↑ Up

Zipperpin---2.1.9999.THM-Ref.s

View TPTP
Problem
Process solution in
SystemOnTSTP
Download .tgz
%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : LCL944^8 : TPTP v9.3.1. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.bYV52buvdE true

% Computer : n031.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon Sep  7 01:37:37 PM UTC 2026

% Result   : Theorem 268.09s 35.44s
% Output   : Refutation 268.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   85 (  27 unt;   0 typ;   0 def)
%            Number of atoms       :  608 (  15 equ;   0 cnn)
%            Maximal formula atoms :   32 (   7 avg)
%            Number of connectives : 1539 (  52   ~;  46   |;   7   &;1019   @)
%                                         (   0 <=>; 241  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (  11 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   24 (  24   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  18 usr;   4 con; 0-3 aty)
%                                         ( 174  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  292 ( 215   ^;  77   !;   0   ?; 292   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mworld_type,type,
    mworld: $tType ).

thf('#form83_type',type,
    '#form83': mworld > $o ).

thf(implies_type,type,
    implies: $i > $i > $i ).

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

thf(or_2_type,type,
    or_2: mworld > $o ).

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

thf(or_type,type,
    or: $i > $i > $i ).

thf(eiw_di_type,type,
    eiw_di: $i > mworld > $o ).

thf(mactual_type,type,
    mactual: mworld ).

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

thf('#sk1_type',type,
    '#sk1': mworld ).

thf('#sk84_type',type,
    '#sk84': mworld > mworld ).

thf(mforall_di_type,type,
    mforall_di: ( $i > mworld > $o ) > mworld > $o ).

thf(mlocal_type,type,
    mlocal: ( mworld > $o ) > $o ).

thf(mrel_type,type,
    mrel: mworld > mworld > $o ).

thf(r2_type,type,
    r2: mworld > $o ).

thf(is_a_theorem_type,type,
    is_a_theorem: $i > mworld > $o ).

thf('#form81_type',type,
    '#form81': mworld > $o ).

thf('#form153_type',type,
    '#form153': mworld > $o ).

thf(mrel_reflexive,axiom,
    ! [W: mworld] : ( mrel @ W @ W ) ).

thf(zip_derived_cl0,plain,
    ( !!
    @ ^ [Y0: mworld] : ( mrel @ Y0 @ Y0 ) ),
    inference(cnf,[status(esa)],[mrel_reflexive]) ).

thf(zip_derived_cl71,plain,
    ! [X2: mworld] : ( mrel @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).

thf(mforall_di_def,axiom,
    ( mforall_di
    = ( ^ [A: $i > mworld > $o,W: mworld] :
        ! [X: $i] :
          ( ( eiw_di @ X @ W )
         => ( A @ X @ W ) ) ) ) ).

thf('0',plain,
    ( mforall_di
    = ( ^ [A: $i > mworld > $o,W: mworld] :
        ! [X: $i] :
          ( ( eiw_di @ X @ W )
         => ( A @ X @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mforall_di_def]) ).

thf('1',plain,
    ( mforall_di
    = ( ^ [V_1: $i > mworld > $o,V_2: mworld] :
        ! [X4: $i] :
          ( ( eiw_di @ X4 @ V_2 )
         => ( V_1 @ X4 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(mbox_def,axiom,
    ( mbox
    = ( ^ [Phi: mworld > $o,W: mworld] :
        ! [V: mworld] :
          ( ( mrel @ W @ V )
         => ( Phi @ V ) ) ) ) ).

thf('2',plain,
    ( mbox
    = ( ^ [Phi: mworld > $o,W: mworld] :
        ! [V: mworld] :
          ( ( mrel @ W @ V )
         => ( Phi @ V ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mbox_def]) ).

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

thf(mimplies_def,axiom,
    ( mimplies
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
         => ( B @ W ) ) ) ) ).

thf('4',plain,
    ( mimplies
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
         => ( B @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies_def]) ).

thf('5',plain,
    ( mimplies
    = ( ^ [V_1: mworld > $o,V_2: mworld > $o,V_3: mworld] :
          ( ( V_1 @ V_3 )
         => ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(mand_def,axiom,
    ( mand
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
          & ( B @ W ) ) ) ) ).

thf('6',plain,
    ( mand
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
          & ( B @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mand_def]) ).

thf('7',plain,
    ( mand
    = ( ^ [V_1: mworld > $o,V_2: mworld > $o,V_3: mworld] :
          ( ( V_1 @ V_3 )
          & ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(mlocal_def,axiom,
    ( mlocal
    = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).

thf('8',plain,
    ( mlocal
    = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mlocal_def]) ).

thf('9',plain,
    ( mlocal
    = ( ^ [V_1: mworld > $o] : ( V_1 @ mactual ) ) ),
    define([status(thm)]) ).

thf(r2_0,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ r2 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [P: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [P: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) ) ) ) )
          @ ( mbox @ r2 ) ) ) ) ) ).

thf(zf_stmt_0,axiom,
    ( ! [X18: mworld] :
        ( ( mrel @ mactual @ X18 )
       => ( ! [X20: mworld] :
              ( ( mrel @ X18 @ X20 )
             => ! [X22: $i] :
                  ( ( eiw_di @ X22 @ X20 )
                 => ! [X24: mworld] :
                      ( ( mrel @ X20 @ X24 )
                     => ! [X26: $i] :
                          ( ( eiw_di @ X26 @ X24 )
                         => ! [X28: mworld] :
                              ( ( mrel @ X24 @ X28 )
                             => ( is_a_theorem @ ( implies @ X26 @ ( or @ X22 @ X26 ) ) @ X28 ) ) ) ) ) )
         => ! [X30: mworld] :
              ( ( mrel @ X18 @ X30 )
             => ( r2 @ X30 ) ) ) )
    & ! [X4: mworld] :
        ( ( mrel @ mactual @ X4 )
       => ( ! [X6: mworld] :
              ( ( mrel @ X4 @ X6 )
             => ( r2 @ X6 ) )
         => ! [X8: mworld] :
              ( ( mrel @ X4 @ X8 )
             => ! [X10: $i] :
                  ( ( eiw_di @ X10 @ X8 )
                 => ! [X12: mworld] :
                      ( ( mrel @ X8 @ X12 )
                     => ! [X14: $i] :
                          ( ( eiw_di @ X14 @ X12 )
                         => ! [X16: mworld] :
                              ( ( mrel @ X12 @ X16 )
                             => ( is_a_theorem @ ( implies @ X14 @ ( or @ X10 @ X14 ) ) @ X16 ) ) ) ) ) ) ) ) ) ).

thf(zip_derived_cl37,plain,
    ( ( !!
      @ ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ( ( !!
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( eiw_di @ Y2 @ Y1 )
                       => ( !!
                          @ ^ [Y3: mworld] :
                              ( ( mrel @ Y1 @ Y3 )
                             => ( !!
                                @ ^ [Y4: $i] :
                                    ( ( eiw_di @ Y4 @ Y3 )
                                   => ( !!
                                      @ ^ [Y5: mworld] :
                                          ( ( mrel @ Y3 @ Y5 )
                                         => ( is_a_theorem @ ( implies @ Y4 @ ( or @ Y2 @ Y4 ) ) @ Y5 ) ) ) ) ) ) ) ) ) ) )
           => ( !!
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( r2 @ Y1 ) ) ) ) ) )
    & ( !!
      @ ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ( ( !!
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( r2 @ Y1 ) ) )
           => ( !!
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( eiw_di @ Y2 @ Y1 )
                       => ( !!
                          @ ^ [Y3: mworld] :
                              ( ( mrel @ Y1 @ Y3 )
                             => ( !!
                                @ ^ [Y4: $i] :
                                    ( ( eiw_di @ Y4 @ Y3 )
                                   => ( !!
                                      @ ^ [Y5: mworld] :
                                          ( ( mrel @ Y3 @ Y5 )
                                         => ( is_a_theorem @ ( implies @ Y4 @ ( or @ Y2 @ Y4 ) ) @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2094,plain,
    ( !!
    @ ^ [Y0: mworld] :
        ( ( mrel @ mactual @ Y0 )
       => ( ( !!
            @ ^ [Y1: mworld] :
                ( ( mrel @ Y0 @ Y1 )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( eiw_di @ Y2 @ Y1 )
                     => ( !!
                        @ ^ [Y3: mworld] :
                            ( ( mrel @ Y1 @ Y3 )
                           => ( !!
                              @ ^ [Y4: $i] :
                                  ( ( eiw_di @ Y4 @ Y3 )
                                 => ( !!
                                    @ ^ [Y5: mworld] :
                                        ( ( mrel @ Y3 @ Y5 )
                                       => ( is_a_theorem @ ( implies @ Y4 @ ( or @ Y2 @ Y4 ) ) @ Y5 ) ) ) ) ) ) ) ) ) ) )
         => ( !!
            @ ^ [Y1: mworld] :
                ( ( mrel @ Y0 @ Y1 )
               => ( r2 @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl2096,plain,
    ! [X2: mworld] :
      ( ( mrel @ mactual @ X2 )
     => ( ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( eiw_di @ Y1 @ Y0 )
                   => ( !!
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y0 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( eiw_di @ Y3 @ Y2 )
                               => ( !!
                                  @ ^ [Y4: mworld] :
                                      ( ( mrel @ Y2 @ Y4 )
                                     => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) )
       => ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( r2 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2094]) ).

thf(zip_derived_cl2098,plain,
    ! [X2: mworld] :
      ( ~ ( mrel @ mactual @ X2 )
      | ( ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( eiw_di @ Y1 @ Y0 )
                   => ( !!
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y0 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( eiw_di @ Y3 @ Y2 )
                               => ( !!
                                  @ ^ [Y4: mworld] :
                                      ( ( mrel @ Y2 @ Y4 )
                                     => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) )
       => ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( r2 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2096]) ).

thf(zip_derived_cl2100,plain,
    ! [X2: mworld] :
      ( ~ ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( eiw_di @ Y1 @ Y0 )
                   => ( !!
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y0 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( eiw_di @ Y3 @ Y2 )
                               => ( !!
                                  @ ^ [Y4: mworld] :
                                      ( ( mrel @ Y2 @ Y4 )
                                     => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( r2 @ Y0 ) ) )
      | ~ ( mrel @ mactual @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2098]) ).

thf(or_2_0,axiom,
    ( mlocal
    @ ( mand
      @ ( mbox
        @ ( mimplies @ ( mbox @ or_2 )
          @ ( mbox
            @ ( mforall_di
              @ ^ [X: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) ) ) ) ) ) )
      @ ( mbox
        @ ( mimplies
          @ ( mbox
            @ ( mforall_di
              @ ^ [X: $i] :
                  ( mbox
                  @ ( mforall_di
                    @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) ) ) ) )
          @ ( mbox @ or_2 ) ) ) ) ) ).

thf(zf_stmt_1,axiom,
    ( ! [X18: mworld] :
        ( ( mrel @ mactual @ X18 )
       => ( ! [X20: mworld] :
              ( ( mrel @ X18 @ X20 )
             => ! [X22: $i] :
                  ( ( eiw_di @ X22 @ X20 )
                 => ! [X24: mworld] :
                      ( ( mrel @ X20 @ X24 )
                     => ! [X26: $i] :
                          ( ( eiw_di @ X26 @ X24 )
                         => ! [X28: mworld] :
                              ( ( mrel @ X24 @ X28 )
                             => ( is_a_theorem @ ( implies @ X26 @ ( or @ X22 @ X26 ) ) @ X28 ) ) ) ) ) )
         => ! [X30: mworld] :
              ( ( mrel @ X18 @ X30 )
             => ( or_2 @ X30 ) ) ) )
    & ! [X4: mworld] :
        ( ( mrel @ mactual @ X4 )
       => ( ! [X6: mworld] :
              ( ( mrel @ X4 @ X6 )
             => ( or_2 @ X6 ) )
         => ! [X8: mworld] :
              ( ( mrel @ X4 @ X8 )
             => ! [X10: $i] :
                  ( ( eiw_di @ X10 @ X8 )
                 => ! [X12: mworld] :
                      ( ( mrel @ X8 @ X12 )
                     => ! [X14: $i] :
                          ( ( eiw_di @ X14 @ X12 )
                         => ! [X16: mworld] :
                              ( ( mrel @ X12 @ X16 )
                             => ( is_a_theorem @ ( implies @ X14 @ ( or @ X10 @ X14 ) ) @ X16 ) ) ) ) ) ) ) ) ) ).

thf(zip_derived_cl25,plain,
    ( ( !!
      @ ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ( ( !!
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( eiw_di @ Y2 @ Y1 )
                       => ( !!
                          @ ^ [Y3: mworld] :
                              ( ( mrel @ Y1 @ Y3 )
                             => ( !!
                                @ ^ [Y4: $i] :
                                    ( ( eiw_di @ Y4 @ Y3 )
                                   => ( !!
                                      @ ^ [Y5: mworld] :
                                          ( ( mrel @ Y3 @ Y5 )
                                         => ( is_a_theorem @ ( implies @ Y4 @ ( or @ Y2 @ Y4 ) ) @ Y5 ) ) ) ) ) ) ) ) ) ) )
           => ( !!
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( or_2 @ Y1 ) ) ) ) ) )
    & ( !!
      @ ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ( ( !!
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( or_2 @ Y1 ) ) )
           => ( !!
              @ ^ [Y1: mworld] :
                  ( ( mrel @ Y0 @ Y1 )
                 => ( !!
                    @ ^ [Y2: $i] :
                        ( ( eiw_di @ Y2 @ Y1 )
                       => ( !!
                          @ ^ [Y3: mworld] :
                              ( ( mrel @ Y1 @ Y3 )
                             => ( !!
                                @ ^ [Y4: $i] :
                                    ( ( eiw_di @ Y4 @ Y3 )
                                   => ( !!
                                      @ ^ [Y5: mworld] :
                                          ( ( mrel @ Y3 @ Y5 )
                                         => ( is_a_theorem @ ( implies @ Y4 @ ( or @ Y2 @ Y4 ) ) @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1297,plain,
    ( !!
    @ ^ [Y0: mworld] :
        ( ( mrel @ mactual @ Y0 )
       => ( ( !!
            @ ^ [Y1: mworld] :
                ( ( mrel @ Y0 @ Y1 )
               => ( or_2 @ Y1 ) ) )
         => ( !!
            @ ^ [Y1: mworld] :
                ( ( mrel @ Y0 @ Y1 )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( eiw_di @ Y2 @ Y1 )
                     => ( !!
                        @ ^ [Y3: mworld] :
                            ( ( mrel @ Y1 @ Y3 )
                           => ( !!
                              @ ^ [Y4: $i] :
                                  ( ( eiw_di @ Y4 @ Y3 )
                                 => ( !!
                                    @ ^ [Y5: mworld] :
                                        ( ( mrel @ Y3 @ Y5 )
                                       => ( is_a_theorem @ ( implies @ Y4 @ ( or @ Y2 @ Y4 ) ) @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl1299,plain,
    ! [X2: mworld] :
      ( ( mrel @ mactual @ X2 )
     => ( ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( or_2 @ Y0 ) ) )
       => ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( eiw_di @ Y1 @ Y0 )
                   => ( !!
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y0 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( eiw_di @ Y3 @ Y2 )
                               => ( !!
                                  @ ^ [Y4: mworld] :
                                      ( ( mrel @ Y2 @ Y4 )
                                     => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1297]) ).

thf(zip_derived_cl1301,plain,
    ! [X2: mworld] :
      ( ~ ( mrel @ mactual @ X2 )
      | ( ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( or_2 @ Y0 ) ) )
       => ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( eiw_di @ Y1 @ Y0 )
                   => ( !!
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y0 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( eiw_di @ Y3 @ Y2 )
                               => ( !!
                                  @ ^ [Y4: mworld] :
                                      ( ( mrel @ Y2 @ Y4 )
                                     => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1299]) ).

thf(zip_derived_cl1303,plain,
    ! [X2: mworld] :
      ( ~ ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( or_2 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( eiw_di @ Y1 @ Y0 )
                 => ( !!
                    @ ^ [Y2: mworld] :
                        ( ( mrel @ Y0 @ Y2 )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( eiw_di @ Y3 @ Y2 )
                             => ( !!
                                @ ^ [Y4: mworld] :
                                    ( ( mrel @ Y2 @ Y4 )
                                   => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) )
      | ~ ( mrel @ mactual @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1301]) ).

thf(zip_derived_cl1303_001,plain,
    ! [X2: mworld] :
      ( ~ ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( or_2 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( eiw_di @ Y1 @ Y0 )
                 => ( !!
                    @ ^ [Y2: mworld] :
                        ( ( mrel @ Y0 @ Y2 )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( eiw_di @ Y3 @ Y2 )
                             => ( !!
                                @ ^ [Y4: mworld] :
                                    ( ( mrel @ Y2 @ Y4 )
                                   => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) )
      | ~ ( mrel @ mactual @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1301]) ).

thf(zip_derived_cl1307,plain,
    ! [X2: mworld] :
      ( ( '#form83' @ X2 )
      | ~ ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( or_2 @ Y0 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl1309,plain,
    ! [X2: mworld] :
      ( ~ ( '#form83' @ X2 )
      | ~ ( mrel @ mactual @ X2 )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( eiw_di @ Y1 @ Y0 )
                 => ( !!
                    @ ^ [Y2: mworld] :
                        ( ( mrel @ Y0 @ Y2 )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( eiw_di @ Y3 @ Y2 )
                             => ( !!
                                @ ^ [Y4: mworld] :
                                    ( ( mrel @ Y2 @ Y4 )
                                   => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl1303,zip_derived_cl1307]) ).

thf(zip_derived_cl1315,plain,
    ! [X2: mworld] :
      ( ~ ( '#form81' @ X2 )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( eiw_di @ Y1 @ Y0 )
                 => ( !!
                    @ ^ [Y2: mworld] :
                        ( ( mrel @ Y0 @ Y2 )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( eiw_di @ Y3 @ Y2 )
                             => ( !!
                                @ ^ [Y4: mworld] :
                                    ( ( mrel @ Y2 @ Y4 )
                                   => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl1296,plain,
    ( !!
    @ ^ [Y0: mworld] :
        ( ( mrel @ mactual @ Y0 )
       => ( ( !!
            @ ^ [Y1: mworld] :
                ( ( mrel @ Y0 @ Y1 )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( eiw_di @ Y2 @ Y1 )
                     => ( !!
                        @ ^ [Y3: mworld] :
                            ( ( mrel @ Y1 @ Y3 )
                           => ( !!
                              @ ^ [Y4: $i] :
                                  ( ( eiw_di @ Y4 @ Y3 )
                                 => ( !!
                                    @ ^ [Y5: mworld] :
                                        ( ( mrel @ Y3 @ Y5 )
                                       => ( is_a_theorem @ ( implies @ Y4 @ ( or @ Y2 @ Y4 ) ) @ Y5 ) ) ) ) ) ) ) ) ) ) )
         => ( !!
            @ ^ [Y1: mworld] :
                ( ( mrel @ Y0 @ Y1 )
               => ( or_2 @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl1298,plain,
    ! [X2: mworld] :
      ( ( mrel @ mactual @ X2 )
     => ( ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( eiw_di @ Y1 @ Y0 )
                   => ( !!
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y0 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( eiw_di @ Y3 @ Y2 )
                               => ( !!
                                  @ ^ [Y4: mworld] :
                                      ( ( mrel @ Y2 @ Y4 )
                                     => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) )
       => ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( or_2 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1296]) ).

thf(zip_derived_cl1300,plain,
    ! [X2: mworld] :
      ( ~ ( mrel @ mactual @ X2 )
      | ( ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( eiw_di @ Y1 @ Y0 )
                   => ( !!
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y0 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( eiw_di @ Y3 @ Y2 )
                               => ( !!
                                  @ ^ [Y4: mworld] :
                                      ( ( mrel @ Y2 @ Y4 )
                                     => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) )
       => ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( or_2 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1298]) ).

thf(zip_derived_cl1302,plain,
    ! [X2: mworld] :
      ( ~ ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( eiw_di @ Y1 @ Y0 )
                   => ( !!
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y0 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( eiw_di @ Y3 @ Y2 )
                               => ( !!
                                  @ ^ [Y4: mworld] :
                                      ( ( mrel @ Y2 @ Y4 )
                                     => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( or_2 @ Y0 ) ) )
      | ~ ( mrel @ mactual @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1300]) ).

thf(zip_derived_cl1304,plain,
    ! [X2: mworld] :
      ( ( '#form81' @ X2 )
      | ~ ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( eiw_di @ Y1 @ Y0 )
                   => ( !!
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y0 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( eiw_di @ Y3 @ Y2 )
                               => ( !!
                                  @ ^ [Y4: mworld] :
                                      ( ( mrel @ Y2 @ Y4 )
                                     => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl2102,plain,
    ! [X2: mworld] :
      ( ~ ( '#form81' @ X2 )
      | ~ ( mrel @ mactual @ X2 )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( r2 @ Y0 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl2100,zip_derived_cl1315,zip_derived_cl1304]) ).

thf(zip_derived_cl2102_002,plain,
    ! [X2: mworld] :
      ( ~ ( '#form81' @ X2 )
      | ~ ( mrel @ mactual @ X2 )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( r2 @ Y0 ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl2100,zip_derived_cl1315,zip_derived_cl1304]) ).

thf(zip_derived_cl2106,plain,
    ! [X2: mworld] :
      ( ~ ( '#form153' @ X2 )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( r2 @ Y0 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl2095,plain,
    ( !!
    @ ^ [Y0: mworld] :
        ( ( mrel @ mactual @ Y0 )
       => ( ( !!
            @ ^ [Y1: mworld] :
                ( ( mrel @ Y0 @ Y1 )
               => ( r2 @ Y1 ) ) )
         => ( !!
            @ ^ [Y1: mworld] :
                ( ( mrel @ Y0 @ Y1 )
               => ( !!
                  @ ^ [Y2: $i] :
                      ( ( eiw_di @ Y2 @ Y1 )
                     => ( !!
                        @ ^ [Y3: mworld] :
                            ( ( mrel @ Y1 @ Y3 )
                           => ( !!
                              @ ^ [Y4: $i] :
                                  ( ( eiw_di @ Y4 @ Y3 )
                                 => ( !!
                                    @ ^ [Y5: mworld] :
                                        ( ( mrel @ Y3 @ Y5 )
                                       => ( is_a_theorem @ ( implies @ Y4 @ ( or @ Y2 @ Y4 ) ) @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl2097,plain,
    ! [X2: mworld] :
      ( ( mrel @ mactual @ X2 )
     => ( ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( r2 @ Y0 ) ) )
       => ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( eiw_di @ Y1 @ Y0 )
                   => ( !!
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y0 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( eiw_di @ Y3 @ Y2 )
                               => ( !!
                                  @ ^ [Y4: mworld] :
                                      ( ( mrel @ Y2 @ Y4 )
                                     => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2095]) ).

thf(zip_derived_cl2099,plain,
    ! [X2: mworld] :
      ( ~ ( mrel @ mactual @ X2 )
      | ( ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( r2 @ Y0 ) ) )
       => ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( eiw_di @ Y1 @ Y0 )
                   => ( !!
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y0 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( eiw_di @ Y3 @ Y2 )
                               => ( !!
                                  @ ^ [Y4: mworld] :
                                      ( ( mrel @ Y2 @ Y4 )
                                     => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2097]) ).

thf(zip_derived_cl2101,plain,
    ! [X2: mworld] :
      ( ~ ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( r2 @ Y0 ) ) )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( eiw_di @ Y1 @ Y0 )
                 => ( !!
                    @ ^ [Y2: mworld] :
                        ( ( mrel @ Y0 @ Y2 )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( eiw_di @ Y3 @ Y2 )
                             => ( !!
                                @ ^ [Y4: mworld] :
                                    ( ( mrel @ Y2 @ Y4 )
                                   => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) )
      | ~ ( mrel @ mactual @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2099]) ).

thf(zip_derived_cl2103,plain,
    ! [X2: mworld] :
      ( ( '#form153' @ X2 )
      | ~ ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( r2 @ Y0 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl2108,plain,
    ! [X2: mworld] :
      ( ( '#form153' @ X2 )
      | ~ ( mrel @ mactual @ X2 )
      | ~ ( '#form81' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl2102,zip_derived_cl2106,zip_derived_cl2103]) ).

thf(zip_derived_cl2113,plain,
    ( ~ ( '#form81' @ mactual )
    | ( '#form153' @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl71,zip_derived_cl2108]) ).

thf(principia_r2,conjecture,
    mlocal @ ( mbox @ r2 ) ).

thf(zf_stmt_2,conjecture,
    ! [X4: mworld] :
      ( ( mrel @ mactual @ X4 )
     => ( r2 @ X4 ) ) ).

thf(zf_stmt_3,negated_conjecture,
    ~ ! [X4: mworld] :
        ( ( mrel @ mactual @ X4 )
       => ( r2 @ X4 ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl67,plain,
    ~ ( !!
      @ ^ [Y0: mworld] :
          ( ( mrel @ mactual @ Y0 )
         => ( r2 @ Y0 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl68,plain,
    ~ ( ( mrel @ mactual @ '#sk1' )
     => ( r2 @ '#sk1' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl67]) ).

thf(zip_derived_cl69,plain,
    mrel @ mactual @ '#sk1',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl2106_003,plain,
    ! [X2: mworld] :
      ( ~ ( '#form153' @ X2 )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( r2 @ Y0 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl2107,plain,
    ! [X2: mworld,X4: mworld] :
      ( ( ( mrel @ X2 @ X4 )
       => ( r2 @ X4 ) )
      | ~ ( '#form153' @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2106]) ).

thf(zip_derived_cl2112,plain,
    ! [X2: mworld,X4: mworld] :
      ( ~ ( mrel @ X2 @ X4 )
      | ( r2 @ X4 )
      | ~ ( '#form153' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2107]) ).

thf(zip_derived_cl2132,plain,
    ( ~ ( '#form153' @ mactual )
    | ( r2 @ '#sk1' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl69,zip_derived_cl2112]) ).

thf(zip_derived_cl70,plain,
    ~ ( r2 @ '#sk1' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl2142,plain,
    ~ ( '#form153' @ mactual ),
    inference(clc,[status(thm)],[zip_derived_cl2132,zip_derived_cl70]) ).

thf(zip_derived_cl2468,plain,
    ~ ( '#form81' @ mactual ),
    inference(clc,[status(thm)],[zip_derived_cl2113,zip_derived_cl2142]) ).

thf(zip_derived_cl71_004,plain,
    ! [X2: mworld] : ( mrel @ X2 @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl1309_005,plain,
    ! [X2: mworld] :
      ( ~ ( '#form83' @ X2 )
      | ~ ( mrel @ mactual @ X2 )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( eiw_di @ Y1 @ Y0 )
                 => ( !!
                    @ ^ [Y2: mworld] :
                        ( ( mrel @ Y0 @ Y2 )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( eiw_di @ Y3 @ Y2 )
                             => ( !!
                                @ ^ [Y4: mworld] :
                                    ( ( mrel @ Y2 @ Y4 )
                                   => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(renaming,[status(thm)],[zip_derived_cl1303,zip_derived_cl1307]) ).

thf(zip_derived_cl1315_006,plain,
    ! [X2: mworld] :
      ( ~ ( '#form81' @ X2 )
      | ( !!
        @ ^ [Y0: mworld] :
            ( ( mrel @ X2 @ Y0 )
           => ( !!
              @ ^ [Y1: $i] :
                  ( ( eiw_di @ Y1 @ Y0 )
                 => ( !!
                    @ ^ [Y2: mworld] :
                        ( ( mrel @ Y0 @ Y2 )
                       => ( !!
                          @ ^ [Y3: $i] :
                              ( ( eiw_di @ Y3 @ Y2 )
                             => ( !!
                                @ ^ [Y4: mworld] :
                                    ( ( mrel @ Y2 @ Y4 )
                                   => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl1304_007,plain,
    ! [X2: mworld] :
      ( ( '#form81' @ X2 )
      | ~ ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( !!
                @ ^ [Y1: $i] :
                    ( ( eiw_di @ Y1 @ Y0 )
                   => ( !!
                      @ ^ [Y2: mworld] :
                          ( ( mrel @ Y0 @ Y2 )
                         => ( !!
                            @ ^ [Y3: $i] :
                                ( ( eiw_di @ Y3 @ Y2 )
                               => ( !!
                                  @ ^ [Y4: mworld] :
                                      ( ( mrel @ Y2 @ Y4 )
                                     => ( is_a_theorem @ ( implies @ Y3 @ ( or @ Y1 @ Y3 ) ) @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl1317,plain,
    ! [X2: mworld] :
      ( ( '#form81' @ X2 )
      | ~ ( mrel @ mactual @ X2 )
      | ~ ( '#form83' @ X2 ) ),
    inference(renaming,[status(thm)],[zip_derived_cl1309,zip_derived_cl1315,zip_derived_cl1304]) ).

thf(zip_derived_cl1362,plain,
    ( ~ ( '#form83' @ mactual )
    | ( '#form81' @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl71,zip_derived_cl1317]) ).

thf(zip_derived_cl2469,plain,
    ~ ( '#form83' @ mactual ),
    inference('sup+',[status(thm)],[zip_derived_cl2468,zip_derived_cl1362]) ).

thf(zip_derived_cl1307_008,plain,
    ! [X2: mworld] :
      ( ( '#form83' @ X2 )
      | ~ ( !!
          @ ^ [Y0: mworld] :
              ( ( mrel @ X2 @ Y0 )
             => ( or_2 @ Y0 ) ) ) ),
    define([status(thm)]) ).

thf(zip_derived_cl1308,plain,
    ! [X2: mworld] :
      ( ~ ( ( mrel @ X2 @ ( '#sk84' @ X2 ) )
         => ( or_2 @ ( '#sk84' @ X2 ) ) )
      | ( '#form83' @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1307]) ).

thf(zip_derived_cl1318,plain,
    ! [X2: mworld] :
      ( ( mrel @ X2 @ ( '#sk84' @ X2 ) )
      | ( '#form83' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1308]) ).

thf(hilbert_or_2,axiom,
    mlocal @ ( mbox @ or_2 ) ).

thf(zf_stmt_4,axiom,
    ! [X4: mworld] :
      ( ( mrel @ mactual @ X4 )
     => ( or_2 @ X4 ) ) ).

thf(zip_derived_cl58,plain,
    ( !!
    @ ^ [Y0: mworld] :
        ( ( mrel @ mactual @ Y0 )
       => ( or_2 @ Y0 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl532,plain,
    ! [X2: mworld] :
      ( ( mrel @ mactual @ X2 )
     => ( or_2 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl533,plain,
    ! [X2: mworld] :
      ( ~ ( mrel @ mactual @ X2 )
      | ( or_2 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl532]) ).

thf(zip_derived_cl7442,plain,
    ( ( '#form83' @ mactual )
    | ( or_2 @ ( '#sk84' @ mactual ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1318,zip_derived_cl533]) ).

thf(zip_derived_cl2469_009,plain,
    ~ ( '#form83' @ mactual ),
    inference('sup+',[status(thm)],[zip_derived_cl2468,zip_derived_cl1362]) ).

thf(zip_derived_cl7544,plain,
    or_2 @ ( '#sk84' @ mactual ),
    inference(demod,[status(thm)],[zip_derived_cl7442,zip_derived_cl2469]) ).

thf(zip_derived_cl1319,plain,
    ! [X2: mworld] :
      ( ~ ( or_2 @ ( '#sk84' @ X2 ) )
      | ( '#form83' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1308]) ).

thf(zip_derived_cl23413,plain,
    '#form83' @ mactual,
    inference('sup-',[status(thm)],[zip_derived_cl7544,zip_derived_cl1319]) ).

thf(zip_derived_cl23414,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl2469,zip_derived_cl23413]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : LCL944^8 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.bYV52buvdE true
% 0.09/0.37  % Computer : n031.cluster.edu
% 0.09/0.37  % Model    : x86_64 x86_64
% 0.09/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37  % Memory   : 8046.5625MB
% 0.09/0.37  % OS       : Linux 6.8.0-71-generic
% 0.09/0.37  % CPULimit : 300
% 0.09/0.37  % WCLimit  : 300
% 0.09/0.37  % DateTime : Sat Sep  5 05:34:54 UTC 2026
% 0.09/0.37  % CPUTime  : 
% 0.09/0.37  % Running portfolio for 300 s
% 0.09/0.37  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37  % Number of cores: 8
% 0.09/0.38  % Python version: Python 3.12.3
% 0.09/0.38  % Running in HO mode
% 0.36/0.61  % Total configuration time : 828
% 0.36/0.61  % Estimated wc time : 1656
% 0.36/0.61  % Estimated cpu time (8 cpus) : 207.0
% 0.42/0.68  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.42/0.74  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.42/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.42/0.74  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.42/0.74  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.42/0.74  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.42/0.74  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.42/0.79  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.45/0.84  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 0.45/0.86  % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 0.46/0.97  % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 30s
% 168.37/23.85  % /export/starexec/sandbox/solver/bin/lams/15_lifting3.sh running for 30s
% 222.40/30.80  % /export/starexec/sandbox/solver/bin/lams/33_shallow_sine.sh running for 66s
% 268.09/35.44  % Solved by lams/15_lifting3.sh.
% 268.09/35.44  % done 1566 iterations in 11.523s
% 268.09/35.44  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 268.09/35.44  % SZS output start Refutation
% See solution above
% 268.09/35.45  
% 268.09/35.45  
% 268.09/35.45  % Terminating...
% 65.21/35.50  % Runner terminated.
% 65.21/35.54  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------