TSTP Solution File: SEV174^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV174^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.FcZ6w99yEp 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 19:59:53 EDT 2023

% Result   : Theorem 20.34s 3.37s
% Output   : Refutation 20.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  113 (  10 unt;   9 typ;   0 def)
%            Number of atoms       :  560 (  57 equ;   0 cnn)
%            Maximal formula atoms :   22 (   5 avg)
%            Number of connectives : 1234 ( 130   ~; 127   |; 149   &; 623   @)
%                                         (  26 <=>;  40  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   8 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  191 ( 191   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   8 usr;   4 con; 0-2 aty)
%                                         (  63  !!;  76  ??;   0 @@+;   0 @@-)
%            Number of variables   :  296 ( 168   ^; 118   !;  10   ?; 296   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf('#sk33_type',type,
    '#sk33': a > $o ).

thf('#form55_type',type,
    '#form55': ( a > $o ) > $o ).

thf('#sk41_type',type,
    '#sk41': a > $o ).

thf('#sk58_type',type,
    '#sk58': a ).

thf(cP_type,type,
    cP: ( a > $o ) > $o ).

thf('#sk19_type',type,
    '#sk19': ( a > $o ) > a ).

thf('#sk5_type',type,
    '#sk5': a > $o ).

thf('#sk10_type',type,
    '#sk10': ( a > $o ) > a ).

thf(cTHM555_pme,conjecture,
    ( ( ! [Xx: a,Xp: a > $o,Xq: a > $o] :
          ( ( ( Xq @ Xx )
            & ( Xp @ Xx )
            & ( cP @ Xq )
            & ( cP @ Xp ) )
         => ( Xp = Xq ) )
      & ! [Xp: a > $o] :
          ( ( cP @ Xp )
         => ? [Xz: a] : ( Xp @ Xz ) ) )
   => ? [S: a > $o] :
        ( ! [Xa: a > $o] :
            ( ( cP @ Xa )
           => ? [Xx: a] : ( Xa @ Xx ) )
        & ! [Xx: a] :
            ( ( S @ Xx )
          <=> ? [S0: a > $o] :
                ( ( cP @ S0 )
                & ( S0 @ Xx ) ) )
        & ! [Xb: a > $o,Xc: a > $o] :
            ( ( ? [Xx: a] :
                  ( ( Xb @ Xx )
                  & ( Xc @ Xx ) )
              & ( cP @ Xc )
              & ( cP @ Xb ) )
           => ( Xb = Xc ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( ( ! [Xx: a,Xp: a > $o,Xq: a > $o] :
            ( ( ( Xq @ Xx )
              & ( Xp @ Xx )
              & ( cP @ Xq )
              & ( cP @ Xp ) )
           => ( Xp = Xq ) )
        & ! [Xp: a > $o] :
            ( ( cP @ Xp )
           => ? [Xz: a] : ( Xp @ Xz ) ) )
     => ? [S: a > $o] :
          ( ! [Xa: a > $o] :
              ( ( cP @ Xa )
             => ? [Xx: a] : ( Xa @ Xx ) )
          & ! [Xx: a] :
              ( ( S @ Xx )
            <=> ? [S0: a > $o] :
                  ( ( cP @ S0 )
                  & ( S0 @ Xx ) ) )
          & ! [Xb: a > $o,Xc: a > $o] :
              ( ( ? [Xx: a] :
                    ( ( Xb @ Xx )
                    & ( Xc @ Xx ) )
                & ( cP @ Xc )
                & ( cP @ Xb ) )
             => ( Xb = Xc ) ) ) ),
    inference('cnf.neg',[status(esa)],[cTHM555_pme]) ).

thf(zip_derived_cl0,plain,
    ~ ( ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( ( Y2 @ Y0 )
                        & ( Y1 @ Y0 )
                        & ( cP @ Y2 )
                        & ( cP @ Y1 ) )
                     => ( Y1 = Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
             => ( ??
                @ ^ [Y1: a] : ( Y0 @ Y1 ) ) ) ) )
     => ( ??
        @ ^ [Y0: a > $o] :
            ( ( !!
              @ ^ [Y1: a > $o] :
                  ( ( cP @ Y1 )
                 => ( ??
                    @ ^ [Y2: a] : ( Y1 @ Y2 ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( ( Y0 @ Y1 )
                <=> ( ??
                    @ ^ [Y2: a > $o] :
                        ( ( cP @ Y2 )
                        & ( Y2 @ Y1 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a > $o] :
                  ( !!
                  @ ^ [Y2: a > $o] :
                      ( ( ( ??
                          @ ^ [Y3: a] :
                              ( ( Y1 @ Y3 )
                              & ( Y2 @ Y3 ) ) )
                        & ( cP @ Y2 )
                        & ( cP @ Y1 ) )
                     => ( Y1 = Y2 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2,plain,
    ~ ( ??
      @ ^ [Y0: a > $o] :
          ( ( !!
            @ ^ [Y1: a > $o] :
                ( ( cP @ Y1 )
               => ( ??
                  @ ^ [Y2: a] : ( Y1 @ Y2 ) ) ) )
          & ( !!
            @ ^ [Y1: a] :
                ( ( Y0 @ Y1 )
              <=> ( ??
                  @ ^ [Y2: a > $o] :
                      ( ( cP @ Y2 )
                      & ( Y2 @ Y1 ) ) ) ) )
          & ( !!
            @ ^ [Y1: a > $o] :
                ( !!
                @ ^ [Y2: a > $o] :
                    ( ( ( ??
                        @ ^ [Y3: a] :
                            ( ( Y1 @ Y3 )
                            & ( Y2 @ Y3 ) ) )
                      & ( cP @ Y2 )
                      & ( cP @ Y1 ) )
                   => ( Y1 = Y2 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl5,plain,
    ! [X2: a > $o] :
      ~ ( ( !!
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
             => ( ??
                @ ^ [Y1: a] : ( Y0 @ Y1 ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a > $o] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( ( ??
                      @ ^ [Y2: a] :
                          ( ( Y0 @ Y2 )
                          & ( Y1 @ Y2 ) ) )
                    & ( cP @ Y1 )
                    & ( cP @ Y0 ) )
                 => ( Y0 = Y1 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl14,plain,
    ! [X2: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
             => ( ??
                @ ^ [Y1: a] : ( Y0 @ Y1 ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( ( ??
                      @ ^ [Y2: a] :
                          ( ( Y0 @ Y2 )
                          & ( Y1 @ Y2 ) ) )
                    & ( cP @ Y1 )
                    & ( cP @ Y0 ) )
                 => ( Y0 = Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl20,plain,
    ! [X2: a > $o] :
      ( ~ ( ( cP @ '#sk5' )
         => ( ??
            @ ^ [Y0: a] : ( '#sk5' @ Y0 ) ) )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( ( ??
                      @ ^ [Y2: a] :
                          ( ( Y0 @ Y2 )
                          & ( Y1 @ Y2 ) ) )
                    & ( cP @ Y1 )
                    & ( cP @ Y0 ) )
                 => ( Y0 = Y1 ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl26,plain,
    ! [X2: a > $o] :
      ( ( cP @ '#sk5' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( ( ??
                      @ ^ [Y2: a] :
                          ( ( Y0 @ Y2 )
                          & ( Y1 @ Y2 ) ) )
                    & ( cP @ Y1 )
                    & ( cP @ Y0 ) )
                 => ( Y0 = Y1 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl29,plain,
    ! [X2: a > $o] :
      ( ~ ( ( X2 @ ( '#sk19' @ X2 ) )
        <=> ( ??
            @ ^ [Y0: a > $o] :
                ( ( cP @ Y0 )
                & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( ( ??
                      @ ^ [Y2: a] :
                          ( ( Y0 @ Y2 )
                          & ( Y1 @ Y2 ) ) )
                    & ( cP @ Y1 )
                    & ( cP @ Y0 ) )
                 => ( Y0 = Y1 ) ) ) )
      | ( cP @ '#sk5' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl33,plain,
    ! [X2: a > $o] :
      ( ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( ( ??
                      @ ^ [Y2: a] :
                          ( ( Y0 @ Y2 )
                          & ( Y1 @ Y2 ) ) )
                    & ( cP @ Y1 )
                    & ( cP @ Y0 ) )
                 => ( Y0 = Y1 ) ) ) )
      | ( cP @ '#sk5' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl34,plain,
    ! [X2: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a > $o] :
              ( ( ( ??
                  @ ^ [Y1: a] :
                      ( ( '#sk33' @ Y1 )
                      & ( Y0 @ Y1 ) ) )
                & ( cP @ Y0 )
                & ( cP @ '#sk33' ) )
             => ( '#sk33' = Y0 ) ) )
      | ( cP @ '#sk5' )
      | ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl36,plain,
    ! [X2: a > $o] :
      ( ~ ( ( ( ??
              @ ^ [Y0: a] :
                  ( ( '#sk33' @ Y0 )
                  & ( '#sk41' @ Y0 ) ) )
            & ( cP @ '#sk41' )
            & ( cP @ '#sk33' ) )
         => ( '#sk33' = '#sk41' ) )
      | ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) )
      | ( cP @ '#sk5' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl38,plain,
    ! [X2: a > $o] :
      ( ( ( ??
          @ ^ [Y0: a] :
              ( ( '#sk33' @ Y0 )
              & ( '#sk41' @ Y0 ) ) )
        & ( cP @ '#sk41' )
        & ( cP @ '#sk33' ) )
      | ( cP @ '#sk5' )
      | ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl42,plain,
    ! [X2: a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ( '#sk33' @ Y0 )
            & ( '#sk41' @ Y0 ) ) )
      | ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) )
      | ( cP @ '#sk5' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl53,plain,
    ! [X2: a > $o] :
      ( ( ( '#sk33' @ '#sk58' )
        & ( '#sk41' @ '#sk58' ) )
      | ( cP @ '#sk5' )
      | ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl59,plain,
    ! [X2: a > $o] :
      ( ( '#sk41' @ '#sk58' )
      | ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) )
      | ( cP @ '#sk5' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl621,plain,
    ( ( cP @ '#sk5' )
    | ( '#sk41' @ '#sk58' ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl59]) ).

thf(zip_derived_cl1,plain,
    ( ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( !!
              @ ^ [Y2: a > $o] :
                  ( ( ( Y2 @ Y0 )
                    & ( Y1 @ Y0 )
                    & ( cP @ Y2 )
                    & ( cP @ Y1 ) )
                 => ( Y1 = Y2 ) ) ) ) )
    & ( !!
      @ ^ [Y0: a > $o] :
          ( ( cP @ Y0 )
         => ( ??
            @ ^ [Y1: a] : ( Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl4,plain,
    ( !!
    @ ^ [Y0: a > $o] :
        ( ( cP @ Y0 )
       => ( ??
          @ ^ [Y1: a] : ( Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl10,plain,
    ! [X2: a > $o] :
      ( ( cP @ X2 )
     => ( ??
        @ ^ [Y0: a] : ( X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl19,plain,
    ! [X2: a > $o] :
      ( ~ ( cP @ X2 )
      | ( ??
        @ ^ [Y0: a] : ( X2 @ Y0 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl25,plain,
    ! [X2: a > $o] :
      ( ( X2 @ ( '#sk10' @ X2 ) )
      | ~ ( cP @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl628,plain,
    ( ( '#sk41' @ '#sk58' )
    | ( '#sk5' @ ( '#sk10' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl621,zip_derived_cl25]) ).

thf(zip_derived_cl27,plain,
    ! [X2: a > $o] :
      ( ~ ( ??
          @ ^ [Y0: a] : ( '#sk5' @ Y0 ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( ( ??
                      @ ^ [Y2: a] :
                          ( ( Y0 @ Y2 )
                          & ( Y1 @ Y2 ) ) )
                    & ( cP @ Y1 )
                    & ( cP @ Y0 ) )
                 => ( Y0 = Y1 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl30,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( '#sk5' @ X4 )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( !!
              @ ^ [Y1: a > $o] :
                  ( ( ( ??
                      @ ^ [Y2: a] :
                          ( ( Y0 @ Y2 )
                          & ( Y1 @ Y2 ) ) )
                    & ( cP @ Y1 )
                    & ( cP @ Y0 ) )
                 => ( Y0 = Y1 ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl35,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( !!
          @ ^ [Y0: a > $o] :
              ( ( ( ??
                  @ ^ [Y1: a] :
                      ( ( '#sk33' @ Y1 )
                      & ( Y0 @ Y1 ) ) )
                & ( cP @ Y0 )
                & ( cP @ '#sk33' ) )
             => ( '#sk33' = Y0 ) ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) )
      | ~ ( '#sk5' @ X4 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl37,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( ( ( ??
              @ ^ [Y0: a] :
                  ( ( '#sk33' @ Y0 )
                  & ( '#sk41' @ Y0 ) ) )
            & ( cP @ '#sk41' )
            & ( cP @ '#sk33' ) )
         => ( '#sk33' = '#sk41' ) )
      | ~ ( '#sk5' @ X4 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl40,plain,
    ! [X2: a > $o,X4: a] :
      ( ( ( ??
          @ ^ [Y0: a] :
              ( ( '#sk33' @ Y0 )
              & ( '#sk41' @ Y0 ) ) )
        & ( cP @ '#sk41' )
        & ( cP @ '#sk33' ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) )
      | ~ ( '#sk5' @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl46,plain,
    ! [X2: a > $o,X4: a] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ( '#sk33' @ Y0 )
            & ( '#sk41' @ Y0 ) ) )
      | ~ ( '#sk5' @ X4 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl41,plain,
    ! [X2: a > $o,X4: a] :
      ( ( '#sk33' != '#sk41' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) )
      | ~ ( '#sk5' @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl49,plain,
    ! [X2: a > $o,X4: a] :
      ( ( '#sk33' != '#sk41' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) )
      | ~ ( '#sk5' @ X4 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl41]) ).

thf(zip_derived_cl50,plain,
    ! [X2: a > $o] :
      ( ( '#form55' @ X2 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl54,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( '#form55'
          @ ^ [Y0: a] : ( X2 @ Y0 ) )
      | ~ ( '#sk5' @ X4 )
      | ( ??
        @ ^ [Y0: a] :
            ( ( '#sk33' @ Y0 )
            & ( '#sk41' @ Y0 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl46,zip_derived_cl50]) ).

thf(zip_derived_cl60,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( '#form55' @ X2 )
      | ~ ( '#sk5' @ X4 )
      | ( ??
        @ ^ [Y0: a] :
            ( ( '#sk33' @ Y0 )
            & ( '#sk41' @ Y0 ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl61,plain,
    ! [X2: a > $o,X4: a] :
      ( ( ( '#sk33' @ '#sk58' )
        & ( '#sk41' @ '#sk58' ) )
      | ~ ( '#sk5' @ X4 )
      | ~ ( '#form55' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl60]) ).

thf(zip_derived_cl65,plain,
    ! [X2: a > $o,X4: a] :
      ( ( '#sk41' @ '#sk58' )
      | ~ ( '#form55' @ X2 )
      | ~ ( '#sk5' @ X4 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl61]) ).

thf(zip_derived_cl754,plain,
    ! [X0: a > $o] :
      ( ( '#sk41' @ '#sk58' )
      | ~ ( '#form55' @ X0 )
      | ( '#sk41' @ '#sk58' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl628,zip_derived_cl65]) ).

thf(zip_derived_cl770,plain,
    ! [X0: a > $o] :
      ( ~ ( '#form55' @ X0 )
      | ( '#sk41' @ '#sk58' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl754]) ).

thf(zip_derived_cl50_001,plain,
    ! [X2: a > $o] :
      ( ( '#form55' @ X2 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl51,plain,
    ! [X2: a > $o] :
      ( ~ ( ( X2 @ ( '#sk19' @ X2 ) )
        <=> ( ??
            @ ^ [Y0: a > $o] :
                ( ( cP @ Y0 )
                & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) )
      | ( '#form55' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl57,plain,
    ! [X2: a > $o] :
      ( ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) )
      | ( '#form55' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl522,plain,
    ( '#form55'
    @ ^ [Y0: a] :
        ( ??
        @ ( ^ [Y1: a,Y2: a > $o] :
              ( ( ^ [Y3: a,Y4: a > $o] :
                    ( cP
                    @ ( ^ [Y5: a,Y6: a > $o,Y7: a] :
                          ( Y6
                          @ ( ^ [Y8: a,Y9: a > $o,Y10: a] : Y10
                            @ Y5
                            @ Y6
                            @ Y7 ) )
                      @ Y3
                      @ Y4 ) )
                @ Y1
                @ Y2 )
              & ( ^ [Y3: a,Y4: a > $o] :
                    ( Y4
                    @ ( ^ [Y5: a,Y6: a > $o] : Y5
                      @ Y3
                      @ Y4 ) )
                @ Y1
                @ Y2 ) )
          @ Y0 ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl527,plain,
    ( '#form55'
    @ ^ [Y0: a] :
        ( ??
        @ ^ [Y1: a > $o] :
            ( ( cP @ Y1 )
            & ( Y1 @ Y0 ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl522]) ).

thf(zip_derived_cl777,plain,
    '#sk41' @ '#sk58',
    inference('sup+',[status(thm)],[zip_derived_cl770,zip_derived_cl527]) ).

thf(zip_derived_cl58,plain,
    ! [X2: a > $o] :
      ( ( '#sk33' @ '#sk58' )
      | ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) )
      | ( cP @ '#sk5' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl575,plain,
    ( ( cP @ '#sk5' )
    | ( '#sk33' @ '#sk58' ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl25_002,plain,
    ! [X2: a > $o] :
      ( ( X2 @ ( '#sk10' @ X2 ) )
      | ~ ( cP @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl592,plain,
    ( ( '#sk33' @ '#sk58' )
    | ( '#sk5' @ ( '#sk10' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl575,zip_derived_cl25]) ).

thf(zip_derived_cl64,plain,
    ! [X2: a > $o,X4: a] :
      ( ( '#sk33' @ '#sk58' )
      | ~ ( '#form55' @ X2 )
      | ~ ( '#sk5' @ X4 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl61]) ).

thf(zip_derived_cl667,plain,
    ! [X0: a > $o] :
      ( ( '#sk33' @ '#sk58' )
      | ~ ( '#form55' @ X0 )
      | ( '#sk33' @ '#sk58' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl592,zip_derived_cl64]) ).

thf(zip_derived_cl685,plain,
    ! [X0: a > $o] :
      ( ~ ( '#form55' @ X0 )
      | ( '#sk33' @ '#sk58' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl667]) ).

thf(zip_derived_cl527_003,plain,
    ( '#form55'
    @ ^ [Y0: a] :
        ( ??
        @ ^ [Y1: a > $o] :
            ( ( cP @ Y1 )
            & ( Y1 @ Y0 ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl522]) ).

thf(zip_derived_cl694,plain,
    '#sk33' @ '#sk58',
    inference('sup+',[status(thm)],[zip_derived_cl685,zip_derived_cl527]) ).

thf(zip_derived_cl3,plain,
    ( !!
    @ ^ [Y0: a] :
        ( !!
        @ ^ [Y1: a > $o] :
            ( !!
            @ ^ [Y2: a > $o] :
                ( ( ( Y2 @ Y0 )
                  & ( Y1 @ Y0 )
                  & ( cP @ Y2 )
                  & ( cP @ Y1 ) )
               => ( Y1 = Y2 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl9,plain,
    ! [X2: a] :
      ( !!
      @ ^ [Y0: a > $o] :
          ( !!
          @ ^ [Y1: a > $o] :
              ( ( ( Y1 @ X2 )
                & ( Y0 @ X2 )
                & ( cP @ Y1 )
                & ( cP @ Y0 ) )
             => ( Y0 = Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl15,plain,
    ! [X2: a,X4: a > $o] :
      ( !!
      @ ^ [Y0: a > $o] :
          ( ( ( Y0 @ X2 )
            & ( X4 @ X2 )
            & ( cP @ Y0 )
            & ( cP @ X4 ) )
         => ( X4 = Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl21,plain,
    ! [X2: a,X4: a > $o,X6: a > $o] :
      ( ( ( X6 @ X2 )
        & ( X4 @ X2 )
        & ( cP @ X6 )
        & ( cP @ X4 ) )
     => ( X4 = X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl28,plain,
    ! [X2: a,X4: a > $o,X6: a > $o] :
      ( ~ ( ( X6 @ X2 )
          & ( X4 @ X2 )
          & ( cP @ X6 )
          & ( cP @ X4 ) )
      | ( X4 = X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl31,plain,
    ! [X2: a,X4: a > $o,X6: a > $o] :
      ( ~ ( ( X6 @ X2 )
          & ( X4 @ X2 )
          & ( cP @ X6 )
          & ( cP @ X4 ) )
      | ( X4 = X6 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl32,plain,
    ! [X2: a,X4: a > $o,X6: a > $o] :
      ( ~ ( X6 @ X2 )
      | ~ ( X4 @ X2 )
      | ~ ( cP @ X6 )
      | ~ ( cP @ X4 )
      | ( X4 = X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl709,plain,
    ! [X0: a > $o] :
      ( ( X0
        = ( ^ [Y0: a] :
              ( '#sk33'
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) ) )
      | ~ ( cP @ X0 )
      | ~ ( cP
          @ ^ [Y0: a] :
              ( '#sk33'
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) )
      | ~ ( X0 @ '#sk58' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl694,zip_derived_cl32]) ).

thf(zip_derived_cl716,plain,
    ! [X0: a > $o] :
      ( ( X0 = '#sk33' )
      | ~ ( cP @ X0 )
      | ~ ( cP @ '#sk33' )
      | ~ ( X0 @ '#sk58' ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl709]) ).

thf(zip_derived_cl44,plain,
    ! [X2: a > $o] :
      ( ( cP @ '#sk33' )
      | ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) )
      | ( cP @ '#sk5' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl432,plain,
    ( ( cP @ '#sk5' )
    | ( cP @ '#sk33' ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl25_004,plain,
    ! [X2: a > $o] :
      ( ( X2 @ ( '#sk10' @ X2 ) )
      | ~ ( cP @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl48,plain,
    ! [X2: a > $o,X4: a] :
      ( ( cP @ '#sk33' )
      | ~ ( '#sk5' @ X4 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl50_005,plain,
    ! [X2: a > $o] :
      ( ( '#form55' @ X2 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl56,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( '#form55'
          @ ^ [Y0: a] : ( X2 @ Y0 ) )
      | ~ ( '#sk5' @ X4 )
      | ( cP @ '#sk33' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl48,zip_derived_cl50]) ).

thf(zip_derived_cl63,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( '#form55' @ X2 )
      | ~ ( '#sk5' @ X4 )
      | ( cP @ '#sk33' ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl56]) ).

thf(zip_derived_cl429,plain,
    ! [X0: a > a,X1: a > $o] :
      ( ~ ( cP
          @ ^ [Y0: a] : ( '#sk5' @ ( X0 @ Y0 ) ) )
      | ( cP @ '#sk33' )
      | ~ ( '#form55' @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl63]) ).

thf(zip_derived_cl869,plain,
    ! [X0: a > $o] :
      ( ( cP @ '#sk33' )
      | ~ ( '#form55' @ X0 )
      | ( cP @ '#sk33' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl432,zip_derived_cl429]) ).

thf(zip_derived_cl874,plain,
    ! [X0: a > $o] :
      ( ~ ( '#form55' @ X0 )
      | ( cP @ '#sk33' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl869]) ).

thf(zip_derived_cl527_006,plain,
    ( '#form55'
    @ ^ [Y0: a] :
        ( ??
        @ ^ [Y1: a > $o] :
            ( ( cP @ Y1 )
            & ( Y1 @ Y0 ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl522]) ).

thf(zip_derived_cl910,plain,
    cP @ '#sk33',
    inference('sup+',[status(thm)],[zip_derived_cl874,zip_derived_cl527]) ).

thf(zip_derived_cl969,plain,
    ! [X0: a > $o] :
      ( ( X0 = '#sk33' )
      | ~ ( cP @ X0 )
      | ~ ( X0 @ '#sk58' ) ),
    inference(demod,[status(thm)],[zip_derived_cl716,zip_derived_cl910]) ).

thf(zip_derived_cl1038,plain,
    ( ~ ( cP
        @ ^ [Y0: a] : ( '#sk41' @ Y0 ) )
    | ( ( ^ [Y0: a] : ( '#sk41' @ Y0 ) )
      = '#sk33' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl777,zip_derived_cl969]) ).

thf(zip_derived_cl1065,plain,
    ( ~ ( cP @ '#sk41' )
    | ( '#sk41' = '#sk33' ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl1038]) ).

thf(zip_derived_cl39,plain,
    ! [X2: a > $o] :
      ( ( '#sk33' != '#sk41' )
      | ( cP @ '#sk5' )
      | ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl45,plain,
    ! [X2: a > $o] :
      ( ( '#sk33' != '#sk41' )
      | ( cP @ '#sk5' )
      | ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl487,plain,
    ( ( cP @ '#sk5' )
    | ( '#sk33' != '#sk41' ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl25_007,plain,
    ! [X2: a > $o] :
      ( ( X2 @ ( '#sk10' @ X2 ) )
      | ~ ( cP @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl489,plain,
    ( ( '#sk33' != '#sk41' )
    | ( '#sk5' @ ( '#sk10' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl487,zip_derived_cl25]) ).

thf(zip_derived_cl49_008,plain,
    ! [X2: a > $o,X4: a] :
      ( ( '#sk33' != '#sk41' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) )
      | ~ ( '#sk5' @ X4 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl41]) ).

thf(zip_derived_cl50_009,plain,
    ! [X2: a > $o] :
      ( ( '#form55' @ X2 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl52,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( '#form55' @ X2 )
      | ~ ( '#sk5' @ X4 )
      | ( '#sk33' != '#sk41' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl49,zip_derived_cl50]) ).

thf(zip_derived_cl800,plain,
    ! [X0: a > $o] :
      ( ( '#sk33' != '#sk41' )
      | ( '#sk33' != '#sk41' )
      | ~ ( '#form55' @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl489,zip_derived_cl52]) ).

thf(zip_derived_cl813,plain,
    ! [X0: a > $o] :
      ( ~ ( '#form55' @ X0 )
      | ( '#sk33' != '#sk41' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl800]) ).

thf(zip_derived_cl527_010,plain,
    ( '#form55'
    @ ^ [Y0: a] :
        ( ??
        @ ^ [Y1: a > $o] :
            ( ( cP @ Y1 )
            & ( Y1 @ Y0 ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl522]) ).

thf(zip_derived_cl824,plain,
    '#sk33' != '#sk41',
    inference('sup+',[status(thm)],[zip_derived_cl813,zip_derived_cl527]) ).

thf(zip_derived_cl1066,plain,
    ~ ( cP @ '#sk41' ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1065,zip_derived_cl824]) ).

thf(zip_derived_cl43,plain,
    ! [X2: a > $o] :
      ( ( cP @ '#sk41' )
      | ( ( X2 @ ( '#sk19' @ X2 ) )
       != ( ??
          @ ^ [Y0: a > $o] :
              ( ( cP @ Y0 )
              & ( Y0 @ ( '#sk19' @ X2 ) ) ) ) )
      | ( cP @ '#sk5' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl373,plain,
    ( ( cP @ '#sk5' )
    | ( cP @ '#sk41' ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl25_011,plain,
    ! [X2: a > $o] :
      ( ( X2 @ ( '#sk10' @ X2 ) )
      | ~ ( cP @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl385,plain,
    ( ( cP @ '#sk41' )
    | ( '#sk5' @ ( '#sk10' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl373,zip_derived_cl25]) ).

thf(zip_derived_cl1088,plain,
    '#sk5' @ ( '#sk10' @ '#sk5' ),
    inference('sup+',[status(thm)],[zip_derived_cl1066,zip_derived_cl385]) ).

thf(zip_derived_cl47,plain,
    ! [X2: a > $o,X4: a] :
      ( ( cP @ '#sk41' )
      | ~ ( '#sk5' @ X4 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl50_012,plain,
    ! [X2: a > $o] :
      ( ( '#form55' @ X2 )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
            <=> ( ??
                @ ^ [Y1: a > $o] :
                    ( ( cP @ Y1 )
                    & ( Y1 @ Y0 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl55,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( '#form55'
          @ ^ [Y0: a] : ( X2 @ Y0 ) )
      | ~ ( '#sk5' @ X4 )
      | ( cP @ '#sk41' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl47,zip_derived_cl50]) ).

thf(zip_derived_cl62,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( '#form55' @ X2 )
      | ~ ( '#sk5' @ X4 )
      | ( cP @ '#sk41' ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl1247,plain,
    ! [X0: a > $o] :
      ( ( cP @ '#sk41' )
      | ~ ( '#form55' @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1088,zip_derived_cl62]) ).

thf(zip_derived_cl1066_013,plain,
    ~ ( cP @ '#sk41' ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1065,zip_derived_cl824]) ).

thf(zip_derived_cl1276,plain,
    ! [X0: a > $o] :
      ~ ( '#form55' @ X0 ),
    inference(clc,[status(thm)],[zip_derived_cl1247,zip_derived_cl1066]) ).

thf(zip_derived_cl527_014,plain,
    ( '#form55'
    @ ^ [Y0: a] :
        ( ??
        @ ^ [Y1: a > $o] :
            ( ( cP @ Y1 )
            & ( Y1 @ Y0 ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl522]) ).

thf(zip_derived_cl1278,plain,
    $false,
    inference('sup+',[status(thm)],[zip_derived_cl1276,zip_derived_cl527]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV174^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.FcZ6w99yEp true
% 0.14/0.33  % Computer : n013.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 300
% 0.14/0.33  % DateTime : Thu Aug 24 02:45:17 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  % Running portfolio for 300 s
% 0.14/0.34  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.34  % Number of cores: 8
% 0.14/0.34  % Python version: Python 3.6.8
% 0.14/0.34  % Running in HO mode
% 0.17/0.61  % Total configuration time : 828
% 0.17/0.61  % Estimated wc time : 1656
% 0.17/0.61  % Estimated cpu time (8 cpus) : 207.0
% 0.17/0.70  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.17/0.70  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.17/0.71  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.17/0.71  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.17/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.17/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.17/0.72  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.17/0.76  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 20.34/3.37  % Solved by lams/30_sp5.sh.
% 20.34/3.37  % done 197 iterations in 2.539s
% 20.34/3.37  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 20.34/3.37  % SZS output start Refutation
% See solution above
% 20.34/3.38  
% 20.34/3.38  
% 20.34/3.38  % Terminating...
% 20.36/3.50  % Runner terminated.
% 20.36/3.52  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------