TSTP Solution File: NUM648^4 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM648^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CjGb1bh89q true

% Computer : n012.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 12:43:04 EDT 2023

% Result   : Theorem 40.19s 5.71s
% Output   : Refutation 40.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   78 (  35 unt;  15 typ;   0 def)
%            Number of atoms       :  260 (  97 equ;   0 cnn)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :  552 (  56   ~;  26   |;   0   &; 358   @)
%                                         (   0 <=>;  87  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   36 (  36   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;   7 con; 0-3 aty)
%                                         (  25  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  124 (  90   ^;  34   !;   0   ?; 124   :)

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

thf(is_of_type,type,
    is_of: $i > ( $i > $o ) > $o ).

thf(in_type,type,
    in: $i > $i > $o ).

thf(nis_type,type,
    nis: $i > $i > $o ).

thf('#sk6416_type',type,
    '#sk6416': $i ).

thf('#sk6418_type',type,
    '#sk6418': $i ).

thf('#sk6415_type',type,
    '#sk6415': $i ).

thf(n_is_type,type,
    n_is: $i > $i > $o ).

thf(imp_type,type,
    imp: $o > $o > $o ).

thf(all_of_type,type,
    all_of: ( $i > $o ) > ( $i > $o ) > $o ).

thf(d_not_type,type,
    d_not: $o > $o ).

thf(amone_type,type,
    amone: $i > ( $i > $o ) > $o ).

thf(e_is_type,type,
    e_is: $i > $i > $i > $o ).

thf('#sk6417_type',type,
    '#sk6417': $i ).

thf(n_pl_type,type,
    n_pl: $i > $i > $i ).

thf(def_n_is,axiom,
    ( n_is
    = ( e_is @ nat ) ) ).

thf(def_e_is,axiom,
    ( e_is
    = ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ) ).

thf('0',plain,
    ( e_is
    = ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_e_is]) ).

thf('1',plain,
    ( e_is
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( V_2 = V_3 ) ) ),
    define([status(thm)]) ).

thf('2',plain,
    ( n_is
    = ( e_is @ nat ) ),
    inference(simplify_rw_rule,[status(thm)],[def_n_is,'1']) ).

thf('3',plain,
    ( n_is
    = ( e_is @ nat ) ),
    define([status(thm)]) ).

thf(def_amone,axiom,
    ( amone
    = ( ^ [X0: $i,X1: $i > $o] :
          ( all_of
          @ ^ [X2: $i] : ( in @ X2 @ X0 )
          @ ^ [X2: $i] :
              ( all_of
              @ ^ [X3: $i] : ( in @ X3 @ X0 )
              @ ^ [X3: $i] :
                  ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( e_is @ X0 @ X2 @ X3 ) ) ) ) ) ) ) ).

thf(def_all_of,axiom,
    ( all_of
    = ( ^ [X0: $i > $o,X1: $i > $o] :
        ! [X2: $i] :
          ( ( is_of @ X2 @ X0 )
         => ( X1 @ X2 ) ) ) ) ).

thf(def_is_of,axiom,
    ( is_of
    = ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ) ).

thf('4',plain,
    ( is_of
    = ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_is_of]) ).

thf('5',plain,
    ( is_of
    = ( ^ [V_1: $i,V_2: $i > $o] : ( V_2 @ V_1 ) ) ),
    define([status(thm)]) ).

thf('6',plain,
    ( all_of
    = ( ^ [X0: $i > $o,X1: $i > $o] :
        ! [X2: $i] :
          ( ( is_of @ X2 @ X0 )
         => ( X1 @ X2 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_all_of,'5']) ).

thf('7',plain,
    ( all_of
    = ( ^ [V_1: $i > $o,V_2: $i > $o] :
        ! [X4: $i] :
          ( ( is_of @ X4 @ V_1 )
         => ( V_2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf('8',plain,
    ( amone
    = ( ^ [X0: $i,X1: $i > $o] :
          ( all_of
          @ ^ [X2: $i] : ( in @ X2 @ X0 )
          @ ^ [X2: $i] :
              ( all_of
              @ ^ [X3: $i] : ( in @ X3 @ X0 )
              @ ^ [X3: $i] :
                  ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( e_is @ X0 @ X2 @ X3 ) ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_amone,'1','7','5']) ).

thf('9',plain,
    ( amone
    = ( ^ [V_1: $i,V_2: $i > $o] :
          ( all_of
          @ ^ [V_3: $i] : ( in @ V_3 @ V_1 )
          @ ^ [V_4: $i] :
              ( all_of
              @ ^ [V_5: $i] : ( in @ V_5 @ V_1 )
              @ ^ [V_6: $i] :
                  ( ( V_2 @ V_4 )
                 => ( ( V_2 @ V_6 )
                   => ( e_is @ V_1 @ V_4 @ V_6 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(satz8b,conjecture,
    ( all_of
    @ ^ [X0: $i] : ( in @ X0 @ nat )
    @ ^ [X0: $i] :
        ( all_of
        @ ^ [X1: $i] : ( in @ X1 @ nat )
        @ ^ [X1: $i] :
            ( amone @ nat
            @ ^ [X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i] :
      ( ( in @ X4 @ nat )
     => ! [X6: $i] :
          ( ( in @ X6 @ nat )
         => ! [X8: $i] :
              ( ( in @ X8 @ nat )
             => ! [X10: $i] :
                  ( ( in @ X10 @ nat )
                 => ( ( X4
                      = ( n_pl @ X6 @ X8 ) )
                   => ( ( X4
                        = ( n_pl @ X6 @ X10 ) )
                     => ( X8 = X10 ) ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i] :
        ( ( in @ X4 @ nat )
       => ! [X6: $i] :
            ( ( in @ X6 @ nat )
           => ! [X8: $i] :
                ( ( in @ X8 @ nat )
               => ! [X10: $i] :
                    ( ( in @ X10 @ nat )
                   => ( ( X4
                        = ( n_pl @ X6 @ X8 ) )
                     => ( ( X4
                          = ( n_pl @ X6 @ X10 ) )
                       => ( X8 = X10 ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl136,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ nat )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ nat )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ nat )
                     => ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ nat )
                           => ( ( Y0
                                = ( n_pl @ Y1 @ Y2 ) )
                             => ( ( Y0
                                  = ( n_pl @ Y1 @ Y3 ) )
                               => ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl4498,plain,
    ~ ( ( in @ '#sk6415' @ nat )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ nat )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ nat )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ nat )
                       => ( ( '#sk6415'
                            = ( n_pl @ Y0 @ Y1 ) )
                         => ( ( '#sk6415'
                              = ( n_pl @ Y0 @ Y2 ) )
                           => ( Y1 = Y2 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl136]) ).

thf(zip_derived_cl4500,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ nat )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ nat )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ nat )
                     => ( ( '#sk6415'
                          = ( n_pl @ Y0 @ Y1 ) )
                       => ( ( '#sk6415'
                            = ( n_pl @ Y0 @ Y2 ) )
                         => ( Y1 = Y2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4498]) ).

thf(zip_derived_cl4501,plain,
    ~ ( ( in @ '#sk6416' @ nat )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ nat )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ nat )
                 => ( ( '#sk6415'
                      = ( n_pl @ '#sk6416' @ Y0 ) )
                   => ( ( '#sk6415'
                        = ( n_pl @ '#sk6416' @ Y1 ) )
                     => ( Y0 = Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4500]) ).

thf(zip_derived_cl4503,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ nat )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ nat )
               => ( ( '#sk6415'
                    = ( n_pl @ '#sk6416' @ Y0 ) )
                 => ( ( '#sk6415'
                      = ( n_pl @ '#sk6416' @ Y1 ) )
                   => ( Y0 = Y1 ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4501]) ).

thf(zip_derived_cl4504,plain,
    ~ ( ( in @ '#sk6417' @ nat )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ nat )
           => ( ( '#sk6415'
                = ( n_pl @ '#sk6416' @ '#sk6417' ) )
             => ( ( '#sk6415'
                  = ( n_pl @ '#sk6416' @ Y0 ) )
               => ( '#sk6417' = Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4503]) ).

thf(zip_derived_cl4506,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ nat )
         => ( ( '#sk6415'
              = ( n_pl @ '#sk6416' @ '#sk6417' ) )
           => ( ( '#sk6415'
                = ( n_pl @ '#sk6416' @ Y0 ) )
             => ( '#sk6417' = Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4504]) ).

thf(zip_derived_cl4507,plain,
    ~ ( ( in @ '#sk6418' @ nat )
     => ( ( '#sk6415'
          = ( n_pl @ '#sk6416' @ '#sk6417' ) )
       => ( ( '#sk6415'
            = ( n_pl @ '#sk6416' @ '#sk6418' ) )
         => ( '#sk6417' = '#sk6418' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4506]) ).

thf(zip_derived_cl4509,plain,
    ~ ( ( '#sk6415'
        = ( n_pl @ '#sk6416' @ '#sk6417' ) )
     => ( ( '#sk6415'
          = ( n_pl @ '#sk6416' @ '#sk6418' ) )
       => ( '#sk6417' = '#sk6418' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4507]) ).

thf(zip_derived_cl4511,plain,
    ~ ( ( '#sk6415'
        = ( n_pl @ '#sk6416' @ '#sk6418' ) )
     => ( '#sk6417' = '#sk6418' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4509]) ).

thf(zip_derived_cl4513,plain,
    ( '#sk6415'
    = ( n_pl @ '#sk6416' @ '#sk6418' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4511]) ).

thf(zip_derived_cl4515,plain,
    ( '#sk6415'
    = ( n_pl @ '#sk6416' @ '#sk6418' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4513]) ).

thf(zip_derived_cl4510,plain,
    ( '#sk6415'
    = ( n_pl @ '#sk6416' @ '#sk6417' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4509]) ).

thf(zip_derived_cl4512,plain,
    ( '#sk6415'
    = ( n_pl @ '#sk6416' @ '#sk6417' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4510]) ).

thf(def_nis,axiom,
    ( nis
    = ( ^ [X0: $i,X1: $i] : ( d_not @ ( n_is @ X0 @ X1 ) ) ) ) ).

thf(def_d_not,axiom,
    ( d_not
    = ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ) ).

thf(def_imp,axiom,
    ( imp
    = ( ^ [X0: $o,X1: $o] :
          ( X0
         => X1 ) ) ) ).

thf('10',plain,
    ( imp
    = ( ^ [X0: $o,X1: $o] :
          ( X0
         => X1 ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_imp]) ).

thf('11',plain,
    ( imp
    = ( ^ [V_1: $o,V_2: $o] :
          ( V_1
         => V_2 ) ) ),
    define([status(thm)]) ).

thf('12',plain,
    ( d_not
    = ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_d_not,'11']) ).

thf('13',plain,
    ( d_not
    = ( ^ [V_1: $o] : ( imp @ V_1 @ $false ) ) ),
    define([status(thm)]) ).

thf('14',plain,
    ( nis
    = ( ^ [X0: $i,X1: $i] : ( d_not @ ( n_is @ X0 @ X1 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_nis,'3','1','13']) ).

thf('15',plain,
    ( nis
    = ( ^ [V_1: $i,V_2: $i] : ( d_not @ ( n_is @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(satz8,axiom,
    ( all_of
    @ ^ [X0: $i] : ( in @ X0 @ nat )
    @ ^ [X0: $i] :
        ( all_of
        @ ^ [X1: $i] : ( in @ X1 @ nat )
        @ ^ [X1: $i] :
            ( all_of
            @ ^ [X2: $i] : ( in @ X2 @ nat )
            @ ^ [X2: $i] :
                ( ( nis @ X1 @ X2 )
               => ( nis @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X0 @ X2 ) ) ) ) ) ) ).

thf(zf_stmt_2,axiom,
    ! [X4: $i] :
      ( ( in @ X4 @ nat )
     => ! [X6: $i] :
          ( ( in @ X6 @ nat )
         => ! [X8: $i] :
              ( ( in @ X8 @ nat )
             => ( ( X6 != X8 )
               => ( ( n_pl @ X4 @ X6 )
                 != ( n_pl @ X4 @ X8 ) ) ) ) ) ) ).

thf(zip_derived_cl134,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( in @ Y0 @ nat )
       => ( !!
          @ ^ [Y1: $i] :
              ( ( in @ Y1 @ nat )
             => ( !!
                @ ^ [Y2: $i] :
                    ( ( in @ Y2 @ nat )
                   => ( ( Y1 != Y2 )
                     => ( ( n_pl @ Y0 @ Y1 )
                       != ( n_pl @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl4096,plain,
    ! [X2: $i] :
      ( ( in @ X2 @ nat )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ nat )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ nat )
                 => ( ( Y0 != Y1 )
                   => ( ( n_pl @ X2 @ Y0 )
                     != ( n_pl @ X2 @ Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl134]) ).

thf(zip_derived_cl4097,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ nat )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ nat )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ nat )
                 => ( ( Y0 != Y1 )
                   => ( ( n_pl @ X2 @ Y0 )
                     != ( n_pl @ X2 @ Y1 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4096]) ).

thf(zip_derived_cl4098,plain,
    ! [X2: $i,X4: $i] :
      ( ( ( in @ X4 @ nat )
       => ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ nat )
             => ( ( X4 != Y0 )
               => ( ( n_pl @ X2 @ X4 )
                 != ( n_pl @ X2 @ Y0 ) ) ) ) ) )
      | ~ ( in @ X2 @ nat ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4097]) ).

thf(zip_derived_cl4099,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( in @ X4 @ nat )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ nat )
           => ( ( X4 != Y0 )
             => ( ( n_pl @ X2 @ X4 )
               != ( n_pl @ X2 @ Y0 ) ) ) ) )
      | ~ ( in @ X2 @ nat ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4098]) ).

thf(zip_derived_cl4100,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( in @ X6 @ nat )
       => ( ( X4 != X6 )
         => ( ( n_pl @ X2 @ X4 )
           != ( n_pl @ X2 @ X6 ) ) ) )
      | ~ ( in @ X2 @ nat )
      | ~ ( in @ X4 @ nat ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4099]) ).

thf(zip_derived_cl4101,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( in @ X6 @ nat )
      | ( ( X4 != X6 )
       => ( ( n_pl @ X2 @ X4 )
         != ( n_pl @ X2 @ X6 ) ) )
      | ~ ( in @ X4 @ nat )
      | ~ ( in @ X2 @ nat ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4100]) ).

thf(zip_derived_cl4102,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( X4 != X6 )
      | ( ( n_pl @ X2 @ X4 )
       != ( n_pl @ X2 @ X6 ) )
      | ~ ( in @ X2 @ nat )
      | ~ ( in @ X4 @ nat )
      | ~ ( in @ X6 @ nat ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4101]) ).

thf(zip_derived_cl4103,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( X4 = X6 )
      | ( ( n_pl @ X2 @ X4 )
       != ( n_pl @ X2 @ X6 ) )
      | ~ ( in @ X2 @ nat )
      | ~ ( in @ X4 @ nat )
      | ~ ( in @ X6 @ nat ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4102]) ).

thf(zip_derived_cl4741,plain,
    ! [X0: $i] :
      ( ( ( n_pl @ '#sk6416' @ X0 )
       != '#sk6415' )
      | ~ ( in @ '#sk6417' @ nat )
      | ~ ( in @ X0 @ nat )
      | ~ ( in @ '#sk6416' @ nat )
      | ( X0 = '#sk6417' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl4512,zip_derived_cl4103]) ).

thf(zip_derived_cl4505,plain,
    in @ '#sk6417' @ nat,
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4504]) ).

thf(zip_derived_cl4502,plain,
    in @ '#sk6416' @ nat,
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4501]) ).

thf(zip_derived_cl4755,plain,
    ! [X0: $i] :
      ( ( ( n_pl @ '#sk6416' @ X0 )
       != '#sk6415' )
      | ~ ( in @ X0 @ nat )
      | ( X0 = '#sk6417' ) ),
    inference(demod,[status(thm)],[zip_derived_cl4741,zip_derived_cl4505,zip_derived_cl4502]) ).

thf(zip_derived_cl4982,plain,
    ( ( '#sk6415' != '#sk6415' )
    | ( '#sk6418' = '#sk6417' )
    | ~ ( in @ '#sk6418' @ nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl4515,zip_derived_cl4755]) ).

thf(zip_derived_cl4508,plain,
    in @ '#sk6418' @ nat,
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4507]) ).

thf(zip_derived_cl4999,plain,
    ( ( '#sk6415' != '#sk6415' )
    | ( '#sk6418' = '#sk6417' ) ),
    inference(demod,[status(thm)],[zip_derived_cl4982,zip_derived_cl4508]) ).

thf(zip_derived_cl5000,plain,
    '#sk6418' = '#sk6417',
    inference(simplify,[status(thm)],[zip_derived_cl4999]) ).

thf(zip_derived_cl4514,plain,
    '#sk6417' != '#sk6418',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4511]) ).

thf(zip_derived_cl4516,plain,
    '#sk6417' != '#sk6418',
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4514]) ).

thf(zip_derived_cl5001,plain,
    $false,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl5000,zip_derived_cl4516]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM648^4 : TPTP v8.1.2. Released v7.1.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CjGb1bh89q true
% 0.13/0.35  % Computer : n012.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Fri Aug 25 15:24:11 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.36  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36  % Number of cores: 8
% 0.13/0.36  % Python version: Python 3.6.8
% 0.13/0.36  % Running in HO mode
% 0.22/0.58  % Total configuration time : 828
% 0.22/0.58  % Estimated wc time : 1656
% 0.22/0.58  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.67  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.67  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.67  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.70  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.70  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.70  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.70  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.71  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 40.19/5.71  % Solved by lams/35_full_unif4.sh.
% 40.19/5.71  % done 492 iterations in 5.009s
% 40.19/5.71  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 40.19/5.71  % SZS output start Refutation
% See solution above
% 40.19/5.71  
% 40.19/5.71  
% 40.19/5.71  % Terminating...
% 40.85/5.85  % Runner terminated.
% 40.85/5.85  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------