TSTP Solution File: NUM694^4 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM694^4 : 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.Wruck5laIC true

% Computer : n010.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 12:43:31 EDT 2023

% Result   : Theorem 65.19s 8.98s
% Output   : Refutation 65.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   59
% Syntax   : Number of formulae    :  123 (  58 unt;  23 typ;   0 def)
%            Number of atoms       :  315 ( 119 equ;   3 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  521 (  72   ~;  30   |;   0   &; 334   @)
%                                         (   0 <=>;  56  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   59 (  59   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  23 usr;   8 con; 0-3 aty)
%                                         (  29  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  146 ( 113   ^;  33   !;   0   ?; 146   :)

% Comments : 
%------------------------------------------------------------------------------
thf(n_1_type,type,
    n_1: $i ).

thf(nat_type,type,
    nat: $i ).

thf(lessis_type,type,
    lessis: $i > $i > $o ).

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(non_type,type,
    non: $i > ( $i > $o ) > $i > $o ).

thf(l_some_type,type,
    l_some: $i > ( $i > $o ) > $o ).

thf(emptyset_type,type,
    emptyset: $i ).

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

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

thf('#sk6395_type',type,
    '#sk6395': $i ).

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

thf(diffprop_type,type,
    diffprop: $i > $i > $i > $o ).

thf(n_some_type,type,
    n_some: ( $i > $o ) > $o ).

thf(l_or_type,type,
    l_or: $o > $o > $o ).

thf(ordsucc_type,type,
    ordsucc: $i > $i ).

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

thf('#sk4661_type',type,
    '#sk4661': $i > $i ).

thf('#sk967_type',type,
    '#sk967': $i ).

thf(iii_type,type,
    iii: $i > $i > $o ).

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

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

thf(def_lessis,axiom,
    ( lessis
    = ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ) ).

thf(def_iii,axiom,
    ( iii
    = ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ) ).

thf(def_diffprop,axiom,
    ( diffprop
    = ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ).

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('4',plain,
    ( diffprop
    = ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_diffprop,'3','1']) ).

thf('5',plain,
    ( diffprop
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( n_is @ V_1 @ ( n_pl @ V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(def_n_some,axiom,
    ( n_some
    = ( l_some @ nat ) ) ).

thf(def_l_some,axiom,
    ( l_some
    = ( ^ [X0: $i,X1: $i > $o] :
          ( d_not
          @ ( all_of
            @ ^ [X2: $i] : ( in @ X2 @ X0 )
            @ ( non @ X0 @ X1 ) ) ) ) ) ).

thf(def_non,axiom,
    ( non
    = ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ) ).

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

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

thf('6',plain,
    ( imp
    = ( ^ [X0: $o,X1: $o] :
          ( X0
         => X1 ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_imp]) ).

thf('7',plain,
    ( imp
    = ( ^ [V_1: $o,V_2: $o] :
          ( V_1
         => V_2 ) ) ),
    define([status(thm)]) ).

thf('8',plain,
    ( d_not
    = ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_d_not,'7']) ).

thf('9',plain,
    ( d_not
    = ( ^ [V_1: $o] : ( imp @ V_1 @ $false ) ) ),
    define([status(thm)]) ).

thf('10',plain,
    ( non
    = ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_non,'9','7']) ).

thf('11',plain,
    ( non
    = ( ^ [V_1: $i,V_2: $i > $o,V_3: $i] : ( d_not @ ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

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

thf('13',plain,
    ( is_of
    = ( ^ [V_1: $i,V_2: $i > $o] : ( V_2 @ V_1 ) ) ),
    define([status(thm)]) ).

thf('14',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,'13']) ).

thf('15',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('16',plain,
    ( l_some
    = ( ^ [X0: $i,X1: $i > $o] :
          ( d_not
          @ ( all_of
            @ ^ [X2: $i] : ( in @ X2 @ X0 )
            @ ( non @ X0 @ X1 ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_l_some,'11','9','7','15','13']) ).

thf('17',plain,
    ( l_some
    = ( ^ [V_1: $i,V_2: $i > $o] :
          ( d_not
          @ ( all_of
            @ ^ [V_3: $i] : ( in @ V_3 @ V_1 )
            @ ( non @ V_1 @ V_2 ) ) ) ) ),
    define([status(thm)]) ).

thf('18',plain,
    ( n_some
    = ( l_some @ nat ) ),
    inference(simplify_rw_rule,[status(thm)],[def_n_some,'17','11','9','7','15','13']) ).

thf('19',plain,
    ( n_some
    = ( l_some @ nat ) ),
    define([status(thm)]) ).

thf('20',plain,
    ( iii
    = ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_iii,'5','19','3','1','17','11','9','7','15','13']) ).

thf('21',plain,
    ( iii
    = ( ^ [V_1: $i,V_2: $i] : ( n_some @ ( diffprop @ V_2 @ V_1 ) ) ) ),
    define([status(thm)]) ).

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

thf('22',plain,
    ( l_or
    = ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_l_or,'9','7']) ).

thf('23',plain,
    ( l_or
    = ( ^ [V_1: $o] : ( imp @ ( d_not @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf('24',plain,
    ( lessis
    = ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_lessis,'21','5','19','3','1','17','11','23','9','7','15','13']) ).

thf('25',plain,
    ( lessis
    = ( ^ [V_1: $i,V_2: $i] : ( l_or @ ( iii @ V_1 @ V_2 ) @ ( n_is @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(satz24a,conjecture,
    ( all_of
    @ ^ [X0: $i] : ( in @ X0 @ nat )
    @ ( lessis @ n_1 ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i] :
      ( ( in @ X4 @ nat )
     => ( ! [X6: $i] :
            ( ( in @ X6 @ nat )
           => ( X4
             != ( n_pl @ n_1 @ X6 ) ) )
       => ( n_1 = X4 ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i] :
        ( ( in @ X4 @ nat )
       => ( ! [X6: $i] :
              ( ( in @ X6 @ nat )
             => ( X4
               != ( n_pl @ n_1 @ X6 ) ) )
         => ( n_1 = X4 ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl194,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ nat )
         => ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ nat )
                 => ( Y0
                   != ( n_pl @ n_1 @ Y1 ) ) ) )
           => ( n_1 = Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1224,plain,
    ~ ( ( in @ '#sk967' @ nat )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ nat )
             => ( '#sk967'
               != ( n_pl @ n_1 @ Y0 ) ) ) )
       => ( n_1 = '#sk967' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl194]) ).

thf(zip_derived_cl1225,plain,
    in @ '#sk967' @ nat,
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1224]) ).

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

thf('26',plain,
    ( nis
    = ( ^ [X0: $i,X1: $i] : ( d_not @ ( n_is @ X0 @ X1 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_nis,'3','1','9']) ).

thf('27',plain,
    ( nis
    = ( ^ [V_1: $i,V_2: $i] : ( d_not @ ( n_is @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(satz3,axiom,
    ( all_of
    @ ^ [X0: $i] : ( in @ X0 @ nat )
    @ ^ [X0: $i] :
        ( ( nis @ X0 @ n_1 )
       => ( n_some
          @ ^ [X1: $i] : ( n_is @ X0 @ ( ordsucc @ X1 ) ) ) ) ) ).

thf(zf_stmt_2,axiom,
    ! [X4: $i] :
      ( ( in @ X4 @ nat )
     => ( ( X4 != n_1 )
       => ~ ! [X6: $i] :
              ( ( in @ X6 @ nat )
             => ( X4
               != ( ordsucc @ X6 ) ) ) ) ) ).

thf(zip_derived_cl117,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( in @ Y0 @ nat )
       => ( ( Y0 != n_1 )
         => ( (~)
            @ ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ nat )
                 => ( Y0
                   != ( ordsucc @ Y1 ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl3605,plain,
    ! [X2: $i] :
      ( ( in @ X2 @ nat )
     => ( ( X2 != n_1 )
       => ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( in @ Y0 @ nat )
               => ( X2
                 != ( ordsucc @ Y0 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl117]) ).

thf(zip_derived_cl3606,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ nat )
      | ( ( X2 != n_1 )
       => ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( in @ Y0 @ nat )
               => ( X2
                 != ( ordsucc @ Y0 ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3605]) ).

thf(zip_derived_cl3607,plain,
    ! [X2: $i] :
      ( ( X2 != n_1 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ nat )
             => ( X2
               != ( ordsucc @ Y0 ) ) ) )
      | ~ ( in @ X2 @ nat ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3606]) ).

thf(zip_derived_cl3608,plain,
    ! [X2: $i] :
      ( ( X2 = n_1 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ nat )
             => ( X2
               != ( ordsucc @ Y0 ) ) ) )
      | ~ ( in @ X2 @ nat ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl3607]) ).

thf(zip_derived_cl3609,plain,
    ! [X2: $i] :
      ( ~ ( ( in @ ( '#sk4661' @ X2 ) @ nat )
         => ( X2
           != ( ordsucc @ ( '#sk4661' @ X2 ) ) ) )
      | ~ ( in @ X2 @ nat )
      | ( X2 = n_1 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3608]) ).

thf(zip_derived_cl3611,plain,
    ! [X2: $i] :
      ( ( X2
       != ( ordsucc @ ( '#sk4661' @ X2 ) ) )
      | ( X2 = n_1 )
      | ~ ( in @ X2 @ nat ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3609]) ).

thf(zip_derived_cl3612,plain,
    ! [X2: $i] :
      ( ( X2
        = ( ordsucc @ ( '#sk4661' @ X2 ) ) )
      | ( X2 = n_1 )
      | ~ ( in @ X2 @ nat ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl3611]) ).

thf(zip_derived_cl9317,plain,
    ( ( '#sk967' = n_1 )
    | ( '#sk967'
      = ( ordsucc @ ( '#sk4661' @ '#sk967' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1225,zip_derived_cl3612]) ).

thf(def_n_1,axiom,
    ( n_1
    = ( ordsucc @ emptyset ) ) ).

thf(zip_derived_cl108,plain,
    ( n_1
    = ( ordsucc @ emptyset ) ),
    inference(cnf,[status(esa)],[def_n_1]) ).

thf(k_In_ind,axiom,
    ! [X0: $i > $o] :
      ( ! [X1: $i] :
          ( ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( X0 @ X2 ) )
         => ( X0 @ X1 ) )
     => ! [X1: $i] : ( X0 @ X1 ) ) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: $i > $o] :
        ( ( !!
          @ ^ [Y1: $i] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( in @ Y2 @ Y1 )
                   => ( Y0 @ Y2 ) ) )
             => ( Y0 @ Y1 ) ) )
       => ( !!
          @ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
    inference(cnf,[status(esa)],[k_In_ind]) ).

thf(zip_derived_cl298,plain,
    ! [X2: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ Y0 )
                 => ( X2 @ Y1 ) ) )
           => ( X2 @ Y0 ) ) )
     => ( !!
        @ ^ [Y0: $i] : ( X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl537,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ Y0 )
               => ( Y1 != emptyset ) ) )
         => ( Y0 != emptyset ) ) )
   => ( !!
      @ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl298]) ).

thf(zip_derived_cl4448,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ Y0 )
                 => ( Y1 != emptyset ) ) )
           => ( Y0 != emptyset ) ) )
    | ( !!
      @ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl537]) ).

thf(zip_derived_cl4449,plain,
    ( ~ ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ '#sk6395' )
             => ( Y0 != emptyset ) ) )
       => ( '#sk6395' != emptyset ) )
    | ( !!
      @ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4448]) ).

thf(zip_derived_cl4451,plain,
    ( ( '#sk6395' != emptyset )
    | ( !!
      @ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4449]) ).

thf(zip_derived_cl4453,plain,
    ( ( '#sk6395' = emptyset )
    | ( !!
      @ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4451]) ).

thf(zip_derived_cl4454,plain,
    ! [X2: $i] :
      ( ( X2 != emptyset )
      | ( '#sk6395' = emptyset ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4453]) ).

thf(zip_derived_cl4456,plain,
    ! [X2: $i] :
      ( ( X2 != emptyset )
      | ( '#sk6395' = emptyset ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4454]) ).

thf(zip_derived_cl4457,plain,
    '#sk6395' = emptyset,
    inference(simplify,[status(thm)],[zip_derived_cl4456]) ).

thf(zip_derived_cl4464,plain,
    ( n_1
    = ( ordsucc @ '#sk6395' ) ),
    inference(demod,[status(thm)],[zip_derived_cl108,zip_derived_cl4457]) ).

thf(zip_derived_cl9357,plain,
    ( ( '#sk967'
      = ( ordsucc @ '#sk6395' ) )
    | ( '#sk967'
      = ( ordsucc @ ( '#sk4661' @ '#sk967' ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl9317,zip_derived_cl4464]) ).

thf(zip_derived_cl1226,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ nat )
           => ( '#sk967'
             != ( n_pl @ n_1 @ Y0 ) ) ) )
     => ( n_1 = '#sk967' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1224]) ).

thf(zip_derived_cl1228,plain,
    n_1 != '#sk967',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1226]) ).

thf(zip_derived_cl1230,plain,
    n_1 != '#sk967',
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl1228]) ).

thf(zip_derived_cl4464_001,plain,
    ( n_1
    = ( ordsucc @ '#sk6395' ) ),
    inference(demod,[status(thm)],[zip_derived_cl108,zip_derived_cl4457]) ).

thf(zip_derived_cl4624,plain,
    ( ( ordsucc @ '#sk6395' )
   != '#sk967' ),
    inference(demod,[status(thm)],[zip_derived_cl1230,zip_derived_cl4464]) ).

thf(zip_derived_cl9397,plain,
    ( '#sk967'
    = ( ordsucc @ ( '#sk4661' @ '#sk967' ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl9357,zip_derived_cl4624]) ).

thf(satz4c,axiom,
    ( all_of
    @ ^ [X0: $i] : ( in @ X0 @ nat )
    @ ^ [X0: $i] : ( n_is @ ( n_pl @ n_1 @ X0 ) @ ( ordsucc @ X0 ) ) ) ).

thf(zf_stmt_3,axiom,
    ! [X4: $i] :
      ( ( in @ X4 @ nat )
     => ( ( n_pl @ n_1 @ X4 )
        = ( ordsucc @ X4 ) ) ) ).

thf(zip_derived_cl125,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( in @ Y0 @ nat )
       => ( ( n_pl @ n_1 @ Y0 )
          = ( ordsucc @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl899,plain,
    ! [X2: $i] :
      ( ( in @ X2 @ nat )
     => ( ( n_pl @ n_1 @ X2 )
        = ( ordsucc @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl125]) ).

thf(zip_derived_cl900,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ nat )
      | ( ( n_pl @ n_1 @ X2 )
        = ( ordsucc @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl899]) ).

thf(zip_derived_cl901,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ nat )
      | ( ( n_pl @ n_1 @ X2 )
        = ( ordsucc @ X2 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl900]) ).

thf(zip_derived_cl1227,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( in @ Y0 @ nat )
       => ( '#sk967'
         != ( n_pl @ n_1 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1226]) ).

thf(zip_derived_cl1229,plain,
    ! [X2: $i] :
      ( ( in @ X2 @ nat )
     => ( '#sk967'
       != ( n_pl @ n_1 @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1227]) ).

thf(zip_derived_cl1231,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ nat )
      | ( '#sk967'
       != ( n_pl @ n_1 @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1229]) ).

thf(zip_derived_cl1232,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ nat )
      | ( '#sk967'
       != ( n_pl @ n_1 @ X2 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl1231]) ).

thf(zip_derived_cl1733,plain,
    ! [X0: $i] :
      ( ( '#sk967'
       != ( ordsucc @ X0 ) )
      | ~ ( in @ X0 @ nat )
      | ~ ( in @ X0 @ nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl901,zip_derived_cl1232]) ).

thf(zip_derived_cl1735,plain,
    ! [X0: $i] :
      ( ~ ( in @ X0 @ nat )
      | ( '#sk967'
       != ( ordsucc @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1733]) ).

thf(zip_derived_cl9414,plain,
    ( ( '#sk967' != '#sk967' )
    | ~ ( in @ ( '#sk4661' @ '#sk967' ) @ nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl9397,zip_derived_cl1735]) ).

thf(zip_derived_cl1225_002,plain,
    in @ '#sk967' @ nat,
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1224]) ).

thf(zip_derived_cl3610,plain,
    ! [X2: $i] :
      ( ( in @ ( '#sk4661' @ X2 ) @ nat )
      | ( X2 = n_1 )
      | ~ ( in @ X2 @ nat ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3609]) ).

thf(zip_derived_cl3614,plain,
    ( ( '#sk967' = n_1 )
    | ( in @ ( '#sk4661' @ '#sk967' ) @ nat ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1225,zip_derived_cl3610]) ).

thf(zip_derived_cl1230_003,plain,
    n_1 != '#sk967',
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl1228]) ).

thf(zip_derived_cl3636,plain,
    in @ ( '#sk4661' @ '#sk967' ) @ nat,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl3614,zip_derived_cl1230]) ).

thf(zip_derived_cl9424,plain,
    '#sk967' != '#sk967',
    inference(demod,[status(thm)],[zip_derived_cl9414,zip_derived_cl3636]) ).

thf(zip_derived_cl9425,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl9424]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14  % Problem  : NUM694^4 : TPTP v8.1.2. Released v7.1.0.
% 0.14/0.15  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Wruck5laIC true
% 0.16/0.37  % Computer : n010.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Fri Aug 25 14:56:05 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.16/0.37  % Running portfolio for 300 s
% 0.16/0.37  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.37  % Number of cores: 8
% 0.16/0.37  % Python version: Python 3.6.8
% 0.16/0.38  % Running in HO mode
% 0.24/0.68  % Total configuration time : 828
% 0.24/0.69  % Estimated wc time : 1656
% 0.24/0.69  % Estimated cpu time (8 cpus) : 207.0
% 0.24/0.75  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.24/0.75  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.24/0.75  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.24/0.80  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.24/0.80  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.24/0.80  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.24/0.80  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.30/0.81  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 35.76/5.25  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 65.19/8.98  % Solved by lams/35_full_unif4.sh.
% 65.19/8.98  % done 953 iterations in 8.167s
% 65.19/8.98  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 65.19/8.98  % SZS output start Refutation
% See solution above
% 65.19/8.98  
% 65.19/8.98  
% 65.19/8.98  % Terminating...
% 65.56/9.14  % Runner terminated.
% 65.56/9.16  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------