TSTP Solution File: SET926^7 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET926^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.gm8Fn82T5m true

% Computer : n005.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 16:16:52 EDT 2023

% Result   : Theorem 1.54s 0.94s
% Output   : Refutation 1.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   78 (  30 unt;  17 typ;   0 def)
%            Number of atoms       :  314 (  21 equ;  59 cnn)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :  972 ( 106   ~;  77   |;   0   &; 733   @)
%                                         (   0 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   8 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   76 (  76   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  16 usr;   7 con; 0-3 aty)
%                                         (  21  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  121 (  69   ^;  52   !;   0   ?; 121   :)

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

thf(in_type,type,
    in: mu > mu > $i > $o ).

thf('#sk5_type',type,
    '#sk5': mu ).

thf('#sk6_type',type,
    '#sk6': mu ).

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

thf(set_difference_type,type,
    set_difference: mu > mu > mu ).

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

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

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

thf(empty_set_type,type,
    empty_set: mu ).

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

thf(exists_in_world_type,type,
    exists_in_world: mu > $i > $o ).

thf(qmltpeq_type,type,
    qmltpeq: mu > mu > $i > $o ).

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

thf(singleton_type,type,
    singleton: mu > mu ).

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

thf('2',plain,
    ( mforall_ind
    = ( ^ [Phi: mu > $i > $o,W: $i] :
        ! [X: mu] :
          ( ( exists_in_world @ X @ W )
         => ( Phi @ X @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mforall_ind]) ).

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

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

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

thf('5',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(t69_zfmisc_1,conjecture,
    ( mvalid
    @ ( mforall_ind
      @ ^ [A: mu] :
          ( mforall_ind
          @ ^ [B: mu] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i,X6: mu] :
      ( ( exists_in_world @ X6 @ X4 )
     => ! [X8: mu] :
          ( ( exists_in_world @ X8 @ X4 )
         => ( ( qmltpeq @ ( set_difference @ ( singleton @ X6 ) @ X8 ) @ ( singleton @ X6 ) @ X4 )
            | ( qmltpeq @ ( set_difference @ ( singleton @ X6 ) @ X8 ) @ empty_set @ X4 ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i,X6: mu] :
        ( ( exists_in_world @ X6 @ X4 )
       => ! [X8: mu] :
            ( ( exists_in_world @ X8 @ X4 )
           => ( ( qmltpeq @ ( set_difference @ ( singleton @ X6 ) @ X8 ) @ ( singleton @ X6 ) @ X4 )
              | ( qmltpeq @ ( set_difference @ ( singleton @ X6 ) @ X8 ) @ empty_set @ X4 ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl22,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: mu] :
              ( ( exists_in_world @ Y1 @ Y0 )
             => ( !!
                @ ^ [Y2: mu] :
                    ( ( exists_in_world @ Y2 @ Y0 )
                   => ( ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 )
                      | ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl64,plain,
    ~ ( !!
      @ ^ [Y0: mu] :
          ( ( exists_in_world @ Y0 @ '#sk4' )
         => ( !!
            @ ^ [Y1: mu] :
                ( ( exists_in_world @ Y1 @ '#sk4' )
               => ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ '#sk4' )
                  | ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ '#sk4' ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl65,plain,
    ~ ( ( exists_in_world @ '#sk5' @ '#sk4' )
     => ( !!
        @ ^ [Y0: mu] :
            ( ( exists_in_world @ Y0 @ '#sk4' )
           => ( ( qmltpeq @ ( set_difference @ ( singleton @ '#sk5' ) @ Y0 ) @ ( singleton @ '#sk5' ) @ '#sk4' )
              | ( qmltpeq @ ( set_difference @ ( singleton @ '#sk5' ) @ Y0 ) @ empty_set @ '#sk4' ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl64]) ).

thf(zip_derived_cl67,plain,
    ~ ( !!
      @ ^ [Y0: mu] :
          ( ( exists_in_world @ Y0 @ '#sk4' )
         => ( ( qmltpeq @ ( set_difference @ ( singleton @ '#sk5' ) @ Y0 ) @ ( singleton @ '#sk5' ) @ '#sk4' )
            | ( qmltpeq @ ( set_difference @ ( singleton @ '#sk5' ) @ Y0 ) @ empty_set @ '#sk4' ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl68,plain,
    ~ ( ( exists_in_world @ '#sk6' @ '#sk4' )
     => ( ( qmltpeq @ ( set_difference @ ( singleton @ '#sk5' ) @ '#sk6' ) @ ( singleton @ '#sk5' ) @ '#sk4' )
        | ( qmltpeq @ ( set_difference @ ( singleton @ '#sk5' ) @ '#sk6' ) @ empty_set @ '#sk4' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl70,plain,
    ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ '#sk5' ) @ '#sk6' ) @ ( singleton @ '#sk5' ) @ '#sk4' )
      | ( qmltpeq @ ( set_difference @ ( singleton @ '#sk5' ) @ '#sk6' ) @ empty_set @ '#sk4' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl72,plain,
    ~ ( qmltpeq @ ( set_difference @ ( singleton @ '#sk5' ) @ '#sk6' ) @ empty_set @ '#sk4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl70]) ).

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

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

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

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

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

thf('8',plain,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies,'5','7']) ).

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

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

thf('10',plain,
    ( mand
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mand,'5','7']) ).

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

thf('12',plain,
    ( mequiv
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mequiv,'9','11','5','7']) ).

thf('13',plain,
    ( mequiv
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ ( mimplies @ V_1 @ V_2 ) @ ( mimplies @ V_2 @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf(l36_zfmisc_1,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [A: mu] :
          ( mforall_ind
          @ ^ [B: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ) ).

thf(zf_stmt_2,axiom,
    ! [X4: $i,X6: mu] :
      ( ( exists_in_world @ X6 @ X4 )
     => ! [X8: mu] :
          ( ( exists_in_world @ X8 @ X4 )
         => ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X6 ) @ X8 ) @ empty_set @ X4 )
                  | ~ ( in @ X6 @ X8 @ X4 ) )
              | ~ ( ( in @ X6 @ X8 @ X4 )
                  | ~ ( qmltpeq @ ( set_difference @ ( singleton @ X6 ) @ X8 ) @ empty_set @ X4 ) ) ) ) ) ).

thf(zip_derived_cl19,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu] :
            ( ( exists_in_world @ Y1 @ Y0 )
           => ( !!
              @ ^ [Y2: mu] :
                  ( ( exists_in_world @ Y2 @ Y0 )
                 => ( (~)
                    @ ( ( (~)
                        @ ( ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 )
                          | ( (~) @ ( in @ Y1 @ Y2 @ Y0 ) ) ) )
                      | ( (~)
                        @ ( ( in @ Y1 @ Y2 @ Y0 )
                          | ( (~) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ empty_set @ Y0 ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl253,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu] :
          ( ( exists_in_world @ Y0 @ X2 )
         => ( !!
            @ ^ [Y1: mu] :
                ( ( exists_in_world @ Y1 @ X2 )
               => ( (~)
                  @ ( ( (~)
                      @ ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ X2 )
                        | ( (~) @ ( in @ Y0 @ Y1 @ X2 ) ) ) )
                    | ( (~)
                      @ ( ( in @ Y0 @ Y1 @ X2 )
                        | ( (~) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ X2 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl254,plain,
    ! [X2: $i,X4: mu] :
      ( ( exists_in_world @ X4 @ X2 )
     => ( !!
        @ ^ [Y0: mu] :
            ( ( exists_in_world @ Y0 @ X2 )
           => ( (~)
              @ ( ( (~)
                  @ ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ Y0 ) @ empty_set @ X2 )
                    | ( (~) @ ( in @ X4 @ Y0 @ X2 ) ) ) )
                | ( (~)
                  @ ( ( in @ X4 @ Y0 @ X2 )
                    | ( (~) @ ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ Y0 ) @ empty_set @ X2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl253]) ).

thf(zip_derived_cl255,plain,
    ! [X2: $i,X4: mu] :
      ( ~ ( exists_in_world @ X4 @ X2 )
      | ( !!
        @ ^ [Y0: mu] :
            ( ( exists_in_world @ Y0 @ X2 )
           => ( (~)
              @ ( ( (~)
                  @ ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ Y0 ) @ empty_set @ X2 )
                    | ( (~) @ ( in @ X4 @ Y0 @ X2 ) ) ) )
                | ( (~)
                  @ ( ( in @ X4 @ Y0 @ X2 )
                    | ( (~) @ ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ Y0 ) @ empty_set @ X2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl254]) ).

thf(zip_derived_cl256,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( ( exists_in_world @ X6 @ X2 )
       => ( (~)
          @ ( ( (~)
              @ ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ empty_set @ X2 )
                | ( (~) @ ( in @ X4 @ X6 @ X2 ) ) ) )
            | ( (~)
              @ ( ( in @ X4 @ X6 @ X2 )
                | ( (~) @ ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ empty_set @ X2 ) ) ) ) ) ) )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl255]) ).

thf(zip_derived_cl257,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( ( (~)
            @ ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ empty_set @ X2 )
              | ( (~) @ ( in @ X4 @ X6 @ X2 ) ) ) )
          | ( (~)
            @ ( ( in @ X4 @ X6 @ X2 )
              | ( (~) @ ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ empty_set @ X2 ) ) ) ) )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl256]) ).

thf(zip_derived_cl258,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ empty_set @ X2 )
      | ( (~) @ ( in @ X4 @ X6 @ X2 ) )
      | ~ ( exists_in_world @ X4 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl257]) ).

thf(zip_derived_cl260,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ empty_set @ X2 )
      | ~ ( in @ X4 @ X6 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl258]) ).

thf(zip_derived_cl268,plain,
    ( ~ ( exists_in_world @ '#sk5' @ '#sk4' )
    | ~ ( exists_in_world @ '#sk6' @ '#sk4' )
    | ~ ( in @ '#sk5' @ '#sk6' @ '#sk4' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl72,zip_derived_cl260]) ).

thf(zip_derived_cl66,plain,
    exists_in_world @ '#sk5' @ '#sk4',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl69,plain,
    exists_in_world @ '#sk6' @ '#sk4',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl276,plain,
    ~ ( in @ '#sk5' @ '#sk6' @ '#sk4' ),
    inference(demod,[status(thm)],[zip_derived_cl268,zip_derived_cl66,zip_derived_cl69]) ).

thf(zip_derived_cl71,plain,
    ~ ( qmltpeq @ ( set_difference @ ( singleton @ '#sk5' ) @ '#sk6' ) @ ( singleton @ '#sk5' ) @ '#sk4' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl70]) ).

thf(l34_zfmisc_1,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [A: mu] :
          ( mforall_ind
          @ ^ [B: mu] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).

thf(zf_stmt_3,axiom,
    ! [X4: $i,X6: mu] :
      ( ( exists_in_world @ X6 @ X4 )
     => ! [X8: mu] :
          ( ( exists_in_world @ X8 @ X4 )
         => ~ ( ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ X6 ) @ X8 ) @ ( singleton @ X6 ) @ X4 )
                  | ( in @ X6 @ X8 @ X4 ) )
              | ~ ( ~ ( in @ X6 @ X8 @ X4 )
                  | ~ ( qmltpeq @ ( set_difference @ ( singleton @ X6 ) @ X8 ) @ ( singleton @ X6 ) @ X4 ) ) ) ) ) ).

thf(zip_derived_cl18,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu] :
            ( ( exists_in_world @ Y1 @ Y0 )
           => ( !!
              @ ^ [Y2: mu] :
                  ( ( exists_in_world @ Y2 @ Y0 )
                 => ( (~)
                    @ ( ( (~)
                        @ ( ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 )
                          | ( in @ Y1 @ Y2 @ Y0 ) ) )
                      | ( (~)
                        @ ( ( (~) @ ( in @ Y1 @ Y2 @ Y0 ) )
                          | ( (~) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y1 ) @ Y2 ) @ ( singleton @ Y1 ) @ Y0 ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl290,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu] :
          ( ( exists_in_world @ Y0 @ X2 )
         => ( !!
            @ ^ [Y1: mu] :
                ( ( exists_in_world @ Y1 @ X2 )
               => ( (~)
                  @ ( ( (~)
                      @ ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ X2 )
                        | ( in @ Y0 @ Y1 @ X2 ) ) )
                    | ( (~)
                      @ ( ( (~) @ ( in @ Y0 @ Y1 @ X2 ) )
                        | ( (~) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ X2 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl291,plain,
    ! [X2: $i,X4: mu] :
      ( ( exists_in_world @ X4 @ X2 )
     => ( !!
        @ ^ [Y0: mu] :
            ( ( exists_in_world @ Y0 @ X2 )
           => ( (~)
              @ ( ( (~)
                  @ ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ Y0 ) @ ( singleton @ X4 ) @ X2 )
                    | ( in @ X4 @ Y0 @ X2 ) ) )
                | ( (~)
                  @ ( ( (~) @ ( in @ X4 @ Y0 @ X2 ) )
                    | ( (~) @ ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ Y0 ) @ ( singleton @ X4 ) @ X2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl290]) ).

thf(zip_derived_cl292,plain,
    ! [X2: $i,X4: mu] :
      ( ~ ( exists_in_world @ X4 @ X2 )
      | ( !!
        @ ^ [Y0: mu] :
            ( ( exists_in_world @ Y0 @ X2 )
           => ( (~)
              @ ( ( (~)
                  @ ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ Y0 ) @ ( singleton @ X4 ) @ X2 )
                    | ( in @ X4 @ Y0 @ X2 ) ) )
                | ( (~)
                  @ ( ( (~) @ ( in @ X4 @ Y0 @ X2 ) )
                    | ( (~) @ ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ Y0 ) @ ( singleton @ X4 ) @ X2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl291]) ).

thf(zip_derived_cl293,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( ( exists_in_world @ X6 @ X2 )
       => ( (~)
          @ ( ( (~)
              @ ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ ( singleton @ X4 ) @ X2 )
                | ( in @ X4 @ X6 @ X2 ) ) )
            | ( (~)
              @ ( ( (~) @ ( in @ X4 @ X6 @ X2 ) )
                | ( (~) @ ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ ( singleton @ X4 ) @ X2 ) ) ) ) ) ) )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl292]) ).

thf(zip_derived_cl294,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( ( (~)
            @ ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ ( singleton @ X4 ) @ X2 )
              | ( in @ X4 @ X6 @ X2 ) ) )
          | ( (~)
            @ ( ( (~) @ ( in @ X4 @ X6 @ X2 ) )
              | ( (~) @ ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ ( singleton @ X4 ) @ X2 ) ) ) ) )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl293]) ).

thf(zip_derived_cl295,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ ( singleton @ X4 ) @ X2 )
      | ( in @ X4 @ X6 @ X2 )
      | ~ ( exists_in_world @ X4 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl294]) ).

thf(zip_derived_cl297,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ ( singleton @ X4 ) @ X2 )
      | ( in @ X4 @ X6 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl295]) ).

thf(zip_derived_cl305,plain,
    ( ~ ( exists_in_world @ '#sk5' @ '#sk4' )
    | ~ ( exists_in_world @ '#sk6' @ '#sk4' )
    | ( in @ '#sk5' @ '#sk6' @ '#sk4' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl71,zip_derived_cl297]) ).

thf(zip_derived_cl66_001,plain,
    exists_in_world @ '#sk5' @ '#sk4',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl69_002,plain,
    exists_in_world @ '#sk6' @ '#sk4',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl313,plain,
    in @ '#sk5' @ '#sk6' @ '#sk4',
    inference(demod,[status(thm)],[zip_derived_cl305,zip_derived_cl66,zip_derived_cl69]) ).

thf(zip_derived_cl327,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl276,zip_derived_cl313]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET926^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.gm8Fn82T5m true
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat Aug 26 16:12:53 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  % Running portfolio for 300 s
% 0.12/0.34  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34  % Number of cores: 8
% 0.12/0.35  % Python version: Python 3.6.8
% 0.12/0.35  % Running in HO mode
% 0.20/0.67  % Total configuration time : 828
% 0.20/0.67  % Estimated wc time : 1656
% 0.20/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.72  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.93/0.74  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.93/0.75  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.93/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.93/0.77  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.36/0.80  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.54/0.94  % Solved by lams/35_full_unif4.sh.
% 1.54/0.94  % done 39 iterations in 0.137s
% 1.54/0.94  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.54/0.94  % SZS output start Refutation
% See solution above
% 1.54/0.94  
% 1.54/0.94  
% 1.54/0.94  % Terminating...
% 1.89/1.05  % Runner terminated.
% 1.89/1.06  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------