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Zipperpin---2.1.9999.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : PHI004^2 : TPTP v9.2.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.6ApaTgZeyi true

% Computer : n023.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 Oct  2 04:49:03 PM UTC 2025

% Result   : Theorem 4.02s 1.26s
% Output   : Refutation 4.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   31
% Syntax   : Number of formulae    :  124 (  48 unt;   0 typ;   0 def)
%            Number of atoms       :  447 (  41 equ;  43 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives : 1176 ( 128   ~;  89   |;   9   &; 788   @)
%                                         (   7 <=>;  83  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  263 ( 263   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  20 usr;   8 con; 0-3 aty)
%                                         (  72  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  291 ( 205   ^;  86   !;   0   ?; 291   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mu_type,type,
    mu: $tType ).

thf('#sk122_type',type,
    '#sk122': mu ).

thf('#sk125_type',type,
    '#sk125': mu > $i > $o ).

thf(essence_type,type,
    essence: ( mu > $i > $o ) > mu > $i > $o ).

thf(mand_type,type,
    mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(rel_type,type,
    rel: $i > $i > $o ).

thf(positive_type,type,
    positive: ( mu > $i > $o ) > $i > $o ).

thf('#sk130_type',type,
    '#sk130': mu ).

thf('#sk128_type',type,
    '#sk128': mu > $i > $o ).

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

thf(mforall_ind_type,type,
    mforall_ind: ( mu > $i > $o ) > $i > $o ).

thf(mbox_generic_type,type,
    mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf('#sk129_type',type,
    '#sk129': $i ).

thf(mequiv_type,type,
    mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(mforall_indset_type,type,
    mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).

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

thf(god_type,type,
    god: mu > $i > $o ).

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

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

thf('#form131_type',type,
    '#form131': $o ).

thf('#sk121_type',type,
    '#sk121': $i ).

thf(defD2,axiom,
    ( essence
    = ( ^ [Phi: mu > $i > $o,X: mu] :
          ( mand @ ( Phi @ X )
          @ ( mforall_indset
            @ ^ [Psi: mu > $i > $o] :
                ( mimplies @ ( Psi @ X )
                @ ( mbox
                  @ ( mforall_ind
                    @ ^ [Y: mu] : ( mimplies @ ( Phi @ Y ) @ ( Psi @ Y ) ) ) ) ) ) ) ) ) ).

thf(mbox,axiom,
    ( mbox
    = ( mbox_generic @ rel ) ) ).

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

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

thf('1',plain,
    ( mbox_generic
    = ( ^ [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('2',plain,
    ( mbox
    = ( mbox_generic @ rel ) ),
    inference(simplify_rw_rule,[status(thm)],[mbox,'1']) ).

thf('3',plain,
    ( mbox
    = ( mbox_generic @ rel ) ),
    define([status(thm)]) ).

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

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

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

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

thf('6',plain,
    ( mforall_ind
    = ( ^ [Phi: mu > $i > $o,W: $i] :
        ! [X: mu] : ( Phi @ X @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mforall_ind]) ).

thf('7',plain,
    ( mforall_ind
    = ( ^ [V_1: mu > $i > $o,V_2: $i] :
        ! [X4: mu] : ( V_1 @ X4 @ V_2 ) ) ),
    define([status(thm)]) ).

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

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

thf('9',plain,
    ( mimplies
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
          ( ( V_1 @ V_3 )
         => ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

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

thf('10',plain,
    ( mand
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          & ( Psi @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mand]) ).

thf('11',plain,
    ( mand
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
          ( ( V_1 @ V_3 )
          & ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf('12',plain,
    ( essence
    = ( ^ [Phi: mu > $i > $o,X: mu] :
          ( mand @ ( Phi @ X )
          @ ( mforall_indset
            @ ^ [Psi: mu > $i > $o] :
                ( mimplies @ ( Psi @ X )
                @ ( mbox
                  @ ( mforall_ind
                    @ ^ [Y: mu] : ( mimplies @ ( Phi @ Y ) @ ( Psi @ Y ) ) ) ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[defD2,'3','1','5','7','9','11']) ).

thf('13',plain,
    ( essence
    = ( ^ [V_1: mu > $i > $o,V_2: mu] :
          ( mand @ ( V_1 @ V_2 )
          @ ( mforall_indset
            @ ^ [V_3: mu > $i > $o] :
                ( mimplies @ ( V_3 @ V_2 )
                @ ( mbox
                  @ ( mforall_ind
                    @ ^ [V_4: mu] : ( mimplies @ ( V_1 @ V_4 ) @ ( V_3 @ V_4 ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(defD1,axiom,
    ( god
    = ( ^ [X: mu] :
          ( mforall_indset
          @ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ) ).

thf('14',plain,
    ( god
    = ( ^ [X: mu] :
          ( mforall_indset
          @ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[defD1,'5','9']) ).

thf('15',plain,
    ( god
    = ( ^ [V_1: mu] :
          ( mforall_indset
          @ ^ [V_2: mu > $i > $o] : ( mimplies @ ( positive @ V_2 ) @ ( V_2 @ V_1 ) ) ) ) ),
    define([status(thm)]) ).

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

thf('16',plain,
    ( mvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mvalid]) ).

thf('17',plain,
    ( mvalid
    = ( ^ [V_1: $i > $o] :
        ! [X4: $i] : ( V_1 @ X4 ) ) ),
    define([status(thm)]) ).

thf(thmT2,conjecture,
    ( mvalid
    @ ( mforall_ind
      @ ^ [X: mu] : ( mimplies @ ( god @ X ) @ ( essence @ god @ X ) ) ) ) ).

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

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

thf(zip_derived_cl2,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: mu] :
              ( ( !!
                @ ^ [Y2: mu > $i > $o] :
                    ( ( positive @ Y2 @ Y0 )
                   => ( Y2 @ Y1 @ Y0 ) ) )
             => ( ( !!
                  @ ^ [Y2: mu > $i > $o] :
                      ( ( Y2 @ Y1 @ Y0 )
                     => ( !!
                        @ ^ [Y3: $i] :
                            ( ( (~) @ ( rel @ Y0 @ Y3 ) )
                            | ( !!
                              @ ^ [Y4: mu] :
                                  ( ( !!
                                    @ ^ [Y5: mu > $i > $o] :
                                        ( ( positive @ Y5 @ Y3 )
                                       => ( Y5 @ Y4 @ Y3 ) ) )
                                 => ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) )
                & ( !!
                  @ ^ [Y2: mu > $i > $o] :
                      ( ( positive @ Y2 @ Y0 )
                     => ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl33,plain,
    ~ ( !!
      @ ^ [Y0: mu] :
          ( ( !!
            @ ^ [Y1: mu > $i > $o] :
                ( ( positive @ Y1 @ '#sk121' )
               => ( Y1 @ Y0 @ '#sk121' ) ) )
         => ( ( !!
              @ ^ [Y1: mu > $i > $o] :
                  ( ( Y1 @ Y0 @ '#sk121' )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( (~) @ ( rel @ '#sk121' @ Y2 ) )
                        | ( !!
                          @ ^ [Y3: mu] :
                              ( ( !!
                                @ ^ [Y4: mu > $i > $o] :
                                    ( ( positive @ Y4 @ Y2 )
                                   => ( Y4 @ Y3 @ Y2 ) ) )
                             => ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
            & ( !!
              @ ^ [Y1: mu > $i > $o] :
                  ( ( positive @ Y1 @ '#sk121' )
                 => ( Y1 @ Y0 @ '#sk121' ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl34,plain,
    ~ ( ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) )
     => ( ( !!
          @ ^ [Y0: mu > $i > $o] :
              ( ( Y0 @ '#sk122' @ '#sk121' )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel @ '#sk121' @ Y1 ) )
                    | ( !!
                      @ ^ [Y2: mu] :
                          ( ( !!
                            @ ^ [Y3: mu > $i > $o] :
                                ( ( positive @ Y3 @ Y1 )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                         => ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
        & ( !!
          @ ^ [Y0: mu > $i > $o] :
              ( ( positive @ Y0 @ '#sk121' )
             => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl36,plain,
    ~ ( ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( Y0 @ '#sk122' @ '#sk121' )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel @ '#sk121' @ Y1 ) )
                  | ( !!
                    @ ^ [Y2: mu] :
                        ( ( !!
                          @ ^ [Y3: mu > $i > $o] :
                              ( ( positive @ Y3 @ Y1 )
                             => ( Y3 @ Y2 @ Y1 ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
      & ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl39,plain,
    ( ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( Y0 @ '#sk122' @ '#sk121' )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel @ '#sk121' @ Y1 ) )
                  | ( !!
                    @ ^ [Y2: mu] :
                        ( ( !!
                          @ ^ [Y3: mu > $i > $o] :
                              ( ( positive @ Y3 @ Y1 )
                             => ( Y3 @ Y2 @ Y1 ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl44,plain,
    ( ~ ( ( '#sk125' @ '#sk122' @ '#sk121' )
       => ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel @ '#sk121' @ Y0 ) )
              | ( !!
                @ ^ [Y1: mu] :
                    ( ( !!
                      @ ^ [Y2: mu > $i > $o] :
                          ( ( positive @ Y2 @ Y0 )
                         => ( Y2 @ Y1 @ Y0 ) ) )
                   => ( '#sk125' @ Y1 @ Y0 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl39]) ).

thf(zip_derived_cl46,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel @ '#sk121' @ Y0 ) )
            | ( !!
              @ ^ [Y1: mu] :
                  ( ( !!
                    @ ^ [Y2: mu > $i > $o] :
                        ( ( positive @ Y2 @ Y0 )
                       => ( Y2 @ Y1 @ Y0 ) ) )
                 => ( '#sk125' @ Y1 @ Y0 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl51,plain,
    ( ~ ( ( (~) @ ( rel @ '#sk121' @ '#sk129' ) )
        | ( !!
          @ ^ [Y0: mu] :
              ( ( !!
                @ ^ [Y1: mu > $i > $o] :
                    ( ( positive @ Y1 @ '#sk129' )
                   => ( Y1 @ Y0 @ '#sk129' ) ) )
             => ( '#sk125' @ Y0 @ '#sk129' ) ) ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl55,plain,
    ( ~ ( !!
        @ ^ [Y0: mu] :
            ( ( !!
              @ ^ [Y1: mu > $i > $o] :
                  ( ( positive @ Y1 @ '#sk129' )
                 => ( Y1 @ Y0 @ '#sk129' ) ) )
           => ( '#sk125' @ Y0 @ '#sk129' ) ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl57,plain,
    ( ~ ( ( !!
          @ ^ [Y0: mu > $i > $o] :
              ( ( positive @ Y0 @ '#sk129' )
             => ( Y0 @ '#sk130' @ '#sk129' ) ) )
       => ( '#sk125' @ '#sk130' @ '#sk129' ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl55]) ).

thf(zip_derived_cl60,plain,
    ( ( !!
      @ ^ [Y0: mu > $i > $o] :
          ( ( positive @ Y0 @ '#sk129' )
         => ( Y0 @ '#sk130' @ '#sk129' ) ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl62,plain,
    ! [X2: mu > $i > $o] :
      ( ( ( positive @ X2 @ '#sk129' )
       => ( X2 @ '#sk130' @ '#sk129' ) )
      | ~ ( !!
          @ ^ [Y0: mu > $i > $o] :
              ( ( positive @ Y0 @ '#sk121' )
             => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl60]) ).

thf(zip_derived_cl64,plain,
    ( ( ( positive @ '#sk125' @ '#sk129' )
     => ( '#sk125' @ '#sk130' @ '#sk129' ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl62]) ).

thf(zip_derived_cl61,plain,
    ( ~ ( '#sk125' @ '#sk130' @ '#sk129' )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl61_001,plain,
    ( ~ ( '#sk125' @ '#sk130' @ '#sk129' )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).

thf(zip_derived_cl66,plain,
    ( '#form131'
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl68,plain,
    ( ~ '#form131'
    | ~ ( '#sk125' @ '#sk130' @ '#sk129' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl61,zip_derived_cl66]) ).

thf(zip_derived_cl66_002,plain,
    ( '#form131'
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl67,plain,
    ( ~ ( ( positive @ '#sk128' @ '#sk121' )
       => ( '#sk128' @ '#sk122' @ '#sk121' ) )
    | '#form131' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl66]) ).

thf(zip_derived_cl70,plain,
    ( ( positive @ '#sk128' @ '#sk121' )
    | '#form131' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl35,plain,
    ( !!
    @ ^ [Y0: mu > $i > $o] :
        ( ( positive @ Y0 @ '#sk121' )
       => ( Y0 @ '#sk122' @ '#sk121' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl37,plain,
    ! [X2: mu > $i > $o] :
      ( ( positive @ X2 @ '#sk121' )
     => ( X2 @ '#sk122' @ '#sk121' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl40,plain,
    ! [X2: mu > $i > $o] :
      ( ~ ( positive @ X2 @ '#sk121' )
      | ( X2 @ '#sk122' @ '#sk121' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl89,plain,
    ( '#form131'
    | ( '#sk128' @ '#sk122' @ '#sk121' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl70,zip_derived_cl40]) ).

thf(zip_derived_cl71,plain,
    ( ~ ( '#sk128' @ '#sk122' @ '#sk121' )
    | '#form131' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl106,plain,
    '#form131',
    inference(clc,[status(thm)],[zip_derived_cl89,zip_derived_cl71]) ).

thf(zip_derived_cl107,plain,
    ~ ( '#sk125' @ '#sk130' @ '#sk129' ),
    inference(demod,[status(thm)],[zip_derived_cl68,zip_derived_cl106]) ).

thf(zip_derived_cl136,plain,
    ( ( ( positive @ '#sk125' @ '#sk129' )
     => $false )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl64,zip_derived_cl107]) ).

thf(zip_derived_cl137,plain,
    ( ( (~) @ ( positive @ '#sk125' @ '#sk129' ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl136]) ).

thf(zip_derived_cl138,plain,
    ( ~ ( positive @ '#sk125' @ '#sk129' )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl137]) ).

thf(zip_derived_cl66_003,plain,
    ( '#form131'
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl139,plain,
    ( ~ '#form131'
    | ~ ( positive @ '#sk125' @ '#sk129' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl138,zip_derived_cl66]) ).

thf(zip_derived_cl106_004,plain,
    '#form131',
    inference(clc,[status(thm)],[zip_derived_cl89,zip_derived_cl71]) ).

thf(zip_derived_cl140,plain,
    ~ ( positive @ '#sk125' @ '#sk129' ),
    inference(demod,[status(thm)],[zip_derived_cl139,zip_derived_cl106]) ).

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

thf('18',plain,
    ( mequiv
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
        <=> ( Psi @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mequiv]) ).

thf('19',plain,
    ( mequiv
    = ( ^ [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('20',plain,
    ( mnot
    = ( ^ [Phi: $i > $o,W: $i] :
          ~ ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mnot]) ).

thf('21',plain,
    ( mnot
    = ( ^ [V_1: $i > $o,V_2: $i] :
          ~ ( V_1 @ V_2 ) ) ),
    define([status(thm)]) ).

thf(axA1,axiom,
    ( mvalid
    @ ( mforall_indset
      @ ^ [Phi: mu > $i > $o] :
          ( mequiv
          @ ( positive
            @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) )
          @ ( mnot @ ( positive @ Phi ) ) ) ) ) ).

thf(zf_stmt_2,axiom,
    ! [X4: $i,X6: mu > $i > $o] :
      ( ( positive
        @ ^ [V_1: mu,V_2: $i] :
            ~ ( X6 @ V_1 @ V_2 )
        @ X4 )
    <=> ~ ( positive @ X6 @ X4 ) ) ).

thf(zip_derived_cl0,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu > $i > $o] :
            ( ( positive
              @ ^ [Y2: mu,Y3: $i] : ( (~) @ ( Y1 @ Y2 @ Y3 ) )
              @ Y0 )
          <=> ( (~) @ ( positive @ Y1 @ Y0 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl3,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu > $i > $o] :
          ( ( positive
            @ ^ [Y1: mu,Y2: $i] : ( (~) @ ( Y0 @ Y1 @ Y2 ) )
            @ X2 )
        <=> ( (~) @ ( positive @ Y0 @ X2 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl4,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
        @ X2 )
    <=> ( (~) @ ( positive @ X4 @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl5,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
        @ X2 )
     != ( positive @ X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl7,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
        @ X2 )
      | ( positive @ X4 @ X2 ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl7_005,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
        @ X2 )
      | ( positive @ X4 @ X2 ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl40_006,plain,
    ! [X2: mu > $i > $o] :
      ( ~ ( positive @ X2 @ '#sk121' )
      | ( X2 @ '#sk122' @ '#sk121' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl74,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X0 @ Y0 @ Y1 ) )
        @ '#sk121' )
      | ( X0 @ '#sk122' @ '#sk121' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl40]) ).

thf(zip_derived_cl54,plain,
    ( ( rel @ '#sk121' @ '#sk129' )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl56,plain,
    ( ~ ( ( positive @ '#sk128' @ '#sk121' )
       => ( '#sk128' @ '#sk122' @ '#sk121' ) )
    | ( rel @ '#sk121' @ '#sk129' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl58,plain,
    ( ( positive @ '#sk128' @ '#sk121' )
    | ( rel @ '#sk121' @ '#sk129' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl56]) ).

thf(zip_derived_cl5_007,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
        @ X2 )
     != ( positive @ X4 @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl8,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ~ ( positive
          @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
          @ X2 )
      | ~ ( positive @ X4 @ X2 ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl127,plain,
    ! [X0: mu > $i > $o] :
      ( ( ( ^ [Y0: mu,Y1: $i] : ( '#sk128' @ Y0 @ Y1 ) )
       != ( ^ [Y0: mu,Y1: $i] : ( (~) @ ( X0 @ Y0 @ Y1 ) ) ) )
      | ( rel @ '#sk121' @ '#sk129' )
      | ~ ( positive @ X0 @ '#sk121' ) ),
    inference(ext_sup,[status(thm)],[zip_derived_cl58,zip_derived_cl8]) ).

thf(zip_derived_cl128,plain,
    ! [X0: mu > $i > $o] :
      ( ( '#sk128'
       != ( ^ [Y0: mu,Y1: $i] : ( (~) @ ( X0 @ Y0 @ Y1 ) ) ) )
      | ( rel @ '#sk121' @ '#sk129' )
      | ~ ( positive @ X0 @ '#sk121' ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl127]) ).

thf(zip_derived_cl257,plain,
    ! [X0: mu > $i > $o] :
      ( ( X0 @ '#sk122' @ '#sk121' )
      | ( rel @ '#sk121' @ '#sk129' )
      | ( '#sk128'
       != ( ^ [Y0: mu,Y1: $i] :
              ( (~)
              @ ( ^ [Y2: mu,Y3: $i] : ( (~) @ ( X0 @ Y2 @ Y3 ) )
                @ Y0
                @ Y1 ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl74,zip_derived_cl128]) ).

thf(zip_derived_cl265,plain,
    ! [X0: mu > $i > $o] :
      ( ( X0 @ '#sk122' @ '#sk121' )
      | ( rel @ '#sk121' @ '#sk129' )
      | ( '#sk128'
       != ( ^ [Y0: mu,Y1: $i] : ( (~) @ ( (~) @ ( X0 @ Y0 @ Y1 ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl257]) ).

thf(zip_derived_cl266,plain,
    ! [X0: mu > $i > $o] :
      ( ( X0 @ '#sk122' @ '#sk121' )
      | ( rel @ '#sk121' @ '#sk129' )
      | ( '#sk128'
       != ( ^ [Y0: mu,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl265]) ).

thf(zip_derived_cl267,plain,
    ! [X0: mu > $i > $o] :
      ( ( X0 @ '#sk122' @ '#sk121' )
      | ( rel @ '#sk121' @ '#sk129' )
      | ( '#sk128' != X0 ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl266]) ).

thf(zip_derived_cl332,plain,
    ( ( rel @ '#sk121' @ '#sk129' )
    | ( '#sk128' @ '#sk122' @ '#sk121' ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl267]) ).

thf(zip_derived_cl59,plain,
    ( ~ ( '#sk128' @ '#sk122' @ '#sk121' )
    | ( rel @ '#sk121' @ '#sk129' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl56]) ).

thf(zip_derived_cl360,plain,
    rel @ '#sk121' @ '#sk129',
    inference(clc,[status(thm)],[zip_derived_cl332,zip_derived_cl59]) ).

thf(zip_derived_cl7_008,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
        @ X2 )
      | ( positive @ X4 @ X2 ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl5]) ).

thf(axA4,axiom,
    ( mvalid
    @ ( mforall_indset
      @ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( mbox @ ( positive @ Phi ) ) ) ) ) ).

thf(zf_stmt_3,axiom,
    ! [X4: $i,X6: mu > $i > $o] :
      ( ( positive @ X6 @ X4 )
     => ! [X8: $i] :
          ( ~ ( rel @ X4 @ X8 )
          | ( positive @ X6 @ X8 ) ) ) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu > $i > $o] :
            ( ( positive @ Y1 @ Y0 )
           => ( !!
              @ ^ [Y2: $i] :
                  ( ( (~) @ ( rel @ Y0 @ Y2 ) )
                  | ( positive @ Y1 @ Y2 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl22,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu > $i > $o] :
          ( ( positive @ Y0 @ X2 )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( rel @ X2 @ Y1 ) )
                | ( positive @ Y0 @ Y1 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl23,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ( positive @ X4 @ X2 )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel @ X2 @ Y0 ) )
            | ( positive @ X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl25,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ~ ( positive @ X4 @ X2 )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel @ X2 @ Y0 ) )
            | ( positive @ X4 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl26,plain,
    ! [X2: $i,X4: mu > $i > $o,X6: $i] :
      ( ( (~) @ ( rel @ X2 @ X6 ) )
      | ( positive @ X4 @ X6 )
      | ~ ( positive @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl27,plain,
    ! [X2: $i,X4: mu > $i > $o,X6: $i] :
      ( ~ ( rel @ X2 @ X6 )
      | ( positive @ X4 @ X6 )
      | ~ ( positive @ X4 @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl28,plain,
    ! [X0: $i,X1: mu > $i > $o,X2: $i] :
      ( ( positive @ X1 @ X0 )
      | ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X1 @ Y0 @ Y1 ) )
        @ X2 )
      | ~ ( rel @ X0 @ X2 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl27]) ).

thf(zip_derived_cl361,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X0 @ Y0 @ Y1 ) )
        @ '#sk129' )
      | ( positive @ X0 @ '#sk121' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl360,zip_derived_cl28]) ).

thf(zip_derived_cl8_009,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ~ ( positive
          @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
          @ X2 )
      | ~ ( positive @ X4 @ X2 ) ),
    inference(eq_elim,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl375,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive @ X0 @ '#sk121' )
      | ~ ( positive
          @ ^ [Y0: mu,Y1: $i] :
              ( (~)
              @ ( ^ [Y2: mu,Y3: $i] : ( (~) @ ( X0 @ Y2 @ Y3 ) )
                @ Y0
                @ Y1 ) )
          @ '#sk129' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl361,zip_derived_cl8]) ).

thf(zip_derived_cl397,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive @ X0 @ '#sk121' )
      | ~ ( positive
          @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( (~) @ ( X0 @ Y0 @ Y1 ) ) )
          @ '#sk129' ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl375]) ).

thf(zip_derived_cl398,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive @ X0 @ '#sk121' )
      | ~ ( positive
          @ ^ [Y0: mu,Y1: $i] : ( X0 @ Y0 @ Y1 )
          @ '#sk129' ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl397]) ).

thf(zip_derived_cl399,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive @ X0 @ '#sk121' )
      | ~ ( positive @ X0 @ '#sk129' ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl398]) ).

thf(zip_derived_cl406,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive @ X0 @ '#sk129' )
      | ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X0 @ Y0 @ Y1 ) )
        @ '#sk121' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl399]) ).

thf(zip_derived_cl40_010,plain,
    ! [X2: mu > $i > $o] :
      ( ~ ( positive @ X2 @ '#sk121' )
      | ( X2 @ '#sk122' @ '#sk121' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl483,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive @ X0 @ '#sk129' )
      | ( ^ [Y0: mu,Y1: $i] : ( (~) @ ( X0 @ Y0 @ Y1 ) )
        @ '#sk122'
        @ '#sk121' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl406,zip_derived_cl40]) ).

thf(zip_derived_cl503,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive @ X0 @ '#sk129' )
      | ( (~) @ ( X0 @ '#sk122' @ '#sk121' ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl483]) ).

thf(zip_derived_cl504,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive @ X0 @ '#sk129' )
      | ~ ( X0 @ '#sk122' @ '#sk121' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl503]) ).

thf(zip_derived_cl605,plain,
    ~ ( '#sk125' @ '#sk122' @ '#sk121' ),
    inference('sup+',[status(thm)],[zip_derived_cl140,zip_derived_cl504]) ).

thf(zip_derived_cl45,plain,
    ( ( '#sk125' @ '#sk122' @ '#sk121' )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk121' )
           => ( Y0 @ '#sk122' @ '#sk121' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl50,plain,
    ( ~ ( ( positive @ '#sk128' @ '#sk121' )
       => ( '#sk128' @ '#sk122' @ '#sk121' ) )
    | ( '#sk125' @ '#sk122' @ '#sk121' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl52,plain,
    ( ( positive @ '#sk128' @ '#sk121' )
    | ( '#sk125' @ '#sk122' @ '#sk121' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl40_011,plain,
    ! [X2: mu > $i > $o] :
      ( ~ ( positive @ X2 @ '#sk121' )
      | ( X2 @ '#sk122' @ '#sk121' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl112,plain,
    ( ( '#sk125' @ '#sk122' @ '#sk121' )
    | ( '#sk128' @ '#sk122' @ '#sk121' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl52,zip_derived_cl40]) ).

thf(zip_derived_cl53,plain,
    ( ~ ( '#sk128' @ '#sk122' @ '#sk121' )
    | ( '#sk125' @ '#sk122' @ '#sk121' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl132,plain,
    '#sk125' @ '#sk122' @ '#sk121',
    inference(clc,[status(thm)],[zip_derived_cl112,zip_derived_cl53]) ).

thf(zip_derived_cl619,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl605,zip_derived_cl132]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem  : PHI004^2 : TPTP v9.2.0. Released v6.1.0.
% 0.10/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.6ApaTgZeyi true
% 0.13/0.35  % Computer : n023.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 : Wed Oct  1 16:57:23 EDT 2025
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.36  % Python version: Python 3.6.8
% 0.13/0.36  % Running in HO mode
% 0.54/0.67  % Total configuration time : 828
% 0.54/0.67  % Estimated wc time : 1656
% 0.54/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.58/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.58/0.78  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.58/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.58/0.79  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.58/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.58/0.81  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.58/0.82  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.58/0.83  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.58/0.84  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 4.02/1.26  % Solved by lams/35_full_unif4.sh.
% 4.02/1.26  % done 72 iterations in 0.411s
% 4.02/1.26  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 4.02/1.26  % SZS output start Refutation
% See solution above
% 4.02/1.26  
% 4.02/1.26  
% 4.02/1.26  % Terminating...
% 4.85/1.54  % Runner terminated.
% 4.87/1.55  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------