TSTP Solution File: SEU820^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU820^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.KNnaiN1CJS true

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 19:18:27 EDT 2023

% Result   : Theorem 1.48s 0.84s
% Output   : Refutation 1.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   47
% Syntax   : Number of formulae    :  117 (  43 unt;  20 typ;   0 def)
%            Number of atoms       :  842 (  93 equ;  18 cnn)
%            Maximal formula atoms :   42 (   8 avg)
%            Number of connectives : 2041 ( 151   ~; 161   |;  76   &;1194   @)
%                                         (   0 <=>; 285  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  20 usr;  16 con; 0-2 aty)
%                                         ( 167  !!;   7  ??;   0 @@+;   0 @@-)
%            Number of variables   :  283 ( 190   ^;  88   !;   5   ?; 283   :)

% Comments : 
%------------------------------------------------------------------------------
thf(powersetE1_type,type,
    powersetE1: $o ).

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

thf(subset_type,type,
    subset: $i > $i > $o ).

thf('#form8_type',type,
    '#form8': $o ).

thf(powerset_type,type,
    powerset: $i > $i ).

thf(subsetemptysetimpeq_type,type,
    subsetemptysetimpeq: $o ).

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

thf(ordinal_type,type,
    ordinal: $i > $o ).

thf('#form4_type',type,
    '#form4': $o ).

thf('#form6_type',type,
    '#form6': $o ).

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

thf(vacuousDall_type,type,
    vacuousDall: $o ).

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

thf(nonempty_type,type,
    nonempty: $i > $o ).

thf('#sk7_type',type,
    '#sk7': $i ).

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

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

thf(wellorderedByIn_type,type,
    wellorderedByIn: $i > $o ).

thf(stricttotalorderedByIn_type,type,
    stricttotalorderedByIn: $i > $o ).

thf(transitiveset_type,type,
    transitiveset: $i > $o ).

thf(ordinal,axiom,
    ( ordinal
    = ( ^ [Xx: $i] :
          ( ( transitiveset @ Xx )
          & ( wellorderedByIn @ Xx ) ) ) ) ).

thf(wellorderedByIn,axiom,
    ( wellorderedByIn
    = ( ^ [A: $i] :
          ( ( stricttotalorderedByIn @ A )
          & ! [X: $i] :
              ( ( in @ X @ ( powerset @ A ) )
             => ( ( nonempty @ X )
               => ? [Xx: $i] :
                    ( ! [Y: $i] :
                        ( ( in @ Y @ X )
                       => ( ( Xx = Y )
                          | ( in @ Xx @ Y ) ) )
                    & ( in @ Xx @ X ) ) ) ) ) ) ) ).

thf(stricttotalorderedByIn,axiom,
    ( stricttotalorderedByIn
    = ( ^ [A: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [X: $i] :
                  ( ( in @ X @ A )
                 => ! [Y: $i] :
                      ( ( in @ Y @ A )
                     => ( ( ( in @ Xx @ X )
                          & ( in @ X @ Y ) )
                       => ( in @ Xx @ Y ) ) ) ) )
          & ! [X: $i] :
              ( ( in @ X @ A )
             => ! [Y: $i] :
                  ( ( in @ Y @ A )
                 => ( ( X = Y )
                    | ( in @ X @ Y )
                    | ( in @ Y @ X ) ) ) )
          & ! [X: $i] :
              ( ( in @ X @ A )
             => ~ ( in @ X @ X ) ) ) ) ) ).

thf('0',plain,
    ( stricttotalorderedByIn
    = ( ^ [A: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ! [X: $i] :
                  ( ( in @ X @ A )
                 => ! [Y: $i] :
                      ( ( in @ Y @ A )
                     => ( ( ( in @ Xx @ X )
                          & ( in @ X @ Y ) )
                       => ( in @ Xx @ Y ) ) ) ) )
          & ! [X: $i] :
              ( ( in @ X @ A )
             => ! [Y: $i] :
                  ( ( in @ Y @ A )
                 => ( ( X = Y )
                    | ( in @ X @ Y )
                    | ( in @ Y @ X ) ) ) )
          & ! [X: $i] :
              ( ( in @ X @ A )
             => ~ ( in @ X @ X ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[stricttotalorderedByIn]) ).

thf('1',plain,
    ( stricttotalorderedByIn
    = ( ^ [V_1: $i] :
          ( ! [X4: $i] :
              ( ( in @ X4 @ V_1 )
             => ! [X6: $i] :
                  ( ( in @ X6 @ V_1 )
                 => ! [X8: $i] :
                      ( ( in @ X8 @ V_1 )
                     => ( ( ( in @ X4 @ X6 )
                          & ( in @ X6 @ X8 ) )
                       => ( in @ X4 @ X8 ) ) ) ) )
          & ! [X10: $i] :
              ( ( in @ X10 @ V_1 )
             => ! [X12: $i] :
                  ( ( in @ X12 @ V_1 )
                 => ( ( X10 = X12 )
                    | ( in @ X10 @ X12 )
                    | ( in @ X12 @ X10 ) ) ) )
          & ! [X14: $i] :
              ( ( in @ X14 @ V_1 )
             => ~ ( in @ X14 @ X14 ) ) ) ) ),
    define([status(thm)]) ).

thf(nonempty,axiom,
    ( nonempty
    = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).

thf('2',plain,
    ( nonempty
    = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
    inference(simplify_rw_rule,[status(thm)],[nonempty]) ).

thf('3',plain,
    ( nonempty
    = ( ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
    define([status(thm)]) ).

thf('4',plain,
    ( wellorderedByIn
    = ( ^ [A: $i] :
          ( ( stricttotalorderedByIn @ A )
          & ! [X: $i] :
              ( ( in @ X @ ( powerset @ A ) )
             => ( ( nonempty @ X )
               => ? [Xx: $i] :
                    ( ! [Y: $i] :
                        ( ( in @ Y @ X )
                       => ( ( Xx = Y )
                          | ( in @ Xx @ Y ) ) )
                    & ( in @ Xx @ X ) ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[wellorderedByIn,'1','3']) ).

thf('5',plain,
    ( wellorderedByIn
    = ( ^ [V_1: $i] :
          ( ( stricttotalorderedByIn @ V_1 )
          & ! [X4: $i] :
              ( ( in @ X4 @ ( powerset @ V_1 ) )
             => ( ( nonempty @ X4 )
               => ? [X6: $i] :
                    ( ! [X8: $i] :
                        ( ( in @ X8 @ X4 )
                       => ( ( X6 = X8 )
                          | ( in @ X6 @ X8 ) ) )
                    & ( in @ X6 @ X4 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf('6',plain,
    ( ordinal
    = ( ^ [Xx: $i] :
          ( ( transitiveset @ Xx )
          & ( wellorderedByIn @ Xx ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[ordinal,'5','1','3']) ).

thf('7',plain,
    ( ordinal
    = ( ^ [V_1: $i] :
          ( ( transitiveset @ V_1 )
          & ( wellorderedByIn @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf(transitiveset,axiom,
    ( transitiveset
    = ( ^ [A: $i] :
        ! [X: $i] :
          ( ( in @ X @ A )
         => ( subset @ X @ A ) ) ) ) ).

thf('8',plain,
    ( transitiveset
    = ( ^ [A: $i] :
        ! [X: $i] :
          ( ( in @ X @ A )
         => ( subset @ X @ A ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[transitiveset]) ).

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

thf(powersetE1,axiom,
    ( powersetE1
    = ( ! [A: $i,B: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( subset @ B @ A ) ) ) ) ).

thf('10',plain,
    ( powersetE1
    = ( ! [X4: $i,X6: $i] :
          ( ( in @ X6 @ ( powerset @ X4 ) )
         => ( subset @ X6 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(subsetemptysetimpeq,axiom,
    ( subsetemptysetimpeq
    = ( ! [A: $i] :
          ( ( subset @ A @ emptyset )
         => ( A = emptyset ) ) ) ) ).

thf('11',plain,
    ( subsetemptysetimpeq
    = ( ! [X4: $i] :
          ( ( subset @ X4 @ emptyset )
         => ( X4 = emptyset ) ) ) ),
    define([status(thm)]) ).

thf(vacuousDall,axiom,
    ( vacuousDall
    = ( ! [Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ( Xphi @ Xx ) ) ) ) ).

thf('12',plain,
    ( vacuousDall
    = ( ! [X4: $i > $o,X6: $i] :
          ( ( in @ X6 @ emptyset )
         => ( X4 @ X6 ) ) ) ),
    define([status(thm)]) ).

thf(emptysetOrdinal,conjecture,
    ( vacuousDall
   => ( subsetemptysetimpeq
     => ( powersetE1
       => ( ordinal @ emptyset ) ) ) ) ).

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

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

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

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: $i > $o] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( in @ Y1 @ emptyset )
           => ( Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl3,plain,
    ! [X2: $i > $o] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ emptyset )
         => ( X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl6,plain,
    ! [X2: $i > $o,X4: $i] :
      ( ( in @ X4 @ emptyset )
     => ( X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl10,plain,
    ! [X2: $o,X4: $i] :
      ( ( in @ X4 @ emptyset )
     => ( ^ [Y0: $i] : X2
        @ X4 ) ),
    inference(prune_arg_fun,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl11,plain,
    ! [X2: $o,X4: $i] :
      ( ( in @ X4 @ emptyset )
     => X2 ),
    inference(ho_norm,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl12,plain,
    ! [X2: $o,X4: $i] :
      ( ~ ( in @ X4 @ emptyset )
      | X2 ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl93,plain,
    ! [X0: $i] :
      ~ ( in @ X0 @ emptyset ),
    inference('ho.refine',[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl2,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( ( subset @ Y0 @ emptyset )
           => ( Y0 = emptyset ) ) )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ ( powerset @ Y0 ) )
                 => ( subset @ Y1 @ Y0 ) ) ) )
       => ( ( !!
            @ ^ [Y0: $i] :
                ( ( in @ Y0 @ ( powerset @ emptyset ) )
               => ( ( Y0 != emptyset )
                 => ( ??
                    @ ^ [Y1: $i] :
                        ( ( in @ Y1 @ Y0 )
                        & ( !!
                          @ ^ [Y2: $i] :
                              ( ( in @ Y2 @ Y0 )
                             => ( ( in @ Y1 @ Y2 )
                                | ( Y1 = Y2 ) ) ) ) ) ) ) ) )
          & ( !!
            @ ^ [Y0: $i] :
                ( ( in @ Y0 @ emptyset )
               => ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
          & ( !!
            @ ^ [Y0: $i] :
                ( ( in @ Y0 @ emptyset )
               => ( !!
                  @ ^ [Y1: $i] :
                      ( ( in @ Y1 @ emptyset )
                     => ( ( in @ Y1 @ Y0 )
                        | ( in @ Y0 @ Y1 )
                        | ( Y0 = Y1 ) ) ) ) ) )
          & ( !!
            @ ^ [Y0: $i] :
                ( ( in @ Y0 @ emptyset )
               => ( !!
                  @ ^ [Y1: $i] :
                      ( ( in @ Y1 @ emptyset )
                     => ( !!
                        @ ^ [Y2: $i] :
                            ( ( in @ Y2 @ emptyset )
                           => ( ( ( in @ Y1 @ Y2 )
                                & ( in @ Y0 @ Y1 ) )
                             => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
          & ( !!
            @ ^ [Y0: $i] :
                ( ( in @ Y0 @ emptyset )
               => ( subset @ Y0 @ emptyset ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl5,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ ( powerset @ Y0 ) )
               => ( subset @ Y1 @ Y0 ) ) ) )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ ( powerset @ emptyset ) )
             => ( ( Y0 != emptyset )
               => ( ??
                  @ ^ [Y1: $i] :
                      ( ( in @ Y1 @ Y0 )
                      & ( !!
                        @ ^ [Y2: $i] :
                            ( ( in @ Y2 @ Y0 )
                           => ( ( in @ Y1 @ Y2 )
                              | ( Y1 = Y2 ) ) ) ) ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ emptyset )
             => ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ emptyset )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( in @ Y1 @ emptyset )
                   => ( ( in @ Y1 @ Y0 )
                      | ( in @ Y0 @ Y1 )
                      | ( Y0 = Y1 ) ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ emptyset )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( in @ Y1 @ emptyset )
                   => ( !!
                      @ ^ [Y2: $i] :
                          ( ( in @ Y2 @ emptyset )
                         => ( ( ( in @ Y1 @ Y2 )
                              & ( in @ Y0 @ Y1 ) )
                           => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ emptyset )
             => ( subset @ Y0 @ emptyset ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl9,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ ( powerset @ emptyset ) )
           => ( ( Y0 != emptyset )
             => ( ??
                @ ^ [Y1: $i] :
                    ( ( in @ Y1 @ Y0 )
                    & ( !!
                      @ ^ [Y2: $i] :
                          ( ( in @ Y2 @ Y0 )
                         => ( ( in @ Y1 @ Y2 )
                            | ( Y1 = Y2 ) ) ) ) ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl15,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ ( powerset @ emptyset ) )
           => ( ( Y0 != emptyset )
             => ( ??
                @ ^ [Y1: $i] :
                    ( ( in @ Y1 @ Y0 )
                    & ( !!
                      @ ^ [Y2: $i] :
                          ( ( in @ Y2 @ Y0 )
                         => ( ( in @ Y1 @ Y2 )
                            | ( Y1 = Y2 ) ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl18,plain,
    ( ~ ( ( in @ '#sk2' @ ( powerset @ emptyset ) )
       => ( ( '#sk2' != emptyset )
         => ( ??
            @ ^ [Y0: $i] :
                ( ( in @ Y0 @ '#sk2' )
                & ( !!
                  @ ^ [Y1: $i] :
                      ( ( in @ Y1 @ '#sk2' )
                     => ( ( in @ Y0 @ Y1 )
                        | ( Y0 = Y1 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl20,plain,
    ( ( in @ '#sk2' @ ( powerset @ emptyset ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl22,plain,
    ( ~ ( ( in @ '#sk3' @ emptyset )
       => ( (~) @ ( in @ '#sk3' @ '#sk3' ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) )
    | ( in @ '#sk2' @ ( powerset @ emptyset ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl25,plain,
    ( ( in @ '#sk3' @ emptyset )
    | ( in @ '#sk2' @ ( powerset @ emptyset ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl25_001,plain,
    ( ( in @ '#sk3' @ emptyset )
    | ( in @ '#sk2' @ ( powerset @ emptyset ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl32,plain,
    ( '#form6'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl34,plain,
    ( ~ '#form6'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ( in @ '#sk2' @ ( powerset @ emptyset ) )
    | ( in @ '#sk3' @ emptyset ) ),
    inference(renaming,[status(thm)],[zip_derived_cl25,zip_derived_cl32]) ).

thf(zip_derived_cl21,plain,
    ( ~ ( ( '#sk2' != emptyset )
       => ( ??
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ '#sk2' )
              & ( !!
                @ ^ [Y1: $i] :
                    ( ( in @ Y1 @ '#sk2' )
                   => ( ( in @ Y0 @ Y1 )
                      | ( Y0 = Y1 ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl23,plain,
    ( ( '#sk2' != emptyset )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl27,plain,
    ( ( '#sk2' != emptyset )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl28,plain,
    ( '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl40,plain,
    ( ~ '#form4'
    | ( in @ '#sk3' @ emptyset )
    | ( in @ '#sk2' @ ( powerset @ emptyset ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ '#form6' ),
    inference(renaming,[status(thm)],[zip_derived_cl34,zip_derived_cl28]) ).

thf(zip_derived_cl27_002,plain,
    ( ( '#sk2' != emptyset )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl28_003,plain,
    ( '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl30,plain,
    ( ~ '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ( '#sk2' != emptyset ) ),
    inference(renaming,[status(thm)],[zip_derived_cl27,zip_derived_cl28]) ).

thf(zip_derived_cl32_004,plain,
    ( '#form6'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl36,plain,
    ( ~ '#form6'
    | ( '#sk2' != emptyset )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
    | ~ '#form4' ),
    inference(renaming,[status(thm)],[zip_derived_cl30,zip_derived_cl32]) ).

thf(zip_derived_cl44,plain,
    ( '#form8'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl48,plain,
    ( ~ '#form8'
    | ~ '#form6'
    | ( in @ '#sk2' @ ( powerset @ emptyset ) )
    | ( in @ '#sk3' @ emptyset )
    | ~ '#form4' ),
    inference(renaming,[status(thm)],[zip_derived_cl40,zip_derived_cl44]) ).

thf(zip_derived_cl44_005,plain,
    ( '#form8'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl45,plain,
    ( ~ ( ( in @ '#sk9' @ emptyset )
       => ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ emptyset )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( in @ Y1 @ emptyset )
                   => ( ( ( in @ Y0 @ Y1 )
                        & ( in @ '#sk9' @ Y0 ) )
                     => ( in @ '#sk9' @ Y1 ) ) ) ) ) ) )
    | '#form8' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl52,plain,
    ( ( in @ '#sk9' @ emptyset )
    | '#form8' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl93_006,plain,
    ! [X0: $i] :
      ~ ( in @ X0 @ emptyset ),
    inference('ho.refine',[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl100,plain,
    '#form8',
    inference(clc,[status(thm)],[zip_derived_cl52,zip_derived_cl93]) ).

thf(zip_derived_cl32_007,plain,
    ( '#form6'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( ( in @ Y1 @ Y0 )
                    | ( in @ Y0 @ Y1 )
                    | ( Y0 = Y1 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl33,plain,
    ( ~ ( ( in @ '#sk7' @ emptyset )
       => ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ emptyset )
             => ( ( in @ Y0 @ '#sk7' )
                | ( in @ '#sk7' @ Y0 )
                | ( '#sk7' = Y0 ) ) ) ) )
    | '#form6' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl41,plain,
    ( ( in @ '#sk7' @ emptyset )
    | '#form6' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl93_008,plain,
    ! [X0: $i] :
      ~ ( in @ X0 @ emptyset ),
    inference('ho.refine',[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl99,plain,
    '#form6',
    inference(clc,[status(thm)],[zip_derived_cl41,zip_derived_cl93]) ).

thf(zip_derived_cl93_009,plain,
    ! [X0: $i] :
      ~ ( in @ X0 @ emptyset ),
    inference('ho.refine',[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl28_010,plain,
    ( '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( subset @ Y0 @ emptyset ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl29,plain,
    ( ~ ( ( in @ '#sk5' @ emptyset )
       => ( subset @ '#sk5' @ emptyset ) )
    | '#form4' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl37,plain,
    ( ( in @ '#sk5' @ emptyset )
    | '#form4' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl93_011,plain,
    ! [X0: $i] :
      ~ ( in @ X0 @ emptyset ),
    inference('ho.refine',[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl98,plain,
    '#form4',
    inference(clc,[status(thm)],[zip_derived_cl37,zip_derived_cl93]) ).

thf(zip_derived_cl115,plain,
    in @ '#sk2' @ ( powerset @ emptyset ),
    inference(demod,[status(thm)],[zip_derived_cl48,zip_derived_cl100,zip_derived_cl99,zip_derived_cl93,zip_derived_cl98]) ).

thf(zip_derived_cl8,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( in @ Y1 @ ( powerset @ Y0 ) )
           => ( subset @ Y1 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl14,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ ( powerset @ X2 ) )
         => ( subset @ Y0 @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl17,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ X4 @ ( powerset @ X2 ) )
     => ( subset @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl19,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( in @ X4 @ ( powerset @ X2 ) )
      | ( subset @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl116,plain,
    subset @ '#sk2' @ emptyset,
    inference('sup-',[status(thm)],[zip_derived_cl115,zip_derived_cl19]) ).

thf(zip_derived_cl4,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( subset @ Y0 @ emptyset )
       => ( Y0 = emptyset ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl7,plain,
    ! [X2: $i] :
      ( ( subset @ X2 @ emptyset )
     => ( X2 = emptyset ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl13,plain,
    ! [X2: $i] :
      ( ~ ( subset @ X2 @ emptyset )
      | ( X2 = emptyset ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl16,plain,
    ! [X2: $i] :
      ( ~ ( subset @ X2 @ emptyset )
      | ( X2 = emptyset ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl120,plain,
    '#sk2' = emptyset,
    inference('sup-',[status(thm)],[zip_derived_cl116,zip_derived_cl16]) ).

thf(zip_derived_cl125,plain,
    ! [X0: $i] :
      ~ ( in @ X0 @ '#sk2' ),
    inference(demod,[status(thm)],[zip_derived_cl93,zip_derived_cl120]) ).

thf(zip_derived_cl36_012,plain,
    ( ~ '#form6'
    | ( '#sk2' != emptyset )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
    | ~ '#form4' ),
    inference(renaming,[status(thm)],[zip_derived_cl30,zip_derived_cl32]) ).

thf(zip_derived_cl44_013,plain,
    ( '#form8'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ emptyset )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ emptyset )
                       => ( ( ( in @ Y1 @ Y2 )
                            & ( in @ Y0 @ Y1 ) )
                         => ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl46,plain,
    ( ~ '#form8'
    | ~ '#form4'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ emptyset )
           => ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
    | ( '#sk2' != emptyset )
    | ~ '#form6' ),
    inference(renaming,[status(thm)],[zip_derived_cl36,zip_derived_cl44]) ).

thf(zip_derived_cl51,plain,
    ( ~ ( ( in @ '#sk3' @ emptyset )
       => ( (~) @ ( in @ '#sk3' @ '#sk3' ) ) )
    | ~ '#form6'
    | ( '#sk2' != emptyset )
    | ~ '#form4'
    | ~ '#form8' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl57,plain,
    ( ~ ( ( in @ '#sk3' @ '#sk2' )
       => ( (~) @ ( in @ '#sk3' @ '#sk3' ) ) )
    | ~ '#form6'
    | ( '#sk2' != emptyset )
    | ~ '#form4'
    | ~ '#form8' ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl58,plain,
    ( ( in @ '#sk3' @ '#sk2' )
    | ~ '#form8'
    | ~ '#form4'
    | ( '#sk2' != emptyset )
    | ~ '#form6' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl100_014,plain,
    '#form8',
    inference(clc,[status(thm)],[zip_derived_cl52,zip_derived_cl93]) ).

thf(zip_derived_cl98_015,plain,
    '#form4',
    inference(clc,[status(thm)],[zip_derived_cl37,zip_derived_cl93]) ).

thf(zip_derived_cl99_016,plain,
    '#form6',
    inference(clc,[status(thm)],[zip_derived_cl41,zip_derived_cl93]) ).

thf(zip_derived_cl113,plain,
    ( ( in @ '#sk3' @ '#sk2' )
    | ( '#sk2' != emptyset ) ),
    inference(demod,[status(thm)],[zip_derived_cl58,zip_derived_cl100,zip_derived_cl98,zip_derived_cl99]) ).

thf(zip_derived_cl120_017,plain,
    '#sk2' = emptyset,
    inference('sup-',[status(thm)],[zip_derived_cl116,zip_derived_cl16]) ).

thf(zip_derived_cl126,plain,
    ( ( in @ '#sk3' @ '#sk2' )
    | ( '#sk2' != '#sk2' ) ),
    inference(demod,[status(thm)],[zip_derived_cl113,zip_derived_cl120]) ).

thf(zip_derived_cl127,plain,
    in @ '#sk3' @ '#sk2',
    inference(simplify,[status(thm)],[zip_derived_cl126]) ).

thf(zip_derived_cl132,plain,
    $false,
    inference('sup+',[status(thm)],[zip_derived_cl125,zip_derived_cl127]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU820^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.KNnaiN1CJS true
% 0.13/0.34  % Computer : n016.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 : Wed Aug 23 19:26:52 EDT 2023
% 0.20/0.35  % CPUTime  : 
% 0.20/0.35  % Running portfolio for 300 s
% 0.20/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35  % Number of cores: 8
% 0.20/0.35  % Python version: Python 3.6.8
% 0.20/0.35  % Running in HO mode
% 0.21/0.64  % Total configuration time : 828
% 0.21/0.64  % Estimated wc time : 1656
% 0.21/0.64  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.73  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.73  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.48/0.84  % Solved by lams/35_full_unif4.sh.
% 1.48/0.84  % done 23 iterations in 0.059s
% 1.48/0.84  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.48/0.84  % SZS output start Refutation
% See solution above
% 1.48/0.84  
% 1.48/0.84  
% 1.48/0.84  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.48/0.84  % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 1.48/0.84  % Terminating...
% 1.95/0.94  % Runner terminated.
% 1.95/0.95  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------