TSTP Solution File: NUM737^1 by LEO-II---1.7.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : NUM737^1 : 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 : n008.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 11:54:50 EDT 2022

% Result   : Theorem 177.40s 177.67s
% Output   : CNFRefutation 177.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   83 (  51 unt;  10 typ;   0 def)
%            Number of atoms       :  292 ( 137 equ;   0 cnn)
%            Maximal formula atoms :    3 (   4 avg)
%            Number of connectives :  771 (  18   ~;  33   |;   0   &; 714   @)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :  141 (   0   ^ 141   !;   0   ?; 141   :)

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

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

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

thf(tp_more,type,
    more: nat > nat > $o ).

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

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

thf(tp_u,type,
    u: frac ).

thf(tp_x,type,
    x: frac ).

thf(tp_y,type,
    y: frac ).

thf(tp_z,type,
    z: frac ).

thf(1,axiom,
    ! [Xx: frac,Xy: frac] :
      ( ( ( ts @ ( num @ Xx ) @ ( den @ Xy ) )
        = ( ts @ ( num @ Xy ) @ ( den @ Xx ) ) )
     => ( ( ts @ ( num @ Xy ) @ ( den @ Xx ) )
        = ( ts @ ( num @ Xx ) @ ( den @ Xy ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz38) ).

thf(2,axiom,
    ! [Xx: nat,Xy: nat,Xz: nat] :
      ( ( ts @ ( ts @ Xx @ Xy ) @ Xz )
      = ( ts @ Xx @ ( ts @ Xy @ Xz ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz31) ).

thf(3,axiom,
    ! [Xx: nat,Xy: nat] :
      ( ( ts @ Xx @ Xy )
      = ( ts @ Xy @ Xx ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29) ).

thf(4,axiom,
    ! [Xx: nat,Xy: nat,Xz: nat] :
      ( ( more @ Xx @ Xy )
     => ( more @ ( ts @ Xz @ Xx ) @ ( ts @ Xz @ Xy ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz32d) ).

thf(5,axiom,
    ! [Xx: nat,Xy: nat,Xz: nat] :
      ( ( more @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xz ) )
     => ( more @ Xx @ Xy ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz33a) ).

thf(6,axiom,
    ( ( ts @ ( num @ y ) @ ( den @ u ) )
    = ( ts @ ( num @ u ) @ ( den @ y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f) ).

thf(7,axiom,
    ( ( ts @ ( num @ x ) @ ( den @ z ) )
    = ( ts @ ( num @ z ) @ ( den @ x ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).

thf(8,axiom,
    more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).

thf(9,conjecture,
    more @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ z ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44) ).

thf(10,negated_conjecture,
    ( ( more @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ z ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[9]) ).

thf(11,plain,
    ( ( more @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ z ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[10]) ).

thf(12,plain,
    ( ( ! [Xx: frac,Xy: frac] :
          ( ( ( ts @ ( num @ Xx ) @ ( den @ Xy ) )
            = ( ts @ ( num @ Xy ) @ ( den @ Xx ) ) )
         => ( ( ts @ ( num @ Xy ) @ ( den @ Xx ) )
            = ( ts @ ( num @ Xx ) @ ( den @ Xy ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1]) ).

thf(13,plain,
    ( ( ! [Xx: nat,Xy: nat,Xz: nat] :
          ( ( ts @ ( ts @ Xx @ Xy ) @ Xz )
          = ( ts @ Xx @ ( ts @ Xy @ Xz ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2]) ).

thf(14,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( ts @ Xx @ Xy )
          = ( ts @ Xy @ Xx ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(15,plain,
    ( ( ! [Xx: nat,Xy: nat,Xz: nat] :
          ( ( more @ Xx @ Xy )
         => ( more @ ( ts @ Xz @ Xx ) @ ( ts @ Xz @ Xy ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4]) ).

thf(16,plain,
    ( ( ! [Xx: nat,Xy: nat,Xz: nat] :
          ( ( more @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xz ) )
         => ( more @ Xx @ Xy ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5]) ).

thf(17,plain,
    ( ( ( ts @ ( num @ y ) @ ( den @ u ) )
      = ( ts @ ( num @ u ) @ ( den @ y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6]) ).

thf(18,plain,
    ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
      = ( ts @ ( num @ z ) @ ( den @ x ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7]) ).

thf(19,plain,
    ( ( more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8]) ).

thf(20,plain,
    ( ( ~ ( more @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ z ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[11]) ).

thf(21,plain,
    ( ( ! [Xx: frac,Xy: frac] :
          ( ( ( ts @ ( num @ Xx ) @ ( den @ Xy ) )
           != ( ts @ ( num @ Xy ) @ ( den @ Xx ) ) )
          | ( ( ts @ ( num @ Xy ) @ ( den @ Xx ) )
            = ( ts @ ( num @ Xx ) @ ( den @ Xy ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[12]) ).

thf(22,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ~ ( more @ Xx @ Xy )
          | ! [Xz: nat] : ( more @ ( ts @ Xz @ Xx ) @ ( ts @ Xz @ Xy ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[15]) ).

thf(23,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ! [Xz: nat] :
              ~ ( more @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xz ) )
          | ( more @ Xx @ Xy ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[16]) ).

thf(24,plain,
    ( ( more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) )
    = $true ),
    inference(copy,[status(thm)],[19]) ).

thf(25,plain,
    ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
      = ( ts @ ( num @ z ) @ ( den @ x ) ) )
    = $true ),
    inference(copy,[status(thm)],[18]) ).

thf(26,plain,
    ( ( ( ts @ ( num @ y ) @ ( den @ u ) )
      = ( ts @ ( num @ u ) @ ( den @ y ) ) )
    = $true ),
    inference(copy,[status(thm)],[17]) ).

thf(27,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ! [Xz: nat] :
              ~ ( more @ ( ts @ Xx @ Xz ) @ ( ts @ Xy @ Xz ) )
          | ( more @ Xx @ Xy ) ) )
    = $true ),
    inference(copy,[status(thm)],[23]) ).

thf(28,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ~ ( more @ Xx @ Xy )
          | ! [Xz: nat] : ( more @ ( ts @ Xz @ Xx ) @ ( ts @ Xz @ Xy ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[22]) ).

thf(29,plain,
    ( ( ! [Xx: nat,Xy: nat] :
          ( ( ts @ Xx @ Xy )
          = ( ts @ Xy @ Xx ) ) )
    = $true ),
    inference(copy,[status(thm)],[14]) ).

thf(30,plain,
    ( ( ! [Xx: nat,Xy: nat,Xz: nat] :
          ( ( ts @ ( ts @ Xx @ Xy ) @ Xz )
          = ( ts @ Xx @ ( ts @ Xy @ Xz ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[13]) ).

thf(31,plain,
    ( ( ! [Xx: frac,Xy: frac] :
          ( ( ( ts @ ( num @ Xx ) @ ( den @ Xy ) )
           != ( ts @ ( num @ Xy ) @ ( den @ Xx ) ) )
          | ( ( ts @ ( num @ Xy ) @ ( den @ Xx ) )
            = ( ts @ ( num @ Xx ) @ ( den @ Xy ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[21]) ).

thf(32,plain,
    ( ( ~ ( more @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[20]) ).

thf(33,plain,
    ! [SV1: nat] :
      ( ( ! [SY48: nat] :
            ( ! [SY49: nat] :
                ~ ( more @ ( ts @ SV1 @ SY49 ) @ ( ts @ SY48 @ SY49 ) )
            | ( more @ SV1 @ SY48 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(34,plain,
    ! [SV2: nat] :
      ( ( ! [SY50: nat] :
            ( ~ ( more @ SV2 @ SY50 )
            | ! [SY51: nat] : ( more @ ( ts @ SY51 @ SV2 ) @ ( ts @ SY51 @ SY50 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(35,plain,
    ! [SV3: nat] :
      ( ( ! [SY52: nat] :
            ( ( ts @ SV3 @ SY52 )
            = ( ts @ SY52 @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[29]) ).

thf(36,plain,
    ! [SV4: nat] :
      ( ( ! [SY53: nat,SY54: nat] :
            ( ( ts @ ( ts @ SV4 @ SY53 ) @ SY54 )
            = ( ts @ SV4 @ ( ts @ SY53 @ SY54 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[30]) ).

thf(37,plain,
    ! [SV5: frac] :
      ( ( ! [SY55: frac] :
            ( ( ( ts @ ( num @ SV5 ) @ ( den @ SY55 ) )
             != ( ts @ ( num @ SY55 ) @ ( den @ SV5 ) ) )
            | ( ( ts @ ( num @ SY55 ) @ ( den @ SV5 ) )
              = ( ts @ ( num @ SV5 ) @ ( den @ SY55 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[31]) ).

thf(38,plain,
    ( ( more @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ z ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(39,plain,
    ! [SV6: nat,SV1: nat] :
      ( ( ! [SY56: nat] :
            ~ ( more @ ( ts @ SV1 @ SY56 ) @ ( ts @ SV6 @ SY56 ) )
        | ( more @ SV1 @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(40,plain,
    ! [SV7: nat,SV2: nat] :
      ( ( ~ ( more @ SV2 @ SV7 )
        | ! [SY57: nat] : ( more @ ( ts @ SY57 @ SV2 ) @ ( ts @ SY57 @ SV7 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[34]) ).

thf(41,plain,
    ! [SV8: nat,SV3: nat] :
      ( ( ( ts @ SV3 @ SV8 )
        = ( ts @ SV8 @ SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[35]) ).

thf(42,plain,
    ! [SV9: nat,SV4: nat] :
      ( ( ! [SY58: nat] :
            ( ( ts @ ( ts @ SV4 @ SV9 ) @ SY58 )
            = ( ts @ SV4 @ ( ts @ SV9 @ SY58 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(43,plain,
    ! [SV10: frac,SV5: frac] :
      ( ( ( ( ts @ ( num @ SV5 ) @ ( den @ SV10 ) )
         != ( ts @ ( num @ SV10 ) @ ( den @ SV5 ) ) )
        | ( ( ts @ ( num @ SV10 ) @ ( den @ SV5 ) )
          = ( ts @ ( num @ SV5 ) @ ( den @ SV10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[37]) ).

thf(44,plain,
    ! [SV6: nat,SV1: nat] :
      ( ( ( ! [SY56: nat] :
              ~ ( more @ ( ts @ SV1 @ SY56 ) @ ( ts @ SV6 @ SY56 ) ) )
        = $true )
      | ( ( more @ SV1 @ SV6 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[39]) ).

thf(45,plain,
    ! [SV7: nat,SV2: nat] :
      ( ( ( ~ ( more @ SV2 @ SV7 ) )
        = $true )
      | ( ( ! [SY57: nat] : ( more @ ( ts @ SY57 @ SV2 ) @ ( ts @ SY57 @ SV7 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[40]) ).

thf(46,plain,
    ! [SV11: nat,SV9: nat,SV4: nat] :
      ( ( ( ts @ ( ts @ SV4 @ SV9 ) @ SV11 )
        = ( ts @ SV4 @ ( ts @ SV9 @ SV11 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(47,plain,
    ! [SV10: frac,SV5: frac] :
      ( ( ( ( ( ts @ ( num @ SV5 ) @ ( den @ SV10 ) )
           != ( ts @ ( num @ SV10 ) @ ( den @ SV5 ) ) ) )
        = $true )
      | ( ( ( ts @ ( num @ SV10 ) @ ( den @ SV5 ) )
          = ( ts @ ( num @ SV5 ) @ ( den @ SV10 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[43]) ).

thf(48,plain,
    ! [SV6: nat,SV12: nat,SV1: nat] :
      ( ( ( ~ ( more @ ( ts @ SV1 @ SV12 ) @ ( ts @ SV6 @ SV12 ) ) )
        = $true )
      | ( ( more @ SV1 @ SV6 )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[44]) ).

thf(49,plain,
    ! [SV7: nat,SV2: nat] :
      ( ( ( more @ SV2 @ SV7 )
        = $false )
      | ( ( ! [SY57: nat] : ( more @ ( ts @ SY57 @ SV2 ) @ ( ts @ SY57 @ SV7 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[45]) ).

thf(50,plain,
    ! [SV10: frac,SV5: frac] :
      ( ( ( ( ts @ ( num @ SV5 ) @ ( den @ SV10 ) )
          = ( ts @ ( num @ SV10 ) @ ( den @ SV5 ) ) )
        = $false )
      | ( ( ( ts @ ( num @ SV10 ) @ ( den @ SV5 ) )
          = ( ts @ ( num @ SV5 ) @ ( den @ SV10 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[47]) ).

thf(51,plain,
    ! [SV6: nat,SV12: nat,SV1: nat] :
      ( ( ( more @ ( ts @ SV1 @ SV12 ) @ ( ts @ SV6 @ SV12 ) )
        = $false )
      | ( ( more @ SV1 @ SV6 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[48]) ).

thf(52,plain,
    ! [SV7: nat,SV2: nat,SV13: nat] :
      ( ( ( more @ ( ts @ SV13 @ SV2 ) @ ( ts @ SV13 @ SV7 ) )
        = $true )
      | ( ( more @ SV2 @ SV7 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[49]) ).

thf(57,plain,
    ! [SV14: nat,SV15: nat] :
      ( ( ( ts @ SV15 @ SV14 )
        = ( ts @ SV14 @ SV15 ) )
      = $true ),
    inference(rename,[status(thm)],[41]) ).

thf(59,plain,
    ! [SV16: nat,SV17: nat,SV18: nat] :
      ( ( ( ts @ ( ts @ SV18 @ SV17 ) @ SV16 )
        = ( ts @ SV18 @ ( ts @ SV17 @ SV16 ) ) )
      = $true ),
    inference(rename,[status(thm)],[46]) ).

thf(61,plain,
    ! [SV19: frac,SV20: frac] :
      ( ( ( ( ts @ ( num @ SV20 ) @ ( den @ SV19 ) )
          = ( ts @ ( num @ SV19 ) @ ( den @ SV20 ) ) )
        = $false )
      | ( ( ( ts @ ( num @ SV19 ) @ ( den @ SV20 ) )
          = ( ts @ ( num @ SV20 ) @ ( den @ SV19 ) ) )
        = $true ) ),
    inference(rename,[status(thm)],[50]) ).

thf(67,plain,
    ! [SV19: frac,SV20: frac] :
      ( ( ( ( ( ts @ ( num @ SV20 ) @ ( den @ SV19 ) )
            = ( ts @ ( num @ SV19 ) @ ( den @ SV20 ) ) )
          = ( ( ts @ ( num @ y ) @ ( den @ u ) )
            = ( ts @ ( num @ u ) @ ( den @ y ) ) ) )
        = $false )
      | ( ( ( ts @ ( num @ SV19 ) @ ( den @ SV20 ) )
          = ( ts @ ( num @ SV20 ) @ ( den @ SV19 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[61,26]) ).

thf(68,plain,
    ! [SV19: frac,SV20: frac] :
      ( ( ( ( ( ts @ ( num @ SV20 ) @ ( den @ SV19 ) )
            = ( ts @ ( num @ SV19 ) @ ( den @ SV20 ) ) )
          = ( ( ts @ ( num @ x ) @ ( den @ z ) )
            = ( ts @ ( num @ z ) @ ( den @ x ) ) ) )
        = $false )
      | ( ( ( ts @ ( num @ SV19 ) @ ( den @ SV20 ) )
          = ( ts @ ( num @ SV20 ) @ ( den @ SV19 ) ) )
        = $true ) ),
    inference(res,[status(thm)],[61,25]) ).

thf(70,plain,
    ( ( ( ts @ ( num @ x ) @ ( den @ z ) )
      = ( ts @ ( num @ z ) @ ( den @ x ) ) )
    = $true ),
    inference(extuni,[status(esa)],[68:[bind(SV20,$thf( z )),bind(SV19,$thf( x ))]]) ).

thf(71,plain,
    ( ( ( ts @ ( num @ z ) @ ( den @ x ) )
      = ( ts @ ( num @ x ) @ ( den @ z ) ) )
    = $true ),
    inference(extuni,[status(esa)],[68:[bind(SV19,$thf( z )),bind(SV20,$thf( x ))]]) ).

thf(72,plain,
    ( ( ( ts @ ( num @ y ) @ ( den @ u ) )
      = ( ts @ ( num @ u ) @ ( den @ y ) ) )
    = $true ),
    inference(extuni,[status(esa)],[67:[bind(SV20,$thf( u )),bind(SV19,$thf( y ))]]) ).

thf(73,plain,
    ( ( ( ts @ ( num @ u ) @ ( den @ y ) )
      = ( ts @ ( num @ y ) @ ( den @ u ) ) )
    = $true ),
    inference(extuni,[status(esa)],[67:[bind(SV19,$thf( u )),bind(SV20,$thf( y ))]]) ).

thf(79,plain,
    ! [SV21: nat,SV22: nat,SV23: nat] :
      ( ( ( more @ ( ts @ SV23 @ SV22 ) @ ( ts @ SV21 @ SV22 ) )
        = $false )
      | ( ( more @ SV23 @ SV21 )
        = $true ) ),
    inference(rename,[status(thm)],[51]) ).

thf(86,plain,
    ! [SV21: nat,SV22: nat,SV23: nat] :
      ( ( ( ( more @ SV23 @ SV21 )
          = ( more @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ ( ts @ ( num @ u ) @ ( den @ z ) ) ) )
        = $false )
      | ( ( more @ ( ts @ SV23 @ SV22 ) @ ( ts @ SV21 @ SV22 ) )
        = $false ) ),
    inference(res,[status(thm)],[79,38]) ).

thf(90,plain,
    ! [SV22: nat] :
      ( ( more @ ( ts @ ( ts @ ( num @ z ) @ ( den @ u ) ) @ SV22 ) @ ( ts @ ( ts @ ( num @ u ) @ ( den @ z ) ) @ SV22 ) )
      = $false ),
    inference(extuni,[status(esa)],[86:[bind(SV21,$thf( ts @ ( num @ u ) @ ( den @ z ) )),bind(SV23,$thf( ts @ ( num @ z ) @ ( den @ u ) ))]]) ).

thf(91,plain,
    ! [SV24: nat,SV25: nat,SV26: nat] :
      ( ( ( more @ ( ts @ SV26 @ SV25 ) @ ( ts @ SV26 @ SV24 ) )
        = $true )
      | ( ( more @ SV25 @ SV24 )
        = $false ) ),
    inference(rename,[status(thm)],[52]) ).

thf(94,plain,
    ! [SV24: nat,SV25: nat,SV26: nat,SV21: nat,SV22: nat,SV23: nat] :
      ( ( ( ( more @ SV25 @ SV24 )
          = ( more @ SV23 @ SV21 ) )
        = $false )
      | ( ( more @ ( ts @ SV26 @ SV25 ) @ ( ts @ SV26 @ SV24 ) )
        = $true )
      | ( ( more @ ( ts @ SV23 @ SV22 ) @ ( ts @ SV21 @ SV22 ) )
        = $false ) ),
    inference(res,[status(thm)],[91,79]) ).

thf(95,plain,
    ! [SV24: nat,SV25: nat,SV26: nat,SV21: nat,SV22: nat,SV23: nat] :
      ( ( ( ( more @ ( ts @ SV26 @ SV25 ) @ ( ts @ SV26 @ SV24 ) )
          = ( more @ ( ts @ SV23 @ SV22 ) @ ( ts @ SV21 @ SV22 ) ) )
        = $false )
      | ( ( more @ SV25 @ SV24 )
        = $false )
      | ( ( more @ SV23 @ SV21 )
        = $true ) ),
    inference(res,[status(thm)],[91,79]) ).

thf(103,plain,
    ! [SV24: nat,SV25: nat,SV26: nat] :
      ( ( ( ( more @ SV25 @ SV24 )
          = ( more @ ( ts @ ( num @ x ) @ ( den @ y ) ) @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
        = $false )
      | ( ( more @ ( ts @ SV26 @ SV25 ) @ ( ts @ SV26 @ SV24 ) )
        = $true ) ),
    inference(res,[status(thm)],[91,24]) ).

thf(104,plain,
    ! [SV26: nat] :
      ( ( more @ ( ts @ SV26 @ ( ts @ ( num @ x ) @ ( den @ y ) ) ) @ ( ts @ SV26 @ ( ts @ ( num @ y ) @ ( den @ x ) ) ) )
      = $true ),
    inference(extuni,[status(esa)],[103:[bind(SV24,$thf( ts @ ( num @ y ) @ ( den @ x ) )),bind(SV25,$thf( ts @ ( num @ x ) @ ( den @ y ) ))]]) ).

thf(105,plain,
    ! [SV22: nat,SV21: nat] :
      ( ( ( more @ SV21 @ SV21 )
        = $true )
      | ( ( more @ SV22 @ SV22 )
        = $false ) ),
    inference(extuni,[status(esa)],[95:[bind(SV24,$thf( SV22 )),bind(SV23,$thf( SV21 )),bind(SV25,$thf( SV22 )),bind(SV26,$thf( SV21 ))]]) ).

thf(106,plain,
    ! [SV26: nat,SV21: nat,SV22: nat,SV23: nat] :
      ( ( ( more @ ( ts @ SV23 @ SV22 ) @ ( ts @ SV21 @ SV22 ) )
        = $false )
      | ( ( more @ ( ts @ SV26 @ SV23 ) @ ( ts @ SV26 @ SV21 ) )
        = $true ) ),
    inference(extuni,[status(esa)],[94:[bind(SV24,$thf( SV21 )),bind(SV25,$thf( SV23 ))]]) ).

thf(107,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[24,106,105,104,91,90,79,73,72,71,70,61,59,57,38,26,25]) ).

thf(108,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[107]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM737^1 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34  % Computer : n008.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Wed Jul  6 03:14:38 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  
% 0.14/0.35   No.of.Axioms: 8
% 0.14/0.35  
% 0.14/0.35   Length.of.Defs: 0
% 0.14/0.35  
% 0.14/0.35   Contains.Choice.Funs: false
% 0.14/0.35  (rf:0,axioms:8,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:10,loop_count:0,foatp_calls:0,translation:fof_full)..eprover: CPU time limit exceeded, terminating
% 25.26/25.43  .eprover: CPU time limit exceeded, terminating
% 50.32/50.51  .....eprover: CPU time limit exceeded, terminating
% 74.68/74.88  .
% 75.06/75.25  (rf:0,axioms:8,ps:2,u:1,ude:false,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:10,loop_count:0,foatp_calls:0,translation:fof_full)..eprover: CPU time limit exceeded, terminating
% 100.06/100.36  .eprover: CPU time limit exceeded, terminating
% 125.18/125.44  .....eprover: CPU time limit exceeded, terminating
% 150.19/150.41  
% 150.19/150.41  (rf:0,axioms:8,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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:10,loop_count:0,foatp_calls:0,translation:fof_full)...eprover: CPU time limit exceeded, terminating
% 175.27/175.53  ..
% 177.40/177.67  
% 177.40/177.67  ********************************
% 177.40/177.67  *   All subproblems solved!    *
% 177.40/177.67  ********************************
% 177.40/177.67  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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:107,loop_count:10,foatp_calls:2,translation:fof_full)
% 177.40/177.68  
% 177.40/177.68  %**** Beginning of derivation protocol ****
% 177.40/177.68  % SZS output start CNFRefutation
% See solution above
% 177.40/177.68  
% 177.40/177.68  %**** End of derivation protocol ****
% 177.40/177.68  %**** no. of clauses in derivation: 73 ****
% 177.40/177.68  %**** clause counter: 107 ****
% 177.40/177.68  
% 177.40/177.68  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:8,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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:107,loop_count:10,foatp_calls:2,translation:fof_full)
%------------------------------------------------------------------------------