TSTP Solution File: SEV208^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV208^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Vt4lk2cEvx true

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 20:00:01 EDT 2023

% Result   : Theorem 49.35s 7.23s
% Output   : Refutation 49.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   34
% Syntax   : Number of formulae    :  132 (   4 unt;  19 typ;   0 def)
%            Number of atoms       :  870 ( 477 equ;   0 cnn)
%            Maximal formula atoms :   51 (   7 avg)
%            Number of connectives : 3068 (  67   ~; 260   |; 362   &;2052   @)
%                                         (   0 <=>;  49  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   34 (  14 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  331 ( 331   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  18 usr;   8 con; 0-3 aty)
%                                         (  59  !!; 219  ??;   0 @@+;   0 @@-)
%            Number of variables   :  513 ( 278   ^; 199   !;  36   ?; 513   :)

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

thf('#form1044_type',type,
    '#form1044': ( a > a > a > $o ) > $o ).

thf(w_type,type,
    w: a ).

thf('#sk804_type',type,
    '#sk804': ( a > a > a > $o ) > a ).

thf('#sk344_type',type,
    '#sk344': ( a > a > a > $o ) > a ).

thf('#sk692_type',type,
    '#sk692': ( a > a > a > $o ) > a ).

thf('#sk416_type',type,
    '#sk416': ( a > a > a > $o ) > a ).

thf(y_type,type,
    y: a ).

thf(c0_type,type,
    c0: a ).

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

thf('#sk59_type',type,
    '#sk59': ( a > a > a > $o ) > a ).

thf(x_type,type,
    x: a ).

thf(cP_type,type,
    cP: a > a > a ).

thf(z_type,type,
    z: a ).

thf('#sk590_type',type,
    '#sk590': ( a > a > a > $o ) > a ).

thf('#sk498_type',type,
    '#sk498': ( a > a > a > $o ) > a ).

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

thf('#sk111_type',type,
    '#sk111': ( a > a > a > $o ) > a ).

thf('#form989_type',type,
    '#form989': ( a > a > a > $o ) > $o ).

thf(cS_INCL_LEM1_pme,conjecture,
    ( ( ! [R: a > a > a > $o] :
          ( ! [Xa: a,Xb: a,Xc: a] :
              ( ( ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
                    ( ( Xa
                      = ( cP @ Xx1 @ Xx2 ) )
                    & ( Xb
                      = ( cP @ Xy1 @ Xy2 ) )
                    & ( Xc
                      = ( cP @ Xz1 @ Xz2 ) )
                    & ( R @ Xx1 @ Xy1 @ Xz1 )
                    & ( R @ Xx2 @ Xy2 @ Xz2 ) )
                | ( ( Xa = Xc )
                  & ( Xb = c0 ) )
                | ( ( Xb = Xc )
                  & ( Xa = c0 ) ) )
             => ( R @ Xa @ Xb @ Xc ) )
         => ( R @ w @ z @ z ) )
      & ! [R: a > a > a > $o] :
          ( ! [Xa: a,Xb: a,Xc: a] :
              ( ( ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
                    ( ( Xa
                      = ( cP @ Xx1 @ Xx2 ) )
                    & ( Xb
                      = ( cP @ Xy1 @ Xy2 ) )
                    & ( Xc
                      = ( cP @ Xz1 @ Xz2 ) )
                    & ( R @ Xx1 @ Xy1 @ Xz1 )
                    & ( R @ Xx2 @ Xy2 @ Xz2 ) )
                | ( ( Xa = Xc )
                  & ( Xb = c0 ) )
                | ( ( Xb = Xc )
                  & ( Xa = c0 ) ) )
             => ( R @ Xa @ Xb @ Xc ) )
         => ( R @ x @ y @ y ) ) )
   => ! [R: a > a > a > $o] :
        ( ! [Xa: a,Xb: a,Xc: a] :
            ( ( ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
                  ( ( Xa
                    = ( cP @ Xx1 @ Xx2 ) )
                  & ( Xb
                    = ( cP @ Xy1 @ Xy2 ) )
                  & ( Xc
                    = ( cP @ Xz1 @ Xz2 ) )
                  & ( R @ Xx1 @ Xy1 @ Xz1 )
                  & ( R @ Xx2 @ Xy2 @ Xz2 ) )
              | ( ( Xa = Xc )
                & ( Xb = c0 ) )
              | ( ( Xb = Xc )
                & ( Xa = c0 ) ) )
           => ( R @ Xa @ Xb @ Xc ) )
       => ( R @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( ( ! [R: a > a > a > $o] :
            ( ! [Xa: a,Xb: a,Xc: a] :
                ( ( ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
                      ( ( Xa
                        = ( cP @ Xx1 @ Xx2 ) )
                      & ( Xb
                        = ( cP @ Xy1 @ Xy2 ) )
                      & ( Xc
                        = ( cP @ Xz1 @ Xz2 ) )
                      & ( R @ Xx1 @ Xy1 @ Xz1 )
                      & ( R @ Xx2 @ Xy2 @ Xz2 ) )
                  | ( ( Xa = Xc )
                    & ( Xb = c0 ) )
                  | ( ( Xb = Xc )
                    & ( Xa = c0 ) ) )
               => ( R @ Xa @ Xb @ Xc ) )
           => ( R @ w @ z @ z ) )
        & ! [R: a > a > a > $o] :
            ( ! [Xa: a,Xb: a,Xc: a] :
                ( ( ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
                      ( ( Xa
                        = ( cP @ Xx1 @ Xx2 ) )
                      & ( Xb
                        = ( cP @ Xy1 @ Xy2 ) )
                      & ( Xc
                        = ( cP @ Xz1 @ Xz2 ) )
                      & ( R @ Xx1 @ Xy1 @ Xz1 )
                      & ( R @ Xx2 @ Xy2 @ Xz2 ) )
                  | ( ( Xa = Xc )
                    & ( Xb = c0 ) )
                  | ( ( Xb = Xc )
                    & ( Xa = c0 ) ) )
               => ( R @ Xa @ Xb @ Xc ) )
           => ( R @ x @ y @ y ) ) )
     => ! [R: a > a > a > $o] :
          ( ! [Xa: a,Xb: a,Xc: a] :
              ( ( ? [Xx1: a,Xx2: a,Xy1: a,Xy2: a,Xz1: a,Xz2: a] :
                    ( ( Xa
                      = ( cP @ Xx1 @ Xx2 ) )
                    & ( Xb
                      = ( cP @ Xy1 @ Xy2 ) )
                    & ( Xc
                      = ( cP @ Xz1 @ Xz2 ) )
                    & ( R @ Xx1 @ Xy1 @ Xz1 )
                    & ( R @ Xx2 @ Xy2 @ Xz2 ) )
                | ( ( Xa = Xc )
                  & ( Xb = c0 ) )
                | ( ( Xb = Xc )
                  & ( Xa = c0 ) ) )
             => ( R @ Xa @ Xb @ Xc ) )
         => ( R @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ),
    inference('cnf.neg',[status(esa)],[cS_INCL_LEM1_pme]) ).

thf(zip_derived_cl0,plain,
    ~ ( ( ( !!
          @ ^ [Y0: a > a > a > $o] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( ??
                                @ ^ [Y4: a] :
                                    ( ??
                                    @ ^ [Y5: a] :
                                        ( ??
                                        @ ^ [Y6: a] :
                                            ( ??
                                            @ ^ [Y7: a] :
                                                ( ??
                                                @ ^ [Y8: a] :
                                                    ( ??
                                                    @ ^ [Y9: a] :
                                                        ( ( Y1
                                                          = ( cP @ Y4 @ Y5 ) )
                                                        & ( Y2
                                                          = ( cP @ Y6 @ Y7 ) )
                                                        & ( Y3
                                                          = ( cP @ Y8 @ Y9 ) )
                                                        & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                        & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                              | ( ( Y1 = Y3 )
                                & ( Y2 = c0 ) )
                              | ( ( Y2 = Y3 )
                                & ( Y1 = c0 ) ) )
                           => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
             => ( Y0 @ w @ z @ z ) ) )
        & ( !!
          @ ^ [Y0: a > a > a > $o] :
              ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( ??
                                @ ^ [Y4: a] :
                                    ( ??
                                    @ ^ [Y5: a] :
                                        ( ??
                                        @ ^ [Y6: a] :
                                            ( ??
                                            @ ^ [Y7: a] :
                                                ( ??
                                                @ ^ [Y8: a] :
                                                    ( ??
                                                    @ ^ [Y9: a] :
                                                        ( ( Y1
                                                          = ( cP @ Y4 @ Y5 ) )
                                                        & ( Y2
                                                          = ( cP @ Y6 @ Y7 ) )
                                                        & ( Y3
                                                          = ( cP @ Y8 @ Y9 ) )
                                                        & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                        & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                              | ( ( Y1 = Y3 )
                                & ( Y2 = c0 ) )
                              | ( ( Y2 = Y3 )
                                & ( Y1 = c0 ) ) )
                           => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
             => ( Y0 @ x @ y @ y ) ) ) )
     => ( !!
        @ ^ [Y0: a > a > a > $o] :
            ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( ??
                              @ ^ [Y4: a] :
                                  ( ??
                                  @ ^ [Y5: a] :
                                      ( ??
                                      @ ^ [Y6: a] :
                                          ( ??
                                          @ ^ [Y7: a] :
                                              ( ??
                                              @ ^ [Y8: a] :
                                                  ( ??
                                                  @ ^ [Y9: a] :
                                                      ( ( Y1
                                                        = ( cP @ Y4 @ Y5 ) )
                                                      & ( Y2
                                                        = ( cP @ Y6 @ Y7 ) )
                                                      & ( Y3
                                                        = ( cP @ Y8 @ Y9 ) )
                                                      & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                      & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                            | ( ( Y1 = Y3 )
                              & ( Y2 = c0 ) )
                            | ( ( Y2 = Y3 )
                              & ( Y1 = c0 ) ) )
                         => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
           => ( Y0 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2,plain,
    ~ ( !!
      @ ^ [Y0: a > a > a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( !!
                    @ ^ [Y3: a] :
                        ( ( ( ??
                            @ ^ [Y4: a] :
                                ( ??
                                @ ^ [Y5: a] :
                                    ( ??
                                    @ ^ [Y6: a] :
                                        ( ??
                                        @ ^ [Y7: a] :
                                            ( ??
                                            @ ^ [Y8: a] :
                                                ( ??
                                                @ ^ [Y9: a] :
                                                    ( ( Y1
                                                      = ( cP @ Y4 @ Y5 ) )
                                                    & ( Y2
                                                      = ( cP @ Y6 @ Y7 ) )
                                                    & ( Y3
                                                      = ( cP @ Y8 @ Y9 ) )
                                                    & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                    & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                          | ( ( Y1 = Y3 )
                            & ( Y2 = c0 ) )
                          | ( ( Y2 = Y3 )
                            & ( Y1 = c0 ) ) )
                       => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
         => ( Y0 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl5,plain,
    ~ ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( ??
                        @ ^ [Y3: a] :
                            ( ??
                            @ ^ [Y4: a] :
                                ( ??
                                @ ^ [Y5: a] :
                                    ( ??
                                    @ ^ [Y6: a] :
                                        ( ??
                                        @ ^ [Y7: a] :
                                            ( ??
                                            @ ^ [Y8: a] :
                                                ( ( Y0
                                                  = ( cP @ Y3 @ Y4 ) )
                                                & ( Y1
                                                  = ( cP @ Y5 @ Y6 ) )
                                                & ( Y2
                                                  = ( cP @ Y7 @ Y8 ) )
                                                & ( '#sk1' @ Y3 @ Y5 @ Y7 )
                                                & ( '#sk1' @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
                      | ( ( Y0 = Y2 )
                        & ( Y1 = c0 ) )
                      | ( ( Y1 = Y2 )
                        & ( Y0 = c0 ) ) )
                   => ( '#sk1' @ Y0 @ Y1 @ Y2 ) ) ) ) )
     => ( '#sk1' @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl10,plain,
    ( !!
    @ ^ [Y0: a] :
        ( !!
        @ ^ [Y1: a] :
            ( !!
            @ ^ [Y2: a] :
                ( ( ( ??
                    @ ^ [Y3: a] :
                        ( ??
                        @ ^ [Y4: a] :
                            ( ??
                            @ ^ [Y5: a] :
                                ( ??
                                @ ^ [Y6: a] :
                                    ( ??
                                    @ ^ [Y7: a] :
                                        ( ??
                                        @ ^ [Y8: a] :
                                            ( ( Y0
                                              = ( cP @ Y3 @ Y4 ) )
                                            & ( Y1
                                              = ( cP @ Y5 @ Y6 ) )
                                            & ( Y2
                                              = ( cP @ Y7 @ Y8 ) )
                                            & ( '#sk1' @ Y3 @ Y5 @ Y7 )
                                            & ( '#sk1' @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
                  | ( ( Y0 = Y2 )
                    & ( Y1 = c0 ) )
                  | ( ( Y1 = Y2 )
                    & ( Y0 = c0 ) ) )
               => ( '#sk1' @ Y0 @ Y1 @ Y2 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl14,plain,
    ! [X2: a] :
      ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( ( ??
                  @ ^ [Y2: a] :
                      ( ??
                      @ ^ [Y3: a] :
                          ( ??
                          @ ^ [Y4: a] :
                              ( ??
                              @ ^ [Y5: a] :
                                  ( ??
                                  @ ^ [Y6: a] :
                                      ( ??
                                      @ ^ [Y7: a] :
                                          ( ( X2
                                            = ( cP @ Y2 @ Y3 ) )
                                          & ( Y0
                                            = ( cP @ Y4 @ Y5 ) )
                                          & ( Y1
                                            = ( cP @ Y6 @ Y7 ) )
                                          & ( '#sk1' @ Y2 @ Y4 @ Y6 )
                                          & ( '#sk1' @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
                | ( ( X2 = Y1 )
                  & ( Y0 = c0 ) )
                | ( ( Y0 = Y1 )
                  & ( X2 = c0 ) ) )
             => ( '#sk1' @ X2 @ Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl17,plain,
    ! [X2: a,X4: a] :
      ( !!
      @ ^ [Y0: a] :
          ( ( ( ??
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a] :
                      ( ??
                      @ ^ [Y3: a] :
                          ( ??
                          @ ^ [Y4: a] :
                              ( ??
                              @ ^ [Y5: a] :
                                  ( ??
                                  @ ^ [Y6: a] :
                                      ( ( X2
                                        = ( cP @ Y1 @ Y2 ) )
                                      & ( X4
                                        = ( cP @ Y3 @ Y4 ) )
                                      & ( Y0
                                        = ( cP @ Y5 @ Y6 ) )
                                      & ( '#sk1' @ Y1 @ Y3 @ Y5 )
                                      & ( '#sk1' @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
            | ( ( X2 = Y0 )
              & ( X4 = c0 ) )
            | ( ( X4 = Y0 )
              & ( X2 = c0 ) ) )
         => ( '#sk1' @ X2 @ X4 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl20,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ( ( ??
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a] :
                      ( ??
                      @ ^ [Y3: a] :
                          ( ??
                          @ ^ [Y4: a] :
                              ( ??
                              @ ^ [Y5: a] :
                                  ( ( X2
                                    = ( cP @ Y0 @ Y1 ) )
                                  & ( X4
                                    = ( cP @ Y2 @ Y3 ) )
                                  & ( X6
                                    = ( cP @ Y4 @ Y5 ) )
                                  & ( '#sk1' @ Y0 @ Y2 @ Y4 )
                                  & ( '#sk1' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
        | ( ( X2 = X6 )
          & ( X4 = c0 ) )
        | ( ( X4 = X6 )
          & ( X2 = c0 ) ) )
     => ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl23,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( ( ??
            @ ^ [Y0: a] :
                ( ??
                @ ^ [Y1: a] :
                    ( ??
                    @ ^ [Y2: a] :
                        ( ??
                        @ ^ [Y3: a] :
                            ( ??
                            @ ^ [Y4: a] :
                                ( ??
                                @ ^ [Y5: a] :
                                    ( ( X2
                                      = ( cP @ Y0 @ Y1 ) )
                                    & ( X4
                                      = ( cP @ Y2 @ Y3 ) )
                                    & ( X6
                                      = ( cP @ Y4 @ Y5 ) )
                                    & ( '#sk1' @ Y0 @ Y2 @ Y4 )
                                    & ( '#sk1' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
          | ( ( X2 = X6 )
            & ( X4 = c0 ) )
          | ( ( X4 = X6 )
            & ( X2 = c0 ) ) )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl30,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( ( X4 = X6 )
          & ( X2 = c0 ) )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl35,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ( X4 != X6 )
      | ( X2 != c0 )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl41,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ( X4 != X6 )
      | ( X2 != c0 )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl42,plain,
    ! [X6: a] : ( '#sk1' @ c0 @ X6 @ X6 ),
    inference(simplify,[status(thm)],[zip_derived_cl41]) ).

thf(zip_derived_cl29,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( ( X2 = X6 )
          & ( X4 = c0 ) )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl34,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ( X2 != X6 )
      | ( X4 != c0 )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl39,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ( X2 != X6 )
      | ( X4 != c0 )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl40,plain,
    ! [X6: a] : ( '#sk1' @ X6 @ c0 @ X6 ),
    inference(simplify,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl1,plain,
    ( ( !!
      @ ^ [Y0: a > a > a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( !!
                    @ ^ [Y3: a] :
                        ( ( ( ??
                            @ ^ [Y4: a] :
                                ( ??
                                @ ^ [Y5: a] :
                                    ( ??
                                    @ ^ [Y6: a] :
                                        ( ??
                                        @ ^ [Y7: a] :
                                            ( ??
                                            @ ^ [Y8: a] :
                                                ( ??
                                                @ ^ [Y9: a] :
                                                    ( ( Y1
                                                      = ( cP @ Y4 @ Y5 ) )
                                                    & ( Y2
                                                      = ( cP @ Y6 @ Y7 ) )
                                                    & ( Y3
                                                      = ( cP @ Y8 @ Y9 ) )
                                                    & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                    & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                          | ( ( Y1 = Y3 )
                            & ( Y2 = c0 ) )
                          | ( ( Y2 = Y3 )
                            & ( Y1 = c0 ) ) )
                       => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
         => ( Y0 @ w @ z @ z ) ) )
    & ( !!
      @ ^ [Y0: a > a > a > $o] :
          ( ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( !!
                    @ ^ [Y3: a] :
                        ( ( ( ??
                            @ ^ [Y4: a] :
                                ( ??
                                @ ^ [Y5: a] :
                                    ( ??
                                    @ ^ [Y6: a] :
                                        ( ??
                                        @ ^ [Y7: a] :
                                            ( ??
                                            @ ^ [Y8: a] :
                                                ( ??
                                                @ ^ [Y9: a] :
                                                    ( ( Y1
                                                      = ( cP @ Y4 @ Y5 ) )
                                                    & ( Y2
                                                      = ( cP @ Y6 @ Y7 ) )
                                                    & ( Y3
                                                      = ( cP @ Y8 @ Y9 ) )
                                                    & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                    & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                          | ( ( Y1 = Y3 )
                            & ( Y2 = c0 ) )
                          | ( ( Y2 = Y3 )
                            & ( Y1 = c0 ) ) )
                       => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
         => ( Y0 @ x @ y @ y ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl3,plain,
    ( !!
    @ ^ [Y0: a > a > a > $o] :
        ( ( !!
          @ ^ [Y1: a] :
              ( !!
              @ ^ [Y2: a] :
                  ( !!
                  @ ^ [Y3: a] :
                      ( ( ( ??
                          @ ^ [Y4: a] :
                              ( ??
                              @ ^ [Y5: a] :
                                  ( ??
                                  @ ^ [Y6: a] :
                                      ( ??
                                      @ ^ [Y7: a] :
                                          ( ??
                                          @ ^ [Y8: a] :
                                              ( ??
                                              @ ^ [Y9: a] :
                                                  ( ( Y1
                                                    = ( cP @ Y4 @ Y5 ) )
                                                  & ( Y2
                                                    = ( cP @ Y6 @ Y7 ) )
                                                  & ( Y3
                                                    = ( cP @ Y8 @ Y9 ) )
                                                  & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                  & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                        | ( ( Y1 = Y3 )
                          & ( Y2 = c0 ) )
                        | ( ( Y2 = Y3 )
                          & ( Y1 = c0 ) ) )
                     => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
       => ( Y0 @ w @ z @ z ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl6,plain,
    ! [X2: a > a > a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( ??
                        @ ^ [Y3: a] :
                            ( ??
                            @ ^ [Y4: a] :
                                ( ??
                                @ ^ [Y5: a] :
                                    ( ??
                                    @ ^ [Y6: a] :
                                        ( ??
                                        @ ^ [Y7: a] :
                                            ( ??
                                            @ ^ [Y8: a] :
                                                ( ( Y0
                                                  = ( cP @ Y3 @ Y4 ) )
                                                & ( Y1
                                                  = ( cP @ Y5 @ Y6 ) )
                                                & ( Y2
                                                  = ( cP @ Y7 @ Y8 ) )
                                                & ( X2 @ Y3 @ Y5 @ Y7 )
                                                & ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
                      | ( ( Y0 = Y2 )
                        & ( Y1 = c0 ) )
                      | ( ( Y1 = Y2 )
                        & ( Y0 = c0 ) ) )
                   => ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
     => ( X2 @ w @ z @ z ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl12,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( ??
                          @ ^ [Y3: a] :
                              ( ??
                              @ ^ [Y4: a] :
                                  ( ??
                                  @ ^ [Y5: a] :
                                      ( ??
                                      @ ^ [Y6: a] :
                                          ( ??
                                          @ ^ [Y7: a] :
                                              ( ??
                                              @ ^ [Y8: a] :
                                                  ( ( Y0
                                                    = ( cP @ Y3 @ Y4 ) )
                                                  & ( Y1
                                                    = ( cP @ Y5 @ Y6 ) )
                                                  & ( Y2
                                                    = ( cP @ Y7 @ Y8 ) )
                                                  & ( X2 @ Y3 @ Y5 @ Y7 )
                                                  & ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
                        | ( ( Y0 = Y2 )
                          & ( Y1 = c0 ) )
                        | ( ( Y1 = Y2 )
                          & ( Y0 = c0 ) ) )
                     => ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
      | ( X2 @ w @ z @ z ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl15,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( ??
                      @ ^ [Y2: a] :
                          ( ??
                          @ ^ [Y3: a] :
                              ( ??
                              @ ^ [Y4: a] :
                                  ( ??
                                  @ ^ [Y5: a] :
                                      ( ??
                                      @ ^ [Y6: a] :
                                          ( ??
                                          @ ^ [Y7: a] :
                                              ( ( ( '#sk29' @ X2 )
                                                = ( cP @ Y2 @ Y3 ) )
                                              & ( Y0
                                                = ( cP @ Y4 @ Y5 ) )
                                              & ( Y1
                                                = ( cP @ Y6 @ Y7 ) )
                                              & ( X2 @ Y2 @ Y4 @ Y6 )
                                              & ( X2 @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
                    | ( ( ( '#sk29' @ X2 )
                        = Y1 )
                      & ( Y0 = c0 ) )
                    | ( ( Y0 = Y1 )
                      & ( ( '#sk29' @ X2 )
                        = c0 ) ) )
                 => ( X2 @ ( '#sk29' @ X2 ) @ Y0 @ Y1 ) ) ) )
      | ( X2 @ w @ z @ z ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl18,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( ( ??
                  @ ^ [Y1: a] :
                      ( ??
                      @ ^ [Y2: a] :
                          ( ??
                          @ ^ [Y3: a] :
                              ( ??
                              @ ^ [Y4: a] :
                                  ( ??
                                  @ ^ [Y5: a] :
                                      ( ??
                                      @ ^ [Y6: a] :
                                          ( ( ( '#sk29' @ X2 )
                                            = ( cP @ Y1 @ Y2 ) )
                                          & ( ( '#sk59' @ X2 )
                                            = ( cP @ Y3 @ Y4 ) )
                                          & ( Y0
                                            = ( cP @ Y5 @ Y6 ) )
                                          & ( X2 @ Y1 @ Y3 @ Y5 )
                                          & ( X2 @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
                | ( ( ( '#sk29' @ X2 )
                    = Y0 )
                  & ( ( '#sk59' @ X2 )
                    = c0 ) )
                | ( ( ( '#sk59' @ X2 )
                    = Y0 )
                  & ( ( '#sk29' @ X2 )
                    = c0 ) ) )
             => ( X2 @ ( '#sk29' @ X2 ) @ ( '#sk59' @ X2 ) @ Y0 ) ) )
      | ( X2 @ w @ z @ z ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl21,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( ( ( ??
              @ ^ [Y0: a] :
                  ( ??
                  @ ^ [Y1: a] :
                      ( ??
                      @ ^ [Y2: a] :
                          ( ??
                          @ ^ [Y3: a] :
                              ( ??
                              @ ^ [Y4: a] :
                                  ( ??
                                  @ ^ [Y5: a] :
                                      ( ( ( '#sk29' @ X2 )
                                        = ( cP @ Y0 @ Y1 ) )
                                      & ( ( '#sk59' @ X2 )
                                        = ( cP @ Y2 @ Y3 ) )
                                      & ( ( '#sk111' @ X2 )
                                        = ( cP @ Y4 @ Y5 ) )
                                      & ( X2 @ Y0 @ Y2 @ Y4 )
                                      & ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
            | ( ( ( '#sk29' @ X2 )
                = ( '#sk111' @ X2 ) )
              & ( ( '#sk59' @ X2 )
                = c0 ) )
            | ( ( ( '#sk59' @ X2 )
                = ( '#sk111' @ X2 ) )
              & ( ( '#sk29' @ X2 )
                = c0 ) ) )
         => ( X2 @ ( '#sk29' @ X2 ) @ ( '#sk59' @ X2 ) @ ( '#sk111' @ X2 ) ) )
      | ( X2 @ w @ z @ z ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl24,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a] :
                ( ??
                @ ^ [Y2: a] :
                    ( ??
                    @ ^ [Y3: a] :
                        ( ??
                        @ ^ [Y4: a] :
                            ( ??
                            @ ^ [Y5: a] :
                                ( ( ( '#sk29' @ X2 )
                                  = ( cP @ Y0 @ Y1 ) )
                                & ( ( '#sk59' @ X2 )
                                  = ( cP @ Y2 @ Y3 ) )
                                & ( ( '#sk111' @ X2 )
                                  = ( cP @ Y4 @ Y5 ) )
                                & ( X2 @ Y0 @ Y2 @ Y4 )
                                & ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( X2 @ w @ z @ z ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl31,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a] :
                ( ??
                @ ^ [Y2: a] :
                    ( ??
                    @ ^ [Y3: a] :
                        ( ??
                        @ ^ [Y4: a] :
                            ( ??
                            @ ^ [Y5: a] :
                                ( ( ( '#sk29' @ X2 )
                                  = ( cP @ Y0 @ Y1 ) )
                                & ( ( '#sk59' @ X2 )
                                  = ( cP @ Y2 @ Y3 ) )
                                & ( ( '#sk111' @ X2 )
                                  = ( cP @ Y4 @ Y5 ) )
                                & ( X2 @ Y0 @ Y2 @ Y4 )
                                & ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( X2 @ w @ z @ z ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl36,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a] :
                ( ??
                @ ^ [Y2: a] :
                    ( ??
                    @ ^ [Y3: a] :
                        ( ??
                        @ ^ [Y4: a] :
                            ( ( ( '#sk29' @ X2 )
                              = ( cP @ ( '#sk344' @ X2 ) @ Y0 ) )
                            & ( ( '#sk59' @ X2 )
                              = ( cP @ Y1 @ Y2 ) )
                            & ( ( '#sk111' @ X2 )
                              = ( cP @ Y3 @ Y4 ) )
                            & ( X2 @ ( '#sk344' @ X2 ) @ Y1 @ Y3 )
                            & ( X2 @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
      | ( X2 @ w @ z @ z )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl43,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a] :
                ( ??
                @ ^ [Y2: a] :
                    ( ??
                    @ ^ [Y3: a] :
                        ( ( ( '#sk29' @ X2 )
                          = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
                        & ( ( '#sk59' @ X2 )
                          = ( cP @ Y0 @ Y1 ) )
                        & ( ( '#sk111' @ X2 )
                          = ( cP @ Y2 @ Y3 ) )
                        & ( X2 @ ( '#sk344' @ X2 ) @ Y0 @ Y2 )
                        & ( X2 @ ( '#sk416' @ X2 ) @ Y1 @ Y3 ) ) ) ) ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( X2 @ w @ z @ z ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl46,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a] :
                ( ??
                @ ^ [Y2: a] :
                    ( ( ( '#sk29' @ X2 )
                      = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
                    & ( ( '#sk59' @ X2 )
                      = ( cP @ ( '#sk498' @ X2 ) @ Y0 ) )
                    & ( ( '#sk111' @ X2 )
                      = ( cP @ Y1 @ Y2 ) )
                    & ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ Y1 )
                    & ( X2 @ ( '#sk416' @ X2 ) @ Y0 @ Y2 ) ) ) ) )
      | ( X2 @ w @ z @ z )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl49,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a] :
                ( ( ( '#sk29' @ X2 )
                  = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
                & ( ( '#sk59' @ X2 )
                  = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
                & ( ( '#sk111' @ X2 )
                  = ( cP @ Y0 @ Y1 ) )
                & ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ Y0 )
                & ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ Y1 ) ) ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( X2 @ w @ z @ z ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl52,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ( ( '#sk29' @ X2 )
              = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
            & ( ( '#sk59' @ X2 )
              = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
            & ( ( '#sk111' @ X2 )
              = ( cP @ ( '#sk692' @ X2 ) @ Y0 ) )
            & ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
            & ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ Y0 ) ) )
      | ( X2 @ w @ z @ z )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).

thf(zip_derived_cl55,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( ( '#sk29' @ X2 )
          = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
        & ( ( '#sk59' @ X2 )
          = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
        & ( ( '#sk111' @ X2 )
          = ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
        & ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
        & ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( X2 @ w @ z @ z ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl58,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk29' @ X2 )
        = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
      | ( X2 @ w @ z @ z )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl69,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk29' @ X2 )
        = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
      | ( X2 @ w @ z @ z )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl70,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form1044' @ X2 )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl71,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk59' @ X2 )
        = ( '#sk111' @ X2 ) )
      | ~ ( '#form1044' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl70]) ).

thf(zip_derived_cl84,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk59' @ X2 )
        = ( '#sk111' @ X2 ) )
      | ~ ( '#form1044' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl11,plain,
    ~ ( '#sk1' @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl4,plain,
    ( !!
    @ ^ [Y0: a > a > a > $o] :
        ( ( !!
          @ ^ [Y1: a] :
              ( !!
              @ ^ [Y2: a] :
                  ( !!
                  @ ^ [Y3: a] :
                      ( ( ( ??
                          @ ^ [Y4: a] :
                              ( ??
                              @ ^ [Y5: a] :
                                  ( ??
                                  @ ^ [Y6: a] :
                                      ( ??
                                      @ ^ [Y7: a] :
                                          ( ??
                                          @ ^ [Y8: a] :
                                              ( ??
                                              @ ^ [Y9: a] :
                                                  ( ( Y1
                                                    = ( cP @ Y4 @ Y5 ) )
                                                  & ( Y2
                                                    = ( cP @ Y6 @ Y7 ) )
                                                  & ( Y3
                                                    = ( cP @ Y8 @ Y9 ) )
                                                  & ( Y0 @ Y4 @ Y6 @ Y8 )
                                                  & ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
                        | ( ( Y1 = Y3 )
                          & ( Y2 = c0 ) )
                        | ( ( Y2 = Y3 )
                          & ( Y1 = c0 ) ) )
                     => ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
       => ( Y0 @ x @ y @ y ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl8,plain,
    ! [X2: a > a > a > $o] :
      ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( ??
                        @ ^ [Y3: a] :
                            ( ??
                            @ ^ [Y4: a] :
                                ( ??
                                @ ^ [Y5: a] :
                                    ( ??
                                    @ ^ [Y6: a] :
                                        ( ??
                                        @ ^ [Y7: a] :
                                            ( ??
                                            @ ^ [Y8: a] :
                                                ( ( Y0
                                                  = ( cP @ Y3 @ Y4 ) )
                                                & ( Y1
                                                  = ( cP @ Y5 @ Y6 ) )
                                                & ( Y2
                                                  = ( cP @ Y7 @ Y8 ) )
                                                & ( X2 @ Y3 @ Y5 @ Y7 )
                                                & ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
                      | ( ( Y0 = Y2 )
                        & ( Y1 = c0 ) )
                      | ( ( Y1 = Y2 )
                        & ( Y0 = c0 ) ) )
                   => ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
     => ( X2 @ x @ y @ y ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl13,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( ??
                          @ ^ [Y3: a] :
                              ( ??
                              @ ^ [Y4: a] :
                                  ( ??
                                  @ ^ [Y5: a] :
                                      ( ??
                                      @ ^ [Y6: a] :
                                          ( ??
                                          @ ^ [Y7: a] :
                                              ( ??
                                              @ ^ [Y8: a] :
                                                  ( ( Y0
                                                    = ( cP @ Y3 @ Y4 ) )
                                                  & ( Y1
                                                    = ( cP @ Y5 @ Y6 ) )
                                                  & ( Y2
                                                    = ( cP @ Y7 @ Y8 ) )
                                                  & ( X2 @ Y3 @ Y5 @ Y7 )
                                                  & ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
                        | ( ( Y0 = Y2 )
                          & ( Y1 = c0 ) )
                        | ( ( Y1 = Y2 )
                          & ( Y0 = c0 ) ) )
                     => ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
      | ( X2 @ x @ y @ y ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl16,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( ??
                      @ ^ [Y2: a] :
                          ( ??
                          @ ^ [Y3: a] :
                              ( ??
                              @ ^ [Y4: a] :
                                  ( ??
                                  @ ^ [Y5: a] :
                                      ( ??
                                      @ ^ [Y6: a] :
                                          ( ??
                                          @ ^ [Y7: a] :
                                              ( ( ( '#sk29' @ X2 )
                                                = ( cP @ Y2 @ Y3 ) )
                                              & ( Y0
                                                = ( cP @ Y4 @ Y5 ) )
                                              & ( Y1
                                                = ( cP @ Y6 @ Y7 ) )
                                              & ( X2 @ Y2 @ Y4 @ Y6 )
                                              & ( X2 @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
                    | ( ( ( '#sk29' @ X2 )
                        = Y1 )
                      & ( Y0 = c0 ) )
                    | ( ( Y0 = Y1 )
                      & ( ( '#sk29' @ X2 )
                        = c0 ) ) )
                 => ( X2 @ ( '#sk29' @ X2 ) @ Y0 @ Y1 ) ) ) )
      | ( X2 @ x @ y @ y ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl19,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( !!
          @ ^ [Y0: a] :
              ( ( ( ??
                  @ ^ [Y1: a] :
                      ( ??
                      @ ^ [Y2: a] :
                          ( ??
                          @ ^ [Y3: a] :
                              ( ??
                              @ ^ [Y4: a] :
                                  ( ??
                                  @ ^ [Y5: a] :
                                      ( ??
                                      @ ^ [Y6: a] :
                                          ( ( ( '#sk29' @ X2 )
                                            = ( cP @ Y1 @ Y2 ) )
                                          & ( ( '#sk59' @ X2 )
                                            = ( cP @ Y3 @ Y4 ) )
                                          & ( Y0
                                            = ( cP @ Y5 @ Y6 ) )
                                          & ( X2 @ Y1 @ Y3 @ Y5 )
                                          & ( X2 @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
                | ( ( ( '#sk29' @ X2 )
                    = Y0 )
                  & ( ( '#sk59' @ X2 )
                    = c0 ) )
                | ( ( ( '#sk59' @ X2 )
                    = Y0 )
                  & ( ( '#sk29' @ X2 )
                    = c0 ) ) )
             => ( X2 @ ( '#sk29' @ X2 ) @ ( '#sk59' @ X2 ) @ Y0 ) ) )
      | ( X2 @ x @ y @ y ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl22,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( ( ( ??
              @ ^ [Y0: a] :
                  ( ??
                  @ ^ [Y1: a] :
                      ( ??
                      @ ^ [Y2: a] :
                          ( ??
                          @ ^ [Y3: a] :
                              ( ??
                              @ ^ [Y4: a] :
                                  ( ??
                                  @ ^ [Y5: a] :
                                      ( ( ( '#sk29' @ X2 )
                                        = ( cP @ Y0 @ Y1 ) )
                                      & ( ( '#sk59' @ X2 )
                                        = ( cP @ Y2 @ Y3 ) )
                                      & ( ( '#sk111' @ X2 )
                                        = ( cP @ Y4 @ Y5 ) )
                                      & ( X2 @ Y0 @ Y2 @ Y4 )
                                      & ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
            | ( ( ( '#sk29' @ X2 )
                = ( '#sk111' @ X2 ) )
              & ( ( '#sk59' @ X2 )
                = c0 ) )
            | ( ( ( '#sk59' @ X2 )
                = ( '#sk111' @ X2 ) )
              & ( ( '#sk29' @ X2 )
                = c0 ) ) )
         => ( X2 @ ( '#sk29' @ X2 ) @ ( '#sk59' @ X2 ) @ ( '#sk111' @ X2 ) ) )
      | ( X2 @ x @ y @ y ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl26,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a] :
                ( ??
                @ ^ [Y2: a] :
                    ( ??
                    @ ^ [Y3: a] :
                        ( ??
                        @ ^ [Y4: a] :
                            ( ??
                            @ ^ [Y5: a] :
                                ( ( ( '#sk29' @ X2 )
                                  = ( cP @ Y0 @ Y1 ) )
                                & ( ( '#sk59' @ X2 )
                                  = ( cP @ Y2 @ Y3 ) )
                                & ( ( '#sk111' @ X2 )
                                  = ( cP @ Y4 @ Y5 ) )
                                & ( X2 @ Y0 @ Y2 @ Y4 )
                                & ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( X2 @ x @ y @ y ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl32,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a] :
                ( ??
                @ ^ [Y2: a] :
                    ( ??
                    @ ^ [Y3: a] :
                        ( ??
                        @ ^ [Y4: a] :
                            ( ??
                            @ ^ [Y5: a] :
                                ( ( ( '#sk29' @ X2 )
                                  = ( cP @ Y0 @ Y1 ) )
                                & ( ( '#sk59' @ X2 )
                                  = ( cP @ Y2 @ Y3 ) )
                                & ( ( '#sk111' @ X2 )
                                  = ( cP @ Y4 @ Y5 ) )
                                & ( X2 @ Y0 @ Y2 @ Y4 )
                                & ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( X2 @ x @ y @ y ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl37,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a] :
                ( ??
                @ ^ [Y2: a] :
                    ( ??
                    @ ^ [Y3: a] :
                        ( ??
                        @ ^ [Y4: a] :
                            ( ( ( '#sk29' @ X2 )
                              = ( cP @ ( '#sk344' @ X2 ) @ Y0 ) )
                            & ( ( '#sk59' @ X2 )
                              = ( cP @ Y1 @ Y2 ) )
                            & ( ( '#sk111' @ X2 )
                              = ( cP @ Y3 @ Y4 ) )
                            & ( X2 @ ( '#sk344' @ X2 ) @ Y1 @ Y3 )
                            & ( X2 @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
      | ( X2 @ x @ y @ y )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl44,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a] :
                ( ??
                @ ^ [Y2: a] :
                    ( ??
                    @ ^ [Y3: a] :
                        ( ( ( '#sk29' @ X2 )
                          = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
                        & ( ( '#sk59' @ X2 )
                          = ( cP @ Y0 @ Y1 ) )
                        & ( ( '#sk111' @ X2 )
                          = ( cP @ Y2 @ Y3 ) )
                        & ( X2 @ ( '#sk344' @ X2 ) @ Y0 @ Y2 )
                        & ( X2 @ ( '#sk416' @ X2 ) @ Y1 @ Y3 ) ) ) ) ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( X2 @ x @ y @ y ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl47,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a] :
                ( ??
                @ ^ [Y2: a] :
                    ( ( ( '#sk29' @ X2 )
                      = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
                    & ( ( '#sk59' @ X2 )
                      = ( cP @ ( '#sk498' @ X2 ) @ Y0 ) )
                    & ( ( '#sk111' @ X2 )
                      = ( cP @ Y1 @ Y2 ) )
                    & ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ Y1 )
                    & ( X2 @ ( '#sk416' @ X2 ) @ Y0 @ Y2 ) ) ) ) )
      | ( X2 @ x @ y @ y )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl50,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ??
            @ ^ [Y1: a] :
                ( ( ( '#sk29' @ X2 )
                  = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
                & ( ( '#sk59' @ X2 )
                  = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
                & ( ( '#sk111' @ X2 )
                  = ( cP @ Y0 @ Y1 ) )
                & ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ Y0 )
                & ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ Y1 ) ) ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( X2 @ x @ y @ y ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl53,plain,
    ! [X2: a > a > a > $o] :
      ( ( ??
        @ ^ [Y0: a] :
            ( ( ( '#sk29' @ X2 )
              = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
            & ( ( '#sk59' @ X2 )
              = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
            & ( ( '#sk111' @ X2 )
              = ( cP @ ( '#sk692' @ X2 ) @ Y0 ) )
            & ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
            & ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ Y0 ) ) )
      | ( X2 @ x @ y @ y )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl56,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( ( '#sk29' @ X2 )
          = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
        & ( ( '#sk59' @ X2 )
          = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
        & ( ( '#sk111' @ X2 )
          = ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
        & ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
        & ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( X2 @ x @ y @ y ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl63,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form989' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl64,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk29' @ X2 )
        = ( '#sk111' @ X2 ) )
      | ~ ( '#form989' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl81,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk29' @ X2 )
        = ( '#sk111' @ X2 ) )
      | ~ ( '#form989' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl64]) ).

thf(zip_derived_cl56_001,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( ( '#sk29' @ X2 )
          = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
        & ( ( '#sk59' @ X2 )
          = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
        & ( ( '#sk111' @ X2 )
          = ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
        & ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
        & ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( X2 @ x @ y @ y ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl63_002,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form989' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl66,plain,
    ! [X2: a > a > a > $o] :
      ( ( '#form989' @ X2 )
      | ( X2 @ x @ y @ y )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
        & ( ( '#sk59' @ X2 )
          = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
        & ( ( '#sk111' @ X2 )
          = ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
        & ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
        & ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl56,zip_derived_cl63]) ).

thf(zip_derived_cl70_003,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form1044' @ X2 )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl80,plain,
    ! [X2: a > a > a > $o] :
      ( ( '#form1044' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
        & ( ( '#sk59' @ X2 )
          = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
        & ( ( '#sk111' @ X2 )
          = ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
        & ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
        & ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) ) )
      | ( X2 @ x @ y @ y )
      | ( '#form989' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl66,zip_derived_cl70]) ).

thf(zip_derived_cl90,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk29' @ X2 )
        = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
      | ( '#form989' @ X2 )
      | ( X2 @ x @ y @ y )
      | ( '#form1044' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl95,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk29' @ X2 )
        = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
      | ( '#form989' @ X2 )
      | ( X2 @ x @ y @ y )
      | ( '#form1044' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl90]) ).

thf(zip_derived_cl65,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk59' @ X2 )
        = c0 )
      | ~ ( '#form989' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl82,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk59' @ X2 )
        = c0 )
      | ~ ( '#form989' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl27,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( X2 @ ( '#sk29' @ X2 ) @ ( '#sk59' @ X2 ) @ ( '#sk111' @ X2 ) )
      | ( X2 @ x @ y @ y ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl91,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk59' @ X2 )
        = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
      | ( '#form989' @ X2 )
      | ( X2 @ x @ y @ y )
      | ( '#form1044' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl96,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk59' @ X2 )
        = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
      | ( '#form989' @ X2 )
      | ( X2 @ x @ y @ y )
      | ( '#form1044' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl91]) ).

thf(zip_derived_cl69_004,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk29' @ X2 )
        = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
      | ( X2 @ w @ z @ z )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl70_005,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form1044' @ X2 )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl73,plain,
    ! [X2: a > a > a > $o] :
      ( ( '#form1044' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( X2 @ w @ z @ z )
      | ( ( '#sk29' @ X2 )
        = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl69,zip_derived_cl70]) ).

thf(zip_derived_cl63_006,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form989' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl83,plain,
    ! [X2: a > a > a > $o] :
      ( ( '#form989' @ X2 )
      | ( ( '#sk29' @ X2 )
        = ( cP @ ( '#sk344' @ X2 ) @ ( '#sk416' @ X2 ) ) )
      | ( X2 @ w @ z @ z )
      | ( '#form1044' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl73,zip_derived_cl63]) ).

thf(zip_derived_cl72,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk29' @ X2 )
        = c0 )
      | ~ ( '#form1044' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl70]) ).

thf(zip_derived_cl85,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk29' @ X2 )
        = c0 )
      | ~ ( '#form1044' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl72]) ).

thf(zip_derived_cl92,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk111' @ X2 )
        = ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
      | ( '#form989' @ X2 )
      | ( X2 @ x @ y @ y )
      | ( '#form1044' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl97,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk111' @ X2 )
        = ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
      | ( '#form989' @ X2 )
      | ( X2 @ x @ y @ y )
      | ( '#form1044' @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl92]) ).

thf(zip_derived_cl25,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( X2 @ ( '#sk29' @ X2 ) @ ( '#sk59' @ X2 ) @ ( '#sk111' @ X2 ) )
      | ( X2 @ w @ z @ z ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl59,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk59' @ X2 )
        = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
      | ( X2 @ w @ z @ z )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl74,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk59' @ X2 )
        = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
      | ( X2 @ w @ z @ z )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl59]) ).

thf(zip_derived_cl70_007,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form1044' @ X2 )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl75,plain,
    ! [X2: a > a > a > $o] :
      ( ( '#form1044' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( X2 @ w @ z @ z )
      | ( ( '#sk59' @ X2 )
        = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl74,zip_derived_cl70]) ).

thf(zip_derived_cl63_008,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form989' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl86,plain,
    ! [X2: a > a > a > $o] :
      ( ( '#form989' @ X2 )
      | ( ( '#sk59' @ X2 )
        = ( cP @ ( '#sk498' @ X2 ) @ ( '#sk590' @ X2 ) ) )
      | ( X2 @ w @ z @ z )
      | ( '#form1044' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl75,zip_derived_cl63]) ).

thf(zip_derived_cl93,plain,
    ! [X2: a > a > a > $o] :
      ( ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
      | ( '#form989' @ X2 )
      | ( X2 @ x @ y @ y )
      | ( '#form1044' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl60,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk111' @ X2 )
        = ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
      | ( X2 @ w @ z @ z )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl76,plain,
    ! [X2: a > a > a > $o] :
      ( ( ( '#sk111' @ X2 )
        = ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
      | ( X2 @ w @ z @ z )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl60]) ).

thf(zip_derived_cl70_009,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form1044' @ X2 )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl77,plain,
    ! [X2: a > a > a > $o] :
      ( ( '#form1044' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( X2 @ w @ z @ z )
      | ( ( '#sk111' @ X2 )
        = ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl76,zip_derived_cl70]) ).

thf(zip_derived_cl63_010,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form989' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl87,plain,
    ! [X2: a > a > a > $o] :
      ( ( '#form989' @ X2 )
      | ( ( '#sk111' @ X2 )
        = ( cP @ ( '#sk692' @ X2 ) @ ( '#sk804' @ X2 ) ) )
      | ( X2 @ w @ z @ z )
      | ( '#form1044' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl77,zip_derived_cl63]) ).

thf(zip_derived_cl94,plain,
    ! [X2: a > a > a > $o] :
      ( ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) )
      | ( '#form989' @ X2 )
      | ( X2 @ x @ y @ y )
      | ( '#form1044' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl61,plain,
    ! [X2: a > a > a > $o] :
      ( ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
      | ( X2 @ w @ z @ z )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl70_011,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form1044' @ X2 )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl78,plain,
    ! [X2: a > a > a > $o] :
      ( ( '#form1044' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( X2 @ w @ z @ z )
      | ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl61,zip_derived_cl70]) ).

thf(zip_derived_cl63_012,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form989' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl88,plain,
    ! [X2: a > a > a > $o] :
      ( ( '#form989' @ X2 )
      | ( X2 @ ( '#sk344' @ X2 ) @ ( '#sk498' @ X2 ) @ ( '#sk692' @ X2 ) )
      | ( X2 @ w @ z @ z )
      | ( '#form1044' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl78,zip_derived_cl63]) ).

thf(zip_derived_cl62,plain,
    ! [X2: a > a > a > $o] :
      ( ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) )
      | ( X2 @ w @ z @ z )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl70_013,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form1044' @ X2 )
      | ( ( ( '#sk59' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk29' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl79,plain,
    ! [X2: a > a > a > $o] :
      ( ( '#form1044' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) )
      | ( X2 @ w @ z @ z )
      | ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl62,zip_derived_cl70]) ).

thf(zip_derived_cl63_014,plain,
    ! [X2: a > a > a > $o] :
      ( ~ ( '#form989' @ X2 )
      | ( ( ( '#sk29' @ X2 )
          = ( '#sk111' @ X2 ) )
        & ( ( '#sk59' @ X2 )
          = c0 ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl89,plain,
    ! [X2: a > a > a > $o] :
      ( ( '#form989' @ X2 )
      | ( X2 @ ( '#sk416' @ X2 ) @ ( '#sk590' @ X2 ) @ ( '#sk804' @ X2 ) )
      | ( X2 @ w @ z @ z )
      | ( '#form1044' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl79,zip_derived_cl63]) ).

thf(zip_derived_cl28,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( ??
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a] :
                      ( ??
                      @ ^ [Y3: a] :
                          ( ??
                          @ ^ [Y4: a] :
                              ( ??
                              @ ^ [Y5: a] :
                                  ( ( X2
                                    = ( cP @ Y0 @ Y1 ) )
                                  & ( X4
                                    = ( cP @ Y2 @ Y3 ) )
                                  & ( X6
                                    = ( cP @ Y4 @ Y5 ) )
                                  & ( '#sk1' @ Y0 @ Y2 @ Y4 )
                                  & ( '#sk1' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl33,plain,
    ! [X2: a,X4: a,X6: a,X8: a] :
      ( ~ ( ??
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a] :
                      ( ??
                      @ ^ [Y3: a] :
                          ( ??
                          @ ^ [Y4: a] :
                              ( ( X2
                                = ( cP @ X8 @ Y0 ) )
                              & ( X4
                                = ( cP @ Y1 @ Y2 ) )
                              & ( X6
                                = ( cP @ Y3 @ Y4 ) )
                              & ( '#sk1' @ X8 @ Y1 @ Y3 )
                              & ( '#sk1' @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl38,plain,
    ! [X2: a,X4: a,X6: a,X8: a,X10: a] :
      ( ~ ( ??
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a] :
                      ( ??
                      @ ^ [Y3: a] :
                          ( ( X2
                            = ( cP @ X8 @ X10 ) )
                          & ( X4
                            = ( cP @ Y0 @ Y1 ) )
                          & ( X6
                            = ( cP @ Y2 @ Y3 ) )
                          & ( '#sk1' @ X8 @ Y0 @ Y2 )
                          & ( '#sk1' @ X10 @ Y1 @ Y3 ) ) ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl45,plain,
    ! [X2: a,X4: a,X6: a,X8: a,X10: a,X12: a] :
      ( ~ ( ??
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a] :
                  ( ??
                  @ ^ [Y2: a] :
                      ( ( X2
                        = ( cP @ X8 @ X10 ) )
                      & ( X4
                        = ( cP @ X12 @ Y0 ) )
                      & ( X6
                        = ( cP @ Y1 @ Y2 ) )
                      & ( '#sk1' @ X8 @ X12 @ Y1 )
                      & ( '#sk1' @ X10 @ Y0 @ Y2 ) ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl48,plain,
    ! [X2: a,X4: a,X6: a,X8: a,X10: a,X12: a,X14: a] :
      ( ~ ( ??
          @ ^ [Y0: a] :
              ( ??
              @ ^ [Y1: a] :
                  ( ( X2
                    = ( cP @ X8 @ X10 ) )
                  & ( X4
                    = ( cP @ X12 @ X14 ) )
                  & ( X6
                    = ( cP @ Y0 @ Y1 ) )
                  & ( '#sk1' @ X8 @ X12 @ Y0 )
                  & ( '#sk1' @ X10 @ X14 @ Y1 ) ) ) )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl51,plain,
    ! [X2: a,X4: a,X6: a,X8: a,X10: a,X12: a,X14: a,X16: a] :
      ( ~ ( ??
          @ ^ [Y0: a] :
              ( ( X2
                = ( cP @ X8 @ X10 ) )
              & ( X4
                = ( cP @ X12 @ X14 ) )
              & ( X6
                = ( cP @ X16 @ Y0 ) )
              & ( '#sk1' @ X8 @ X12 @ X16 )
              & ( '#sk1' @ X10 @ X14 @ Y0 ) ) )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl54,plain,
    ! [X2: a,X4: a,X6: a,X8: a,X10: a,X12: a,X14: a,X16: a,X18: a] :
      ( ~ ( ( X2
            = ( cP @ X8 @ X10 ) )
          & ( X4
            = ( cP @ X12 @ X14 ) )
          & ( X6
            = ( cP @ X16 @ X18 ) )
          & ( '#sk1' @ X8 @ X12 @ X16 )
          & ( '#sk1' @ X10 @ X14 @ X18 ) )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl57,plain,
    ! [X2: a,X4: a,X6: a,X8: a,X10: a,X12: a,X14: a,X16: a,X18: a] :
      ( ( X2
       != ( cP @ X8 @ X10 ) )
      | ( X4
       != ( cP @ X12 @ X14 ) )
      | ( X6
       != ( cP @ X16 @ X18 ) )
      | ~ ( '#sk1' @ X8 @ X12 @ X16 )
      | ~ ( '#sk1' @ X10 @ X14 @ X18 )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl67,plain,
    ! [X2: a,X4: a,X6: a,X8: a,X10: a,X12: a,X14: a,X16: a,X18: a] :
      ( ( X2
       != ( cP @ X8 @ X10 ) )
      | ( X4
       != ( cP @ X12 @ X14 ) )
      | ( X6
       != ( cP @ X16 @ X18 ) )
      | ~ ( '#sk1' @ X8 @ X12 @ X16 )
      | ~ ( '#sk1' @ X10 @ X14 @ X18 )
      | ( '#sk1' @ X2 @ X4 @ X6 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl68,plain,
    ! [X8: a,X10: a,X12: a,X14: a,X16: a,X18: a] :
      ( ( '#sk1' @ ( cP @ X8 @ X10 ) @ ( cP @ X12 @ X14 ) @ ( cP @ X16 @ X18 ) )
      | ~ ( '#sk1' @ X10 @ X14 @ X18 )
      | ~ ( '#sk1' @ X8 @ X12 @ X16 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl5349,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl42,zip_derived_cl40,zip_derived_cl84,zip_derived_cl11,zip_derived_cl81,zip_derived_cl95,zip_derived_cl82,zip_derived_cl27,zip_derived_cl96,zip_derived_cl83,zip_derived_cl85,zip_derived_cl97,zip_derived_cl25,zip_derived_cl86,zip_derived_cl93,zip_derived_cl87,zip_derived_cl94,zip_derived_cl88,zip_derived_cl89,zip_derived_cl68]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV208^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Vt4lk2cEvx true
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug 24 02:09:37 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in HO mode
% 0.20/0.67  % Total configuration time : 828
% 0.20/0.67  % Estimated wc time : 1656
% 0.20/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.73  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.56/0.76  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.56/0.76  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.56/0.76  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.56/0.76  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.56/0.77  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.56/0.78  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 49.35/7.23  % Solved by lams/20_acsne_simpl.sh.
% 49.35/7.23  % done 491 iterations in 6.341s
% 49.35/7.23  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 49.35/7.23  % SZS output start Refutation
% See solution above
% 49.35/7.23  
% 49.35/7.23  
% 49.35/7.23  % Terminating...
% 51.47/7.34  % Runner terminated.
% 51.49/7.35  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------