% 3.18/1.84  
% 3.18/1.84  % (31932)Memory used [KB]: 2558
% 3.18/1.84  % (31932)Time elapsed: 0.028 s
% 3.18/1.84  % (31932)Instructions burned: 103 (million)
% 3.18/1.84  % (31932)------------------------------
% 3.18/1.84  % (31932)------------------------------
% 3.18/1.84  % (31937)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_31682 for (2997ds/86Mi)
% 3.18/1.85  % (31940)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_31682 for (2997ds/107Mi)
% 3.18/1.87  % (31937)Instruction limit reached!
% 3.18/1.87  % (31937)------------------------------
% 3.18/1.87  % (31937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.87  % (31937)Termination reason: Unknown
% 3.18/1.87  % (31937)Termination phase: Property scanning
% 3.18/1.87  
% 3.18/1.87  % (31937)Memory used [KB]: 2558
% 3.18/1.87  % (31937)Time elapsed: 0.025 s
% 3.18/1.87  % (31937)Instructions burned: 86 (million)
% 3.18/1.87  % (31937)------------------------------
% 3.18/1.87  % (31937)------------------------------
% 3.18/1.88  % (31954)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_31682 for (2997ds/39Mi)
% 3.18/1.88  % (31940)Instruction limit reached!
% 3.18/1.88  % (31940)------------------------------
% 3.18/1.88  % (31940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.88  % (31940)Termination reason: Unknown
% 3.18/1.88  % (31940)Termination phase: Property scanning
% 3.18/1.88  
% 3.18/1.88  % (31940)Memory used [KB]: 2942
% 3.18/1.88  % (31940)Time elapsed: 0.031 s
% 3.18/1.88  % (31940)Instructions burned: 107 (million)
% 3.18/1.88  % (31940)------------------------------
% 3.18/1.88  % (31940)------------------------------
% 3.18/1.89  % (31960)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_31682 for (2997ds/448Mi)
% 3.18/1.89  % (31954)Instruction limit reached!
% 3.18/1.89  % (31954)------------------------------
% 3.18/1.89  % (31954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.89  % (31954)Termination reason: Unknown
% 3.18/1.89  % (31954)Termination phase: shuffling
% 3.18/1.89  
% 3.18/1.89  % (31954)Memory used [KB]: 2302
% 3.18/1.89  % (31954)Time elapsed: 0.012 s
% 3.18/1.89  % (31954)Instructions burned: 40 (million)
% 3.18/1.89  % (31954)------------------------------
% 3.18/1.89  % (31954)------------------------------
% 3.18/1.90  % (31965)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_31682 for (2997ds/46Mi)
% 3.18/1.91  % (31965)Instruction limit reached!
% 3.18/1.91  % (31965)------------------------------
% 3.18/1.91  % (31965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.91  % (31965)Termination reason: Unknown
% 3.18/1.91  % (31965)Termination phase: SInE selection
% 3.18/1.91  
% 3.18/1.91  % (31965)Memory used [KB]: 2046
% 3.18/1.91  % (31965)Time elapsed: 0.015 s
% 3.18/1.91  % (31965)Instructions burned: 49 (million)
% 3.18/1.91  % (31965)------------------------------
% 3.18/1.91  % (31965)------------------------------
% 3.18/1.92  % (31920)Instruction limit reached!
% 3.18/1.92  % (31920)------------------------------
% 3.18/1.92  % (31920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.92  % (31920)Termination reason: Unknown
% 3.18/1.92  % (31920)Termination phase: Saturation
% 3.18/1.92  
% 3.18/1.92  % (31920)Memory used [KB]: 9850
% 3.18/1.92  % (31920)Time elapsed: 0.221 s
% 3.18/1.92  % (31920)Instructions burned: 779 (million)
% 3.18/1.92  % (31920)------------------------------
% 3.18/1.92  % (31920)------------------------------
% 3.18/1.92  % (31979)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_31682 for (2996ds/98Mi)
% 3.18/1.93  % (31903)Instruction limit reached!
% 3.18/1.93  % (31903)------------------------------
% 3.18/1.93  % (31903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.93  % (31903)Termination reason: Unknown
% 3.18/1.93  % (31903)Termination phase: Saturation
% 3.18/1.93  
% 3.18/1.93  % (31903)Memory used [KB]: 8315
% 3.18/1.93  % (31903)Time elapsed: 0.260 s
% 3.18/1.93  % (31903)Instructions burned: 904 (million)
% 3.18/1.93  % (31903)------------------------------
% 3.18/1.93  % (31903)------------------------------
% 3.18/1.93  % (31981)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_31682 for (2996ds/507Mi)
% 3.18/1.93  % (31901)Instruction limit reached!
% 3.18/1.93  % (31901)------------------------------
% 3.18/1.93  % (31901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.93  % (31901)Termination reason: Unknown
% 3.18/1.93  % (31901)Termination phase: Saturation
% 3.18/1.93  
% 3.18/1.93  % (31901)Memory used [KB]: 8443
% 3.18/1.93  % (31901)Time elapsed: 0.268 s
% 3.18/1.93  % (31901)Instructions burned: 710 (million)
% 3.18/1.93  % (31901)------------------------------
% 3.18/1.93  % (31901)------------------------------
% 3.18/1.94  % (31986)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_31682 for (2996ds/39Mi)
% 3.18/1.94  % (31984)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_31682 for (2996ds/149Mi)
% 3.18/1.95  % (31979)Instruction limit reached!
% 3.18/1.95  % (31979)------------------------------
% 3.18/1.95  % (31979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.95  % (31979)Termination reason: Unknown
% 3.18/1.95  % (31979)Termination phase: Property scanning
% 3.18/1.95  
% 3.18/1.95  % (31979)Memory used [KB]: 2558
% 3.18/1.95  % (31979)Time elapsed: 0.027 s
% 3.18/1.95  % (31979)Instructions burned: 99 (million)
% 3.18/1.95  % (31979)------------------------------
% 3.18/1.95  % (31979)------------------------------
% 3.18/1.95  % (31986)Instruction limit reached!
% 3.18/1.95  % (31986)------------------------------
% 3.18/1.95  % (31986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.95  % (31986)Termination reason: Unknown
% 3.18/1.95  % (31986)Termination phase: Property scanning
% 3.18/1.95  
% 3.18/1.95  % (31986)Memory used [KB]: 2046
% 3.18/1.95  % (31986)Time elapsed: 0.014 s
% 3.18/1.95  % (31986)Instructions burned: 40 (million)
% 3.18/1.95  % (31986)------------------------------
% 3.18/1.95  % (31986)------------------------------
% 3.18/1.96  % (31996)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_31682 for (2996ds/6Mi)
% 3.18/1.96  % (31996)Instruction limit reached!
% 3.18/1.96  % (31996)------------------------------
% 3.18/1.96  % (31996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.96  % (31996)Termination reason: Unknown
% 3.18/1.96  % (31996)Termination phase: shuffling
% 3.18/1.96  
% 3.18/1.96  % (31996)Memory used [KB]: 1535
% 3.18/1.96  % (31996)Time elapsed: 0.003 s
% 3.18/1.96  % (31996)Instructions burned: 7 (million)
% 3.18/1.96  % (31996)------------------------------
% 3.18/1.96  % (31996)------------------------------
% 3.18/1.96  % (31997)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_31682 for (2996ds/1087Mi)
% 3.18/1.97  % (31924)Instruction limit reached!
% 3.18/1.97  % (31924)------------------------------
% 3.18/1.97  % (31924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.97  % (31924)Termination reason: Unknown
% 3.18/1.97  % (31924)Termination phase: Saturation
% 3.18/1.97  
% 3.18/1.97  % (31924)Memory used [KB]: 8315
% 3.18/1.97  % (31924)Time elapsed: 0.253 s
% 3.18/1.97  % (31924)Instructions burned: 881 (million)
% 3.18/1.97  % (31924)------------------------------
% 3.18/1.97  % (31924)------------------------------
% 3.18/1.97  % (32001)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_31682 for (2996ds/47Mi)
% 3.18/1.98  % (32004)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_31682 for (2996ds/44Mi)
% 3.18/1.98  % (32001)Instruction limit reached!
% 3.18/1.98  % (32001)------------------------------
% 3.18/1.98  % (32001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.98  % (32001)Termination reason: Unknown
% 3.18/1.98  % (32001)Termination phase: Naming
% 3.18/1.98  
% 3.18/1.98  % (32001)Memory used [KB]: 2174
% 3.18/1.98  % (32001)Time elapsed: 0.015 s
% 3.18/1.98  % (32001)Instructions burned: 47 (million)
% 3.18/1.98  % (32001)------------------------------
% 3.18/1.98  % (32001)------------------------------
% 3.18/1.99  % (31890)Instruction limit reached!
% 3.18/1.99  % (31890)------------------------------
% 3.18/1.99  % (31890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.99  % (31890)Termination reason: Unknown
% 3.18/1.99  % (31890)Termination phase: Saturation
% 3.18/1.99  
% 3.18/1.99  % (31890)Memory used [KB]: 10106
% 3.18/1.99  % (31890)Time elapsed: 0.354 s
% 3.18/1.99  % (31890)Instructions burned: 1043 (million)
% 3.18/1.99  % (31890)------------------------------
% 3.18/1.99  % (31890)------------------------------
% 3.18/1.99  % (32004)Instruction limit reached!
% 3.18/1.99  % (32004)------------------------------
% 3.18/1.99  % (32004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.99  % (32004)Termination reason: Unknown
% 3.18/1.99  % (32004)Termination phase: shuffling
% 3.18/1.99  
% 3.18/1.99  % (32004)Memory used [KB]: 2302
% 3.18/1.99  % (32004)Time elapsed: 0.013 s
% 3.18/1.99  % (32004)Instructions burned: 45 (million)
% 3.18/1.99  % (32004)------------------------------
% 3.18/1.99  % (32004)------------------------------
% 3.18/1.99  % (32012)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_31682 for (2996ds/432Mi)
% 3.18/2.00  % (32015)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_31682 for (2996ds/62Mi)
% 3.18/2.00  % (32016)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_31682 for (2996ds/31Mi)
% 3.18/2.01  % (32016)Instruction limit reached!
% 3.18/2.01  % (32016)------------------------------
% 3.18/2.01  % (32016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/2.01  % (32016)Termination reason: Unknown
% 3.18/2.01  % (32016)Termination phase: Property scanning
% 3.18/2.01  
% 3.18/2.01  % (32016)Memory used [KB]: 2046
% 3.18/2.01  % (32016)Time elapsed: 0.012 s
% 3.18/2.01  % (32016)Instructions burned: 35 (million)
% 3.18/2.01  % (32016)------------------------------
% 3.18/2.01  % (32016)------------------------------
% 3.18/2.01  % (31960)Instruction limit reached!
% 3.18/2.01  % (31960)------------------------------
% 3.18/2.01  % (31960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/2.01  % (31960)Termination reason: Unknown
% 3.18/2.01  % (31960)Termination phase: Saturation
% 3.18/2.01  
% 3.18/2.01  % (31960)Memory used [KB]: 8187
% 3.18/2.01  % (31960)Time elapsed: 0.122 s
% 3.18/2.01  % (31960)Instructions burned: 448 (million)
% 3.18/2.01  % (31960)------------------------------
% 3.18/2.01  % (31960)------------------------------
% 3.18/2.01  % (31984)Instruction limit reached!
% 3.18/2.01  % (31984)------------------------------
% 3.18/2.01  % (31984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/2.01  % (31984)Termination reason: Unknown
% 3.18/2.01  % (31984)Termination phase: Property scanning
% 3.18/2.01  
% 3.18/2.01  % (31984)Memory used [KB]: 2942
% 3.18/2.01  % (31984)Time elapsed: 0.069 s
% 3.18/2.01  % (31984)Instructions burned: 150 (million)
% 3.18/2.01  % (31984)------------------------------
% 3.18/2.01  % (31984)------------------------------
% 5.95/2.01  % (32015)Instruction limit reached!
% 5.95/2.01  % (32015)------------------------------
% 5.95/2.01  % (32015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.01  % (32015)Termination reason: Unknown
% 5.95/2.01  % (32015)Termination phase: Property scanning
% 5.95/2.01  
% 5.95/2.01  % (32015)Memory used [KB]: 2430
% 5.95/2.01  % (32015)Time elapsed: 0.018 s
% 5.95/2.01  % (32015)Instructions burned: 62 (million)
% 5.95/2.01  % (32015)------------------------------
% 5.95/2.01  % (32015)------------------------------
% 5.95/2.02  % (32025)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_31682 for (2995ds/96Mi)
% 5.95/2.02  % (32028)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_31682 for (2995ds/453Mi)
% 5.95/2.02  % (32029)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_31682 for (2995ds/71Mi)
% 5.95/2.02  % (32031)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_31682 for (2995ds/83Mi)
% 5.95/2.04  % (32029)Instruction limit reached!
% 5.95/2.04  % (32029)------------------------------
% 5.95/2.04  % (32029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.04  % (32029)Termination reason: Unknown
% 5.95/2.04  % (32029)Termination phase: Property scanning
% 5.95/2.04  
% 5.95/2.04  % (32029)Memory used [KB]: 2558
% 5.95/2.04  % (32029)Time elapsed: 0.022 s
% 5.95/2.04  % (32029)Instructions burned: 72 (million)
% 5.95/2.04  % (32029)------------------------------
% 5.95/2.04  % (32029)------------------------------
% 5.95/2.04  % (32025)Instruction limit reached!
% 5.95/2.04  % (32025)------------------------------
% 5.95/2.04  % (32025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.04  % (32025)Termination reason: Unknown
% 5.95/2.04  % (32025)Termination phase: Function definition elimination
% 5.95/2.04  
% 5.95/2.04  % (32025)Memory used [KB]: 2814
% 5.95/2.04  % (32025)Time elapsed: 0.028 s
% 5.95/2.04  % (32025)Instructions burned: 97 (million)
% 5.95/2.04  % (32025)------------------------------
% 5.95/2.04  % (32025)------------------------------
% 5.95/2.05  % (32031)Instruction limit reached!
% 5.95/2.05  % (32031)------------------------------
% 5.95/2.05  % (32031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.05  % (32031)Termination reason: Unknown
% 5.95/2.05  % (32031)Termination phase: Property scanning
% 5.95/2.05  
% 5.95/2.05  % (32031)Memory used [KB]: 2558
% 5.95/2.05  % (32031)Time elapsed: 0.025 s
% 5.95/2.05  % (32031)Instructions burned: 85 (million)
% 5.95/2.05  % (32031)------------------------------
% 5.95/2.05  % (32031)------------------------------
% 5.95/2.05  % (32041)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_31682 for (2995ds/11Mi)
% 5.95/2.05  % (32042)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_31682 for (2995ds/41Mi)
% 5.95/2.06  % (32043)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31682 for (2995ds/6Mi)
% 5.95/2.06  % (32041)Instruction limit reached!
% 5.95/2.06  % (32041)------------------------------
% 5.95/2.06  % (32041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.06  % (32041)Termination reason: Unknown
% 5.95/2.06  % (32041)Termination phase: shuffling
% 5.95/2.06  
% 5.95/2.06  % (32041)Memory used [KB]: 1663
% 5.95/2.06  % (32041)Time elapsed: 0.005 s
% 5.95/2.06  % (32041)Instructions burned: 13 (million)
% 5.95/2.06  % (32041)------------------------------
% 5.95/2.06  % (32041)------------------------------
% 5.95/2.06  % (32043)Instruction limit reached!
% 5.95/2.06  % (32043)------------------------------
% 5.95/2.06  % (32043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.06  % (32043)Termination reason: Unknown
% 5.95/2.06  % (32043)Termination phase: shuffling
% 5.95/2.06  
% 5.95/2.06  % (32043)Memory used [KB]: 1663
% 5.95/2.06  % (32043)Time elapsed: 0.004 s
% 5.95/2.06  % (32043)Instructions burned: 9 (million)
% 5.95/2.06  % (32043)------------------------------
% 5.95/2.06  % (32043)------------------------------
% 5.95/2.06  % (32054)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_31682 for (2995ds/150Mi)
% 5.95/2.07  % (32042)Instruction limit reached!
% 5.95/2.07  % (32042)------------------------------
% 5.95/2.07  % (32042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.07  % (32042)Termination reason: Unknown
% 5.95/2.07  % (32042)Termination phase: shuffling
% 5.95/2.07  
% 5.95/2.07  % (32042)Memory used [KB]: 2302
% 5.95/2.07  % (32042)Time elapsed: 0.013 s
% 5.95/2.07  % (32042)Instructions burned: 44 (million)
% 5.95/2.07  % (32042)------------------------------
% 5.95/2.07  % (32042)------------------------------
% 5.95/2.07  % (32057)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_31682 for (2995ds/343Mi)
% 5.95/2.07  % (31981)Instruction limit reached!
% 5.95/2.07  % (31981)------------------------------
% 5.95/2.07  % (31981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.07  % (31981)Termination reason: Unknown
% 5.95/2.07  % (31981)Termination phase: Saturation
% 5.95/2.07  
% 5.95/2.07  % (31981)Memory used [KB]: 8827
% 5.95/2.07  % (31981)Time elapsed: 0.143 s
% 5.95/2.07  % (31981)Instructions burned: 510 (million)
% 5.95/2.07  % (31981)------------------------------
% 5.95/2.07  % (31981)------------------------------
% 5.95/2.08  % (32062)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_31682 for (2995ds/109Mi)
% 5.95/2.08  % (32066)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_31682 for (2995ds/253Mi)
% 5.95/2.11  % (32054)Instruction limit reached!
% 5.95/2.11  % (32054)------------------------------
% 5.95/2.11  % (32054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.11  % (32054)Termination reason: Unknown
% 5.95/2.11  % (32054)Termination phase: Property scanning
% 5.95/2.11  
% 5.95/2.11  % (32054)Memory used [KB]: 3070
% 5.95/2.11  % (32054)Time elapsed: 0.042 s
% 5.95/2.11  % (32054)Instructions burned: 154 (million)
% 5.95/2.11  % (32054)------------------------------
% 5.95/2.11  % (32054)------------------------------
% 5.95/2.11  % (32062)Instruction limit reached!
% 5.95/2.11  % (32062)------------------------------
% 5.95/2.11  % (32062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.11  % (32062)Termination reason: Unknown
% 5.95/2.11  % (32062)Termination phase: Property scanning
% 5.95/2.11  
% 5.95/2.11  % (32062)Memory used [KB]: 2814
% 5.95/2.11  % (32062)Time elapsed: 0.032 s
% 5.95/2.11  % (32062)Instructions burned: 111 (million)
% 5.95/2.11  % (32062)------------------------------
% 5.95/2.11  % (32062)------------------------------
% 6.54/2.11  % (32012)Instruction limit reached!
% 6.54/2.11  % (32012)------------------------------
% 6.54/2.11  % (32012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.11  % (32012)Termination reason: Unknown
% 6.54/2.11  % (32012)Termination phase: Saturation
% 6.54/2.11  
% 6.54/2.11  % (32012)Memory used [KB]: 4605
% 6.54/2.11  % (32012)Time elapsed: 0.146 s
% 6.54/2.11  % (32012)Instructions burned: 432 (million)
% 6.54/2.11  % (32012)------------------------------
% 6.54/2.11  % (32012)------------------------------
% 6.54/2.12  % (32085)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_31682 for (2994ds/140Mi)
% 6.54/2.12  % (32087)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_31682 for (2994ds/614Mi)
% 6.54/2.12  % (32089)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_31682 for (2994ds/202Mi)
% 6.54/2.14  % (32028)Instruction limit reached!
% 6.54/2.14  % (32028)------------------------------
% 6.54/2.14  % (32028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.14  % (32028)Termination reason: Unknown
% 6.54/2.14  % (32028)Termination phase: Saturation
% 6.54/2.14  
% 6.54/2.14  % (32028)Memory used [KB]: 8187
% 6.54/2.14  % (32028)Time elapsed: 0.149 s
% 6.54/2.14  % (32028)Instructions burned: 453 (million)
% 6.54/2.14  % (32028)------------------------------
% 6.54/2.14  % (32028)------------------------------
% 6.54/2.15  % (32066)Instruction limit reached!
% 6.54/2.15  % (32066)------------------------------
% 6.54/2.15  % (32066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.15  % (32066)Termination reason: Unknown
% 6.54/2.15  % (32066)Termination phase: Saturation
% 6.54/2.15  
% 6.54/2.15  % (32066)Memory used [KB]: 8059
% 6.54/2.15  % (32066)Time elapsed: 0.074 s
% 6.54/2.15  % (32066)Instructions burned: 253 (million)
% 6.54/2.15  % (32066)------------------------------
% 6.54/2.15  % (32066)------------------------------
% 6.54/2.15  % (32103)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_31682 for (2994ds/339Mi)
% 6.54/2.16  % (32085)Instruction limit reached!
% 6.54/2.16  % (32085)------------------------------
% 6.54/2.16  % (32085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.16  % (32085)Termination reason: Unknown
% 6.54/2.16  % (32085)Termination phase: Saturation
% 6.54/2.16  
% 6.54/2.16  % (32085)Memory used [KB]: 7036
% 6.54/2.16  % (32085)Time elapsed: 0.045 s
% 6.54/2.16  % (32085)Instructions burned: 140 (million)
% 6.54/2.16  % (32085)------------------------------
% 6.54/2.16  % (32085)------------------------------
% 6.54/2.16  % (32107)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_31682 for (2994ds/283Mi)
% 6.54/2.17  % (32057)Instruction limit reached!
% 6.54/2.17  % (32057)------------------------------
% 6.54/2.17  % (32057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.17  % (32057)Termination reason: Unknown
% 6.54/2.17  % (32057)Termination phase: Saturation
% 6.54/2.17  
% 6.54/2.17  % (32057)Memory used [KB]: 8059
% 6.54/2.17  % (32057)Time elapsed: 0.099 s
% 6.54/2.17  % (32057)Instructions burned: 344 (million)
% 6.54/2.17  % (32057)------------------------------
% 6.54/2.17  % (32057)------------------------------
% 6.54/2.17  % (32089)First to succeed.
% 6.54/2.17  % (32110)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_31682 for (2994ds/134Mi)
% 6.54/2.17  % (32089)Refutation found. Thanks to Tanya!
% 6.54/2.17  % SZS status Theorem for DTF2THF_31682
% 6.54/2.17  % SZS output start Proof for DTF2THF_31682
% 6.54/2.17  thf(type_def_5, type, set_int: $tType).
% 6.54/2.17  thf(type_def_7, type, set_poly_int: $tType).
% 6.54/2.17  thf(type_def_8, type, set_poly_poly_real: $tType).
% 6.54/2.17  thf(type_def_9, type, set_poly_real: $tType).
% 6.54/2.17  thf(type_def_10, type, set_real: $tType).
% 6.54/2.17  thf(type_def_11, type, set_set_int: $tType).
% 6.54/2.17  thf(type_def_12, type, set_set_real: $tType).
% 6.54/2.17  thf(type_def_13, type, int: $tType).
% 6.54/2.17  thf(type_def_14, type, poly_real: $tType).
% 6.54/2.17  thf(type_def_15, type, poly_int: $tType).
% 6.54/2.17  thf(type_def_16, type, poly_poly_int: $tType).
% 6.54/2.17  thf(type_def_17, type, poly_poly_poly_real: $tType).
% 6.54/2.17  thf(type_def_18, type, poly_poly_real: $tType).
% 6.54/2.17  thf(type_def_19, type, real: $tType).
% 6.54/2.17  thf(type_def_20, type, nat: $tType).
% 6.54/2.17  thf(func_def_0, type, poly_poly_poly_real: $tType).
% 6.54/2.17  thf(func_def_1, type, set_poly_poly_real: $tType).
% 6.54/2.17  thf(func_def_2, type, poly_poly_real: $tType).
% 6.54/2.17  thf(func_def_3, type, poly_poly_int: $tType).
% 6.54/2.17  thf(func_def_4, type, set_poly_real: $tType).
% 6.54/2.17  thf(func_def_5, type, set_poly_int: $tType).
% 6.54/2.17  thf(func_def_6, type, set_set_real: $tType).
% 6.54/2.17  thf(func_def_7, type, set_set_int: $tType).
% 6.54/2.17  thf(func_def_8, type, poly_real: $tType).
% 6.54/2.17  thf(func_def_9, type, poly_int: $tType).
% 6.54/2.17  thf(func_def_10, type, set_real: $tType).
% 6.54/2.17  thf(func_def_11, type, set_int: $tType).
% 6.54/2.17  thf(func_def_12, type, real: $tType).
% 6.54/2.17  thf(func_def_13, type, nat: $tType).
% 6.54/2.17  thf(func_def_14, type, int: $tType).
% 6.54/2.17  thf(func_def_15, type, finite_finite_int: set_int > $o).
% 6.54/2.17  thf(func_def_16, type, finite385822667ly_int: set_poly_int > $o).
% 6.54/2.17  thf(func_def_17, type, finite1328464339y_real: set_poly_poly_real > $o).
% 6.54/2.17  thf(func_def_18, type, finite1810960971y_real: set_poly_real > $o).
% 6.54/2.17  thf(func_def_19, type, finite_finite_real: set_real > $o).
% 6.54/2.17  thf(func_def_20, type, finite26677625et_int: set_set_int > $o).
% 6.54/2.17  thf(func_def_21, type, finite475462905t_real: set_set_real > $o).
% 6.54/2.17  thf(func_def_22, type, one_one_int: int).
% 6.54/2.17  thf(func_def_23, type, one_one_poly_real: poly_real).
% 6.54/2.17  thf(func_def_24, type, zero_zero_int: int).
% 6.54/2.17  thf(func_def_25, type, zero_zero_poly_int: poly_int).
% 6.54/2.17  thf(func_def_26, type, zero_z1549157189ly_int: poly_poly_int).
% 6.54/2.17  thf(func_def_27, type, zero_z935034829y_real: poly_poly_poly_real).
% 6.54/2.17  thf(func_def_28, type, zero_z1423781445y_real: poly_poly_real).
% 6.54/2.17  thf(func_def_29, type, zero_zero_poly_real: poly_real).
% 6.54/2.17  thf(func_def_30, type, zero_zero_real: real).
% 6.54/2.17  thf(func_def_31, type, groups2051521940al_int: (real > int) > set_real > int).
% 6.54/2.17  thf(func_def_32, type, ord_less_int: int > int > $o).
% 6.54/2.17  thf(func_def_33, type, ord_less_poly_int: poly_int > poly_int > $o).
% 6.54/2.17  thf(func_def_34, type, ord_le38482960y_real: poly_poly_real > poly_poly_real > $o).
% 6.54/2.17  thf(func_def_35, type, ord_less_poly_real: poly_real > poly_real > $o).
% 6.54/2.17  thf(func_def_36, type, ord_less_real: real > real > $o).
% 6.54/2.17  thf(func_def_37, type, ord_less_set_int: set_int > set_int > $o).
% 6.54/2.17  thf(func_def_38, type, ord_less_set_real: set_real > set_real > $o).
% 6.54/2.17  thf(func_def_39, type, ord_less_eq_real_o: (real > $o) > (real > $o) > $o).
% 6.54/2.17  thf(func_def_40, type, ord_less_eq_int: int > int > $o).
% 6.54/2.17  thf(func_def_41, type, ord_less_eq_poly_int: poly_int > poly_int > $o).
% 6.54/2.17  thf(func_def_42, type, ord_le893774876y_real: poly_poly_real > poly_poly_real > $o).
% 6.54/2.17  thf(func_def_43, type, ord_le1180086932y_real: poly_real > poly_real > $o).
% 6.54/2.17  thf(func_def_44, type, ord_less_eq_real: real > real > $o).
% 6.54/2.17  thf(func_def_45, type, ord_less_eq_set_int: set_int > set_int > $o).
% 6.54/2.17  thf(func_def_46, type, ord_less_eq_set_real: set_real > set_real > $o).
% 6.54/2.17  thf(func_def_47, type, is_zero_int: poly_int > $o).
% 6.54/2.17  thf(func_def_48, type, is_zero_poly_real: poly_poly_real > $o).
% 6.54/2.17  thf(func_def_49, type, is_zero_real: poly_real > $o).
% 6.54/2.17  thf(func_def_50, type, poly_int2: poly_int > int > int).
% 6.54/2.17  thf(func_def_51, type, poly_poly_int2: poly_poly_int > poly_int > poly_int).
% 6.54/2.17  thf(func_def_52, type, poly_poly_poly_real2: poly_poly_poly_real > poly_poly_real > poly_poly_real).
% 6.54/2.17  thf(func_def_53, type, poly_poly_real2: poly_poly_real > poly_real > poly_real).
% 6.54/2.17  thf(func_def_54, type, poly_real2: poly_real > real > real).
% 6.54/2.17  thf(func_def_55, type, poly_cutoff_int: nat > poly_int > poly_int).
% 6.54/2.17  thf(func_def_56, type, poly_c1404107022y_real: nat > poly_poly_real > poly_poly_real).
% 6.54/2.17  thf(func_def_57, type, poly_cutoff_real: nat > poly_real > poly_real).
% 6.54/2.17  thf(func_def_58, type, collect_int: (int > $o) > set_int).
% 6.54/2.17  thf(func_def_59, type, collect_poly_int: (poly_int > $o) > set_poly_int).
% 6.54/2.17  thf(func_def_60, type, collec927113489y_real: (poly_poly_real > $o) > set_poly_poly_real).
% 6.54/2.17  thf(func_def_61, type, collect_poly_real: (poly_real > $o) > set_poly_real).
% 6.54/2.17  thf(func_def_62, type, collect_real: (real > $o) > set_real).
% 6.54/2.17  thf(func_def_63, type, collect_set_int: (set_int > $o) > set_set_int).
% 6.54/2.17  thf(func_def_64, type, collect_set_real: (set_real > $o) > set_set_real).
% 6.54/2.17  thf(func_def_65, type, sturm_308542325x_poly: real > real > poly_real > poly_real > int).
% 6.54/2.17  thf(func_def_66, type, sturm_1953858694_cross: poly_real > real > real > int).
% 6.54/2.17  thf(func_def_67, type, sturm_276991412p_poly: poly_real > poly_real > real > int).
% 6.54/2.17  thf(func_def_68, type, member_int: int > set_int > $o).
% 6.54/2.17  thf(func_def_69, type, member_real: real > set_real > $o).
% 6.54/2.17  thf(func_def_70, type, a: real).
% 6.54/2.17  thf(func_def_71, type, a2: real).
% 6.54/2.17  thf(func_def_72, type, b: real).
% 6.54/2.17  thf(func_def_73, type, b2: real).
% 6.54/2.17  thf(func_def_74, type, p: poly_real).
% 6.54/2.17  thf(func_def_90, type, diff: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > X0)).
% 6.54/2.17  thf(func_def_91, type, sP0: (real > $o) > (real > $o) > (real > $o) > (real > $o) > $o).
% 6.54/2.17  thf(func_def_92, type, sP1: (real > $o) > (real > $o) > (real > $o) > (real > $o) > $o).
% 6.54/2.17  thf(func_def_93, type, sP2: (real > $o) > (real > $o) > (real > $o) > (real > $o) > $o).
% 6.54/2.17  thf(func_def_94, type, sP3: (real > $o) > (real > $o) > (real > $o) > (real > $o) > $o).
% 6.54/2.17  thf(func_def_95, type, sK4: (real > int) > real).
% 6.54/2.17  thf(func_def_96, type, sK5: (real > int) > real).
% 6.54/2.17  thf(func_def_97, type, sK6: real > real).
% 6.54/2.17  thf(func_def_98, type, sK7: real > real > real > real).
% 6.54/2.17  thf(func_def_99, type, sK8: real > real).
% 6.54/2.17  thf(func_def_100, type, sK9: real > real).
% 6.54/2.17  thf(func_def_101, type, sK10: real > set_real > real).
% 6.54/2.17  thf(func_def_102, type, sK11: set_real > real).
% 6.54/2.17  thf(func_def_103, type, sK12: real > set_real > real).
% 6.54/2.17  thf(func_def_104, type, sK13: real > real).
% 6.54/2.17  thf(func_def_105, type, sK14: set_real > real > real).
% 6.54/2.17  thf(func_def_106, type, sK15: (int > real) > int).
% 6.54/2.17  thf(func_def_107, type, sK16: (int > real) > int).
% 6.54/2.17  thf(func_def_108, type, sK17: (int > real) > int).
% 6.54/2.17  thf(func_def_109, type, sK18: (int > real) > int).
% 6.54/2.17  thf(func_def_110, type, sK19: (int > real) > int).
% 6.54/2.17  thf(func_def_111, type, sK20: (int > real) > int).
% 6.54/2.17  thf(func_def_112, type, sK21: (int > real) > int).
% 6.54/2.17  thf(func_def_113, type, sK22: (int > real) > int).
% 6.54/2.17  thf(func_def_114, type, sK23: set_real > real > real).
% 6.54/2.17  thf(func_def_115, type, sK24: (real > int) > real).
% 6.54/2.17  thf(func_def_116, type, sK25: (real > int) > real).
% 6.54/2.17  thf(func_def_117, type, sK26: real > real).
% 6.54/2.17  thf(func_def_118, type, sK27: real > real > real).
% 6.54/2.17  thf(func_def_119, type, sK28: real > real).
% 6.54/2.17  thf(func_def_120, type, sK29: real > real).
% 6.54/2.17  thf(func_def_121, type, sK30: (real > $o) > (real > $o) > (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_122, type, sK31: real > (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_123, type, sK32: real > (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_124, type, sK33: real > real).
% 6.54/2.17  thf(func_def_125, type, sK34: (real > real) > real).
% 6.54/2.17  thf(func_def_126, type, sK35: (real > real) > real).
% 6.54/2.17  thf(func_def_127, type, sK36: poly_real > real > real > real).
% 6.54/2.17  thf(func_def_128, type, sK37: (real > int) > real).
% 6.54/2.17  thf(func_def_129, type, sK38: (real > int) > real).
% 6.54/2.17  thf(func_def_130, type, sK39: (real > real > $o) > real).
% 6.54/2.17  thf(func_def_131, type, sK40: (real > real > $o) > real).
% 6.54/2.17  thf(func_def_132, type, sK41: (real > real > $o) > real).
% 6.54/2.17  thf(func_def_133, type, sK42: (real > real > $o) > real).
% 6.54/2.17  thf(func_def_134, type, sK43: (real > real > $o) > real).
% 6.54/2.17  thf(func_def_135, type, sK44: (real > real) > real).
% 6.54/2.17  thf(func_def_136, type, sK45: (real > real) > real).
% 6.54/2.17  thf(func_def_137, type, sK46: (real > real) > real).
% 6.54/2.17  thf(func_def_138, type, sK47: (real > real) > real).
% 6.54/2.17  thf(func_def_139, type, sK48: poly_real > real).
% 6.54/2.17  thf(func_def_140, type, sK49: real > real).
% 6.54/2.17  thf(func_def_141, type, sK50: (real > int) > real).
% 6.54/2.17  thf(func_def_142, type, sK51: (real > int) > real).
% 6.54/2.17  thf(func_def_143, type, sK52: set_int > (int > real > $o) > set_real > real).
% 6.54/2.17  thf(func_def_144, type, sK53: set_int > (int > real > $o) > set_real > int).
% 6.54/2.17  thf(func_def_145, type, sK54: (real > int > $o) > set_real > set_int > int).
% 6.54/2.17  thf(func_def_146, type, sK55: (real > int > $o) > set_real > set_int > real).
% 6.54/2.17  thf(func_def_147, type, sK56: (real > $o) > real).
% 6.54/2.17  thf(func_def_148, type, sK57: poly_real > real > real).
% 6.54/2.17  thf(func_def_149, type, sK58: real > poly_real > real > real).
% 6.54/2.17  thf(func_def_150, type, sK59: real > poly_real > real > real).
% 6.54/2.17  thf(func_def_151, type, sK60: real > poly_real > real > real).
% 6.54/2.17  thf(func_def_152, type, sK61: poly_real > real > real > real).
% 6.54/2.17  thf(func_def_153, type, sK62: poly_real > real > real > real).
% 6.54/2.17  thf(func_def_154, type, sK63: poly_real > real > real > real).
% 6.54/2.17  thf(func_def_155, type, sK64: (int > real) > int).
% 6.54/2.17  thf(func_def_156, type, sK65: (int > real) > int).
% 6.54/2.17  thf(func_def_157, type, sK66: real > real).
% 6.54/2.17  thf(func_def_158, type, sK67: (real > int) > real).
% 6.54/2.17  thf(func_def_159, type, sK68: (real > int) > real).
% 6.54/2.17  thf(func_def_160, type, sK69: (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_161, type, sK70: poly_real > real > real > real).
% 6.54/2.17  thf(func_def_162, type, sK71: (real > int) > real).
% 6.54/2.17  thf(func_def_163, type, sK72: (real > int) > real).
% 6.54/2.17  thf(func_def_164, type, sK73: (real > $o) > real > real > real).
% 6.54/2.17  thf(func_def_165, type, sK74: real > (real > $o) > real > real).
% 6.54/2.17  thf(func_def_166, type, sK75: (real > real > $o) > set_real > set_real > real).
% 6.54/2.17  thf(func_def_167, type, sK76: (real > real > $o) > set_real > set_real > real).
% 6.54/2.17  thf(func_def_168, type, sK77: real > real).
% 6.54/2.17  thf(func_def_169, type, sK78: (real > $o) > (real > $o) > (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_170, type, sK79: real > (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_171, type, sK80: real > (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_172, type, sK81: (int > real) > int).
% 6.54/2.17  thf(func_def_173, type, sK82: (int > real) > int).
% 6.54/2.17  thf(func_def_174, type, sK83: (int > real) > int).
% 6.54/2.17  thf(func_def_175, type, sK84: (int > real) > int).
% 6.54/2.17  thf(func_def_176, type, sK85: (int > real) > int).
% 6.54/2.17  thf(func_def_177, type, sK86: (int > real) > int).
% 6.54/2.17  thf(func_def_178, type, sK87: (real > real) > real).
% 6.54/2.17  thf(func_def_179, type, sK88: (real > real) > real).
% 6.54/2.17  thf(func_def_180, type, sK89: (real > $o) > (real > $o) > (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_181, type, sK90: real > (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_182, type, sK91: real > (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_183, type, sK92: real > real > real).
% 6.54/2.17  thf(func_def_184, type, sK93: (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_185, type, sK94: (real > real) > real).
% 6.54/2.17  thf(func_def_186, type, sK95: (real > real) > real).
% 6.54/2.17  thf(func_def_187, type, sK96: (real > real) > real).
% 6.54/2.17  thf(func_def_188, type, sK97: (real > real) > real).
% 6.54/2.17  thf(func_def_189, type, sK98: real > poly_real > real).
% 6.54/2.17  thf(func_def_190, type, sK99: (real > $o) > (real > $o) > (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_191, type, sK100: real > (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_192, type, sK101: real > (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_193, type, sK102: (real > real) > real).
% 6.54/2.17  thf(func_def_194, type, sK103: (real > real) > real).
% 6.54/2.17  thf(func_def_195, type, sK104: (real > real) > real).
% 6.54/2.17  thf(func_def_196, type, sK105: (real > real) > real).
% 6.54/2.17  thf(func_def_197, type, sK106: real > real > real > real).
% 6.54/2.17  thf(func_def_198, type, sK107: (real > $o) > (real > $o) > real).
% 6.54/2.17  thf(func_def_199, type, sK108: real > real > real).
% 6.54/2.17  thf(func_def_200, type, sK109: real > real > real).
% 6.54/2.17  thf(func_def_202, type, ph111: !>[X0: $tType]:(X0)).
% 6.54/2.17  thf(f1781,plain,(
% 6.54/2.17    $false),
% 6.54/2.17    inference(subsumption_resolution,[status(thm)],[f1770,f1492])).
% 6.54/2.17  thf(f1492,plain,(
% 6.54/2.17    ((finite_finite_real @ (collect_real @ (^[Y0 : real]: ((poly_real2 @ p @ Y0) = zero_zero_real)))) = $true)),
% 6.54/2.17    inference(cnf_transformation,[status(thm)],[f637])).
% 6.54/2.17  thf(f637,plain,(
% 6.54/2.17    ((finite_finite_real @ (collect_real @ (^[Y0 : real]: ((poly_real2 @ p @ Y0) = zero_zero_real)))) = $true)),
% 6.54/2.17    inference(fool_elimination,[status(thm)],[f636])).
% 6.54/2.17  thf(f636,plain,(
% 6.54/2.17    (finite_finite_real @ (collect_real @ (^[X0 : real] : (((poly_real2 @ p @ X0) = zero_zero_real)))))),
% 6.54/2.17    inference(rectify,[status(thm)],[f1])).
% 6.54/2.17  thf(f1,axiom,(
% 6.54/2.17    (finite_finite_real @ (collect_real @ (^[X0 : real] : (((poly_real2 @ p @ X0) = zero_zero_real)))))),
% 6.54/2.17    file('/export/starexec/sandbox/tmp/tmp.JM2D9zVyZJ/DTF2THF_31682.p',fact_0__092_060open_062finite_A_123x_O_Apoly_Ap_Ax_A_061_A0_125_092_060close_062)).
% 6.54/2.17  thf(f1770,plain,(
% 6.54/2.17    ((finite_finite_real @ (collect_real @ (^[Y0 : real]: ((poly_real2 @ p @ Y0) = zero_zero_real)))) != $true)),
% 6.54/2.17    inference(trivial_inequality_removal,[status(thm)],[f1761])).
% 6.54/2.17  thf(f1761,plain,(
% 6.54/2.17    ((finite_finite_real @ (collect_real @ (^[Y0 : real]: ((poly_real2 @ p @ Y0) = zero_zero_real)))) != $true) | ($true != $true)),
% 6.54/2.17    inference(superposition,[status(thm)],[f1727,f1468])).
% 6.54/2.17  thf(f1468,plain,(
% 6.54/2.17    ( ! [X0 : real > $o,X1 : real > $o] : (((finite_finite_real @ (collect_real @ (^[Y0 : real]: ((X1 @ Y0) & (X0 @ Y0))))) = $true) | ((finite_finite_real @ (collect_real @ X1)) != $true)) )),
% 6.54/2.17    inference(cnf_transformation,[status(thm)],[f1114])).
% 6.54/2.17  thf(f1114,plain,(
% 6.54/2.17    ! [X0 : real > $o,X1 : real > $o] : ((((finite_finite_real @ (collect_real @ X1)) != $true) & ((finite_finite_real @ (collect_real @ X0)) != $true)) | ((finite_finite_real @ (collect_real @ (^[Y0 : real]: ((X1 @ Y0) & (X0 @ Y0))))) = $true))),
% 6.54/2.17    inference(ennf_transformation,[status(thm)],[f903])).
% 6.54/2.17  thf(f903,plain,(
% 6.54/2.17    ! [X0 : real > $o,X1 : real > $o] : ((((finite_finite_real @ (collect_real @ X0)) = $true) | ((finite_finite_real @ (collect_real @ X1)) = $true)) => ((finite_finite_real @ (collect_real @ (^[Y0 : real]: ((X1 @ Y0) & (X0 @ Y0))))) = $true))),
% 6.54/2.17    inference(fool_elimination,[status(thm)],[f902])).
% 6.54/2.17  thf(f902,plain,(
% 6.54/2.17    ! [X0 : real > $o,X1 : real > $o] : (((finite_finite_real @ (collect_real @ X0)) | (finite_finite_real @ (collect_real @ X1))) => (finite_finite_real @ (collect_real @ (^[X2 : real] : ((X0 @ X2) & (X1 @ X2))))))),
% 6.54/2.17    inference(rectify,[status(thm)],[f12])).
% 6.54/2.17  thf(f12,axiom,(
% 6.54/2.17    ! [X3 : real > $o,X4 : real > $o] : (((finite_finite_real @ (collect_real @ X3)) | (finite_finite_real @ (collect_real @ X4))) => (finite_finite_real @ (collect_real @ (^[X0 : real] : ((X3 @ X0) & (X4 @ X0))))))),
% 6.54/2.17    file('/export/starexec/sandbox/tmp/tmp.JM2D9zVyZJ/DTF2THF_31682.p',fact_11_finite__Collect__conjI)).
% 6.54/2.17  thf(f1727,plain,(
% 6.54/2.17    ((finite_finite_real @ (collect_real @ (^[Y0 : real]: (((poly_real2 @ p @ Y0) = zero_zero_real) & (ord_less_real @ a @ Y0))))) != $true)),
% 6.54/2.17    inference(trivial_inequality_removal,[status(thm)],[f1725])).
% 6.54/2.17  thf(f1725,plain,(
% 6.54/2.17    ((finite_finite_real @ (collect_real @ (^[Y0 : real]: (((poly_real2 @ p @ Y0) = zero_zero_real) & (ord_less_real @ a @ Y0))))) != $true) | ($true != $true)),
% 6.54/2.17    inference(superposition,[status(thm)],[f1677,f1468])).
% 6.54/2.17  thf(f1677,plain,(
% 6.54/2.17    ((finite_finite_real @ (collect_real @ (^[Y0 : real]: ((((poly_real2 @ p @ Y0) = zero_zero_real) & (ord_less_real @ a @ Y0)) & (ord_less_real @ Y0 @ b))))) != $true)),
% 6.54/2.17    inference(cnf_transformation,[status(thm)],[f1017])).
% 6.54/2.17  thf(f1017,plain,(
% 6.54/2.17    ((finite_finite_real @ (collect_real @ (^[Y0 : real]: ((((poly_real2 @ p @ Y0) = zero_zero_real) & (ord_less_real @ a @ Y0)) & (ord_less_real @ Y0 @ b))))) != $true)),
% 6.54/2.17    inference(flattening,[status(thm)],[f745])).
% 6.54/2.17  thf(f745,plain,(
% 6.54/2.17    ~((finite_finite_real @ (collect_real @ (^[Y0 : real]: ((((poly_real2 @ p @ Y0) = zero_zero_real) & (ord_less_real @ a @ Y0)) & (ord_less_real @ Y0 @ b))))) = $true)),
% 6.54/2.17    inference(fool_elimination,[status(thm)],[f744])).
% 6.54/2.17  thf(f744,plain,(
% 6.54/2.17    ~(finite_finite_real @ (collect_real @ (^[X0 : real] : ((ord_less_real @ X0 @ b) & (ord_less_real @ a @ X0) & ((poly_real2 @ p @ X0) = zero_zero_real)))))),
% 6.54/2.17    inference(rectify,[status(thm)],[f352])).
% 6.54/2.17  thf(f352,negated_conjecture,(
% 6.54/2.17    ~(finite_finite_real @ (collect_real @ (^[X0 : real] : ((ord_less_real @ X0 @ b) & (ord_less_real @ a @ X0) & ((poly_real2 @ p @ X0) = zero_zero_real)))))),
% 6.54/2.17    inference(negated_conjecture,[status(cth)],[f351])).
% 6.54/2.17  thf(f351,conjecture,(
% 6.54/2.17    (finite_finite_real @ (collect_real @ (^[X0 : real] : ((ord_less_real @ X0 @ b) & (ord_less_real @ a @ X0) & ((poly_real2 @ p @ X0) = zero_zero_real)))))),
% 6.54/2.17    file('/export/starexec/sandbox/tmp/tmp.JM2D9zVyZJ/DTF2THF_31682.p',conj_0)).
% 6.54/2.17  % SZS output end Proof for DTF2THF_31682
% 6.54/2.17  % (32089)------------------------------
% 6.54/2.17  % (32089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.54/2.17  % (32089)Termination reason: Refutation
% 6.54/2.17  
% 6.54/2.17  % (32089)Memory used [KB]: 7675
% 6.54/2.17  % (32089)Time elapsed: 0.045 s
% 6.54/2.17  % (32089)Instructions burned: 144 (million)
% 6.54/2.17  % (32089)------------------------------
% 6.54/2.17  % (32089)------------------------------
% 6.54/2.17  % (31873)Success in time 0.58 s
%------------------------------------------------------------------------------