TSTP Solution File: ALG272^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : ALG272^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.XFivht7x8M true

% Computer : n004.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 : Wed Aug 30 17:12:40 EDT 2023

% Result   : Theorem 1.40s 0.85s
% Output   : Refutation 1.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   42
% Syntax   : Number of formulae    :  143 (  48 unt;  20 typ;   0 def)
%            Number of atoms       :  688 ( 330 equ;   0 cnn)
%            Maximal formula atoms :   22 (   5 avg)
%            Number of connectives : 1981 ( 139   ~; 126   |; 128   &;1323   @)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   81 (  81   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  19 usr;  12 con; 0-2 aty)
%                                         ( 221  !!;  38  ??;   0 @@+;   0 @@-)
%            Number of variables   :  433 ( 298   ^; 125   !;  10   ?; 433   :)

% Comments : 
%------------------------------------------------------------------------------
thf(g_type,type,
    g: $tType ).

thf(cGRP_INVERSE_type,type,
    cGRP_INVERSE: ( g > g > g ) > g > $o ).

thf('#sk4_type',type,
    '#sk4': g > g ).

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

thf('#sk11_type',type,
    '#sk11': g ).

thf(cGROUP2_type,type,
    cGROUP2: ( g > g > g ) > g > $o ).

thf(cGRP_LEFT_UNIT_type,type,
    cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).

thf(cGRP_UNIT_type,type,
    cGRP_UNIT: ( g > g > g ) > g > $o ).

thf('#sk10_type',type,
    '#sk10': g ).

thf('#sk9_type',type,
    '#sk9': g ).

thf(cGRP_LEFT_INVERSE_type,type,
    cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).

thf(cGRP_ASSOC_type,type,
    cGRP_ASSOC: ( g > g > g ) > $o ).

thf('#sk1_type',type,
    '#sk1': g > g > g ).

thf('#sk5_type',type,
    '#sk5': g > g ).

thf(cGROUP1_type,type,
    cGROUP1: ( g > g > g ) > g > $o ).

thf('#sk12_type',type,
    '#sk12': g ).

thf('#form3_type',type,
    '#form3': $o ).

thf('#sk8_type',type,
    '#sk8': g ).

thf('#sk7_type',type,
    '#sk7': g ).

thf('#sk6_type',type,
    '#sk6': g ).

thf(cGROUP2_def,axiom,
    ( cGROUP2
    = ( ^ [Xf: g > g > g,Xe: g] :
          ( ( cGRP_ASSOC @ Xf )
          & ( cGRP_LEFT_UNIT @ Xf @ Xe )
          & ( cGRP_LEFT_INVERSE @ Xf @ Xe ) ) ) ) ).

thf(cGRP_LEFT_UNIT_def,axiom,
    ( cGRP_LEFT_UNIT
    = ( ^ [Xf: g > g > g,Xe: g] :
        ! [Xa: g] :
          ( ( Xf @ Xe @ Xa )
          = Xa ) ) ) ).

thf('0',plain,
    ( cGRP_LEFT_UNIT
    = ( ^ [Xf: g > g > g,Xe: g] :
        ! [Xa: g] :
          ( ( Xf @ Xe @ Xa )
          = Xa ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cGRP_LEFT_UNIT_def]) ).

thf('1',plain,
    ( cGRP_LEFT_UNIT
    = ( ^ [V_1: g > g > g,V_2: g] :
        ! [X4: g] :
          ( ( V_1 @ V_2 @ X4 )
          = X4 ) ) ),
    define([status(thm)]) ).

thf(cGRP_LEFT_INVERSE_def,axiom,
    ( cGRP_LEFT_INVERSE
    = ( ^ [Xf: g > g > g,Xe: g] :
        ! [Xa: g] :
        ? [Xb: g] :
          ( ( Xf @ Xb @ Xa )
          = Xe ) ) ) ).

thf('2',plain,
    ( cGRP_LEFT_INVERSE
    = ( ^ [Xf: g > g > g,Xe: g] :
        ! [Xa: g] :
        ? [Xb: g] :
          ( ( Xf @ Xb @ Xa )
          = Xe ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cGRP_LEFT_INVERSE_def]) ).

thf('3',plain,
    ( cGRP_LEFT_INVERSE
    = ( ^ [V_1: g > g > g,V_2: g] :
        ! [X4: g] :
        ? [X6: g] :
          ( ( V_1 @ X6 @ X4 )
          = V_2 ) ) ),
    define([status(thm)]) ).

thf(cGRP_ASSOC_def,axiom,
    ( cGRP_ASSOC
    = ( ^ [Xf: g > g > g] :
        ! [Xa: g,Xb: g,Xc: g] :
          ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
          = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ) ).

thf('4',plain,
    ( cGRP_ASSOC
    = ( ^ [Xf: g > g > g] :
        ! [Xa: g,Xb: g,Xc: g] :
          ( ( Xf @ ( Xf @ Xa @ Xb ) @ Xc )
          = ( Xf @ Xa @ ( Xf @ Xb @ Xc ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cGRP_ASSOC_def]) ).

thf('5',plain,
    ( cGRP_ASSOC
    = ( ^ [V_1: g > g > g] :
        ! [X4: g,X6: g,X8: g] :
          ( ( V_1 @ ( V_1 @ X4 @ X6 ) @ X8 )
          = ( V_1 @ X4 @ ( V_1 @ X6 @ X8 ) ) ) ) ),
    define([status(thm)]) ).

thf('6',plain,
    ( cGROUP2
    = ( ^ [Xf: g > g > g,Xe: g] :
          ( ( cGRP_ASSOC @ Xf )
          & ( cGRP_LEFT_UNIT @ Xf @ Xe )
          & ( cGRP_LEFT_INVERSE @ Xf @ Xe ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cGROUP2_def,'1','3','5']) ).

thf('7',plain,
    ( cGROUP2
    = ( ^ [V_1: g > g > g,V_2: g] :
          ( ( cGRP_ASSOC @ V_1 )
          & ( cGRP_LEFT_UNIT @ V_1 @ V_2 )
          & ( cGRP_LEFT_INVERSE @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(cGROUP1_def,axiom,
    ( cGROUP1
    = ( ^ [Xf: g > g > g,Xe: g] :
          ( ( cGRP_ASSOC @ Xf )
          & ( cGRP_UNIT @ Xf @ Xe )
          & ( cGRP_INVERSE @ Xf @ Xe ) ) ) ) ).

thf(cGRP_UNIT_def,axiom,
    ( cGRP_UNIT
    = ( ^ [Xf: g > g > g,Xe: g] :
        ! [Xa: g] :
          ( ( ( Xf @ Xa @ Xe )
            = Xa )
          & ( ( Xf @ Xe @ Xa )
            = Xa ) ) ) ) ).

thf('8',plain,
    ( cGRP_UNIT
    = ( ^ [Xf: g > g > g,Xe: g] :
        ! [Xa: g] :
          ( ( ( Xf @ Xa @ Xe )
            = Xa )
          & ( ( Xf @ Xe @ Xa )
            = Xa ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cGRP_UNIT_def]) ).

thf('9',plain,
    ( cGRP_UNIT
    = ( ^ [V_1: g > g > g,V_2: g] :
        ! [X4: g] :
          ( ( ( V_1 @ X4 @ V_2 )
            = X4 )
          & ( ( V_1 @ V_2 @ X4 )
            = X4 ) ) ) ),
    define([status(thm)]) ).

thf(cGRP_INVERSE_def,axiom,
    ( cGRP_INVERSE
    = ( ^ [Xf: g > g > g,Xe: g] :
        ! [Xa: g] :
        ? [Xb: g] :
          ( ( ( Xf @ Xb @ Xa )
            = Xe )
          & ( ( Xf @ Xa @ Xb )
            = Xe ) ) ) ) ).

thf('10',plain,
    ( cGRP_INVERSE
    = ( ^ [Xf: g > g > g,Xe: g] :
        ! [Xa: g] :
        ? [Xb: g] :
          ( ( ( Xf @ Xb @ Xa )
            = Xe )
          & ( ( Xf @ Xa @ Xb )
            = Xe ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cGRP_INVERSE_def]) ).

thf('11',plain,
    ( cGRP_INVERSE
    = ( ^ [V_1: g > g > g,V_2: g] :
        ! [X4: g] :
        ? [X6: g] :
          ( ( ( V_1 @ X6 @ X4 )
            = V_2 )
          & ( ( V_1 @ X4 @ X6 )
            = V_2 ) ) ) ),
    define([status(thm)]) ).

thf('12',plain,
    ( cGROUP1
    = ( ^ [Xf: g > g > g,Xe: g] :
          ( ( cGRP_ASSOC @ Xf )
          & ( cGRP_UNIT @ Xf @ Xe )
          & ( cGRP_INVERSE @ Xf @ Xe ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[cGROUP1_def,'9','11','5']) ).

thf('13',plain,
    ( cGROUP1
    = ( ^ [V_1: g > g > g,V_2: g] :
          ( ( cGRP_ASSOC @ V_1 )
          & ( cGRP_UNIT @ V_1 @ V_2 )
          & ( cGRP_INVERSE @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(cEQUIV_01_02,conjecture,
    ! [Xf: g > g > g,Xe: g] :
      ( ( cGROUP1 @ Xf @ Xe )
    <=> ( cGROUP2 @ Xf @ Xe ) ) ).

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

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

thf(zip_derived_cl0,plain,
    ~ ( !!
      @ ^ [Y0: g > g > g] :
          ( !!
          @ ^ [Y1: g] :
              ( ( ( !!
                  @ ^ [Y2: g] :
                      ( ??
                      @ ^ [Y3: g] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            = Y1 )
                          & ( ( Y0 @ Y3 @ Y2 )
                            = Y1 ) ) ) )
                & ( !!
                  @ ^ [Y2: g] :
                      ( ( ( Y0 @ Y1 @ Y2 )
                        = Y2 )
                      & ( ( Y0 @ Y2 @ Y1 )
                        = Y2 ) ) )
                & ( !!
                  @ ^ [Y2: g] :
                      ( !!
                      @ ^ [Y3: g] :
                          ( !!
                          @ ^ [Y4: g] :
                              ( ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y4 )
                              = ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) )
            <=> ( ( !!
                  @ ^ [Y2: g] :
                      ( ??
                      @ ^ [Y3: g] :
                          ( ( Y0 @ Y3 @ Y2 )
                          = Y1 ) ) )
                & ( !!
                  @ ^ [Y2: g] :
                      ( ( Y0 @ Y1 @ Y2 )
                      = Y2 ) )
                & ( !!
                  @ ^ [Y2: g] :
                      ( !!
                      @ ^ [Y3: g] :
                          ( !!
                          @ ^ [Y4: g] :
                              ( ( Y0 @ ( Y0 @ Y2 @ Y3 ) @ Y4 )
                              = ( Y0 @ Y2 @ ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

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

thf(zip_derived_cl2,plain,
    ~ ( ( ( !!
          @ ^ [Y0: g] :
              ( ??
              @ ^ [Y1: g] :
                  ( ( ( '#sk1' @ Y0 @ Y1 )
                    = '#sk2' )
                  & ( ( '#sk1' @ Y1 @ Y0 )
                    = '#sk2' ) ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) )
    <=> ( ( !!
          @ ^ [Y0: g] :
              ( ??
              @ ^ [Y1: g] :
                  ( ( '#sk1' @ Y1 @ Y0 )
                  = '#sk2' ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( ( '#sk1' @ '#sk2' @ Y0 )
              = Y0 ) )
        & ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl3,plain,
    ( ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( ( '#sk1' @ Y0 @ Y1 )
                  = '#sk2' )
                & ( ( '#sk1' @ Y1 @ Y0 )
                  = '#sk2' ) ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( ( '#sk1' @ '#sk2' @ Y0 )
              = Y0 )
            & ( ( '#sk1' @ Y0 @ '#sk2' )
              = Y0 ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) )
   != ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl4,plain,
    ( ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( ( '#sk1' @ Y0 @ Y1 )
                  = '#sk2' )
                & ( ( '#sk1' @ Y1 @ Y0 )
                  = '#sk2' ) ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( ( '#sk1' @ '#sk2' @ Y0 )
              = Y0 )
            & ( ( '#sk1' @ Y0 @ '#sk2' )
              = Y0 ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl6,plain,
    ( ( !!
      @ ^ [Y0: g] :
          ( ??
          @ ^ [Y1: g] :
              ( ( ( '#sk1' @ Y0 @ Y1 )
                = '#sk2' )
              & ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) ) )
    | ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl9,plain,
    ( ~ '#form3'
    | ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl10,plain,
    ( ( !!
      @ ^ [Y0: g] :
          ( ??
          @ ^ [Y1: g] :
              ( ( '#sk1' @ Y1 @ Y0 )
              = '#sk2' ) ) )
    | ~ '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl19,plain,
    ! [X2: g] :
      ( ( ??
        @ ^ [Y0: g] :
            ( ( '#sk1' @ Y0 @ X2 )
            = '#sk2' ) )
      | ~ '#form3' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl25,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ ( '#sk5' @ X2 ) @ X2 )
        = '#sk2' )
      | ~ '#form3' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl33,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ ( '#sk5' @ X2 ) @ X2 )
        = '#sk2' )
      | ~ '#form3' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl6_001,plain,
    ( ( !!
      @ ^ [Y0: g] :
          ( ??
          @ ^ [Y1: g] :
              ( ( ( '#sk1' @ Y0 @ Y1 )
                = '#sk2' )
              & ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) ) )
    | ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl9_002,plain,
    ( ~ '#form3'
    | ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl13,plain,
    ( '#form3'
    | ( !!
      @ ^ [Y0: g] :
          ( ??
          @ ^ [Y1: g] :
              ( ( ( '#sk1' @ Y0 @ Y1 )
                = '#sk2' )
              & ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl6,zip_derived_cl9]) ).

thf(zip_derived_cl18,plain,
    ! [X2: g] :
      ( ( ??
        @ ^ [Y0: g] :
            ( ( ( '#sk1' @ X2 @ Y0 )
              = '#sk2' )
            & ( ( '#sk1' @ Y0 @ X2 )
              = '#sk2' ) ) )
      | '#form3' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl24,plain,
    ! [X2: g] :
      ( ( ( ( '#sk1' @ X2 @ ( '#sk4' @ X2 ) )
          = '#sk2' )
        & ( ( '#sk1' @ ( '#sk4' @ X2 ) @ X2 )
          = '#sk2' ) )
      | '#form3' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl32,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ ( '#sk4' @ X2 ) @ X2 )
        = '#sk2' )
      | '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl39,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ ( '#sk4' @ X2 ) @ X2 )
        = '#sk2' )
      | '#form3' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl3_003,plain,
    ( ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( ( '#sk1' @ Y0 @ Y1 )
                  = '#sk2' )
                & ( ( '#sk1' @ Y1 @ Y0 )
                  = '#sk2' ) ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( ( '#sk1' @ '#sk2' @ Y0 )
              = Y0 )
            & ( ( '#sk1' @ Y0 @ '#sk2' )
              = Y0 ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) )
   != ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl5,plain,
    ( ~ ( ( !!
          @ ^ [Y0: g] :
              ( ??
              @ ^ [Y1: g] :
                  ( ( ( '#sk1' @ Y0 @ Y1 )
                    = '#sk2' )
                  & ( ( '#sk1' @ Y1 @ Y0 )
                    = '#sk2' ) ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) )
    | ~ ( ( !!
          @ ^ [Y0: g] :
              ( ??
              @ ^ [Y1: g] :
                  ( ( '#sk1' @ Y1 @ Y0 )
                  = '#sk2' ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( ( '#sk1' @ '#sk2' @ Y0 )
              = Y0 ) )
        & ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl92,plain,
    ( '#form3'
    | ~ ( ( !!
          @ ^ [Y0: g] :
              ( ??
              @ ^ [Y1: g] :
                  ( ( '#sk1' @ Y1 @ Y0 )
                  = '#sk2' ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( ( '#sk1' @ '#sk2' @ Y0 )
              = Y0 ) )
        & ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl93,plain,
    ( ~ ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
    | ~ ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
    | ~ ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
    | '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl92]) ).

thf(zip_derived_cl96,plain,
    ( ~ ( ??
        @ ^ [Y0: g] :
            ( ( '#sk1' @ Y0 @ '#sk6' )
            = '#sk2' ) )
    | '#form3'
    | ~ ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl93]) ).

thf(zip_derived_cl98,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ X2 @ '#sk6' )
       != '#sk2' )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( ( '#sk1' @ '#sk2' @ Y0 )
              = Y0 ) )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
      | '#form3' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl96]) ).

thf(zip_derived_cl100,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ X2 @ '#sk6' )
       != '#sk2' )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( ( '#sk1' @ '#sk2' @ Y0 )
              = Y0 ) )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
      | '#form3' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl98]) ).

thf(zip_derived_cl101,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk2' @ '#sk8' )
       != '#sk8' )
      | '#form3'
      | ~ ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
      | ( ( '#sk1' @ X2 @ '#sk6' )
       != '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl100]) ).

thf(zip_derived_cl103,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk2' @ '#sk8' )
       != '#sk8' )
      | '#form3'
      | ~ ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
      | ( ( '#sk1' @ X2 @ '#sk6' )
       != '#sk2' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl101]) ).

thf(zip_derived_cl7,plain,
    ( ( !!
      @ ^ [Y0: g] :
          ( ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 )
          & ( ( '#sk1' @ Y0 @ '#sk2' )
            = Y0 ) ) )
    | ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl9_004,plain,
    ( ~ '#form3'
    | ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl14,plain,
    ( '#form3'
    | ( !!
      @ ^ [Y0: g] :
          ( ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 )
          & ( ( '#sk1' @ Y0 @ '#sk2' )
            = Y0 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl7,zip_derived_cl9]) ).

thf(zip_derived_cl22,plain,
    ! [X2: g] :
      ( ( ( ( '#sk1' @ '#sk2' @ X2 )
          = X2 )
        & ( ( '#sk1' @ X2 @ '#sk2' )
          = X2 ) )
      | '#form3' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl28,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk2' @ X2 )
        = X2 )
      | '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl35,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk2' @ X2 )
        = X2 )
      | '#form3' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl11,plain,
    ( ( !!
      @ ^ [Y0: g] :
          ( ( '#sk1' @ '#sk2' @ Y0 )
          = Y0 ) )
    | ~ '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl20,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk2' @ X2 )
        = X2 )
      | ~ '#form3' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl26,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk2' @ X2 )
        = X2 )
      | ~ '#form3' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl41,plain,
    ! [X2: g] :
      ( ( '#sk1' @ '#sk2' @ X2 )
      = X2 ),
    inference(clc,[status(thm)],[zip_derived_cl35,zip_derived_cl26]) ).

thf(zip_derived_cl104,plain,
    ! [X2: g] :
      ( ( '#sk8' != '#sk8' )
      | '#form3'
      | ~ ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
      | ( ( '#sk1' @ X2 @ '#sk6' )
       != '#sk2' ) ),
    inference(demod,[status(thm)],[zip_derived_cl103,zip_derived_cl41]) ).

thf(zip_derived_cl105,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ X2 @ '#sk6' )
       != '#sk2' )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
      | '#form3' ),
    inference(simplify,[status(thm)],[zip_derived_cl104]) ).

thf(zip_derived_cl106,plain,
    ! [X2: g] :
      ( ~ ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( ( '#sk1' @ ( '#sk1' @ '#sk9' @ Y0 ) @ Y1 )
                  = ( '#sk1' @ '#sk9' @ ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
      | '#form3'
      | ( ( '#sk1' @ X2 @ '#sk6' )
       != '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl105]) ).

thf(zip_derived_cl109,plain,
    ! [X2: g] :
      ( ~ ( !!
          @ ^ [Y0: g] :
              ( ( '#sk1' @ ( '#sk1' @ '#sk9' @ '#sk10' ) @ Y0 )
              = ( '#sk1' @ '#sk9' @ ( '#sk1' @ '#sk10' @ Y0 ) ) ) )
      | ( ( '#sk1' @ X2 @ '#sk6' )
       != '#sk2' )
      | '#form3' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl106]) ).

thf(zip_derived_cl111,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ ( '#sk1' @ '#sk9' @ '#sk10' ) @ '#sk11' )
       != ( '#sk1' @ '#sk9' @ ( '#sk1' @ '#sk10' @ '#sk11' ) ) )
      | '#form3'
      | ( ( '#sk1' @ X2 @ '#sk6' )
       != '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl109]) ).

thf(zip_derived_cl113,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ ( '#sk1' @ '#sk9' @ '#sk10' ) @ '#sk11' )
       != ( '#sk1' @ '#sk9' @ ( '#sk1' @ '#sk10' @ '#sk11' ) ) )
      | '#form3'
      | ( ( '#sk1' @ X2 @ '#sk6' )
       != '#sk2' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl111]) ).

thf(zip_derived_cl8,plain,
    ( ( !!
      @ ^ [Y0: g] :
          ( !!
          @ ^ [Y1: g] :
              ( !!
              @ ^ [Y2: g] :
                  ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                  = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl15,plain,
    ( ( !!
      @ ^ [Y0: g] :
          ( !!
          @ ^ [Y1: g] :
              ( !!
              @ ^ [Y2: g] :
                  ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                  = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
    | ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
      & $false ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl16,plain,
    ( !!
    @ ^ [Y0: g] :
        ( !!
        @ ^ [Y1: g] :
            ( !!
            @ ^ [Y2: g] :
                ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl17,plain,
    ! [X2: g] :
      ( !!
      @ ^ [Y0: g] :
          ( !!
          @ ^ [Y1: g] :
              ( ( '#sk1' @ ( '#sk1' @ X2 @ Y0 ) @ Y1 )
              = ( '#sk1' @ X2 @ ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl23,plain,
    ! [X2: g,X4: g] :
      ( !!
      @ ^ [Y0: g] :
          ( ( '#sk1' @ ( '#sk1' @ X2 @ X4 ) @ Y0 )
          = ( '#sk1' @ X2 @ ( '#sk1' @ X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl30,plain,
    ! [X2: g,X4: g,X6: g] :
      ( ( '#sk1' @ ( '#sk1' @ X2 @ X4 ) @ X6 )
      = ( '#sk1' @ X2 @ ( '#sk1' @ X4 @ X6 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl37,plain,
    ! [X2: g,X4: g,X6: g] :
      ( ( '#sk1' @ ( '#sk1' @ X2 @ X4 ) @ X6 )
      = ( '#sk1' @ X2 @ ( '#sk1' @ X4 @ X6 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl114,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk9' @ ( '#sk1' @ '#sk10' @ '#sk11' ) )
       != ( '#sk1' @ '#sk9' @ ( '#sk1' @ '#sk10' @ '#sk11' ) ) )
      | '#form3'
      | ( ( '#sk1' @ X2 @ '#sk6' )
       != '#sk2' ) ),
    inference(demod,[status(thm)],[zip_derived_cl113,zip_derived_cl37]) ).

thf(zip_derived_cl115,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ X2 @ '#sk6' )
       != '#sk2' )
      | '#form3' ),
    inference(simplify,[status(thm)],[zip_derived_cl114]) ).

thf(zip_derived_cl124,plain,
    ( ( '#sk2' != '#sk2' )
    | '#form3'
    | '#form3' ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl115]) ).

thf(zip_derived_cl132,plain,
    '#form3',
    inference(simplify,[status(thm)],[zip_derived_cl124]) ).

thf(zip_derived_cl135,plain,
    ! [X2: g] :
      ( ( '#sk1' @ ( '#sk5' @ X2 ) @ X2 )
      = '#sk2' ),
    inference(demod,[status(thm)],[zip_derived_cl33,zip_derived_cl132]) ).

thf(zip_derived_cl135_005,plain,
    ! [X2: g] :
      ( ( '#sk1' @ ( '#sk5' @ X2 ) @ X2 )
      = '#sk2' ),
    inference(demod,[status(thm)],[zip_derived_cl33,zip_derived_cl132]) ).

thf(zip_derived_cl37_006,plain,
    ! [X2: g,X4: g,X6: g] :
      ( ( '#sk1' @ ( '#sk1' @ X2 @ X4 ) @ X6 )
      = ( '#sk1' @ X2 @ ( '#sk1' @ X4 @ X6 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl136,plain,
    ! [X0: g,X1: g] :
      ( ( '#sk1' @ '#sk2' @ X0 )
      = ( '#sk1' @ ( '#sk5' @ X1 ) @ ( '#sk1' @ X1 @ X0 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl135,zip_derived_cl37]) ).

thf(zip_derived_cl41_007,plain,
    ! [X2: g] :
      ( ( '#sk1' @ '#sk2' @ X2 )
      = X2 ),
    inference(clc,[status(thm)],[zip_derived_cl35,zip_derived_cl26]) ).

thf(zip_derived_cl138,plain,
    ! [X0: g,X1: g] :
      ( X0
      = ( '#sk1' @ ( '#sk5' @ X1 ) @ ( '#sk1' @ X1 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl136,zip_derived_cl41]) ).

thf(zip_derived_cl143,plain,
    ! [X0: g] :
      ( X0
      = ( '#sk1' @ ( '#sk5' @ ( '#sk5' @ X0 ) ) @ '#sk2' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl135,zip_derived_cl138]) ).

thf(zip_derived_cl138_008,plain,
    ! [X0: g,X1: g] :
      ( X0
      = ( '#sk1' @ ( '#sk5' @ X1 ) @ ( '#sk1' @ X1 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl136,zip_derived_cl41]) ).

thf(zip_derived_cl138_009,plain,
    ! [X0: g,X1: g] :
      ( X0
      = ( '#sk1' @ ( '#sk5' @ X1 ) @ ( '#sk1' @ X1 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl136,zip_derived_cl41]) ).

thf(zip_derived_cl140,plain,
    ! [X0: g,X1: g] :
      ( ( '#sk1' @ X1 @ X0 )
      = ( '#sk1' @ ( '#sk5' @ ( '#sk5' @ X1 ) ) @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl138,zip_derived_cl138]) ).

thf(zip_derived_cl193,plain,
    ! [X0: g] :
      ( ( '#sk1' @ X0 @ '#sk2' )
      = X0 ),
    inference('sup+',[status(thm)],[zip_derived_cl143,zip_derived_cl140]) ).

thf(zip_derived_cl143_010,plain,
    ! [X0: g] :
      ( X0
      = ( '#sk1' @ ( '#sk5' @ ( '#sk5' @ X0 ) ) @ '#sk2' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl135,zip_derived_cl138]) ).

thf(zip_derived_cl208,plain,
    ! [X0: g] :
      ( X0
      = ( '#sk5' @ ( '#sk5' @ X0 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl193,zip_derived_cl143]) ).

thf(zip_derived_cl135_011,plain,
    ! [X2: g] :
      ( ( '#sk1' @ ( '#sk5' @ X2 ) @ X2 )
      = '#sk2' ),
    inference(demod,[status(thm)],[zip_derived_cl33,zip_derived_cl132]) ).

thf(zip_derived_cl235,plain,
    ! [X0: g] :
      ( ( '#sk1' @ X0 @ ( '#sk5' @ X0 ) )
      = '#sk2' ),
    inference('sup+',[status(thm)],[zip_derived_cl208,zip_derived_cl135]) ).

thf(zip_derived_cl5_012,plain,
    ( ~ ( ( !!
          @ ^ [Y0: g] :
              ( ??
              @ ^ [Y1: g] :
                  ( ( ( '#sk1' @ Y0 @ Y1 )
                    = '#sk2' )
                  & ( ( '#sk1' @ Y1 @ Y0 )
                    = '#sk2' ) ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) )
    | ~ ( ( !!
          @ ^ [Y0: g] :
              ( ??
              @ ^ [Y1: g] :
                  ( ( '#sk1' @ Y1 @ Y0 )
                  = '#sk2' ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( ( '#sk1' @ '#sk2' @ Y0 )
              = Y0 ) )
        & ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl92_013,plain,
    ( '#form3'
    | ~ ( ( !!
          @ ^ [Y0: g] :
              ( ??
              @ ^ [Y1: g] :
                  ( ( '#sk1' @ Y1 @ Y0 )
                  = '#sk2' ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( ( '#sk1' @ '#sk2' @ Y0 )
              = Y0 ) )
        & ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl9_014,plain,
    ( ~ '#form3'
    | ( ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( '#sk1' @ Y1 @ Y0 )
                = '#sk2' ) ) )
      & ( !!
        @ ^ [Y0: g] :
            ( ( '#sk1' @ '#sk2' @ Y0 )
            = Y0 ) )
      & ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl94,plain,
    ( ~ '#form3'
    | ~ ( ( !!
          @ ^ [Y0: g] :
              ( ??
              @ ^ [Y1: g] :
                  ( ( ( '#sk1' @ Y0 @ Y1 )
                    = '#sk2' )
                  & ( ( '#sk1' @ Y1 @ Y0 )
                    = '#sk2' ) ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) )
        & ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl5,zip_derived_cl92,zip_derived_cl9]) ).

thf(zip_derived_cl95,plain,
    ( ~ ( !!
        @ ^ [Y0: g] :
            ( ??
            @ ^ [Y1: g] :
                ( ( ( '#sk1' @ Y0 @ Y1 )
                  = '#sk2' )
                & ( ( '#sk1' @ Y1 @ Y0 )
                  = '#sk2' ) ) ) )
    | ~ ( !!
        @ ^ [Y0: g] :
            ( ( ( '#sk1' @ '#sk2' @ Y0 )
              = Y0 )
            & ( ( '#sk1' @ Y0 @ '#sk2' )
              = Y0 ) ) )
    | ~ ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
    | ~ '#form3' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl94]) ).

thf(zip_derived_cl97,plain,
    ( ~ ( ??
        @ ^ [Y0: g] :
            ( ( ( '#sk1' @ '#sk7' @ Y0 )
              = '#sk2' )
            & ( ( '#sk1' @ Y0 @ '#sk7' )
              = '#sk2' ) ) )
    | ~ '#form3'
    | ~ ( !!
        @ ^ [Y0: g] :
            ( !!
            @ ^ [Y1: g] :
                ( !!
                @ ^ [Y2: g] :
                    ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: g] :
            ( ( ( '#sk1' @ '#sk2' @ Y0 )
              = Y0 )
            & ( ( '#sk1' @ Y0 @ '#sk2' )
              = Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl95]) ).

thf(zip_derived_cl99,plain,
    ! [X2: g] :
      ( ~ ( ( ( '#sk1' @ '#sk7' @ X2 )
            = '#sk2' )
          & ( ( '#sk1' @ X2 @ '#sk7' )
            = '#sk2' ) )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
      | ~ '#form3' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl97]) ).

thf(zip_derived_cl102,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' )
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ~ '#form3'
      | ~ ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl99]) ).

thf(zip_derived_cl107,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' )
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ~ '#form3'
      | ~ ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( !!
                  @ ^ [Y2: g] :
                      ( ( '#sk1' @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                      = ( '#sk1' @ Y0 @ ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl102]) ).

thf(zip_derived_cl108,plain,
    ! [X2: g] :
      ( ~ ( !!
          @ ^ [Y0: g] :
              ( !!
              @ ^ [Y1: g] :
                  ( ( '#sk1' @ ( '#sk1' @ '#sk9' @ Y0 ) @ Y1 )
                  = ( '#sk1' @ '#sk9' @ ( '#sk1' @ Y0 @ Y1 ) ) ) ) )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) )
      | ~ '#form3'
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl107]) ).

thf(zip_derived_cl110,plain,
    ! [X2: g] :
      ( ~ ( !!
          @ ^ [Y0: g] :
              ( ( '#sk1' @ ( '#sk1' @ '#sk9' @ '#sk10' ) @ Y0 )
              = ( '#sk1' @ '#sk9' @ ( '#sk1' @ '#sk10' @ Y0 ) ) ) )
      | ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' )
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ~ '#form3'
      | ~ ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl108]) ).

thf(zip_derived_cl112,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ ( '#sk1' @ '#sk9' @ '#sk10' ) @ '#sk11' )
       != ( '#sk1' @ '#sk9' @ ( '#sk1' @ '#sk10' @ '#sk11' ) ) )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) )
      | ~ '#form3'
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl110]) ).

thf(zip_derived_cl116,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ ( '#sk1' @ '#sk9' @ '#sk10' ) @ '#sk11' )
       != ( '#sk1' @ '#sk9' @ ( '#sk1' @ '#sk10' @ '#sk11' ) ) )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) )
      | ~ '#form3'
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl112]) ).

thf(zip_derived_cl37_015,plain,
    ! [X2: g,X4: g,X6: g] :
      ( ( '#sk1' @ ( '#sk1' @ X2 @ X4 ) @ X6 )
      = ( '#sk1' @ X2 @ ( '#sk1' @ X4 @ X6 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl117,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk9' @ ( '#sk1' @ '#sk10' @ '#sk11' ) )
       != ( '#sk1' @ '#sk9' @ ( '#sk1' @ '#sk10' @ '#sk11' ) ) )
      | ~ ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) )
      | ~ '#form3'
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' ) ),
    inference(demod,[status(thm)],[zip_derived_cl116,zip_derived_cl37]) ).

thf(zip_derived_cl118,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' )
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ~ '#form3'
      | ~ ( !!
          @ ^ [Y0: g] :
              ( ( ( '#sk1' @ '#sk2' @ Y0 )
                = Y0 )
              & ( ( '#sk1' @ Y0 @ '#sk2' )
                = Y0 ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl117]) ).

thf(zip_derived_cl119,plain,
    ! [X2: g] :
      ( ~ ( ( ( '#sk1' @ '#sk2' @ '#sk12' )
            = '#sk12' )
          & ( ( '#sk1' @ '#sk12' @ '#sk2' )
            = '#sk12' ) )
      | ~ '#form3'
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl118]) ).

thf(zip_derived_cl41_016,plain,
    ! [X2: g] :
      ( ( '#sk1' @ '#sk2' @ X2 )
      = X2 ),
    inference(clc,[status(thm)],[zip_derived_cl35,zip_derived_cl26]) ).

thf(zip_derived_cl120,plain,
    ! [X2: g] :
      ( ~ ( ( '#sk12' = '#sk12' )
          & ( ( '#sk1' @ '#sk12' @ '#sk2' )
            = '#sk12' ) )
      | ~ '#form3'
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' ) ),
    inference(demod,[status(thm)],[zip_derived_cl119,zip_derived_cl41]) ).

thf(zip_derived_cl121,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk12' @ '#sk2' )
       != '#sk12' )
      | ~ '#form3'
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl120]) ).

thf(zip_derived_cl122,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk12' @ '#sk2' )
       != '#sk12' )
      | ~ '#form3'
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl121]) ).

thf(zip_derived_cl132_017,plain,
    '#form3',
    inference(simplify,[status(thm)],[zip_derived_cl124]) ).

thf(zip_derived_cl160,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk12' @ '#sk2' )
       != '#sk12' )
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' ) ),
    inference(demod,[status(thm)],[zip_derived_cl122,zip_derived_cl132]) ).

thf(zip_derived_cl193_018,plain,
    ! [X0: g] :
      ( ( '#sk1' @ X0 @ '#sk2' )
      = X0 ),
    inference('sup+',[status(thm)],[zip_derived_cl143,zip_derived_cl140]) ).

thf(zip_derived_cl206,plain,
    ! [X2: g] :
      ( ( '#sk12' != '#sk12' )
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' )
      | ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' ) ),
    inference(demod,[status(thm)],[zip_derived_cl160,zip_derived_cl193]) ).

thf(zip_derived_cl207,plain,
    ! [X2: g] :
      ( ( ( '#sk1' @ '#sk7' @ X2 )
       != '#sk2' )
      | ( ( '#sk1' @ X2 @ '#sk7' )
       != '#sk2' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl206]) ).

thf(zip_derived_cl243,plain,
    ( ( '#sk2' != '#sk2' )
    | ( ( '#sk1' @ ( '#sk5' @ '#sk7' ) @ '#sk7' )
     != '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl235,zip_derived_cl207]) ).

thf(zip_derived_cl135_019,plain,
    ! [X2: g] :
      ( ( '#sk1' @ ( '#sk5' @ X2 ) @ X2 )
      = '#sk2' ),
    inference(demod,[status(thm)],[zip_derived_cl33,zip_derived_cl132]) ).

thf(zip_derived_cl257,plain,
    ( ( '#sk2' != '#sk2' )
    | ( '#sk2' != '#sk2' ) ),
    inference(demod,[status(thm)],[zip_derived_cl243,zip_derived_cl135]) ).

thf(zip_derived_cl258,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl257]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ALG272^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.XFivht7x8M true
% 0.13/0.34  % Computer : n004.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 : Mon Aug 28 02:29:22 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in HO mode
% 0.20/0.58  % Total configuration time : 828
% 0.20/0.58  % Estimated wc time : 1656
% 0.20/0.58  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.69  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.70  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.70  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.70  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.70  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.17/0.74  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.17/0.77  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.40/0.85  % Solved by lams/20_acsne_simpl.sh.
% 1.40/0.85  % done 54 iterations in 0.054s
% 1.40/0.85  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.40/0.85  % SZS output start Refutation
% See solution above
% 1.40/0.86  
% 1.40/0.86  
% 1.40/0.86  % Terminating...
% 1.51/0.94  % Runner terminated.
% 1.51/0.94  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------