TSTP Solution File: ITP133^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : ITP133^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HgqkEC0hyl true

% Computer : n013.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  : 300s
% DateTime : Thu Aug 31 05:22:23 EDT 2023

% Result   : Theorem 21.01s 3.52s
% Output   : Refutation 21.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   18
% Syntax   : Number of formulae    :  150 (  28 unt;  12 typ;   0 def)
%            Number of atoms       :  359 ( 134 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  941 (  89   ~; 212   |;   4   &; 631   @)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   68 (  19   ^;  49   !;   0   ?;  68   :)

% Comments : 
%------------------------------------------------------------------------------
thf(nat_type,type,
    nat: $tType ).

thf(set_nat_type,type,
    set_nat: $tType ).

thf(sk__18_type,type,
    sk__18: nat ).

thf(times_times_nat_type,type,
    times_times_nat: nat > nat > nat ).

thf(ord_less_eq_nat_type,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(set_ord_atMost_nat_type,type,
    set_ord_atMost_nat: nat > set_nat ).

thf(groups1842438620at_nat_type,type,
    groups1842438620at_nat: ( nat > nat ) > set_nat > nat ).

thf(zero_zero_nat_type,type,
    zero_zero_nat: nat ).

thf(one_one_nat_type,type,
    one_one_nat: nat ).

thf(sk__17_type,type,
    sk__17: nat ).

thf('#sk649_type',type,
    '#sk649': nat ).

thf(p_type,type,
    p: nat > nat ).

thf(fact_75_not__one__le__zero,axiom,
    ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).

thf(zip_derived_cl110,plain,
    ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_75_not__one__le__zero]) ).

thf(conj_0,conjecture,
    ( ( ( ( groups1842438620at_nat
          @ ^ [I2: nat] : ( times_times_nat @ ( p @ I2 ) @ I2 )
          @ ( set_ord_atMost_nat @ zero_zero_nat ) )
        = zero_zero_nat )
      & ! [I2: nat] :
          ( ( ( p @ I2 )
           != zero_zero_nat )
         => ( ( ord_less_eq_nat @ one_one_nat @ I2 )
            & ( ord_less_eq_nat @ I2 @ zero_zero_nat ) ) ) )
  <=> ! [I2: nat] :
        ( ( p @ I2 )
        = zero_zero_nat ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( ( ( ( groups1842438620at_nat
            @ ^ [I2: nat] : ( times_times_nat @ ( p @ I2 ) @ I2 )
            @ ( set_ord_atMost_nat @ zero_zero_nat ) )
          = zero_zero_nat )
        & ! [I2: nat] :
            ( ( ( p @ I2 )
             != zero_zero_nat )
           => ( ( ord_less_eq_nat @ one_one_nat @ I2 )
              & ( ord_less_eq_nat @ I2 @ zero_zero_nat ) ) ) )
    <=> ! [I2: nat] :
          ( ( p @ I2 )
          = zero_zero_nat ) ),
    inference('cnf.neg',[status(esa)],[conj_0]) ).

thf(zip_derived_cl181,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ X1 @ zero_zero_nat )
      | ( ( p @ X1 )
        = zero_zero_nat ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl695,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(condensation,[status(thm)],[zip_derived_cl181]) ).

thf(zip_derived_cl695_001,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(condensation,[status(thm)],[zip_derived_cl181]) ).

thf(zip_derived_cl695_002,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(condensation,[status(thm)],[zip_derived_cl181]) ).

thf(fact_0_sum_Oneutral__const,axiom,
    ! [A: set_nat] :
      ( ( groups1842438620at_nat
        @ ^ [Uu: nat] : zero_zero_nat
        @ A )
      = zero_zero_nat ) ).

thf(zip_derived_cl0,plain,
    ! [X0: set_nat] :
      ( ( groups1842438620at_nat
        @ ^ [Y0: nat] : zero_zero_nat
        @ X0 )
      = zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_0_sum_Oneutral__const]) ).

thf(zip_derived_cl183,plain,
    ( ( ( p @ sk__17 )
     != zero_zero_nat )
    | ( ( p @ sk__18 )
     != zero_zero_nat )
    | ( ( groups1842438620at_nat
        @ ^ [Y0: nat] : ( times_times_nat @ ( p @ Y0 ) @ Y0 )
        @ ( set_ord_atMost_nat @ zero_zero_nat ) )
     != zero_zero_nat ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl186,plain,
    ( ( ( ^ [Y0: nat] : zero_zero_nat )
     != ( ^ [Y0: nat] : ( times_times_nat @ ( p @ Y0 ) @ Y0 ) ) )
    | ( ( p @ sk__17 )
     != zero_zero_nat )
    | ( ( p @ sk__18 )
     != zero_zero_nat )
    | ( zero_zero_nat != zero_zero_nat ) ),
    inference(ext_sup,[status(thm)],[zip_derived_cl0,zip_derived_cl183]) ).

thf(zip_derived_cl187,plain,
    ( ( ( p @ sk__18 )
     != zero_zero_nat )
    | ( ( p @ sk__17 )
     != zero_zero_nat )
    | ( ( ^ [Y0: nat] : zero_zero_nat )
     != ( ^ [Y0: nat] : ( times_times_nat @ ( p @ Y0 ) @ Y0 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl186]) ).

thf(zip_derived_cl696,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( ( ^ [Y0: nat] : zero_zero_nat )
     != ( ^ [Y0: nat] : ( times_times_nat @ ( p @ Y0 ) @ Y0 ) ) )
    | ( ( p @ sk__17 )
     != zero_zero_nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl695,zip_derived_cl187]) ).

thf(zip_derived_cl704,plain,
    ( ( ( p @ sk__17 )
     != zero_zero_nat )
    | ( ( ^ [Y0: nat] : zero_zero_nat )
     != ( ^ [Y0: nat] : ( times_times_nat @ ( p @ Y0 ) @ Y0 ) ) )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl696]) ).

thf(zip_derived_cl744,plain,
    ( ( ( p @ sk__17 )
     != zero_zero_nat )
    | ( zero_zero_nat
     != ( times_times_nat @ ( p @ '#sk649' ) @ '#sk649' ) )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference(neg_ext,[status(thm)],[zip_derived_cl704]) ).

thf(fact_143_mult_Ocommute,axiom,
    ! [A4: nat,B4: nat] :
      ( ( times_times_nat @ A4 @ B4 )
      = ( times_times_nat @ B4 @ A4 ) ) ).

thf(zip_derived_cl132,plain,
    ! [X0: nat,X1: nat] :
      ( ( times_times_nat @ X1 @ X0 )
      = ( times_times_nat @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[fact_143_mult_Ocommute]) ).

thf(zip_derived_cl745,plain,
    ( ( ( p @ sk__17 )
     != zero_zero_nat )
    | ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference(demod,[status(thm)],[zip_derived_cl744,zip_derived_cl132]) ).

thf(zip_derived_cl1980,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl695,zip_derived_cl745]) ).

thf(zip_derived_cl1995,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1980]) ).

thf(zip_derived_cl2956,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ zero_zero_nat ) )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl695,zip_derived_cl1995]) ).

thf(fact_14_mult__zero__right,axiom,
    ! [A2: nat] :
      ( ( times_times_nat @ A2 @ zero_zero_nat )
      = zero_zero_nat ) ).

thf(zip_derived_cl22,plain,
    ! [X0: nat] :
      ( ( times_times_nat @ X0 @ zero_zero_nat )
      = zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_14_mult__zero__right]) ).

thf(zip_derived_cl2977,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference(demod,[status(thm)],[zip_derived_cl2956,zip_derived_cl22]) ).

thf(zip_derived_cl2978,plain,
    ( ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2977]) ).

thf(fact_45_bot__nat__0_Oextremum__uniqueI,axiom,
    ! [A2: nat] :
      ( ( ord_less_eq_nat @ A2 @ zero_zero_nat )
     => ( A2 = zero_zero_nat ) ) ).

thf(zip_derived_cl77,plain,
    ! [X0: nat] :
      ( ( X0 = zero_zero_nat )
      | ~ ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(cnf,[status(esa)],[fact_45_bot__nat__0_Oextremum__uniqueI]) ).

thf(zip_derived_cl3638,plain,
    ( ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( sk__17 = zero_zero_nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2978,zip_derived_cl77]) ).

thf(zip_derived_cl77_003,plain,
    ! [X0: nat] :
      ( ( X0 = zero_zero_nat )
      | ~ ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(cnf,[status(esa)],[fact_45_bot__nat__0_Oextremum__uniqueI]) ).

thf(zip_derived_cl3659,plain,
    ( ( sk__17 = zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( sk__18 = zero_zero_nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3638,zip_derived_cl77]) ).

thf(zip_derived_cl695_004,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(condensation,[status(thm)],[zip_derived_cl181]) ).

thf(zip_derived_cl182,plain,
    ! [X0: nat,X1: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ one_one_nat @ X1 )
      | ( ( p @ X1 )
        = zero_zero_nat ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl712,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ one_one_nat @ X0 ) ),
    inference(condensation,[status(thm)],[zip_derived_cl182]) ).

thf(zip_derived_cl745_005,plain,
    ( ( ( p @ sk__17 )
     != zero_zero_nat )
    | ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference(demod,[status(thm)],[zip_derived_cl744,zip_derived_cl132]) ).

thf(zip_derived_cl1979,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl712,zip_derived_cl745]) ).

thf(zip_derived_cl1994,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1979]) ).

thf(zip_derived_cl2418,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ zero_zero_nat ) )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl695,zip_derived_cl1994]) ).

thf(zip_derived_cl22_006,plain,
    ! [X0: nat] :
      ( ( times_times_nat @ X0 @ zero_zero_nat )
      = zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_14_mult__zero__right]) ).

thf(zip_derived_cl2437,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference(demod,[status(thm)],[zip_derived_cl2418,zip_derived_cl22]) ).

thf(zip_derived_cl2438,plain,
    ( ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2437]) ).

thf(zip_derived_cl3902,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat )
    | ( sk__18 = zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference('sup+',[status(thm)],[zip_derived_cl3659,zip_derived_cl2438]) ).

thf(zip_derived_cl110_007,plain,
    ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_75_not__one__le__zero]) ).

thf(zip_derived_cl3914,plain,
    ( ( sk__18 = zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference(demod,[status(thm)],[zip_derived_cl3902,zip_derived_cl110]) ).

thf(zip_derived_cl3915,plain,
    ( ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( sk__18 = zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3914]) ).

thf(zip_derived_cl77_008,plain,
    ! [X0: nat] :
      ( ( X0 = zero_zero_nat )
      | ~ ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(cnf,[status(esa)],[fact_45_bot__nat__0_Oextremum__uniqueI]) ).

thf(zip_derived_cl4091,plain,
    ( ( sk__18 = zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat ) ),
    inference(clc,[status(thm)],[zip_derived_cl3915,zip_derived_cl77]) ).

thf(zip_derived_cl4091_009,plain,
    ( ( sk__18 = zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat ) ),
    inference(clc,[status(thm)],[zip_derived_cl3915,zip_derived_cl77]) ).

thf(zip_derived_cl695_010,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(condensation,[status(thm)],[zip_derived_cl181]) ).

thf(zip_derived_cl695_011,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(condensation,[status(thm)],[zip_derived_cl181]) ).

thf(zip_derived_cl712_012,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ one_one_nat @ X0 ) ),
    inference(condensation,[status(thm)],[zip_derived_cl182]) ).

thf(zip_derived_cl187_013,plain,
    ( ( ( p @ sk__18 )
     != zero_zero_nat )
    | ( ( p @ sk__17 )
     != zero_zero_nat )
    | ( ( ^ [Y0: nat] : zero_zero_nat )
     != ( ^ [Y0: nat] : ( times_times_nat @ ( p @ Y0 ) @ Y0 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl186]) ).

thf(zip_derived_cl713,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( ( ^ [Y0: nat] : zero_zero_nat )
     != ( ^ [Y0: nat] : ( times_times_nat @ ( p @ Y0 ) @ Y0 ) ) )
    | ( ( p @ sk__17 )
     != zero_zero_nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl712,zip_derived_cl187]) ).

thf(zip_derived_cl721,plain,
    ( ( ( p @ sk__17 )
     != zero_zero_nat )
    | ( ( ^ [Y0: nat] : zero_zero_nat )
     != ( ^ [Y0: nat] : ( times_times_nat @ ( p @ Y0 ) @ Y0 ) ) )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl713]) ).

thf(zip_derived_cl748,plain,
    ( ( ( p @ sk__17 )
     != zero_zero_nat )
    | ( zero_zero_nat
     != ( times_times_nat @ ( p @ '#sk649' ) @ '#sk649' ) )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference(neg_ext,[status(thm)],[zip_derived_cl721]) ).

thf(zip_derived_cl132_014,plain,
    ! [X0: nat,X1: nat] :
      ( ( times_times_nat @ X1 @ X0 )
      = ( times_times_nat @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[fact_143_mult_Ocommute]) ).

thf(zip_derived_cl749,plain,
    ( ( ( p @ sk__17 )
     != zero_zero_nat )
    | ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference(demod,[status(thm)],[zip_derived_cl748,zip_derived_cl132]) ).

thf(zip_derived_cl2015,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl695,zip_derived_cl749]) ).

thf(zip_derived_cl2027,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2015]) ).

thf(zip_derived_cl7482,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ zero_zero_nat ) )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl695,zip_derived_cl2027]) ).

thf(zip_derived_cl22_015,plain,
    ! [X0: nat] :
      ( ( times_times_nat @ X0 @ zero_zero_nat )
      = zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_14_mult__zero__right]) ).

thf(zip_derived_cl7595,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference(demod,[status(thm)],[zip_derived_cl7482,zip_derived_cl22]) ).

thf(zip_derived_cl7596,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl7595]) ).

thf(zip_derived_cl8004,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat ) ),
    inference('sup+',[status(thm)],[zip_derived_cl4091,zip_derived_cl7596]) ).

thf(zip_derived_cl110_016,plain,
    ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_75_not__one__le__zero]) ).

thf(zip_derived_cl8019,plain,
    ( ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat ) ),
    inference(demod,[status(thm)],[zip_derived_cl8004,zip_derived_cl110]) ).

thf(zip_derived_cl8020,plain,
    ( ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8019]) ).

thf(zip_derived_cl77_017,plain,
    ! [X0: nat] :
      ( ( X0 = zero_zero_nat )
      | ~ ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(cnf,[status(esa)],[fact_45_bot__nat__0_Oextremum__uniqueI]) ).

thf(zip_derived_cl8028,plain,
    ( ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( sk__17 = zero_zero_nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl8020,zip_derived_cl77]) ).

thf(zip_derived_cl695_018,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(condensation,[status(thm)],[zip_derived_cl181]) ).

thf(zip_derived_cl712_019,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ one_one_nat @ X0 ) ),
    inference(condensation,[status(thm)],[zip_derived_cl182]) ).

thf(zip_derived_cl749_020,plain,
    ( ( ( p @ sk__17 )
     != zero_zero_nat )
    | ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference(demod,[status(thm)],[zip_derived_cl748,zip_derived_cl132]) ).

thf(zip_derived_cl2014,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl712,zip_derived_cl749]) ).

thf(zip_derived_cl2026,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2014]) ).

thf(zip_derived_cl6984,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ zero_zero_nat ) )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl695,zip_derived_cl2026]) ).

thf(zip_derived_cl22_021,plain,
    ! [X0: nat] :
      ( ( times_times_nat @ X0 @ zero_zero_nat )
      = zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_14_mult__zero__right]) ).

thf(zip_derived_cl7009,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6984,zip_derived_cl22]) ).

thf(zip_derived_cl7010,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl7009]) ).

thf(zip_derived_cl8059,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl8028,zip_derived_cl7010]) ).

thf(zip_derived_cl110_022,plain,
    ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_75_not__one__le__zero]) ).

thf(zip_derived_cl8077,plain,
    ( ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference(demod,[status(thm)],[zip_derived_cl8059,zip_derived_cl110]) ).

thf(zip_derived_cl8078,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8077]) ).

thf(zip_derived_cl8096,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat ) ),
    inference('sup+',[status(thm)],[zip_derived_cl4091,zip_derived_cl8078]) ).

thf(zip_derived_cl8123,plain,
    ( ( ord_less_eq_nat @ '#sk649' @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl8096]) ).

thf(zip_derived_cl110_023,plain,
    ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_75_not__one__le__zero]) ).

thf(zip_derived_cl8146,plain,
    ord_less_eq_nat @ '#sk649' @ zero_zero_nat,
    inference(clc,[status(thm)],[zip_derived_cl8123,zip_derived_cl110]) ).

thf(zip_derived_cl77_024,plain,
    ! [X0: nat] :
      ( ( X0 = zero_zero_nat )
      | ~ ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(cnf,[status(esa)],[fact_45_bot__nat__0_Oextremum__uniqueI]) ).

thf(zip_derived_cl8149,plain,
    '#sk649' = zero_zero_nat,
    inference('sup-',[status(thm)],[zip_derived_cl8146,zip_derived_cl77]) ).

thf(zip_derived_cl712_025,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ one_one_nat @ X0 ) ),
    inference(condensation,[status(thm)],[zip_derived_cl182]) ).

thf(zip_derived_cl1995_026,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1980]) ).

thf(zip_derived_cl2955,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ zero_zero_nat ) )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl712,zip_derived_cl1995]) ).

thf(zip_derived_cl22_027,plain,
    ! [X0: nat] :
      ( ( times_times_nat @ X0 @ zero_zero_nat )
      = zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_14_mult__zero__right]) ).

thf(zip_derived_cl2975,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference(demod,[status(thm)],[zip_derived_cl2955,zip_derived_cl22]) ).

thf(zip_derived_cl2976,plain,
    ( ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2975]) ).

thf(zip_derived_cl77_028,plain,
    ! [X0: nat] :
      ( ( X0 = zero_zero_nat )
      | ~ ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(cnf,[status(esa)],[fact_45_bot__nat__0_Oextremum__uniqueI]) ).

thf(zip_derived_cl3098,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( sk__17 = zero_zero_nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2976,zip_derived_cl77]) ).

thf(zip_derived_cl77_029,plain,
    ! [X0: nat] :
      ( ( X0 = zero_zero_nat )
      | ~ ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(cnf,[status(esa)],[fact_45_bot__nat__0_Oextremum__uniqueI]) ).

thf(zip_derived_cl3124,plain,
    ( ( sk__17 = zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( sk__18 = zero_zero_nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3098,zip_derived_cl77]) ).

thf(zip_derived_cl712_030,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ one_one_nat @ X0 ) ),
    inference(condensation,[status(thm)],[zip_derived_cl182]) ).

thf(zip_derived_cl1994_031,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1979]) ).

thf(zip_derived_cl2417,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ zero_zero_nat ) )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl712,zip_derived_cl1994]) ).

thf(zip_derived_cl22_032,plain,
    ! [X0: nat] :
      ( ( times_times_nat @ X0 @ zero_zero_nat )
      = zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_14_mult__zero__right]) ).

thf(zip_derived_cl2435,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference(demod,[status(thm)],[zip_derived_cl2417,zip_derived_cl22]) ).

thf(zip_derived_cl2436,plain,
    ( ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2435]) ).

thf(zip_derived_cl3150,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat )
    | ( sk__18 = zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference('sup+',[status(thm)],[zip_derived_cl3124,zip_derived_cl2436]) ).

thf(zip_derived_cl110_033,plain,
    ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_75_not__one__le__zero]) ).

thf(zip_derived_cl3159,plain,
    ( ( sk__18 = zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ sk__18 @ zero_zero_nat ) ),
    inference(demod,[status(thm)],[zip_derived_cl3150,zip_derived_cl110]) ).

thf(zip_derived_cl3160,plain,
    ( ( ord_less_eq_nat @ sk__18 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( sk__18 = zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3159]) ).

thf(zip_derived_cl77_034,plain,
    ! [X0: nat] :
      ( ( X0 = zero_zero_nat )
      | ~ ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(cnf,[status(esa)],[fact_45_bot__nat__0_Oextremum__uniqueI]) ).

thf(zip_derived_cl3631,plain,
    ( ( sk__18 = zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' ) ),
    inference(clc,[status(thm)],[zip_derived_cl3160,zip_derived_cl77]) ).

thf(zip_derived_cl3631_035,plain,
    ( ( sk__18 = zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' ) ),
    inference(clc,[status(thm)],[zip_derived_cl3160,zip_derived_cl77]) ).

thf(zip_derived_cl712_036,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ one_one_nat @ X0 ) ),
    inference(condensation,[status(thm)],[zip_derived_cl182]) ).

thf(zip_derived_cl2027_037,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2015]) ).

thf(zip_derived_cl7481,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ zero_zero_nat ) )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl712,zip_derived_cl2027]) ).

thf(zip_derived_cl22_038,plain,
    ! [X0: nat] :
      ( ( times_times_nat @ X0 @ zero_zero_nat )
      = zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_14_mult__zero__right]) ).

thf(zip_derived_cl7593,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference(demod,[status(thm)],[zip_derived_cl7481,zip_derived_cl22]) ).

thf(zip_derived_cl7594,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl7593]) ).

thf(zip_derived_cl7767,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat ) ),
    inference('sup+',[status(thm)],[zip_derived_cl3631,zip_derived_cl7594]) ).

thf(zip_derived_cl110_039,plain,
    ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_75_not__one__le__zero]) ).

thf(zip_derived_cl7784,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ sk__17 @ zero_zero_nat ) ),
    inference(demod,[status(thm)],[zip_derived_cl7767,zip_derived_cl110]) ).

thf(zip_derived_cl7785,plain,
    ( ( ord_less_eq_nat @ sk__17 @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl7784]) ).

thf(zip_derived_cl77_040,plain,
    ! [X0: nat] :
      ( ( X0 = zero_zero_nat )
      | ~ ( ord_less_eq_nat @ X0 @ zero_zero_nat ) ),
    inference(cnf,[status(esa)],[fact_45_bot__nat__0_Oextremum__uniqueI]) ).

thf(zip_derived_cl7794,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( sk__17 = zero_zero_nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl7785,zip_derived_cl77]) ).

thf(zip_derived_cl712_041,plain,
    ! [X0: nat] :
      ( ( ( p @ X0 )
        = zero_zero_nat )
      | ( ord_less_eq_nat @ one_one_nat @ X0 ) ),
    inference(condensation,[status(thm)],[zip_derived_cl182]) ).

thf(zip_derived_cl2026_042,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ ( p @ '#sk649' ) ) )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl2014]) ).

thf(zip_derived_cl6983,plain,
    ( ( zero_zero_nat
     != ( times_times_nat @ '#sk649' @ zero_zero_nat ) )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl712,zip_derived_cl2026]) ).

thf(zip_derived_cl22_043,plain,
    ! [X0: nat] :
      ( ( times_times_nat @ X0 @ zero_zero_nat )
      = zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_14_mult__zero__right]) ).

thf(zip_derived_cl7007,plain,
    ( ( zero_zero_nat != zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference(demod,[status(thm)],[zip_derived_cl6983,zip_derived_cl22]) ).

thf(zip_derived_cl7008,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( ord_less_eq_nat @ one_one_nat @ sk__17 )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl7007]) ).

thf(zip_derived_cl7842,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl7794,zip_derived_cl7008]) ).

thf(zip_derived_cl110_044,plain,
    ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_75_not__one__le__zero]) ).

thf(zip_derived_cl7892,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ sk__18 ) ),
    inference(demod,[status(thm)],[zip_derived_cl7842,zip_derived_cl110]) ).

thf(zip_derived_cl7893,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ sk__18 )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl7892]) ).

thf(zip_derived_cl7941,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ '#sk649' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl3631,zip_derived_cl7893]) ).

thf(zip_derived_cl7956,plain,
    ( ( ord_less_eq_nat @ one_one_nat @ '#sk649' )
    | ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ),
    inference(simplify,[status(thm)],[zip_derived_cl7941]) ).

thf(zip_derived_cl110_045,plain,
    ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ),
    inference(cnf,[status(esa)],[fact_75_not__one__le__zero]) ).

thf(zip_derived_cl7973,plain,
    ord_less_eq_nat @ one_one_nat @ '#sk649',
    inference(clc,[status(thm)],[zip_derived_cl7956,zip_derived_cl110]) ).

thf(zip_derived_cl8173,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl110,zip_derived_cl8149,zip_derived_cl7973]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : ITP133^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.15  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HgqkEC0hyl true
% 0.15/0.37  % Computer : n013.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Sun Aug 27 13:41:02 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.15/0.37  % Running portfolio for 300 s
% 0.15/0.37  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37  % Number of cores: 8
% 0.23/0.37  % Python version: Python 3.6.8
% 0.23/0.38  % Running in HO mode
% 0.24/0.67  % Total configuration time : 828
% 0.24/0.67  % Estimated wc time : 1656
% 0.24/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.24/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.24/0.77  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.24/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.24/0.77  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.24/0.78  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.24/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.24/0.78  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.24/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.44/0.91  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 21.01/3.52  % Solved by lams/40_c_ic.sh.
% 21.01/3.52  % done 568 iterations in 2.692s
% 21.01/3.52  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 21.01/3.52  % SZS output start Refutation
% See solution above
% 21.01/3.53  
% 21.01/3.53  
% 21.01/3.53  % Terminating...
% 22.36/3.64  % Runner terminated.
% 22.36/3.64  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------