TSTP Solution File: NUM343+1 by LEO-II---1.7.0

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%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM343+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% 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  : 600s
% DateTime : Mon Jul 18 11:48:33 EDT 2022

% Result   : Theorem 0.54s 0.76s
% Output   : CNFRefutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :  289
% Syntax   : Number of formulae    :  461 ( 137 unt; 270 typ;   0 def)
%            Number of atoms       :  952 ( 320 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives : 1581 ( 279   ~; 245   |;  30   &;1005   @)
%                                         (   6 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   29 (  29   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  273 ( 270 usr; 258 con; 0-4 aty)
%            Number of variables   :  474 (   0   ^ 470   !;   4   ?; 474   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_difference,type,
    difference: $i > $i > $i > $o ).

thf(tp_less,type,
    less: $i > $i > $o ).

thf(tp_less_or_equal,type,
    less_or_equal: $i > $i > $o ).

thf(tp_n0,type,
    n0: $i ).

thf(tp_n1,type,
    n1: $i ).

thf(tp_n10,type,
    n10: $i ).

thf(tp_n100,type,
    n100: $i ).

thf(tp_n101,type,
    n101: $i ).

thf(tp_n102,type,
    n102: $i ).

thf(tp_n103,type,
    n103: $i ).

thf(tp_n104,type,
    n104: $i ).

thf(tp_n105,type,
    n105: $i ).

thf(tp_n106,type,
    n106: $i ).

thf(tp_n107,type,
    n107: $i ).

thf(tp_n108,type,
    n108: $i ).

thf(tp_n109,type,
    n109: $i ).

thf(tp_n11,type,
    n11: $i ).

thf(tp_n110,type,
    n110: $i ).

thf(tp_n111,type,
    n111: $i ).

thf(tp_n112,type,
    n112: $i ).

thf(tp_n113,type,
    n113: $i ).

thf(tp_n114,type,
    n114: $i ).

thf(tp_n115,type,
    n115: $i ).

thf(tp_n116,type,
    n116: $i ).

thf(tp_n117,type,
    n117: $i ).

thf(tp_n118,type,
    n118: $i ).

thf(tp_n119,type,
    n119: $i ).

thf(tp_n12,type,
    n12: $i ).

thf(tp_n120,type,
    n120: $i ).

thf(tp_n121,type,
    n121: $i ).

thf(tp_n122,type,
    n122: $i ).

thf(tp_n123,type,
    n123: $i ).

thf(tp_n124,type,
    n124: $i ).

thf(tp_n125,type,
    n125: $i ).

thf(tp_n126,type,
    n126: $i ).

thf(tp_n127,type,
    n127: $i ).

thf(tp_n13,type,
    n13: $i ).

thf(tp_n14,type,
    n14: $i ).

thf(tp_n15,type,
    n15: $i ).

thf(tp_n16,type,
    n16: $i ).

thf(tp_n17,type,
    n17: $i ).

thf(tp_n18,type,
    n18: $i ).

thf(tp_n19,type,
    n19: $i ).

thf(tp_n2,type,
    n2: $i ).

thf(tp_n20,type,
    n20: $i ).

thf(tp_n21,type,
    n21: $i ).

thf(tp_n22,type,
    n22: $i ).

thf(tp_n23,type,
    n23: $i ).

thf(tp_n24,type,
    n24: $i ).

thf(tp_n25,type,
    n25: $i ).

thf(tp_n26,type,
    n26: $i ).

thf(tp_n27,type,
    n27: $i ).

thf(tp_n28,type,
    n28: $i ).

thf(tp_n29,type,
    n29: $i ).

thf(tp_n3,type,
    n3: $i ).

thf(tp_n30,type,
    n30: $i ).

thf(tp_n31,type,
    n31: $i ).

thf(tp_n32,type,
    n32: $i ).

thf(tp_n33,type,
    n33: $i ).

thf(tp_n34,type,
    n34: $i ).

thf(tp_n35,type,
    n35: $i ).

thf(tp_n36,type,
    n36: $i ).

thf(tp_n37,type,
    n37: $i ).

thf(tp_n38,type,
    n38: $i ).

thf(tp_n39,type,
    n39: $i ).

thf(tp_n4,type,
    n4: $i ).

thf(tp_n40,type,
    n40: $i ).

thf(tp_n41,type,
    n41: $i ).

thf(tp_n42,type,
    n42: $i ).

thf(tp_n43,type,
    n43: $i ).

thf(tp_n44,type,
    n44: $i ).

thf(tp_n45,type,
    n45: $i ).

thf(tp_n46,type,
    n46: $i ).

thf(tp_n47,type,
    n47: $i ).

thf(tp_n48,type,
    n48: $i ).

thf(tp_n49,type,
    n49: $i ).

thf(tp_n5,type,
    n5: $i ).

thf(tp_n50,type,
    n50: $i ).

thf(tp_n51,type,
    n51: $i ).

thf(tp_n52,type,
    n52: $i ).

thf(tp_n53,type,
    n53: $i ).

thf(tp_n54,type,
    n54: $i ).

thf(tp_n55,type,
    n55: $i ).

thf(tp_n56,type,
    n56: $i ).

thf(tp_n57,type,
    n57: $i ).

thf(tp_n58,type,
    n58: $i ).

thf(tp_n59,type,
    n59: $i ).

thf(tp_n6,type,
    n6: $i ).

thf(tp_n60,type,
    n60: $i ).

thf(tp_n61,type,
    n61: $i ).

thf(tp_n62,type,
    n62: $i ).

thf(tp_n63,type,
    n63: $i ).

thf(tp_n64,type,
    n64: $i ).

thf(tp_n65,type,
    n65: $i ).

thf(tp_n66,type,
    n66: $i ).

thf(tp_n67,type,
    n67: $i ).

thf(tp_n68,type,
    n68: $i ).

thf(tp_n69,type,
    n69: $i ).

thf(tp_n7,type,
    n7: $i ).

thf(tp_n70,type,
    n70: $i ).

thf(tp_n71,type,
    n71: $i ).

thf(tp_n72,type,
    n72: $i ).

thf(tp_n73,type,
    n73: $i ).

thf(tp_n74,type,
    n74: $i ).

thf(tp_n75,type,
    n75: $i ).

thf(tp_n76,type,
    n76: $i ).

thf(tp_n77,type,
    n77: $i ).

thf(tp_n78,type,
    n78: $i ).

thf(tp_n79,type,
    n79: $i ).

thf(tp_n8,type,
    n8: $i ).

thf(tp_n80,type,
    n80: $i ).

thf(tp_n81,type,
    n81: $i ).

thf(tp_n82,type,
    n82: $i ).

thf(tp_n83,type,
    n83: $i ).

thf(tp_n84,type,
    n84: $i ).

thf(tp_n85,type,
    n85: $i ).

thf(tp_n86,type,
    n86: $i ).

thf(tp_n87,type,
    n87: $i ).

thf(tp_n88,type,
    n88: $i ).

thf(tp_n89,type,
    n89: $i ).

thf(tp_n9,type,
    n9: $i ).

thf(tp_n90,type,
    n90: $i ).

thf(tp_n91,type,
    n91: $i ).

thf(tp_n92,type,
    n92: $i ).

thf(tp_n93,type,
    n93: $i ).

thf(tp_n94,type,
    n94: $i ).

thf(tp_n95,type,
    n95: $i ).

thf(tp_n96,type,
    n96: $i ).

thf(tp_n97,type,
    n97: $i ).

thf(tp_n98,type,
    n98: $i ).

thf(tp_n99,type,
    n99: $i ).

thf(tp_nn1,type,
    nn1: $i ).

thf(tp_nn10,type,
    nn10: $i ).

thf(tp_nn100,type,
    nn100: $i ).

thf(tp_nn101,type,
    nn101: $i ).

thf(tp_nn102,type,
    nn102: $i ).

thf(tp_nn103,type,
    nn103: $i ).

thf(tp_nn104,type,
    nn104: $i ).

thf(tp_nn105,type,
    nn105: $i ).

thf(tp_nn106,type,
    nn106: $i ).

thf(tp_nn107,type,
    nn107: $i ).

thf(tp_nn108,type,
    nn108: $i ).

thf(tp_nn109,type,
    nn109: $i ).

thf(tp_nn11,type,
    nn11: $i ).

thf(tp_nn110,type,
    nn110: $i ).

thf(tp_nn111,type,
    nn111: $i ).

thf(tp_nn112,type,
    nn112: $i ).

thf(tp_nn113,type,
    nn113: $i ).

thf(tp_nn114,type,
    nn114: $i ).

thf(tp_nn115,type,
    nn115: $i ).

thf(tp_nn116,type,
    nn116: $i ).

thf(tp_nn117,type,
    nn117: $i ).

thf(tp_nn118,type,
    nn118: $i ).

thf(tp_nn119,type,
    nn119: $i ).

thf(tp_nn12,type,
    nn12: $i ).

thf(tp_nn120,type,
    nn120: $i ).

thf(tp_nn121,type,
    nn121: $i ).

thf(tp_nn122,type,
    nn122: $i ).

thf(tp_nn123,type,
    nn123: $i ).

thf(tp_nn124,type,
    nn124: $i ).

thf(tp_nn125,type,
    nn125: $i ).

thf(tp_nn126,type,
    nn126: $i ).

thf(tp_nn127,type,
    nn127: $i ).

thf(tp_nn128,type,
    nn128: $i ).

thf(tp_nn13,type,
    nn13: $i ).

thf(tp_nn14,type,
    nn14: $i ).

thf(tp_nn15,type,
    nn15: $i ).

thf(tp_nn16,type,
    nn16: $i ).

thf(tp_nn17,type,
    nn17: $i ).

thf(tp_nn18,type,
    nn18: $i ).

thf(tp_nn19,type,
    nn19: $i ).

thf(tp_nn2,type,
    nn2: $i ).

thf(tp_nn20,type,
    nn20: $i ).

thf(tp_nn21,type,
    nn21: $i ).

thf(tp_nn22,type,
    nn22: $i ).

thf(tp_nn23,type,
    nn23: $i ).

thf(tp_nn24,type,
    nn24: $i ).

thf(tp_nn25,type,
    nn25: $i ).

thf(tp_nn26,type,
    nn26: $i ).

thf(tp_nn27,type,
    nn27: $i ).

thf(tp_nn28,type,
    nn28: $i ).

thf(tp_nn29,type,
    nn29: $i ).

thf(tp_nn3,type,
    nn3: $i ).

thf(tp_nn30,type,
    nn30: $i ).

thf(tp_nn31,type,
    nn31: $i ).

thf(tp_nn32,type,
    nn32: $i ).

thf(tp_nn33,type,
    nn33: $i ).

thf(tp_nn34,type,
    nn34: $i ).

thf(tp_nn35,type,
    nn35: $i ).

thf(tp_nn36,type,
    nn36: $i ).

thf(tp_nn37,type,
    nn37: $i ).

thf(tp_nn38,type,
    nn38: $i ).

thf(tp_nn39,type,
    nn39: $i ).

thf(tp_nn4,type,
    nn4: $i ).

thf(tp_nn40,type,
    nn40: $i ).

thf(tp_nn41,type,
    nn41: $i ).

thf(tp_nn42,type,
    nn42: $i ).

thf(tp_nn43,type,
    nn43: $i ).

thf(tp_nn44,type,
    nn44: $i ).

thf(tp_nn45,type,
    nn45: $i ).

thf(tp_nn46,type,
    nn46: $i ).

thf(tp_nn47,type,
    nn47: $i ).

thf(tp_nn48,type,
    nn48: $i ).

thf(tp_nn49,type,
    nn49: $i ).

thf(tp_nn5,type,
    nn5: $i ).

thf(tp_nn50,type,
    nn50: $i ).

thf(tp_nn51,type,
    nn51: $i ).

thf(tp_nn52,type,
    nn52: $i ).

thf(tp_nn53,type,
    nn53: $i ).

thf(tp_nn54,type,
    nn54: $i ).

thf(tp_nn55,type,
    nn55: $i ).

thf(tp_nn56,type,
    nn56: $i ).

thf(tp_nn57,type,
    nn57: $i ).

thf(tp_nn58,type,
    nn58: $i ).

thf(tp_nn59,type,
    nn59: $i ).

thf(tp_nn6,type,
    nn6: $i ).

thf(tp_nn60,type,
    nn60: $i ).

thf(tp_nn61,type,
    nn61: $i ).

thf(tp_nn62,type,
    nn62: $i ).

thf(tp_nn63,type,
    nn63: $i ).

thf(tp_nn64,type,
    nn64: $i ).

thf(tp_nn65,type,
    nn65: $i ).

thf(tp_nn66,type,
    nn66: $i ).

thf(tp_nn67,type,
    nn67: $i ).

thf(tp_nn68,type,
    nn68: $i ).

thf(tp_nn69,type,
    nn69: $i ).

thf(tp_nn7,type,
    nn7: $i ).

thf(tp_nn70,type,
    nn70: $i ).

thf(tp_nn71,type,
    nn71: $i ).

thf(tp_nn72,type,
    nn72: $i ).

thf(tp_nn73,type,
    nn73: $i ).

thf(tp_nn74,type,
    nn74: $i ).

thf(tp_nn75,type,
    nn75: $i ).

thf(tp_nn76,type,
    nn76: $i ).

thf(tp_nn77,type,
    nn77: $i ).

thf(tp_nn78,type,
    nn78: $i ).

thf(tp_nn79,type,
    nn79: $i ).

thf(tp_nn8,type,
    nn8: $i ).

thf(tp_nn80,type,
    nn80: $i ).

thf(tp_nn81,type,
    nn81: $i ).

thf(tp_nn82,type,
    nn82: $i ).

thf(tp_nn83,type,
    nn83: $i ).

thf(tp_nn84,type,
    nn84: $i ).

thf(tp_nn85,type,
    nn85: $i ).

thf(tp_nn86,type,
    nn86: $i ).

thf(tp_nn87,type,
    nn87: $i ).

thf(tp_nn88,type,
    nn88: $i ).

thf(tp_nn89,type,
    nn89: $i ).

thf(tp_nn9,type,
    nn9: $i ).

thf(tp_nn90,type,
    nn90: $i ).

thf(tp_nn91,type,
    nn91: $i ).

thf(tp_nn92,type,
    nn92: $i ).

thf(tp_nn93,type,
    nn93: $i ).

thf(tp_nn94,type,
    nn94: $i ).

thf(tp_nn95,type,
    nn95: $i ).

thf(tp_nn96,type,
    nn96: $i ).

thf(tp_nn97,type,
    nn97: $i ).

thf(tp_nn98,type,
    nn98: $i ).

thf(tp_nn99,type,
    nn99: $i ).

thf(tp_rdn,type,
    rdn: $i > $i > $i ).

thf(tp_rdn_add_with_carry,type,
    rdn_add_with_carry: $i > $i > $i > $i > $o ).

thf(tp_rdn_digit_add,type,
    rdn_digit_add: $i > $i > $i > $i > $o ).

thf(tp_rdn_neg,type,
    rdn_neg: $i > $i ).

thf(tp_rdn_non_zero,type,
    rdn_non_zero: $i > $o ).

thf(tp_rdn_non_zero_digit,type,
    rdn_non_zero_digit: $i > $o ).

thf(tp_rdn_pos,type,
    rdn_pos: $i > $i ).

thf(tp_rdn_positive_less,type,
    rdn_positive_less: $i > $i > $o ).

thf(tp_rdn_translate,type,
    rdn_translate: $i > $i > $o ).

thf(tp_rdnn,type,
    rdnn: $i > $i ).

thf(tp_sum,type,
    sum: $i > $i > $i > $o ).

thf(106,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( sum @ Y @ Z @ X )
    <=> ( difference @ X @ Y @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',minus_entry_point) ).

thf(107,axiom,
    ! [X: $i,Y1: $i,Y2: $i,Z: $i] :
      ( ( ( sum @ X @ Y1 @ Z )
        & ( sum @ X @ Y2 @ Z ) )
     => ( Y1 = Y2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_RHS) ).

thf(108,axiom,
    ! [X1: $i,X2: $i,Y: $i,Z: $i] :
      ( ( ( sum @ X1 @ Y @ Z )
        & ( sum @ X2 @ Y @ Z ) )
     => ( X1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_LHS) ).

thf(109,axiom,
    ! [X: $i,Y: $i,Z1: $i,Z2: $i] :
      ( ( ( sum @ X @ Y @ Z1 )
        & ( sum @ X @ Y @ Z2 ) )
     => ( Z1 = Z2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_sum) ).

thf(116,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( ( sum @ X @ n1 @ Y )
        & ( less @ Z @ Y ) )
     => ( less_or_equal @ Z @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_successor) ).

thf(117,axiom,
    ! [X: $i,Y: $i] :
      ( ( less_or_equal @ X @ Y )
    <=> ( ( less @ X @ Y )
        | ( X = Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal) ).

thf(118,axiom,
    ! [X: $i,Y: $i] :
      ( ( less @ X @ Y )
    <=> ( ~ ( less @ Y @ X )
        & ( Y != X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_property) ).

thf(123,axiom,
    ! [X: $i] :
      ( ( rdn_non_zero_digit @ ( rdnn @ X ) )
     => ( rdn_non_zero @ ( rdnn @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_non_zero_by_digit) ).

thf(127,axiom,
    ! [X: $i,Y: $i,Z: $i] :
      ( ( ( rdn_positive_less @ ( rdnn @ X ) @ ( rdnn @ Y ) )
        & ( rdn_positive_less @ ( rdnn @ Y ) @ ( rdnn @ Z ) ) )
     => ( rdn_positive_less @ ( rdnn @ X ) @ ( rdnn @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_positive_less_transitivity) ).

thf(137,axiom,
    rdn_non_zero_digit @ ( rdnn @ n9 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit9) ).

thf(138,axiom,
    rdn_non_zero_digit @ ( rdnn @ n8 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit8) ).

thf(139,axiom,
    rdn_non_zero_digit @ ( rdnn @ n7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit7) ).

thf(140,axiom,
    rdn_non_zero_digit @ ( rdnn @ n6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit6) ).

thf(141,axiom,
    rdn_non_zero_digit @ ( rdnn @ n5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit5) ).

thf(142,axiom,
    rdn_non_zero_digit @ ( rdnn @ n4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit4) ).

thf(143,axiom,
    rdn_non_zero_digit @ ( rdnn @ n3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit3) ).

thf(144,axiom,
    rdn_non_zero_digit @ ( rdnn @ n2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit2) ).

thf(145,axiom,
    rdn_non_zero_digit @ ( rdnn @ n1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rdn_digit1) ).

thf(402,conjecture,
    ? [X: $i] :
      ( ( ( less @ nn1 @ X )
        & ( less @ X @ n1 ) )
     => ( sum @ n21 @ X @ n21 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_something_n0_samething) ).

thf(403,negated_conjecture,
    ( ( ? [X: $i] :
          ( ( ( less @ nn1 @ X )
            & ( less @ X @ n1 ) )
         => ( sum @ n21 @ X @ n21 ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[402]) ).

thf(404,plain,
    ( ( ? [X: $i] :
          ( ( ( less @ nn1 @ X )
            & ( less @ X @ n1 ) )
         => ( sum @ n21 @ X @ n21 ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[403]) ).

thf(405,plain,
    ( ( ! [X: $i] :
          ( ( rdn_non_zero_digit @ ( rdnn @ X ) )
         => ( rdn_non_zero @ ( rdnn @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[123]) ).

thf(406,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( ( rdn_positive_less @ ( rdnn @ X ) @ ( rdnn @ Y ) )
            & ( rdn_positive_less @ ( rdnn @ Y ) @ ( rdnn @ Z ) ) )
         => ( rdn_positive_less @ ( rdnn @ X ) @ ( rdnn @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[127]) ).

thf(407,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n9 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[137]) ).

thf(408,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n8 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[138]) ).

thf(409,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n7 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[139]) ).

thf(410,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n6 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[140]) ).

thf(411,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n5 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[141]) ).

thf(412,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n4 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[142]) ).

thf(413,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n3 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[143]) ).

thf(414,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[144]) ).

thf(415,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( sum @ Y @ Z @ X )
        <=> ( difference @ X @ Y @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[106]) ).

thf(416,plain,
    ( ( ! [X: $i,Y1: $i,Y2: $i,Z: $i] :
          ( ( ( sum @ X @ Y1 @ Z )
            & ( sum @ X @ Y2 @ Z ) )
         => ( Y1 = Y2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[107]) ).

thf(417,plain,
    ( ( ! [X1: $i,X2: $i,Y: $i,Z: $i] :
          ( ( ( sum @ X1 @ Y @ Z )
            & ( sum @ X2 @ Y @ Z ) )
         => ( X1 = X2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[108]) ).

thf(418,plain,
    ( ( ! [X: $i,Y: $i,Z1: $i,Z2: $i] :
          ( ( ( sum @ X @ Y @ Z1 )
            & ( sum @ X @ Y @ Z2 ) )
         => ( Z1 = Z2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[109]) ).

thf(419,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ( ( sum @ X @ n1 @ Y )
            & ( less @ Z @ Y ) )
         => ( less_or_equal @ Z @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[116]) ).

thf(420,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( less_or_equal @ X @ Y )
        <=> ( ( less @ X @ Y )
            | ( X = Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[117]) ).

thf(421,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( less @ X @ Y )
        <=> ( ~ ( less @ Y @ X )
            & ( Y != X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[118]) ).

thf(422,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[145]) ).

thf(423,plain,
    ( ( ~ ? [X: $i] :
            ( ( ( less @ nn1 @ X )
              & ( less @ X @ n1 ) )
           => ( sum @ n21 @ X @ n21 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[404]) ).

thf(424,plain,
    ( ( ! [X: $i] : ( less @ nn1 @ X )
      & ! [X: $i] : ( less @ X @ n1 )
      & ! [X: $i] :
          ~ ( sum @ n21 @ X @ n21 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[423]) ).

thf(425,plain,
    ( ( ! [X: $i] :
          ( ~ ( rdn_non_zero_digit @ ( rdnn @ X ) )
          | ( rdn_non_zero @ ( rdnn @ X ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[405]) ).

thf(426,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( rdn_positive_less @ ( rdnn @ X ) @ ( rdnn @ Y ) )
          | ~ ( rdn_positive_less @ ( rdnn @ Y ) @ ( rdnn @ Z ) )
          | ( rdn_positive_less @ ( rdnn @ X ) @ ( rdnn @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[406]) ).

thf(427,plain,
    ( ( ! [X: $i] :
          ( ! [Y: $i,Z: $i] :
              ( ~ ( difference @ X @ Y @ Z )
              | ( sum @ Y @ Z @ X ) )
          & ! [Y: $i,Z: $i] :
              ( ~ ( sum @ Y @ Z @ X )
              | ( difference @ X @ Y @ Z ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[415]) ).

thf(428,plain,
    ( ( ! [X: $i,Y1: $i,Y2: $i] :
          ( ! [Z: $i] :
              ( ~ ( sum @ X @ Y1 @ Z )
              | ~ ( sum @ X @ Y2 @ Z ) )
          | ( Y1 = Y2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[416]) ).

thf(429,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ! [Y: $i,Z: $i] :
              ( ~ ( sum @ X1 @ Y @ Z )
              | ~ ( sum @ X2 @ Y @ Z ) )
          | ( X1 = X2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[417]) ).

thf(430,plain,
    ( ( ! [X: $i,Y: $i,Z1: $i,Z2: $i] :
          ( ~ ( sum @ X @ Y @ Z1 )
          | ~ ( sum @ X @ Y @ Z2 )
          | ( Z1 = Z2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[418]) ).

thf(431,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( less @ Z @ Y )
          | ~ ( sum @ X @ n1 @ Y )
          | ( less_or_equal @ Z @ X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[419]) ).

thf(432,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_or_equal @ X @ Y )
          | ( X = Y )
          | ( less @ X @ Y ) )
      & ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( less_or_equal @ X @ Y ) )
      & ! [X: $i,Y: $i] :
          ( ~ ( less @ X @ Y )
          | ( less_or_equal @ X @ Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[420]) ).

thf(433,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( less @ Y @ X )
          | ( Y = X )
          | ( less @ X @ Y ) )
      & ! [X: $i,Y: $i] :
          ( ~ ( less @ X @ Y )
          | ~ ( less @ Y @ X ) )
      & ! [X: $i,Y: $i] :
          ( ~ ( less @ X @ Y )
          | ( Y != X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[421]) ).

thf(434,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n1 ) )
    = $true ),
    inference(copy,[status(thm)],[422]) ).

thf(435,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( less @ Y @ X )
          | ( Y = X )
          | ( less @ X @ Y ) )
      & ! [X: $i,Y: $i] :
          ( ~ ( less @ X @ Y )
          | ~ ( less @ Y @ X ) )
      & ! [X: $i,Y: $i] :
          ( ~ ( less @ X @ Y )
          | ( Y != X ) ) )
    = $true ),
    inference(copy,[status(thm)],[433]) ).

thf(436,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( less_or_equal @ X @ Y )
          | ( X = Y )
          | ( less @ X @ Y ) )
      & ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( less_or_equal @ X @ Y ) )
      & ! [X: $i,Y: $i] :
          ( ~ ( less @ X @ Y )
          | ( less_or_equal @ X @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[432]) ).

thf(437,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( less @ Z @ Y )
          | ~ ( sum @ X @ n1 @ Y )
          | ( less_or_equal @ Z @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[431]) ).

thf(438,plain,
    ( ( ! [X: $i,Y: $i,Z1: $i,Z2: $i] :
          ( ~ ( sum @ X @ Y @ Z1 )
          | ~ ( sum @ X @ Y @ Z2 )
          | ( Z1 = Z2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[430]) ).

thf(439,plain,
    ( ( ! [X1: $i,X2: $i] :
          ( ! [Y: $i,Z: $i] :
              ( ~ ( sum @ X1 @ Y @ Z )
              | ~ ( sum @ X2 @ Y @ Z ) )
          | ( X1 = X2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[429]) ).

thf(440,plain,
    ( ( ! [X: $i,Y1: $i,Y2: $i] :
          ( ! [Z: $i] :
              ( ~ ( sum @ X @ Y1 @ Z )
              | ~ ( sum @ X @ Y2 @ Z ) )
          | ( Y1 = Y2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[428]) ).

thf(441,plain,
    ( ( ! [X: $i] :
          ( ! [Y: $i,Z: $i] :
              ( ~ ( difference @ X @ Y @ Z )
              | ( sum @ Y @ Z @ X ) )
          & ! [Y: $i,Z: $i] :
              ( ~ ( sum @ Y @ Z @ X )
              | ( difference @ X @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[427]) ).

thf(442,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n2 ) )
    = $true ),
    inference(copy,[status(thm)],[414]) ).

thf(443,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n3 ) )
    = $true ),
    inference(copy,[status(thm)],[413]) ).

thf(444,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n4 ) )
    = $true ),
    inference(copy,[status(thm)],[412]) ).

thf(445,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n5 ) )
    = $true ),
    inference(copy,[status(thm)],[411]) ).

thf(446,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n6 ) )
    = $true ),
    inference(copy,[status(thm)],[410]) ).

thf(447,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n7 ) )
    = $true ),
    inference(copy,[status(thm)],[409]) ).

thf(448,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n8 ) )
    = $true ),
    inference(copy,[status(thm)],[408]) ).

thf(449,plain,
    ( ( rdn_non_zero_digit @ ( rdnn @ n9 ) )
    = $true ),
    inference(copy,[status(thm)],[407]) ).

thf(450,plain,
    ( ( ! [X: $i,Y: $i,Z: $i] :
          ( ~ ( rdn_positive_less @ ( rdnn @ X ) @ ( rdnn @ Y ) )
          | ~ ( rdn_positive_less @ ( rdnn @ Y ) @ ( rdnn @ Z ) )
          | ( rdn_positive_less @ ( rdnn @ X ) @ ( rdnn @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[426]) ).

thf(451,plain,
    ( ( ! [X: $i] :
          ( ~ ( rdn_non_zero_digit @ ( rdnn @ X ) )
          | ( rdn_non_zero @ ( rdnn @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[425]) ).

thf(452,plain,
    ( ( ! [X: $i] : ( less @ nn1 @ X )
      & ! [X: $i] : ( less @ X @ n1 )
      & ! [X: $i] :
          ~ ( sum @ n21 @ X @ n21 ) )
    = $true ),
    inference(copy,[status(thm)],[424]) ).

thf(453,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( less_or_equal @ SX0 @ SX1 )
                | ( SX0 = SX1 )
                | ( less @ SX0 @ SX1 ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ( SX0 != SX1 )
                      | ( less_or_equal @ SX0 @ SX1 ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( less @ SX0 @ SX1 )
                      | ( less_or_equal @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[436]) ).

thf(454,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( less @ SX1 @ SX0 )
                | ( SX1 = SX0 )
                | ( less @ SX0 @ SX1 ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( less @ SX0 @ SX1 )
                      | ~ ( less @ SX1 @ SX0 ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( less @ SX0 @ SX1 )
                      | ( SX1 != SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[435]) ).

thf(455,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i] : ( less @ nn1 @ SX0 )
                | ~ ! [SX0: $i] : ( less @ SX0 @ n1 ) )
          | ~ ! [SX0: $i] :
                ~ ( sum @ n21 @ SX0 @ n21 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[452]) ).

thf(456,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( difference @ SX0 @ SX1 @ SX2 )
                  | ( sum @ SX1 @ SX2 @ SX0 ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( sum @ SX1 @ SX2 @ SX0 )
                  | ( difference @ SX0 @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[441]) ).

thf(457,plain,
    ! [SV1: $i] :
      ( ( ! [SY27: $i,SY28: $i] :
            ( ~ ( less @ SY28 @ SY27 )
            | ~ ( sum @ SV1 @ n1 @ SY27 )
            | ( less_or_equal @ SY28 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[437]) ).

thf(458,plain,
    ! [SV2: $i] :
      ( ( ! [SY29: $i,SY30: $i,SY31: $i] :
            ( ~ ( sum @ SV2 @ SY29 @ SY30 )
            | ~ ( sum @ SV2 @ SY29 @ SY31 )
            | ( SY30 = SY31 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[438]) ).

thf(459,plain,
    ! [SV3: $i] :
      ( ( ! [SY32: $i] :
            ( ! [SY33: $i,SY34: $i] :
                ( ~ ( sum @ SV3 @ SY33 @ SY34 )
                | ~ ( sum @ SY32 @ SY33 @ SY34 ) )
            | ( SV3 = SY32 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[439]) ).

thf(460,plain,
    ! [SV4: $i] :
      ( ( ! [SY35: $i,SY36: $i] :
            ( ! [SY37: $i] :
                ( ~ ( sum @ SV4 @ SY35 @ SY37 )
                | ~ ( sum @ SV4 @ SY36 @ SY37 ) )
            | ( SY35 = SY36 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[440]) ).

thf(461,plain,
    ! [SV5: $i] :
      ( ( ! [SY38: $i,SY39: $i] :
            ( ~ ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SY38 ) )
            | ~ ( rdn_positive_less @ ( rdnn @ SY38 ) @ ( rdnn @ SY39 ) )
            | ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SY39 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[450]) ).

thf(462,plain,
    ! [SV6: $i] :
      ( ( ~ ( rdn_non_zero_digit @ ( rdnn @ SV6 ) )
        | ( rdn_non_zero @ ( rdnn @ SV6 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[451]) ).

thf(463,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less_or_equal @ SX0 @ SX1 )
            | ( SX0 = SX1 )
            | ( less @ SX0 @ SX1 ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ( SX0 != SX1 )
                  | ( less_or_equal @ SX0 @ SX1 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( less @ SX0 @ SX1 )
                  | ( less_or_equal @ SX0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[453]) ).

thf(464,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( less @ SX1 @ SX0 )
            | ( SX1 = SX0 )
            | ( less @ SX0 @ SX1 ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( less @ SX0 @ SX1 )
                  | ~ ( less @ SX1 @ SX0 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( less @ SX0 @ SX1 )
                  | ( SX1 != SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[454]) ).

thf(465,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] : ( less @ nn1 @ SX0 )
            | ~ ! [SX0: $i] : ( less @ SX0 @ n1 ) )
      | ~ ! [SX0: $i] :
            ~ ( sum @ n21 @ SX0 @ n21 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[455]) ).

thf(466,plain,
    ! [SV7: $i] :
      ( ( ~ ( ~ ! [SY40: $i,SY41: $i] :
                  ( ~ ( difference @ SV7 @ SY40 @ SY41 )
                  | ( sum @ SY40 @ SY41 @ SV7 ) )
            | ~ ! [SY42: $i,SY43: $i] :
                  ( ~ ( sum @ SY42 @ SY43 @ SV7 )
                  | ( difference @ SV7 @ SY42 @ SY43 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[456]) ).

thf(467,plain,
    ! [SV1: $i,SV8: $i] :
      ( ( ! [SY44: $i] :
            ( ~ ( less @ SY44 @ SV8 )
            | ~ ( sum @ SV1 @ n1 @ SV8 )
            | ( less_or_equal @ SY44 @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[457]) ).

thf(468,plain,
    ! [SV9: $i,SV2: $i] :
      ( ( ! [SY45: $i,SY46: $i] :
            ( ~ ( sum @ SV2 @ SV9 @ SY45 )
            | ~ ( sum @ SV2 @ SV9 @ SY46 )
            | ( SY45 = SY46 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[458]) ).

thf(469,plain,
    ! [SV10: $i,SV3: $i] :
      ( ( ! [SY47: $i,SY48: $i] :
            ( ~ ( sum @ SV3 @ SY47 @ SY48 )
            | ~ ( sum @ SV10 @ SY47 @ SY48 ) )
        | ( SV3 = SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[459]) ).

thf(470,plain,
    ! [SV11: $i,SV4: $i] :
      ( ( ! [SY49: $i] :
            ( ! [SY50: $i] :
                ( ~ ( sum @ SV4 @ SV11 @ SY50 )
                | ~ ( sum @ SV4 @ SY49 @ SY50 ) )
            | ( SV11 = SY49 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[460]) ).

thf(471,plain,
    ! [SV12: $i,SV5: $i] :
      ( ( ! [SY51: $i] :
            ( ~ ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SV12 ) )
            | ~ ( rdn_positive_less @ ( rdnn @ SV12 ) @ ( rdnn @ SY51 ) )
            | ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SY51 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[461]) ).

thf(472,plain,
    ! [SV6: $i] :
      ( ( ( ~ ( rdn_non_zero_digit @ ( rdnn @ SV6 ) ) )
        = $true )
      | ( ( rdn_non_zero @ ( rdnn @ SV6 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[462]) ).

thf(473,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less_or_equal @ SX0 @ SX1 )
            | ( SX0 = SX1 )
            | ( less @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[463]) ).

thf(474,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ( SX0 != SX1 )
                  | ( less_or_equal @ SX0 @ SX1 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( less @ SX0 @ SX1 )
                  | ( less_or_equal @ SX0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[463]) ).

thf(475,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( less @ SX1 @ SX0 )
            | ( SX1 = SX0 )
            | ( less @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[464]) ).

thf(476,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( less @ SX0 @ SX1 )
                  | ~ ( less @ SX1 @ SX0 ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( less @ SX0 @ SX1 )
                  | ( SX1 != SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[464]) ).

thf(477,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] : ( less @ nn1 @ SX0 )
            | ~ ! [SX0: $i] : ( less @ SX0 @ n1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[465]) ).

thf(478,plain,
    ( ( ~ ! [SX0: $i] :
            ~ ( sum @ n21 @ SX0 @ n21 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[465]) ).

thf(479,plain,
    ! [SV7: $i] :
      ( ( ~ ! [SY40: $i,SY41: $i] :
              ( ~ ( difference @ SV7 @ SY40 @ SY41 )
              | ( sum @ SY40 @ SY41 @ SV7 ) )
        | ~ ! [SY42: $i,SY43: $i] :
              ( ~ ( sum @ SY42 @ SY43 @ SV7 )
              | ( difference @ SV7 @ SY42 @ SY43 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[466]) ).

thf(480,plain,
    ! [SV1: $i,SV8: $i,SV13: $i] :
      ( ( ~ ( less @ SV13 @ SV8 )
        | ~ ( sum @ SV1 @ n1 @ SV8 )
        | ( less_or_equal @ SV13 @ SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[467]) ).

thf(481,plain,
    ! [SV14: $i,SV9: $i,SV2: $i] :
      ( ( ! [SY52: $i] :
            ( ~ ( sum @ SV2 @ SV9 @ SV14 )
            | ~ ( sum @ SV2 @ SV9 @ SY52 )
            | ( SV14 = SY52 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[468]) ).

thf(482,plain,
    ! [SV10: $i,SV3: $i] :
      ( ( ( ! [SY47: $i,SY48: $i] :
              ( ~ ( sum @ SV3 @ SY47 @ SY48 )
              | ~ ( sum @ SV10 @ SY47 @ SY48 ) ) )
        = $true )
      | ( ( SV3 = SV10 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[469]) ).

thf(483,plain,
    ! [SV15: $i,SV11: $i,SV4: $i] :
      ( ( ! [SY53: $i] :
            ( ~ ( sum @ SV4 @ SV11 @ SY53 )
            | ~ ( sum @ SV4 @ SV15 @ SY53 ) )
        | ( SV11 = SV15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[470]) ).

thf(484,plain,
    ! [SV16: $i,SV12: $i,SV5: $i] :
      ( ( ~ ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SV12 ) )
        | ~ ( rdn_positive_less @ ( rdnn @ SV12 ) @ ( rdnn @ SV16 ) )
        | ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SV16 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[471]) ).

thf(485,plain,
    ! [SV6: $i] :
      ( ( ( rdn_non_zero_digit @ ( rdnn @ SV6 ) )
        = $false )
      | ( ( rdn_non_zero @ ( rdnn @ SV6 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[472]) ).

thf(486,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( less_or_equal @ SX0 @ SX1 )
          | ( SX0 = SX1 )
          | ( less @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[473]) ).

thf(487,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != SX1 )
                | ( less_or_equal @ SX0 @ SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( less @ SX0 @ SX1 )
                | ( less_or_equal @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[474]) ).

thf(488,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( less @ SX1 @ SX0 )
          | ( SX1 = SX0 )
          | ( less @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[475]) ).

thf(489,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( less @ SX0 @ SX1 )
                | ~ ( less @ SX1 @ SX0 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( less @ SX0 @ SX1 )
                | ( SX1 != SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[476]) ).

thf(490,plain,
    ( ( ~ ( ~ ! [SX0: $i] : ( less @ nn1 @ SX0 )
          | ~ ! [SX0: $i] : ( less @ SX0 @ n1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[477]) ).

thf(491,plain,
    ( ( ! [SX0: $i] :
          ~ ( sum @ n21 @ SX0 @ n21 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[478]) ).

thf(492,plain,
    ! [SV7: $i] :
      ( ( ~ ! [SY40: $i,SY41: $i] :
              ( ~ ( difference @ SV7 @ SY40 @ SY41 )
              | ( sum @ SY40 @ SY41 @ SV7 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[479]) ).

thf(493,plain,
    ! [SV7: $i] :
      ( ( ~ ! [SY42: $i,SY43: $i] :
              ( ~ ( sum @ SY42 @ SY43 @ SV7 )
              | ( difference @ SV7 @ SY42 @ SY43 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[479]) ).

thf(494,plain,
    ! [SV1: $i,SV8: $i,SV13: $i] :
      ( ( ( ~ ( less @ SV13 @ SV8 )
          | ~ ( sum @ SV1 @ n1 @ SV8 ) )
        = $true )
      | ( ( less_or_equal @ SV13 @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[480]) ).

thf(495,plain,
    ! [SV17: $i,SV14: $i,SV9: $i,SV2: $i] :
      ( ( ~ ( sum @ SV2 @ SV9 @ SV14 )
        | ~ ( sum @ SV2 @ SV9 @ SV17 )
        | ( SV14 = SV17 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[481]) ).

thf(496,plain,
    ! [SV10: $i,SV18: $i,SV3: $i] :
      ( ( ( ! [SY54: $i] :
              ( ~ ( sum @ SV3 @ SV18 @ SY54 )
              | ~ ( sum @ SV10 @ SV18 @ SY54 ) ) )
        = $true )
      | ( ( SV3 = SV10 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[482]) ).

thf(497,plain,
    ! [SV15: $i,SV11: $i,SV4: $i] :
      ( ( ( ! [SY53: $i] :
              ( ~ ( sum @ SV4 @ SV11 @ SY53 )
              | ~ ( sum @ SV4 @ SV15 @ SY53 ) ) )
        = $true )
      | ( ( SV11 = SV15 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[483]) ).

thf(498,plain,
    ! [SV16: $i,SV12: $i,SV5: $i] :
      ( ( ( ~ ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SV12 ) )
          | ~ ( rdn_positive_less @ ( rdnn @ SV12 ) @ ( rdnn @ SV16 ) ) )
        = $true )
      | ( ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SV16 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[484]) ).

thf(499,plain,
    ! [SV19: $i] :
      ( ( ! [SY55: $i] :
            ( ~ ( less_or_equal @ SV19 @ SY55 )
            | ( SV19 = SY55 )
            | ( less @ SV19 @ SY55 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[486]) ).

thf(500,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( less_or_equal @ SX0 @ SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less @ SX0 @ SX1 )
            | ( less_or_equal @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[487]) ).

thf(501,plain,
    ! [SV20: $i] :
      ( ( ! [SY56: $i] :
            ( ( less @ SY56 @ SV20 )
            | ( SY56 = SV20 )
            | ( less @ SV20 @ SY56 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[488]) ).

thf(502,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less @ SX0 @ SX1 )
            | ~ ( less @ SX1 @ SX0 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less @ SX0 @ SX1 )
            | ( SX1 != SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[489]) ).

thf(503,plain,
    ( ( ~ ! [SX0: $i] : ( less @ nn1 @ SX0 )
      | ~ ! [SX0: $i] : ( less @ SX0 @ n1 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[490]) ).

thf(504,plain,
    ! [SV21: $i] :
      ( ( ~ ( sum @ n21 @ SV21 @ n21 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[491]) ).

thf(505,plain,
    ! [SV7: $i] :
      ( ( ! [SY40: $i,SY41: $i] :
            ( ~ ( difference @ SV7 @ SY40 @ SY41 )
            | ( sum @ SY40 @ SY41 @ SV7 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[492]) ).

thf(506,plain,
    ! [SV7: $i] :
      ( ( ! [SY42: $i,SY43: $i] :
            ( ~ ( sum @ SY42 @ SY43 @ SV7 )
            | ( difference @ SV7 @ SY42 @ SY43 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[493]) ).

thf(507,plain,
    ! [SV1: $i,SV8: $i,SV13: $i] :
      ( ( ( ~ ( less @ SV13 @ SV8 ) )
        = $true )
      | ( ( ~ ( sum @ SV1 @ n1 @ SV8 ) )
        = $true )
      | ( ( less_or_equal @ SV13 @ SV1 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[494]) ).

thf(508,plain,
    ! [SV17: $i,SV14: $i,SV9: $i,SV2: $i] :
      ( ( ( ~ ( sum @ SV2 @ SV9 @ SV14 )
          | ~ ( sum @ SV2 @ SV9 @ SV17 ) )
        = $true )
      | ( ( SV14 = SV17 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[495]) ).

thf(509,plain,
    ! [SV10: $i,SV22: $i,SV18: $i,SV3: $i] :
      ( ( ( ~ ( sum @ SV3 @ SV18 @ SV22 )
          | ~ ( sum @ SV10 @ SV18 @ SV22 ) )
        = $true )
      | ( ( SV3 = SV10 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[496]) ).

thf(510,plain,
    ! [SV15: $i,SV23: $i,SV11: $i,SV4: $i] :
      ( ( ( ~ ( sum @ SV4 @ SV11 @ SV23 )
          | ~ ( sum @ SV4 @ SV15 @ SV23 ) )
        = $true )
      | ( ( SV11 = SV15 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[497]) ).

thf(511,plain,
    ! [SV16: $i,SV12: $i,SV5: $i] :
      ( ( ( ~ ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SV12 ) ) )
        = $true )
      | ( ( ~ ( rdn_positive_less @ ( rdnn @ SV12 ) @ ( rdnn @ SV16 ) ) )
        = $true )
      | ( ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SV16 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[498]) ).

thf(512,plain,
    ! [SV24: $i,SV19: $i] :
      ( ( ~ ( less_or_equal @ SV19 @ SV24 )
        | ( SV19 = SV24 )
        | ( less @ SV19 @ SV24 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[499]) ).

thf(513,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( less_or_equal @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[500]) ).

thf(514,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less @ SX0 @ SX1 )
            | ( less_or_equal @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[500]) ).

thf(515,plain,
    ! [SV20: $i,SV25: $i] :
      ( ( ( less @ SV25 @ SV20 )
        | ( SV25 = SV20 )
        | ( less @ SV20 @ SV25 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[501]) ).

thf(516,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less @ SX0 @ SX1 )
            | ~ ( less @ SX1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[502]) ).

thf(517,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less @ SX0 @ SX1 )
            | ( SX1 != SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[502]) ).

thf(518,plain,
    ( ( ~ ! [SX0: $i] : ( less @ nn1 @ SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[503]) ).

thf(519,plain,
    ( ( ~ ! [SX0: $i] : ( less @ SX0 @ n1 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[503]) ).

thf(520,plain,
    ! [SV21: $i] :
      ( ( sum @ n21 @ SV21 @ n21 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[504]) ).

thf(521,plain,
    ! [SV26: $i,SV7: $i] :
      ( ( ! [SY57: $i] :
            ( ~ ( difference @ SV7 @ SV26 @ SY57 )
            | ( sum @ SV26 @ SY57 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[505]) ).

thf(522,plain,
    ! [SV7: $i,SV27: $i] :
      ( ( ! [SY58: $i] :
            ( ~ ( sum @ SV27 @ SY58 @ SV7 )
            | ( difference @ SV7 @ SV27 @ SY58 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[506]) ).

thf(523,plain,
    ! [SV1: $i,SV8: $i,SV13: $i] :
      ( ( ( less @ SV13 @ SV8 )
        = $false )
      | ( ( ~ ( sum @ SV1 @ n1 @ SV8 ) )
        = $true )
      | ( ( less_or_equal @ SV13 @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[507]) ).

thf(524,plain,
    ! [SV17: $i,SV14: $i,SV9: $i,SV2: $i] :
      ( ( ( ~ ( sum @ SV2 @ SV9 @ SV14 ) )
        = $true )
      | ( ( ~ ( sum @ SV2 @ SV9 @ SV17 ) )
        = $true )
      | ( ( SV14 = SV17 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[508]) ).

thf(525,plain,
    ! [SV10: $i,SV22: $i,SV18: $i,SV3: $i] :
      ( ( ( ~ ( sum @ SV3 @ SV18 @ SV22 ) )
        = $true )
      | ( ( ~ ( sum @ SV10 @ SV18 @ SV22 ) )
        = $true )
      | ( ( SV3 = SV10 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[509]) ).

thf(526,plain,
    ! [SV15: $i,SV23: $i,SV11: $i,SV4: $i] :
      ( ( ( ~ ( sum @ SV4 @ SV11 @ SV23 ) )
        = $true )
      | ( ( ~ ( sum @ SV4 @ SV15 @ SV23 ) )
        = $true )
      | ( ( SV11 = SV15 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[510]) ).

thf(527,plain,
    ! [SV16: $i,SV12: $i,SV5: $i] :
      ( ( ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SV12 ) )
        = $false )
      | ( ( ~ ( rdn_positive_less @ ( rdnn @ SV12 ) @ ( rdnn @ SV16 ) ) )
        = $true )
      | ( ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SV16 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[511]) ).

thf(528,plain,
    ! [SV24: $i,SV19: $i] :
      ( ( ( ~ ( less_or_equal @ SV19 @ SV24 ) )
        = $true )
      | ( ( ( SV19 = SV24 )
          | ( less @ SV19 @ SV24 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[512]) ).

thf(529,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( less_or_equal @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[513]) ).

thf(530,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( less @ SX0 @ SX1 )
          | ( less_or_equal @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[514]) ).

thf(531,plain,
    ! [SV20: $i,SV25: $i] :
      ( ( ( ( less @ SV25 @ SV20 )
          | ( SV25 = SV20 ) )
        = $true )
      | ( ( less @ SV20 @ SV25 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[515]) ).

thf(532,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( less @ SX0 @ SX1 )
          | ~ ( less @ SX1 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[516]) ).

thf(533,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( less @ SX0 @ SX1 )
          | ( SX1 != SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[517]) ).

thf(534,plain,
    ( ( ! [SX0: $i] : ( less @ nn1 @ SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[518]) ).

thf(535,plain,
    ( ( ! [SX0: $i] : ( less @ SX0 @ n1 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[519]) ).

thf(536,plain,
    ! [SV28: $i,SV26: $i,SV7: $i] :
      ( ( ~ ( difference @ SV7 @ SV26 @ SV28 )
        | ( sum @ SV26 @ SV28 @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[521]) ).

thf(537,plain,
    ! [SV7: $i,SV29: $i,SV27: $i] :
      ( ( ~ ( sum @ SV27 @ SV29 @ SV7 )
        | ( difference @ SV7 @ SV27 @ SV29 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[522]) ).

thf(538,plain,
    ! [SV13: $i,SV8: $i,SV1: $i] :
      ( ( ( sum @ SV1 @ n1 @ SV8 )
        = $false )
      | ( ( less @ SV13 @ SV8 )
        = $false )
      | ( ( less_or_equal @ SV13 @ SV1 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[523]) ).

thf(539,plain,
    ! [SV17: $i,SV14: $i,SV9: $i,SV2: $i] :
      ( ( ( sum @ SV2 @ SV9 @ SV14 )
        = $false )
      | ( ( ~ ( sum @ SV2 @ SV9 @ SV17 ) )
        = $true )
      | ( ( SV14 = SV17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[524]) ).

thf(540,plain,
    ! [SV10: $i,SV22: $i,SV18: $i,SV3: $i] :
      ( ( ( sum @ SV3 @ SV18 @ SV22 )
        = $false )
      | ( ( ~ ( sum @ SV10 @ SV18 @ SV22 ) )
        = $true )
      | ( ( SV3 = SV10 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[525]) ).

thf(541,plain,
    ! [SV15: $i,SV23: $i,SV11: $i,SV4: $i] :
      ( ( ( sum @ SV4 @ SV11 @ SV23 )
        = $false )
      | ( ( ~ ( sum @ SV4 @ SV15 @ SV23 ) )
        = $true )
      | ( ( SV11 = SV15 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[526]) ).

thf(542,plain,
    ! [SV5: $i,SV16: $i,SV12: $i] :
      ( ( ( rdn_positive_less @ ( rdnn @ SV12 ) @ ( rdnn @ SV16 ) )
        = $false )
      | ( ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SV12 ) )
        = $false )
      | ( ( rdn_positive_less @ ( rdnn @ SV5 ) @ ( rdnn @ SV16 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[527]) ).

thf(543,plain,
    ! [SV24: $i,SV19: $i] :
      ( ( ( less_or_equal @ SV19 @ SV24 )
        = $false )
      | ( ( ( SV19 = SV24 )
          | ( less @ SV19 @ SV24 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[528]) ).

thf(544,plain,
    ! [SV30: $i] :
      ( ( ! [SY59: $i] :
            ( ( SV30 != SY59 )
            | ( less_or_equal @ SV30 @ SY59 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[529]) ).

thf(545,plain,
    ! [SV31: $i] :
      ( ( ! [SY60: $i] :
            ( ~ ( less @ SV31 @ SY60 )
            | ( less_or_equal @ SV31 @ SY60 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[530]) ).

thf(546,plain,
    ! [SV20: $i,SV25: $i] :
      ( ( ( less @ SV25 @ SV20 )
        = $true )
      | ( ( SV25 = SV20 )
        = $true )
      | ( ( less @ SV20 @ SV25 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[531]) ).

thf(547,plain,
    ! [SV32: $i] :
      ( ( ! [SY61: $i] :
            ( ~ ( less @ SV32 @ SY61 )
            | ~ ( less @ SY61 @ SV32 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[532]) ).

thf(548,plain,
    ! [SV33: $i] :
      ( ( ! [SY62: $i] :
            ( ~ ( less @ SV33 @ SY62 )
            | ( SY62 != SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[533]) ).

thf(549,plain,
    ! [SV34: $i] :
      ( ( less @ nn1 @ SV34 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[534]) ).

thf(550,plain,
    ! [SV35: $i] :
      ( ( less @ SV35 @ n1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[535]) ).

thf(551,plain,
    ! [SV28: $i,SV26: $i,SV7: $i] :
      ( ( ( ~ ( difference @ SV7 @ SV26 @ SV28 ) )
        = $true )
      | ( ( sum @ SV26 @ SV28 @ SV7 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[536]) ).

thf(552,plain,
    ! [SV7: $i,SV29: $i,SV27: $i] :
      ( ( ( ~ ( sum @ SV27 @ SV29 @ SV7 ) )
        = $true )
      | ( ( difference @ SV7 @ SV27 @ SV29 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[537]) ).

thf(553,plain,
    ! [SV14: $i,SV17: $i,SV9: $i,SV2: $i] :
      ( ( ( sum @ SV2 @ SV9 @ SV17 )
        = $false )
      | ( ( sum @ SV2 @ SV9 @ SV14 )
        = $false )
      | ( ( SV14 = SV17 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[539]) ).

thf(554,plain,
    ! [SV3: $i,SV22: $i,SV18: $i,SV10: $i] :
      ( ( ( sum @ SV10 @ SV18 @ SV22 )
        = $false )
      | ( ( sum @ SV3 @ SV18 @ SV22 )
        = $false )
      | ( ( SV3 = SV10 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[540]) ).

thf(555,plain,
    ! [SV11: $i,SV23: $i,SV15: $i,SV4: $i] :
      ( ( ( sum @ SV4 @ SV15 @ SV23 )
        = $false )
      | ( ( sum @ SV4 @ SV11 @ SV23 )
        = $false )
      | ( ( SV11 = SV15 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[541]) ).

thf(556,plain,
    ! [SV24: $i,SV19: $i] :
      ( ( ( SV19 = SV24 )
        = $true )
      | ( ( less @ SV19 @ SV24 )
        = $true )
      | ( ( less_or_equal @ SV19 @ SV24 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[543]) ).

thf(557,plain,
    ! [SV36: $i,SV30: $i] :
      ( ( ( SV30 != SV36 )
        | ( less_or_equal @ SV30 @ SV36 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[544]) ).

thf(558,plain,
    ! [SV37: $i,SV31: $i] :
      ( ( ~ ( less @ SV31 @ SV37 )
        | ( less_or_equal @ SV31 @ SV37 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[545]) ).

thf(559,plain,
    ! [SV38: $i,SV32: $i] :
      ( ( ~ ( less @ SV32 @ SV38 )
        | ~ ( less @ SV38 @ SV32 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[547]) ).

thf(560,plain,
    ! [SV39: $i,SV33: $i] :
      ( ( ~ ( less @ SV33 @ SV39 )
        | ( SV39 != SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[548]) ).

thf(561,plain,
    ! [SV28: $i,SV26: $i,SV7: $i] :
      ( ( ( difference @ SV7 @ SV26 @ SV28 )
        = $false )
      | ( ( sum @ SV26 @ SV28 @ SV7 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[551]) ).

thf(562,plain,
    ! [SV7: $i,SV29: $i,SV27: $i] :
      ( ( ( sum @ SV27 @ SV29 @ SV7 )
        = $false )
      | ( ( difference @ SV7 @ SV27 @ SV29 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[552]) ).

thf(563,plain,
    ! [SV36: $i,SV30: $i] :
      ( ( ( ( SV30 != SV36 ) )
        = $true )
      | ( ( less_or_equal @ SV30 @ SV36 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[557]) ).

thf(564,plain,
    ! [SV37: $i,SV31: $i] :
      ( ( ( ~ ( less @ SV31 @ SV37 ) )
        = $true )
      | ( ( less_or_equal @ SV31 @ SV37 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[558]) ).

thf(565,plain,
    ! [SV38: $i,SV32: $i] :
      ( ( ( ~ ( less @ SV32 @ SV38 ) )
        = $true )
      | ( ( ~ ( less @ SV38 @ SV32 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[559]) ).

thf(566,plain,
    ! [SV39: $i,SV33: $i] :
      ( ( ( ~ ( less @ SV33 @ SV39 ) )
        = $true )
      | ( ( ( SV39 != SV33 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[560]) ).

thf(567,plain,
    ! [SV36: $i,SV30: $i] :
      ( ( ( SV30 = SV36 )
        = $false )
      | ( ( less_or_equal @ SV30 @ SV36 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[563]) ).

thf(568,plain,
    ! [SV37: $i,SV31: $i] :
      ( ( ( less @ SV31 @ SV37 )
        = $false )
      | ( ( less_or_equal @ SV31 @ SV37 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[564]) ).

thf(569,plain,
    ! [SV38: $i,SV32: $i] :
      ( ( ( less @ SV32 @ SV38 )
        = $false )
      | ( ( ~ ( less @ SV38 @ SV32 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[565]) ).

thf(570,plain,
    ! [SV39: $i,SV33: $i] :
      ( ( ( less @ SV33 @ SV39 )
        = $false )
      | ( ( ( SV39 != SV33 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[566]) ).

thf(571,plain,
    ! [SV32: $i,SV38: $i] :
      ( ( ( less @ SV38 @ SV32 )
        = $false )
      | ( ( less @ SV32 @ SV38 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[569]) ).

thf(572,plain,
    ! [SV33: $i,SV39: $i] :
      ( ( ( SV39 = SV33 )
        = $false )
      | ( ( less @ SV33 @ SV39 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[570]) ).

thf(573,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[434,572,571,568,567,562,561,556,555,554,553,550,549,546,542,538,520,485,449,448,447,446,445,444,443,442]) ).

thf(574,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[573]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NUM343+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n010.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Wed Jul  6 06:37:02 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.42  ..
% 0.45/0.62  
% 0.45/0.62   No.of.Axioms: 401
% 0.45/0.62  
% 0.45/0.62   Length.of.Defs: 0
% 0.45/0.62  
% 0.45/0.62   Contains.Choice.Funs: false
% 0.47/0.67  ...........
% 0.47/0.69  (rf:2,axioms:18,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:403,loop_count:0,foatp_calls:0,translation:fof_full)...........
% 0.54/0.76  
% 0.54/0.76  ********************************
% 0.54/0.76  *   All subproblems solved!    *
% 0.54/0.76  ********************************
% 0.54/0.76  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:18,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:573,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.54/0.76  
% 0.54/0.76  %**** Beginning of derivation protocol ****
% 0.54/0.76  % SZS output start CNFRefutation
% See solution above
% 0.54/0.76  
% 0.54/0.76  %**** End of derivation protocol ****
% 0.54/0.76  %**** no. of clauses in derivation: 191 ****
% 0.54/0.76  %**** clause counter: 573 ****
% 0.54/0.76  
% 0.54/0.76  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:18,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:573,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------