TSTP Solution File: NUM741^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM741^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n006.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 11:54:53 EDT 2022

% Result   : Theorem 34.36s 34.55s
% Output   : CNFRefutation 34.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   16
% Syntax   : Number of formulae    :  145 (  44 unt;   9 typ;   0 def)
%            Number of atoms       :  853 ( 427 equ;   0 cnn)
%            Maximal formula atoms :    5 (   6 avg)
%            Number of connectives : 1471 (  22   ~; 151   |;   0   &;1292   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  259 (   0   ^ 259   !;   0   ?; 259   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_frac,type,
    frac: $tType ).

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

thf(tp_den,type,
    den: frac > nat ).

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

thf(tp_num,type,
    num: frac > nat ).

thf(tp_ts,type,
    ts: nat > nat > nat ).

thf(tp_x,type,
    x: frac ).

thf(tp_y,type,
    y: frac ).

thf(tp_z,type,
    z: frac ).

thf(1,axiom,
    ! [Xx: nat,Xy: nat,Xz: nat] :
      ( ( ts @ ( ts @ Xx @ Xy ) @ Xz )
      = ( ts @ Xx @ ( ts @ Xy @ Xz ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz31) ).

thf(2,axiom,
    ! [Xx: nat,Xy: nat] :
      ( ( ts @ Xx @ Xy )
      = ( ts @ Xy @ Xx ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz29) ).

thf(3,axiom,
    ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
      ( ( less @ Xx @ Xy )
     => ( ( less @ Xz @ Xu )
       => ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz34a) ).

thf(4,axiom,
    ! [Xx: nat,Xy: nat,Xz: nat] :
      ( ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xz ) )
     => ( less @ Xx @ Xy ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz33c) ).

thf(5,axiom,
    less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).

thf(6,axiom,
    less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).

thf(7,conjecture,
    less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz50) ).

thf(8,negated_conjecture,
    ( ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[7]) ).

thf(9,plain,
    ( ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(10,plain,
    ( ( ! [Xx: nat,Xy: nat,Xz: nat] :
          ( ( ts @ ( ts @ Xx @ Xy ) @ Xz )
          = ( ts @ Xx @ ( ts @ Xy @ Xz ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(11,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( ts @ Xx @ Xy )
          = ( ts @ Xy @ Xx ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(12,plain,
    ( ( ! [Xx: nat,Xy: nat,Xz: nat,Xu: nat] :
          ( ( less @ Xx @ Xy )
         => ( ( less @ Xz @ Xu )
           => ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(13,plain,
    ( ( ! [Xx: nat,Xy: nat,Xz: nat] :
          ( ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xz ) )
         => ( less @ Xx @ Xy ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(14,plain,
    ( ( less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(15,plain,
    ( ( less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(16,plain,
    ( ( ~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[9]) ).

thf(17,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ~ ( less @ Xx @ Xy )
          | ! [Xz: nat,Xu: nat] :
              ( ~ ( less @ Xz @ Xu )
              | ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(18,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ! [Xz: nat] :
              ~ ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xz ) )
          | ( less @ Xx @ Xy ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[13]) ).

thf(19,plain,
    ( ( less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) )
    = $true ),
    inference(copy,[status(thm)],[15]) ).

thf(20,plain,
    ( ( less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(21,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ! [Xz: nat] :
              ~ ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xz ) )
          | ( less @ Xx @ Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(22,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ~ ( less @ Xx @ Xy )
          | ! [Xz: nat,Xu: nat] :
              ( ~ ( less @ Xz @ Xu )
              | ( less @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xu ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(23,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( ts @ Xx @ Xy )
          = ( ts @ Xy @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[11]) ).

thf(24,plain,
    ( ( ! [Xx: nat,Xy: nat,Xz: nat] :
          ( ( ts @ ( ts @ Xx @ Xy ) @ Xz )
          = ( ts @ Xx @ ( ts @ Xy @ Xz ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10]) ).

thf(25,plain,
    ( ( ~ ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[16]) ).

thf(26,plain,
    ! [SV1: nat] :
      ( ( ! [SY12: nat] :
            ( ! [SY13: nat] :
                ~ ( less @ ( ts @ SV1 @ SY13 ) @ ( ts @ SY12 @ SY13 ) )
            | ( less @ SV1 @ SY12 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(27,plain,
    ! [SV2: nat] :
      ( ( ! [SY14: nat] :
            ( ~ ( less @ SV2 @ SY14 )
            | ! [SY15: nat,SY16: nat] :
                ( ~ ( less @ SY15 @ SY16 )
                | ( less @ ( ts @ SV2 @ SY15 ) @ ( ts @ SY14 @ SY16 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[22]) ).

thf(28,plain,
    ! [SV3: nat] :
      ( ( ! [SY17: nat] :
            ( ( ts @ SV3 @ SY17 )
            = ( ts @ SY17 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(29,plain,
    ! [SV4: nat] :
      ( ( ! [SY18: nat,SY19: nat] :
            ( ( ts @ ( ts @ SV4 @ SY18 ) @ SY19 )
            = ( ts @ SV4 @ ( ts @ SY18 @ SY19 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(30,plain,
    ( ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(31,plain,
    ! [SV5: nat,SV1: nat] :
      ( ( ! [SY20: nat] :
            ~ ( less @ ( ts @ SV1 @ SY20 ) @ ( ts @ SV5 @ SY20 ) )
        | ( less @ SV1 @ SV5 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[26]) ).

thf(32,plain,
    ! [SV6: nat,SV2: nat] :
      ( ( ~ ( less @ SV2 @ SV6 )
        | ! [SY21: nat,SY22: nat] :
            ( ~ ( less @ SY21 @ SY22 )
            | ( less @ ( ts @ SV2 @ SY21 ) @ ( ts @ SV6 @ SY22 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(33,plain,
    ! [SV7: nat,SV3: nat] :
      ( ( ( ts @ SV3 @ SV7 )
        = ( ts @ SV7 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(34,plain,
    ! [SV8: nat,SV4: nat] :
      ( ( ! [SY23: nat] :
            ( ( ts @ ( ts @ SV4 @ SV8 ) @ SY23 )
            = ( ts @ SV4 @ ( ts @ SV8 @ SY23 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(35,plain,
    ! [SV5: nat,SV1: nat] :
      ( ( ( ! [SY20: nat] :
              ~ ( less @ ( ts @ SV1 @ SY20 ) @ ( ts @ SV5 @ SY20 ) ) )
        = $true )
      | ( ( less @ SV1 @ SV5 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(36,plain,
    ! [SV6: nat,SV2: nat] :
      ( ( ( ~ ( less @ SV2 @ SV6 ) )
        = $true )
      | ( ( ! [SY21: nat,SY22: nat] :
              ( ~ ( less @ SY21 @ SY22 )
              | ( less @ ( ts @ SV2 @ SY21 ) @ ( ts @ SV6 @ SY22 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[32]) ).

thf(37,plain,
    ! [SV9: nat,SV8: nat,SV4: nat] :
      ( ( ( ts @ ( ts @ SV4 @ SV8 ) @ SV9 )
        = ( ts @ SV4 @ ( ts @ SV8 @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(38,plain,
    ! [SV5: nat,SV10: nat,SV1: nat] :
      ( ( ( ~ ( less @ ( ts @ SV1 @ SV10 ) @ ( ts @ SV5 @ SV10 ) ) )
        = $true )
      | ( ( less @ SV1 @ SV5 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(39,plain,
    ! [SV6: nat,SV2: nat] :
      ( ( ( less @ SV2 @ SV6 )
        = $false )
      | ( ( ! [SY21: nat,SY22: nat] :
              ( ~ ( less @ SY21 @ SY22 )
              | ( less @ ( ts @ SV2 @ SY21 ) @ ( ts @ SV6 @ SY22 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[36]) ).

thf(40,plain,
    ! [SV5: nat,SV10: nat,SV1: nat] :
      ( ( ( less @ ( ts @ SV1 @ SV10 ) @ ( ts @ SV5 @ SV10 ) )
        = $false )
      | ( ( less @ SV1 @ SV5 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[38]) ).

thf(41,plain,
    ! [SV6: nat,SV2: nat,SV11: nat] :
      ( ( ( ! [SY24: nat] :
              ( ~ ( less @ SV11 @ SY24 )
              | ( less @ ( ts @ SV2 @ SV11 ) @ ( ts @ SV6 @ SY24 ) ) ) )
        = $true )
      | ( ( less @ SV2 @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[39]) ).

thf(42,plain,
    ! [SV6: nat,SV2: nat,SV12: nat,SV11: nat] :
      ( ( ( ~ ( less @ SV11 @ SV12 )
          | ( less @ ( ts @ SV2 @ SV11 ) @ ( ts @ SV6 @ SV12 ) ) )
        = $true )
      | ( ( less @ SV2 @ SV6 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[41]) ).

thf(43,plain,
    ! [SV6: nat,SV2: nat,SV12: nat,SV11: nat] :
      ( ( ( ~ ( less @ SV11 @ SV12 ) )
        = $true )
      | ( ( less @ ( ts @ SV2 @ SV11 ) @ ( ts @ SV6 @ SV12 ) )
        = $true )
      | ( ( less @ SV2 @ SV6 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[42]) ).

thf(44,plain,
    ! [SV6: nat,SV2: nat,SV12: nat,SV11: nat] :
      ( ( ( less @ SV11 @ SV12 )
        = $false )
      | ( ( less @ ( ts @ SV2 @ SV11 ) @ ( ts @ SV6 @ SV12 ) )
        = $true )
      | ( ( less @ SV2 @ SV6 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[43]) ).

thf(45,plain,
    ( ( ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) )
      = ( less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
    = $false ),
    inference(res,[status(thm)],[30,20]) ).

thf(46,plain,
    ( ( ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) )
      = ( less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
    = $false ),
    inference(res,[status(thm)],[30,19]) ).

thf(47,plain,
    ( ( ( z = y )
      = $false )
    | ( ( z = y )
      = $false ) ),
    inference(extuni,[status(esa)],[46]) ).

thf(48,plain,
    ( ( ( ( num @ z )
        = ( num @ y ) )
      = $false )
    | ( ( z = y )
      = $false ) ),
    inference(extuni,[status(esa)],[46]) ).

thf(49,plain,
    ( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
        = ( ts @ ( num @ y ) @ ( den @ x ) ) )
      = $false )
    | ( ( z = y )
      = $false ) ),
    inference(extuni,[status(esa)],[46]) ).

thf(50,plain,
    ( ( ( z = y )
      = $false )
    | ( ( ( den @ z )
        = ( den @ y ) )
      = $false ) ),
    inference(extuni,[status(esa)],[46]) ).

thf(51,plain,
    ( ( ( ( num @ z )
        = ( num @ y ) )
      = $false )
    | ( ( ( den @ z )
        = ( den @ y ) )
      = $false ) ),
    inference(extuni,[status(esa)],[46]) ).

thf(52,plain,
    ( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
        = ( ts @ ( num @ y ) @ ( den @ x ) ) )
      = $false )
    | ( ( ( den @ z )
        = ( den @ y ) )
      = $false ) ),
    inference(extuni,[status(esa)],[46]) ).

thf(53,plain,
    ( ( ( z = y )
      = $false )
    | ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
        = ( ts @ ( num @ x ) @ ( den @ y ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[46]) ).

thf(54,plain,
    ( ( ( ( num @ z )
        = ( num @ y ) )
      = $false )
    | ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
        = ( ts @ ( num @ x ) @ ( den @ y ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[46]) ).

thf(55,plain,
    ( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
        = ( ts @ ( num @ y ) @ ( den @ x ) ) )
      = $false )
    | ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
        = ( ts @ ( num @ x ) @ ( den @ y ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[46]) ).

thf(56,plain,
    ( ( ( x = y )
      = $false )
    | ( ( x = y )
      = $false ) ),
    inference(extuni,[status(esa)],[45]) ).

thf(57,plain,
    ( ( ( ( den @ x )
        = ( den @ y ) )
      = $false )
    | ( ( x = y )
      = $false ) ),
    inference(extuni,[status(esa)],[45]) ).

thf(58,plain,
    ( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
        = ( ts @ ( num @ z ) @ ( den @ y ) ) )
      = $false )
    | ( ( x = y )
      = $false ) ),
    inference(extuni,[status(esa)],[45]) ).

thf(59,plain,
    ( ( ( x = y )
      = $false )
    | ( ( ( num @ x )
        = ( num @ y ) )
      = $false ) ),
    inference(extuni,[status(esa)],[45]) ).

thf(60,plain,
    ( ( ( ( den @ x )
        = ( den @ y ) )
      = $false )
    | ( ( ( num @ x )
        = ( num @ y ) )
      = $false ) ),
    inference(extuni,[status(esa)],[45]) ).

thf(61,plain,
    ( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
        = ( ts @ ( num @ z ) @ ( den @ y ) ) )
      = $false )
    | ( ( ( num @ x )
        = ( num @ y ) )
      = $false ) ),
    inference(extuni,[status(esa)],[45]) ).

thf(62,plain,
    ( ( ( x = y )
      = $false )
    | ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
        = ( ts @ ( num @ y ) @ ( den @ z ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[45]) ).

thf(63,plain,
    ( ( ( ( den @ x )
        = ( den @ y ) )
      = $false )
    | ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
        = ( ts @ ( num @ y ) @ ( den @ z ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[45]) ).

thf(64,plain,
    ( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
        = ( ts @ ( num @ z ) @ ( den @ y ) ) )
      = $false )
    | ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
        = ( ts @ ( num @ y ) @ ( den @ z ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[45]) ).

thf(65,plain,
    ( ( z = y )
    = $false ),
    inference(sim,[status(thm)],[47]) ).

thf(66,plain,
    ( ( x = y )
    = $false ),
    inference(sim,[status(thm)],[56]) ).

thf(67,plain,
    ! [SV13: nat,SV14: nat] :
      ( ( ( ts @ SV14 @ SV13 )
        = ( ts @ SV13 @ SV14 ) )
      = $true ),
    inference(rename,[status(thm)],[33]) ).

thf(69,plain,
    ! [SV15: nat,SV16: nat,SV17: nat] :
      ( ( ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 )
        = ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) )
      = $true ),
    inference(rename,[status(thm)],[37]) ).

thf(71,plain,
    ! [SV18: nat,SV19: nat,SV20: nat] :
      ( ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
        = $false )
      | ( ( less @ SV20 @ SV18 )
        = $true ) ),
    inference(rename,[status(thm)],[40]) ).

thf(76,plain,
    ! [SV18: nat,SV19: nat,SV20: nat] :
      ( ( ( ( less @ SV20 @ SV18 )
          = ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
        = $false )
      | ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
        = $false ) ),
    inference(res,[status(thm)],[71,30]) ).

thf(77,plain,
    ! [SV18: nat,SV19: nat,SV20: nat] :
      ( ( ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
          = ( less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
        = $false )
      | ( ( less @ SV20 @ SV18 )
        = $true ) ),
    inference(res,[status(thm)],[71,20]) ).

thf(78,plain,
    ! [SV18: nat,SV19: nat,SV20: nat] :
      ( ( ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
          = ( less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
        = $false )
      | ( ( less @ SV20 @ SV18 )
        = $true ) ),
    inference(res,[status(thm)],[71,19]) ).

thf(79,plain,
    ( ( ( less @ ( num @ x ) @ ( num @ y ) )
      = $true )
    | ( ( y = x )
      = $false ) ),
    inference(extuni,[status(esa)],[78:[bind(SV18,$thf( num @ y )),bind(SV19,$thf( den @ y )),bind(SV20,$thf( num @ x ))]]) ).

thf(80,plain,
    ( ( ( less @ ( num @ x ) @ ( num @ y ) )
      = $true )
    | ( ( ( den @ y )
        = ( den @ x ) )
      = $false ) ),
    inference(extuni,[status(esa)],[78:[bind(SV18,$thf( num @ y )),bind(SV19,$thf( den @ y )),bind(SV20,$thf( num @ x ))]]) ).

thf(81,plain,
    ! [SV18: nat] :
      ( ( ( less @ ( num @ x ) @ SV18 )
        = $true )
      | ( ( ( ts @ SV18 @ ( den @ y ) )
          = ( ts @ ( num @ y ) @ ( den @ x ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[78:[bind(SV19,$thf( den @ y )),bind(SV20,$thf( num @ x ))]]) ).

thf(82,plain,
    ! [SV20: nat] :
      ( ( ( less @ SV20 @ ( num @ y ) )
        = $true )
      | ( ( ( ts @ SV20 @ ( den @ x ) )
          = ( ts @ ( num @ x ) @ ( den @ y ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[78:[bind(SV19,$thf( den @ x )),bind(SV18,$thf( num @ y ))]]) ).

thf(83,plain,
    ! [SV19: nat,SV18: nat,SV20: nat] :
      ( ( ( less @ SV20 @ SV18 )
        = $true )
      | ( ( ( ts @ SV18 @ SV19 )
          = ( ts @ ( num @ y ) @ ( den @ x ) ) )
        = $false )
      | ( ( ( ts @ SV20 @ SV19 )
          = ( ts @ ( num @ x ) @ ( den @ y ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[78]) ).

thf(84,plain,
    ( ( ( less @ ( num @ y ) @ ( num @ z ) )
      = $true )
    | ( ( z = y )
      = $false ) ),
    inference(extuni,[status(esa)],[77:[bind(SV18,$thf( num @ z )),bind(SV19,$thf( den @ z )),bind(SV20,$thf( num @ y ))]]) ).

thf(85,plain,
    ( ( ( less @ ( num @ y ) @ ( num @ z ) )
      = $true )
    | ( ( ( den @ z )
        = ( den @ y ) )
      = $false ) ),
    inference(extuni,[status(esa)],[77:[bind(SV18,$thf( num @ z )),bind(SV19,$thf( den @ z )),bind(SV20,$thf( num @ y ))]]) ).

thf(86,plain,
    ! [SV18: nat] :
      ( ( ( less @ ( num @ y ) @ SV18 )
        = $true )
      | ( ( ( ts @ SV18 @ ( den @ z ) )
          = ( ts @ ( num @ z ) @ ( den @ y ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[77:[bind(SV19,$thf( den @ z )),bind(SV20,$thf( num @ y ))]]) ).

thf(87,plain,
    ! [SV20: nat] :
      ( ( ( less @ SV20 @ ( num @ z ) )
        = $true )
      | ( ( ( ts @ SV20 @ ( den @ y ) )
          = ( ts @ ( num @ y ) @ ( den @ z ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[77:[bind(SV19,$thf( den @ y )),bind(SV18,$thf( num @ z ))]]) ).

thf(88,plain,
    ! [SV19: nat,SV18: nat,SV20: nat] :
      ( ( ( less @ SV20 @ SV18 )
        = $true )
      | ( ( ( ts @ SV18 @ SV19 )
          = ( ts @ ( num @ z ) @ ( den @ y ) ) )
        = $false )
      | ( ( ( ts @ SV20 @ SV19 )
          = ( ts @ ( num @ y ) @ ( den @ z ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[77]) ).

thf(89,plain,
    ! [SV19: nat] :
      ( ( less @ ( ts @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ SV19 ) @ ( ts @ ( ts @ ( num @ z ) @ ( den @ x ) ) @ SV19 ) )
      = $false ),
    inference(extuni,[status(esa)],[76:[bind(SV18,$thf( ts @ ( num @ z ) @ ( den @ x ) )),bind(SV20,$thf( ts @ ( num @ x ) @ ( den @ z ) ))]]) ).

thf(90,plain,
    ! [SV21: nat,SV22: nat,SV23: nat,SV24: nat] :
      ( ( ( less @ SV24 @ SV23 )
        = $false )
      | ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
        = $true )
      | ( ( less @ SV22 @ SV21 )
        = $false ) ),
    inference(rename,[status(thm)],[44]) ).

thf(95,plain,
    ! [SV21: nat,SV22: nat,SV23: nat,SV24: nat,SV18: nat,SV19: nat,SV20: nat] :
      ( ( ( ( less @ SV22 @ SV21 )
          = ( less @ SV20 @ SV18 ) )
        = $false )
      | ( ( less @ SV24 @ SV23 )
        = $false )
      | ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
        = $true )
      | ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
        = $false ) ),
    inference(res,[status(thm)],[90,71]) ).

thf(96,plain,
    ! [SV21: nat,SV22: nat,SV23: nat,SV24: nat,SV18: nat,SV19: nat,SV20: nat] :
      ( ( ( ( less @ SV24 @ SV23 )
          = ( less @ SV20 @ SV18 ) )
        = $false )
      | ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
        = $true )
      | ( ( less @ SV22 @ SV21 )
        = $false )
      | ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
        = $false ) ),
    inference(res,[status(thm)],[90,71]) ).

thf(97,plain,
    ! [SV21: nat,SV22: nat,SV23: nat,SV24: nat,SV18: nat,SV19: nat,SV20: nat] :
      ( ( ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
          = ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) ) )
        = $false )
      | ( ( less @ SV24 @ SV23 )
        = $false )
      | ( ( less @ SV22 @ SV21 )
        = $false )
      | ( ( less @ SV20 @ SV18 )
        = $true ) ),
    inference(res,[status(thm)],[90,71]) ).

thf(102,plain,
    ! [SV21: nat,SV22: nat,SV23: nat,SV24: nat] :
      ( ( ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
          = ( less @ ( ts @ ( num @ x ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
        = $false )
      | ( ( less @ SV24 @ SV23 )
        = $false )
      | ( ( less @ SV22 @ SV21 )
        = $false ) ),
    inference(res,[status(thm)],[90,30]) ).

thf(103,plain,
    ! [SV21: nat,SV22: nat,SV23: nat,SV24: nat] :
      ( ( ( ( less @ SV22 @ SV21 )
          = ( less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
        = $false )
      | ( ( less @ SV24 @ SV23 )
        = $false )
      | ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
        = $true ) ),
    inference(res,[status(thm)],[90,20]) ).

thf(104,plain,
    ! [SV21: nat,SV22: nat,SV23: nat,SV24: nat] :
      ( ( ( ( less @ SV24 @ SV23 )
          = ( less @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
        = $false )
      | ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
        = $true )
      | ( ( less @ SV22 @ SV21 )
        = $false ) ),
    inference(res,[status(thm)],[90,20]) ).

thf(105,plain,
    ! [SV21: nat,SV22: nat,SV23: nat,SV24: nat] :
      ( ( ( ( less @ SV22 @ SV21 )
          = ( less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
        = $false )
      | ( ( less @ SV24 @ SV23 )
        = $false )
      | ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
        = $true ) ),
    inference(res,[status(thm)],[90,19]) ).

thf(106,plain,
    ! [SV21: nat,SV22: nat,SV23: nat,SV24: nat] :
      ( ( ( ( less @ SV24 @ SV23 )
          = ( less @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
        = $false )
      | ( ( less @ ( ts @ SV22 @ SV24 ) @ ( ts @ SV21 @ SV23 ) )
        = $true )
      | ( ( less @ SV22 @ SV21 )
        = $false ) ),
    inference(res,[status(thm)],[90,19]) ).

thf(107,plain,
    ! [SV21: nat,SV22: nat] :
      ( ( ( less @ SV22 @ SV21 )
        = $false )
      | ( ( less @ ( ts @ SV22 @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ SV21 @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
        = $true ) ),
    inference(extuni,[status(esa)],[106:[bind(SV23,$thf( ts @ ( num @ y ) @ ( den @ x ) )),bind(SV24,$thf( ts @ ( num @ x ) @ ( den @ y ) ))]]) ).

thf(108,plain,
    ! [SV23: nat,SV24: nat] :
      ( ( ( less @ ( ts @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ SV24 ) @ ( ts @ ( ts @ ( num @ y ) @ ( den @ x ) ) @ SV23 ) )
        = $true )
      | ( ( less @ SV24 @ SV23 )
        = $false ) ),
    inference(extuni,[status(esa)],[105:[bind(SV21,$thf( ts @ ( num @ y ) @ ( den @ x ) )),bind(SV22,$thf( ts @ ( num @ x ) @ ( den @ y ) ))]]) ).

thf(109,plain,
    ! [SV21: nat,SV22: nat] :
      ( ( ( less @ SV22 @ SV21 )
        = $false )
      | ( ( less @ ( ts @ SV22 @ ( ts @ ( num @ y ) @ ( den @ z ) ) ) @ ( ts @ SV21 @ ( ts @ ( num @ z ) @ ( den @ y ) ) ) )
        = $true ) ),
    inference(extuni,[status(esa)],[104:[bind(SV23,$thf( ts @ ( num @ z ) @ ( den @ y ) )),bind(SV24,$thf( ts @ ( num @ y ) @ ( den @ z ) ))]]) ).

thf(110,plain,
    ! [SV23: nat,SV24: nat] :
      ( ( ( less @ ( ts @ ( ts @ ( num @ y ) @ ( den @ z ) ) @ SV24 ) @ ( ts @ ( ts @ ( num @ z ) @ ( den @ y ) ) @ SV23 ) )
        = $true )
      | ( ( less @ SV24 @ SV23 )
        = $false ) ),
    inference(extuni,[status(esa)],[103:[bind(SV21,$thf( ts @ ( num @ z ) @ ( den @ y ) )),bind(SV22,$thf( ts @ ( num @ y ) @ ( den @ z ) ))]]) ).

thf(111,plain,
    ( ( ( less @ ( num @ x ) @ ( num @ z ) )
      = $false )
    | ( ( less @ ( den @ z ) @ ( den @ x ) )
      = $false ) ),
    inference(extuni,[status(esa)],[102:[bind(SV23,$thf( den @ x )),bind(SV21,$thf( num @ z )),bind(SV24,$thf( den @ z )),bind(SV22,$thf( num @ x ))]]) ).

thf(112,plain,
    ! [SV23: nat,SV21: nat] :
      ( ( ( less @ ( num @ x ) @ SV21 )
        = $false )
      | ( ( less @ ( den @ z ) @ SV23 )
        = $false )
      | ( ( ( ts @ SV21 @ SV23 )
          = ( ts @ ( num @ z ) @ ( den @ x ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[102:[bind(SV24,$thf( den @ z )),bind(SV22,$thf( num @ x ))]]) ).

thf(113,plain,
    ! [SV24: nat,SV22: nat] :
      ( ( ( less @ SV22 @ ( num @ z ) )
        = $false )
      | ( ( less @ SV24 @ ( den @ x ) )
        = $false )
      | ( ( ( ts @ SV22 @ SV24 )
          = ( ts @ ( num @ x ) @ ( den @ z ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[102:[bind(SV23,$thf( den @ x )),bind(SV21,$thf( num @ z ))]]) ).

thf(114,plain,
    ! [SV23: nat,SV24: nat,SV21: nat,SV22: nat] :
      ( ( ( less @ SV22 @ SV21 )
        = $false )
      | ( ( less @ SV24 @ SV23 )
        = $false )
      | ( ( ( ts @ SV21 @ SV23 )
          = ( ts @ ( num @ z ) @ ( den @ x ) ) )
        = $false )
      | ( ( ( ts @ SV22 @ SV24 )
          = ( ts @ ( num @ x ) @ ( den @ z ) ) )
        = $false ) ),
    inference(extuni,[status(esa)],[102]) ).

thf(116,plain,
    ! [SV23: nat,SV19: nat,SV21: nat,SV18: nat,SV20: nat] :
      ( ( ( less @ SV20 @ SV18 )
        = $true )
      | ( ( less @ SV20 @ SV21 )
        = $false )
      | ( ( less @ SV19 @ SV23 )
        = $false )
      | ( ( ( ts @ SV21 @ SV23 )
          = ( ts @ SV18 @ SV19 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[97:[bind(SV24,$thf( SV19 )),bind(SV22,$thf( SV20 ))]]) ).

thf(117,plain,
    ! [SV19: nat,SV24: nat,SV22: nat,SV18: nat,SV20: nat] :
      ( ( ( less @ SV20 @ SV18 )
        = $true )
      | ( ( less @ SV22 @ SV18 )
        = $false )
      | ( ( less @ SV24 @ SV19 )
        = $false )
      | ( ( ( ts @ SV22 @ SV24 )
          = ( ts @ SV20 @ SV19 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[97:[bind(SV23,$thf( SV19 )),bind(SV21,$thf( SV18 ))]]) ).

thf(118,plain,
    ! [SV19: nat,SV23: nat,SV24: nat,SV21: nat,SV22: nat,SV18: nat,SV20: nat] :
      ( ( ( less @ SV20 @ SV18 )
        = $true )
      | ( ( less @ SV22 @ SV21 )
        = $false )
      | ( ( less @ SV24 @ SV23 )
        = $false )
      | ( ( ( ts @ SV21 @ SV23 )
          = ( ts @ SV18 @ SV19 ) )
        = $false )
      | ( ( ( ts @ SV22 @ SV24 )
          = ( ts @ SV20 @ SV19 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[97]) ).

thf(119,plain,
    ! [SV21: nat,SV22: nat,SV18: nat,SV19: nat,SV20: nat] :
      ( ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
        = $false )
      | ( ( less @ SV22 @ SV21 )
        = $false )
      | ( ( less @ ( ts @ SV22 @ SV20 ) @ ( ts @ SV21 @ SV18 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[96:[bind(SV23,$thf( SV18 )),bind(SV24,$thf( SV20 ))]]) ).

thf(120,plain,
    ! [SV23: nat,SV24: nat,SV18: nat,SV19: nat,SV20: nat] :
      ( ( ( less @ ( ts @ SV20 @ SV19 ) @ ( ts @ SV18 @ SV19 ) )
        = $false )
      | ( ( less @ ( ts @ SV20 @ SV24 ) @ ( ts @ SV18 @ SV23 ) )
        = $true )
      | ( ( less @ SV24 @ SV23 )
        = $false ) ),
    inference(extuni,[status(esa)],[95:[bind(SV21,$thf( SV18 )),bind(SV22,$thf( SV20 ))]]) ).

thf(126,plain,
    ! [SV15: nat,SV16: nat,SV17: nat] :
      ( ( ( ( ( num @ z )
            = ( num @ y ) )
          = ( ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 )
            = ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) ) )
        = $false )
      | ( ( z = y )
        = $false ) ),
    inference(res,[status(thm)],[48,69]) ).

thf(128,plain,
    ! [SV13: nat,SV14: nat] :
      ( ( ( ( ( num @ z )
            = ( num @ y ) )
          = ( ( ts @ SV14 @ SV13 )
            = ( ts @ SV13 @ SV14 ) ) )
        = $false )
      | ( ( z = y )
        = $false ) ),
    inference(res,[status(thm)],[48,67]) ).

thf(134,plain,
    ! [SV14: nat,SV13: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( num @ z )
          = ( ts @ SV13 @ SV14 ) )
        = $false )
      | ( ( ( num @ y )
          = ( ts @ SV14 @ SV13 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[128]) ).

thf(135,plain,
    ! [SV14: nat,SV13: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( num @ y )
          = ( ts @ SV13 @ SV14 ) )
        = $false )
      | ( ( ( num @ z )
          = ( ts @ SV14 @ SV13 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[128]) ).

thf(136,plain,
    ! [SV15: nat,SV16: nat,SV17: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( num @ z )
          = ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) )
        = $false )
      | ( ( ( num @ y )
          = ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[126]) ).

thf(137,plain,
    ! [SV15: nat,SV16: nat,SV17: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( num @ y )
          = ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) )
        = $false )
      | ( ( ( num @ z )
          = ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[126]) ).

thf(138,plain,
    ( ( ( z = y )
      = $false )
    | ( ( z = y )
      = $false ) ),
    inference(extuni,[status(esa)],[48]) ).

thf(139,plain,
    ( ( z = y )
    = $false ),
    inference(sim,[status(thm)],[138]) ).

thf(145,plain,
    ! [SV15: nat,SV16: nat,SV17: nat] :
      ( ( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
            = ( ts @ ( num @ y ) @ ( den @ x ) ) )
          = ( ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 )
            = ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) ) )
        = $false )
      | ( ( z = y )
        = $false ) ),
    inference(res,[status(thm)],[49,69]) ).

thf(147,plain,
    ! [SV13: nat,SV14: nat] :
      ( ( ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
            = ( ts @ ( num @ y ) @ ( den @ x ) ) )
          = ( ( ts @ SV14 @ SV13 )
            = ( ts @ SV13 @ SV14 ) ) )
        = $false )
      | ( ( z = y )
        = $false ) ),
    inference(res,[status(thm)],[49,67]) ).

thf(153,plain,
    ( ( ( z = y )
      = $false )
    | ( ( ( den @ x )
        = ( num @ y ) )
      = $false )
    | ( ( ( num @ z )
        = ( den @ x ) )
      = $false ) ),
    inference(extuni,[status(esa)],[147:[bind(SV13,$thf( den @ x )),bind(SV14,$thf( num @ y ))]]) ).

thf(154,plain,
    ( ( ( z = y )
      = $false )
    | ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
        = ( ts @ ( den @ x ) @ ( num @ y ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[147:[bind(SV13,$thf( den @ x )),bind(SV14,$thf( num @ y ))]]) ).

thf(155,plain,
    ( ( ( z = y )
      = $false )
    | ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
        = ( ts @ ( den @ x ) @ ( num @ z ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[147:[bind(SV14,$thf( den @ x )),bind(SV13,$thf( num @ z ))]]) ).

thf(156,plain,
    ! [SV14: nat,SV13: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
          = ( ts @ SV13 @ SV14 ) )
        = $false )
      | ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
          = ( ts @ SV14 @ SV13 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[147]) ).

thf(157,plain,
    ( ( ( z = y )
      = $false )
    | ( ( ( den @ x )
        = ( num @ z ) )
      = $false )
    | ( ( ( num @ y )
        = ( den @ x ) )
      = $false ) ),
    inference(extuni,[status(esa)],[147:[bind(SV13,$thf( den @ x )),bind(SV14,$thf( num @ z ))]]) ).

thf(158,plain,
    ( ( ( z = y )
      = $false )
    | ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
        = ( ts @ ( den @ x ) @ ( num @ z ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[147:[bind(SV13,$thf( den @ x )),bind(SV14,$thf( num @ z ))]]) ).

thf(159,plain,
    ( ( ( z = y )
      = $false )
    | ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
        = ( ts @ ( den @ x ) @ ( num @ y ) ) )
      = $false ) ),
    inference(extuni,[status(esa)],[147:[bind(SV14,$thf( den @ x )),bind(SV13,$thf( num @ y ))]]) ).

thf(160,plain,
    ! [SV14: nat,SV13: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
          = ( ts @ SV13 @ SV14 ) )
        = $false )
      | ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
          = ( ts @ SV14 @ SV13 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[147]) ).

thf(161,plain,
    ! [SV16: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( den @ x )
          = ( ts @ SV16 @ ( den @ x ) ) )
        = $false )
      | ( ( ( num @ y )
          = ( ts @ ( num @ z ) @ SV16 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[145:[bind(SV17,$thf( num @ z )),bind(SV15,$thf( den @ x ))]]) ).

thf(162,plain,
    ! [SV16: nat,SV17: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
          = ( ts @ SV17 @ ( ts @ SV16 @ ( den @ x ) ) ) )
        = $false )
      | ( ( ( num @ y )
          = ( ts @ SV17 @ SV16 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[145:[bind(SV15,$thf( den @ x ))]]) ).

thf(163,plain,
    ! [SV15: nat,SV16: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( den @ x )
          = ( ts @ SV16 @ SV15 ) )
        = $false )
      | ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
          = ( ts @ ( ts @ ( num @ z ) @ SV16 ) @ SV15 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[145:[bind(SV17,$thf( num @ z ))]]) ).

thf(164,plain,
    ! [SV15: nat,SV16: nat,SV17: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
          = ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) )
        = $false )
      | ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
          = ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[145]) ).

thf(165,plain,
    ! [SV16: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( den @ x )
          = ( ts @ SV16 @ ( den @ x ) ) )
        = $false )
      | ( ( ( num @ z )
          = ( ts @ ( num @ y ) @ SV16 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[145:[bind(SV17,$thf( num @ y )),bind(SV15,$thf( den @ x ))]]) ).

thf(166,plain,
    ! [SV16: nat,SV17: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
          = ( ts @ SV17 @ ( ts @ SV16 @ ( den @ x ) ) ) )
        = $false )
      | ( ( ( num @ z )
          = ( ts @ SV17 @ SV16 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[145:[bind(SV15,$thf( den @ x ))]]) ).

thf(167,plain,
    ! [SV15: nat,SV16: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( den @ x )
          = ( ts @ SV16 @ SV15 ) )
        = $false )
      | ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
          = ( ts @ ( ts @ ( num @ y ) @ SV16 ) @ SV15 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[145:[bind(SV17,$thf( num @ y ))]]) ).

thf(168,plain,
    ! [SV15: nat,SV16: nat,SV17: nat] :
      ( ( ( z = y )
        = $false )
      | ( ( ( ts @ ( num @ y ) @ ( den @ x ) )
          = ( ts @ SV17 @ ( ts @ SV16 @ SV15 ) ) )
        = $false )
      | ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
          = ( ts @ ( ts @ SV17 @ SV16 ) @ SV15 ) )
        = $false ) ),
    inference(extuni,[status(esa)],[145]) ).

thf(169,plain,
    ( ( ( z = y )
      = $false )
    | ( ( z = y )
      = $false ) ),
    inference(extuni,[status(esa)],[49]) ).

thf(170,plain,
    ( ( ( z = y )
      = $false )
    | ( ( ( num @ z )
        = ( num @ y ) )
      = $false ) ),
    inference(extuni,[status(esa)],[49]) ).

thf(171,plain,
    ( ( z = y )
    = $false ),
    inference(sim,[status(thm)],[169]) ).

thf(172,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[19,171,170,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,139,137,136,135,134,120,119,118,117,116,114,113,112,111,110,109,108,107,90,89,88,87,86,85,84,83,82,81,80,79,71,69,67,66,65,64,63,62,61,60,59,58,57,55,54,53,52,51,50,49,48,30,20]) ).

thf(173,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[172]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM741^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34  % Computer : n006.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 : Thu Jul  7 01:27:36 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  
% 0.13/0.35   No.of.Axioms: 6
% 0.13/0.35  
% 0.13/0.35   Length.of.Defs: 0
% 0.13/0.35  
% 0.13/0.35   Contains.Choice.Funs: false
% 0.13/0.35  (rf:0,axioms:6,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:8,loop_count:0,foatp_calls:0,translation:fof_full)..eprover: CPU time limit exceeded, terminating
% 25.27/25.47  ...
% 34.36/34.55  
% 34.36/34.55  ********************************
% 34.36/34.55  *   All subproblems solved!    *
% 34.36/34.55  ********************************
% 34.36/34.55  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:172,loop_count:10,foatp_calls:2,translation:fof_full)
% 34.36/34.57  
% 34.36/34.57  %**** Beginning of derivation protocol ****
% 34.36/34.57  % SZS output start CNFRefutation
% See solution above
% 34.36/34.57  
% 34.36/34.57  %**** End of derivation protocol ****
% 34.36/34.57  %**** no. of clauses in derivation: 136 ****
% 34.36/34.57  %**** clause counter: 172 ****
% 34.36/34.57  
% 34.36/34.57  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:6,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:172,loop_count:10,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------