TSTP Solution File: SEU463^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU463^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.utSov65BKU true

% Computer : n026.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 19:13:12 EDT 2023

% Result   : Theorem 1.44s 1.40s
% Output   : Refutation 1.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   98 (  16 unt;  14 typ;   0 def)
%            Number of atoms       :  504 (   9 equ;   0 cnn)
%            Maximal formula atoms :   25 (   6 avg)
%            Number of connectives : 1735 (  68   ~;  67   |; 119   &;1096   @)
%                                         (   0 <=>; 147  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   29 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  166 ( 166   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  14 usr;   5 con; 0-3 aty)
%                                         ( 238  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  366 ( 256   ^; 110   !;   0   ?; 366   :)

% Comments : 
%------------------------------------------------------------------------------
thf('#sk117_type',type,
    '#sk117': ( $i > $i > $o ) > $i ).

thf(subrel_type,type,
    subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).

thf('#form116_type',type,
    '#form116': ( $i > $i > $o ) > $o ).

thf('#sk213_type',type,
    '#sk213': ( $i > $i > $o ) > $i ).

thf('#sk66_type',type,
    '#sk66': ( $i > $i > $o ) > $i ).

thf('#sk164_type',type,
    '#sk164': ( $i > $i > $o ) > $i ).

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

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

thf('#sk46_type',type,
    '#sk46': ( $i > $i > $o ) > $i ).

thf(tc_type,type,
    tc: ( $i > $i > $o ) > $i > $i > $o ).

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

thf(trans_type,type,
    trans: ( $i > $i > $o ) > $o ).

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

thf('#sk4_type',type,
    '#sk4': $i ).

thf(transitive_closure,axiom,
    ( tc
    = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
        ! [S: $i > $i > $o] :
          ( ( ( trans @ S )
            & ( subrel @ R @ S ) )
         => ( S @ X @ Y ) ) ) ) ).

thf(transitive,axiom,
    ( trans
    = ( ^ [R: $i > $i > $o] :
        ! [X: $i,Y: $i,Z: $i] :
          ( ( ( R @ X @ Y )
            & ( R @ Y @ Z ) )
         => ( R @ X @ Z ) ) ) ) ).

thf('0',plain,
    ( trans
    = ( ^ [R: $i > $i > $o] :
        ! [X: $i,Y: $i,Z: $i] :
          ( ( ( R @ X @ Y )
            & ( R @ Y @ Z ) )
         => ( R @ X @ Z ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[transitive]) ).

thf('1',plain,
    ( trans
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i,X6: $i,X8: $i] :
          ( ( ( V_1 @ X4 @ X6 )
            & ( V_1 @ X6 @ X8 ) )
         => ( V_1 @ X4 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(subrel,axiom,
    ( subrel
    = ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
        ! [X: $i,Y: $i] :
          ( ( R @ X @ Y )
         => ( S @ X @ Y ) ) ) ) ).

thf('2',plain,
    ( subrel
    = ( ^ [R: $i > $i > $o,S: $i > $i > $o] :
        ! [X: $i,Y: $i] :
          ( ( R @ X @ Y )
         => ( S @ X @ Y ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[subrel]) ).

thf('3',plain,
    ( subrel
    = ( ^ [V_1: $i > $i > $o,V_2: $i > $i > $o] :
        ! [X4: $i,X6: $i] :
          ( ( V_1 @ X4 @ X6 )
         => ( V_2 @ X4 @ X6 ) ) ) ),
    define([status(thm)]) ).

thf('4',plain,
    ( tc
    = ( ^ [R: $i > $i > $o,X: $i,Y: $i] :
        ! [S: $i > $i > $o] :
          ( ( ( trans @ S )
            & ( subrel @ R @ S ) )
         => ( S @ X @ Y ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[transitive_closure,'1','3']) ).

thf('5',plain,
    ( tc
    = ( ^ [V_1: $i > $i > $o,V_2: $i,V_3: $i] :
        ! [X4: $i > $i > $o] :
          ( ( ( trans @ X4 )
            & ( subrel @ V_1 @ X4 ) )
         => ( X4 @ V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(transitive_closure_is_transitive3,conjecture,
    ! [R: $i > $i > $o,X: $i,Y: $i,Z: $i,S: $i > $i > $o] :
      ( ( ( trans @ S )
        & ( subrel @ R @ S )
        & ( tc @ R @ X @ Y )
        & ( tc @ R @ Y @ Z ) )
     => ( S @ X @ Z ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i > $i > $o,X6: $i,X8: $i,X10: $i,X12: $i > $i > $o] :
      ( ( ! [X36: $i > $i > $o] :
            ( ( ! [X44: $i,X46: $i] :
                  ( ( X4 @ X44 @ X46 )
                 => ( X36 @ X44 @ X46 ) )
              & ! [X38: $i,X40: $i,X42: $i] :
                  ( ( ( X36 @ X40 @ X42 )
                    & ( X36 @ X38 @ X40 ) )
                 => ( X36 @ X38 @ X42 ) ) )
           => ( X36 @ X8 @ X10 ) )
        & ! [X24: $i > $i > $o] :
            ( ( ! [X32: $i,X34: $i] :
                  ( ( X4 @ X32 @ X34 )
                 => ( X24 @ X32 @ X34 ) )
              & ! [X26: $i,X28: $i,X30: $i] :
                  ( ( ( X24 @ X28 @ X30 )
                    & ( X24 @ X26 @ X28 ) )
                 => ( X24 @ X26 @ X30 ) ) )
           => ( X24 @ X6 @ X8 ) )
        & ! [X20: $i,X22: $i] :
            ( ( X4 @ X20 @ X22 )
           => ( X12 @ X20 @ X22 ) )
        & ! [X14: $i,X16: $i,X18: $i] :
            ( ( ( X12 @ X16 @ X18 )
              & ( X12 @ X14 @ X16 ) )
           => ( X12 @ X14 @ X18 ) ) )
     => ( X12 @ X6 @ X10 ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i > $i > $o,X6: $i,X8: $i,X10: $i,X12: $i > $i > $o] :
        ( ( ! [X36: $i > $i > $o] :
              ( ( ! [X44: $i,X46: $i] :
                    ( ( X4 @ X44 @ X46 )
                   => ( X36 @ X44 @ X46 ) )
                & ! [X38: $i,X40: $i,X42: $i] :
                    ( ( ( X36 @ X40 @ X42 )
                      & ( X36 @ X38 @ X40 ) )
                   => ( X36 @ X38 @ X42 ) ) )
             => ( X36 @ X8 @ X10 ) )
          & ! [X24: $i > $i > $o] :
              ( ( ! [X32: $i,X34: $i] :
                    ( ( X4 @ X32 @ X34 )
                   => ( X24 @ X32 @ X34 ) )
                & ! [X26: $i,X28: $i,X30: $i] :
                    ( ( ( X24 @ X28 @ X30 )
                      & ( X24 @ X26 @ X28 ) )
                   => ( X24 @ X26 @ X30 ) ) )
             => ( X24 @ X6 @ X8 ) )
          & ! [X20: $i,X22: $i] :
              ( ( X4 @ X20 @ X22 )
             => ( X12 @ X20 @ X22 ) )
          & ! [X14: $i,X16: $i,X18: $i] :
              ( ( ( X12 @ X16 @ X18 )
                & ( X12 @ X14 @ X16 ) )
             => ( X12 @ X14 @ X18 ) ) )
       => ( X12 @ X6 @ X10 ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl0,plain,
    ~ ( !!
      @ ^ [Y0: $i > $i > $o] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( !!
                  @ ^ [Y3: $i] :
                      ( !!
                      @ ^ [Y4: $i > $i > $o] :
                          ( ( ( !!
                              @ ^ [Y5: $i > $i > $o] :
                                  ( ( ( !!
                                      @ ^ [Y6: $i] :
                                          ( !!
                                          @ ^ [Y7: $i] :
                                              ( ( Y0 @ Y6 @ Y7 )
                                             => ( Y5 @ Y6 @ Y7 ) ) ) )
                                    & ( !!
                                      @ ^ [Y6: $i] :
                                          ( !!
                                          @ ^ [Y7: $i] :
                                              ( !!
                                              @ ^ [Y8: $i] :
                                                  ( ( ( Y5 @ Y7 @ Y8 )
                                                    & ( Y5 @ Y6 @ Y7 ) )
                                                 => ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
                                 => ( Y5 @ Y2 @ Y3 ) ) )
                            & ( !!
                              @ ^ [Y5: $i > $i > $o] :
                                  ( ( ( !!
                                      @ ^ [Y6: $i] :
                                          ( !!
                                          @ ^ [Y7: $i] :
                                              ( ( Y0 @ Y6 @ Y7 )
                                             => ( Y5 @ Y6 @ Y7 ) ) ) )
                                    & ( !!
                                      @ ^ [Y6: $i] :
                                          ( !!
                                          @ ^ [Y7: $i] :
                                              ( !!
                                              @ ^ [Y8: $i] :
                                                  ( ( ( Y5 @ Y7 @ Y8 )
                                                    & ( Y5 @ Y6 @ Y7 ) )
                                                 => ( Y5 @ Y6 @ Y8 ) ) ) ) ) )
                                 => ( Y5 @ Y1 @ Y2 ) ) )
                            & ( !!
                              @ ^ [Y5: $i] :
                                  ( !!
                                  @ ^ [Y6: $i] :
                                      ( ( Y0 @ Y5 @ Y6 )
                                     => ( Y4 @ Y5 @ Y6 ) ) ) )
                            & ( !!
                              @ ^ [Y5: $i] :
                                  ( !!
                                  @ ^ [Y6: $i] :
                                      ( !!
                                      @ ^ [Y7: $i] :
                                          ( ( ( Y4 @ Y6 @ Y7 )
                                            & ( Y4 @ Y5 @ Y6 ) )
                                         => ( Y4 @ Y5 @ Y7 ) ) ) ) ) )
                         => ( Y4 @ Y1 @ Y3 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

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

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

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

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

thf(zip_derived_cl5,plain,
    ~ ( ( ( !!
          @ ^ [Y0: $i > $i > $o] :
              ( ( ( !!
                  @ ^ [Y1: $i] :
                      ( !!
                      @ ^ [Y2: $i] :
                          ( ( '#sk1' @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) )
                & ( !!
                  @ ^ [Y1: $i] :
                      ( !!
                      @ ^ [Y2: $i] :
                          ( !!
                          @ ^ [Y3: $i] :
                              ( ( ( Y0 @ Y2 @ Y3 )
                                & ( Y0 @ Y1 @ Y2 ) )
                             => ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
             => ( Y0 @ '#sk3' @ '#sk4' ) ) )
        & ( !!
          @ ^ [Y0: $i > $i > $o] :
              ( ( ( !!
                  @ ^ [Y1: $i] :
                      ( !!
                      @ ^ [Y2: $i] :
                          ( ( '#sk1' @ Y1 @ Y2 )
                         => ( Y0 @ Y1 @ Y2 ) ) ) )
                & ( !!
                  @ ^ [Y1: $i] :
                      ( !!
                      @ ^ [Y2: $i] :
                          ( !!
                          @ ^ [Y3: $i] :
                              ( ( ( Y0 @ Y2 @ Y3 )
                                & ( Y0 @ Y1 @ Y2 ) )
                             => ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
             => ( Y0 @ '#sk2' @ '#sk3' ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk5' @ Y0 @ Y1 ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk5' @ Y1 @ Y2 )
                        & ( '#sk5' @ Y0 @ Y1 ) )
                     => ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) )
     => ( '#sk5' @ '#sk2' @ '#sk4' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl6,plain,
    ( ( !!
      @ ^ [Y0: $i > $i > $o] :
          ( ( ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( '#sk1' @ Y1 @ Y2 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) )
            & ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( !!
                      @ ^ [Y3: $i] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
         => ( Y0 @ '#sk3' @ '#sk4' ) ) )
    & ( !!
      @ ^ [Y0: $i > $i > $o] :
          ( ( ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( '#sk1' @ Y1 @ Y2 )
                     => ( Y0 @ Y1 @ Y2 ) ) ) )
            & ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( !!
                      @ ^ [Y3: $i] :
                          ( ( ( Y0 @ Y2 @ Y3 )
                            & ( Y0 @ Y1 @ Y2 ) )
                         => ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
         => ( Y0 @ '#sk2' @ '#sk3' ) ) )
    & ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( '#sk1' @ Y0 @ Y1 )
             => ( '#sk5' @ Y0 @ Y1 ) ) ) )
    & ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( '#sk5' @ Y1 @ Y2 )
                    & ( '#sk5' @ Y0 @ Y1 ) )
                 => ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl9,plain,
    ( !!
    @ ^ [Y0: $i > $i > $o] :
        ( ( ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( '#sk1' @ Y1 @ Y2 )
                   => ( Y0 @ Y1 @ Y2 ) ) ) )
          & ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( !!
                    @ ^ [Y3: $i] :
                        ( ( ( Y0 @ Y2 @ Y3 )
                          & ( Y0 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
       => ( Y0 @ '#sk2' @ '#sk3' ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl15,plain,
    ! [X2: $i > $i > $o] :
      ( ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( X2 @ Y0 @ Y1 ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) ) )
     => ( X2 @ '#sk2' @ '#sk3' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl16,plain,
    ( ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) )
   => ( '#sk5' @ '#sk2' @ '#sk3' ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl158,plain,
    ( ~ ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk5' @ Y0 @ Y1 ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk5' @ Y1 @ Y2 )
                        & ( '#sk5' @ Y0 @ Y1 ) )
                     => ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) )
    | ( '#sk5' @ '#sk2' @ '#sk3' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl159,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
    | ( '#sk5' @ '#sk2' @ '#sk3' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl158]) ).

thf(zip_derived_cl8,plain,
    ( !!
    @ ^ [Y0: $i > $i > $o] :
        ( ( ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( '#sk1' @ Y1 @ Y2 )
                   => ( Y0 @ Y1 @ Y2 ) ) ) )
          & ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( !!
                    @ ^ [Y3: $i] :
                        ( ( ( Y0 @ Y2 @ Y3 )
                          & ( Y0 @ Y1 @ Y2 ) )
                       => ( Y0 @ Y1 @ Y3 ) ) ) ) ) )
       => ( Y0 @ '#sk3' @ '#sk4' ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl12,plain,
    ! [X2: $i > $i > $o] :
      ( ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( X2 @ Y0 @ Y1 ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) ) )
     => ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl20,plain,
    ! [X2: $i > $i > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: $i] :
                ( !!
                @ ^ [Y1: $i] :
                    ( ( '#sk1' @ Y0 @ Y1 )
                   => ( X2 @ Y0 @ Y1 ) ) ) )
          & ( !!
            @ ^ [Y0: $i] :
                ( !!
                @ ^ [Y1: $i] :
                    ( !!
                    @ ^ [Y2: $i] :
                        ( ( ( X2 @ Y1 @ Y2 )
                          & ( X2 @ Y0 @ Y1 ) )
                       => ( X2 @ Y0 @ Y2 ) ) ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl24,plain,
    ! [X2: $i > $i > $o] :
      ( ~ ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( X2 @ Y0 @ Y1 ) ) ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl28,plain,
    ! [X2: $i > $i > $o] :
      ( ~ ( !!
          @ ^ [Y0: $i] :
              ( ( '#sk1' @ ( '#sk46' @ X2 ) @ Y0 )
             => ( X2 @ ( '#sk46' @ X2 ) @ Y0 ) ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl24]) ).

thf(zip_derived_cl31,plain,
    ! [X2: $i > $i > $o] :
      ( ~ ( ( '#sk1' @ ( '#sk46' @ X2 ) @ ( '#sk66' @ X2 ) )
         => ( X2 @ ( '#sk46' @ X2 ) @ ( '#sk66' @ X2 ) ) )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) )
      | ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl34,plain,
    ! [X2: $i > $i > $o] :
      ( ( '#sk1' @ ( '#sk46' @ X2 ) @ ( '#sk66' @ X2 ) )
      | ( X2 @ '#sk3' @ '#sk4' )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl38,plain,
    ! [X2: $i > $i > $o] :
      ( ( '#form116' @ X2 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl160,plain,
    ( ~ ( '#form116' @ '#sk5' )
    | ( '#sk5' @ '#sk2' @ '#sk3' )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl159,zip_derived_cl38]) ).

thf(zip_derived_cl161,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ ( '#sk46' @ '#sk5' ) @ Y0 )
           => ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ Y0 ) ) )
    | ( '#sk5' @ '#sk2' @ '#sk3' )
    | ~ ( '#form116' @ '#sk5' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl160]) ).

thf(zip_derived_cl162,plain,
    ( ~ ( ( '#sk1' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) )
       => ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) ) )
    | ~ ( '#form116' @ '#sk5' )
    | ( '#sk5' @ '#sk2' @ '#sk3' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl161]) ).

thf(zip_derived_cl163,plain,
    ( ( '#sk1' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) )
    | ( '#sk5' @ '#sk2' @ '#sk3' )
    | ~ ( '#form116' @ '#sk5' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl162]) ).

thf(zip_derived_cl10,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( '#sk1' @ Y0 @ Y1 )
           => ( '#sk5' @ Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl18,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( '#sk1' @ X2 @ Y0 )
         => ( '#sk5' @ X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl22,plain,
    ! [X2: $i,X4: $i] :
      ( ( '#sk1' @ X2 @ X4 )
     => ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl26,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl165,plain,
    ( ~ ( '#form116' @ '#sk5' )
    | ( '#sk5' @ '#sk2' @ '#sk3' )
    | ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl163,zip_derived_cl26]) ).

thf(zip_derived_cl164,plain,
    ( ~ ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) )
    | ( '#sk5' @ '#sk2' @ '#sk3' )
    | ~ ( '#form116' @ '#sk5' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl162]) ).

thf(zip_derived_cl197,plain,
    ( ( '#sk5' @ '#sk2' @ '#sk3' )
    | ~ ( '#form116' @ '#sk5' ) ),
    inference(clc,[status(thm)],[zip_derived_cl165,zip_derived_cl164]) ).

thf(zip_derived_cl12_001,plain,
    ! [X2: $i > $i > $o] :
      ( ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( X2 @ Y0 @ Y1 ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) ) )
     => ( X2 @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl13,plain,
    ( ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) )
      & ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) )
   => ( '#sk5' @ '#sk3' @ '#sk4' ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl94,plain,
    ( ~ ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( '#sk1' @ Y0 @ Y1 )
                 => ( '#sk5' @ Y0 @ Y1 ) ) ) )
        & ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( '#sk5' @ Y1 @ Y2 )
                        & ( '#sk5' @ Y0 @ Y1 ) )
                     => ( '#sk5' @ Y0 @ Y2 ) ) ) ) ) )
    | ( '#sk5' @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl95,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk5' @ Y1 @ Y2 )
                      & ( '#sk5' @ Y0 @ Y1 ) )
                   => ( '#sk5' @ Y0 @ Y2 ) ) ) ) )
    | ( '#sk5' @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl94]) ).

thf(zip_derived_cl38_002,plain,
    ! [X2: $i > $i > $o] :
      ( ( '#form116' @ X2 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl96,plain,
    ( ~ ( '#form116' @ '#sk5' )
    | ( '#sk5' @ '#sk3' @ '#sk4' )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( '#sk1' @ Y0 @ Y1 )
               => ( '#sk5' @ Y0 @ Y1 ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl95,zip_derived_cl38]) ).

thf(zip_derived_cl97,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( '#sk1' @ ( '#sk46' @ '#sk5' ) @ Y0 )
           => ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ Y0 ) ) )
    | ( '#sk5' @ '#sk3' @ '#sk4' )
    | ~ ( '#form116' @ '#sk5' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl96]) ).

thf(zip_derived_cl98,plain,
    ( ~ ( ( '#sk1' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) )
       => ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) ) )
    | ~ ( '#form116' @ '#sk5' )
    | ( '#sk5' @ '#sk3' @ '#sk4' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl97]) ).

thf(zip_derived_cl99,plain,
    ( ( '#sk1' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) )
    | ( '#sk5' @ '#sk3' @ '#sk4' )
    | ~ ( '#form116' @ '#sk5' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl98]) ).

thf(zip_derived_cl26_003,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( '#sk1' @ X2 @ X4 )
      | ( '#sk5' @ X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl101,plain,
    ( ~ ( '#form116' @ '#sk5' )
    | ( '#sk5' @ '#sk3' @ '#sk4' )
    | ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl99,zip_derived_cl26]) ).

thf(zip_derived_cl100,plain,
    ( ~ ( '#sk5' @ ( '#sk46' @ '#sk5' ) @ ( '#sk66' @ '#sk5' ) )
    | ( '#sk5' @ '#sk3' @ '#sk4' )
    | ~ ( '#form116' @ '#sk5' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl98]) ).

thf(zip_derived_cl130,plain,
    ( ( '#sk5' @ '#sk3' @ '#sk4' )
    | ~ ( '#form116' @ '#sk5' ) ),
    inference(clc,[status(thm)],[zip_derived_cl101,zip_derived_cl100]) ).

thf(zip_derived_cl11,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( !!
            @ ^ [Y2: $i] :
                ( ( ( '#sk5' @ Y1 @ Y2 )
                  & ( '#sk5' @ Y0 @ Y1 ) )
               => ( '#sk5' @ Y0 @ Y2 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl19,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( ( '#sk5' @ Y0 @ Y1 )
                & ( '#sk5' @ X2 @ Y0 ) )
             => ( '#sk5' @ X2 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl23,plain,
    ! [X2: $i,X4: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( ( '#sk5' @ X4 @ Y0 )
            & ( '#sk5' @ X2 @ X4 ) )
         => ( '#sk5' @ X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl27,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( '#sk5' @ X4 @ X6 )
        & ( '#sk5' @ X2 @ X4 ) )
     => ( '#sk5' @ X2 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl30,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( '#sk5' @ X4 @ X6 )
          & ( '#sk5' @ X2 @ X4 ) )
      | ( '#sk5' @ X2 @ X6 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl33,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( '#sk5' @ X4 @ X6 )
      | ~ ( '#sk5' @ X2 @ X4 )
      | ( '#sk5' @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl131,plain,
    ! [X0: $i] :
      ( ~ ( '#form116' @ '#sk5' )
      | ( '#sk5' @ X0 @ '#sk4' )
      | ~ ( '#sk5' @ X0 @ '#sk3' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl130,zip_derived_cl33]) ).

thf(zip_derived_cl198,plain,
    ( ~ ( '#form116' @ '#sk5' )
    | ( '#sk5' @ '#sk2' @ '#sk4' )
    | ~ ( '#form116' @ '#sk5' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl197,zip_derived_cl131]) ).

thf(zip_derived_cl202,plain,
    ( ( '#sk5' @ '#sk2' @ '#sk4' )
    | ~ ( '#form116' @ '#sk5' ) ),
    inference(simplify,[status(thm)],[zip_derived_cl198]) ).

thf(zip_derived_cl7,plain,
    ~ ( '#sk5' @ '#sk2' @ '#sk4' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl204,plain,
    ~ ( '#form116' @ '#sk5' ),
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl7]) ).

thf(zip_derived_cl38_004,plain,
    ! [X2: $i > $i > $o] :
      ( ( '#form116' @ X2 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: $i] :
                      ( ( ( X2 @ Y1 @ Y2 )
                        & ( X2 @ Y0 @ Y1 ) )
                     => ( X2 @ Y0 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl39,plain,
    ! [X2: $i > $i > $o] :
      ( ~ ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: $i] :
                  ( ( ( X2 @ Y0 @ Y1 )
                    & ( X2 @ ( '#sk117' @ X2 ) @ Y0 ) )
                 => ( X2 @ ( '#sk117' @ X2 ) @ Y1 ) ) ) )
      | ( '#form116' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl44,plain,
    ! [X2: $i > $i > $o] :
      ( ~ ( !!
          @ ^ [Y0: $i] :
              ( ( ( X2 @ ( '#sk164' @ X2 ) @ Y0 )
                & ( X2 @ ( '#sk117' @ X2 ) @ ( '#sk164' @ X2 ) ) )
             => ( X2 @ ( '#sk117' @ X2 ) @ Y0 ) ) )
      | ( '#form116' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl48,plain,
    ! [X2: $i > $i > $o] :
      ( ~ ( ( ( X2 @ ( '#sk164' @ X2 ) @ ( '#sk213' @ X2 ) )
            & ( X2 @ ( '#sk117' @ X2 ) @ ( '#sk164' @ X2 ) ) )
         => ( X2 @ ( '#sk117' @ X2 ) @ ( '#sk213' @ X2 ) ) )
      | ( '#form116' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl49,plain,
    ! [X2: $i > $i > $o] :
      ( ( ( X2 @ ( '#sk164' @ X2 ) @ ( '#sk213' @ X2 ) )
        & ( X2 @ ( '#sk117' @ X2 ) @ ( '#sk164' @ X2 ) ) )
      | ( '#form116' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl52,plain,
    ! [X2: $i > $i > $o] :
      ( ( X2 @ ( '#sk117' @ X2 ) @ ( '#sk164' @ X2 ) )
      | ( '#form116' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl49]) ).

thf(zip_derived_cl51,plain,
    ! [X2: $i > $i > $o] :
      ( ( X2 @ ( '#sk164' @ X2 ) @ ( '#sk213' @ X2 ) )
      | ( '#form116' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl49]) ).

thf(zip_derived_cl33_005,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( '#sk5' @ X4 @ X6 )
      | ~ ( '#sk5' @ X2 @ X4 )
      | ( '#sk5' @ X2 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl57,plain,
    ! [X0: $i] :
      ( ( '#form116' @ '#sk5' )
      | ( '#sk5' @ X0 @ ( '#sk213' @ '#sk5' ) )
      | ~ ( '#sk5' @ X0 @ ( '#sk164' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl33]) ).

thf(zip_derived_cl204_006,plain,
    ~ ( '#form116' @ '#sk5' ),
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl7]) ).

thf(zip_derived_cl341,plain,
    ! [X0: $i] :
      ( ( '#sk5' @ X0 @ ( '#sk213' @ '#sk5' ) )
      | ~ ( '#sk5' @ X0 @ ( '#sk164' @ '#sk5' ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl57,zip_derived_cl204]) ).

thf(zip_derived_cl342,plain,
    ( ( '#form116' @ '#sk5' )
    | ( '#sk5' @ ( '#sk117' @ '#sk5' ) @ ( '#sk213' @ '#sk5' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl52,zip_derived_cl341]) ).

thf(zip_derived_cl204_007,plain,
    ~ ( '#form116' @ '#sk5' ),
    inference(clc,[status(thm)],[zip_derived_cl202,zip_derived_cl7]) ).

thf(zip_derived_cl343,plain,
    '#sk5' @ ( '#sk117' @ '#sk5' ) @ ( '#sk213' @ '#sk5' ),
    inference(demod,[status(thm)],[zip_derived_cl342,zip_derived_cl204]) ).

thf(zip_derived_cl50,plain,
    ! [X2: $i > $i > $o] :
      ( ~ ( X2 @ ( '#sk117' @ X2 ) @ ( '#sk213' @ X2 ) )
      | ( '#form116' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl441,plain,
    '#form116' @ '#sk5',
    inference('sup-',[status(thm)],[zip_derived_cl343,zip_derived_cl50]) ).

thf(zip_derived_cl448,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl204,zip_derived_cl441]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU463^1 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.utSov65BKU true
% 0.13/0.35  % Computer : n026.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug 24 01:22:01 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
% 0.20/0.68  % Total configuration time : 828
% 0.20/0.68  % Estimated wc time : 1656
% 0.20/0.68  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.75  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.20/0.75  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.20/0.76  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.20/0.77  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.20/0.77  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.20/0.77  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.20/0.77  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.44/1.40  % Solved by lams/35_full_unif4.sh.
% 1.44/1.40  % done 53 iterations in 0.596s
% 1.44/1.40  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.44/1.40  % SZS output start Refutation
% See solution above
% 1.44/1.40  
% 1.44/1.40  
% 1.44/1.40  % Terminating...
% 6.85/1.51  % Runner terminated.
% 6.85/1.52  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------