TSTP Solution File: SEV109^5 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEV109^5 : 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.nXOhyrD3QX 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 : Thu Aug 31 19:59:38 EDT 2023

% Result   : Theorem 2.01s 1.05s
% Output   : Refutation 2.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   14
% Syntax   : Number of formulae    :  101 (   2 unt;  13 typ;   0 def)
%            Number of atoms       :  763 (   0 equ;   1 cnn)
%            Maximal formula atoms :   30 (   8 avg)
%            Number of connectives : 2423 (  60   ~; 111   |; 124   &;1591   @)
%                                         (   0 <=>; 204  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   35 (  12 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :  137 ( 137   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  12 usr;   5 con; 0-4 aty)
%                                         ( 333  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  466 ( 333   ^; 133   !;   0   ?; 466   :)

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

thf('#sk3_type',type,
    '#sk3': a ).

thf('#sk86_type',type,
    '#sk86': a > a > a > a > $o ).

thf('#sk87_type',type,
    '#sk87': a > a > a > a > $o ).

thf('#sk41_type',type,
    '#sk41': ( a > a > $o ) > a ).

thf('#sk4_type',type,
    '#sk4': a ).

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

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

thf('#sk54_type',type,
    '#sk54': ( a > a > $o ) > a ).

thf('#sk85_type',type,
    '#sk85': ( a > a > $o ) > a ).

thf('#sk30_type',type,
    '#sk30': ( a > a > $o ) > a ).

thf('#sk5_type',type,
    '#sk5': a > a > $o ).

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

thf(cTHM251F_pme,conjecture,
    ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
      ( ! [Xq1: a > a > $o] :
          ( ( ! [Xx0: a,Xy0: a,Xz: a] :
                ( ( ( Xq1 @ Xy0 @ Xz )
                  & ( Xq1 @ Xx0 @ Xy0 ) )
               => ( Xq1 @ Xx0 @ Xz ) )
            & ! [Xs: a,Xt: a] :
                ( ( ( S @ Xs @ Xt )
                  | ( R @ Xs @ Xt ) )
               => ( Xq1 @ Xs @ Xt ) ) )
         => ( Xq1 @ Xx @ Xy ) )
     => ! [Xp1: a > a > $o] :
          ( ( ! [Xx0: a,Xy0: a,Xz: a] :
                ( ( ( Xp1 @ Xy0 @ Xz )
                  & ( Xp1 @ Xx0 @ Xy0 ) )
               => ( Xp1 @ Xx0 @ Xz ) )
            & ! [Xss: a,Xtt: a] :
                ( ( ! [Xq3: a > a > $o] :
                      ( ( ! [Xx0: a,Xy0: a,Xz: a] :
                            ( ( ( Xq3 @ Xy0 @ Xz )
                              & ( Xq3 @ Xx0 @ Xy0 ) )
                           => ( Xq3 @ Xx0 @ Xz ) )
                        & ! [Xssss: a,Xtttt: a] :
                            ( ( S @ Xssss @ Xtttt )
                           => ( Xq3 @ Xssss @ Xtttt ) ) )
                     => ( Xq3 @ Xss @ Xtt ) )
                  | ! [Xq2: a > a > $o] :
                      ( ( ! [Xx0: a,Xy0: a,Xz: a] :
                            ( ( ( Xq2 @ Xy0 @ Xz )
                              & ( Xq2 @ Xx0 @ Xy0 ) )
                           => ( Xq2 @ Xx0 @ Xz ) )
                        & ! [Xsss: a,Xttt: a] :
                            ( ( R @ Xsss @ Xttt )
                           => ( Xq2 @ Xsss @ Xttt ) ) )
                     => ( Xq2 @ Xss @ Xtt ) ) )
               => ( Xp1 @ Xss @ Xtt ) ) )
         => ( Xp1 @ Xx @ Xy ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
        ( ! [Xq1: a > a > $o] :
            ( ( ! [Xx0: a,Xy0: a,Xz: a] :
                  ( ( ( Xq1 @ Xy0 @ Xz )
                    & ( Xq1 @ Xx0 @ Xy0 ) )
                 => ( Xq1 @ Xx0 @ Xz ) )
              & ! [Xs: a,Xt: a] :
                  ( ( ( S @ Xs @ Xt )
                    | ( R @ Xs @ Xt ) )
                 => ( Xq1 @ Xs @ Xt ) ) )
           => ( Xq1 @ Xx @ Xy ) )
       => ! [Xp1: a > a > $o] :
            ( ( ! [Xx0: a,Xy0: a,Xz: a] :
                  ( ( ( Xp1 @ Xy0 @ Xz )
                    & ( Xp1 @ Xx0 @ Xy0 ) )
                 => ( Xp1 @ Xx0 @ Xz ) )
              & ! [Xss: a,Xtt: a] :
                  ( ( ! [Xq3: a > a > $o] :
                        ( ( ! [Xx0: a,Xy0: a,Xz: a] :
                              ( ( ( Xq3 @ Xy0 @ Xz )
                                & ( Xq3 @ Xx0 @ Xy0 ) )
                             => ( Xq3 @ Xx0 @ Xz ) )
                          & ! [Xssss: a,Xtttt: a] :
                              ( ( S @ Xssss @ Xtttt )
                             => ( Xq3 @ Xssss @ Xtttt ) ) )
                       => ( Xq3 @ Xss @ Xtt ) )
                    | ! [Xq2: a > a > $o] :
                        ( ( ! [Xx0: a,Xy0: a,Xz: a] :
                              ( ( ( Xq2 @ Xy0 @ Xz )
                                & ( Xq2 @ Xx0 @ Xy0 ) )
                             => ( Xq2 @ Xx0 @ Xz ) )
                          & ! [Xsss: a,Xttt: a] :
                              ( ( R @ Xsss @ Xttt )
                             => ( Xq2 @ Xsss @ Xttt ) ) )
                       => ( Xq2 @ Xss @ Xtt ) ) )
                 => ( Xp1 @ Xss @ Xtt ) ) )
           => ( Xp1 @ Xx @ Xy ) ) ),
    inference('cnf.neg',[status(esa)],[cTHM251F_pme]) ).

thf(zip_derived_cl0,plain,
    ~ ( !!
      @ ^ [Y0: a > a > $o] :
          ( !!
          @ ^ [Y1: a > a > $o] :
              ( !!
              @ ^ [Y2: a] :
                  ( !!
                  @ ^ [Y3: a] :
                      ( ( !!
                        @ ^ [Y4: a > a > $o] :
                            ( ( ( !!
                                @ ^ [Y5: a] :
                                    ( !!
                                    @ ^ [Y6: a] :
                                        ( !!
                                        @ ^ [Y7: a] :
                                            ( ( ( Y4 @ Y6 @ Y7 )
                                              & ( Y4 @ Y5 @ Y6 ) )
                                           => ( Y4 @ Y5 @ Y7 ) ) ) ) )
                              & ( !!
                                @ ^ [Y5: a] :
                                    ( !!
                                    @ ^ [Y6: a] :
                                        ( ( ( Y1 @ Y5 @ Y6 )
                                          | ( Y0 @ Y5 @ Y6 ) )
                                       => ( Y4 @ Y5 @ Y6 ) ) ) ) )
                           => ( Y4 @ Y2 @ Y3 ) ) )
                     => ( !!
                        @ ^ [Y4: a > a > $o] :
                            ( ( ( !!
                                @ ^ [Y5: a] :
                                    ( !!
                                    @ ^ [Y6: a] :
                                        ( !!
                                        @ ^ [Y7: a] :
                                            ( ( ( Y4 @ Y6 @ Y7 )
                                              & ( Y4 @ Y5 @ Y6 ) )
                                           => ( Y4 @ Y5 @ Y7 ) ) ) ) )
                              & ( !!
                                @ ^ [Y5: a] :
                                    ( !!
                                    @ ^ [Y6: a] :
                                        ( ( ( !!
                                            @ ^ [Y7: a > a > $o] :
                                                ( ( ( !!
                                                    @ ^ [Y8: a] :
                                                        ( !!
                                                        @ ^ [Y9: a] :
                                                            ( !!
                                                            @ ^ [Y10: a] :
                                                                ( ( ( Y7 @ Y9 @ Y10 )
                                                                  & ( Y7 @ Y8 @ Y9 ) )
                                                               => ( Y7 @ Y8 @ Y10 ) ) ) ) )
                                                  & ( !!
                                                    @ ^ [Y8: a] :
                                                        ( !!
                                                        @ ^ [Y9: a] :
                                                            ( ( Y1 @ Y8 @ Y9 )
                                                           => ( Y7 @ Y8 @ Y9 ) ) ) ) )
                                               => ( Y7 @ Y5 @ Y6 ) ) )
                                          | ( !!
                                            @ ^ [Y7: a > a > $o] :
                                                ( ( ( !!
                                                    @ ^ [Y8: a] :
                                                        ( !!
                                                        @ ^ [Y9: a] :
                                                            ( !!
                                                            @ ^ [Y10: a] :
                                                                ( ( ( Y7 @ Y9 @ Y10 )
                                                                  & ( Y7 @ Y8 @ Y9 ) )
                                                               => ( Y7 @ Y8 @ Y10 ) ) ) ) )
                                                  & ( !!
                                                    @ ^ [Y8: a] :
                                                        ( !!
                                                        @ ^ [Y9: a] :
                                                            ( ( Y0 @ Y8 @ Y9 )
                                                           => ( Y7 @ Y8 @ Y9 ) ) ) ) )
                                               => ( Y7 @ Y5 @ Y6 ) ) ) )
                                       => ( Y4 @ Y5 @ Y6 ) ) ) ) )
                           => ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl1,plain,
    ~ ( !!
      @ ^ [Y0: a > a > $o] :
          ( !!
          @ ^ [Y1: a] :
              ( !!
              @ ^ [Y2: a] :
                  ( ( !!
                    @ ^ [Y3: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( !!
                                    @ ^ [Y6: a] :
                                        ( ( ( Y3 @ Y5 @ Y6 )
                                          & ( Y3 @ Y4 @ Y5 ) )
                                       => ( Y3 @ Y4 @ Y6 ) ) ) ) )
                          & ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( ( ( Y0 @ Y4 @ Y5 )
                                      | ( '#sk1' @ Y4 @ Y5 ) )
                                   => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                       => ( Y3 @ Y1 @ Y2 ) ) )
                 => ( !!
                    @ ^ [Y3: a > a > $o] :
                        ( ( ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( !!
                                    @ ^ [Y6: a] :
                                        ( ( ( Y3 @ Y5 @ Y6 )
                                          & ( Y3 @ Y4 @ Y5 ) )
                                       => ( Y3 @ Y4 @ Y6 ) ) ) ) )
                          & ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( ( ( !!
                                        @ ^ [Y6: a > a > $o] :
                                            ( ( ( !!
                                                @ ^ [Y7: a] :
                                                    ( !!
                                                    @ ^ [Y8: a] :
                                                        ( !!
                                                        @ ^ [Y9: a] :
                                                            ( ( ( Y6 @ Y8 @ Y9 )
                                                              & ( Y6 @ Y7 @ Y8 ) )
                                                           => ( Y6 @ Y7 @ Y9 ) ) ) ) )
                                              & ( !!
                                                @ ^ [Y7: a] :
                                                    ( !!
                                                    @ ^ [Y8: a] :
                                                        ( ( Y0 @ Y7 @ Y8 )
                                                       => ( Y6 @ Y7 @ Y8 ) ) ) ) )
                                           => ( Y6 @ Y4 @ Y5 ) ) )
                                      | ( !!
                                        @ ^ [Y6: a > a > $o] :
                                            ( ( ( !!
                                                @ ^ [Y7: a] :
                                                    ( !!
                                                    @ ^ [Y8: a] :
                                                        ( !!
                                                        @ ^ [Y9: a] :
                                                            ( ( ( Y6 @ Y8 @ Y9 )
                                                              & ( Y6 @ Y7 @ Y8 ) )
                                                           => ( Y6 @ Y7 @ Y9 ) ) ) ) )
                                              & ( !!
                                                @ ^ [Y7: a] :
                                                    ( !!
                                                    @ ^ [Y8: a] :
                                                        ( ( '#sk1' @ Y7 @ Y8 )
                                                       => ( Y6 @ Y7 @ Y8 ) ) ) ) )
                                           => ( Y6 @ Y4 @ Y5 ) ) ) )
                                   => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                       => ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl2,plain,
    ~ ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( !!
                @ ^ [Y2: a > a > $o] :
                    ( ( ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( ( ( Y2 @ Y4 @ Y5 )
                                      & ( Y2 @ Y3 @ Y4 ) )
                                   => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( ( '#sk2' @ Y3 @ Y4 )
                                  | ( '#sk1' @ Y3 @ Y4 ) )
                               => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                   => ( Y2 @ Y0 @ Y1 ) ) )
             => ( !!
                @ ^ [Y2: a > a > $o] :
                    ( ( ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( ( ( Y2 @ Y4 @ Y5 )
                                      & ( Y2 @ Y3 @ Y4 ) )
                                   => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( ( !!
                                    @ ^ [Y5: a > a > $o] :
                                        ( ( ( !!
                                            @ ^ [Y6: a] :
                                                ( !!
                                                @ ^ [Y7: a] :
                                                    ( !!
                                                    @ ^ [Y8: a] :
                                                        ( ( ( Y5 @ Y7 @ Y8 )
                                                          & ( Y5 @ Y6 @ Y7 ) )
                                                       => ( Y5 @ Y6 @ Y8 ) ) ) ) )
                                          & ( !!
                                            @ ^ [Y6: a] :
                                                ( !!
                                                @ ^ [Y7: a] :
                                                    ( ( '#sk2' @ Y6 @ Y7 )
                                                   => ( Y5 @ Y6 @ Y7 ) ) ) ) )
                                       => ( Y5 @ Y3 @ Y4 ) ) )
                                  | ( !!
                                    @ ^ [Y5: a > a > $o] :
                                        ( ( ( !!
                                            @ ^ [Y6: a] :
                                                ( !!
                                                @ ^ [Y7: a] :
                                                    ( !!
                                                    @ ^ [Y8: a] :
                                                        ( ( ( Y5 @ Y7 @ Y8 )
                                                          & ( Y5 @ Y6 @ Y7 ) )
                                                       => ( Y5 @ Y6 @ Y8 ) ) ) ) )
                                          & ( !!
                                            @ ^ [Y6: a] :
                                                ( !!
                                                @ ^ [Y7: a] :
                                                    ( ( '#sk1' @ Y6 @ Y7 )
                                                   => ( Y5 @ Y6 @ Y7 ) ) ) ) )
                                       => ( Y5 @ Y3 @ Y4 ) ) ) )
                               => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                   => ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl3,plain,
    ~ ( !!
      @ ^ [Y0: a] :
          ( ( !!
            @ ^ [Y1: a > a > $o] :
                ( ( ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( ( Y1 @ Y3 @ Y4 )
                                  & ( Y1 @ Y2 @ Y3 ) )
                               => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                  & ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( '#sk2' @ Y2 @ Y3 )
                              | ( '#sk1' @ Y2 @ Y3 ) )
                           => ( Y1 @ Y2 @ Y3 ) ) ) ) )
               => ( Y1 @ '#sk3' @ Y0 ) ) )
         => ( !!
            @ ^ [Y1: a > a > $o] :
                ( ( ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( ( Y1 @ Y3 @ Y4 )
                                  & ( Y1 @ Y2 @ Y3 ) )
                               => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                  & ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( !!
                                @ ^ [Y4: a > a > $o] :
                                    ( ( ( !!
                                        @ ^ [Y5: a] :
                                            ( !!
                                            @ ^ [Y6: a] :
                                                ( !!
                                                @ ^ [Y7: a] :
                                                    ( ( ( Y4 @ Y6 @ Y7 )
                                                      & ( Y4 @ Y5 @ Y6 ) )
                                                   => ( Y4 @ Y5 @ Y7 ) ) ) ) )
                                      & ( !!
                                        @ ^ [Y5: a] :
                                            ( !!
                                            @ ^ [Y6: a] :
                                                ( ( '#sk2' @ Y5 @ Y6 )
                                               => ( Y4 @ Y5 @ Y6 ) ) ) ) )
                                   => ( Y4 @ Y2 @ Y3 ) ) )
                              | ( !!
                                @ ^ [Y4: a > a > $o] :
                                    ( ( ( !!
                                        @ ^ [Y5: a] :
                                            ( !!
                                            @ ^ [Y6: a] :
                                                ( !!
                                                @ ^ [Y7: a] :
                                                    ( ( ( Y4 @ Y6 @ Y7 )
                                                      & ( Y4 @ Y5 @ Y6 ) )
                                                   => ( Y4 @ Y5 @ Y7 ) ) ) ) )
                                      & ( !!
                                        @ ^ [Y5: a] :
                                            ( !!
                                            @ ^ [Y6: a] :
                                                ( ( '#sk1' @ Y5 @ Y6 )
                                               => ( Y4 @ Y5 @ Y6 ) ) ) ) )
                                   => ( Y4 @ Y2 @ Y3 ) ) ) )
                           => ( Y1 @ Y2 @ Y3 ) ) ) ) )
               => ( Y1 @ '#sk3' @ Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl4,plain,
    ~ ( ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( '#sk2' @ Y1 @ Y2 )
                          | ( '#sk1' @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ '#sk3' @ '#sk4' ) ) )
     => ( !!
        @ ^ [Y0: a > a > $o] :
            ( ( ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( !!
                        @ ^ [Y3: a] :
                            ( ( ( Y0 @ Y2 @ Y3 )
                              & ( Y0 @ Y1 @ Y2 ) )
                           => ( Y0 @ Y1 @ Y3 ) ) ) ) )
              & ( !!
                @ ^ [Y1: a] :
                    ( !!
                    @ ^ [Y2: a] :
                        ( ( ( !!
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !!
                                    @ ^ [Y4: a] :
                                        ( !!
                                        @ ^ [Y5: a] :
                                            ( !!
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y5 @ Y6 )
                                                  & ( Y3 @ Y4 @ Y5 ) )
                                               => ( Y3 @ Y4 @ Y6 ) ) ) ) )
                                  & ( !!
                                    @ ^ [Y4: a] :
                                        ( !!
                                        @ ^ [Y5: a] :
                                            ( ( '#sk2' @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) )
                          | ( !!
                            @ ^ [Y3: a > a > $o] :
                                ( ( ( !!
                                    @ ^ [Y4: a] :
                                        ( !!
                                        @ ^ [Y5: a] :
                                            ( !!
                                            @ ^ [Y6: a] :
                                                ( ( ( Y3 @ Y5 @ Y6 )
                                                  & ( Y3 @ Y4 @ Y5 ) )
                                               => ( Y3 @ Y4 @ Y6 ) ) ) ) )
                                  & ( !!
                                    @ ^ [Y4: a] :
                                        ( !!
                                        @ ^ [Y5: a] :
                                            ( ( '#sk1' @ Y4 @ Y5 )
                                           => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                               => ( Y3 @ Y1 @ Y2 ) ) ) )
                       => ( Y0 @ Y1 @ Y2 ) ) ) ) )
           => ( Y0 @ '#sk3' @ '#sk4' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl5,plain,
    ( !!
    @ ^ [Y0: a > a > $o] :
        ( ( ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( !!
                    @ ^ [Y3: a] :
                        ( ( ( Y0 @ Y2 @ Y3 )
                          & ( Y0 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y3 ) ) ) ) )
          & ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk2' @ Y1 @ Y2 )
                      | ( '#sk1' @ Y1 @ Y2 ) )
                   => ( Y0 @ Y1 @ Y2 ) ) ) ) )
       => ( Y0 @ '#sk3' @ '#sk4' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl7,plain,
    ! [X2: a > a > $o] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( '#sk2' @ Y0 @ Y1 )
                    | ( '#sk1' @ Y0 @ Y1 ) )
                 => ( X2 @ Y0 @ Y1 ) ) ) ) )
     => ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl10,plain,
    ( ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk2' @ Y0 @ Y1 )
                  | ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
   => ( '#sk5' @ '#sk3' @ '#sk4' ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl6,plain,
    ~ ( !!
      @ ^ [Y0: a > a > $o] :
          ( ( ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( !!
                      @ ^ [Y3: a] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) )
            & ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( !!
                          @ ^ [Y3: a > a > $o] :
                              ( ( ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( !!
                                          @ ^ [Y6: a] :
                                              ( ( ( Y3 @ Y5 @ Y6 )
                                                & ( Y3 @ Y4 @ Y5 ) )
                                             => ( Y3 @ Y4 @ Y6 ) ) ) ) )
                                & ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( '#sk2' @ Y4 @ Y5 )
                                         => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                             => ( Y3 @ Y1 @ Y2 ) ) )
                        | ( !!
                          @ ^ [Y3: a > a > $o] :
                              ( ( ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( !!
                                          @ ^ [Y6: a] :
                                              ( ( ( Y3 @ Y5 @ Y6 )
                                                & ( Y3 @ Y4 @ Y5 ) )
                                             => ( Y3 @ Y4 @ Y6 ) ) ) ) )
                                & ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( '#sk1' @ Y4 @ Y5 )
                                         => ( Y3 @ Y4 @ Y5 ) ) ) ) )
                             => ( Y3 @ Y1 @ Y2 ) ) ) )
                     => ( Y0 @ Y1 @ Y2 ) ) ) ) )
         => ( Y0 @ '#sk3' @ '#sk4' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl11,plain,
    ~ ( ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( '#sk5' @ Y1 @ Y2 )
                        & ( '#sk5' @ Y0 @ Y1 ) )
                     => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk2' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) )
                    | ( !!
                      @ ^ [Y2: a > a > $o] :
                          ( ( ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( !!
                                      @ ^ [Y5: a] :
                                          ( ( ( Y2 @ Y4 @ Y5 )
                                            & ( Y2 @ Y3 @ Y4 ) )
                                         => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                            & ( !!
                              @ ^ [Y3: a] :
                                  ( !!
                                  @ ^ [Y4: a] :
                                      ( ( '#sk1' @ Y3 @ Y4 )
                                     => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                         => ( Y2 @ Y0 @ Y1 ) ) ) )
                 => ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
     => ( '#sk5' @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl14,plain,
    ~ ( '#sk5' @ '#sk3' @ '#sk4' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl142,plain,
    ( ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk2' @ Y0 @ Y1 )
                  | ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) )
   => $false ),
    inference(demod,[status(thm)],[zip_derived_cl10,zip_derived_cl14]) ).

thf(zip_derived_cl143,plain,
    ( (~)
    @ ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk2' @ Y0 @ Y1 )
                  | ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl142]) ).

thf(zip_derived_cl144,plain,
    ~ ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
      & ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk2' @ Y0 @ Y1 )
                  | ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl143]) ).

thf(zip_derived_cl145,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( !!
                @ ^ [Y2: a] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk2' @ Y0 @ Y1 )
                  | ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl144]) ).

thf(zip_derived_cl146,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk5' @ Y0 @ Y1 )
                  & ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ Y0 ) )
               => ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ Y1 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk2' @ Y0 @ Y1 )
                  | ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl145]) ).

thf(zip_derived_cl147,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( ( '#sk5' @ ( '#sk41' @ '#sk5' ) @ Y0 )
              & ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk41' @ '#sk5' ) ) )
           => ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ Y0 ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk2' @ Y0 @ Y1 )
                  | ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl146]) ).

thf(zip_derived_cl148,plain,
    ( ~ ( ( ( '#sk5' @ ( '#sk41' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) )
          & ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk41' @ '#sk5' ) ) )
       => ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk2' @ Y0 @ Y1 )
                  | ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl147]) ).

thf(zip_derived_cl150,plain,
    ( ~ ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk2' @ Y0 @ Y1 )
                  | ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl148]) ).

thf(zip_derived_cl153,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ Y0 )
              | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ Y0 ) )
           => ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ Y0 ) ) )
    | ~ ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl150]) ).

thf(zip_derived_cl156,plain,
    ( ~ ( ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
          | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) ) )
       => ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) ) )
    | ~ ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl153]) ).

thf(zip_derived_cl160,plain,
    ( ~ ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ~ ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl156]) ).

thf(zip_derived_cl149,plain,
    ( ( ( '#sk5' @ ( '#sk41' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) )
      & ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk41' @ '#sk5' ) ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk2' @ Y0 @ Y1 )
                  | ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl148]) ).

thf(zip_derived_cl152,plain,
    ( ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk41' @ '#sk5' ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk2' @ Y0 @ Y1 )
                  | ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl149]) ).

thf(zip_derived_cl155,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ Y0 )
              | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ Y0 ) )
           => ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ Y0 ) ) )
    | ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk41' @ '#sk5' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl152]) ).

thf(zip_derived_cl158,plain,
    ( ~ ( ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
          | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) ) )
       => ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) ) )
    | ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk41' @ '#sk5' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl155]) ).

thf(zip_derived_cl163,plain,
    ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk41' @ '#sk5' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl158]) ).

thf(zip_derived_cl167,plain,
    ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk41' @ '#sk5' ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl163]) ).

thf(zip_derived_cl13,plain,
    ( ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( !!
              @ ^ [Y2: a] :
                  ( ( ( '#sk5' @ Y1 @ Y2 )
                    & ( '#sk5' @ Y0 @ Y1 ) )
                 => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
    & ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( ( !!
                  @ ^ [Y2: a > a > $o] :
                      ( ( ( !!
                          @ ^ [Y3: a] :
                              ( !!
                              @ ^ [Y4: a] :
                                  ( !!
                                  @ ^ [Y5: a] :
                                      ( ( ( Y2 @ Y4 @ Y5 )
                                        & ( Y2 @ Y3 @ Y4 ) )
                                     => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                        & ( !!
                          @ ^ [Y3: a] :
                              ( !!
                              @ ^ [Y4: a] :
                                  ( ( '#sk2' @ Y3 @ Y4 )
                                 => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                     => ( Y2 @ Y0 @ Y1 ) ) )
                | ( !!
                  @ ^ [Y2: a > a > $o] :
                      ( ( ( !!
                          @ ^ [Y3: a] :
                              ( !!
                              @ ^ [Y4: a] :
                                  ( !!
                                  @ ^ [Y5: a] :
                                      ( ( ( Y2 @ Y4 @ Y5 )
                                        & ( Y2 @ Y3 @ Y4 ) )
                                     => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                        & ( !!
                          @ ^ [Y3: a] :
                              ( !!
                              @ ^ [Y4: a] :
                                  ( ( '#sk1' @ Y3 @ Y4 )
                                 => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                     => ( Y2 @ Y0 @ Y1 ) ) ) )
             => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl17,plain,
    ( !!
    @ ^ [Y0: a] :
        ( !!
        @ ^ [Y1: a] :
            ( ( ( !!
                @ ^ [Y2: a > a > $o] :
                    ( ( ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( ( ( Y2 @ Y4 @ Y5 )
                                      & ( Y2 @ Y3 @ Y4 ) )
                                   => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk2' @ Y3 @ Y4 )
                               => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                   => ( Y2 @ Y0 @ Y1 ) ) )
              | ( !!
                @ ^ [Y2: a > a > $o] :
                    ( ( ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( !!
                                @ ^ [Y5: a] :
                                    ( ( ( Y2 @ Y4 @ Y5 )
                                      & ( Y2 @ Y3 @ Y4 ) )
                                   => ( Y2 @ Y3 @ Y5 ) ) ) ) )
                      & ( !!
                        @ ^ [Y3: a] :
                            ( !!
                            @ ^ [Y4: a] :
                                ( ( '#sk1' @ Y3 @ Y4 )
                               => ( Y2 @ Y3 @ Y4 ) ) ) ) )
                   => ( Y2 @ Y0 @ Y1 ) ) ) )
           => ( '#sk5' @ Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl20,plain,
    ! [X2: a] :
      ( !!
      @ ^ [Y0: a] :
          ( ( ( !!
              @ ^ [Y1: a > a > $o] :
                  ( ( ( !!
                      @ ^ [Y2: a] :
                          ( !!
                          @ ^ [Y3: a] :
                              ( !!
                              @ ^ [Y4: a] :
                                  ( ( ( Y1 @ Y3 @ Y4 )
                                    & ( Y1 @ Y2 @ Y3 ) )
                                 => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                    & ( !!
                      @ ^ [Y2: a] :
                          ( !!
                          @ ^ [Y3: a] :
                              ( ( '#sk2' @ Y2 @ Y3 )
                             => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                 => ( Y1 @ X2 @ Y0 ) ) )
            | ( !!
              @ ^ [Y1: a > a > $o] :
                  ( ( ( !!
                      @ ^ [Y2: a] :
                          ( !!
                          @ ^ [Y3: a] :
                              ( !!
                              @ ^ [Y4: a] :
                                  ( ( ( Y1 @ Y3 @ Y4 )
                                    & ( Y1 @ Y2 @ Y3 ) )
                                 => ( Y1 @ Y2 @ Y4 ) ) ) ) )
                    & ( !!
                      @ ^ [Y2: a] :
                          ( !!
                          @ ^ [Y3: a] :
                              ( ( '#sk1' @ Y2 @ Y3 )
                             => ( Y1 @ Y2 @ Y3 ) ) ) ) )
                 => ( Y1 @ X2 @ Y0 ) ) ) )
         => ( '#sk5' @ X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl23,plain,
    ! [X2: a,X4: a] :
      ( ( ( !!
          @ ^ [Y0: a > a > $o] :
              ( ( ( !!
                  @ ^ [Y1: a] :
                      ( !!
                      @ ^ [Y2: a] :
                          ( !!
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y2 @ Y3 )
                                & ( Y0 @ Y1 @ Y2 ) )
                             => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                & ( !!
                  @ ^ [Y1: a] :
                      ( !!
                      @ ^ [Y2: a] :
                          ( ( '#sk2' @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ X2 @ X4 ) ) )
        | ( !!
          @ ^ [Y0: a > a > $o] :
              ( ( ( !!
                  @ ^ [Y1: a] :
                      ( !!
                      @ ^ [Y2: a] :
                          ( !!
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y2 @ Y3 )
                                & ( Y0 @ Y1 @ Y2 ) )
                             => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                & ( !!
                  @ ^ [Y1: a] :
                      ( !!
                      @ ^ [Y2: a] :
                          ( ( '#sk1' @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ X2 @ X4 ) ) ) )
     => ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl26,plain,
    ! [X2: a,X4: a] :
      ( ~ ( ( !!
            @ ^ [Y0: a > a > $o] :
                ( ( ( !!
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( ( ( Y0 @ Y2 @ Y3 )
                                  & ( Y0 @ Y1 @ Y2 ) )
                               => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                  & ( !!
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a] :
                            ( ( '#sk2' @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ X2 @ X4 ) ) )
          | ( !!
            @ ^ [Y0: a > a > $o] :
                ( ( ( !!
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a] :
                            ( !!
                            @ ^ [Y3: a] :
                                ( ( ( Y0 @ Y2 @ Y3 )
                                  & ( Y0 @ Y1 @ Y2 ) )
                               => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                  & ( !!
                    @ ^ [Y1: a] :
                        ( !!
                        @ ^ [Y2: a] :
                            ( ( '#sk1' @ Y1 @ Y2 )
                           => ( Y0 @ Y1 @ Y2 ) ) ) ) )
               => ( Y0 @ X2 @ X4 ) ) ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl31,plain,
    ! [X2: a,X4: a] :
      ( ~ ( !!
          @ ^ [Y0: a > a > $o] :
              ( ( ( !!
                  @ ^ [Y1: a] :
                      ( !!
                      @ ^ [Y2: a] :
                          ( !!
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y2 @ Y3 )
                                & ( Y0 @ Y1 @ Y2 ) )
                             => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                & ( !!
                  @ ^ [Y1: a] :
                      ( !!
                      @ ^ [Y2: a] :
                          ( ( '#sk1' @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ X2 @ X4 ) ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl39,plain,
    ! [X2: a,X4: a] :
      ( ~ ( ( ( !!
              @ ^ [Y0: a] :
                  ( !!
                  @ ^ [Y1: a] :
                      ( !!
                      @ ^ [Y2: a] :
                          ( ( ( '#sk87' @ X2 @ X4 @ Y1 @ Y2 )
                            & ( '#sk87' @ X2 @ X4 @ Y0 @ Y1 ) )
                         => ( '#sk87' @ X2 @ X4 @ Y0 @ Y2 ) ) ) ) )
            & ( !!
              @ ^ [Y0: a] :
                  ( !!
                  @ ^ [Y1: a] :
                      ( ( '#sk1' @ Y0 @ Y1 )
                     => ( '#sk87' @ X2 @ X4 @ Y0 @ Y1 ) ) ) ) )
         => ( '#sk87' @ X2 @ X4 @ X2 @ X4 ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl46,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk87' @ X2 @ X4 @ X2 @ X4 )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl45,plain,
    ! [X2: a,X4: a] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( '#sk87' @ X2 @ X4 @ Y1 @ Y2 )
                        & ( '#sk87' @ X2 @ X4 @ Y0 @ Y1 ) )
                     => ( '#sk87' @ X2 @ X4 @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk87' @ X2 @ X4 @ Y0 @ Y1 ) ) ) ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl54,plain,
    ! [X2: a,X4: a] :
      ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk87' @ X2 @ X4 @ Y0 @ Y1 ) ) ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl63,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( '#sk1' @ X6 @ Y0 )
           => ( '#sk87' @ X2 @ X4 @ X6 @ Y0 ) ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl69,plain,
    ! [X2: a,X4: a,X6: a,X8: a] :
      ( ( ( '#sk1' @ X6 @ X8 )
       => ( '#sk87' @ X2 @ X4 @ X6 @ X8 ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).

thf(zip_derived_cl73,plain,
    ! [X2: a,X4: a,X6: a,X8: a] :
      ( ~ ( '#sk1' @ X6 @ X8 )
      | ( '#sk87' @ X2 @ X4 @ X6 @ X8 )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl69]) ).

thf(zip_derived_cl87,plain,
    ! [X0: a,X1: a] :
      ( ( '#sk5' @ X1 @ X0 )
      | ( '#sk5' @ X1 @ X0 )
      | ~ ( '#sk1' @ X1 @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl46,zip_derived_cl73]) ).

thf(zip_derived_cl90,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk1' @ X1 @ X0 )
      | ( '#sk5' @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl87]) ).

thf(zip_derived_cl282,plain,
    ( ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk41' @ '#sk5' ) )
    | ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl167,zip_derived_cl90]) ).

thf(zip_derived_cl30,plain,
    ! [X2: a,X4: a] :
      ( ~ ( !!
          @ ^ [Y0: a > a > $o] :
              ( ( ( !!
                  @ ^ [Y1: a] :
                      ( !!
                      @ ^ [Y2: a] :
                          ( !!
                          @ ^ [Y3: a] :
                              ( ( ( Y0 @ Y2 @ Y3 )
                                & ( Y0 @ Y1 @ Y2 ) )
                             => ( Y0 @ Y1 @ Y3 ) ) ) ) )
                & ( !!
                  @ ^ [Y1: a] :
                      ( !!
                      @ ^ [Y2: a] :
                          ( ( '#sk2' @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) ) )
             => ( Y0 @ X2 @ X4 ) ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl37,plain,
    ! [X2: a,X4: a] :
      ( ~ ( ( ( !!
              @ ^ [Y0: a] :
                  ( !!
                  @ ^ [Y1: a] :
                      ( !!
                      @ ^ [Y2: a] :
                          ( ( ( '#sk86' @ X2 @ X4 @ Y1 @ Y2 )
                            & ( '#sk86' @ X2 @ X4 @ Y0 @ Y1 ) )
                         => ( '#sk86' @ X2 @ X4 @ Y0 @ Y2 ) ) ) ) )
            & ( !!
              @ ^ [Y0: a] :
                  ( !!
                  @ ^ [Y1: a] :
                      ( ( '#sk2' @ Y0 @ Y1 )
                     => ( '#sk86' @ X2 @ X4 @ Y0 @ Y1 ) ) ) ) )
         => ( '#sk86' @ X2 @ X4 @ X2 @ X4 ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl44,plain,
    ! [X2: a,X4: a] :
      ( ~ ( '#sk86' @ X2 @ X4 @ X2 @ X4 )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl43,plain,
    ! [X2: a,X4: a] :
      ( ( ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( !!
                  @ ^ [Y2: a] :
                      ( ( ( '#sk86' @ X2 @ X4 @ Y1 @ Y2 )
                        & ( '#sk86' @ X2 @ X4 @ Y0 @ Y1 ) )
                     => ( '#sk86' @ X2 @ X4 @ Y0 @ Y2 ) ) ) ) )
        & ( !!
          @ ^ [Y0: a] :
              ( !!
              @ ^ [Y1: a] :
                  ( ( '#sk2' @ Y0 @ Y1 )
                 => ( '#sk86' @ X2 @ X4 @ Y0 @ Y1 ) ) ) ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl52,plain,
    ! [X2: a,X4: a] :
      ( ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( '#sk2' @ Y0 @ Y1 )
               => ( '#sk86' @ X2 @ X4 @ Y0 @ Y1 ) ) ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl61,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ( !!
        @ ^ [Y0: a] :
            ( ( '#sk2' @ X6 @ Y0 )
           => ( '#sk86' @ X2 @ X4 @ X6 @ Y0 ) ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl67,plain,
    ! [X2: a,X4: a,X6: a,X8: a] :
      ( ( ( '#sk2' @ X6 @ X8 )
       => ( '#sk86' @ X2 @ X4 @ X6 @ X8 ) )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl61]) ).

thf(zip_derived_cl71,plain,
    ! [X2: a,X4: a,X6: a,X8: a] :
      ( ~ ( '#sk2' @ X6 @ X8 )
      | ( '#sk86' @ X2 @ X4 @ X6 @ X8 )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl79,plain,
    ! [X0: a,X1: a] :
      ( ( '#sk5' @ X1 @ X0 )
      | ( '#sk5' @ X1 @ X0 )
      | ~ ( '#sk2' @ X1 @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl44,zip_derived_cl71]) ).

thf(zip_derived_cl82,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk2' @ X1 @ X0 )
      | ( '#sk5' @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl79]) ).

thf(zip_derived_cl287,plain,
    ( ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk41' @ '#sk5' ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl282,zip_derived_cl82]) ).

thf(zip_derived_cl164,plain,
    ( ~ ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk41' @ '#sk5' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl158]) ).

thf(zip_derived_cl288,plain,
    '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk41' @ '#sk5' ),
    inference(clc,[status(thm)],[zip_derived_cl287,zip_derived_cl164]) ).

thf(zip_derived_cl151,plain,
    ( ( '#sk5' @ ( '#sk41' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) )
    | ~ ( !!
        @ ^ [Y0: a] :
            ( !!
            @ ^ [Y1: a] :
                ( ( ( '#sk2' @ Y0 @ Y1 )
                  | ( '#sk1' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl149]) ).

thf(zip_derived_cl154,plain,
    ( ~ ( !!
        @ ^ [Y0: a] :
            ( ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ Y0 )
              | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ Y0 ) )
           => ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ Y0 ) ) )
    | ( '#sk5' @ ( '#sk41' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl151]) ).

thf(zip_derived_cl157,plain,
    ( ~ ( ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
          | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) ) )
       => ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) ) )
    | ( '#sk5' @ ( '#sk41' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl154]) ).

thf(zip_derived_cl161,plain,
    ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk41' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl157]) ).

thf(zip_derived_cl166,plain,
    ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk41' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl161]) ).

thf(zip_derived_cl90_001,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk1' @ X1 @ X0 )
      | ( '#sk5' @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl87]) ).

thf(zip_derived_cl279,plain,
    ( ( '#sk5' @ ( '#sk41' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) )
    | ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl166,zip_derived_cl90]) ).

thf(zip_derived_cl82_002,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk2' @ X1 @ X0 )
      | ( '#sk5' @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl79]) ).

thf(zip_derived_cl284,plain,
    ( ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk41' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl279,zip_derived_cl82]) ).

thf(zip_derived_cl162,plain,
    ( ~ ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk41' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl157]) ).

thf(zip_derived_cl285,plain,
    '#sk5' @ ( '#sk41' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ),
    inference(clc,[status(thm)],[zip_derived_cl284,zip_derived_cl162]) ).

thf(zip_derived_cl16,plain,
    ( !!
    @ ^ [Y0: a] :
        ( !!
        @ ^ [Y1: a] :
            ( !!
            @ ^ [Y2: a] :
                ( ( ( '#sk5' @ Y1 @ Y2 )
                  & ( '#sk5' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y2 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl19,plain,
    ! [X2: a] :
      ( !!
      @ ^ [Y0: a] :
          ( !!
          @ ^ [Y1: a] :
              ( ( ( '#sk5' @ Y0 @ Y1 )
                & ( '#sk5' @ X2 @ Y0 ) )
             => ( '#sk5' @ X2 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl22,plain,
    ! [X2: a,X4: a] :
      ( !!
      @ ^ [Y0: a] :
          ( ( ( '#sk5' @ X4 @ Y0 )
            & ( '#sk5' @ X2 @ X4 ) )
         => ( '#sk5' @ X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl25,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ( ( '#sk5' @ X4 @ X6 )
        & ( '#sk5' @ X2 @ X4 ) )
     => ( '#sk5' @ X2 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl29,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( ( '#sk5' @ X4 @ X6 )
          & ( '#sk5' @ X2 @ X4 ) )
      | ( '#sk5' @ X2 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl35,plain,
    ! [X2: a,X4: a,X6: a] :
      ( ~ ( '#sk5' @ X4 @ X6 )
      | ~ ( '#sk5' @ X2 @ X4 )
      | ( '#sk5' @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl286,plain,
    ! [X0: a] :
      ( ( '#sk5' @ X0 @ ( '#sk54' @ '#sk5' ) )
      | ~ ( '#sk5' @ X0 @ ( '#sk41' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl285,zip_derived_cl35]) ).

thf(zip_derived_cl302,plain,
    '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ),
    inference('sup-',[status(thm)],[zip_derived_cl288,zip_derived_cl286]) ).

thf(zip_derived_cl303,plain,
    ~ ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) ),
    inference(demod,[status(thm)],[zip_derived_cl160,zip_derived_cl302]) ).

thf(zip_derived_cl159,plain,
    ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ~ ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl156]) ).

thf(zip_derived_cl165,plain,
    ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ~ ( '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl159]) ).

thf(zip_derived_cl302_003,plain,
    '#sk5' @ ( '#sk30' @ '#sk5' ) @ ( '#sk54' @ '#sk5' ),
    inference('sup-',[status(thm)],[zip_derived_cl288,zip_derived_cl286]) ).

thf(zip_derived_cl304,plain,
    ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk1' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl165,zip_derived_cl302]) ).

thf(zip_derived_cl90_004,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk1' @ X1 @ X0 )
      | ( '#sk5' @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl87]) ).

thf(zip_derived_cl348,plain,
    ( ( '#sk2' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) )
    | ( '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl304,zip_derived_cl90]) ).

thf(zip_derived_cl82_005,plain,
    ! [X0: a,X1: a] :
      ( ~ ( '#sk2' @ X1 @ X0 )
      | ( '#sk5' @ X1 @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl79]) ).

thf(zip_derived_cl352,plain,
    '#sk5' @ ( '#sk85' @ '#sk5' ) @ ( '#sk111' @ '#sk5' ),
    inference(clc,[status(thm)],[zip_derived_cl348,zip_derived_cl82]) ).

thf(zip_derived_cl353,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl303,zip_derived_cl352]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEV109^5 : 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.nXOhyrD3QX true
% 0.13/0.33  % Computer : n004.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu Aug 24 02:51:23 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34  % Number of cores: 8
% 0.13/0.34  % Python version: Python 3.6.8
% 0.13/0.34  % Running in HO mode
% 0.20/0.65  % Total configuration time : 828
% 0.20/0.65  % Estimated wc time : 1656
% 0.20/0.65  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.70  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.72  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.75  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.75  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.20/0.79  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 2.01/1.05  % Solved by lams/35_full_unif4.sh.
% 2.01/1.05  % done 43 iterations in 0.282s
% 2.01/1.05  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.01/1.05  % SZS output start Refutation
% See solution above
% 2.01/1.05  
% 2.01/1.05  
% 2.01/1.05  % Terminating...
% 2.10/1.19  % Runner terminated.
% 2.10/1.19  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------