TSTP Solution File: SEV010^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV010^5 : 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.3KiOpWdBTt true

% Computer : n029.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 19:59:16 EDT 2023

% Result   : Theorem 26.23s 3.95s
% Output   : Refutation 26.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   49
%            Number of leaves      :    9
% Syntax   : Number of formulae    :  201 (  16 unt;   8 typ;   0 def)
%            Number of atoms       : 1088 (  89 equ;   0 cnn)
%            Maximal formula atoms :   24 (   5 avg)
%            Number of connectives : 3037 ( 192   ~; 250   |;  93   &;2220   @)
%                                         (  45 <=>;  84  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (   8 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   83 (  83   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   7 usr;   4 con; 0-2 aty)
%                                         ( 121  !!;  32  ??;   0 @@+;   0 @@-)
%            Number of variables   :  507 ( 301   ^; 196   !;  10   ?; 507   :)

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

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

thf('#sk2_type',type,
    '#sk2': a ).

thf('#sk24_type',type,
    '#sk24': ( a > $o ) > a > $o ).

thf('#sk28_type',type,
    '#sk28': ( a > $o ) > a ).

thf('#_fresh_sk90_type',type,
    '#_fresh_sk90': ( a > $o ) > a ).

thf('#_fresh_sk52_type',type,
    '#_fresh_sk52': ( a > $o ) > a ).

thf('#sk17_type',type,
    '#sk17': ( a > $o ) > a ).

thf(cTHM260_pme,conjecture,
    ! [R: a > a > $o] :
      ( ( ! [Xx: a,Xy: a,Xz: a] :
            ( ( ( R @ Xy @ Xz )
              & ( R @ Xx @ Xy ) )
           => ( R @ Xx @ Xz ) )
        & ! [Xx: a,Xy: a] :
            ( ( R @ Xx @ Xy )
           => ( R @ Xy @ Xx ) )
        & ! [Xx: a] : ( R @ Xx @ Xx ) )
     => ( ! [Xx: a] :
          ? [Xp: a > $o] :
            ( ? [Xz: a] : ( Xp @ Xz )
            & ! [Xx0: a] :
                ( ( Xp @ Xx0 )
               => ! [Xy: a] :
                    ( ( Xp @ Xy )
                  <=> ( R @ Xx0 @ Xy ) ) )
            & ( Xp @ Xx )
            & ! [Xq: a > $o] :
                ( ( ( Xq @ Xx )
                  & ! [Xx0: a] :
                      ( ( Xq @ Xx0 )
                     => ! [Xy: a] :
                          ( ( Xq @ Xy )
                        <=> ( R @ Xx0 @ Xy ) ) )
                  & ? [Xz: a] : ( Xq @ Xz ) )
               => ( Xq = Xp ) ) )
        & ! [Xp: a > $o] :
            ( ( ! [Xx: a] :
                  ( ( Xp @ Xx )
                 => ! [Xy: a] :
                      ( ( Xp @ Xy )
                    <=> ( R @ Xx @ Xy ) ) )
              & ? [Xz: a] : ( Xp @ Xz ) )
           => ? [Xz: a] : ( Xp @ Xz ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [R: a > a > $o] :
        ( ( ! [Xx: a,Xy: a,Xz: a] :
              ( ( ( R @ Xy @ Xz )
                & ( R @ Xx @ Xy ) )
             => ( R @ Xx @ Xz ) )
          & ! [Xx: a,Xy: a] :
              ( ( R @ Xx @ Xy )
             => ( R @ Xy @ Xx ) )
          & ! [Xx: a] : ( R @ Xx @ Xx ) )
       => ( ! [Xx: a] :
            ? [Xp: a > $o] :
              ( ? [Xz: a] : ( Xp @ Xz )
              & ! [Xx0: a] :
                  ( ( Xp @ Xx0 )
                 => ! [Xy: a] :
                      ( ( Xp @ Xy )
                    <=> ( R @ Xx0 @ Xy ) ) )
              & ( Xp @ Xx )
              & ! [Xq: a > $o] :
                  ( ( ( Xq @ Xx )
                    & ! [Xx0: a] :
                        ( ( Xq @ Xx0 )
                       => ! [Xy: a] :
                            ( ( Xq @ Xy )
                          <=> ( R @ Xx0 @ Xy ) ) )
                    & ? [Xz: a] : ( Xq @ Xz ) )
                 => ( Xq = Xp ) ) )
          & ! [Xp: a > $o] :
              ( ( ! [Xx: a] :
                    ( ( Xp @ Xx )
                   => ! [Xy: a] :
                        ( ( Xp @ Xy )
                      <=> ( R @ Xx @ Xy ) ) )
                & ? [Xz: a] : ( Xp @ Xz ) )
             => ? [Xz: a] : ( Xp @ Xz ) ) ) ),
    inference('cnf.neg',[status(esa)],[cTHM260_pme]) ).

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

thf(zip_derived_cl1,plain,
    ~ ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( Y0 @ Y1 @ Y2 )
                     => ( Y0 @ Y2 @ Y1 ) ) ) )
            & ( !!
              @ ^ [Y1: a] : ( Y0 @ Y1 @ Y1 ) ) )
         => ( !!
            @ ^ [Y1: a] :
                ( ??
                @ ^ [Y2: a > $o] :
                    ( ( ??
                      @ ^ [Y3: a] : ( Y2 @ Y3 ) )
                    & ( !!
                      @ ^ [Y3: a] :
                          ( ( Y2 @ Y3 )
                         => ( !!
                            @ ^ [Y4: a] :
                                ( ( Y2 @ Y4 )
                              <=> ( Y0 @ Y3 @ Y4 ) ) ) ) )
                    & ( Y2 @ Y1 )
                    & ( !!
                      @ ^ [Y3: a > $o] :
                          ( ( ( Y3 @ Y1 )
                            & ( !!
                              @ ^ [Y4: a] :
                                  ( ( Y3 @ Y4 )
                                 => ( !!
                                    @ ^ [Y5: a] :
                                        ( ( Y3 @ Y5 )
                                      <=> ( Y0 @ Y4 @ Y5 ) ) ) ) )
                            & ( ??
                              @ ^ [Y4: a] : ( Y3 @ Y4 ) ) )
                         => ( Y3 = Y2 ) ) ) ) ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl0]) ).

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

thf(zip_derived_cl3,plain,
    ( ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( !!
              @ ^ [Y2: a] :
                  ( ( ( '#sk1' @ Y1 @ Y2 )
                    & ( '#sk1' @ Y0 @ Y1 ) )
                 => ( '#sk1' @ Y0 @ Y2 ) ) ) ) )
    & ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( '#sk1' @ Y0 @ Y1 )
             => ( '#sk1' @ Y1 @ Y0 ) ) ) )
    & ( !!
      @ ^ [Y0: a] : ( '#sk1' @ Y0 @ Y0 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl7,plain,
    ( !!
    @ ^ [Y0: a] : ( '#sk1' @ Y0 @ Y0 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl11,plain,
    ! [X2: a] : ( '#sk1' @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl4,plain,
    ~ ( !!
      @ ^ [Y0: a] :
          ( ??
          @ ^ [Y1: a > $o] :
              ( ( ??
                @ ^ [Y2: a] : ( Y1 @ Y2 ) )
              & ( !!
                @ ^ [Y2: a] :
                    ( ( Y1 @ Y2 )
                   => ( !!
                      @ ^ [Y3: a] :
                          ( ( Y1 @ Y3 )
                        <=> ( '#sk1' @ Y2 @ Y3 ) ) ) ) )
              & ( Y1 @ Y0 )
              & ( !!
                @ ^ [Y2: a > $o] :
                    ( ( ( Y2 @ Y0 )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( ( Y2 @ Y3 )
                           => ( !!
                              @ ^ [Y4: a] :
                                  ( ( Y2 @ Y4 )
                                <=> ( '#sk1' @ Y3 @ Y4 ) ) ) ) )
                      & ( ??
                        @ ^ [Y3: a] : ( Y2 @ Y3 ) ) )
                   => ( Y2 = Y1 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl8,plain,
    ~ ( ??
      @ ^ [Y0: a > $o] :
          ( ( ??
            @ ^ [Y1: a] : ( Y0 @ Y1 ) )
          & ( !!
            @ ^ [Y1: a] :
                ( ( Y0 @ Y1 )
               => ( !!
                  @ ^ [Y2: a] :
                      ( ( Y0 @ Y2 )
                    <=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
          & ( Y0 @ '#sk2' )
          & ( !!
            @ ^ [Y1: a > $o] :
                ( ( ( Y1 @ '#sk2' )
                  & ( !!
                    @ ^ [Y2: a] :
                        ( ( Y1 @ Y2 )
                       => ( !!
                          @ ^ [Y3: a] :
                              ( ( Y1 @ Y3 )
                            <=> ( '#sk1' @ Y2 @ Y3 ) ) ) ) )
                  & ( ??
                    @ ^ [Y2: a] : ( Y1 @ Y2 ) ) )
               => ( Y1 = Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl12,plain,
    ! [X2: a > $o] :
      ~ ( ( ??
          @ ^ [Y0: a] : ( X2 @ Y0 ) )
        & ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
             => ( !!
                @ ^ [Y1: a] :
                    ( ( X2 @ Y1 )
                  <=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
        & ( X2 @ '#sk2' )
        & ( !!
          @ ^ [Y0: a > $o] :
              ( ( ( Y0 @ '#sk2' )
                & ( !!
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: a] :
                            ( ( Y0 @ Y2 )
                          <=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
                & ( ??
                  @ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
             => ( Y0 = X2 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl15,plain,
    ! [X2: a > $o] :
      ( ~ ( ??
          @ ^ [Y0: a] : ( X2 @ Y0 ) )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
             => ( !!
                @ ^ [Y1: a] :
                    ( ( X2 @ Y1 )
                  <=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
      | ~ ( X2 @ '#sk2' )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( ( ( Y0 @ '#sk2' )
                & ( !!
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: a] :
                            ( ( Y0 @ Y2 )
                          <=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
                & ( ??
                  @ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
             => ( Y0 = X2 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl18,plain,
    ! [X2: a > $o,X4: a] :
      ( ~ ( X2 @ X4 )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( ( ( Y0 @ '#sk2' )
                & ( !!
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: a] :
                            ( ( Y0 @ Y2 )
                          <=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
                & ( ??
                  @ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
             => ( Y0 = X2 ) ) )
      | ~ ( X2 @ '#sk2' )
      | ~ ( !!
          @ ^ [Y0: a] :
              ( ( X2 @ Y0 )
             => ( !!
                @ ^ [Y1: a] :
                    ( ( X2 @ Y1 )
                  <=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl20,plain,
    ! [X0: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( X0 @ Y0 )
             => ( !!
                @ ^ [Y1: a] :
                    ( ( X0 @ Y1 )
                  <=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( ( ( Y0 @ '#sk2' )
                & ( !!
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: a] :
                            ( ( Y0 @ Y2 )
                          <=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
                & ( ??
                  @ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
             => ( Y0 = X0 ) ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference(condensation,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl21,plain,
    ! [X0: a > $o] :
      ( ~ ( ( X0 @ ( '#sk17' @ X0 ) )
         => ( !!
            @ ^ [Y0: a] :
                ( ( X0 @ Y0 )
              <=> ( '#sk1' @ ( '#sk17' @ X0 ) @ Y0 ) ) ) )
      | ~ ( X0 @ '#sk2' )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( ( ( Y0 @ '#sk2' )
                & ( !!
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: a] :
                            ( ( Y0 @ Y2 )
                          <=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
                & ( ??
                  @ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
             => ( Y0 = X0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl24,plain,
    ! [X0: a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( X0 @ Y0 )
            <=> ( '#sk1' @ ( '#sk17' @ X0 ) @ Y0 ) ) )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( ( ( Y0 @ '#sk2' )
                & ( !!
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: a] :
                            ( ( Y0 @ Y2 )
                          <=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
                & ( ??
                  @ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
             => ( Y0 = X0 ) ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl27,plain,
    ! [X0: a > $o] :
      ( ~ ( ( X0 @ ( '#sk28' @ X0 ) )
        <=> ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
      | ~ ( X0 @ '#sk2' )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( ( ( Y0 @ '#sk2' )
                & ( !!
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: a] :
                            ( ( Y0 @ Y2 )
                          <=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
                & ( ??
                  @ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
             => ( Y0 = X0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl30,plain,
    ! [X0: a > $o] :
      ( ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
      | ~ ( X0 @ '#sk2' )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( ( ( Y0 @ '#sk2' )
                & ( !!
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: a] :
                            ( ( Y0 @ Y2 )
                          <=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
                & ( ??
                  @ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
             => ( Y0 = X0 ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl31,plain,
    ! [X0: a > $o] :
      ( ~ ( ( ( '#sk24' @ X0 @ '#sk2' )
            & ( !!
              @ ^ [Y0: a] :
                  ( ( '#sk24' @ X0 @ Y0 )
                 => ( !!
                    @ ^ [Y1: a] :
                        ( ( '#sk24' @ X0 @ Y1 )
                      <=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
            & ( ??
              @ ^ [Y0: a] : ( '#sk24' @ X0 @ Y0 ) ) )
         => ( ( '#sk24' @ X0 )
            = X0 ) )
      | ~ ( X0 @ '#sk2' )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl38,plain,
    ! [X0: a > $o] :
      ( ( ( '#sk24' @ X0 )
       != X0 )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl44,plain,
    ! [X0: a > $o] :
      ( ( ( '#sk24' @ X0 )
       != X0 )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl45,plain,
    ! [X0: a > $o] :
      ( ( ( '#sk24' @ X0 @ ( '#_fresh_sk90' @ X0 ) )
       != ( X0 @ ( '#_fresh_sk90' @ X0 ) ) )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference(neg_ext_simpl,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl148,plain,
    ( ( ( ^ [Y0: a] :
            ( '#sk1'
            @ ( ^ [Y1: a] :
                  ( ^ [Y2: a] : '#sk2'
                  @ Y1 )
              @ Y0 )
            @ ( ^ [Y1: a] : Y1
              @ Y0 ) )
        @ ( '#sk28'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) ) )
     != ( '#sk1'
        @ ( '#sk17'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) )
        @ ( '#sk28'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) ) ) )
    | ( ( '#sk24'
        @ ^ [Y0: a] :
            ( '#sk1'
            @ ( ^ [Y1: a] :
                  ( ^ [Y2: a] : '#sk2'
                  @ Y1 )
              @ Y0 )
            @ ( ^ [Y1: a] : Y1
              @ Y0 ) )
        @ ( '#_fresh_sk90'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) ) )
     != ( ^ [Y0: a] :
            ( '#sk1'
            @ ( ^ [Y1: a] :
                  ( ^ [Y2: a] : '#sk2'
                  @ Y1 )
              @ Y0 )
            @ ( ^ [Y1: a] : Y1
              @ Y0 ) )
        @ ( '#_fresh_sk90'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl45]) ).

thf(zip_derived_cl153,plain,
    ( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
    | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl148]) ).

thf(zip_derived_cl11_001,plain,
    ! [X2: a] : ( '#sk1' @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl23,plain,
    ! [X0: a > $o] :
      ( ( X0 @ ( '#sk17' @ X0 ) )
      | ~ ( !!
          @ ^ [Y0: a > $o] :
              ( ( ( Y0 @ '#sk2' )
                & ( !!
                  @ ^ [Y1: a] :
                      ( ( Y0 @ Y1 )
                     => ( !!
                        @ ^ [Y2: a] :
                            ( ( Y0 @ Y2 )
                          <=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) )
                & ( ??
                  @ ^ [Y1: a] : ( Y0 @ Y1 ) ) )
             => ( Y0 = X0 ) ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl26,plain,
    ! [X0: a > $o] :
      ( ~ ( ( ( '#sk24' @ X0 @ '#sk2' )
            & ( !!
              @ ^ [Y0: a] :
                  ( ( '#sk24' @ X0 @ Y0 )
                 => ( !!
                    @ ^ [Y1: a] :
                        ( ( '#sk24' @ X0 @ Y1 )
                      <=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
            & ( ??
              @ ^ [Y0: a] : ( '#sk24' @ X0 @ Y0 ) ) )
         => ( ( '#sk24' @ X0 )
            = X0 ) )
      | ~ ( X0 @ '#sk2' )
      | ( X0 @ ( '#sk17' @ X0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl28,plain,
    ! [X0: a > $o] :
      ( ( ( '#sk24' @ X0 @ '#sk2' )
        & ( !!
          @ ^ [Y0: a] :
              ( ( '#sk24' @ X0 @ Y0 )
             => ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk24' @ X0 @ Y1 )
                  <=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
        & ( ??
          @ ^ [Y0: a] : ( '#sk24' @ X0 @ Y0 ) ) )
      | ( X0 @ ( '#sk17' @ X0 ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl32,plain,
    ! [X0: a > $o] :
      ( ( '#sk24' @ X0 @ '#sk2' )
      | ~ ( X0 @ '#sk2' )
      | ( X0 @ ( '#sk17' @ X0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl85,plain,
    ( ( ^ [Y0: a] :
          ( '#sk1'
          @ ( ^ [Y1: a] :
                ( ^ [Y2: a] : '#sk2'
                @ Y1 )
            @ Y0 )
          @ ( ^ [Y1: a] : Y1
            @ Y0 ) )
      @ ( '#sk17'
        @ ^ [Y0: a] :
            ( '#sk1'
            @ ( ^ [Y1: a] :
                  ( ^ [Y2: a] : '#sk2'
                  @ Y1 )
              @ Y0 )
            @ ( ^ [Y1: a] : Y1
              @ Y0 ) ) ) )
    | ( '#sk24'
      @ ^ [Y0: a] :
          ( '#sk1'
          @ ( ^ [Y1: a] :
                ( ^ [Y2: a] : '#sk2'
                @ Y1 )
            @ Y0 )
          @ ( ^ [Y1: a] : Y1
            @ Y0 ) )
      @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl32]) ).

thf(zip_derived_cl89,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl85]) ).

thf(zip_derived_cl11_002,plain,
    ! [X2: a] : ( '#sk1' @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl33,plain,
    ! [X0: a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( '#sk24' @ X0 @ Y0 )
           => ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk24' @ X0 @ Y1 )
                <=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
      | ~ ( X0 @ '#sk2' )
      | ( X0 @ ( '#sk17' @ X0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl39,plain,
    ! [X0: a > $o,X2: a] :
      ( ( ( '#sk24' @ X0 @ X2 )
       => ( !!
          @ ^ [Y0: a] :
              ( ( '#sk24' @ X0 @ Y0 )
            <=> ( '#sk1' @ X2 @ Y0 ) ) ) )
      | ( X0 @ ( '#sk17' @ X0 ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl46,plain,
    ! [X0: a > $o,X2: a] :
      ( ~ ( '#sk24' @ X0 @ X2 )
      | ( !!
        @ ^ [Y0: a] :
            ( ( '#sk24' @ X0 @ Y0 )
          <=> ( '#sk1' @ X2 @ Y0 ) ) )
      | ~ ( X0 @ '#sk2' )
      | ( X0 @ ( '#sk17' @ X0 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl49,plain,
    ! [X0: a > $o,X2: a,X4: a] :
      ( ( ( '#sk24' @ X0 @ X4 )
      <=> ( '#sk1' @ X2 @ X4 ) )
      | ( X0 @ ( '#sk17' @ X0 ) )
      | ~ ( X0 @ '#sk2' )
      | ~ ( '#sk24' @ X0 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl51,plain,
    ! [X0: a > $o,X2: a,X4: a] :
      ( ( ( '#sk24' @ X0 @ X4 )
        = ( '#sk1' @ X2 @ X4 ) )
      | ( X0 @ ( '#sk17' @ X0 ) )
      | ~ ( X0 @ '#sk2' )
      | ~ ( '#sk24' @ X0 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl49]) ).

thf(zip_derived_cl244,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk24'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) )
          @ X0 )
      | ( ^ [Y0: a] :
            ( '#sk1'
            @ ( ^ [Y1: a] :
                  ( ^ [Y2: a] : '#sk2'
                  @ Y1 )
              @ Y0 )
            @ ( ^ [Y1: a] : Y1
              @ Y0 ) )
        @ ( '#sk17'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) ) )
      | ( ( '#sk24'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) )
          @ X1 )
        = ( '#sk1' @ X0 @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl51]) ).

thf(zip_derived_cl248,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
      | ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
      | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
        = ( '#sk1' @ X0 @ X1 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl244]) ).

thf(zip_derived_cl1309,plain,
    ! [X0: a] :
      ( ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
      | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
        = ( '#sk1' @ '#sk2' @ X0 ) )
      | ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl248]) ).

thf(zip_derived_cl1326,plain,
    ! [X0: a] :
      ( ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
        = ( '#sk1' @ '#sk2' @ X0 ) )
      | ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1309]) ).

thf(zip_derived_cl11_003,plain,
    ! [X2: a] : ( '#sk1' @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl29,plain,
    ! [X0: a > $o] :
      ( ( ( '#sk24' @ X0 )
       != X0 )
      | ( X0 @ ( '#sk17' @ X0 ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl35,plain,
    ! [X0: a > $o] :
      ( ( ( '#sk24' @ X0 )
       != X0 )
      | ( X0 @ ( '#sk17' @ X0 ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl36,plain,
    ! [X0: a > $o] :
      ( ( ( '#sk24' @ X0 @ ( '#_fresh_sk52' @ X0 ) )
       != ( X0 @ ( '#_fresh_sk52' @ X0 ) ) )
      | ( X0 @ ( '#sk17' @ X0 ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference(neg_ext_simpl,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl136,plain,
    ( ( ^ [Y0: a] :
          ( '#sk1'
          @ ( ^ [Y1: a] :
                ( ^ [Y2: a] : '#sk2'
                @ Y1 )
            @ Y0 )
          @ ( ^ [Y1: a] : Y1
            @ Y0 ) )
      @ ( '#sk17'
        @ ^ [Y0: a] :
            ( '#sk1'
            @ ( ^ [Y1: a] :
                  ( ^ [Y2: a] : '#sk2'
                  @ Y1 )
              @ Y0 )
            @ ( ^ [Y1: a] : Y1
              @ Y0 ) ) ) )
    | ( ( '#sk24'
        @ ^ [Y0: a] :
            ( '#sk1'
            @ ( ^ [Y1: a] :
                  ( ^ [Y2: a] : '#sk2'
                  @ Y1 )
              @ Y0 )
            @ ( ^ [Y1: a] : Y1
              @ Y0 ) )
        @ ( '#_fresh_sk52'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) ) )
     != ( ^ [Y0: a] :
            ( '#sk1'
            @ ( ^ [Y1: a] :
                  ( ^ [Y2: a] : '#sk2'
                  @ Y1 )
              @ Y0 )
            @ ( ^ [Y1: a] : Y1
              @ Y0 ) )
        @ ( '#_fresh_sk52'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl36]) ).

thf(zip_derived_cl141,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
    | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk52' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ '#sk2' @ ( '#_fresh_sk52' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl136]) ).

thf(zip_derived_cl1338,plain,
    ( ( ( '#sk1' @ '#sk2' @ ( '#_fresh_sk52' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ '#sk2' @ ( '#_fresh_sk52' @ ( '#sk1' @ '#sk2' ) ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1326,zip_derived_cl141]) ).

thf(zip_derived_cl1371,plain,
    '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1338]) ).

thf(zip_derived_cl6,plain,
    ( !!
    @ ^ [Y0: a] :
        ( !!
        @ ^ [Y1: a] :
            ( ( '#sk1' @ Y0 @ Y1 )
           => ( '#sk1' @ Y1 @ Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl10,plain,
    ! [X2: a] :
      ( !!
      @ ^ [Y0: a] :
          ( ( '#sk1' @ X2 @ Y0 )
         => ( '#sk1' @ Y0 @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl14,plain,
    ! [X2: a,X4: a] :
      ( ( '#sk1' @ X2 @ X4 )
     => ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl17,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl1401,plain,
    '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2',
    inference('sup-',[status(thm)],[zip_derived_cl1371,zip_derived_cl17]) ).

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

thf(zip_derived_cl9,plain,
    ! [X2: a] :
      ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( ( '#sk1' @ Y0 @ Y1 )
                & ( '#sk1' @ X2 @ Y0 ) )
             => ( '#sk1' @ X2 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl13,plain,
    ! [X2: a,X4: a] :
      ( !!
      @ ^ [Y0: a] :
          ( ( ( '#sk1' @ X4 @ Y0 )
            & ( '#sk1' @ X2 @ X4 ) )
         => ( '#sk1' @ X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl16,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ( ( '#sk1' @ X4 @ X6 )
        & ( '#sk1' @ X2 @ X4 ) )
     => ( '#sk1' @ X2 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl19,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( ( '#sk1' @ X4 @ X6 )
          & ( '#sk1' @ X2 @ X4 ) )
      | ( '#sk1' @ X2 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl22,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( '#sk1' @ X4 @ X6 )
      | ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl1420,plain,
    ! [X0: a] :
      ( ( '#sk1' @ X0 @ '#sk2' )
      | ~ ( '#sk1' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1401,zip_derived_cl22]) ).

thf(zip_derived_cl11_004,plain,
    ! [X2: a] : ( '#sk1' @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl37,plain,
    ! [X0: a > $o] :
      ( ( ( '#sk24' @ X0 @ '#sk2' )
        & ( !!
          @ ^ [Y0: a] :
              ( ( '#sk24' @ X0 @ Y0 )
             => ( !!
                @ ^ [Y1: a] :
                    ( ( '#sk24' @ X0 @ Y1 )
                  <=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
        & ( ??
          @ ^ [Y0: a] : ( '#sk24' @ X0 @ Y0 ) ) )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl41,plain,
    ! [X0: a > $o] :
      ( ( '#sk24' @ X0 @ '#sk2' )
      | ~ ( X0 @ '#sk2' )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl147,plain,
    ( ( ( ^ [Y0: a] :
            ( '#sk1'
            @ ( ^ [Y1: a] :
                  ( ^ [Y2: a] : '#sk2'
                  @ Y1 )
              @ Y0 )
            @ ( ^ [Y1: a] : Y1
              @ Y0 ) )
        @ ( '#sk28'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) ) )
     != ( '#sk1'
        @ ( '#sk17'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) )
        @ ( '#sk28'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) ) ) )
    | ( '#sk24'
      @ ^ [Y0: a] :
          ( '#sk1'
          @ ( ^ [Y1: a] :
                ( ^ [Y2: a] : '#sk2'
                @ Y1 )
            @ Y0 )
          @ ( ^ [Y1: a] : Y1
            @ Y0 ) )
      @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl41]) ).

thf(zip_derived_cl152,plain,
    ( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl147]) ).

thf(zip_derived_cl223,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl152]) ).

thf(zip_derived_cl17_005,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl251,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' )
    | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl223,zip_derived_cl17]) ).

thf(zip_derived_cl1564,plain,
    ( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
    | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl1420,zip_derived_cl251]) ).

thf(zip_derived_cl17_006,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl2562,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' )
    | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1564,zip_derived_cl17]) ).

thf(zip_derived_cl11_007,plain,
    ! [X2: a] : ( '#sk1' @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl42,plain,
    ! [X0: a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( '#sk24' @ X0 @ Y0 )
           => ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk24' @ X0 @ Y1 )
                <=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
      | ~ ( X0 @ '#sk2' )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl47,plain,
    ! [X0: a > $o,X2: a] :
      ( ( ( '#sk24' @ X0 @ X2 )
       => ( !!
          @ ^ [Y0: a] :
              ( ( '#sk24' @ X0 @ Y0 )
            <=> ( '#sk1' @ X2 @ Y0 ) ) ) )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
      | ~ ( X0 @ '#sk2' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl50,plain,
    ! [X0: a > $o,X2: a] :
      ( ~ ( '#sk24' @ X0 @ X2 )
      | ( !!
        @ ^ [Y0: a] :
            ( ( '#sk24' @ X0 @ Y0 )
          <=> ( '#sk1' @ X2 @ Y0 ) ) )
      | ~ ( X0 @ '#sk2' )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl52,plain,
    ! [X0: a > $o,X2: a,X4: a] :
      ( ( ( '#sk24' @ X0 @ X4 )
      <=> ( '#sk1' @ X2 @ X4 ) )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
      | ~ ( X0 @ '#sk2' )
      | ~ ( '#sk24' @ X0 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl53,plain,
    ! [X0: a > $o,X2: a,X4: a] :
      ( ( ( '#sk24' @ X0 @ X4 )
        = ( '#sk1' @ X2 @ X4 ) )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
      | ~ ( X0 @ '#sk2' )
      | ~ ( '#sk24' @ X0 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl322,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk24'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) )
          @ X0 )
      | ( ( ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) )
          @ ( '#sk28'
            @ ^ [Y0: a] :
                ( '#sk1'
                @ ( ^ [Y1: a] :
                      ( ^ [Y2: a] : '#sk2'
                      @ Y1 )
                  @ Y0 )
                @ ( ^ [Y1: a] : Y1
                  @ Y0 ) ) ) )
       != ( '#sk1'
          @ ( '#sk17'
            @ ^ [Y0: a] :
                ( '#sk1'
                @ ( ^ [Y1: a] :
                      ( ^ [Y2: a] : '#sk2'
                      @ Y1 )
                  @ Y0 )
                @ ( ^ [Y1: a] : Y1
                  @ Y0 ) ) )
          @ ( '#sk28'
            @ ^ [Y0: a] :
                ( '#sk1'
                @ ( ^ [Y1: a] :
                      ( ^ [Y2: a] : '#sk2'
                      @ Y1 )
                  @ Y0 )
                @ ( ^ [Y1: a] : Y1
                  @ Y0 ) ) ) ) )
      | ( ( '#sk24'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) )
          @ X1 )
        = ( '#sk1' @ X0 @ X1 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl53]) ).

thf(zip_derived_cl327,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
      | ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
       != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
      | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
        = ( '#sk1' @ X0 @ X1 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl322]) ).

thf(zip_derived_cl2522,plain,
    ! [X0: a,X1: a] :
      ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
      | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
      | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
        = ( '#sk1' @ X0 @ X1 ) )
      | ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl327]) ).

thf(zip_derived_cl3524,plain,
    ! [X0: a] :
      ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
      | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
        = ( '#sk1' @ '#sk2' @ X0 ) )
      | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
      | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2562,zip_derived_cl2522]) ).

thf(zip_derived_cl3539,plain,
    ! [X0: a] :
      ( ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
      | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
        = ( '#sk1' @ '#sk2' @ X0 ) )
      | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3524]) ).

thf(zip_derived_cl17_008,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl3564,plain,
    ! [X0: a] :
      ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
      | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
        = ( '#sk1' @ '#sk2' @ X0 ) )
      | ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3539,zip_derived_cl17]) ).

thf(zip_derived_cl1420_009,plain,
    ! [X0: a] :
      ( ( '#sk1' @ X0 @ '#sk2' )
      | ~ ( '#sk1' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1401,zip_derived_cl22]) ).

thf(zip_derived_cl3591,plain,
    ! [X0: a] :
      ( ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
        = ( '#sk1' @ '#sk2' @ X0 ) )
      | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
      | ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3564,zip_derived_cl1420]) ).

thf(zip_derived_cl17_010,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl3613,plain,
    ! [X0: a] :
      ( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
      | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
        = ( '#sk1' @ '#sk2' @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl3591,zip_derived_cl17]) ).

thf(zip_derived_cl17_011,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl3621,plain,
    ! [X0: a] :
      ( ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
        = ( '#sk1' @ '#sk2' @ X0 ) )
      | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3613,zip_derived_cl17]) ).

thf(zip_derived_cl153_012,plain,
    ( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
    | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl148]) ).

thf(zip_derived_cl378,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl153]) ).

thf(zip_derived_cl3675,plain,
    ( ( ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3621,zip_derived_cl378]) ).

thf(zip_derived_cl3699,plain,
    ( ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3675]) ).

thf(zip_derived_cl17_013,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl3751,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3699,zip_derived_cl17]) ).

thf(zip_derived_cl1420_014,plain,
    ! [X0: a] :
      ( ( '#sk1' @ X0 @ '#sk2' )
      | ~ ( '#sk1' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1401,zip_derived_cl22]) ).

thf(zip_derived_cl3921,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3751,zip_derived_cl1420]) ).

thf(zip_derived_cl17_015,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl3935,plain,
    '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2',
    inference(clc,[status(thm)],[zip_derived_cl3921,zip_derived_cl17]) ).

thf(zip_derived_cl17_016,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl3942,plain,
    '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3935,zip_derived_cl17]) ).

thf(zip_derived_cl3950,plain,
    ( ~ ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl153,zip_derived_cl3942]) ).

thf(zip_derived_cl3935_017,plain,
    '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2',
    inference(clc,[status(thm)],[zip_derived_cl3921,zip_derived_cl17]) ).

thf(zip_derived_cl1371_018,plain,
    '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1338]) ).

thf(zip_derived_cl22_019,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( '#sk1' @ X4 @ X6 )
      | ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl1400,plain,
    ! [X0: a] :
      ( ( '#sk1' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
      | ~ ( '#sk1' @ X0 @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1371,zip_derived_cl22]) ).

thf(zip_derived_cl17_020,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl1629,plain,
    ! [X0: a] :
      ( ~ ( '#sk1' @ X0 @ '#sk2' )
      | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1400,zip_derived_cl17]) ).

thf(zip_derived_cl3936,plain,
    '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3935,zip_derived_cl1629]) ).

thf(zip_derived_cl4005,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
   != ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl3950,zip_derived_cl3936]) ).

thf(zip_derived_cl153_021,plain,
    ( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
    | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl148]) ).

thf(zip_derived_cl380,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl153]) ).

thf(zip_derived_cl3179,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl380]) ).

thf(zip_derived_cl17_022,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl3251,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3179,zip_derived_cl17]) ).

thf(zip_derived_cl1420_023,plain,
    ! [X0: a] :
      ( ( '#sk1' @ X0 @ '#sk2' )
      | ~ ( '#sk1' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1401,zip_derived_cl22]) ).

thf(zip_derived_cl3285,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3251,zip_derived_cl1420]) ).

thf(zip_derived_cl17_024,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl3299,plain,
    ( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl3285,zip_derived_cl17]) ).

thf(zip_derived_cl1629_025,plain,
    ! [X0: a] :
      ( ~ ( '#sk1' @ X0 @ '#sk2' )
      | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1400,zip_derived_cl17]) ).

thf(zip_derived_cl3300,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3299,zip_derived_cl1629]) ).

thf(zip_derived_cl380_026,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl153]) ).

thf(zip_derived_cl3340,plain,
    ( ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3300,zip_derived_cl380]) ).

thf(zip_derived_cl3370,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3340]) ).

thf(zip_derived_cl3299_027,plain,
    ( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl3285,zip_derived_cl17]) ).

thf(zip_derived_cl17_028,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl3306,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3299,zip_derived_cl17]) ).

thf(zip_derived_cl3398,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl3370,zip_derived_cl3306]) ).

thf(zip_derived_cl152_029,plain,
    ( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl147]) ).

thf(zip_derived_cl224,plain,
    ( ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ~ ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl152]) ).

thf(zip_derived_cl11_030,plain,
    ! [X2: a] : ( '#sk1' @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl3613_031,plain,
    ! [X0: a] :
      ( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
      | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
        = ( '#sk1' @ '#sk2' @ X0 ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl3591,zip_derived_cl17]) ).

thf(zip_derived_cl3622,plain,
    ! [X0: a] :
      ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
      | ~ ( '#sk1' @ '#sk2' @ X0 )
      | ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl3613]) ).

thf(zip_derived_cl3838,plain,
    ( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl3622]) ).

thf(zip_derived_cl1629_032,plain,
    ! [X0: a] :
      ( ~ ( '#sk1' @ X0 @ '#sk2' )
      | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1400,zip_derived_cl17]) ).

thf(zip_derived_cl3846,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' )
    | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3838,zip_derived_cl1629]) ).

thf(zip_derived_cl3878,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' )
    | ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl224,zip_derived_cl3846]) ).

thf(zip_derived_cl3898,plain,
    ( ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3878]) ).

thf(zip_derived_cl2562_033,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2' )
    | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1564,zip_derived_cl17]) ).

thf(zip_derived_cl3904,plain,
    '#sk24' @ ( '#sk1' @ '#sk2' ) @ '#sk2',
    inference(clc,[status(thm)],[zip_derived_cl3898,zip_derived_cl2562]) ).

thf(zip_derived_cl327_034,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
      | ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
       != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
      | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
        = ( '#sk1' @ X0 @ X1 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl322]) ).

thf(zip_derived_cl2525,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
      | ( '#sk1' @ X0 @ X1 )
      | ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
       != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
      | ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl327]) ).

thf(zip_derived_cl3942_035,plain,
    '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3935,zip_derived_cl17]) ).

thf(zip_derived_cl3959,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
      | ( '#sk1' @ X0 @ X1 )
      | ~ ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
      | ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2525,zip_derived_cl3942]) ).

thf(zip_derived_cl3936_036,plain,
    '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3935,zip_derived_cl1629]) ).

thf(zip_derived_cl4066,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
      | ( '#sk1' @ X0 @ X1 )
      | ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3959,zip_derived_cl3936]) ).

thf(zip_derived_cl4069,plain,
    ! [X0: a] :
      ( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
      | ( '#sk1' @ X0 @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3904,zip_derived_cl4066]) ).

thf(zip_derived_cl4081,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3398,zip_derived_cl4069]) ).

thf(zip_derived_cl17_037,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl4127,plain,
    '#sk1' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2',
    inference(clc,[status(thm)],[zip_derived_cl4081,zip_derived_cl17]) ).

thf(zip_derived_cl17_038,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl4134,plain,
    '#sk1' @ '#sk2' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl4127,zip_derived_cl17]) ).

thf(zip_derived_cl4142,plain,
    ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4005,zip_derived_cl4134]) ).

thf(zip_derived_cl11_039,plain,
    ! [X2: a] : ( '#sk1' @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl1371_040,plain,
    '#sk1' @ '#sk2' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl1338]) ).

thf(zip_derived_cl53_041,plain,
    ! [X0: a > $o,X2: a,X4: a] :
      ( ( ( '#sk24' @ X0 @ X4 )
        = ( '#sk1' @ X2 @ X4 ) )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
      | ~ ( X0 @ '#sk2' )
      | ~ ( '#sk24' @ X0 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl312,plain,
    ! [X0: a > $o,X2: a,X4: a] :
      ( ( '#sk24' @ X0 @ X4 )
      | ~ ( '#sk1' @ X2 @ X4 )
      | ~ ( '#sk24' @ X0 @ X2 )
      | ~ ( X0 @ '#sk2' )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl2641,plain,
    ! [X0: a > $o] :
      ( ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) )
      | ~ ( X0 @ '#sk2' )
      | ~ ( '#sk24' @ X0 @ '#sk2' )
      | ( '#sk24' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1371,zip_derived_cl312]) ).

thf(zip_derived_cl41_042,plain,
    ! [X0: a > $o] :
      ( ( '#sk24' @ X0 @ '#sk2' )
      | ~ ( X0 @ '#sk2' )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl2664,plain,
    ! [X0: a > $o] :
      ( ( '#sk24' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
      | ~ ( X0 @ '#sk2' )
      | ( ( X0 @ ( '#sk28' @ X0 ) )
       != ( '#sk1' @ ( '#sk17' @ X0 ) @ ( '#sk28' @ X0 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl2641,zip_derived_cl41]) ).

thf(zip_derived_cl2670,plain,
    ( ( ( ^ [Y0: a] :
            ( '#sk1'
            @ ( ^ [Y1: a] :
                  ( ^ [Y2: a] : '#sk2'
                  @ Y1 )
              @ Y0 )
            @ ( ^ [Y1: a] : Y1
              @ Y0 ) )
        @ ( '#sk28'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) ) )
     != ( '#sk1'
        @ ( '#sk17'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) )
        @ ( '#sk28'
          @ ^ [Y0: a] :
              ( '#sk1'
              @ ( ^ [Y1: a] :
                    ( ^ [Y2: a] : '#sk2'
                    @ Y1 )
                @ Y0 )
              @ ( ^ [Y1: a] : Y1
                @ Y0 ) ) ) ) )
    | ( '#sk24'
      @ ^ [Y0: a] :
          ( '#sk1'
          @ ( ^ [Y1: a] :
                ( ^ [Y2: a] : '#sk2'
                @ Y1 )
            @ Y0 )
          @ ( ^ [Y1: a] : Y1
            @ Y0 ) )
      @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl2664]) ).

thf(zip_derived_cl2674,plain,
    ( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl2670]) ).

thf(zip_derived_cl2677,plain,
    ( ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ~ ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl2674]) ).

thf(zip_derived_cl2674_043,plain,
    ( ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
     != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl2670]) ).

thf(zip_derived_cl2676,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl2674]) ).

thf(zip_derived_cl17_044,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl3037,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2676,zip_derived_cl17]) ).

thf(zip_derived_cl1420_045,plain,
    ! [X0: a] :
      ( ( '#sk1' @ X0 @ '#sk2' )
      | ~ ( '#sk1' @ X0 @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1401,zip_derived_cl22]) ).

thf(zip_derived_cl3064,plain,
    ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3037,zip_derived_cl1420]) ).

thf(zip_derived_cl17_046,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl3078,plain,
    ( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl3064,zip_derived_cl17]) ).

thf(zip_derived_cl1629_047,plain,
    ! [X0: a] :
      ( ~ ( '#sk1' @ X0 @ '#sk2' )
      | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1400,zip_derived_cl17]) ).

thf(zip_derived_cl3079,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3078,zip_derived_cl1629]) ).

thf(zip_derived_cl3107,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
    | ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl2677,zip_derived_cl3079]) ).

thf(zip_derived_cl3127,plain,
    ( ~ ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl3107]) ).

thf(zip_derived_cl3078_048,plain,
    ( ( '#sk1' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2' )
    | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl3064,zip_derived_cl17]) ).

thf(zip_derived_cl17_049,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk1' @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl3085,plain,
    ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) )
    | ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3078,zip_derived_cl17]) ).

thf(zip_derived_cl3148,plain,
    '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ),
    inference(clc,[status(thm)],[zip_derived_cl3127,zip_derived_cl3085]) ).

thf(zip_derived_cl327_050,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 )
      | ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
       != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
      | ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
        = ( '#sk1' @ X0 @ X1 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl322]) ).

thf(zip_derived_cl2524,plain,
    ! [X0: a,X1: a] :
      ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
      | ~ ( '#sk1' @ X0 @ X1 )
      | ( ( '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
       != ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) ) )
      | ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl327]) ).

thf(zip_derived_cl3942_051,plain,
    '#sk1' @ '#sk2' @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3935,zip_derived_cl17]) ).

thf(zip_derived_cl3958,plain,
    ! [X0: a,X1: a] :
      ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
      | ~ ( '#sk1' @ X0 @ X1 )
      | ~ ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ) )
      | ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2524,zip_derived_cl3942]) ).

thf(zip_derived_cl3936_052,plain,
    '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#sk28' @ ( '#sk1' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3935,zip_derived_cl1629]) ).

thf(zip_derived_cl4359,plain,
    ! [X0: a,X1: a] :
      ( ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X1 )
      | ~ ( '#sk1' @ X0 @ X1 )
      | ~ ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl3958,zip_derived_cl3936]) ).

thf(zip_derived_cl4360,plain,
    ! [X0: a] :
      ( ~ ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ X0 )
      | ( '#sk24' @ ( '#sk1' @ '#sk2' ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3148,zip_derived_cl4359]) ).

thf(zip_derived_cl4127_053,plain,
    '#sk1' @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ) @ '#sk2',
    inference(clc,[status(thm)],[zip_derived_cl4081,zip_derived_cl17]) ).

thf(zip_derived_cl1629_054,plain,
    ! [X0: a] :
      ( ~ ( '#sk1' @ X0 @ '#sk2' )
      | ( '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1400,zip_derived_cl17]) ).

thf(zip_derived_cl4128,plain,
    '#sk1' @ ( '#sk17' @ ( '#sk1' @ '#sk2' ) ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl4127,zip_derived_cl1629]) ).

thf(zip_derived_cl4371,plain,
    '#sk24' @ ( '#sk1' @ '#sk2' ) @ ( '#_fresh_sk90' @ ( '#sk1' @ '#sk2' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl4360,zip_derived_cl4128]) ).

thf(zip_derived_cl4399,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl4142,zip_derived_cl4371]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SEV010^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.3KiOpWdBTt true
% 0.14/0.35  % Computer : n029.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 02:46:08 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
% 0.20/0.64  % Total configuration time : 828
% 0.20/0.64  % Estimated wc time : 1656
% 0.20/0.64  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 26.23/3.95  % Solved by lams/20_acsne_simpl.sh.
% 26.23/3.95  % done 1215 iterations in 3.166s
% 26.23/3.95  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 26.23/3.95  % SZS output start Refutation
% See solution above
% 26.23/3.95  
% 26.23/3.95  
% 26.23/3.95  % Terminating...
% 26.77/4.06  % Runner terminated.
% 26.77/4.09  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------