TSTP Solution File: LCL864^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : LCL864^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.GWx6QVIG34 true

% Computer : n014.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 09:02:27 EDT 2023

% Result   : Theorem 2.18s 0.93s
% Output   : Refutation 2.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   33
%            Number of leaves      :   45
% Syntax   : Number of formulae    :  173 (  37 unt;  20 typ;   0 def)
%            Number of atoms       :  951 (  17 equ;   0 cnn)
%            Maximal formula atoms :   27 (   6 avg)
%            Number of connectives : 2408 ( 201   ~; 201   |; 155   &;1374   @)
%                                         (   5 <=>; 125  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   56 (  56   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  20 usr;  16 con; 0-2 aty)
%                                         ( 310  !!;  37  ??;   0 @@+;   0 @@-)
%            Number of variables   :  486 ( 362   ^; 119   !;   5   ?; 486   :)

% Comments : 
%------------------------------------------------------------------------------
thf('#sk13_type',type,
    '#sk13': $i ).

thf(meuclidean_type,type,
    meuclidean: ( $i > $i > $o ) > $o ).

thf('#form7_type',type,
    '#form7': $o ).

thf('#sk8_type',type,
    '#sk8': $i ).

thf('#sk14_type',type,
    '#sk14': $i ).

thf('#sk9_type',type,
    '#sk9': $i ).

thf(mreflexive_type,type,
    mreflexive: ( $i > $i > $o ) > $o ).

thf('#form10_type',type,
    '#form10': $o ).

thf('#sk5_type',type,
    '#sk5': $i ).

thf('#sk11_type',type,
    '#sk11': $i ).

thf('#form2_type',type,
    '#form2': $o ).

thf('#sk1_type',type,
    '#sk1': $i > $i > $o ).

thf('#sk12_type',type,
    '#sk12': $i ).

thf(mtransitive_type,type,
    mtransitive: ( $i > $i > $o ) > $o ).

thf('#sk15_type',type,
    '#sk15': $i ).

thf('#sk3_type',type,
    '#sk3': $i > $i ).

thf(mserial_type,type,
    mserial: ( $i > $i > $o ) > $o ).

thf(msymmetric_type,type,
    msymmetric: ( $i > $i > $o ) > $o ).

thf('#sk4_type',type,
    '#sk4': $i ).

thf('#sk6_type',type,
    '#sk6': $i ).

thf(meuclidean,axiom,
    ( meuclidean
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ S @ U ) )
         => ( R @ T @ U ) ) ) ) ).

thf('0',plain,
    ( meuclidean
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ S @ U ) )
         => ( R @ T @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[meuclidean]) ).

thf('1',plain,
    ( meuclidean
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i,X6: $i,X8: $i] :
          ( ( ( V_1 @ X4 @ X6 )
            & ( V_1 @ X4 @ X8 ) )
         => ( V_1 @ X6 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(mtransitive,axiom,
    ( mtransitive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ T @ U ) )
         => ( R @ S @ U ) ) ) ) ).

thf('2',plain,
    ( mtransitive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i,U: $i] :
          ( ( ( R @ S @ T )
            & ( R @ T @ U ) )
         => ( R @ S @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mtransitive]) ).

thf('3',plain,
    ( mtransitive
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i,X6: $i,X8: $i] :
          ( ( ( V_1 @ X4 @ X6 )
            & ( V_1 @ X6 @ X8 ) )
         => ( V_1 @ X4 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(mserial,axiom,
    ( mserial
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] :
        ? [T: $i] : ( R @ S @ T ) ) ) ).

thf('4',plain,
    ( mserial
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] :
        ? [T: $i] : ( R @ S @ T ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mserial]) ).

thf('5',plain,
    ( mserial
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i] :
        ? [X6: $i] : ( V_1 @ X4 @ X6 ) ) ),
    define([status(thm)]) ).

thf(msymmetric,axiom,
    ( msymmetric
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i] :
          ( ( R @ S @ T )
         => ( R @ T @ S ) ) ) ) ).

thf('6',plain,
    ( msymmetric
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i] :
          ( ( R @ S @ T )
         => ( R @ T @ S ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[msymmetric]) ).

thf('7',plain,
    ( msymmetric
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i,X6: $i] :
          ( ( V_1 @ X4 @ X6 )
         => ( V_1 @ X6 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(mreflexive,axiom,
    ( mreflexive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] : ( R @ S @ S ) ) ) ).

thf('8',plain,
    ( mreflexive
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i] : ( R @ S @ S ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mreflexive]) ).

thf('9',plain,
    ( mreflexive
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i] : ( V_1 @ X4 @ X4 ) ) ),
    define([status(thm)]) ).

thf(conj,conjecture,
    ! [R: $i > $i > $o] :
      ( ( ( mreflexive @ R )
        & ( meuclidean @ R ) )
    <=> ( ( mserial @ R )
        & ( mtransitive @ R )
        & ( msymmetric @ R )
        & ( meuclidean @ R ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i > $i > $o] :
      ( ( ! [X8: $i,X10: $i,X12: $i] :
            ( ( ( X4 @ X8 @ X12 )
              & ( X4 @ X8 @ X10 ) )
           => ( X4 @ X10 @ X12 ) )
        & ! [X6: $i] : ( X4 @ X6 @ X6 ) )
    <=> ( ! [X28: $i,X30: $i,X32: $i] :
            ( ( ( X4 @ X28 @ X32 )
              & ( X4 @ X28 @ X30 ) )
           => ( X4 @ X30 @ X32 ) )
        & ! [X24: $i,X26: $i] :
            ( ( X4 @ X24 @ X26 )
           => ( X4 @ X26 @ X24 ) )
        & ! [X18: $i,X20: $i,X22: $i] :
            ( ( ( X4 @ X20 @ X22 )
              & ( X4 @ X18 @ X20 ) )
           => ( X4 @ X18 @ X22 ) )
        & ! [X14: $i] :
          ? [X16: $i] : ( X4 @ X14 @ X16 ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i > $i > $o] :
        ( ( ! [X8: $i,X10: $i,X12: $i] :
              ( ( ( X4 @ X8 @ X12 )
                & ( X4 @ X8 @ X10 ) )
             => ( X4 @ X10 @ X12 ) )
          & ! [X6: $i] : ( X4 @ X6 @ X6 ) )
      <=> ( ! [X28: $i,X30: $i,X32: $i] :
              ( ( ( X4 @ X28 @ X32 )
                & ( X4 @ X28 @ X30 ) )
             => ( X4 @ X30 @ X32 ) )
          & ! [X24: $i,X26: $i] :
              ( ( X4 @ X24 @ X26 )
             => ( X4 @ X26 @ X24 ) )
          & ! [X18: $i,X20: $i,X22: $i] :
              ( ( ( X4 @ X20 @ X22 )
                & ( X4 @ X18 @ X20 ) )
             => ( X4 @ X18 @ X22 ) )
          & ! [X14: $i] :
            ? [X16: $i] : ( X4 @ X14 @ X16 ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl0,plain,
    ~ ( !!
      @ ^ [Y0: $i > $i > $o] :
          ( ( ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( !!
                      @ ^ [Y3: $i] :
                          ( ( ( Y0 @ Y1 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y2 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) )
        <=> ( ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( !!
                      @ ^ [Y3: $i] :
                          ( ( ( Y0 @ Y1 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y2 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y0 @ Y1 @ Y2 )
                     => ( Y0 @ Y2 @ Y1 ) ) ) )
            & ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( !!
                      @ ^ [Y3: $i] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ~ ( ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y0 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) )
    <=> ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y0 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk1' @ Y1 @ Y0 ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y1 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl2,plain,
    ( ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) )
   != ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl4,plain,
    ( ~ ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y0 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) )
    | ~ ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y0 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk1' @ Y1 @ Y0 ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y1 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl81,plain,
    ( '#form2'
    | ~ ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y0 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk1' @ Y1 @ Y0 ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y1 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl82,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | '#form2' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl81]) ).

thf(zip_derived_cl85,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( ( '#sk1' @ '#sk4' @ Y1 )
                  & ( '#sk1' @ '#sk4' @ Y0 ) )
               => ( '#sk1' @ Y0 @ Y1 ) ) ) )
    | '#form2'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl82]) ).

thf(zip_derived_cl87,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( ( '#sk1' @ '#sk4' @ Y0 )
              & ( '#sk1' @ '#sk4' @ '#sk5' ) )
           => ( '#sk1' @ '#sk5' @ Y0 ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | '#form2' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl85]) ).

thf(zip_derived_cl89,plain,
    ( ~ ( ( ( '#sk1' @ '#sk4' @ '#sk6' )
          & ( '#sk1' @ '#sk4' @ '#sk5' ) )
       => ( '#sk1' @ '#sk5' @ '#sk6' ) )
    | '#form2'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl87]) ).

thf(zip_derived_cl91,plain,
    ( ( ( '#sk1' @ '#sk4' @ '#sk6' )
      & ( '#sk1' @ '#sk4' @ '#sk5' ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | '#form2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl95,plain,
    ( ( '#sk1' @ '#sk4' @ '#sk6' )
    | '#form2'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).

thf(zip_derived_cl103,plain,
    ( '#form10'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl104,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( ( '#sk1' @ Y0 @ Y1 )
                  & ( '#sk1' @ '#sk11' @ Y0 ) )
               => ( '#sk1' @ '#sk11' @ Y1 ) ) ) )
    | '#form10' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl103]) ).

thf(zip_derived_cl113,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( ( '#sk1' @ '#sk13' @ Y0 )
              & ( '#sk1' @ '#sk11' @ '#sk13' ) )
           => ( '#sk1' @ '#sk11' @ Y0 ) ) )
    | '#form10' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl104]) ).

thf(zip_derived_cl121,plain,
    ( ~ ( ( ( '#sk1' @ '#sk13' @ '#sk15' )
          & ( '#sk1' @ '#sk11' @ '#sk13' ) )
       => ( '#sk1' @ '#sk11' @ '#sk15' ) )
    | '#form10' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl113]) ).

thf(zip_derived_cl126,plain,
    ( ~ ( '#sk1' @ '#sk11' @ '#sk15' )
    | '#form10' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).

thf(zip_derived_cl2_001,plain,
    ( ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) )
   != ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl3,plain,
    ( ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) )
    | ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl6,plain,
    ( ( !!
      @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
    | ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl10,plain,
    ( ~ '#form2'
    | ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl14,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | ~ '#form2' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl21,plain,
    ! [X2: $i] :
      ( ( ??
        @ ^ [Y0: $i] : ( '#sk1' @ X2 @ Y0 ) )
      | ~ '#form2' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl26,plain,
    ! [X2: $i] :
      ( ( '#sk1' @ X2 @ ( '#sk3' @ X2 ) )
      | ~ '#form2' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl12,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( '#sk1' @ Y0 @ Y1 )
             => ( '#sk1' @ Y1 @ Y0 ) ) ) )
    | ~ '#form2' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl19,plain,
    ! [X2: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ X2 @ Y0 )
           => ( '#sk1' @ Y0 @ X2 ) ) )
      | ~ '#form2' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl24,plain,
    ! [X2: $i,X4: $i] :
      ( ( ( '#sk1' @ X2 @ X4 )
       => ( '#sk1' @ X4 @ X2 ) )
      | ~ '#form2' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl29,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 )
      | ~ '#form2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl36,plain,
    ! [X0: $i] :
      ( ~ '#form2'
      | ~ '#form2'
      | ( '#sk1' @ ( '#sk3' @ X0 ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl29]) ).

thf(zip_derived_cl42,plain,
    ! [X0: $i] :
      ( ( '#sk1' @ ( '#sk3' @ X0 ) @ X0 )
      | ~ '#form2' ),
    inference(simplify,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl5,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( '#sk1' @ Y0 @ Y2 )
                    & ( '#sk1' @ Y0 @ Y1 ) )
                 => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl7,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( '#sk1' @ Y0 @ Y2 )
                    & ( '#sk1' @ Y0 @ Y1 ) )
                 => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
    | ( $false
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl8,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( ( '#sk1' @ Y0 @ Y2 )
                  & ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl9,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( ( '#sk1' @ X2 @ Y1 )
                & ( '#sk1' @ X2 @ Y0 ) )
             => ( '#sk1' @ Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl16,plain,
    ! [X2: $i,X4: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( ( '#sk1' @ X2 @ Y0 )
            & ( '#sk1' @ X2 @ X4 ) )
         => ( '#sk1' @ X4 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl22,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( '#sk1' @ X2 @ X6 )
        & ( '#sk1' @ X2 @ X4 ) )
     => ( '#sk1' @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl27,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( '#sk1' @ X2 @ X6 )
          & ( '#sk1' @ X2 @ X4 ) )
      | ( '#sk1' @ X4 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl31,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( '#sk1' @ X2 @ X6 )
      | ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl47,plain,
    ! [X0: $i,X1: $i] :
      ( ( '#sk1' @ X0 @ X0 )
      | ~ ( '#sk1' @ X1 @ X0 ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl58,plain,
    ! [X0: $i] :
      ( ~ '#form2'
      | ( '#sk1' @ X0 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl42,zip_derived_cl47]) ).

thf(zip_derived_cl6_002,plain,
    ( ( !!
      @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
    | ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl10_003,plain,
    ( ~ '#form2'
    | ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl15,plain,
    ( '#form2'
    | ( !!
      @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl6,zip_derived_cl10]) ).

thf(zip_derived_cl17,plain,
    ! [X2: $i] :
      ( ( '#sk1' @ X2 @ X2 )
      | '#form2' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl66,plain,
    ! [X0: $i] : ( '#sk1' @ X0 @ X0 ),
    inference(clc,[status(thm)],[zip_derived_cl58,zip_derived_cl17]) ).

thf(zip_derived_cl66_004,plain,
    ! [X0: $i] : ( '#sk1' @ X0 @ X0 ),
    inference(clc,[status(thm)],[zip_derived_cl58,zip_derived_cl17]) ).

thf(zip_derived_cl96,plain,
    ( ( '#sk1' @ '#sk4' @ '#sk5' )
    | '#form2'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).

thf(zip_derived_cl103_005,plain,
    ( '#form10'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl106,plain,
    ( ~ '#form10'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | '#form2'
    | ( '#sk1' @ '#sk4' @ '#sk5' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl96,zip_derived_cl103]) ).

thf(zip_derived_cl92,plain,
    ( ~ ( '#sk1' @ '#sk5' @ '#sk6' )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | '#form2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl97,plain,
    ( '#form7'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl114,plain,
    ( ~ '#form7'
    | ( '#sk1' @ '#sk4' @ '#sk5' )
    | '#form2'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | ~ '#form10' ),
    inference(renaming,[status(thm)],[zip_derived_cl106,zip_derived_cl97]) ).

thf(zip_derived_cl122,plain,
    ( ~ ( ??
        @ ^ [Y0: $i] : ( '#sk1' @ '#sk14' @ Y0 ) )
    | ~ '#form10'
    | '#form2'
    | ( '#sk1' @ '#sk4' @ '#sk5' )
    | ~ '#form7' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl114]) ).

thf(zip_derived_cl127,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk14' @ X2 )
      | ~ '#form7'
      | ( '#sk1' @ '#sk4' @ '#sk5' )
      | '#form2'
      | ~ '#form10' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl122]) ).

thf(zip_derived_cl97_006,plain,
    ( '#form7'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl98,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ '#sk8' @ Y0 )
           => ( '#sk1' @ Y0 @ '#sk8' ) ) )
    | '#form7' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl97]) ).

thf(zip_derived_cl108,plain,
    ( ~ ( ( '#sk1' @ '#sk8' @ '#sk12' )
       => ( '#sk1' @ '#sk12' @ '#sk8' ) )
    | '#form7' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl98]) ).

thf(zip_derived_cl117,plain,
    ( ~ ( '#sk1' @ '#sk12' @ '#sk8' )
    | '#form7' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl108]) ).

thf(zip_derived_cl116,plain,
    ( ( '#sk1' @ '#sk8' @ '#sk12' )
    | '#form7' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl108]) ).

thf(zip_derived_cl66_007,plain,
    ! [X0: $i] : ( '#sk1' @ X0 @ X0 ),
    inference(clc,[status(thm)],[zip_derived_cl58,zip_derived_cl17]) ).

thf(zip_derived_cl31_008,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( '#sk1' @ X2 @ X6 )
      | ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl67,plain,
    ! [X0: $i,X1: $i] :
      ( ( '#sk1' @ X1 @ X0 )
      | ~ ( '#sk1' @ X0 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl31]) ).

thf(zip_derived_cl130,plain,
    ( '#form7'
    | ( '#sk1' @ '#sk12' @ '#sk8' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl116,zip_derived_cl67]) ).

thf(zip_derived_cl150,plain,
    '#form7',
    inference(clc,[status(thm)],[zip_derived_cl117,zip_derived_cl130]) ).

thf(zip_derived_cl4_009,plain,
    ( ~ ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y0 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) )
    | ~ ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y0 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk1' @ Y1 @ Y0 ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y1 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl81_010,plain,
    ( '#form2'
    | ~ ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y0 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk1' @ Y1 @ Y0 ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y1 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl10_011,plain,
    ( ~ '#form2'
    | ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl83,plain,
    ( ~ '#form2'
    | ~ ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk1' @ Y0 @ Y2 )
                        & ( '#sk1' @ Y0 @ Y1 ) )
                     => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl4,zip_derived_cl81,zip_derived_cl10]) ).

thf(zip_derived_cl84,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
    | ~ '#form2' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl83]) ).

thf(zip_derived_cl86,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( ( '#sk1' @ '#sk4' @ Y1 )
                  & ( '#sk1' @ '#sk4' @ Y0 ) )
               => ( '#sk1' @ Y0 @ Y1 ) ) ) )
    | ~ '#form2'
    | ~ ( !!
        @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl84]) ).

thf(zip_derived_cl88,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( ( '#sk1' @ '#sk4' @ Y0 )
              & ( '#sk1' @ '#sk4' @ '#sk5' ) )
           => ( '#sk1' @ '#sk5' @ Y0 ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
    | ~ '#form2' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl86]) ).

thf(zip_derived_cl90,plain,
    ( ~ ( ( ( '#sk1' @ '#sk4' @ '#sk6' )
          & ( '#sk1' @ '#sk4' @ '#sk5' ) )
       => ( '#sk1' @ '#sk5' @ '#sk6' ) )
    | ~ '#form2'
    | ~ ( !!
        @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl88]) ).

thf(zip_derived_cl93,plain,
    ( ( ( '#sk1' @ '#sk4' @ '#sk6' )
      & ( '#sk1' @ '#sk4' @ '#sk5' ) )
    | ~ ( !!
        @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
    | ~ '#form2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl90]) ).

thf(zip_derived_cl101,plain,
    ( ( '#sk1' @ '#sk4' @ '#sk5' )
    | ~ '#form2'
    | ~ ( !!
        @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl93]) ).

thf(zip_derived_cl110,plain,
    ( ~ ( '#sk1' @ '#sk9' @ '#sk9' )
    | ~ '#form2'
    | ( '#sk1' @ '#sk4' @ '#sk5' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl101]) ).

thf(zip_derived_cl66_012,plain,
    ! [X0: $i] : ( '#sk1' @ X0 @ X0 ),
    inference(clc,[status(thm)],[zip_derived_cl58,zip_derived_cl17]) ).

thf(zip_derived_cl119,plain,
    ( ~ '#form2'
    | ( '#sk1' @ '#sk4' @ '#sk5' ) ),
    inference(demod,[status(thm)],[zip_derived_cl110,zip_derived_cl66]) ).

thf(zip_derived_cl100,plain,
    ( ( '#sk1' @ '#sk4' @ '#sk6' )
    | ~ '#form2'
    | ~ ( !!
        @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl93]) ).

thf(zip_derived_cl109,plain,
    ( ~ ( '#sk1' @ '#sk9' @ '#sk9' )
    | ~ '#form2'
    | ( '#sk1' @ '#sk4' @ '#sk6' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl100]) ).

thf(zip_derived_cl66_013,plain,
    ! [X0: $i] : ( '#sk1' @ X0 @ X0 ),
    inference(clc,[status(thm)],[zip_derived_cl58,zip_derived_cl17]) ).

thf(zip_derived_cl118,plain,
    ( ~ '#form2'
    | ( '#sk1' @ '#sk4' @ '#sk6' ) ),
    inference(demod,[status(thm)],[zip_derived_cl109,zip_derived_cl66]) ).

thf(zip_derived_cl31_014,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( '#sk1' @ X2 @ X6 )
      | ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl164,plain,
    ! [X0: $i] :
      ( ~ '#form2'
      | ( '#sk1' @ X0 @ '#sk6' )
      | ~ ( '#sk1' @ '#sk4' @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl118,zip_derived_cl31]) ).

thf(zip_derived_cl187,plain,
    ( ~ '#form2'
    | ( '#sk1' @ '#sk5' @ '#sk6' )
    | ~ '#form2' ),
    inference('sup-',[status(thm)],[zip_derived_cl119,zip_derived_cl164]) ).

thf(zip_derived_cl195,plain,
    ( ( '#sk1' @ '#sk5' @ '#sk6' )
    | ~ '#form2' ),
    inference(simplify,[status(thm)],[zip_derived_cl187]) ).

thf(zip_derived_cl94,plain,
    ( ~ ( '#sk1' @ '#sk5' @ '#sk6' )
    | ~ ( !!
        @ ^ [Y0: $i] : ( '#sk1' @ Y0 @ Y0 ) )
    | ~ '#form2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl90]) ).

thf(zip_derived_cl102,plain,
    ( ~ ( '#sk1' @ '#sk9' @ '#sk9' )
    | ~ '#form2'
    | ~ ( '#sk1' @ '#sk5' @ '#sk6' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl94]) ).

thf(zip_derived_cl66_015,plain,
    ! [X0: $i] : ( '#sk1' @ X0 @ X0 ),
    inference(clc,[status(thm)],[zip_derived_cl58,zip_derived_cl17]) ).

thf(zip_derived_cl111,plain,
    ( ~ '#form2'
    | ~ ( '#sk1' @ '#sk5' @ '#sk6' ) ),
    inference(demod,[status(thm)],[zip_derived_cl102,zip_derived_cl66]) ).

thf(zip_derived_cl255,plain,
    ~ '#form2',
    inference(clc,[status(thm)],[zip_derived_cl195,zip_derived_cl111]) ).

thf(zip_derived_cl300,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk14' @ X2 )
      | ( '#sk1' @ '#sk4' @ '#sk5' )
      | ~ '#form10' ),
    inference(demod,[status(thm)],[zip_derived_cl127,zip_derived_cl150,zip_derived_cl255]) ).

thf(zip_derived_cl301,plain,
    ( ~ '#form10'
    | ( '#sk1' @ '#sk4' @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl300]) ).

thf(zip_derived_cl66_016,plain,
    ! [X0: $i] : ( '#sk1' @ X0 @ X0 ),
    inference(clc,[status(thm)],[zip_derived_cl58,zip_derived_cl17]) ).

thf(zip_derived_cl95_017,plain,
    ( ( '#sk1' @ '#sk4' @ '#sk6' )
    | '#form2'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).

thf(zip_derived_cl103_018,plain,
    ( '#form10'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl105,plain,
    ( ~ '#form10'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | '#form2'
    | ( '#sk1' @ '#sk4' @ '#sk6' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl95,zip_derived_cl103]) ).

thf(zip_derived_cl97_019,plain,
    ( '#form7'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl112,plain,
    ( ~ '#form7'
    | ( '#sk1' @ '#sk4' @ '#sk6' )
    | '#form2'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | ~ '#form10' ),
    inference(renaming,[status(thm)],[zip_derived_cl105,zip_derived_cl97]) ).

thf(zip_derived_cl120,plain,
    ( ~ ( ??
        @ ^ [Y0: $i] : ( '#sk1' @ '#sk14' @ Y0 ) )
    | ~ '#form10'
    | '#form2'
    | ( '#sk1' @ '#sk4' @ '#sk6' )
    | ~ '#form7' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl112]) ).

thf(zip_derived_cl124,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk14' @ X2 )
      | ~ '#form7'
      | ( '#sk1' @ '#sk4' @ '#sk6' )
      | '#form2'
      | ~ '#form10' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl120]) ).

thf(zip_derived_cl150_020,plain,
    '#form7',
    inference(clc,[status(thm)],[zip_derived_cl117,zip_derived_cl130]) ).

thf(zip_derived_cl255_021,plain,
    ~ '#form2',
    inference(clc,[status(thm)],[zip_derived_cl195,zip_derived_cl111]) ).

thf(zip_derived_cl274,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk14' @ X2 )
      | ( '#sk1' @ '#sk4' @ '#sk6' )
      | ~ '#form10' ),
    inference(demod,[status(thm)],[zip_derived_cl124,zip_derived_cl150,zip_derived_cl255]) ).

thf(zip_derived_cl275,plain,
    ( ~ '#form10'
    | ( '#sk1' @ '#sk4' @ '#sk6' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl274]) ).

thf(zip_derived_cl31_022,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( '#sk1' @ X2 @ X6 )
      | ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl278,plain,
    ! [X0: $i] :
      ( ~ '#form10'
      | ( '#sk1' @ X0 @ '#sk6' )
      | ~ ( '#sk1' @ '#sk4' @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl275,zip_derived_cl31]) ).

thf(zip_derived_cl303,plain,
    ( ~ '#form10'
    | ( '#sk1' @ '#sk5' @ '#sk6' )
    | ~ '#form10' ),
    inference('sup-',[status(thm)],[zip_derived_cl301,zip_derived_cl278]) ).

thf(zip_derived_cl309,plain,
    ( ( '#sk1' @ '#sk5' @ '#sk6' )
    | ~ '#form10' ),
    inference(simplify,[status(thm)],[zip_derived_cl303]) ).

thf(zip_derived_cl92_023,plain,
    ( ~ ( '#sk1' @ '#sk5' @ '#sk6' )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | '#form2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl97_024,plain,
    ( '#form7'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1' @ Y1 @ Y0 ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl99,plain,
    ( ~ '#form7'
    | '#form2'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( '#sk1' @ '#sk5' @ '#sk6' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl92,zip_derived_cl97]) ).

thf(zip_derived_cl103_025,plain,
    ( '#form10'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y1 @ Y2 )
                      & ( '#sk1' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y0 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl107,plain,
    ( ~ '#form10'
    | ~ ( '#sk1' @ '#sk5' @ '#sk6' )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i] : ( '#sk1' @ Y0 @ Y1 ) ) )
    | '#form2'
    | ~ '#form7' ),
    inference(renaming,[status(thm)],[zip_derived_cl99,zip_derived_cl103]) ).

thf(zip_derived_cl115,plain,
    ( ~ ( ??
        @ ^ [Y0: $i] : ( '#sk1' @ '#sk14' @ Y0 ) )
    | ~ '#form7'
    | '#form2'
    | ~ ( '#sk1' @ '#sk5' @ '#sk6' )
    | ~ '#form10' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl107]) ).

thf(zip_derived_cl123,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk14' @ X2 )
      | ~ '#form10'
      | ~ ( '#sk1' @ '#sk5' @ '#sk6' )
      | '#form2'
      | ~ '#form7' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl115]) ).

thf(zip_derived_cl150_026,plain,
    '#form7',
    inference(clc,[status(thm)],[zip_derived_cl117,zip_derived_cl130]) ).

thf(zip_derived_cl151,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk14' @ X2 )
      | ~ '#form10'
      | ~ ( '#sk1' @ '#sk5' @ '#sk6' )
      | '#form2' ),
    inference(demod,[status(thm)],[zip_derived_cl123,zip_derived_cl150]) ).

thf(zip_derived_cl111_027,plain,
    ( ~ '#form2'
    | ~ ( '#sk1' @ '#sk5' @ '#sk6' ) ),
    inference(demod,[status(thm)],[zip_derived_cl102,zip_derived_cl66]) ).

thf(zip_derived_cl152,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk5' @ '#sk6' )
      | ~ '#form10'
      | ~ ( '#sk1' @ '#sk14' @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl151,zip_derived_cl111]) ).

thf(zip_derived_cl315,plain,
    ! [X0: $i] :
      ( ~ '#form10'
      | ~ ( '#sk1' @ '#sk14' @ X0 )
      | ~ '#form10' ),
    inference('sup-',[status(thm)],[zip_derived_cl309,zip_derived_cl152]) ).

thf(zip_derived_cl321,plain,
    ! [X0: $i] :
      ( ~ ( '#sk1' @ '#sk14' @ X0 )
      | ~ '#form10' ),
    inference(simplify,[status(thm)],[zip_derived_cl315]) ).

thf(zip_derived_cl323,plain,
    ~ '#form10',
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl321]) ).

thf(zip_derived_cl325,plain,
    ~ ( '#sk1' @ '#sk11' @ '#sk15' ),
    inference(demod,[status(thm)],[zip_derived_cl126,zip_derived_cl323]) ).

thf(zip_derived_cl125,plain,
    ( ( ( '#sk1' @ '#sk13' @ '#sk15' )
      & ( '#sk1' @ '#sk11' @ '#sk13' ) )
    | '#form10' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).

thf(zip_derived_cl129,plain,
    ( ( '#sk1' @ '#sk11' @ '#sk13' )
    | '#form10' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl125]) ).

thf(zip_derived_cl67_028,plain,
    ! [X0: $i,X1: $i] :
      ( ( '#sk1' @ X1 @ X0 )
      | ~ ( '#sk1' @ X0 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl31]) ).

thf(zip_derived_cl138,plain,
    ( '#form10'
    | ( '#sk1' @ '#sk13' @ '#sk11' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl129,zip_derived_cl67]) ).

thf(zip_derived_cl323_029,plain,
    ~ '#form10',
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl321]) ).

thf(zip_derived_cl329,plain,
    '#sk1' @ '#sk13' @ '#sk11',
    inference(demod,[status(thm)],[zip_derived_cl138,zip_derived_cl323]) ).

thf(zip_derived_cl128,plain,
    ( ( '#sk1' @ '#sk13' @ '#sk15' )
    | '#form10' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl125]) ).

thf(zip_derived_cl323_030,plain,
    ~ '#form10',
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl321]) ).

thf(zip_derived_cl326,plain,
    '#sk1' @ '#sk13' @ '#sk15',
    inference(demod,[status(thm)],[zip_derived_cl128,zip_derived_cl323]) ).

thf(zip_derived_cl31_031,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( '#sk1' @ X2 @ X6 )
      | ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl332,plain,
    ! [X0: $i] :
      ( ( '#sk1' @ X0 @ '#sk15' )
      | ~ ( '#sk1' @ '#sk13' @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl326,zip_derived_cl31]) ).

thf(zip_derived_cl347,plain,
    '#sk1' @ '#sk11' @ '#sk15',
    inference('sup-',[status(thm)],[zip_derived_cl329,zip_derived_cl332]) ).

thf(zip_derived_cl368,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl325,zip_derived_cl347]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL864^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.GWx6QVIG34 true
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug 24 18:31:33 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in HO mode
% 0.20/0.65  % Total configuration time : 828
% 0.20/0.65  % Estimated wc time : 1656
% 0.20/0.65  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.72  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.75  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.48/0.81  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.48/0.83  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 2.18/0.93  % Solved by lams/20_acsne_simpl.sh.
% 2.18/0.93  % done 126 iterations in 0.083s
% 2.18/0.93  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 2.18/0.93  % SZS output start Refutation
% See solution above
% 2.18/0.93  
% 2.18/0.93  
% 2.18/0.93  % Terminating...
% 2.53/1.05  % Runner terminated.
% 2.53/1.07  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------