TSTP Solution File: NUM852+2 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM852+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 : n028.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 11:56:05 EDT 2022

% Result   : Theorem 0.69s 0.88s
% Output   : CNFRefutation 0.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  175 ( 116 unt;  11 typ;   0 def)
%            Number of atoms       :  674 ( 313 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives : 1283 ( 132   ~; 130   |;   4   &; 999   @)
%                                         (   4 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :  354 (   0   ^ 350   !;   4   ?; 354   :)

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

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

thf(tp_sK1_Vd196,type,
    sK1_Vd196: $i > $i > $i ).

thf(tp_sK2_Vd201,type,
    sK2_Vd201: $i > $i > $i ).

thf(tp_vd469,type,
    vd469: $i ).

thf(tp_vd480,type,
    vd480: $i ).

thf(tp_vd481,type,
    vd481: $i ).

thf(tp_vmul,type,
    vmul: $i > $i > $i ).

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

thf(tp_vskolem9,type,
    vskolem9: $i > $i > $i ).

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

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

thf(2,axiom,
    ! [Vd198: $i,Vd199: $i] :
      ( ( less @ Vd199 @ Vd198 )
    <=> ? [Vd201: $i] :
          ( Vd198
          = ( vplus @ Vd199 @ Vd201 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).

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

thf(4,axiom,
    ! [Vd203: $i,Vd204: $i] :
      ( ~ ( greater @ Vd203 @ Vd204 )
      | ~ ( less @ Vd203 @ Vd204 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).

thf(5,axiom,
    ! [Vd203: $i,Vd204: $i] :
      ( ( Vd203 != Vd204 )
      | ~ ( less @ Vd203 @ Vd204 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).

thf(6,axiom,
    ! [Vd203: $i,Vd204: $i] :
      ( ( Vd203 = Vd204 )
      | ( greater @ Vd203 @ Vd204 )
      | ( less @ Vd203 @ Vd204 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).

thf(7,axiom,
    ! [Vd208: $i,Vd209: $i] :
      ( ( greater @ Vd208 @ Vd209 )
     => ( less @ Vd209 @ Vd208 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).

thf(8,axiom,
    ! [Vd226: $i,Vd227: $i] :
      ( ( less @ Vd226 @ Vd227 )
     => ( greater @ Vd227 @ Vd226 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).

thf(9,axiom,
    ! [Vd408: $i,Vd409: $i] :
      ( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
      = ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).

thf(10,axiom,
    ! [Vd418: $i,Vd419: $i] :
      ( ( vmul @ Vd418 @ Vd419 )
      = ( vmul @ Vd419 @ Vd418 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).

thf(11,axiom,
    ! [Vd432: $i,Vd433: $i,Vd434: $i] :
      ( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
      = ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).

thf(12,axiom,
    ! [Vd444: $i,Vd445: $i,Vd446: $i] :
      ( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
      = ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).

thf(13,axiom,
    ! [Vd470: $i,Vd471: $i] :
      ( ( greater @ Vd470 @ Vd471 )
     => ( Vd470
        = ( vplus @ Vd471 @ ( vskolem9 @ Vd470 @ Vd471 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 3)') ).

thf(14,axiom,
    ! [Vd470: $i,Vd471: $i] :
      ( ( greater @ Vd470 @ Vd471 )
     => ( ( vmul @ Vd470 @ vd469 )
        = ( vmul @ ( vplus @ Vd471 @ ( vskolem9 @ Vd470 @ Vd471 ) ) @ vd469 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 2)') ).

thf(15,axiom,
    ! [Vd470: $i,Vd471: $i] :
      ( ( greater @ Vd470 @ Vd471 )
     => ( ( vmul @ ( vplus @ Vd471 @ ( vskolem9 @ Vd470 @ Vd471 ) ) @ vd469 )
        = ( vplus @ ( vmul @ Vd471 @ vd469 ) @ ( vmul @ ( vskolem9 @ Vd470 @ Vd471 ) @ vd469 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 1)') ).

thf(16,axiom,
    ! [Vd470: $i,Vd471: $i] :
      ( ( greater @ Vd470 @ Vd471 )
     => ( greater @ ( vplus @ ( vmul @ Vd471 @ vd469 ) @ ( vmul @ ( vskolem9 @ Vd470 @ Vd471 ) @ vd469 ) ) @ ( vmul @ Vd471 @ vd469 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 0)') ).

thf(17,axiom,
    ! [Vd476: $i,Vd477: $i] :
      ( ( Vd476 = Vd477 )
     => ( ( vmul @ Vd476 @ vd469 )
        = ( vmul @ Vd477 @ vd469 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(303, 0), 0)') ).

thf(18,axiom,
    less @ vd480 @ vd481,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(antec(304), 482, 0)') ).

thf(19,axiom,
    greater @ vd481 @ vd480,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(304)), 483, 0)') ).

thf(20,conjecture,
    greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)') ).

thf(21,negated_conjecture,
    ( ( greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[20]) ).

thf(22,plain,
    ( ( greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ) )
    = $false ),
    inference(unfold_def,[status(thm)],[21]) ).

thf(23,plain,
    ( ( ! [Vd193: $i,Vd194: $i] :
          ( ( greater @ Vd194 @ Vd193 )
        <=> ? [Vd196: $i] :
              ( Vd194
              = ( vplus @ Vd193 @ Vd196 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(24,plain,
    ( ( ! [Vd198: $i,Vd199: $i] :
          ( ( less @ Vd199 @ Vd198 )
        <=> ? [Vd201: $i] :
              ( Vd198
              = ( vplus @ Vd199 @ Vd201 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(25,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 != Vd204 )
          | ~ ( greater @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(26,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ~ ( greater @ Vd203 @ Vd204 )
          | ~ ( less @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(27,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 != Vd204 )
          | ~ ( less @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(28,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 = Vd204 )
          | ( greater @ Vd203 @ Vd204 )
          | ( less @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(29,plain,
    ( ( ! [Vd208: $i,Vd209: $i] :
          ( ( greater @ Vd208 @ Vd209 )
         => ( less @ Vd209 @ Vd208 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(30,plain,
    ( ( ! [Vd226: $i,Vd227: $i] :
          ( ( less @ Vd226 @ Vd227 )
         => ( greater @ Vd227 @ Vd226 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(31,plain,
    ( ( ! [Vd408: $i,Vd409: $i] :
          ( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
          = ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9]) ).

thf(32,plain,
    ( ( ! [Vd418: $i,Vd419: $i] :
          ( ( vmul @ Vd418 @ Vd419 )
          = ( vmul @ Vd419 @ Vd418 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(33,plain,
    ( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
          ( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
          = ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11]) ).

thf(34,plain,
    ( ( ! [Vd444: $i,Vd445: $i,Vd446: $i] :
          ( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
          = ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(35,plain,
    ( ( ! [Vd470: $i,Vd471: $i] :
          ( ( greater @ Vd470 @ Vd471 )
         => ( Vd470
            = ( vplus @ Vd471 @ ( vskolem9 @ Vd470 @ Vd471 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[13]) ).

thf(36,plain,
    ( ( ! [Vd470: $i,Vd471: $i] :
          ( ( greater @ Vd470 @ Vd471 )
         => ( ( vmul @ Vd470 @ vd469 )
            = ( vmul @ ( vplus @ Vd471 @ ( vskolem9 @ Vd470 @ Vd471 ) ) @ vd469 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(37,plain,
    ( ( ! [Vd470: $i,Vd471: $i] :
          ( ( greater @ Vd470 @ Vd471 )
         => ( ( vmul @ ( vplus @ Vd471 @ ( vskolem9 @ Vd470 @ Vd471 ) ) @ vd469 )
            = ( vplus @ ( vmul @ Vd471 @ vd469 ) @ ( vmul @ ( vskolem9 @ Vd470 @ Vd471 ) @ vd469 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[15]) ).

thf(38,plain,
    ( ( ! [Vd470: $i,Vd471: $i] :
          ( ( greater @ Vd470 @ Vd471 )
         => ( greater @ ( vplus @ ( vmul @ Vd471 @ vd469 ) @ ( vmul @ ( vskolem9 @ Vd470 @ Vd471 ) @ vd469 ) ) @ ( vmul @ Vd471 @ vd469 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[16]) ).

thf(39,plain,
    ( ( ! [Vd476: $i,Vd477: $i] :
          ( ( Vd476 = Vd477 )
         => ( ( vmul @ Vd476 @ vd469 )
            = ( vmul @ Vd477 @ vd469 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[17]) ).

thf(40,plain,
    ( ( less @ vd480 @ vd481 )
    = $true ),
    inference(unfold_def,[status(thm)],[18]) ).

thf(41,plain,
    ( ( greater @ vd481 @ vd480 )
    = $true ),
    inference(unfold_def,[status(thm)],[19]) ).

thf(42,plain,
    ( ( ~ ( greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[22]) ).

thf(43,plain,
    ( ( ! [Vd193: $i,Vd194: $i] :
          ( ! [Vd196: $i] :
              ( Vd194
             != ( vplus @ Vd193 @ Vd196 ) )
          | ( greater @ Vd194 @ Vd193 ) )
      & ! [Vd193: $i,Vd194: $i] :
          ( ~ ( greater @ Vd194 @ Vd193 )
          | ( Vd194
            = ( vplus @ Vd193 @ ( sK1_Vd196 @ Vd194 @ Vd193 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[23]) ).

thf(44,plain,
    ( ( ! [Vd198: $i,Vd199: $i] :
          ( ! [Vd201: $i] :
              ( Vd198
             != ( vplus @ Vd199 @ Vd201 ) )
          | ( less @ Vd199 @ Vd198 ) )
      & ! [Vd198: $i,Vd199: $i] :
          ( ~ ( less @ Vd199 @ Vd198 )
          | ( Vd198
            = ( vplus @ Vd199 @ ( sK2_Vd201 @ Vd199 @ Vd198 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[24]) ).

thf(45,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 != Vd204 )
          | ~ ( greater @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[25]) ).

thf(46,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 != Vd204 )
          | ~ ( less @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[27]) ).

thf(47,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( less @ Vd203 @ Vd204 )
          | ( Vd203 = Vd204 )
          | ( greater @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[28]) ).

thf(48,plain,
    ( ( ! [Vd208: $i,Vd209: $i] :
          ( ~ ( greater @ Vd208 @ Vd209 )
          | ( less @ Vd209 @ Vd208 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[29]) ).

thf(49,plain,
    ( ( ! [Vd226: $i,Vd227: $i] :
          ( ~ ( less @ Vd226 @ Vd227 )
          | ( greater @ Vd227 @ Vd226 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[30]) ).

thf(50,plain,
    ( ( ! [Vd470: $i,Vd471: $i] :
          ( ~ ( greater @ Vd470 @ Vd471 )
          | ( Vd470
            = ( vplus @ Vd471 @ ( vskolem9 @ Vd470 @ Vd471 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[35]) ).

thf(51,plain,
    ( ( ! [Vd470: $i,Vd471: $i] :
          ( ~ ( greater @ Vd470 @ Vd471 )
          | ( ( vmul @ Vd470 @ vd469 )
            = ( vmul @ ( vplus @ Vd471 @ ( vskolem9 @ Vd470 @ Vd471 ) ) @ vd469 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[36]) ).

thf(52,plain,
    ( ( ! [Vd470: $i,Vd471: $i] :
          ( ~ ( greater @ Vd470 @ Vd471 )
          | ( ( vmul @ ( vplus @ Vd471 @ ( vskolem9 @ Vd470 @ Vd471 ) ) @ vd469 )
            = ( vplus @ ( vmul @ Vd471 @ vd469 ) @ ( vmul @ ( vskolem9 @ Vd470 @ Vd471 ) @ vd469 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[37]) ).

thf(53,plain,
    ( ( ! [Vd470: $i,Vd471: $i] :
          ( ~ ( greater @ Vd470 @ Vd471 )
          | ( greater @ ( vplus @ ( vmul @ Vd471 @ vd469 ) @ ( vmul @ ( vskolem9 @ Vd470 @ Vd471 ) @ vd469 ) ) @ ( vmul @ Vd471 @ vd469 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[38]) ).

thf(54,plain,
    ( ( ! [Vd476: $i,Vd477: $i] :
          ( ( Vd476 != Vd477 )
          | ( ( vmul @ Vd476 @ vd469 )
            = ( vmul @ Vd477 @ vd469 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[39]) ).

thf(55,plain,
    ( ( greater @ vd481 @ vd480 )
    = $true ),
    inference(copy,[status(thm)],[41]) ).

thf(56,plain,
    ( ( less @ vd480 @ vd481 )
    = $true ),
    inference(copy,[status(thm)],[40]) ).

thf(57,plain,
    ( ( ! [Vd476: $i,Vd477: $i] :
          ( ( Vd476 != Vd477 )
          | ( ( vmul @ Vd476 @ vd469 )
            = ( vmul @ Vd477 @ vd469 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[54]) ).

thf(58,plain,
    ( ( ! [Vd470: $i,Vd471: $i] :
          ( ~ ( greater @ Vd470 @ Vd471 )
          | ( greater @ ( vplus @ ( vmul @ Vd471 @ vd469 ) @ ( vmul @ ( vskolem9 @ Vd470 @ Vd471 ) @ vd469 ) ) @ ( vmul @ Vd471 @ vd469 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[53]) ).

thf(59,plain,
    ( ( ! [Vd470: $i,Vd471: $i] :
          ( ~ ( greater @ Vd470 @ Vd471 )
          | ( ( vmul @ ( vplus @ Vd471 @ ( vskolem9 @ Vd470 @ Vd471 ) ) @ vd469 )
            = ( vplus @ ( vmul @ Vd471 @ vd469 ) @ ( vmul @ ( vskolem9 @ Vd470 @ Vd471 ) @ vd469 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[52]) ).

thf(60,plain,
    ( ( ! [Vd470: $i,Vd471: $i] :
          ( ~ ( greater @ Vd470 @ Vd471 )
          | ( ( vmul @ Vd470 @ vd469 )
            = ( vmul @ ( vplus @ Vd471 @ ( vskolem9 @ Vd470 @ Vd471 ) ) @ vd469 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[51]) ).

thf(61,plain,
    ( ( ! [Vd470: $i,Vd471: $i] :
          ( ~ ( greater @ Vd470 @ Vd471 )
          | ( Vd470
            = ( vplus @ Vd471 @ ( vskolem9 @ Vd470 @ Vd471 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[50]) ).

thf(62,plain,
    ( ( ! [Vd444: $i,Vd445: $i,Vd446: $i] :
          ( ( vmul @ ( vmul @ Vd444 @ Vd445 ) @ Vd446 )
          = ( vmul @ Vd444 @ ( vmul @ Vd445 @ Vd446 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[34]) ).

thf(63,plain,
    ( ( ! [Vd432: $i,Vd433: $i,Vd434: $i] :
          ( ( vmul @ Vd432 @ ( vplus @ Vd433 @ Vd434 ) )
          = ( vplus @ ( vmul @ Vd432 @ Vd433 ) @ ( vmul @ Vd432 @ Vd434 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[33]) ).

thf(64,plain,
    ( ( ! [Vd418: $i,Vd419: $i] :
          ( ( vmul @ Vd418 @ Vd419 )
          = ( vmul @ Vd419 @ Vd418 ) ) )
    = $true ),
    inference(copy,[status(thm)],[32]) ).

thf(65,plain,
    ( ( ! [Vd408: $i,Vd409: $i] :
          ( ( vmul @ ( vsucc @ Vd408 ) @ Vd409 )
          = ( vplus @ ( vmul @ Vd408 @ Vd409 ) @ Vd409 ) ) )
    = $true ),
    inference(copy,[status(thm)],[31]) ).

thf(66,plain,
    ( ( ! [Vd226: $i,Vd227: $i] :
          ( ~ ( less @ Vd226 @ Vd227 )
          | ( greater @ Vd227 @ Vd226 ) ) )
    = $true ),
    inference(copy,[status(thm)],[49]) ).

thf(67,plain,
    ( ( ! [Vd208: $i,Vd209: $i] :
          ( ~ ( greater @ Vd208 @ Vd209 )
          | ( less @ Vd209 @ Vd208 ) ) )
    = $true ),
    inference(copy,[status(thm)],[48]) ).

thf(68,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( less @ Vd203 @ Vd204 )
          | ( Vd203 = Vd204 )
          | ( greater @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(copy,[status(thm)],[47]) ).

thf(69,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 != Vd204 )
          | ~ ( less @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(copy,[status(thm)],[46]) ).

thf(70,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ~ ( greater @ Vd203 @ Vd204 )
          | ~ ( less @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(copy,[status(thm)],[26]) ).

thf(71,plain,
    ( ( ! [Vd203: $i,Vd204: $i] :
          ( ( Vd203 != Vd204 )
          | ~ ( greater @ Vd203 @ Vd204 ) ) )
    = $true ),
    inference(copy,[status(thm)],[45]) ).

thf(72,plain,
    ( ( ! [Vd198: $i,Vd199: $i] :
          ( ! [Vd201: $i] :
              ( Vd198
             != ( vplus @ Vd199 @ Vd201 ) )
          | ( less @ Vd199 @ Vd198 ) )
      & ! [Vd198: $i,Vd199: $i] :
          ( ~ ( less @ Vd199 @ Vd198 )
          | ( Vd198
            = ( vplus @ Vd199 @ ( sK2_Vd201 @ Vd199 @ Vd198 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[44]) ).

thf(73,plain,
    ( ( ! [Vd193: $i,Vd194: $i] :
          ( ! [Vd196: $i] :
              ( Vd194
             != ( vplus @ Vd193 @ Vd196 ) )
          | ( greater @ Vd194 @ Vd193 ) )
      & ! [Vd193: $i,Vd194: $i] :
          ( ~ ( greater @ Vd194 @ Vd193 )
          | ( Vd194
            = ( vplus @ Vd193 @ ( sK1_Vd196 @ Vd194 @ Vd193 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[43]) ).

thf(74,plain,
    ( ( ~ ( greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ) ) )
    = $true ),
    inference(copy,[status(thm)],[42]) ).

thf(75,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ! [SX2: $i] :
                    ( SX0
                   != ( vplus @ SX1 @ SX2 ) )
                | ( less @ SX1 @ SX0 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( less @ SX1 @ SX0 )
                | ( SX0
                  = ( vplus @ SX1 @ ( sK2_Vd201 @ SX1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[72]) ).

thf(76,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ! [SX2: $i] :
                    ( SX1
                   != ( vplus @ SX0 @ SX2 ) )
                | ( greater @ SX1 @ SX0 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( greater @ SX1 @ SX0 )
                | ( SX1
                  = ( vplus @ SX0 @ ( sK1_Vd196 @ SX1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[73]) ).

thf(77,plain,
    ! [SV1: $i] :
      ( ( ! [SY38: $i] :
            ( ( SV1 != SY38 )
            | ( ( vmul @ SV1 @ vd469 )
              = ( vmul @ SY38 @ vd469 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(78,plain,
    ! [SV2: $i] :
      ( ( ! [SY39: $i] :
            ( ~ ( greater @ SV2 @ SY39 )
            | ( greater @ ( vplus @ ( vmul @ SY39 @ vd469 ) @ ( vmul @ ( vskolem9 @ SV2 @ SY39 ) @ vd469 ) ) @ ( vmul @ SY39 @ vd469 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[58]) ).

thf(79,plain,
    ! [SV3: $i] :
      ( ( ! [SY40: $i] :
            ( ~ ( greater @ SV3 @ SY40 )
            | ( ( vmul @ ( vplus @ SY40 @ ( vskolem9 @ SV3 @ SY40 ) ) @ vd469 )
              = ( vplus @ ( vmul @ SY40 @ vd469 ) @ ( vmul @ ( vskolem9 @ SV3 @ SY40 ) @ vd469 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[59]) ).

thf(80,plain,
    ! [SV4: $i] :
      ( ( ! [SY41: $i] :
            ( ~ ( greater @ SV4 @ SY41 )
            | ( ( vmul @ SV4 @ vd469 )
              = ( vmul @ ( vplus @ SY41 @ ( vskolem9 @ SV4 @ SY41 ) ) @ vd469 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[60]) ).

thf(81,plain,
    ! [SV5: $i] :
      ( ( ! [SY42: $i] :
            ( ~ ( greater @ SV5 @ SY42 )
            | ( SV5
              = ( vplus @ SY42 @ ( vskolem9 @ SV5 @ SY42 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[61]) ).

thf(82,plain,
    ! [SV6: $i] :
      ( ( ! [SY43: $i,SY44: $i] :
            ( ( vmul @ ( vmul @ SV6 @ SY43 ) @ SY44 )
            = ( vmul @ SV6 @ ( vmul @ SY43 @ SY44 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[62]) ).

thf(83,plain,
    ! [SV7: $i] :
      ( ( ! [SY45: $i,SY46: $i] :
            ( ( vmul @ SV7 @ ( vplus @ SY45 @ SY46 ) )
            = ( vplus @ ( vmul @ SV7 @ SY45 ) @ ( vmul @ SV7 @ SY46 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(84,plain,
    ! [SV8: $i] :
      ( ( ! [SY47: $i] :
            ( ( vmul @ SV8 @ SY47 )
            = ( vmul @ SY47 @ SV8 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[64]) ).

thf(85,plain,
    ! [SV9: $i] :
      ( ( ! [SY48: $i] :
            ( ( vmul @ ( vsucc @ SV9 ) @ SY48 )
            = ( vplus @ ( vmul @ SV9 @ SY48 ) @ SY48 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[65]) ).

thf(86,plain,
    ! [SV10: $i] :
      ( ( ! [SY49: $i] :
            ( ~ ( less @ SV10 @ SY49 )
            | ( greater @ SY49 @ SV10 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[66]) ).

thf(87,plain,
    ! [SV11: $i] :
      ( ( ! [SY50: $i] :
            ( ~ ( greater @ SV11 @ SY50 )
            | ( less @ SY50 @ SV11 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[67]) ).

thf(88,plain,
    ! [SV12: $i] :
      ( ( ! [SY51: $i] :
            ( ( less @ SV12 @ SY51 )
            | ( SV12 = SY51 )
            | ( greater @ SV12 @ SY51 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[68]) ).

thf(89,plain,
    ! [SV13: $i] :
      ( ( ! [SY52: $i] :
            ( ( SV13 != SY52 )
            | ~ ( less @ SV13 @ SY52 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[69]) ).

thf(90,plain,
    ! [SV14: $i] :
      ( ( ! [SY53: $i] :
            ( ~ ( greater @ SV14 @ SY53 )
            | ~ ( less @ SV14 @ SY53 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(91,plain,
    ! [SV15: $i] :
      ( ( ! [SY54: $i] :
            ( ( SV15 != SY54 )
            | ~ ( greater @ SV15 @ SY54 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[71]) ).

thf(92,plain,
    ( ( greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[74]) ).

thf(93,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( SX0
               != ( vplus @ SX1 @ SX2 ) )
            | ( less @ SX1 @ SX0 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less @ SX1 @ SX0 )
            | ( SX0
              = ( vplus @ SX1 @ ( sK2_Vd201 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[75]) ).

thf(94,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( SX1
               != ( vplus @ SX0 @ SX2 ) )
            | ( greater @ SX1 @ SX0 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( greater @ SX1 @ SX0 )
            | ( SX1
              = ( vplus @ SX0 @ ( sK1_Vd196 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[76]) ).

thf(95,plain,
    ! [SV16: $i,SV1: $i] :
      ( ( ( SV1 != SV16 )
        | ( ( vmul @ SV1 @ vd469 )
          = ( vmul @ SV16 @ vd469 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[77]) ).

thf(96,plain,
    ! [SV17: $i,SV2: $i] :
      ( ( ~ ( greater @ SV2 @ SV17 )
        | ( greater @ ( vplus @ ( vmul @ SV17 @ vd469 ) @ ( vmul @ ( vskolem9 @ SV2 @ SV17 ) @ vd469 ) ) @ ( vmul @ SV17 @ vd469 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[78]) ).

thf(97,plain,
    ! [SV18: $i,SV3: $i] :
      ( ( ~ ( greater @ SV3 @ SV18 )
        | ( ( vmul @ ( vplus @ SV18 @ ( vskolem9 @ SV3 @ SV18 ) ) @ vd469 )
          = ( vplus @ ( vmul @ SV18 @ vd469 ) @ ( vmul @ ( vskolem9 @ SV3 @ SV18 ) @ vd469 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(98,plain,
    ! [SV19: $i,SV4: $i] :
      ( ( ~ ( greater @ SV4 @ SV19 )
        | ( ( vmul @ SV4 @ vd469 )
          = ( vmul @ ( vplus @ SV19 @ ( vskolem9 @ SV4 @ SV19 ) ) @ vd469 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[80]) ).

thf(99,plain,
    ! [SV20: $i,SV5: $i] :
      ( ( ~ ( greater @ SV5 @ SV20 )
        | ( SV5
          = ( vplus @ SV20 @ ( vskolem9 @ SV5 @ SV20 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[81]) ).

thf(100,plain,
    ! [SV21: $i,SV6: $i] :
      ( ( ! [SY55: $i] :
            ( ( vmul @ ( vmul @ SV6 @ SV21 ) @ SY55 )
            = ( vmul @ SV6 @ ( vmul @ SV21 @ SY55 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[82]) ).

thf(101,plain,
    ! [SV22: $i,SV7: $i] :
      ( ( ! [SY56: $i] :
            ( ( vmul @ SV7 @ ( vplus @ SV22 @ SY56 ) )
            = ( vplus @ ( vmul @ SV7 @ SV22 ) @ ( vmul @ SV7 @ SY56 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[83]) ).

thf(102,plain,
    ! [SV23: $i,SV8: $i] :
      ( ( ( vmul @ SV8 @ SV23 )
        = ( vmul @ SV23 @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(103,plain,
    ! [SV24: $i,SV9: $i] :
      ( ( ( vmul @ ( vsucc @ SV9 ) @ SV24 )
        = ( vplus @ ( vmul @ SV9 @ SV24 ) @ SV24 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(104,plain,
    ! [SV25: $i,SV10: $i] :
      ( ( ~ ( less @ SV10 @ SV25 )
        | ( greater @ SV25 @ SV10 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[86]) ).

thf(105,plain,
    ! [SV26: $i,SV11: $i] :
      ( ( ~ ( greater @ SV11 @ SV26 )
        | ( less @ SV26 @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[87]) ).

thf(106,plain,
    ! [SV27: $i,SV12: $i] :
      ( ( ( less @ SV12 @ SV27 )
        | ( SV12 = SV27 )
        | ( greater @ SV12 @ SV27 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[88]) ).

thf(107,plain,
    ! [SV28: $i,SV13: $i] :
      ( ( ( SV13 != SV28 )
        | ~ ( less @ SV13 @ SV28 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(108,plain,
    ! [SV29: $i,SV14: $i] :
      ( ( ~ ( greater @ SV14 @ SV29 )
        | ~ ( less @ SV14 @ SV29 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(109,plain,
    ! [SV30: $i,SV15: $i] :
      ( ( ( SV15 != SV30 )
        | ~ ( greater @ SV15 @ SV30 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(110,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( SX0
               != ( vplus @ SX1 @ SX2 ) )
            | ( less @ SX1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[93]) ).

thf(111,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( less @ SX1 @ SX0 )
            | ( SX0
              = ( vplus @ SX1 @ ( sK2_Vd201 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[93]) ).

thf(112,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ! [SX2: $i] :
                ( SX1
               != ( vplus @ SX0 @ SX2 ) )
            | ( greater @ SX1 @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[94]) ).

thf(113,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( greater @ SX1 @ SX0 )
            | ( SX1
              = ( vplus @ SX0 @ ( sK1_Vd196 @ SX1 @ SX0 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[94]) ).

thf(114,plain,
    ! [SV16: $i,SV1: $i] :
      ( ( ( ( SV1 != SV16 ) )
        = $true )
      | ( ( ( vmul @ SV1 @ vd469 )
          = ( vmul @ SV16 @ vd469 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[95]) ).

thf(115,plain,
    ! [SV17: $i,SV2: $i] :
      ( ( ( ~ ( greater @ SV2 @ SV17 ) )
        = $true )
      | ( ( greater @ ( vplus @ ( vmul @ SV17 @ vd469 ) @ ( vmul @ ( vskolem9 @ SV2 @ SV17 ) @ vd469 ) ) @ ( vmul @ SV17 @ vd469 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[96]) ).

thf(116,plain,
    ! [SV18: $i,SV3: $i] :
      ( ( ( ~ ( greater @ SV3 @ SV18 ) )
        = $true )
      | ( ( ( vmul @ ( vplus @ SV18 @ ( vskolem9 @ SV3 @ SV18 ) ) @ vd469 )
          = ( vplus @ ( vmul @ SV18 @ vd469 ) @ ( vmul @ ( vskolem9 @ SV3 @ SV18 ) @ vd469 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[97]) ).

thf(117,plain,
    ! [SV19: $i,SV4: $i] :
      ( ( ( ~ ( greater @ SV4 @ SV19 ) )
        = $true )
      | ( ( ( vmul @ SV4 @ vd469 )
          = ( vmul @ ( vplus @ SV19 @ ( vskolem9 @ SV4 @ SV19 ) ) @ vd469 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[98]) ).

thf(118,plain,
    ! [SV20: $i,SV5: $i] :
      ( ( ( ~ ( greater @ SV5 @ SV20 ) )
        = $true )
      | ( ( SV5
          = ( vplus @ SV20 @ ( vskolem9 @ SV5 @ SV20 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[99]) ).

thf(119,plain,
    ! [SV31: $i,SV21: $i,SV6: $i] :
      ( ( ( vmul @ ( vmul @ SV6 @ SV21 ) @ SV31 )
        = ( vmul @ SV6 @ ( vmul @ SV21 @ SV31 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[100]) ).

thf(120,plain,
    ! [SV32: $i,SV22: $i,SV7: $i] :
      ( ( ( vmul @ SV7 @ ( vplus @ SV22 @ SV32 ) )
        = ( vplus @ ( vmul @ SV7 @ SV22 ) @ ( vmul @ SV7 @ SV32 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[101]) ).

thf(121,plain,
    ! [SV25: $i,SV10: $i] :
      ( ( ( ~ ( less @ SV10 @ SV25 ) )
        = $true )
      | ( ( greater @ SV25 @ SV10 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[104]) ).

thf(122,plain,
    ! [SV26: $i,SV11: $i] :
      ( ( ( ~ ( greater @ SV11 @ SV26 ) )
        = $true )
      | ( ( less @ SV26 @ SV11 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[105]) ).

thf(123,plain,
    ! [SV27: $i,SV12: $i] :
      ( ( ( less @ SV12 @ SV27 )
        = $true )
      | ( ( ( SV12 = SV27 )
          | ( greater @ SV12 @ SV27 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[106]) ).

thf(124,plain,
    ! [SV28: $i,SV13: $i] :
      ( ( ( ( SV13 != SV28 ) )
        = $true )
      | ( ( ~ ( less @ SV13 @ SV28 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[107]) ).

thf(125,plain,
    ! [SV29: $i,SV14: $i] :
      ( ( ( ~ ( greater @ SV14 @ SV29 ) )
        = $true )
      | ( ( ~ ( less @ SV14 @ SV29 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[108]) ).

thf(126,plain,
    ! [SV30: $i,SV15: $i] :
      ( ( ( ( SV15 != SV30 ) )
        = $true )
      | ( ( ~ ( greater @ SV15 @ SV30 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[109]) ).

thf(127,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ! [SX2: $i] :
              ( SX0
             != ( vplus @ SX1 @ SX2 ) )
          | ( less @ SX1 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[110]) ).

thf(128,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( less @ SX1 @ SX0 )
          | ( SX0
            = ( vplus @ SX1 @ ( sK2_Vd201 @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[111]) ).

thf(129,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ! [SX2: $i] :
              ( SX1
             != ( vplus @ SX0 @ SX2 ) )
          | ( greater @ SX1 @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[112]) ).

thf(130,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( greater @ SX1 @ SX0 )
          | ( SX1
            = ( vplus @ SX0 @ ( sK1_Vd196 @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[113]) ).

thf(131,plain,
    ! [SV16: $i,SV1: $i] :
      ( ( ( SV1 = SV16 )
        = $false )
      | ( ( ( vmul @ SV1 @ vd469 )
          = ( vmul @ SV16 @ vd469 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[114]) ).

thf(132,plain,
    ! [SV17: $i,SV2: $i] :
      ( ( ( greater @ SV2 @ SV17 )
        = $false )
      | ( ( greater @ ( vplus @ ( vmul @ SV17 @ vd469 ) @ ( vmul @ ( vskolem9 @ SV2 @ SV17 ) @ vd469 ) ) @ ( vmul @ SV17 @ vd469 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[115]) ).

thf(133,plain,
    ! [SV18: $i,SV3: $i] :
      ( ( ( greater @ SV3 @ SV18 )
        = $false )
      | ( ( ( vmul @ ( vplus @ SV18 @ ( vskolem9 @ SV3 @ SV18 ) ) @ vd469 )
          = ( vplus @ ( vmul @ SV18 @ vd469 ) @ ( vmul @ ( vskolem9 @ SV3 @ SV18 ) @ vd469 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[116]) ).

thf(134,plain,
    ! [SV19: $i,SV4: $i] :
      ( ( ( greater @ SV4 @ SV19 )
        = $false )
      | ( ( ( vmul @ SV4 @ vd469 )
          = ( vmul @ ( vplus @ SV19 @ ( vskolem9 @ SV4 @ SV19 ) ) @ vd469 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[117]) ).

thf(135,plain,
    ! [SV20: $i,SV5: $i] :
      ( ( ( greater @ SV5 @ SV20 )
        = $false )
      | ( ( SV5
          = ( vplus @ SV20 @ ( vskolem9 @ SV5 @ SV20 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[118]) ).

thf(136,plain,
    ! [SV25: $i,SV10: $i] :
      ( ( ( less @ SV10 @ SV25 )
        = $false )
      | ( ( greater @ SV25 @ SV10 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[121]) ).

thf(137,plain,
    ! [SV26: $i,SV11: $i] :
      ( ( ( greater @ SV11 @ SV26 )
        = $false )
      | ( ( less @ SV26 @ SV11 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[122]) ).

thf(138,plain,
    ! [SV27: $i,SV12: $i] :
      ( ( ( SV12 = SV27 )
        = $true )
      | ( ( greater @ SV12 @ SV27 )
        = $true )
      | ( ( less @ SV12 @ SV27 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[123]) ).

thf(139,plain,
    ! [SV28: $i,SV13: $i] :
      ( ( ( SV13 = SV28 )
        = $false )
      | ( ( ~ ( less @ SV13 @ SV28 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[124]) ).

thf(140,plain,
    ! [SV29: $i,SV14: $i] :
      ( ( ( greater @ SV14 @ SV29 )
        = $false )
      | ( ( ~ ( less @ SV14 @ SV29 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[125]) ).

thf(141,plain,
    ! [SV30: $i,SV15: $i] :
      ( ( ( SV15 = SV30 )
        = $false )
      | ( ( ~ ( greater @ SV15 @ SV30 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[126]) ).

thf(142,plain,
    ! [SV33: $i] :
      ( ( ! [SY57: $i] :
            ( ! [SY58: $i] :
                ( SV33
               != ( vplus @ SY57 @ SY58 ) )
            | ( less @ SY57 @ SV33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[127]) ).

thf(143,plain,
    ! [SV34: $i] :
      ( ( ! [SY59: $i] :
            ( ~ ( less @ SY59 @ SV34 )
            | ( SV34
              = ( vplus @ SY59 @ ( sK2_Vd201 @ SY59 @ SV34 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[128]) ).

thf(144,plain,
    ! [SV35: $i] :
      ( ( ! [SY60: $i] :
            ( ! [SY61: $i] :
                ( SY60
               != ( vplus @ SV35 @ SY61 ) )
            | ( greater @ SY60 @ SV35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[129]) ).

thf(145,plain,
    ! [SV36: $i] :
      ( ( ! [SY62: $i] :
            ( ~ ( greater @ SY62 @ SV36 )
            | ( SY62
              = ( vplus @ SV36 @ ( sK1_Vd196 @ SY62 @ SV36 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[130]) ).

thf(146,plain,
    ! [SV28: $i,SV13: $i] :
      ( ( ( less @ SV13 @ SV28 )
        = $false )
      | ( ( SV13 = SV28 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[139]) ).

thf(147,plain,
    ! [SV29: $i,SV14: $i] :
      ( ( ( less @ SV14 @ SV29 )
        = $false )
      | ( ( greater @ SV14 @ SV29 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[140]) ).

thf(148,plain,
    ! [SV30: $i,SV15: $i] :
      ( ( ( greater @ SV15 @ SV30 )
        = $false )
      | ( ( SV15 = SV30 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[141]) ).

thf(149,plain,
    ! [SV37: $i,SV33: $i] :
      ( ( ! [SY63: $i] :
            ( SV33
           != ( vplus @ SV37 @ SY63 ) )
        | ( less @ SV37 @ SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[142]) ).

thf(150,plain,
    ! [SV34: $i,SV38: $i] :
      ( ( ~ ( less @ SV38 @ SV34 )
        | ( SV34
          = ( vplus @ SV38 @ ( sK2_Vd201 @ SV38 @ SV34 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[143]) ).

thf(151,plain,
    ! [SV35: $i,SV39: $i] :
      ( ( ! [SY64: $i] :
            ( SV39
           != ( vplus @ SV35 @ SY64 ) )
        | ( greater @ SV39 @ SV35 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[144]) ).

thf(152,plain,
    ! [SV36: $i,SV40: $i] :
      ( ( ~ ( greater @ SV40 @ SV36 )
        | ( SV40
          = ( vplus @ SV36 @ ( sK1_Vd196 @ SV40 @ SV36 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[145]) ).

thf(153,plain,
    ! [SV37: $i,SV33: $i] :
      ( ( ( ! [SY63: $i] :
              ( SV33
             != ( vplus @ SV37 @ SY63 ) ) )
        = $true )
      | ( ( less @ SV37 @ SV33 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[149]) ).

thf(154,plain,
    ! [SV34: $i,SV38: $i] :
      ( ( ( ~ ( less @ SV38 @ SV34 ) )
        = $true )
      | ( ( SV34
          = ( vplus @ SV38 @ ( sK2_Vd201 @ SV38 @ SV34 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[150]) ).

thf(155,plain,
    ! [SV35: $i,SV39: $i] :
      ( ( ( ! [SY64: $i] :
              ( SV39
             != ( vplus @ SV35 @ SY64 ) ) )
        = $true )
      | ( ( greater @ SV39 @ SV35 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[151]) ).

thf(156,plain,
    ! [SV36: $i,SV40: $i] :
      ( ( ( ~ ( greater @ SV40 @ SV36 ) )
        = $true )
      | ( ( SV40
          = ( vplus @ SV36 @ ( sK1_Vd196 @ SV40 @ SV36 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[152]) ).

thf(157,plain,
    ! [SV41: $i,SV37: $i,SV33: $i] :
      ( ( ( ( SV33
           != ( vplus @ SV37 @ SV41 ) ) )
        = $true )
      | ( ( less @ SV37 @ SV33 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[153]) ).

thf(158,plain,
    ! [SV34: $i,SV38: $i] :
      ( ( ( less @ SV38 @ SV34 )
        = $false )
      | ( ( SV34
          = ( vplus @ SV38 @ ( sK2_Vd201 @ SV38 @ SV34 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[154]) ).

thf(159,plain,
    ! [SV42: $i,SV35: $i,SV39: $i] :
      ( ( ( ( SV39
           != ( vplus @ SV35 @ SV42 ) ) )
        = $true )
      | ( ( greater @ SV39 @ SV35 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[155]) ).

thf(160,plain,
    ! [SV36: $i,SV40: $i] :
      ( ( ( greater @ SV40 @ SV36 )
        = $false )
      | ( ( SV40
          = ( vplus @ SV36 @ ( sK1_Vd196 @ SV40 @ SV36 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[156]) ).

thf(161,plain,
    ! [SV41: $i,SV37: $i,SV33: $i] :
      ( ( ( SV33
          = ( vplus @ SV37 @ SV41 ) )
        = $false )
      | ( ( less @ SV37 @ SV33 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[157]) ).

thf(162,plain,
    ! [SV42: $i,SV35: $i,SV39: $i] :
      ( ( ( SV39
          = ( vplus @ SV35 @ SV42 ) )
        = $false )
      | ( ( greater @ SV39 @ SV35 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[159]) ).

thf(163,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[55,162,161,160,158,148,147,146,138,137,136,135,134,133,132,131,120,119,103,102,92,56]) ).

thf(164,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[163]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : NUM852+2 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n028.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 21:34:21 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 19
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.36  (rf:0,axioms:19,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:21,loop_count:0,foatp_calls:0,translation:fof_full).........
% 0.69/0.88  
% 0.69/0.88  ********************************
% 0.69/0.88  *   All subproblems solved!    *
% 0.69/0.88  ********************************
% 0.69/0.88  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:19,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:163,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.72/0.89  
% 0.72/0.89  %**** Beginning of derivation protocol ****
% 0.72/0.89  % SZS output start CNFRefutation
% See solution above
% 0.72/0.89  
% 0.72/0.89  %**** End of derivation protocol ****
% 0.72/0.89  %**** no. of clauses in derivation: 164 ****
% 0.72/0.89  %**** clause counter: 163 ****
% 0.72/0.89  
% 0.72/0.89  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:19,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:163,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------