TSTP Solution File: NUM840+2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM840+2 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n015.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 11:55:55 EDT 2022

% Result   : Theorem 5.88s 6.10s
% Output   : CNFRefutation 5.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  238 ( 151 unt;  12 typ;   0 def)
%            Number of atoms       :  953 ( 509 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives : 1471 ( 201   ~; 185   |;   8   &;1057   @)
%                                         (   4 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :  533 (   0   ^ 517   !;  16   ?; 533   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_greater,type,
    greater: $i > $i > $o ).

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

thf(tp_sK1_Vd123,type,
    sK1_Vd123: $i > $i > $i ).

thf(tp_sK2_Vd125,type,
    sK2_Vd125: $i > $i > $i ).

thf(tp_sK3_Vd196,type,
    sK3_Vd196: $i > $i > $i ).

thf(tp_sK4_Vd201,type,
    sK4_Vd201: $i > $i > $i ).

thf(tp_v1,type,
    v1: $i ).

thf(tp_vd328,type,
    vd328: $i ).

thf(tp_vd329,type,
    vd329: $i ).

thf(tp_vd330,type,
    vd330: $i ).

thf(tp_vplus,type,
    vplus: $i > $i > $i ).

thf(tp_vsucc,type,
    vsucc: $i > $i ).

thf(1,axiom,
    ! [Vd42: $i,Vd43: $i] :
      ( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
        = ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
      & ( ( vplus @ Vd42 @ v1 )
        = ( vsucc @ Vd42 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).

thf(2,axiom,
    ! [Vd46: $i,Vd47: $i,Vd48: $i] :
      ( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
      = ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).

thf(3,axiom,
    ! [Vd59: $i] :
      ( ( vplus @ v1 @ Vd59 )
      = ( vsucc @ Vd59 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).

thf(4,axiom,
    ! [Vd68: $i,Vd69: $i] :
      ( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
      = ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).

thf(5,axiom,
    ! [Vd78: $i,Vd79: $i] :
      ( ( vplus @ Vd79 @ Vd78 )
      = ( vplus @ Vd78 @ Vd79 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).

thf(6,axiom,
    ! [Vd92: $i,Vd93: $i] :
      ( Vd93
     != ( vplus @ Vd92 @ Vd93 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).

thf(7,axiom,
    ! [Vd104: $i,Vd105: $i] :
      ( ( Vd104 != Vd105 )
     => ! [Vd107: $i] :
          ( ( vplus @ Vd107 @ Vd104 )
         != ( vplus @ Vd107 @ Vd105 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).

thf(8,axiom,
    ! [Vd120: $i,Vd121: $i] :
      ( ( Vd120 != Vd121 )
      | ~ ? [Vd123: $i] :
            ( Vd120
            = ( vplus @ Vd121 @ Vd123 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).

thf(9,axiom,
    ! [Vd120: $i,Vd121: $i] :
      ( ~ ? [Vd123: $i] :
            ( Vd120
            = ( vplus @ Vd121 @ Vd123 ) )
      | ~ ? [Vd125: $i] :
            ( Vd121
            = ( vplus @ Vd120 @ Vd125 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).

thf(10,axiom,
    ! [Vd120: $i,Vd121: $i] :
      ( ( Vd120 != Vd121 )
      | ~ ? [Vd125: $i] :
            ( Vd121
            = ( vplus @ Vd120 @ Vd125 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).

thf(11,axiom,
    ! [Vd120: $i,Vd121: $i] :
      ( ( Vd120 = Vd121 )
      | ? [Vd123: $i] :
          ( Vd120
          = ( vplus @ Vd121 @ Vd123 ) )
      | ? [Vd125: $i] :
          ( Vd121
          = ( vplus @ Vd120 @ Vd125 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).

thf(12,axiom,
    ! [Vd193: $i,Vd194: $i] :
      ( ( greater @ Vd194 @ Vd193 )
    <=> ? [Vd196: $i] :
          ( Vd194
          = ( vplus @ Vd193 @ Vd196 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).

thf(13,axiom,
    ! [Vd198: $i,Vd199: $i] :
      ( ( less @ Vd199 @ Vd198 )
    <=> ? [Vd201: $i] :
          ( Vd198
          = ( vplus @ Vd199 @ Vd201 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).

thf(14,axiom,
    ! [Vd203: $i,Vd204: $i] :
      ( ( Vd203 != Vd204 )
      | ~ ( greater @ Vd203 @ Vd204 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).

thf(15,axiom,
    ! [Vd203: $i,Vd204: $i] :
      ( ~ ( greater @ Vd203 @ Vd204 )
      | ~ ( less @ Vd203 @ Vd204 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).

thf(16,axiom,
    ! [Vd203: $i,Vd204: $i] :
      ( ( Vd203 != Vd204 )
      | ~ ( less @ Vd203 @ Vd204 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).

thf(17,axiom,
    ! [Vd203: $i,Vd204: $i] :
      ( ( Vd203 = Vd204 )
      | ( greater @ Vd203 @ Vd204 )
      | ( less @ Vd203 @ Vd204 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).

thf(18,axiom,
    ! [Vd208: $i,Vd209: $i] :
      ( ( greater @ Vd208 @ Vd209 )
     => ( less @ Vd209 @ Vd208 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).

thf(19,axiom,
    ! [Vd226: $i,Vd227: $i] :
      ( ( less @ Vd226 @ Vd227 )
     => ( greater @ Vd227 @ Vd226 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).

thf(20,axiom,
    ! [Vd301: $i,Vd302: $i,Vd303: $i] :
      ( ( greater @ Vd301 @ Vd302 )
     => ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 2)') ).

thf(21,axiom,
    ! [Vd301: $i,Vd302: $i,Vd303: $i] :
      ( ( Vd301 = Vd302 )
     => ( ( vplus @ Vd301 @ Vd303 )
        = ( vplus @ Vd302 @ Vd303 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 1)') ).

thf(22,axiom,
    ! [Vd301: $i,Vd302: $i,Vd303: $i] :
      ( ( less @ Vd301 @ Vd302 )
     => ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(193), 0), 0)') ).

thf(23,axiom,
    ( ( greater @ ( vplus @ vd328 @ vd330 ) @ ( vplus @ vd329 @ vd330 ) )
   => ( greater @ vd328 @ vd329 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conjunct1(204), 0), 0)') ).

thf(24,axiom,
    ( ( ( vplus @ vd328 @ vd330 )
      = ( vplus @ vd329 @ vd330 ) )
   => ( vd328 = vd329 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(conjunct1(conjunct2(204)), 0), 0)') ).

thf(25,axiom,
    less @ ( vplus @ vd328 @ vd330 ) @ ( vplus @ vd329 @ vd330 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(conjunct2(conjunct2(204))), 335, 0)') ).

thf(26,conjecture,
    less @ vd328 @ vd329,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(conjunct2(conjunct2(204))), 336, 0)') ).

thf(27,negated_conjecture,
    ( ( less @ vd328 @ vd329 )
    = $false ),
    inference(negate_conjecture,[status(cth)],[26]) ).

thf(28,plain,
    ( ( less @ vd328 @ vd329 )
    = $false ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(29,plain,
    ( ( ! [Vd42: $i,Vd43: $i] :
          ( ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
            = ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
          & ( ( vplus @ Vd42 @ v1 )
            = ( vsucc @ Vd42 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(30,plain,
    ( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
          ( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
          = ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(31,plain,
    ( ( ! [Vd59: $i] :
          ( ( vplus @ v1 @ Vd59 )
          = ( vsucc @ Vd59 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(32,plain,
    ( ( ! [Vd68: $i,Vd69: $i] :
          ( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
          = ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(33,plain,
    ( ( ! [Vd78: $i,Vd79: $i] :
          ( ( vplus @ Vd79 @ Vd78 )
          = ( vplus @ Vd78 @ Vd79 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(34,plain,
    ( ( ! [Vd92: $i,Vd93: $i] :
          ( Vd93
         != ( vplus @ Vd92 @ Vd93 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(35,plain,
    ( ( ! [Vd104: $i,Vd105: $i] :
          ( ( Vd104 != Vd105 )
         => ! [Vd107: $i] :
              ( ( vplus @ Vd107 @ Vd104 )
             != ( vplus @ Vd107 @ Vd105 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(36,plain,
    ( ( ! [Vd120: $i,Vd121: $i] :
          ( ( Vd120 != Vd121 )
          | ~ ? [Vd123: $i] :
                ( Vd120
                = ( vplus @ Vd121 @ Vd123 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(37,plain,
    ( ( ! [Vd120: $i,Vd121: $i] :
          ( ~ ? [Vd123: $i] :
                ( Vd120
                = ( vplus @ Vd121 @ Vd123 ) )
          | ~ ? [Vd125: $i] :
                ( Vd121
                = ( vplus @ Vd120 @ Vd125 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(38,plain,
    ( ( ! [Vd120: $i,Vd121: $i] :
          ( ( Vd120 != Vd121 )
          | ~ ? [Vd125: $i] :
                ( Vd121
                = ( vplus @ Vd120 @ Vd125 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(39,plain,
    ( ( ! [Vd120: $i,Vd121: $i] :
          ( ( Vd120 = Vd121 )
          | ? [Vd123: $i] :
              ( Vd120
              = ( vplus @ Vd121 @ Vd123 ) )
          | ? [Vd125: $i] :
              ( Vd121
              = ( vplus @ Vd120 @ Vd125 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(40,plain,
    ( ( ! [Vd193: $i,Vd194: $i] :
          ( ( greater @ Vd194 @ Vd193 )
        <=> ? [Vd196: $i] :
              ( Vd194
              = ( vplus @ Vd193 @ Vd196 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(41,plain,
    ( ( ! [Vd198: $i,Vd199: $i] :
          ( ( less @ Vd199 @ Vd198 )
        <=> ? [Vd201: $i] :
              ( Vd198
              = ( vplus @ Vd199 @ Vd201 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(42,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 != Vd204 )
          | ~ ( greater @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(43,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ~ ( greater @ Vd203 @ Vd204 )
          | ~ ( less @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(44,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 != Vd204 )
          | ~ ( less @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(45,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 = Vd204 )
          | ( greater @ Vd203 @ Vd204 )
          | ( less @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(46,plain,
    ( ( ! [Vd208: $i,Vd209: $i] :
          ( ( greater @ Vd208 @ Vd209 )
         => ( less @ Vd209 @ Vd208 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(47,plain,
    ( ( ! [Vd226: $i,Vd227: $i] :
          ( ( less @ Vd226 @ Vd227 )
         => ( greater @ Vd227 @ Vd226 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(48,plain,
    ( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
          ( ( greater @ Vd301 @ Vd302 )
         => ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[20]) ).

thf(49,plain,
    ( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
          ( ( Vd301 = Vd302 )
         => ( ( vplus @ Vd301 @ Vd303 )
            = ( vplus @ Vd302 @ Vd303 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(50,plain,
    ( ( ! [Vd301: $i,Vd302: $i,Vd303: $i] :
          ( ( less @ Vd301 @ Vd302 )
         => ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(51,plain,
    ( ( ( greater @ ( vplus @ vd328 @ vd330 ) @ ( vplus @ vd329 @ vd330 ) )
     => ( greater @ vd328 @ vd329 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[23]) ).

thf(52,plain,
    ( ( ( ( vplus @ vd328 @ vd330 )
        = ( vplus @ vd329 @ vd330 ) )
     => ( vd328 = vd329 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[24]) ).

thf(53,plain,
    ( ( less @ ( vplus @ vd328 @ vd330 ) @ ( vplus @ vd329 @ vd330 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(54,plain,
    ( ( ~ ( less @ vd328 @ vd329 ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[28]) ).

thf(55,plain,
    ( ( ! [Vd42: $i,Vd43: $i] :
          ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
          = ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
      & ! [Vd42: $i] :
          ( ( vplus @ Vd42 @ v1 )
          = ( vsucc @ Vd42 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[29]) ).

thf(56,plain,
    ( ( ! [Vd92: $i,Vd93: $i] :
          ( Vd93
         != ( vplus @ Vd92 @ Vd93 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[34]) ).

thf(57,plain,
    ( ( ! [Vd104: $i,Vd105: $i] :
          ( ( Vd104 = Vd105 )
          | ! [Vd107: $i] :
              ( ( vplus @ Vd107 @ Vd104 )
             != ( vplus @ Vd107 @ Vd105 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[35]) ).

thf(58,plain,
    ( ( ! [Vd120: $i,Vd121: $i] :
          ( ( Vd120 != Vd121 )
          | ! [Vd123: $i] :
              ( Vd120
             != ( vplus @ Vd121 @ Vd123 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[36]) ).

thf(59,plain,
    ( ( ! [Vd120: $i,Vd121: $i] :
          ( ! [Vd123: $i] :
              ( Vd120
             != ( vplus @ Vd121 @ Vd123 ) )
          | ! [Vd125: $i] :
              ( Vd121
             != ( vplus @ Vd120 @ Vd125 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[37]) ).

thf(60,plain,
    ( ( ! [Vd120: $i,Vd121: $i] :
          ( ( Vd120 != Vd121 )
          | ! [Vd125: $i] :
              ( Vd121
             != ( vplus @ Vd120 @ Vd125 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[38]) ).

thf(61,plain,
    ( ( ! [Vd120: $i,Vd121: $i] :
          ( ( Vd121
            = ( vplus @ Vd120 @ ( sK2_Vd125 @ Vd121 @ Vd120 ) ) )
          | ( Vd120 = Vd121 )
          | ( Vd120
            = ( vplus @ Vd121 @ ( sK1_Vd123 @ Vd121 @ Vd120 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[39]) ).

thf(62,plain,
    ( ( ! [Vd193: $i,Vd194: $i] :
          ( ! [Vd196: $i] :
              ( Vd194
             != ( vplus @ Vd193 @ Vd196 ) )
          | ( greater @ Vd194 @ Vd193 ) )
      & ! [Vd193: $i,Vd194: $i] :
          ( ~ ( greater @ Vd194 @ Vd193 )
          | ( Vd194
            = ( vplus @ Vd193 @ ( sK3_Vd196 @ Vd194 @ Vd193 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[40]) ).

thf(63,plain,
    ( ( ! [Vd198: $i,Vd199: $i] :
          ( ! [Vd201: $i] :
              ( Vd198
             != ( vplus @ Vd199 @ Vd201 ) )
          | ( less @ Vd199 @ Vd198 ) )
      & ! [Vd198: $i,Vd199: $i] :
          ( ~ ( less @ Vd199 @ Vd198 )
          | ( Vd198
            = ( vplus @ Vd199 @ ( sK4_Vd201 @ Vd199 @ Vd198 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[41]) ).

thf(64,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 != Vd204 )
          | ~ ( greater @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[42]) ).

thf(65,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 != Vd204 )
          | ~ ( less @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[44]) ).

thf(66,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( less @ Vd203 @ Vd204 )
          | ( Vd203 = Vd204 )
          | ( greater @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[45]) ).

thf(67,plain,
    ( ( ! [Vd208: $i,Vd209: $i] :
          ( ~ ( greater @ Vd208 @ Vd209 )
          | ( less @ Vd209 @ Vd208 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[46]) ).

thf(68,plain,
    ( ( ! [Vd226: $i,Vd227: $i] :
          ( ~ ( less @ Vd226 @ Vd227 )
          | ( greater @ Vd227 @ Vd226 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[47]) ).

thf(69,plain,
    ( ( ! [Vd301: $i,Vd302: $i] :
          ( ~ ( greater @ Vd301 @ Vd302 )
          | ! [Vd303: $i] : ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[48]) ).

thf(70,plain,
    ( ( ! [Vd301: $i,Vd302: $i] :
          ( ( Vd301 != Vd302 )
          | ! [Vd303: $i] :
              ( ( vplus @ Vd301 @ Vd303 )
              = ( vplus @ Vd302 @ Vd303 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[49]) ).

thf(71,plain,
    ( ( ! [Vd301: $i,Vd302: $i] :
          ( ~ ( less @ Vd301 @ Vd302 )
          | ! [Vd303: $i] : ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[50]) ).

thf(72,plain,
    ( ( ~ ( greater @ ( vplus @ vd328 @ vd330 ) @ ( vplus @ vd329 @ vd330 ) )
      | ( greater @ vd328 @ vd329 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[51]) ).

thf(73,plain,
    ( ( ( ( vplus @ vd328 @ vd330 )
       != ( vplus @ vd329 @ vd330 ) )
      | ( vd328 = vd329 ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[52]) ).

thf(74,plain,
    ( ( less @ ( vplus @ vd328 @ vd330 ) @ ( vplus @ vd329 @ vd330 ) )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(75,plain,
    ( ( ( ( vplus @ vd328 @ vd330 )
       != ( vplus @ vd329 @ vd330 ) )
      | ( vd328 = vd329 ) )
    = $true ),
    inference(copy,[status(thm)],[73]) ).

thf(76,plain,
    ( ( ~ ( greater @ ( vplus @ vd328 @ vd330 ) @ ( vplus @ vd329 @ vd330 ) )
      | ( greater @ vd328 @ vd329 ) )
    = $true ),
    inference(copy,[status(thm)],[72]) ).

thf(77,plain,
    ( ( ! [Vd301: $i,Vd302: $i] :
          ( ~ ( less @ Vd301 @ Vd302 )
          | ! [Vd303: $i] : ( less @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[71]) ).

thf(78,plain,
    ( ( ! [Vd301: $i,Vd302: $i] :
          ( ( Vd301 != Vd302 )
          | ! [Vd303: $i] :
              ( ( vplus @ Vd301 @ Vd303 )
              = ( vplus @ Vd302 @ Vd303 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[70]) ).

thf(79,plain,
    ( ( ! [Vd301: $i,Vd302: $i] :
          ( ~ ( greater @ Vd301 @ Vd302 )
          | ! [Vd303: $i] : ( greater @ ( vplus @ Vd301 @ Vd303 ) @ ( vplus @ Vd302 @ Vd303 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[69]) ).

thf(80,plain,
    ( ( ! [Vd226: $i,Vd227: $i] :
          ( ~ ( less @ Vd226 @ Vd227 )
          | ( greater @ Vd227 @ Vd226 ) ) )
    = $true ),
    inference(copy,[status(thm)],[68]) ).

thf(81,plain,
    ( ( ! [Vd208: $i,Vd209: $i] :
          ( ~ ( greater @ Vd208 @ Vd209 )
          | ( less @ Vd209 @ Vd208 ) ) )
    = $true ),
    inference(copy,[status(thm)],[67]) ).

thf(82,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( less @ Vd203 @ Vd204 )
          | ( Vd203 = Vd204 )
          | ( greater @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(copy,[status(thm)],[66]) ).

thf(83,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 != Vd204 )
          | ~ ( less @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(copy,[status(thm)],[65]) ).

thf(84,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ~ ( greater @ Vd203 @ Vd204 )
          | ~ ( less @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(85,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 != Vd204 )
          | ~ ( greater @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(copy,[status(thm)],[64]) ).

thf(86,plain,
    ( ( ! [Vd198: $i,Vd199: $i] :
          ( ! [Vd201: $i] :
              ( Vd198
             != ( vplus @ Vd199 @ Vd201 ) )
          | ( less @ Vd199 @ Vd198 ) )
      & ! [Vd198: $i,Vd199: $i] :
          ( ~ ( less @ Vd199 @ Vd198 )
          | ( Vd198
            = ( vplus @ Vd199 @ ( sK4_Vd201 @ Vd199 @ Vd198 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[63]) ).

thf(87,plain,
    ( ( ! [Vd193: $i,Vd194: $i] :
          ( ! [Vd196: $i] :
              ( Vd194
             != ( vplus @ Vd193 @ Vd196 ) )
          | ( greater @ Vd194 @ Vd193 ) )
      & ! [Vd193: $i,Vd194: $i] :
          ( ~ ( greater @ Vd194 @ Vd193 )
          | ( Vd194
            = ( vplus @ Vd193 @ ( sK3_Vd196 @ Vd194 @ Vd193 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[62]) ).

thf(88,plain,
    ( ( ! [Vd120: $i,Vd121: $i] :
          ( ( Vd121
            = ( vplus @ Vd120 @ ( sK2_Vd125 @ Vd121 @ Vd120 ) ) )
          | ( Vd120 = Vd121 )
          | ( Vd120
            = ( vplus @ Vd121 @ ( sK1_Vd123 @ Vd121 @ Vd120 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[61]) ).

thf(89,plain,
    ( ( ! [Vd120: $i,Vd121: $i] :
          ( ( Vd120 != Vd121 )
          | ! [Vd125: $i] :
              ( Vd121
             != ( vplus @ Vd120 @ Vd125 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[60]) ).

thf(90,plain,
    ( ( ! [Vd120: $i,Vd121: $i] :
          ( ! [Vd123: $i] :
              ( Vd120
             != ( vplus @ Vd121 @ Vd123 ) )
          | ! [Vd125: $i] :
              ( Vd121
             != ( vplus @ Vd120 @ Vd125 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[59]) ).

thf(91,plain,
    ( ( ! [Vd120: $i,Vd121: $i] :
          ( ( Vd120 != Vd121 )
          | ! [Vd123: $i] :
              ( Vd120
             != ( vplus @ Vd121 @ Vd123 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[58]) ).

thf(92,plain,
    ( ( ! [Vd104: $i,Vd105: $i] :
          ( ( Vd104 = Vd105 )
          | ! [Vd107: $i] :
              ( ( vplus @ Vd107 @ Vd104 )
             != ( vplus @ Vd107 @ Vd105 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[57]) ).

thf(93,plain,
    ( ( ! [Vd92: $i,Vd93: $i] :
          ( Vd93
         != ( vplus @ Vd92 @ Vd93 ) ) )
    = $true ),
    inference(copy,[status(thm)],[56]) ).

thf(94,plain,
    ( ( ! [Vd78: $i,Vd79: $i] :
          ( ( vplus @ Vd79 @ Vd78 )
          = ( vplus @ Vd78 @ Vd79 ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(95,plain,
    ( ( ! [Vd68: $i,Vd69: $i] :
          ( ( vplus @ ( vsucc @ Vd68 ) @ Vd69 )
          = ( vsucc @ ( vplus @ Vd68 @ Vd69 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(96,plain,
    ( ( ! [Vd59: $i] :
          ( ( vplus @ v1 @ Vd59 )
          = ( vsucc @ Vd59 ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(97,plain,
    ( ( ! [Vd46: $i,Vd47: $i,Vd48: $i] :
          ( ( vplus @ ( vplus @ Vd46 @ Vd47 ) @ Vd48 )
          = ( vplus @ Vd46 @ ( vplus @ Vd47 @ Vd48 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[30]) ).

thf(98,plain,
    ( ( ! [Vd42: $i,Vd43: $i] :
          ( ( vplus @ Vd42 @ ( vsucc @ Vd43 ) )
          = ( vsucc @ ( vplus @ Vd42 @ Vd43 ) ) )
      & ! [Vd42: $i] :
          ( ( vplus @ Vd42 @ v1 )
          = ( vsucc @ Vd42 ) ) )
    = $true ),
    inference(copy,[status(thm)],[55]) ).

thf(99,plain,
    ( ( ~ ( less @ vd328 @ vd329 ) )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(100,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ! [SX2: $i] :
                    ( SX0
                   != ( vplus @ SX1 @ SX2 ) )
                | ( less @ SX1 @ SX0 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( less @ SX1 @ SX0 )
                | ( SX0
                  = ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[86]) ).

thf(101,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ! [SX2: $i] :
                    ( SX1
                   != ( vplus @ SX0 @ SX2 ) )
                | ( greater @ SX1 @ SX0 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( greater @ SX1 @ SX0 )
                | ( SX1
                  = ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[87]) ).

thf(102,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
                = ( vsucc @ ( vplus @ SX0 @ SX1 ) ) )
          | ~ ! [SX0: $i] :
                ( ( vplus @ SX0 @ v1 )
                = ( vsucc @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[98]) ).

thf(103,plain,
    ( ( ( ( ( vplus @ vd328 @ vd330 )
         != ( vplus @ vd329 @ vd330 ) ) )
      = $true )
    | ( ( vd328 = vd329 )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[75]) ).

thf(104,plain,
    ( ( ( ~ ( greater @ ( vplus @ vd328 @ vd330 ) @ ( vplus @ vd329 @ vd330 ) ) )
      = $true )
    | ( ( greater @ vd328 @ vd329 )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[76]) ).

thf(105,plain,
    ! [SV1: $i] :
      ( ( ! [SY56: $i] :
            ( ~ ( less @ SV1 @ SY56 )
            | ! [SY57: $i] : ( less @ ( vplus @ SV1 @ SY57 ) @ ( vplus @ SY56 @ SY57 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(106,plain,
    ! [SV2: $i] :
      ( ( ! [SY58: $i] :
            ( ( SV2 != SY58 )
            | ! [SY59: $i] :
                ( ( vplus @ SV2 @ SY59 )
                = ( vplus @ SY58 @ SY59 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(107,plain,
    ! [SV3: $i] :
      ( ( ! [SY60: $i] :
            ( ~ ( greater @ SV3 @ SY60 )
            | ! [SY61: $i] : ( greater @ ( vplus @ SV3 @ SY61 ) @ ( vplus @ SY60 @ SY61 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(108,plain,
    ! [SV4: $i] :
      ( ( ! [SY62: $i] :
            ( ~ ( less @ SV4 @ SY62 )
            | ( greater @ SY62 @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(109,plain,
    ! [SV5: $i] :
      ( ( ! [SY63: $i] :
            ( ~ ( greater @ SV5 @ SY63 )
            | ( less @ SY63 @ SV5 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(110,plain,
    ! [SV6: $i] :
      ( ( ! [SY64: $i] :
            ( ( less @ SV6 @ SY64 )
            | ( SV6 = SY64 )
            | ( greater @ SV6 @ SY64 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(111,plain,
    ! [SV7: $i] :
      ( ( ! [SY65: $i] :
            ( ( SV7 != SY65 )
            | ~ ( less @ SV7 @ SY65 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(112,plain,
    ! [SV8: $i] :
      ( ( ! [SY66: $i] :
            ( ~ ( greater @ SV8 @ SY66 )
            | ~ ( less @ SV8 @ SY66 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(113,plain,
    ! [SV9: $i] :
      ( ( ! [SY67: $i] :
            ( ( SV9 != SY67 )
            | ~ ( greater @ SV9 @ SY67 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(114,plain,
    ! [SV10: $i] :
      ( ( ! [SY68: $i] :
            ( ( SY68
              = ( vplus @ SV10 @ ( sK2_Vd125 @ SY68 @ SV10 ) ) )
            | ( SV10 = SY68 )
            | ( SV10
              = ( vplus @ SY68 @ ( sK1_Vd123 @ SY68 @ SV10 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(115,plain,
    ! [SV11: $i] :
      ( ( ! [SY69: $i] :
            ( ( SV11 != SY69 )
            | ! [SY70: $i] :
                ( SY69
               != ( vplus @ SV11 @ SY70 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(116,plain,
    ! [SV12: $i] :
      ( ( ! [SY71: $i] :
            ( ! [SY72: $i] :
                ( SV12
               != ( vplus @ SY71 @ SY72 ) )
            | ! [SY73: $i] :
                ( SY71
               != ( vplus @ SV12 @ SY73 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(117,plain,
    ! [SV13: $i] :
      ( ( ! [SY74: $i] :
            ( ( SV13 != SY74 )
            | ! [SY75: $i] :
                ( SV13
               != ( vplus @ SY74 @ SY75 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(118,plain,
    ! [SV14: $i] :
      ( ( ! [SY76: $i] :
            ( ( SV14 = SY76 )
            | ! [SY77: $i] :
                ( ( vplus @ SY77 @ SV14 )
               != ( vplus @ SY77 @ SY76 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[92]) ).

thf(119,plain,
    ! [SV15: $i] :
      ( ( ! [SY78: $i] :
            ( SY78
           != ( vplus @ SV15 @ SY78 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[93]) ).

thf(120,plain,
    ! [SV16: $i] :
      ( ( ! [SY79: $i] :
            ( ( vplus @ SY79 @ SV16 )
            = ( vplus @ SV16 @ SY79 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[94]) ).

thf(121,plain,
    ! [SV17: $i] :
      ( ( ! [SY80: $i] :
            ( ( vplus @ ( vsucc @ SV17 ) @ SY80 )
            = ( vsucc @ ( vplus @ SV17 @ SY80 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[95]) ).

thf(122,plain,
    ! [SV18: $i] :
      ( ( ( vplus @ v1 @ SV18 )
        = ( vsucc @ SV18 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(123,plain,
    ! [SV19: $i] :
      ( ( ! [SY81: $i,SY82: $i] :
            ( ( vplus @ ( vplus @ SV19 @ SY81 ) @ SY82 )
            = ( vplus @ SV19 @ ( vplus @ SY81 @ SY82 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(124,plain,
    ( ( less @ vd328 @ vd329 )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[99]) ).

thf(125,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( SX0
               != ( vplus @ SX1 @ SX2 ) )
            | ( less @ SX1 @ SX0 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less @ SX1 @ SX0 )
            | ( SX0
              = ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[100]) ).

thf(126,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( SX1
               != ( vplus @ SX0 @ SX2 ) )
            | ( greater @ SX1 @ SX0 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( greater @ SX1 @ SX0 )
            | ( SX1
              = ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[101]) ).

thf(127,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
            = ( vsucc @ ( vplus @ SX0 @ SX1 ) ) )
      | ~ ! [SX0: $i] :
            ( ( vplus @ SX0 @ v1 )
            = ( vsucc @ SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[102]) ).

thf(128,plain,
    ( ( ( ( vplus @ vd328 @ vd330 )
        = ( vplus @ vd329 @ vd330 ) )
      = $false )
    | ( ( vd328 = vd329 )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[103]) ).

thf(129,plain,
    ( ( ( greater @ ( vplus @ vd328 @ vd330 ) @ ( vplus @ vd329 @ vd330 ) )
      = $false )
    | ( ( greater @ vd328 @ vd329 )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[104]) ).

thf(130,plain,
    ! [SV20: $i,SV1: $i] :
      ( ( ~ ( less @ SV1 @ SV20 )
        | ! [SY83: $i] : ( less @ ( vplus @ SV1 @ SY83 ) @ ( vplus @ SV20 @ SY83 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[105]) ).

thf(131,plain,
    ! [SV21: $i,SV2: $i] :
      ( ( ( SV2 != SV21 )
        | ! [SY84: $i] :
            ( ( vplus @ SV2 @ SY84 )
            = ( vplus @ SV21 @ SY84 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[106]) ).

thf(132,plain,
    ! [SV22: $i,SV3: $i] :
      ( ( ~ ( greater @ SV3 @ SV22 )
        | ! [SY85: $i] : ( greater @ ( vplus @ SV3 @ SY85 ) @ ( vplus @ SV22 @ SY85 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[107]) ).

thf(133,plain,
    ! [SV23: $i,SV4: $i] :
      ( ( ~ ( less @ SV4 @ SV23 )
        | ( greater @ SV23 @ SV4 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[108]) ).

thf(134,plain,
    ! [SV24: $i,SV5: $i] :
      ( ( ~ ( greater @ SV5 @ SV24 )
        | ( less @ SV24 @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[109]) ).

thf(135,plain,
    ! [SV25: $i,SV6: $i] :
      ( ( ( less @ SV6 @ SV25 )
        | ( SV6 = SV25 )
        | ( greater @ SV6 @ SV25 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[110]) ).

thf(136,plain,
    ! [SV26: $i,SV7: $i] :
      ( ( ( SV7 != SV26 )
        | ~ ( less @ SV7 @ SV26 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[111]) ).

thf(137,plain,
    ! [SV27: $i,SV8: $i] :
      ( ( ~ ( greater @ SV8 @ SV27 )
        | ~ ( less @ SV8 @ SV27 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[112]) ).

thf(138,plain,
    ! [SV28: $i,SV9: $i] :
      ( ( ( SV9 != SV28 )
        | ~ ( greater @ SV9 @ SV28 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[113]) ).

thf(139,plain,
    ! [SV10: $i,SV29: $i] :
      ( ( ( SV29
          = ( vplus @ SV10 @ ( sK2_Vd125 @ SV29 @ SV10 ) ) )
        | ( SV10 = SV29 )
        | ( SV10
          = ( vplus @ SV29 @ ( sK1_Vd123 @ SV29 @ SV10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[114]) ).

thf(140,plain,
    ! [SV30: $i,SV11: $i] :
      ( ( ( SV11 != SV30 )
        | ! [SY86: $i] :
            ( SV30
           != ( vplus @ SV11 @ SY86 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[115]) ).

thf(141,plain,
    ! [SV31: $i,SV12: $i] :
      ( ( ! [SY87: $i] :
            ( SV12
           != ( vplus @ SV31 @ SY87 ) )
        | ! [SY88: $i] :
            ( SV31
           != ( vplus @ SV12 @ SY88 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[116]) ).

thf(142,plain,
    ! [SV32: $i,SV13: $i] :
      ( ( ( SV13 != SV32 )
        | ! [SY89: $i] :
            ( SV13
           != ( vplus @ SV32 @ SY89 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[117]) ).

thf(143,plain,
    ! [SV33: $i,SV14: $i] :
      ( ( ( SV14 = SV33 )
        | ! [SY90: $i] :
            ( ( vplus @ SY90 @ SV14 )
           != ( vplus @ SY90 @ SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[118]) ).

thf(144,plain,
    ! [SV15: $i,SV34: $i] :
      ( ( ( SV34
         != ( vplus @ SV15 @ SV34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[119]) ).

thf(145,plain,
    ! [SV16: $i,SV35: $i] :
      ( ( ( vplus @ SV35 @ SV16 )
        = ( vplus @ SV16 @ SV35 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[120]) ).

thf(146,plain,
    ! [SV36: $i,SV17: $i] :
      ( ( ( vplus @ ( vsucc @ SV17 ) @ SV36 )
        = ( vsucc @ ( vplus @ SV17 @ SV36 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[121]) ).

thf(147,plain,
    ! [SV37: $i,SV19: $i] :
      ( ( ! [SY91: $i] :
            ( ( vplus @ ( vplus @ SV19 @ SV37 ) @ SY91 )
            = ( vplus @ SV19 @ ( vplus @ SV37 @ SY91 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[123]) ).

thf(148,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( SX0
               != ( vplus @ SX1 @ SX2 ) )
            | ( less @ SX1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[125]) ).

thf(149,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less @ SX1 @ SX0 )
            | ( SX0
              = ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[125]) ).

thf(150,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( SX1
               != ( vplus @ SX0 @ SX2 ) )
            | ( greater @ SX1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[126]) ).

thf(151,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( greater @ SX1 @ SX0 )
            | ( SX1
              = ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[126]) ).

thf(152,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
            = ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[127]) ).

thf(153,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( vplus @ SX0 @ v1 )
            = ( vsucc @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[127]) ).

thf(154,plain,
    ! [SV20: $i,SV1: $i] :
      ( ( ( ~ ( less @ SV1 @ SV20 ) )
        = $true )
      | ( ( ! [SY83: $i] : ( less @ ( vplus @ SV1 @ SY83 ) @ ( vplus @ SV20 @ SY83 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[130]) ).

thf(155,plain,
    ! [SV21: $i,SV2: $i] :
      ( ( ( ( SV2 != SV21 ) )
        = $true )
      | ( ( ! [SY84: $i] :
              ( ( vplus @ SV2 @ SY84 )
              = ( vplus @ SV21 @ SY84 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[131]) ).

thf(156,plain,
    ! [SV22: $i,SV3: $i] :
      ( ( ( ~ ( greater @ SV3 @ SV22 ) )
        = $true )
      | ( ( ! [SY85: $i] : ( greater @ ( vplus @ SV3 @ SY85 ) @ ( vplus @ SV22 @ SY85 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[132]) ).

thf(157,plain,
    ! [SV23: $i,SV4: $i] :
      ( ( ( ~ ( less @ SV4 @ SV23 ) )
        = $true )
      | ( ( greater @ SV23 @ SV4 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[133]) ).

thf(158,plain,
    ! [SV24: $i,SV5: $i] :
      ( ( ( ~ ( greater @ SV5 @ SV24 ) )
        = $true )
      | ( ( less @ SV24 @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[134]) ).

thf(159,plain,
    ! [SV25: $i,SV6: $i] :
      ( ( ( less @ SV6 @ SV25 )
        = $true )
      | ( ( ( SV6 = SV25 )
          | ( greater @ SV6 @ SV25 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[135]) ).

thf(160,plain,
    ! [SV26: $i,SV7: $i] :
      ( ( ( ( SV7 != SV26 ) )
        = $true )
      | ( ( ~ ( less @ SV7 @ SV26 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[136]) ).

thf(161,plain,
    ! [SV27: $i,SV8: $i] :
      ( ( ( ~ ( greater @ SV8 @ SV27 ) )
        = $true )
      | ( ( ~ ( less @ SV8 @ SV27 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[137]) ).

thf(162,plain,
    ! [SV28: $i,SV9: $i] :
      ( ( ( ( SV9 != SV28 ) )
        = $true )
      | ( ( ~ ( greater @ SV9 @ SV28 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[138]) ).

thf(163,plain,
    ! [SV10: $i,SV29: $i] :
      ( ( ( SV29
          = ( vplus @ SV10 @ ( sK2_Vd125 @ SV29 @ SV10 ) ) )
        = $true )
      | ( ( ( SV10 = SV29 )
          | ( SV10
            = ( vplus @ SV29 @ ( sK1_Vd123 @ SV29 @ SV10 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[139]) ).

thf(164,plain,
    ! [SV30: $i,SV11: $i] :
      ( ( ( ( SV11 != SV30 ) )
        = $true )
      | ( ( ! [SY86: $i] :
              ( SV30
             != ( vplus @ SV11 @ SY86 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[140]) ).

thf(165,plain,
    ! [SV31: $i,SV12: $i] :
      ( ( ( ! [SY87: $i] :
              ( SV12
             != ( vplus @ SV31 @ SY87 ) ) )
        = $true )
      | ( ( ! [SY88: $i] :
              ( SV31
             != ( vplus @ SV12 @ SY88 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[141]) ).

thf(166,plain,
    ! [SV32: $i,SV13: $i] :
      ( ( ( ( SV13 != SV32 ) )
        = $true )
      | ( ( ! [SY89: $i] :
              ( SV13
             != ( vplus @ SV32 @ SY89 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[142]) ).

thf(167,plain,
    ! [SV33: $i,SV14: $i] :
      ( ( ( SV14 = SV33 )
        = $true )
      | ( ( ! [SY90: $i] :
              ( ( vplus @ SY90 @ SV14 )
             != ( vplus @ SY90 @ SV33 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[143]) ).

thf(168,plain,
    ! [SV15: $i,SV34: $i] :
      ( ( SV34
        = ( vplus @ SV15 @ SV34 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[144]) ).

thf(169,plain,
    ! [SV38: $i,SV37: $i,SV19: $i] :
      ( ( ( vplus @ ( vplus @ SV19 @ SV37 ) @ SV38 )
        = ( vplus @ SV19 @ ( vplus @ SV37 @ SV38 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[147]) ).

thf(170,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ! [SX2: $i] :
              ( SX0
             != ( vplus @ SX1 @ SX2 ) )
          | ( less @ SX1 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[148]) ).

thf(171,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( less @ SX1 @ SX0 )
          | ( SX0
            = ( vplus @ SX1 @ ( sK4_Vd201 @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[149]) ).

thf(172,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ! [SX2: $i] :
              ( SX1
             != ( vplus @ SX0 @ SX2 ) )
          | ( greater @ SX1 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[150]) ).

thf(173,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( greater @ SX1 @ SX0 )
          | ( SX1
            = ( vplus @ SX0 @ ( sK3_Vd196 @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[151]) ).

thf(174,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( vplus @ SX0 @ ( vsucc @ SX1 ) )
          = ( vsucc @ ( vplus @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[152]) ).

thf(175,plain,
    ( ( ! [SX0: $i] :
          ( ( vplus @ SX0 @ v1 )
          = ( vsucc @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[153]) ).

thf(176,plain,
    ! [SV20: $i,SV1: $i] :
      ( ( ( less @ SV1 @ SV20 )
        = $false )
      | ( ( ! [SY83: $i] : ( less @ ( vplus @ SV1 @ SY83 ) @ ( vplus @ SV20 @ SY83 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[154]) ).

thf(177,plain,
    ! [SV21: $i,SV2: $i] :
      ( ( ( SV2 = SV21 )
        = $false )
      | ( ( ! [SY84: $i] :
              ( ( vplus @ SV2 @ SY84 )
              = ( vplus @ SV21 @ SY84 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[155]) ).

thf(178,plain,
    ! [SV22: $i,SV3: $i] :
      ( ( ( greater @ SV3 @ SV22 )
        = $false )
      | ( ( ! [SY85: $i] : ( greater @ ( vplus @ SV3 @ SY85 ) @ ( vplus @ SV22 @ SY85 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[156]) ).

thf(179,plain,
    ! [SV23: $i,SV4: $i] :
      ( ( ( less @ SV4 @ SV23 )
        = $false )
      | ( ( greater @ SV23 @ SV4 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[157]) ).

thf(180,plain,
    ! [SV24: $i,SV5: $i] :
      ( ( ( greater @ SV5 @ SV24 )
        = $false )
      | ( ( less @ SV24 @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[158]) ).

thf(181,plain,
    ! [SV25: $i,SV6: $i] :
      ( ( ( SV6 = SV25 )
        = $true )
      | ( ( greater @ SV6 @ SV25 )
        = $true )
      | ( ( less @ SV6 @ SV25 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[159]) ).

thf(182,plain,
    ! [SV26: $i,SV7: $i] :
      ( ( ( SV7 = SV26 )
        = $false )
      | ( ( ~ ( less @ SV7 @ SV26 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[160]) ).

thf(183,plain,
    ! [SV27: $i,SV8: $i] :
      ( ( ( greater @ SV8 @ SV27 )
        = $false )
      | ( ( ~ ( less @ SV8 @ SV27 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[161]) ).

thf(184,plain,
    ! [SV28: $i,SV9: $i] :
      ( ( ( SV9 = SV28 )
        = $false )
      | ( ( ~ ( greater @ SV9 @ SV28 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[162]) ).

thf(185,plain,
    ! [SV29: $i,SV10: $i] :
      ( ( ( SV10 = SV29 )
        = $true )
      | ( ( SV10
          = ( vplus @ SV29 @ ( sK1_Vd123 @ SV29 @ SV10 ) ) )
        = $true )
      | ( ( SV29
          = ( vplus @ SV10 @ ( sK2_Vd125 @ SV29 @ SV10 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[163]) ).

thf(186,plain,
    ! [SV30: $i,SV11: $i] :
      ( ( ( SV11 = SV30 )
        = $false )
      | ( ( ! [SY86: $i] :
              ( SV30
             != ( vplus @ SV11 @ SY86 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[164]) ).

thf(187,plain,
    ! [SV39: $i,SV31: $i,SV12: $i] :
      ( ( ( ( SV12
           != ( vplus @ SV31 @ SV39 ) ) )
        = $true )
      | ( ( ! [SY88: $i] :
              ( SV31
             != ( vplus @ SV12 @ SY88 ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[165]) ).

thf(188,plain,
    ! [SV32: $i,SV13: $i] :
      ( ( ( SV13 = SV32 )
        = $false )
      | ( ( ! [SY89: $i] :
              ( SV13
             != ( vplus @ SV32 @ SY89 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[166]) ).

thf(189,plain,
    ! [SV33: $i,SV14: $i,SV40: $i] :
      ( ( ( ( ( vplus @ SV40 @ SV14 )
           != ( vplus @ SV40 @ SV33 ) ) )
        = $true )
      | ( ( SV14 = SV33 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[167]) ).

thf(190,plain,
    ! [SV41: $i] :
      ( ( ! [SY92: $i] :
            ( ! [SY93: $i] :
                ( SV41
               != ( vplus @ SY92 @ SY93 ) )
            | ( less @ SY92 @ SV41 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[170]) ).

thf(191,plain,
    ! [SV42: $i] :
      ( ( ! [SY94: $i] :
            ( ~ ( less @ SY94 @ SV42 )
            | ( SV42
              = ( vplus @ SY94 @ ( sK4_Vd201 @ SY94 @ SV42 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[171]) ).

thf(192,plain,
    ! [SV43: $i] :
      ( ( ! [SY95: $i] :
            ( ! [SY96: $i] :
                ( SY95
               != ( vplus @ SV43 @ SY96 ) )
            | ( greater @ SY95 @ SV43 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[172]) ).

thf(193,plain,
    ! [SV44: $i] :
      ( ( ! [SY97: $i] :
            ( ~ ( greater @ SY97 @ SV44 )
            | ( SY97
              = ( vplus @ SV44 @ ( sK3_Vd196 @ SY97 @ SV44 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[173]) ).

thf(194,plain,
    ! [SV45: $i] :
      ( ( ! [SY98: $i] :
            ( ( vplus @ SV45 @ ( vsucc @ SY98 ) )
            = ( vsucc @ ( vplus @ SV45 @ SY98 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[174]) ).

thf(195,plain,
    ! [SV46: $i] :
      ( ( ( vplus @ SV46 @ v1 )
        = ( vsucc @ SV46 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[175]) ).

thf(196,plain,
    ! [SV20: $i,SV47: $i,SV1: $i] :
      ( ( ( less @ ( vplus @ SV1 @ SV47 ) @ ( vplus @ SV20 @ SV47 ) )
        = $true )
      | ( ( less @ SV1 @ SV20 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[176]) ).

thf(197,plain,
    ! [SV21: $i,SV48: $i,SV2: $i] :
      ( ( ( ( vplus @ SV2 @ SV48 )
          = ( vplus @ SV21 @ SV48 ) )
        = $true )
      | ( ( SV2 = SV21 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[177]) ).

thf(198,plain,
    ! [SV22: $i,SV49: $i,SV3: $i] :
      ( ( ( greater @ ( vplus @ SV3 @ SV49 ) @ ( vplus @ SV22 @ SV49 ) )
        = $true )
      | ( ( greater @ SV3 @ SV22 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[178]) ).

thf(199,plain,
    ! [SV26: $i,SV7: $i] :
      ( ( ( less @ SV7 @ SV26 )
        = $false )
      | ( ( SV7 = SV26 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[182]) ).

thf(200,plain,
    ! [SV27: $i,SV8: $i] :
      ( ( ( less @ SV8 @ SV27 )
        = $false )
      | ( ( greater @ SV8 @ SV27 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[183]) ).

thf(201,plain,
    ! [SV28: $i,SV9: $i] :
      ( ( ( greater @ SV9 @ SV28 )
        = $false )
      | ( ( SV9 = SV28 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[184]) ).

thf(202,plain,
    ! [SV50: $i,SV11: $i,SV30: $i] :
      ( ( ( ( SV30
           != ( vplus @ SV11 @ SV50 ) ) )
        = $true )
      | ( ( SV11 = SV30 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[186]) ).

thf(203,plain,
    ! [SV39: $i,SV31: $i,SV12: $i] :
      ( ( ( SV12
          = ( vplus @ SV31 @ SV39 ) )
        = $false )
      | ( ( ! [SY88: $i] :
              ( SV31
             != ( vplus @ SV12 @ SY88 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[187]) ).

thf(204,plain,
    ! [SV51: $i,SV32: $i,SV13: $i] :
      ( ( ( ( SV13
           != ( vplus @ SV32 @ SV51 ) ) )
        = $true )
      | ( ( SV13 = SV32 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[188]) ).

thf(205,plain,
    ! [SV33: $i,SV14: $i,SV40: $i] :
      ( ( ( ( vplus @ SV40 @ SV14 )
          = ( vplus @ SV40 @ SV33 ) )
        = $false )
      | ( ( SV14 = SV33 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[189]) ).

thf(206,plain,
    ! [SV52: $i,SV41: $i] :
      ( ( ! [SY99: $i] :
            ( SV41
           != ( vplus @ SV52 @ SY99 ) )
        | ( less @ SV52 @ SV41 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[190]) ).

thf(207,plain,
    ! [SV42: $i,SV53: $i] :
      ( ( ~ ( less @ SV53 @ SV42 )
        | ( SV42
          = ( vplus @ SV53 @ ( sK4_Vd201 @ SV53 @ SV42 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[191]) ).

thf(208,plain,
    ! [SV43: $i,SV54: $i] :
      ( ( ! [SY100: $i] :
            ( SV54
           != ( vplus @ SV43 @ SY100 ) )
        | ( greater @ SV54 @ SV43 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[192]) ).

thf(209,plain,
    ! [SV44: $i,SV55: $i] :
      ( ( ~ ( greater @ SV55 @ SV44 )
        | ( SV55
          = ( vplus @ SV44 @ ( sK3_Vd196 @ SV55 @ SV44 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[193]) ).

thf(210,plain,
    ! [SV56: $i,SV45: $i] :
      ( ( ( vplus @ SV45 @ ( vsucc @ SV56 ) )
        = ( vsucc @ ( vplus @ SV45 @ SV56 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[194]) ).

thf(211,plain,
    ! [SV50: $i,SV11: $i,SV30: $i] :
      ( ( ( SV30
          = ( vplus @ SV11 @ SV50 ) )
        = $false )
      | ( ( SV11 = SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[202]) ).

thf(212,plain,
    ! [SV39: $i,SV57: $i,SV12: $i,SV31: $i] :
      ( ( ( ( SV31
           != ( vplus @ SV12 @ SV57 ) ) )
        = $true )
      | ( ( SV12
          = ( vplus @ SV31 @ SV39 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[203]) ).

thf(213,plain,
    ! [SV51: $i,SV32: $i,SV13: $i] :
      ( ( ( SV13
          = ( vplus @ SV32 @ SV51 ) )
        = $false )
      | ( ( SV13 = SV32 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[204]) ).

thf(214,plain,
    ! [SV52: $i,SV41: $i] :
      ( ( ( ! [SY99: $i] :
              ( SV41
             != ( vplus @ SV52 @ SY99 ) ) )
        = $true )
      | ( ( less @ SV52 @ SV41 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[206]) ).

thf(215,plain,
    ! [SV42: $i,SV53: $i] :
      ( ( ( ~ ( less @ SV53 @ SV42 ) )
        = $true )
      | ( ( SV42
          = ( vplus @ SV53 @ ( sK4_Vd201 @ SV53 @ SV42 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[207]) ).

thf(216,plain,
    ! [SV43: $i,SV54: $i] :
      ( ( ( ! [SY100: $i] :
              ( SV54
             != ( vplus @ SV43 @ SY100 ) ) )
        = $true )
      | ( ( greater @ SV54 @ SV43 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[208]) ).

thf(217,plain,
    ! [SV44: $i,SV55: $i] :
      ( ( ( ~ ( greater @ SV55 @ SV44 ) )
        = $true )
      | ( ( SV55
          = ( vplus @ SV44 @ ( sK3_Vd196 @ SV55 @ SV44 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[209]) ).

thf(218,plain,
    ! [SV39: $i,SV57: $i,SV12: $i,SV31: $i] :
      ( ( ( SV31
          = ( vplus @ SV12 @ SV57 ) )
        = $false )
      | ( ( SV12
          = ( vplus @ SV31 @ SV39 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[212]) ).

thf(219,plain,
    ! [SV58: $i,SV52: $i,SV41: $i] :
      ( ( ( ( SV41
           != ( vplus @ SV52 @ SV58 ) ) )
        = $true )
      | ( ( less @ SV52 @ SV41 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[214]) ).

thf(220,plain,
    ! [SV42: $i,SV53: $i] :
      ( ( ( less @ SV53 @ SV42 )
        = $false )
      | ( ( SV42
          = ( vplus @ SV53 @ ( sK4_Vd201 @ SV53 @ SV42 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[215]) ).

thf(221,plain,
    ! [SV59: $i,SV43: $i,SV54: $i] :
      ( ( ( ( SV54
           != ( vplus @ SV43 @ SV59 ) ) )
        = $true )
      | ( ( greater @ SV54 @ SV43 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[216]) ).

thf(222,plain,
    ! [SV44: $i,SV55: $i] :
      ( ( ( greater @ SV55 @ SV44 )
        = $false )
      | ( ( SV55
          = ( vplus @ SV44 @ ( sK3_Vd196 @ SV55 @ SV44 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[217]) ).

thf(223,plain,
    ! [SV58: $i,SV52: $i,SV41: $i] :
      ( ( ( SV41
          = ( vplus @ SV52 @ SV58 ) )
        = $false )
      | ( ( less @ SV52 @ SV41 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[219]) ).

thf(224,plain,
    ! [SV59: $i,SV43: $i,SV54: $i] :
      ( ( ( SV54
          = ( vplus @ SV43 @ SV59 ) )
        = $false )
      | ( ( greater @ SV54 @ SV43 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[221]) ).

thf(225,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[74,224,223,222,220,218,213,211,210,205,201,200,199,198,197,196,195,185,181,180,179,169,168,146,145,129,128,124,122]) ).

thf(226,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[225]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : NUM840+2 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n015.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 : Tue Jul  5 06:03:02 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  
% 0.13/0.36   No.of.Axioms: 25
% 0.13/0.36  
% 0.13/0.36   Length.of.Defs: 0
% 0.13/0.36  
% 0.13/0.36   Contains.Choice.Funs: false
% 0.13/0.37  .
% 0.13/0.37  (rf:0,axioms:25,ps:3,u:6,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:27,loop_count:0,foatp_calls:0,translation:fof_full)............
% 5.88/6.10  
% 5.88/6.10  ********************************
% 5.88/6.10  *   All subproblems solved!    *
% 5.88/6.10  ********************************
% 5.88/6.10  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,ps:3,u:6,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:225,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.88/6.12  
% 5.88/6.12  %**** Beginning of derivation protocol ****
% 5.88/6.12  % SZS output start CNFRefutation
% See solution above
% 5.88/6.12  
% 5.88/6.12  %**** End of derivation protocol ****
% 5.88/6.12  %**** no. of clauses in derivation: 226 ****
% 5.88/6.12  %**** clause counter: 225 ****
% 5.88/6.12  
% 5.88/6.12  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:25,ps:3,u:6,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:225,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------