TSTP Solution File: LCL880^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : LCL880^1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.FYlKODQqGl true

% Computer : n009.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 09:02:31 EDT 2023

% Result   : Theorem 6.99s 1.47s
% Output   : Refutation 6.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   38
% Syntax   : Number of formulae    :  119 (  34 unt;  17 typ;   0 def)
%            Number of atoms       :  555 (  20 equ;  81 cnn)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives : 1431 ( 189   ~; 190   |;  35   &; 822   @)
%                                         (   6 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  122 ( 122   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  17 usr;  10 con; 0-3 aty)
%                                         ( 156  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  296 ( 196   ^; 100   !;   0   ?; 296   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mbox_type,type,
    mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf('#sk6_type',type,
    '#sk6': $i ).

thf(mnot_type,type,
    mnot: ( $i > $o ) > $i > $o ).

thf('#sk9_type',type,
    '#sk9': $i ).

thf(mimplies_type,type,
    mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf('#sk8_type',type,
    '#sk8': $i ).

thf('#form7_type',type,
    '#form7': $o ).

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

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

thf('#sk19_type',type,
    '#sk19': ( $i > $o ) > $i > $i ).

thf('#sk10_type',type,
    '#sk10': $i ).

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

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

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

thf(mor_type,type,
    mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mforall_prop_type,type,
    mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).

thf(mvalid_type,type,
    mvalid: ( $i > $o ) > $o ).

thf(mvalid,axiom,
    ( mvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ) ).

thf('0',plain,
    ( mvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mvalid]) ).

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

thf(mbox,axiom,
    ( mbox
    = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
        ! [V: $i] :
          ( ( Phi @ V )
          | ~ ( R @ W @ V ) ) ) ) ).

thf('2',plain,
    ( mbox
    = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
        ! [V: $i] :
          ( ( Phi @ V )
          | ~ ( R @ W @ V ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mbox]) ).

thf('3',plain,
    ( mbox
    = ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
        ! [X4: $i] :
          ( ( V_2 @ X4 )
          | ~ ( V_1 @ V_3 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(mforall_prop,axiom,
    ( mforall_prop
    = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
        ! [P: $i > $o] : ( Phi @ P @ W ) ) ) ).

thf('4',plain,
    ( mforall_prop
    = ( ^ [Phi: ( $i > $o ) > $i > $o,W: $i] :
        ! [P: $i > $o] : ( Phi @ P @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mforall_prop]) ).

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

thf(mimplies,axiom,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).

thf(mor,axiom,
    ( mor
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          | ( Psi @ W ) ) ) ) ).

thf('6',plain,
    ( mor
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          | ( Psi @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mor]) ).

thf('7',plain,
    ( mor
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
          ( ( V_1 @ V_3 )
          | ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(mnot,axiom,
    ( mnot
    = ( ^ [Phi: $i > $o,W: $i] :
          ~ ( Phi @ W ) ) ) ).

thf('8',plain,
    ( mnot
    = ( ^ [Phi: $i > $o,W: $i] :
          ~ ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mnot]) ).

thf('9',plain,
    ( mnot
    = ( ^ [V_1: $i > $o,V_2: $i] :
          ~ ( V_1 @ V_2 ) ) ),
    define([status(thm)]) ).

thf('10',plain,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies,'7','9']) ).

thf('11',plain,
    ( mimplies
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
    define([status(thm)]) ).

thf(conj,conjecture,
    ! [I: $i > $i > $o,J: $i > $i > $o] :
      ( ( mvalid
        @ ( mforall_prop
          @ ^ [Phi: $i > $o] : ( mimplies @ ( mnot @ ( mbox @ I @ Phi ) ) @ ( mbox @ J @ ( mnot @ ( mbox @ I @ Phi ) ) ) ) ) )
    <=> ! [U: $i,V: $i,W: $i] :
          ( ( ( J @ U @ V )
            & ( I @ U @ W ) )
         => ( I @ V @ W ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i > $i > $o,X6: $i > $i > $o] :
      ( ! [X8: $i,X10: $i > $o] :
          ( ! [X14: $i] :
              ( ~ ( X6 @ X8 @ X14 )
              | ~ ! [X16: $i] :
                    ( ~ ( X4 @ X14 @ X16 )
                    | ( X10 @ X16 ) ) )
          | ! [X12: $i] :
              ( ~ ( X4 @ X8 @ X12 )
              | ( X10 @ X12 ) ) )
    <=> ! [X18: $i,X20: $i,X22: $i] :
          ( ( ( X4 @ X18 @ X22 )
            & ( X6 @ X18 @ X20 ) )
         => ( X4 @ X20 @ X22 ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i > $i > $o,X6: $i > $i > $o] :
        ( ! [X8: $i,X10: $i > $o] :
            ( ! [X14: $i] :
                ( ~ ( X6 @ X8 @ X14 )
                | ~ ! [X16: $i] :
                      ( ~ ( X4 @ X14 @ X16 )
                      | ( X10 @ X16 ) ) )
            | ! [X12: $i] :
                ( ~ ( X4 @ X8 @ X12 )
                | ( X10 @ X12 ) ) )
      <=> ! [X18: $i,X20: $i,X22: $i] :
            ( ( ( X4 @ X18 @ X22 )
              & ( X6 @ X18 @ X20 ) )
           => ( X4 @ X20 @ X22 ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

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

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

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

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

thf(zip_derived_cl5,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( (~) @ ( '#sk2' @ Y0 @ Y2 ) )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y3: $i] :
                              ( ( (~) @ ( '#sk1' @ Y2 @ Y3 ) )
                              | ( Y1 @ Y3 ) ) ) ) ) )
                | ( !!
                  @ ^ [Y2: $i] :
                      ( ( (~) @ ( '#sk1' @ Y0 @ Y2 ) )
                      | ( Y1 @ Y2 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl3]) ).

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

thf(zip_derived_cl7,plain,
    ( ~ ( ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( '#sk2' @ '#sk3' @ Y0 ) )
              | ( (~)
                @ ( !!
                  @ ^ [Y1: $i] :
                      ( ( (~) @ ( '#sk1' @ Y0 @ Y1 ) )
                      | ( '#sk4' @ Y1 ) ) ) ) ) )
        | ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( '#sk1' @ '#sk3' @ Y0 ) )
              | ( '#sk4' @ Y0 ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl9,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( '#sk1' @ '#sk3' @ Y0 ) )
            | ( '#sk4' @ Y0 ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl11,plain,
    ( ~ ( ( (~) @ ( '#sk1' @ '#sk3' @ '#sk6' ) )
        | ( '#sk4' @ '#sk6' ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl14,plain,
    ( '#form7'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl15,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( ( '#sk1' @ '#sk8' @ Y1 )
                  & ( '#sk2' @ '#sk8' @ Y0 ) )
               => ( '#sk1' @ Y0 @ Y1 ) ) ) )
    | '#form7' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl21,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( ( '#sk1' @ '#sk8' @ Y0 )
              & ( '#sk2' @ '#sk8' @ '#sk9' ) )
           => ( '#sk1' @ '#sk9' @ Y0 ) ) )
    | '#form7' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl23,plain,
    ( ~ ( ( ( '#sk1' @ '#sk8' @ '#sk10' )
          & ( '#sk2' @ '#sk8' @ '#sk9' ) )
       => ( '#sk1' @ '#sk9' @ '#sk10' ) )
    | '#form7' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl26,plain,
    ( ~ ( '#sk1' @ '#sk9' @ '#sk10' )
    | '#form7' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl8,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( '#sk2' @ '#sk3' @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( '#sk1' @ Y0 @ Y1 ) )
                    | ( '#sk4' @ Y1 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl10,plain,
    ( ~ ( ( (~) @ ( '#sk2' @ '#sk3' @ '#sk5' ) )
        | ( (~)
          @ ( !!
            @ ^ [Y0: $i] :
                ( ( (~) @ ( '#sk1' @ '#sk5' @ Y0 ) )
                | ( '#sk4' @ Y0 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl13,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( '#sk1' @ '#sk5' @ Y0 ) )
          | ( '#sk4' @ Y0 ) ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl14_001,plain,
    ( '#form7'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl18,plain,
    ( ~ '#form7'
    | ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( '#sk1' @ '#sk5' @ Y0 ) )
          | ( '#sk4' @ Y0 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl13,zip_derived_cl14]) ).

thf(zip_derived_cl22,plain,
    ! [X2: $i] :
      ( ( (~) @ ( '#sk1' @ '#sk5' @ X2 ) )
      | ( '#sk4' @ X2 )
      | ~ '#form7' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl24,plain,
    ! [X2: $i] :
      ( ~ ( '#sk1' @ '#sk5' @ X2 )
      | ( '#sk4' @ X2 )
      | ~ '#form7' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl11_002,plain,
    ( ~ ( ( (~) @ ( '#sk1' @ '#sk3' @ '#sk6' ) )
        | ( '#sk4' @ '#sk6' ) )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl14_003,plain,
    ( '#form7'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl16,plain,
    ( ~ '#form7'
    | ~ ( ( (~) @ ( '#sk1' @ '#sk3' @ '#sk6' ) )
        | ( '#sk4' @ '#sk6' ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl11,zip_derived_cl14]) ).

thf(zip_derived_cl19,plain,
    ( ( '#sk1' @ '#sk3' @ '#sk6' )
    | ~ '#form7' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl12,plain,
    ( ( '#sk2' @ '#sk3' @ '#sk5' )
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl14_004,plain,
    ( '#form7'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl17,plain,
    ( ~ '#form7'
    | ( '#sk2' @ '#sk3' @ '#sk5' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl12,zip_derived_cl14]) ).

thf(zip_derived_cl3_005,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( '#sk2' @ Y0 @ Y2 ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y3: $i] :
                            ( ( (~) @ ( '#sk1' @ Y2 @ Y3 ) )
                            | ( Y1 @ Y3 ) ) ) ) ) )
              | ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( '#sk1' @ Y0 @ Y2 ) )
                    | ( Y1 @ Y2 ) ) ) ) ) )
   != ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( '#sk1' @ Y0 @ Y2 )
                    & ( '#sk2' @ Y0 @ Y1 ) )
                 => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl2]) ).

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

thf(zip_derived_cl29,plain,
    ( ~ '#form7'
    | ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( '#sk1' @ Y0 @ Y2 )
                    & ( '#sk2' @ Y0 @ Y1 ) )
                 => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl30,plain,
    ! [X2: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( ( '#sk1' @ X2 @ Y1 )
                  & ( '#sk2' @ X2 @ Y0 ) )
               => ( '#sk1' @ Y0 @ Y1 ) ) ) )
      | ~ '#form7' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).

thf(zip_derived_cl33,plain,
    ! [X2: $i,X4: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( ( '#sk1' @ X2 @ Y0 )
              & ( '#sk2' @ X2 @ X4 ) )
           => ( '#sk1' @ X4 @ Y0 ) ) )
      | ~ '#form7' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl30]) ).

thf(zip_derived_cl38,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ( ( ( '#sk1' @ X2 @ X6 )
          & ( '#sk2' @ X2 @ X4 ) )
       => ( '#sk1' @ X4 @ X6 ) )
      | ~ '#form7' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl40,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( ( '#sk1' @ X2 @ X6 )
          & ( '#sk2' @ X2 @ X4 ) )
      | ( '#sk1' @ X4 @ X6 )
      | ~ '#form7' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl42,plain,
    ! [X2: $i,X4: $i,X6: $i] :
      ( ~ ( '#sk1' @ X2 @ X6 )
      | ~ ( '#sk2' @ X2 @ X4 )
      | ~ '#form7'
      | ( '#sk1' @ X4 @ X6 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl40]) ).

thf(zip_derived_cl52,plain,
    ! [X0: $i] :
      ( ~ '#form7'
      | ( '#sk1' @ '#sk5' @ X0 )
      | ~ '#form7'
      | ~ ( '#sk1' @ '#sk3' @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl42]) ).

thf(zip_derived_cl55,plain,
    ! [X0: $i] :
      ( ~ ( '#sk1' @ '#sk3' @ X0 )
      | ( '#sk1' @ '#sk5' @ X0 )
      | ~ '#form7' ),
    inference(simplify,[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl57,plain,
    ( ~ '#form7'
    | ~ '#form7'
    | ( '#sk1' @ '#sk5' @ '#sk6' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl19,zip_derived_cl55]) ).

thf(zip_derived_cl59,plain,
    ( ( '#sk1' @ '#sk5' @ '#sk6' )
    | ~ '#form7' ),
    inference(simplify,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl62,plain,
    ( ~ '#form7'
    | ( '#sk4' @ '#sk6' )
    | ~ '#form7' ),
    inference('sup+',[status(thm)],[zip_derived_cl24,zip_derived_cl59]) ).

thf(zip_derived_cl65,plain,
    ( ( '#sk4' @ '#sk6' )
    | ~ '#form7' ),
    inference(simplify,[status(thm)],[zip_derived_cl62]) ).

thf(zip_derived_cl20,plain,
    ( ~ ( '#sk4' @ '#sk6' )
    | ~ '#form7' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl69,plain,
    ~ '#form7',
    inference(clc,[status(thm)],[zip_derived_cl65,zip_derived_cl20]) ).

thf(zip_derived_cl70,plain,
    ~ ( '#sk1' @ '#sk9' @ '#sk10' ),
    inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl69]) ).

thf(zip_derived_cl25,plain,
    ( ( ( '#sk1' @ '#sk8' @ '#sk10' )
      & ( '#sk2' @ '#sk8' @ '#sk9' ) )
    | '#form7' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl27,plain,
    ( ( '#sk1' @ '#sk8' @ '#sk10' )
    | '#form7' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl69_006,plain,
    ~ '#form7',
    inference(clc,[status(thm)],[zip_derived_cl65,zip_derived_cl20]) ).

thf(zip_derived_cl71,plain,
    '#sk1' @ '#sk8' @ '#sk10',
    inference(demod,[status(thm)],[zip_derived_cl27,zip_derived_cl69]) ).

thf(zip_derived_cl28,plain,
    ( ( '#sk2' @ '#sk8' @ '#sk9' )
    | '#form7' ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl69_007,plain,
    ~ '#form7',
    inference(clc,[status(thm)],[zip_derived_cl65,zip_derived_cl20]) ).

thf(zip_derived_cl72,plain,
    '#sk2' @ '#sk8' @ '#sk9',
    inference(demod,[status(thm)],[zip_derived_cl28,zip_derived_cl69]) ).

thf(zip_derived_cl4_008,plain,
    ( ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( '#sk2' @ Y0 @ Y2 ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y3: $i] :
                            ( ( (~) @ ( '#sk1' @ Y2 @ Y3 ) )
                            | ( Y1 @ Y3 ) ) ) ) ) )
              | ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( '#sk1' @ Y0 @ Y2 ) )
                    | ( Y1 @ Y2 ) ) ) ) ) )
    | ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( '#sk1' @ Y0 @ Y2 )
                    & ( '#sk2' @ Y0 @ Y1 ) )
                 => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl29_009,plain,
    ( ~ '#form7'
    | ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( !!
              @ ^ [Y2: $i] :
                  ( ( ( '#sk1' @ Y0 @ Y2 )
                    & ( '#sk2' @ Y0 @ Y1 ) )
                 => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl14_010,plain,
    ( '#form7'
    | ~ ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( !!
                @ ^ [Y2: $i] :
                    ( ( ( '#sk1' @ Y0 @ Y2 )
                      & ( '#sk2' @ Y0 @ Y1 ) )
                   => ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl31,plain,
    ( '#form7'
    | ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i > $o] :
              ( ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( '#sk2' @ Y0 @ Y2 ) )
                    | ( (~)
                      @ ( !!
                        @ ^ [Y3: $i] :
                            ( ( (~) @ ( '#sk1' @ Y2 @ Y3 ) )
                            | ( Y1 @ Y3 ) ) ) ) ) )
              | ( !!
                @ ^ [Y2: $i] :
                    ( ( (~) @ ( '#sk1' @ Y0 @ Y2 ) )
                    | ( Y1 @ Y2 ) ) ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl4,zip_derived_cl29,zip_derived_cl14]) ).

thf(zip_derived_cl32,plain,
    ! [X2: $i] :
      ( ( !!
        @ ^ [Y0: $i > $o] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( '#sk2' @ X2 @ Y1 ) )
                  | ( (~)
                    @ ( !!
                      @ ^ [Y2: $i] :
                          ( ( (~) @ ( '#sk1' @ Y1 @ Y2 ) )
                          | ( Y0 @ Y2 ) ) ) ) ) )
            | ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( '#sk1' @ X2 @ Y1 ) )
                  | ( Y0 @ Y1 ) ) ) ) )
      | '#form7' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl34,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( '#sk2' @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( '#sk1' @ Y0 @ Y1 ) )
                    | ( X4 @ Y1 ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( '#sk1' @ X2 @ Y0 ) )
            | ( X4 @ Y0 ) ) )
      | '#form7' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl39,plain,
    ! [X2: $i,X4: $i > $o] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( '#sk2' @ X2 @ Y0 ) )
            | ( (~)
              @ ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( '#sk1' @ Y0 @ Y1 ) )
                    | ( X4 @ Y1 ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( '#sk1' @ X2 @ Y0 ) )
            | ( X4 @ Y0 ) ) )
      | '#form7' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl41,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ( (~) @ ( '#sk2' @ X2 @ X6 ) )
      | ( (~)
        @ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( '#sk1' @ X6 @ Y0 ) )
              | ( X4 @ Y0 ) ) ) )
      | '#form7'
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( '#sk1' @ X2 @ Y0 ) )
            | ( X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl43,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( '#sk2' @ X2 @ X6 )
      | ~ ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( '#sk1' @ X6 @ Y0 ) )
              | ( X4 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( '#sk1' @ X2 @ Y0 ) )
            | ( X4 @ Y0 ) ) )
      | '#form7' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl41]) ).

thf(zip_derived_cl44,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( ( (~) @ ( '#sk1' @ X6 @ ( '#sk19' @ X4 @ X6 ) ) )
          | ( X4 @ ( '#sk19' @ X4 @ X6 ) ) )
      | '#form7'
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( '#sk1' @ X2 @ Y0 ) )
            | ( X4 @ Y0 ) ) )
      | ~ ( '#sk2' @ X2 @ X6 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl45,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ( '#sk1' @ X6 @ ( '#sk19' @ X4 @ X6 ) )
      | ~ ( '#sk2' @ X2 @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( '#sk1' @ X2 @ Y0 ) )
            | ( X4 @ Y0 ) ) )
      | '#form7' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl47,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ( (~) @ ( '#sk1' @ X2 @ X8 ) )
      | ( X4 @ X8 )
      | '#form7'
      | ~ ( '#sk2' @ X2 @ X6 )
      | ( '#sk1' @ X6 @ ( '#sk19' @ X4 @ X6 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl49,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( '#sk1' @ X2 @ X8 )
      | ( X4 @ X8 )
      | ( '#sk1' @ X6 @ ( '#sk19' @ X4 @ X6 ) )
      | ~ ( '#sk2' @ X2 @ X6 )
      | '#form7' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl69_011,plain,
    ~ '#form7',
    inference(clc,[status(thm)],[zip_derived_cl65,zip_derived_cl20]) ).

thf(zip_derived_cl359,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( '#sk1' @ X2 @ X8 )
      | ( X4 @ X8 )
      | ( '#sk1' @ X6 @ ( '#sk19' @ X4 @ X6 ) )
      | ~ ( '#sk2' @ X2 @ X6 ) ),
    inference(demod,[status(thm)],[zip_derived_cl49,zip_derived_cl69]) ).

thf(zip_derived_cl360,plain,
    ! [X0: $i > $o,X1: $i] :
      ( ( '#sk1' @ '#sk9' @ ( '#sk19' @ X0 @ '#sk9' ) )
      | ( X0 @ X1 )
      | ~ ( '#sk1' @ '#sk8' @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl72,zip_derived_cl359]) ).

thf(zip_derived_cl415,plain,
    ! [X0: $i > $o] :
      ( ( X0 @ '#sk10' )
      | ( '#sk1' @ '#sk9' @ ( '#sk19' @ X0 @ '#sk9' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl71,zip_derived_cl360]) ).

thf(zip_derived_cl72_012,plain,
    '#sk2' @ '#sk8' @ '#sk9',
    inference(demod,[status(thm)],[zip_derived_cl28,zip_derived_cl69]) ).

thf(zip_derived_cl71_013,plain,
    '#sk1' @ '#sk8' @ '#sk10',
    inference(demod,[status(thm)],[zip_derived_cl27,zip_derived_cl69]) ).

thf(zip_derived_cl46,plain,
    ! [X2: $i,X4: $i > $o,X6: $i] :
      ( ~ ( X4 @ ( '#sk19' @ X4 @ X6 ) )
      | ~ ( '#sk2' @ X2 @ X6 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( '#sk1' @ X2 @ Y0 ) )
            | ( X4 @ Y0 ) ) )
      | '#form7' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl48,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ( (~) @ ( '#sk1' @ X2 @ X8 ) )
      | ( X4 @ X8 )
      | '#form7'
      | ~ ( '#sk2' @ X2 @ X6 )
      | ~ ( X4 @ ( '#sk19' @ X4 @ X6 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl50,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( '#sk1' @ X2 @ X8 )
      | ( X4 @ X8 )
      | ~ ( X4 @ ( '#sk19' @ X4 @ X6 ) )
      | ~ ( '#sk2' @ X2 @ X6 )
      | '#form7' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl48]) ).

thf(zip_derived_cl69_014,plain,
    ~ '#form7',
    inference(clc,[status(thm)],[zip_derived_cl65,zip_derived_cl20]) ).

thf(zip_derived_cl78,plain,
    ! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
      ( ~ ( '#sk1' @ X2 @ X8 )
      | ( X4 @ X8 )
      | ~ ( X4 @ ( '#sk19' @ X4 @ X6 ) )
      | ~ ( '#sk2' @ X2 @ X6 ) ),
    inference(demod,[status(thm)],[zip_derived_cl50,zip_derived_cl69]) ).

thf(zip_derived_cl79,plain,
    ! [X0: $i,X1: $i > $o] :
      ( ~ ( '#sk2' @ '#sk8' @ X0 )
      | ~ ( X1 @ ( '#sk19' @ X1 @ X0 ) )
      | ( X1 @ '#sk10' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl71,zip_derived_cl78]) ).

thf(zip_derived_cl114,plain,
    ! [X0: $i > $o] :
      ( ( X0 @ '#sk10' )
      | ~ ( X0 @ ( '#sk19' @ X0 @ '#sk9' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl72,zip_derived_cl79]) ).

thf(zip_derived_cl442,plain,
    ( ( '#sk1' @ '#sk9' @ '#sk10' )
    | ( '#sk1' @ '#sk9' @ '#sk10' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl415,zip_derived_cl114]) ).

thf(zip_derived_cl493,plain,
    '#sk1' @ '#sk9' @ '#sk10',
    inference(simplify,[status(thm)],[zip_derived_cl442]) ).

thf(zip_derived_cl551,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl70,zip_derived_cl493]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14  % Problem  : LCL880^1 : TPTP v8.1.2. Released v5.2.0.
% 0.09/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.FYlKODQqGl true
% 0.11/0.34  % Computer : n009.cluster.edu
% 0.11/0.34  % Model    : x86_64 x86_64
% 0.11/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34  % Memory   : 8042.1875MB
% 0.11/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34  % CPULimit : 300
% 0.11/0.34  % WCLimit  : 300
% 0.11/0.34  % DateTime : Fri Aug 25 05:43:06 EDT 2023
% 0.11/0.34  % CPUTime  : 
% 0.11/0.34  % Running portfolio for 300 s
% 0.11/0.34  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.34  % Number of cores: 8
% 0.11/0.34  % Python version: Python 3.6.8
% 0.11/0.34  % Running in HO mode
% 0.16/0.58  % Total configuration time : 828
% 0.16/0.58  % Estimated wc time : 1656
% 0.16/0.58  % Estimated cpu time (8 cpus) : 207.0
% 0.16/0.65  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.16/0.67  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.16/0.67  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.16/0.69  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.16/0.69  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.16/0.69  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.16/0.69  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.16/0.70  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.36/0.83  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 6.99/1.46  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 6.99/1.47  % Solved by lams/30_sp5.sh.
% 6.99/1.47  % done 76 iterations in 0.695s
% 6.99/1.47  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 6.99/1.47  % SZS output start Refutation
% See solution above
% 6.99/1.47  
% 6.99/1.47  
% 6.99/1.47  % Terminating...
% 7.79/1.68  % Runner terminated.
% 7.79/1.69  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------