TSTP Solution File: SEV254^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV254^5 : 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.B6gKofhvN5 true

% Computer : n031.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 20:00:12 EDT 2023

% Result   : Theorem 65.44s 9.08s
% Output   : Refutation 65.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  151 (  13 unt;   8 typ;   0 def)
%            Number of atoms       : 1161 (   3 equ;   0 cnn)
%            Maximal formula atoms :   37 (   8 avg)
%            Number of connectives : 3323 ( 162   ~; 161   |; 217   &;1993   @)
%                                         (   6 <=>; 326  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  247 ( 247   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   8 usr;   6 con; 0-2 aty)
%                                         ( 271  !!; 187  ??;   0 @@+;   0 @@-)
%            Number of variables   :  716 ( 615   ^;  85   !;  16   ?; 716   :)

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

thf('#sk29_type',type,
    '#sk29': ( $i > $o ) > $i ).

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

thf('#sk2_type',type,
    '#sk2': $i ).

thf('#form143_type',type,
    '#form143': $o ).

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

thf('#sk144_type',type,
    '#sk144': $i > $o ).

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

thf(cTHM2C_pme,conjecture,
    ! [K: ( $i > $o ) > $i > $o] :
      ( ( ( ! [Xx: $i] :
              ( ? [S: $i > $o] :
                  ( ! [Xx0: $i] :
                      ( ( S @ Xx0 )
                     => ( K @ S @ Xx0 ) )
                  & ( S @ Xx ) )
             => ( K
                @ ^ [Xx0: $i] :
                  ? [S: $i > $o] :
                    ( ! [Xx1: $i] :
                        ( ( S @ Xx1 )
                       => ( K @ S @ Xx1 ) )
                    & ( S @ Xx0 ) )
                @ Xx ) )
         => ! [Xx: $i] :
              ( ( K
                @ ^ [Xx0: $i] :
                  ? [S: $i > $o] :
                    ( ! [Xx1: $i] :
                        ( ( S @ Xx1 )
                       => ( K @ S @ Xx1 ) )
                    & ( S @ Xx0 ) )
                @ Xx )
             => ( K
                @ ( K
                  @ ^ [Xx0: $i] :
                    ? [S: $i > $o] :
                      ( ! [Xx1: $i] :
                          ( ( S @ Xx1 )
                         => ( K @ S @ Xx1 ) )
                      & ( S @ Xx0 ) ) )
                @ Xx ) ) )
        & ! [Xx: $i > $o] :
            ( ! [Xx0: $i] :
                ( ( Xx @ Xx0 )
               => ? [S: $i > $o] :
                    ( ! [Xx1: $i] :
                        ( ( S @ Xx1 )
                       => ( K @ S @ Xx1 ) )
                    & ( S @ Xx0 ) ) )
           => ! [Xx0: $i] :
                ( ( K @ Xx @ Xx0 )
               => ( K
                  @ ^ [Xx1: $i] :
                    ? [S: $i > $o] :
                      ( ! [Xx2: $i] :
                          ( ( S @ Xx2 )
                         => ( K @ S @ Xx2 ) )
                      & ( S @ Xx1 ) )
                  @ Xx0 ) ) ) )
     => ! [Xx: $i] :
          ( ( K
            @ ^ [Xx0: $i] :
              ? [S: $i > $o] :
                ( ! [Xx1: $i] :
                    ( ( S @ Xx1 )
                   => ( K @ S @ Xx1 ) )
                & ( S @ Xx0 ) )
            @ Xx )
        <=> ? [S: $i > $o] :
              ( ! [Xx0: $i] :
                  ( ( S @ Xx0 )
                 => ( K @ S @ Xx0 ) )
              & ( S @ Xx ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [K: ( $i > $o ) > $i > $o] :
        ( ( ( ! [Xx: $i] :
                ( ? [S: $i > $o] :
                    ( ! [Xx0: $i] :
                        ( ( S @ Xx0 )
                       => ( K @ S @ Xx0 ) )
                    & ( S @ Xx ) )
               => ( K
                  @ ^ [Xx0: $i] :
                    ? [S: $i > $o] :
                      ( ! [Xx1: $i] :
                          ( ( S @ Xx1 )
                         => ( K @ S @ Xx1 ) )
                      & ( S @ Xx0 ) )
                  @ Xx ) )
           => ! [Xx: $i] :
                ( ( K
                  @ ^ [Xx0: $i] :
                    ? [S: $i > $o] :
                      ( ! [Xx1: $i] :
                          ( ( S @ Xx1 )
                         => ( K @ S @ Xx1 ) )
                      & ( S @ Xx0 ) )
                  @ Xx )
               => ( K
                  @ ( K
                    @ ^ [Xx0: $i] :
                      ? [S: $i > $o] :
                        ( ! [Xx1: $i] :
                            ( ( S @ Xx1 )
                           => ( K @ S @ Xx1 ) )
                        & ( S @ Xx0 ) ) )
                  @ Xx ) ) )
          & ! [Xx: $i > $o] :
              ( ! [Xx0: $i] :
                  ( ( Xx @ Xx0 )
                 => ? [S: $i > $o] :
                      ( ! [Xx1: $i] :
                          ( ( S @ Xx1 )
                         => ( K @ S @ Xx1 ) )
                      & ( S @ Xx0 ) ) )
             => ! [Xx0: $i] :
                  ( ( K @ Xx @ Xx0 )
                 => ( K
                    @ ^ [Xx1: $i] :
                      ? [S: $i > $o] :
                        ( ! [Xx2: $i] :
                            ( ( S @ Xx2 )
                           => ( K @ S @ Xx2 ) )
                        & ( S @ Xx1 ) )
                    @ Xx0 ) ) ) )
       => ! [Xx: $i] :
            ( ( K
              @ ^ [Xx0: $i] :
                ? [S: $i > $o] :
                  ( ! [Xx1: $i] :
                      ( ( S @ Xx1 )
                     => ( K @ S @ Xx1 ) )
                  & ( S @ Xx0 ) )
              @ Xx )
          <=> ? [S: $i > $o] :
                ( ! [Xx0: $i] :
                    ( ( S @ Xx0 )
                   => ( K @ S @ Xx0 ) )
                & ( S @ Xx ) ) ) ),
    inference('cnf.neg',[status(esa)],[cTHM2C_pme]) ).

thf(zip_derived_cl0,plain,
    ~ ( !!
      @ ^ [Y0: ( $i > $o ) > $i > $o] :
          ( ( ( ( !!
                @ ^ [Y1: $i] :
                    ( ( ??
                      @ ^ [Y2: $i > $o] :
                          ( ( !!
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                               => ( Y0 @ Y2 @ Y3 ) ) )
                          & ( Y2 @ Y1 ) ) )
                   => ( Y0
                      @ ^ [Y2: $i] :
                          ( ??
                          @ ^ [Y3: $i > $o] :
                              ( ( !!
                                @ ^ [Y4: $i] :
                                    ( ( Y3 @ Y4 )
                                   => ( Y0 @ Y3 @ Y4 ) ) )
                              & ( Y3 @ Y2 ) ) )
                      @ Y1 ) ) )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( Y0
                      @ ^ [Y2: $i] :
                          ( ??
                          @ ^ [Y3: $i > $o] :
                              ( ( !!
                                @ ^ [Y4: $i] :
                                    ( ( Y3 @ Y4 )
                                   => ( Y0 @ Y3 @ Y4 ) ) )
                              & ( Y3 @ Y2 ) ) )
                      @ Y1 )
                   => ( Y0
                      @ ( Y0
                        @ ^ [Y2: $i] :
                            ( ??
                            @ ^ [Y3: $i > $o] :
                                ( ( !!
                                  @ ^ [Y4: $i] :
                                      ( ( Y3 @ Y4 )
                                     => ( Y0 @ Y3 @ Y4 ) ) )
                                & ( Y3 @ Y2 ) ) ) )
                      @ Y1 ) ) ) )
            & ( !!
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( ??
                          @ ^ [Y3: $i > $o] :
                              ( ( !!
                                @ ^ [Y4: $i] :
                                    ( ( Y3 @ Y4 )
                                   => ( Y0 @ Y3 @ Y4 ) ) )
                              & ( Y3 @ Y2 ) ) ) ) )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y0 @ Y1 @ Y2 )
                       => ( Y0
                          @ ^ [Y3: $i] :
                              ( ??
                              @ ^ [Y4: $i > $o] :
                                  ( ( !!
                                    @ ^ [Y5: $i] :
                                        ( ( Y4 @ Y5 )
                                       => ( Y0 @ Y4 @ Y5 ) ) )
                                  & ( Y4 @ Y3 ) ) )
                          @ Y2 ) ) ) ) ) )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( Y0
                  @ ^ [Y2: $i] :
                      ( ??
                      @ ^ [Y3: $i > $o] :
                          ( ( !!
                            @ ^ [Y4: $i] :
                                ( ( Y3 @ Y4 )
                               => ( Y0 @ Y3 @ Y4 ) ) )
                          & ( Y3 @ Y2 ) ) )
                  @ Y1 )
              <=> ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( Y0 @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1,plain,
    ~ ( ( ( ( !!
            @ ^ [Y0: $i] :
                ( ( ??
                  @ ^ [Y1: $i > $o] :
                      ( ( !!
                        @ ^ [Y2: $i] :
                            ( ( Y1 @ Y2 )
                           => ( '#sk1' @ Y1 @ Y2 ) ) )
                      & ( Y1 @ Y0 ) ) )
               => ( '#sk1'
                  @ ^ [Y1: $i] :
                      ( ??
                      @ ^ [Y2: $i > $o] :
                          ( ( !!
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                               => ( '#sk1' @ Y2 @ Y3 ) ) )
                          & ( Y2 @ Y1 ) ) )
                  @ Y0 ) ) )
         => ( !!
            @ ^ [Y0: $i] :
                ( ( '#sk1'
                  @ ^ [Y1: $i] :
                      ( ??
                      @ ^ [Y2: $i > $o] :
                          ( ( !!
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                               => ( '#sk1' @ Y2 @ Y3 ) ) )
                          & ( Y2 @ Y1 ) ) )
                  @ Y0 )
               => ( '#sk1'
                  @ ( '#sk1'
                    @ ^ [Y1: $i] :
                        ( ??
                        @ ^ [Y2: $i > $o] :
                            ( ( !!
                              @ ^ [Y3: $i] :
                                  ( ( Y2 @ Y3 )
                                 => ( '#sk1' @ Y2 @ Y3 ) ) )
                            & ( Y2 @ Y1 ) ) ) )
                  @ Y0 ) ) ) )
        & ( !!
          @ ^ [Y0: $i > $o] :
              ( ( !!
                @ ^ [Y1: $i] :
                    ( ( Y0 @ Y1 )
                   => ( ??
                      @ ^ [Y2: $i > $o] :
                          ( ( !!
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                               => ( '#sk1' @ Y2 @ Y3 ) ) )
                          & ( Y2 @ Y1 ) ) ) ) )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( '#sk1' @ Y0 @ Y1 )
                   => ( '#sk1'
                      @ ^ [Y2: $i] :
                          ( ??
                          @ ^ [Y3: $i > $o] :
                              ( ( !!
                                @ ^ [Y4: $i] :
                                    ( ( Y3 @ Y4 )
                                   => ( '#sk1' @ Y3 @ Y4 ) ) )
                              & ( Y3 @ Y2 ) ) )
                      @ Y1 ) ) ) ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
          <=> ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl3,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 )
        <=> ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl6,plain,
    ~ ( ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ '#sk2' )
    <=> ( ??
        @ ^ [Y0: $i > $o] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                 => ( '#sk1' @ Y0 @ Y1 ) ) )
            & ( Y0 @ '#sk2' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl9,plain,
    ( ( '#sk1'
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                   => ( '#sk1' @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk2' )
   != ( ??
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
               => ( '#sk1' @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk2' ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl43,plain,
    ( ( '#sk1'
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                   => ( '#sk1' @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk2' )
    | ( ??
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
               => ( '#sk1' @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk2' ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl43_001,plain,
    ( ( '#sk1'
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                   => ( '#sk1' @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk2' )
    | ( ??
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
               => ( '#sk1' @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk2' ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl119,plain,
    ( ~ '#form143'
    | ( ??
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
               => ( '#sk1' @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk2' ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl123,plain,
    ( '#form143'
    | ( '#sk1'
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                   => ( '#sk1' @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk2' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl43,zip_derived_cl119]) ).

thf(zip_derived_cl9_002,plain,
    ( ( '#sk1'
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                   => ( '#sk1' @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk2' )
   != ( ??
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
               => ( '#sk1' @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk2' ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl133,plain,
    ( ~ ( ??
        @ ^ [Y0: $i > $o] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                 => ( '#sk1' @ Y0 @ Y1 ) ) )
            & ( Y0 @ '#sk2' ) ) )
    | '#form143' ),
    inference('sup-',[status(thm)],[zip_derived_cl123,zip_derived_cl9]) ).

thf(zip_derived_cl144,plain,
    ! [X2: $i > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: $i] :
                ( ( X2 @ Y0 )
               => ( '#sk1' @ X2 @ Y0 ) ) )
          & ( X2 @ '#sk2' ) )
      | '#form143' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl133]) ).

thf(zip_derived_cl146,plain,
    ( ~ ( ( !!
          @ ^ [Y0: $i] :
              ( ( '#sk1'
                @ ^ [Y1: $i] :
                    ( ??
                    @ ^ [Y2: $i > $o] :
                        ( ( !!
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                             => ( '#sk1' @ Y2 @ Y3 ) ) )
                        & ( Y2 @ Y1 ) ) )
                @ Y0 )
             => ( '#sk1'
                @ ( '#sk1'
                  @ ^ [Y1: $i] :
                      ( ??
                      @ ^ [Y2: $i > $o] :
                          ( ( !!
                            @ ^ [Y3: $i] :
                                ( ( Y2 @ Y3 )
                               => ( '#sk1' @ Y2 @ Y3 ) ) )
                          & ( Y2 @ Y1 ) ) ) )
                @ Y0 ) ) )
        & ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ '#sk2' ) )
    | '#form143' ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl144]) ).

thf(zip_derived_cl2368,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( '#sk1'
              @ ( '#sk1'
                @ ^ [Y1: $i] :
                    ( ??
                    @ ^ [Y2: $i > $o] :
                        ( ( !!
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                             => ( '#sk1' @ Y2 @ Y3 ) ) )
                        & ( Y2 @ Y1 ) ) ) )
              @ Y0 ) ) )
    | ~ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ '#sk2' )
    | '#form143' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl146]) ).

thf(zip_derived_cl123_003,plain,
    ( '#form143'
    | ( '#sk1'
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                   => ( '#sk1' @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk2' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl43,zip_derived_cl119]) ).

thf(zip_derived_cl2369,plain,
    ( '#form143'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( '#sk1'
              @ ( '#sk1'
                @ ^ [Y1: $i] :
                    ( ??
                    @ ^ [Y2: $i > $o] :
                        ( ( !!
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                             => ( '#sk1' @ Y2 @ Y3 ) ) )
                        & ( Y2 @ Y1 ) ) ) )
              @ Y0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl2368,zip_derived_cl123]) ).

thf(zip_derived_cl2370,plain,
    ( ~ ( ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ ( '#sk29'
            @ ( '#sk1'
              @ ^ [Y0: $i] :
                  ( ??
                  @ ^ [Y1: $i > $o] :
                      ( ( !!
                        @ ^ [Y2: $i] :
                            ( ( Y1 @ Y2 )
                           => ( '#sk1' @ Y1 @ Y2 ) ) )
                      & ( Y1 @ Y0 ) ) ) ) ) )
       => ( '#sk1'
          @ ( '#sk1'
            @ ^ [Y0: $i] :
                ( ??
                @ ^ [Y1: $i > $o] :
                    ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( Y1 @ Y2 )
                         => ( '#sk1' @ Y1 @ Y2 ) ) )
                    & ( Y1 @ Y0 ) ) ) )
          @ ( '#sk29'
            @ ( '#sk1'
              @ ^ [Y0: $i] :
                  ( ??
                  @ ^ [Y1: $i > $o] :
                      ( ( !!
                        @ ^ [Y2: $i] :
                            ( ( Y1 @ Y2 )
                           => ( '#sk1' @ Y1 @ Y2 ) ) )
                      & ( Y1 @ Y0 ) ) ) ) ) ) )
    | '#form143' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2369]) ).

thf(zip_derived_cl2371,plain,
    ( ( '#sk1'
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                   => ( '#sk1' @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ ( '#sk29'
        @ ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) ) ) )
    | '#form143' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2370]) ).

thf(zip_derived_cl119_004,plain,
    ( ~ '#form143'
    | ( ??
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
               => ( '#sk1' @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk2' ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl122,plain,
    ( ( ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk144' @ Y0 )
           => ( '#sk1' @ '#sk144' @ Y0 ) ) )
      & ( '#sk144' @ '#sk2' ) )
    | ~ '#form143' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl119]) ).

thf(zip_derived_cl124,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk144' @ Y0 )
         => ( '#sk1' @ '#sk144' @ Y0 ) ) )
    | ~ '#form143' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl122]) ).

thf(zip_derived_cl126,plain,
    ! [X2: $i] :
      ( ( ( '#sk144' @ X2 )
       => ( '#sk1' @ '#sk144' @ X2 ) )
      | ~ '#form143' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl124]) ).

thf(zip_derived_cl127,plain,
    ! [X2: $i] :
      ( ~ ( '#sk144' @ X2 )
      | ( '#sk1' @ '#sk144' @ X2 )
      | ~ '#form143' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl126]) ).

thf(zip_derived_cl127_005,plain,
    ! [X2: $i] :
      ( ~ ( '#sk144' @ X2 )
      | ( '#sk1' @ '#sk144' @ X2 )
      | ~ '#form143' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl126]) ).

thf(zip_derived_cl2,plain,
    ( ( ( !!
        @ ^ [Y0: $i] :
            ( ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
           => ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( '#sk1'
              @ ( '#sk1'
                @ ^ [Y1: $i] :
                    ( ??
                    @ ^ [Y2: $i > $o] :
                        ( ( !!
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                             => ( '#sk1' @ Y2 @ Y3 ) ) )
                        & ( Y2 @ Y1 ) ) ) )
              @ Y0 ) ) ) )
    & ( !!
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
               => ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) ) ) )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk1'
                  @ ^ [Y2: $i] :
                      ( ??
                      @ ^ [Y3: $i > $o] :
                          ( ( !!
                            @ ^ [Y4: $i] :
                                ( ( Y3 @ Y4 )
                               => ( '#sk1' @ Y3 @ Y4 ) ) )
                          & ( Y3 @ Y2 ) ) )
                  @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl5,plain,
    ( !!
    @ ^ [Y0: $i > $o] :
        ( ( !!
          @ ^ [Y1: $i] :
              ( ( Y0 @ Y1 )
             => ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) ) ) )
       => ( !!
          @ ^ [Y1: $i] :
              ( ( '#sk1' @ Y0 @ Y1 )
             => ( '#sk1'
                @ ^ [Y2: $i] :
                    ( ??
                    @ ^ [Y3: $i > $o] :
                        ( ( !!
                          @ ^ [Y4: $i] :
                              ( ( Y3 @ Y4 )
                             => ( '#sk1' @ Y3 @ Y4 ) ) )
                        & ( Y3 @ Y2 ) ) )
                @ Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl8,plain,
    ! [X2: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( X2 @ Y0 )
           => ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ X2 @ Y0 )
           => ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl121,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk144' @ Y0 )
         => ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) ) ) )
   => ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk144' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl447,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk144' @ Y0 )
           => ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk144' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl121]) ).

thf(zip_derived_cl448,plain,
    ( ~ ( ( '#sk144' @ ( '#sk8' @ '#sk144' ) )
       => ( ??
          @ ^ [Y0: $i > $o] :
              ( ( !!
                @ ^ [Y1: $i] :
                    ( ( Y0 @ Y1 )
                   => ( '#sk1' @ Y0 @ Y1 ) ) )
              & ( Y0 @ ( '#sk8' @ '#sk144' ) ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk144' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl447]) ).

thf(zip_derived_cl450,plain,
    ( ~ ( ??
        @ ^ [Y0: $i > $o] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                 => ( '#sk1' @ Y0 @ Y1 ) ) )
            & ( Y0 @ ( '#sk8' @ '#sk144' ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk144' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl448]) ).

thf(zip_derived_cl452,plain,
    ! [X2: $i > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: $i] :
                ( ( X2 @ Y0 )
               => ( '#sk1' @ X2 @ Y0 ) ) )
          & ( X2 @ ( '#sk8' @ '#sk144' ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ '#sk144' @ Y0 )
           => ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl450]) ).

thf(zip_derived_cl453,plain,
    ( ~ ( ( !!
          @ ^ [Y0: $i] :
              ( ( '#sk144' @ Y0 )
             => ( '#sk1' @ '#sk144' @ Y0 ) ) )
        & ( '#sk144' @ ( '#sk8' @ '#sk144' ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk144' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl452]) ).

thf(zip_derived_cl1757,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk144' @ Y0 )
           => ( '#sk1' @ '#sk144' @ Y0 ) ) )
    | ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk144' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl453]) ).

thf(zip_derived_cl1758,plain,
    ( ~ ( ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
       => ( '#sk1' @ '#sk144' @ ( '#sk29' @ '#sk144' ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk144' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) )
    | ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1757]) ).

thf(zip_derived_cl1760,plain,
    ( ~ ( '#sk1' @ '#sk144' @ ( '#sk29' @ '#sk144' ) )
    | ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk144' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1758]) ).

thf(zip_derived_cl1762,plain,
    ! [X2: $i] :
      ( ( ( '#sk1' @ '#sk144' @ X2 )
       => ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X2 ) )
      | ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) )
      | ~ ( '#sk1' @ '#sk144' @ ( '#sk29' @ '#sk144' ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1760]) ).

thf(zip_derived_cl1764,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk144' @ X2 )
      | ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X2 )
      | ~ ( '#sk1' @ '#sk144' @ ( '#sk29' @ '#sk144' ) )
      | ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1762]) ).

thf(zip_derived_cl8_006,plain,
    ! [X2: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( X2 @ Y0 )
           => ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ X2 @ Y0 )
           => ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl11,plain,
    ! [X2: $i > $o] :
      ( ~ ( !!
          @ ^ [Y0: $i] :
              ( ( X2 @ Y0 )
             => ( ??
                @ ^ [Y1: $i > $o] :
                    ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( Y1 @ Y2 )
                         => ( '#sk1' @ Y1 @ Y2 ) ) )
                    & ( Y1 @ Y0 ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ X2 @ Y0 )
           => ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl14,plain,
    ! [X2: $i > $o] :
      ( ~ ( ( X2 @ ( '#sk8' @ X2 ) )
         => ( ??
            @ ^ [Y0: $i > $o] :
                ( ( !!
                  @ ^ [Y1: $i] :
                      ( ( Y0 @ Y1 )
                     => ( '#sk1' @ Y0 @ Y1 ) ) )
                & ( Y0 @ ( '#sk8' @ X2 ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ X2 @ Y0 )
           => ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl18,plain,
    ! [X2: $i > $o] :
      ( ( X2 @ ( '#sk8' @ X2 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ X2 @ Y0 )
           => ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl23,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ( ( '#sk1' @ X2 @ X4 )
       => ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X4 ) )
      | ( X2 @ ( '#sk8' @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl28,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X4 )
      | ( X2 @ ( '#sk8' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl1766,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk144' @ ( '#sk29' @ '#sk144' ) )
      | ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X2 )
      | ~ ( '#sk1' @ '#sk144' @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl1764,zip_derived_cl28]) ).

thf(zip_derived_cl9_007,plain,
    ( ( '#sk1'
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                   => ( '#sk1' @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk2' )
   != ( ??
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
               => ( '#sk1' @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk2' ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl44,plain,
    ( ~ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ '#sk2' )
    | ~ ( ??
        @ ^ [Y0: $i > $o] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                 => ( '#sk1' @ Y0 @ Y1 ) ) )
            & ( Y0 @ '#sk2' ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl44_008,plain,
    ( ~ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ '#sk2' )
    | ~ ( ??
        @ ^ [Y0: $i > $o] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                 => ( '#sk1' @ Y0 @ Y1 ) ) )
            & ( Y0 @ '#sk2' ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl476,plain,
    ( '#form143'
    | ~ ( ??
        @ ^ [Y0: $i > $o] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                 => ( '#sk1' @ Y0 @ Y1 ) ) )
            & ( Y0 @ '#sk2' ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl119_009,plain,
    ( ~ '#form143'
    | ( ??
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
               => ( '#sk1' @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk2' ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl482,plain,
    ( ~ '#form143'
    | ~ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ '#sk2' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl44,zip_derived_cl476,zip_derived_cl119]) ).

thf(zip_derived_cl2411,plain,
    ( ~ ( '#sk1' @ '#sk144' @ '#sk2' )
    | ~ ( '#sk1' @ '#sk144' @ ( '#sk29' @ '#sk144' ) )
    | ~ '#form143' ),
    inference('sup-',[status(thm)],[zip_derived_cl1766,zip_derived_cl482]) ).

thf(zip_derived_cl2429,plain,
    ( ~ '#form143'
    | ~ ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
    | ~ '#form143'
    | ~ ( '#sk1' @ '#sk144' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl127,zip_derived_cl2411]) ).

thf(zip_derived_cl2430,plain,
    ( ~ ( '#sk1' @ '#sk144' @ '#sk2' )
    | ~ ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
    | ~ '#form143' ),
    inference(simplify,[status(thm)],[zip_derived_cl2429]) ).

thf(zip_derived_cl127_010,plain,
    ! [X2: $i] :
      ( ~ ( '#sk144' @ X2 )
      | ( '#sk1' @ '#sk144' @ X2 )
      | ~ '#form143' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl126]) ).

thf(zip_derived_cl1759,plain,
    ( ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
    | ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk144' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1758]) ).

thf(zip_derived_cl1761,plain,
    ! [X2: $i] :
      ( ( ( '#sk1' @ '#sk144' @ X2 )
       => ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X2 ) )
      | ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) )
      | ( '#sk144' @ ( '#sk29' @ '#sk144' ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1759]) ).

thf(zip_derived_cl1763,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk144' @ X2 )
      | ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X2 )
      | ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
      | ~ ( '#sk144' @ ( '#sk8' @ '#sk144' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1761]) ).

thf(zip_derived_cl28_011,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X4 )
      | ( X2 @ ( '#sk8' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl1765,plain,
    ! [X2: $i] :
      ( ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
      | ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X2 )
      | ~ ( '#sk1' @ '#sk144' @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl1763,zip_derived_cl28]) ).

thf(zip_derived_cl482_012,plain,
    ( ~ '#form143'
    | ~ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ '#sk2' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl44,zip_derived_cl476,zip_derived_cl119]) ).

thf(zip_derived_cl1767,plain,
    ( ~ ( '#sk1' @ '#sk144' @ '#sk2' )
    | ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
    | ~ '#form143' ),
    inference('sup-',[status(thm)],[zip_derived_cl1765,zip_derived_cl482]) ).

thf(zip_derived_cl1786,plain,
    ( ~ '#form143'
    | ~ ( '#sk144' @ '#sk2' )
    | ~ '#form143'
    | ( '#sk144' @ ( '#sk29' @ '#sk144' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl127,zip_derived_cl1767]) ).

thf(zip_derived_cl1790,plain,
    ( ( '#sk144' @ ( '#sk29' @ '#sk144' ) )
    | ~ ( '#sk144' @ '#sk2' )
    | ~ '#form143' ),
    inference(simplify,[status(thm)],[zip_derived_cl1786]) ).

thf(zip_derived_cl125,plain,
    ( ( '#sk144' @ '#sk2' )
    | ~ '#form143' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl122]) ).

thf(zip_derived_cl1814,plain,
    ( ~ '#form143'
    | ( '#sk144' @ ( '#sk29' @ '#sk144' ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1790,zip_derived_cl125]) ).

thf(zip_derived_cl2432,plain,
    ( ~ '#form143'
    | ~ ( '#sk1' @ '#sk144' @ '#sk2' ) ),
    inference(clc,[status(thm)],[zip_derived_cl2430,zip_derived_cl1814]) ).

thf(zip_derived_cl2437,plain,
    ( ~ '#form143'
    | ~ ( '#sk144' @ '#sk2' )
    | ~ '#form143' ),
    inference('sup-',[status(thm)],[zip_derived_cl127,zip_derived_cl2432]) ).

thf(zip_derived_cl2442,plain,
    ( ~ ( '#sk144' @ '#sk2' )
    | ~ '#form143' ),
    inference(simplify,[status(thm)],[zip_derived_cl2437]) ).

thf(zip_derived_cl125_013,plain,
    ( ( '#sk144' @ '#sk2' )
    | ~ '#form143' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl122]) ).

thf(zip_derived_cl2452,plain,
    ~ '#form143',
    inference(clc,[status(thm)],[zip_derived_cl2442,zip_derived_cl125]) ).

thf(zip_derived_cl2480,plain,
    ( '#sk1'
    @ ^ [Y0: $i] :
        ( ??
        @ ^ [Y1: $i > $o] :
            ( ( !!
              @ ^ [Y2: $i] :
                  ( ( Y1 @ Y2 )
                 => ( '#sk1' @ Y1 @ Y2 ) ) )
            & ( Y1 @ Y0 ) ) )
    @ ( '#sk29'
      @ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2371,zip_derived_cl2452]) ).

thf(zip_derived_cl4,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) )
   => ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 )
         => ( '#sk1'
            @ ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl7,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
           => ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 )
         => ( '#sk1'
            @ ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl10,plain,
    ( ~ ( ( ??
          @ ^ [Y0: $i > $o] :
              ( ( !!
                @ ^ [Y1: $i] :
                    ( ( Y0 @ Y1 )
                   => ( '#sk1' @ Y0 @ Y1 ) ) )
              & ( Y0 @ '#sk3' ) ) )
       => ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ '#sk3' ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 )
         => ( '#sk1'
            @ ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl12,plain,
    ( ( ??
      @ ^ [Y0: $i > $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( Y0 @ Y1 )
               => ( '#sk1' @ Y0 @ Y1 ) ) )
          & ( Y0 @ '#sk3' ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 )
         => ( '#sk1'
            @ ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl16,plain,
    ( ( ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk9' @ Y0 )
           => ( '#sk1' @ '#sk9' @ Y0 ) ) )
      & ( '#sk9' @ '#sk3' ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 )
         => ( '#sk1'
            @ ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl20,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk9' @ Y0 )
         => ( '#sk1' @ '#sk9' @ Y0 ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 )
         => ( '#sk1'
            @ ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl26,plain,
    ! [X2: $i] :
      ( ( ( '#sk9' @ X2 )
       => ( '#sk1' @ '#sk9' @ X2 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( '#sk1'
              @ ( '#sk1'
                @ ^ [Y1: $i] :
                    ( ??
                    @ ^ [Y2: $i > $o] :
                        ( ( !!
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                             => ( '#sk1' @ Y2 @ Y3 ) ) )
                        & ( Y2 @ Y1 ) ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl30,plain,
    ! [X2: $i] :
      ( ~ ( '#sk9' @ X2 )
      | ( '#sk1' @ '#sk9' @ X2 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 )
           => ( '#sk1'
              @ ( '#sk1'
                @ ^ [Y1: $i] :
                    ( ??
                    @ ^ [Y2: $i > $o] :
                        ( ( !!
                          @ ^ [Y3: $i] :
                              ( ( Y2 @ Y3 )
                             => ( '#sk1' @ Y2 @ Y3 ) ) )
                        & ( Y2 @ Y1 ) ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl33,plain,
    ! [X2: $i,X4: $i] :
      ( ( ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X4 )
       => ( '#sk1'
          @ ( '#sk1'
            @ ^ [Y0: $i] :
                ( ??
                @ ^ [Y1: $i > $o] :
                    ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( Y1 @ Y2 )
                         => ( '#sk1' @ Y1 @ Y2 ) ) )
                    & ( Y1 @ Y0 ) ) ) )
          @ X4 ) )
      | ( '#sk1' @ '#sk9' @ X2 )
      | ~ ( '#sk9' @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl36,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X4 )
      | ( '#sk1'
        @ ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) )
        @ X4 )
      | ~ ( '#sk9' @ X2 )
      | ( '#sk1' @ '#sk9' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl2663,plain,
    ! [X0: $i] :
      ( ( '#sk1' @ '#sk9' @ X0 )
      | ~ ( '#sk9' @ X0 )
      | ( '#sk1'
        @ ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) )
        @ ( '#sk29'
          @ ( '#sk1'
            @ ^ [Y0: $i] :
                ( ??
                @ ^ [Y1: $i > $o] :
                    ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( Y1 @ Y2 )
                         => ( '#sk1' @ Y1 @ Y2 ) ) )
                    & ( Y1 @ Y0 ) ) ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2480,zip_derived_cl36]) ).

thf(zip_derived_cl2372,plain,
    ( ~ ( '#sk1'
        @ ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) )
        @ ( '#sk29'
          @ ( '#sk1'
            @ ^ [Y0: $i] :
                ( ??
                @ ^ [Y1: $i > $o] :
                    ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( Y1 @ Y2 )
                         => ( '#sk1' @ Y1 @ Y2 ) ) )
                    & ( Y1 @ Y0 ) ) ) ) ) )
    | '#form143' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2370]) ).

thf(zip_derived_cl2452_014,plain,
    ~ '#form143',
    inference(clc,[status(thm)],[zip_derived_cl2442,zip_derived_cl125]) ).

thf(zip_derived_cl3116,plain,
    ~ ( '#sk1'
      @ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) ) )
      @ ( '#sk29'
        @ ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2372,zip_derived_cl2452]) ).

thf(zip_derived_cl6411,plain,
    ! [X0: $i] :
      ( ~ ( '#sk9' @ X0 )
      | ( '#sk1' @ '#sk9' @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2663,zip_derived_cl3116]) ).

thf(zip_derived_cl6411_015,plain,
    ! [X0: $i] :
      ( ~ ( '#sk9' @ X0 )
      | ( '#sk1' @ '#sk9' @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2663,zip_derived_cl3116]) ).

thf(zip_derived_cl13,plain,
    ( ~ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ '#sk3' )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 )
         => ( '#sk1'
            @ ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl17,plain,
    ! [X2: $i] :
      ( ( ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X2 )
       => ( '#sk1'
          @ ( '#sk1'
            @ ^ [Y0: $i] :
                ( ??
                @ ^ [Y1: $i > $o] :
                    ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( Y1 @ Y2 )
                         => ( '#sk1' @ Y1 @ Y2 ) ) )
                    & ( Y1 @ Y0 ) ) ) )
          @ X2 ) )
      | ~ ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ '#sk3' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl22,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X2 )
      | ( '#sk1'
        @ ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) )
        @ X2 )
      | ~ ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ '#sk3' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl144_016,plain,
    ! [X2: $i > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: $i] :
                ( ( X2 @ Y0 )
               => ( '#sk1' @ X2 @ Y0 ) ) )
          & ( X2 @ '#sk2' ) )
      | '#form143' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl133]) ).

thf(zip_derived_cl149,plain,
    ! [X2: $i > $o] :
      ( ~ ( !!
          @ ^ [Y0: $i] :
              ( ( X2 @ Y0 )
             => ( '#sk1' @ X2 @ Y0 ) ) )
      | ~ ( X2 @ '#sk2' )
      | '#form143' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl144]) ).

thf(zip_derived_cl150,plain,
    ! [X2: $i > $o] :
      ( ~ ( ( X2 @ ( '#sk29' @ X2 ) )
         => ( '#sk1' @ X2 @ ( '#sk29' @ X2 ) ) )
      | '#form143'
      | ~ ( X2 @ '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl149]) ).

thf(zip_derived_cl152,plain,
    ! [X2: $i > $o] :
      ( ~ ( '#sk1' @ X2 @ ( '#sk29' @ X2 ) )
      | ~ ( X2 @ '#sk2' )
      | '#form143' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl150]) ).

thf(zip_derived_cl2452_017,plain,
    ~ '#form143',
    inference(clc,[status(thm)],[zip_derived_cl2442,zip_derived_cl125]) ).

thf(zip_derived_cl2455,plain,
    ! [X2: $i > $o] :
      ( ~ ( '#sk1' @ X2 @ ( '#sk29' @ X2 ) )
      | ~ ( X2 @ '#sk2' ) ),
    inference(demod,[status(thm)],[zip_derived_cl152,zip_derived_cl2452]) ).

thf(zip_derived_cl2682,plain,
    ( ~ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ '#sk3' )
    | ~ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ ( '#sk29'
          @ ( '#sk1'
            @ ^ [Y0: $i] :
                ( ??
                @ ^ [Y1: $i > $o] :
                    ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( Y1 @ Y2 )
                         => ( '#sk1' @ Y1 @ Y2 ) ) )
                    & ( Y1 @ Y0 ) ) ) ) ) )
    | ~ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl2455]) ).

thf(zip_derived_cl2480_018,plain,
    ( '#sk1'
    @ ^ [Y0: $i] :
        ( ??
        @ ^ [Y1: $i > $o] :
            ( ( !!
              @ ^ [Y2: $i] :
                  ( ( Y1 @ Y2 )
                 => ( '#sk1' @ Y1 @ Y2 ) ) )
            & ( Y1 @ Y0 ) ) )
    @ ( '#sk29'
      @ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2371,zip_derived_cl2452]) ).

thf(zip_derived_cl123_019,plain,
    ( '#form143'
    | ( '#sk1'
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                   => ( '#sk1' @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk2' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl43,zip_derived_cl119]) ).

thf(zip_derived_cl2452_020,plain,
    ~ '#form143',
    inference(clc,[status(thm)],[zip_derived_cl2442,zip_derived_cl125]) ).

thf(zip_derived_cl2453,plain,
    ( '#sk1'
    @ ^ [Y0: $i] :
        ( ??
        @ ^ [Y1: $i > $o] :
            ( ( !!
              @ ^ [Y2: $i] :
                  ( ( Y1 @ Y2 )
                 => ( '#sk1' @ Y1 @ Y2 ) ) )
            & ( Y1 @ Y0 ) ) )
    @ '#sk2' ),
    inference(demod,[status(thm)],[zip_derived_cl123,zip_derived_cl2452]) ).

thf(zip_derived_cl2689,plain,
    ~ ( '#sk1'
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                   => ( '#sk1' @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk3' ),
    inference(demod,[status(thm)],[zip_derived_cl2682,zip_derived_cl2480,zip_derived_cl2453]) ).

thf(zip_derived_cl8_021,plain,
    ! [X2: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( X2 @ Y0 )
           => ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ X2 @ Y0 )
           => ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl15,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk9' @ Y0 )
         => ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) ) ) )
   => ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk9' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl264,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk9' @ Y0 )
           => ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk9' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl265,plain,
    ( ~ ( ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
       => ( ??
          @ ^ [Y0: $i > $o] :
              ( ( !!
                @ ^ [Y1: $i] :
                    ( ( Y0 @ Y1 )
                   => ( '#sk1' @ Y0 @ Y1 ) ) )
              & ( Y0 @ ( '#sk8' @ '#sk9' ) ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk9' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl264]) ).

thf(zip_derived_cl267,plain,
    ( ~ ( ??
        @ ^ [Y0: $i > $o] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( Y0 @ Y1 )
                 => ( '#sk1' @ Y0 @ Y1 ) ) )
            & ( Y0 @ ( '#sk8' @ '#sk9' ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk9' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl265]) ).

thf(zip_derived_cl269,plain,
    ! [X2: $i > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: $i] :
                ( ( X2 @ Y0 )
               => ( '#sk1' @ X2 @ Y0 ) ) )
          & ( X2 @ ( '#sk8' @ '#sk9' ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ '#sk9' @ Y0 )
           => ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) )
              @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl267]) ).

thf(zip_derived_cl273,plain,
    ( ~ ( ( !!
          @ ^ [Y0: $i] :
              ( ( '#sk9' @ Y0 )
             => ( '#sk1' @ '#sk9' @ Y0 ) ) )
        & ( '#sk9' @ ( '#sk8' @ '#sk9' ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk9' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl269]) ).

thf(zip_derived_cl1669,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk9' @ Y0 )
           => ( '#sk1' @ '#sk9' @ Y0 ) ) )
    | ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk9' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl273]) ).

thf(zip_derived_cl1670,plain,
    ( ~ ( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
       => ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk9' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) )
    | ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1669]) ).

thf(zip_derived_cl1672,plain,
    ( ~ ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) )
    | ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk9' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1670]) ).

thf(zip_derived_cl1674,plain,
    ! [X2: $i] :
      ( ( ( '#sk1' @ '#sk9' @ X2 )
       => ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X2 ) )
      | ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
      | ~ ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1672]) ).

thf(zip_derived_cl1676,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk9' @ X2 )
      | ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X2 )
      | ~ ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) )
      | ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1674]) ).

thf(zip_derived_cl28_022,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X4 )
      | ( X2 @ ( '#sk8' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl1678,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) )
      | ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X2 )
      | ~ ( '#sk1' @ '#sk9' @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl1676,zip_derived_cl28]) ).

thf(zip_derived_cl2722,plain,
    ( ~ ( '#sk1' @ '#sk9' @ '#sk3' )
    | ~ ( '#sk1' @ '#sk9' @ ( '#sk29' @ '#sk9' ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl2689,zip_derived_cl1678]) ).

thf(zip_derived_cl6412,plain,
    ( ~ ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
    | ~ ( '#sk1' @ '#sk9' @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl6411,zip_derived_cl2722]) ).

thf(zip_derived_cl2689_023,plain,
    ~ ( '#sk1'
      @ ^ [Y0: $i] :
          ( ??
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( Y1 @ Y2 )
                   => ( '#sk1' @ Y1 @ Y2 ) ) )
              & ( Y1 @ Y0 ) ) )
      @ '#sk3' ),
    inference(demod,[status(thm)],[zip_derived_cl2682,zip_derived_cl2480,zip_derived_cl2453]) ).

thf(zip_derived_cl1671,plain,
    ( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
    | ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ '#sk9' @ Y0 )
         => ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1670]) ).

thf(zip_derived_cl1673,plain,
    ! [X2: $i] :
      ( ( ( '#sk1' @ '#sk9' @ X2 )
       => ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X2 ) )
      | ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) )
      | ( '#sk9' @ ( '#sk29' @ '#sk9' ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1671]) ).

thf(zip_derived_cl1675,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk9' @ X2 )
      | ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X2 )
      | ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
      | ~ ( '#sk9' @ ( '#sk8' @ '#sk9' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1673]) ).

thf(zip_derived_cl28_024,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X4 )
      | ( X2 @ ( '#sk8' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl1677,plain,
    ! [X2: $i] :
      ( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
      | ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ X2 )
      | ~ ( '#sk1' @ '#sk9' @ X2 ) ),
    inference(clc,[status(thm)],[zip_derived_cl1675,zip_derived_cl28]) ).

thf(zip_derived_cl2723,plain,
    ( ~ ( '#sk1' @ '#sk9' @ '#sk3' )
    | ( '#sk9' @ ( '#sk29' @ '#sk9' ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl2689,zip_derived_cl1677]) ).

thf(zip_derived_cl6411_025,plain,
    ! [X0: $i] :
      ( ~ ( '#sk9' @ X0 )
      | ( '#sk1' @ '#sk9' @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl2663,zip_derived_cl3116]) ).

thf(zip_derived_cl6436,plain,
    ( ( '#sk9' @ ( '#sk29' @ '#sk9' ) )
    | ~ ( '#sk9' @ '#sk3' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl2723,zip_derived_cl6411]) ).

thf(zip_derived_cl21,plain,
    ( ( '#sk9' @ '#sk3' )
    | ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1'
            @ ^ [Y1: $i] :
                ( ??
                @ ^ [Y2: $i > $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( Y2 @ Y3 )
                         => ( '#sk1' @ Y2 @ Y3 ) ) )
                    & ( Y2 @ Y1 ) ) )
            @ Y0 )
         => ( '#sk1'
            @ ( '#sk1'
              @ ^ [Y1: $i] :
                  ( ??
                  @ ^ [Y2: $i > $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( Y2 @ Y3 )
                           => ( '#sk1' @ Y2 @ Y3 ) ) )
                      & ( Y2 @ Y1 ) ) ) )
            @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl27,plain,
    ! [X2: $i] :
      ( ( ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X2 )
       => ( '#sk1'
          @ ( '#sk1'
            @ ^ [Y0: $i] :
                ( ??
                @ ^ [Y1: $i > $o] :
                    ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( Y1 @ Y2 )
                         => ( '#sk1' @ Y1 @ Y2 ) ) )
                    & ( Y1 @ Y0 ) ) ) )
          @ X2 ) )
      | ( '#sk9' @ '#sk3' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl31,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) )
          @ X2 )
      | ( '#sk1'
        @ ( '#sk1'
          @ ^ [Y0: $i] :
              ( ??
              @ ^ [Y1: $i > $o] :
                  ( ( !!
                    @ ^ [Y2: $i] :
                        ( ( Y1 @ Y2 )
                       => ( '#sk1' @ Y1 @ Y2 ) ) )
                  & ( Y1 @ Y0 ) ) ) )
        @ X2 )
      | ( '#sk9' @ '#sk3' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl2455_026,plain,
    ! [X2: $i > $o] :
      ( ~ ( '#sk1' @ X2 @ ( '#sk29' @ X2 ) )
      | ~ ( X2 @ '#sk2' ) ),
    inference(demod,[status(thm)],[zip_derived_cl152,zip_derived_cl2452]) ).

thf(zip_derived_cl2681,plain,
    ( ( '#sk9' @ '#sk3' )
    | ~ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ ( '#sk29'
          @ ( '#sk1'
            @ ^ [Y0: $i] :
                ( ??
                @ ^ [Y1: $i > $o] :
                    ( ( !!
                      @ ^ [Y2: $i] :
                          ( ( Y1 @ Y2 )
                         => ( '#sk1' @ Y1 @ Y2 ) ) )
                    & ( Y1 @ Y0 ) ) ) ) ) )
    | ~ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) )
        @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl2455]) ).

thf(zip_derived_cl2480_027,plain,
    ( '#sk1'
    @ ^ [Y0: $i] :
        ( ??
        @ ^ [Y1: $i > $o] :
            ( ( !!
              @ ^ [Y2: $i] :
                  ( ( Y1 @ Y2 )
                 => ( '#sk1' @ Y1 @ Y2 ) ) )
            & ( Y1 @ Y0 ) ) )
    @ ( '#sk29'
      @ ( '#sk1'
        @ ^ [Y0: $i] :
            ( ??
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( Y1 @ Y2 )
                     => ( '#sk1' @ Y1 @ Y2 ) ) )
                & ( Y1 @ Y0 ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2371,zip_derived_cl2452]) ).

thf(zip_derived_cl2453_028,plain,
    ( '#sk1'
    @ ^ [Y0: $i] :
        ( ??
        @ ^ [Y1: $i > $o] :
            ( ( !!
              @ ^ [Y2: $i] :
                  ( ( Y1 @ Y2 )
                 => ( '#sk1' @ Y1 @ Y2 ) ) )
            & ( Y1 @ Y0 ) ) )
    @ '#sk2' ),
    inference(demod,[status(thm)],[zip_derived_cl123,zip_derived_cl2452]) ).

thf(zip_derived_cl2688,plain,
    '#sk9' @ '#sk3',
    inference(demod,[status(thm)],[zip_derived_cl2681,zip_derived_cl2480,zip_derived_cl2453]) ).

thf(zip_derived_cl6442,plain,
    '#sk9' @ ( '#sk29' @ '#sk9' ),
    inference(demod,[status(thm)],[zip_derived_cl6436,zip_derived_cl2688]) ).

thf(zip_derived_cl6548,plain,
    ~ ( '#sk1' @ '#sk9' @ '#sk3' ),
    inference(demod,[status(thm)],[zip_derived_cl6412,zip_derived_cl6442]) ).

thf(zip_derived_cl6558,plain,
    ~ ( '#sk9' @ '#sk3' ),
    inference('sup-',[status(thm)],[zip_derived_cl6411,zip_derived_cl6548]) ).

thf(zip_derived_cl2688_029,plain,
    '#sk9' @ '#sk3',
    inference(demod,[status(thm)],[zip_derived_cl2681,zip_derived_cl2480,zip_derived_cl2453]) ).

thf(zip_derived_cl6565,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl6558,zip_derived_cl2688]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SEV254^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.B6gKofhvN5 true
% 0.14/0.35  % Computer : n031.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug 24 02:23:51 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36  % Number of cores: 8
% 0.14/0.36  % Python version: Python 3.6.8
% 0.14/0.36  % Running in HO mode
% 0.22/0.66  % Total configuration time : 828
% 0.22/0.66  % Estimated wc time : 1656
% 0.22/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.23/0.77  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.23/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.23/0.78  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.23/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 65.44/9.08  % Solved by lams/35_full_unif4.sh.
% 65.44/9.08  % done 847 iterations in 8.274s
% 65.44/9.08  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 65.44/9.08  % SZS output start Refutation
% See solution above
% 65.44/9.09  
% 65.44/9.09  
% 65.44/9.09  % Terminating...
% 66.47/9.21  % Runner terminated.
% 66.47/9.22  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------