TSTP Solution File: PHI004^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : PHI004^1 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WbueJZHSwK true

% Computer : n003.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 12:58:48 EDT 2023

% Result   : Theorem 1.46s 1.29s
% Output   : Refutation 1.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   54
% Syntax   : Number of formulae    :  146 (  51 unt;  21 typ;   0 def)
%            Number of atoms       :  431 (  41 equ;  34 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives : 1128 ( 112   ~;  81   |;   9   &; 760   @)
%                                         (   7 <=>;  86  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  315 ( 315   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   24 (  20 usr;   8 con; 0-3 aty)
%                                         (  73  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  279 ( 196   ^;  83   !;   0   ?; 279   :)

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

thf('#form285_type',type,
    '#form285': $o ).

thf('#sk282_type',type,
    '#sk282': 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('#sk284_type',type,
    '#sk284': mu ).

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

thf('#sk275_type',type,
    '#sk275': $i ).

thf('#sk276_type',type,
    '#sk276': mu ).

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(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('#sk279_type',type,
    '#sk279': mu > $i > $o ).

thf('#sk283_type',type,
    '#sk283': $i ).

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

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

thf('0',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('1',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(mimplies,axiom,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
         => ( Psi @ W ) ) ) ) ).

thf('2',plain,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
         => ( Psi @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies]) ).

thf('3',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('4',plain,
    ( god
    = ( ^ [X: mu] :
          ( mforall_indset
          @ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[defD1,'1','3']) ).

thf('5',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('6',plain,
    ( mvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mvalid]) ).

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

thf(axA3,axiom,
    mvalid @ ( positive @ god ) ).

thf(zf_stmt_0,axiom,
    ! [X4: $i] :
      ( positive
      @ ^ [V_1: mu,V_2: $i] :
        ! [X6: mu > $i > $o] :
          ( ( positive @ X6 @ V_2 )
         => ( X6 @ V_1 @ V_2 ) )
      @ X4 ) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( positive
        @ ^ [Y1: mu,Y2: $i] :
            ( !!
            @ ^ [Y3: mu > $i > $o] :
                ( ( positive @ Y3 @ Y2 )
               => ( Y3 @ Y1 @ Y2 ) ) )
        @ Y0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl6,plain,
    ! [X2: $i] :
      ( positive
      @ ^ [Y0: mu,Y1: $i] :
          ( !!
          @ ^ [Y2: mu > $i > $o] :
              ( ( positive @ Y2 @ Y1 )
             => ( Y2 @ Y0 @ Y1 ) ) )
      @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

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('8',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('9',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('10',plain,
    ( mbox
    = ( mbox_generic @ rel ) ),
    inference(simplify_rw_rule,[status(thm)],[mbox,'9']) ).

thf('11',plain,
    ( mbox
    = ( mbox_generic @ rel ) ),
    define([status(thm)]) ).

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

thf('12',plain,
    ( mforall_ind
    = ( ^ [Phi: mu > $i > $o,W: $i] :
        ! [X: mu] : ( Phi @ X @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mforall_ind]) ).

thf('13',plain,
    ( mforall_ind
    = ( ^ [V_1: mu > $i > $o,V_2: $i] :
        ! [X4: mu] : ( V_1 @ X4 @ V_2 ) ) ),
    define([status(thm)]) ).

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

thf('14',plain,
    ( mand
    = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
          ( ( Phi @ W )
          & ( Psi @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mand]) ).

thf('15',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('16',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,'11','9','1','13','3','15']) ).

thf('17',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(thmT2,conjecture,
    ( mvalid
    @ ( mforall_ind
      @ ^ [X: mu] : ( mimplies @ ( god @ X ) @ ( essence @ god @ X ) ) ) ) ).

thf(zf_stmt_1,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_2,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_1]) ).

thf(zip_derived_cl5,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_2]) ).

thf(zip_derived_cl85,plain,
    ~ ( !!
      @ ^ [Y0: mu] :
          ( ( !!
            @ ^ [Y1: mu > $i > $o] :
                ( ( positive @ Y1 @ '#sk275' )
               => ( Y1 @ Y0 @ '#sk275' ) ) )
         => ( ( !!
              @ ^ [Y1: mu > $i > $o] :
                  ( ( Y1 @ Y0 @ '#sk275' )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( (~) @ ( rel @ '#sk275' @ Y2 ) )
                        | ( !!
                          @ ^ [Y3: mu] :
                              ( ( !!
                                @ ^ [Y4: mu > $i > $o] :
                                    ( ( positive @ Y4 @ Y2 )
                                   => ( Y4 @ Y3 @ Y2 ) ) )
                             => ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) )
            & ( !!
              @ ^ [Y1: mu > $i > $o] :
                  ( ( positive @ Y1 @ '#sk275' )
                 => ( Y1 @ Y0 @ '#sk275' ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl86,plain,
    ~ ( ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) )
     => ( ( !!
          @ ^ [Y0: mu > $i > $o] :
              ( ( Y0 @ '#sk276' @ '#sk275' )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( (~) @ ( rel @ '#sk275' @ Y1 ) )
                    | ( !!
                      @ ^ [Y2: mu] :
                          ( ( !!
                            @ ^ [Y3: mu > $i > $o] :
                                ( ( positive @ Y3 @ Y1 )
                               => ( Y3 @ Y2 @ Y1 ) ) )
                         => ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
        & ( !!
          @ ^ [Y0: mu > $i > $o] :
              ( ( positive @ Y0 @ '#sk275' )
             => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl85]) ).

thf(zip_derived_cl88,plain,
    ~ ( ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( Y0 @ '#sk276' @ '#sk275' )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel @ '#sk275' @ Y1 ) )
                  | ( !!
                    @ ^ [Y2: mu] :
                        ( ( !!
                          @ ^ [Y3: mu > $i > $o] :
                              ( ( positive @ Y3 @ Y1 )
                             => ( Y3 @ Y2 @ Y1 ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
      & ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl86]) ).

thf(zip_derived_cl93,plain,
    ( ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( Y0 @ '#sk276' @ '#sk275' )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( (~) @ ( rel @ '#sk275' @ Y1 ) )
                  | ( !!
                    @ ^ [Y2: mu] :
                        ( ( !!
                          @ ^ [Y3: mu > $i > $o] :
                              ( ( positive @ Y3 @ Y1 )
                             => ( Y3 @ Y2 @ Y1 ) ) )
                       => ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl88]) ).

thf(zip_derived_cl100,plain,
    ( ~ ( ( '#sk279' @ '#sk276' @ '#sk275' )
       => ( !!
          @ ^ [Y0: $i] :
              ( ( (~) @ ( rel @ '#sk275' @ Y0 ) )
              | ( !!
                @ ^ [Y1: mu] :
                    ( ( !!
                      @ ^ [Y2: mu > $i > $o] :
                          ( ( positive @ Y2 @ Y0 )
                         => ( Y2 @ Y1 @ Y0 ) ) )
                   => ( '#sk279' @ Y1 @ Y0 ) ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl93]) ).

thf(zip_derived_cl102,plain,
    ( ~ ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel @ '#sk275' @ Y0 ) )
            | ( !!
              @ ^ [Y1: mu] :
                  ( ( !!
                    @ ^ [Y2: mu > $i > $o] :
                        ( ( positive @ Y2 @ Y0 )
                       => ( Y2 @ Y1 @ Y0 ) ) )
                 => ( '#sk279' @ Y1 @ Y0 ) ) ) ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl100]) ).

thf(zip_derived_cl109,plain,
    ( ~ ( ( (~) @ ( rel @ '#sk275' @ '#sk283' ) )
        | ( !!
          @ ^ [Y0: mu] :
              ( ( !!
                @ ^ [Y1: mu > $i > $o] :
                    ( ( positive @ Y1 @ '#sk283' )
                   => ( Y1 @ Y0 @ '#sk283' ) ) )
             => ( '#sk279' @ Y0 @ '#sk283' ) ) ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl102]) ).

thf(zip_derived_cl113,plain,
    ( ~ ( !!
        @ ^ [Y0: mu] :
            ( ( !!
              @ ^ [Y1: mu > $i > $o] :
                  ( ( positive @ Y1 @ '#sk283' )
                 => ( Y1 @ Y0 @ '#sk283' ) ) )
           => ( '#sk279' @ Y0 @ '#sk283' ) ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl109]) ).

thf(zip_derived_cl115,plain,
    ( ~ ( ( !!
          @ ^ [Y0: mu > $i > $o] :
              ( ( positive @ Y0 @ '#sk283' )
             => ( Y0 @ '#sk284' @ '#sk283' ) ) )
       => ( '#sk279' @ '#sk284' @ '#sk283' ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl113]) ).

thf(zip_derived_cl118,plain,
    ( ( !!
      @ ^ [Y0: mu > $i > $o] :
          ( ( positive @ Y0 @ '#sk283' )
         => ( Y0 @ '#sk284' @ '#sk283' ) ) )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl115]) ).

thf(zip_derived_cl120,plain,
    ! [X2: mu > $i > $o] :
      ( ( ( positive @ X2 @ '#sk283' )
       => ( X2 @ '#sk284' @ '#sk283' ) )
      | ~ ( !!
          @ ^ [Y0: mu > $i > $o] :
              ( ( positive @ Y0 @ '#sk275' )
             => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl118]) ).

thf(zip_derived_cl119,plain,
    ( ~ ( '#sk279' @ '#sk284' @ '#sk283' )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl115]) ).

thf(zip_derived_cl126,plain,
    ( '#form285'
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl129,plain,
    ! [X2: mu > $i > $o] :
      ( ~ '#form285'
      | ( ( positive @ X2 @ '#sk283' )
       => ( X2 @ '#sk284' @ '#sk283' ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl120,zip_derived_cl126]) ).

thf(zip_derived_cl132,plain,
    ! [X2: mu > $i > $o] :
      ( ~ ( positive @ X2 @ '#sk283' )
      | ( X2 @ '#sk284' @ '#sk283' )
      | ~ '#form285' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl129]) ).

thf(zip_derived_cl126_001,plain,
    ( '#form285'
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl127,plain,
    ( ~ ( ( positive @ '#sk282' @ '#sk275' )
       => ( '#sk282' @ '#sk276' @ '#sk275' ) )
    | '#form285' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl126]) ).

thf(zip_derived_cl130,plain,
    ( ( positive @ '#sk282' @ '#sk275' )
    | '#form285' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl127]) ).

thf(zip_derived_cl87,plain,
    ( !!
    @ ^ [Y0: mu > $i > $o] :
        ( ( positive @ Y0 @ '#sk275' )
       => ( Y0 @ '#sk276' @ '#sk275' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl86]) ).

thf(zip_derived_cl89,plain,
    ! [X2: mu > $i > $o] :
      ( ( positive @ X2 @ '#sk275' )
     => ( X2 @ '#sk276' @ '#sk275' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl87]) ).

thf(zip_derived_cl94,plain,
    ! [X2: mu > $i > $o] :
      ( ~ ( positive @ X2 @ '#sk275' )
      | ( X2 @ '#sk276' @ '#sk275' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl162,plain,
    ( '#form285'
    | ( '#sk282' @ '#sk276' @ '#sk275' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl130,zip_derived_cl94]) ).

thf(zip_derived_cl131,plain,
    ( ~ ( '#sk282' @ '#sk276' @ '#sk275' )
    | '#form285' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl127]) ).

thf(zip_derived_cl178,plain,
    '#form285',
    inference(clc,[status(thm)],[zip_derived_cl162,zip_derived_cl131]) ).

thf(zip_derived_cl232,plain,
    ! [X2: mu > $i > $o] :
      ( ~ ( positive @ X2 @ '#sk283' )
      | ( X2 @ '#sk284' @ '#sk283' ) ),
    inference(demod,[status(thm)],[zip_derived_cl132,zip_derived_cl178]) ).

thf(zip_derived_cl234,plain,
    ( ^ [Y0: mu,Y1: $i] :
        ( !!
        @ ^ [Y2: mu > $i > $o] :
            ( ( positive @ Y2 @ Y1 )
           => ( Y2 @ Y0 @ Y1 ) ) )
    @ '#sk284'
    @ '#sk283' ),
    inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl232]) ).

thf(zip_derived_cl246,plain,
    ( !!
    @ ^ [Y0: mu > $i > $o] :
        ( ( positive @ Y0 @ '#sk283' )
       => ( Y0 @ '#sk284' @ '#sk283' ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl234]) ).

thf(zip_derived_cl257,plain,
    ! [X2: mu > $i > $o] :
      ( ( positive @ X2 @ '#sk283' )
     => ( X2 @ '#sk284' @ '#sk283' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl246]) ).

thf(zip_derived_cl259,plain,
    ( ( positive @ '#sk279' @ '#sk283' )
   => ( '#sk279' @ '#sk284' @ '#sk283' ) ),
    inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl257]) ).

thf(zip_derived_cl119_002,plain,
    ( ~ ( '#sk279' @ '#sk284' @ '#sk283' )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl115]) ).

thf(zip_derived_cl126_003,plain,
    ( '#form285'
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl128,plain,
    ( ~ '#form285'
    | ~ ( '#sk279' @ '#sk284' @ '#sk283' ) ),
    inference(renaming,[status(thm)],[zip_derived_cl119,zip_derived_cl126]) ).

thf(zip_derived_cl178_004,plain,
    '#form285',
    inference(clc,[status(thm)],[zip_derived_cl162,zip_derived_cl131]) ).

thf(zip_derived_cl179,plain,
    ~ ( '#sk279' @ '#sk284' @ '#sk283' ),
    inference(demod,[status(thm)],[zip_derived_cl128,zip_derived_cl178]) ).

thf(zip_derived_cl265,plain,
    ( ( positive @ '#sk279' @ '#sk283' )
   => $false ),
    inference(demod,[status(thm)],[zip_derived_cl259,zip_derived_cl179]) ).

thf(zip_derived_cl266,plain,
    (~) @ ( positive @ '#sk279' @ '#sk283' ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl265]) ).

thf(zip_derived_cl267,plain,
    ~ ( positive @ '#sk279' @ '#sk283' ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl266]) ).

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_3,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_3]) ).

thf(zip_derived_cl7,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_cl8,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_cl7]) ).

thf(zip_derived_cl10,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_cl8]) ).

thf(zip_derived_cl14,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_cl10]) ).

thf(zip_derived_cl94_005,plain,
    ! [X2: mu > $i > $o] :
      ( ~ ( positive @ X2 @ '#sk275' )
      | ( X2 @ '#sk276' @ '#sk275' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl136,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X0 @ Y0 @ Y1 ) )
        @ '#sk275' )
      | ( X0 @ '#sk276' @ '#sk275' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl94]) ).

thf(zip_derived_cl112,plain,
    ( ( rel @ '#sk275' @ '#sk283' )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl109]) ).

thf(zip_derived_cl114,plain,
    ( ~ ( ( positive @ '#sk282' @ '#sk275' )
       => ( '#sk282' @ '#sk276' @ '#sk275' ) )
    | ( rel @ '#sk275' @ '#sk283' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl112]) ).

thf(zip_derived_cl116,plain,
    ( ( positive @ '#sk282' @ '#sk275' )
    | ( rel @ '#sk275' @ '#sk283' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl114]) ).

thf(zip_derived_cl10_006,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_cl8]) ).

thf(zip_derived_cl15,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_cl10]) ).

thf(zip_derived_cl211,plain,
    ! [X0: mu > $i > $o] :
      ( ( ( ^ [Y0: mu,Y1: $i] : ( '#sk282' @ Y0 @ Y1 ) )
       != ( ^ [Y0: mu,Y1: $i] : ( (~) @ ( X0 @ Y0 @ Y1 ) ) ) )
      | ( rel @ '#sk275' @ '#sk283' )
      | ~ ( positive @ X0 @ '#sk275' ) ),
    inference(ext_sup,[status(thm)],[zip_derived_cl116,zip_derived_cl15]) ).

thf(zip_derived_cl212,plain,
    ! [X0: mu > $i > $o] :
      ( ( '#sk282'
       != ( ^ [Y0: mu,Y1: $i] : ( (~) @ ( X0 @ Y0 @ Y1 ) ) ) )
      | ( rel @ '#sk275' @ '#sk283' )
      | ~ ( positive @ X0 @ '#sk275' ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl211]) ).

thf(zip_derived_cl554,plain,
    ! [X0: mu > $i > $o] :
      ( ( X0 @ '#sk276' @ '#sk275' )
      | ( rel @ '#sk275' @ '#sk283' )
      | ( '#sk282'
       != ( ^ [Y0: mu,Y1: $i] :
              ( (~)
              @ ( ^ [Y2: mu,Y3: $i] : ( (~) @ ( X0 @ Y2 @ Y3 ) )
                @ Y0
                @ Y1 ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl136,zip_derived_cl212]) ).

thf(zip_derived_cl565,plain,
    ! [X0: mu > $i > $o] :
      ( ( X0 @ '#sk276' @ '#sk275' )
      | ( rel @ '#sk275' @ '#sk283' )
      | ( '#sk282'
       != ( ^ [Y0: mu,Y1: $i] : ( (~) @ ( (~) @ ( X0 @ Y0 @ Y1 ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl554]) ).

thf(zip_derived_cl566,plain,
    ! [X0: mu > $i > $o] :
      ( ( X0 @ '#sk276' @ '#sk275' )
      | ( rel @ '#sk275' @ '#sk283' )
      | ( '#sk282'
       != ( ^ [Y0: mu,Y1: $i] : ( X0 @ Y0 @ Y1 ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl565]) ).

thf(zip_derived_cl567,plain,
    ! [X0: mu > $i > $o] :
      ( ( X0 @ '#sk276' @ '#sk275' )
      | ( rel @ '#sk275' @ '#sk283' )
      | ( '#sk282' != X0 ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl566]) ).

thf(zip_derived_cl586,plain,
    ( ( rel @ '#sk275' @ '#sk283' )
    | ( '#sk282' @ '#sk276' @ '#sk275' ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl567]) ).

thf(zip_derived_cl117,plain,
    ( ~ ( '#sk282' @ '#sk276' @ '#sk275' )
    | ( rel @ '#sk275' @ '#sk283' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl114]) ).

thf(zip_derived_cl590,plain,
    rel @ '#sk275' @ '#sk283',
    inference(clc,[status(thm)],[zip_derived_cl586,zip_derived_cl117]) ).

thf(zip_derived_cl14_007,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_cl10]) ).

thf(zip_derived_cl94_008,plain,
    ! [X2: mu > $i > $o] :
      ( ~ ( positive @ X2 @ '#sk275' )
      | ( X2 @ '#sk276' @ '#sk275' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl135,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive @ X0 @ '#sk275' )
      | ( ^ [Y0: mu,Y1: $i] : ( (~) @ ( X0 @ Y0 @ Y1 ) )
        @ '#sk276'
        @ '#sk275' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl94]) ).

thf(zip_derived_cl147,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive @ X0 @ '#sk275' )
      | ( (~) @ ( X0 @ '#sk276' @ '#sk275' ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl135]) ).

thf(zip_derived_cl148,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive @ X0 @ '#sk275' )
      | ~ ( X0 @ '#sk276' @ '#sk275' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl147]) ).

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

thf(zf_stmt_4,axiom,
    ! [X4: $i,X6: mu > $i > $o] :
      ( ( positive @ X6 @ X4 )
     => ! [X8: $i] :
          ( ~ ( rel @ X4 @ X8 )
          | ( positive @ X6 @ X8 ) ) ) ).

thf(zip_derived_cl3,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu > $i > $o] :
            ( ( positive @ Y1 @ Y0 )
           => ( !!
              @ ^ [Y2: $i] :
                  ( ( (~) @ ( rel @ Y0 @ Y2 ) )
                  | ( positive @ Y1 @ Y2 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl39,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_cl3]) ).

thf(zip_derived_cl40,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_cl39]) ).

thf(zip_derived_cl43,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_cl40]) ).

thf(zip_derived_cl44,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_cl43]) ).

thf(zip_derived_cl45,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_cl44]) ).

thf(zip_derived_cl289,plain,
    ! [X0: mu > $i > $o,X1: $i] :
      ( ~ ( X0 @ '#sk276' @ '#sk275' )
      | ( positive @ X0 @ X1 )
      | ~ ( rel @ '#sk275' @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl148,zip_derived_cl45]) ).

thf(zip_derived_cl591,plain,
    ! [X0: mu > $i > $o] :
      ( ( positive @ X0 @ '#sk283' )
      | ~ ( X0 @ '#sk276' @ '#sk275' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl590,zip_derived_cl289]) ).

thf(zip_derived_cl627,plain,
    ~ ( '#sk279' @ '#sk276' @ '#sk275' ),
    inference('sup+',[status(thm)],[zip_derived_cl267,zip_derived_cl591]) ).

thf(zip_derived_cl101,plain,
    ( ( '#sk279' @ '#sk276' @ '#sk275' )
    | ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk275' )
           => ( Y0 @ '#sk276' @ '#sk275' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl100]) ).

thf(zip_derived_cl108,plain,
    ( ~ ( ( positive @ '#sk282' @ '#sk275' )
       => ( '#sk282' @ '#sk276' @ '#sk275' ) )
    | ( '#sk279' @ '#sk276' @ '#sk275' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl101]) ).

thf(zip_derived_cl110,plain,
    ( ( positive @ '#sk282' @ '#sk275' )
    | ( '#sk279' @ '#sk276' @ '#sk275' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl108]) ).

thf(zip_derived_cl94_009,plain,
    ! [X2: mu > $i > $o] :
      ( ~ ( positive @ X2 @ '#sk275' )
      | ( X2 @ '#sk276' @ '#sk275' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl89]) ).

thf(zip_derived_cl188,plain,
    ( ( '#sk279' @ '#sk276' @ '#sk275' )
    | ( '#sk282' @ '#sk276' @ '#sk275' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl110,zip_derived_cl94]) ).

thf(zip_derived_cl111,plain,
    ( ~ ( '#sk282' @ '#sk276' @ '#sk275' )
    | ( '#sk279' @ '#sk276' @ '#sk275' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl108]) ).

thf(zip_derived_cl231,plain,
    '#sk279' @ '#sk276' @ '#sk275',
    inference(clc,[status(thm)],[zip_derived_cl188,zip_derived_cl111]) ).

thf(zip_derived_cl640,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl627,zip_derived_cl231]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : PHI004^1 : TPTP v8.1.2. Released v6.1.0.
% 0.13/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WbueJZHSwK true
% 0.14/0.36  % Computer : n003.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sun Aug 27 08:58:24 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  % Running portfolio for 300 s
% 0.14/0.36  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36  % Number of cores: 8
% 0.22/0.37  % Python version: Python 3.6.8
% 0.22/0.37  % Running in HO mode
% 0.23/0.66  % Total configuration time : 828
% 0.23/0.66  % Estimated wc time : 1656
% 0.23/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.23/0.71  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.77  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.23/0.77  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.77  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.23/0.77  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.23/0.77  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.23/0.77  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.23/0.80  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.23/0.82  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.46/1.29  % Solved by lams/35_full_unif4.sh.
% 1.46/1.29  % done 88 iterations in 0.479s
% 1.46/1.29  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.46/1.29  % SZS output start Refutation
% See solution above
% 1.46/1.29  
% 1.46/1.29  
% 1.46/1.29  % Terminating...
% 1.97/1.37  % Runner terminated.
% 1.97/1.38  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------