TSTP Solution File: PHI005^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : PHI005^2 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.EGtArhmBNu true

% Computer : n028.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 12:58:49 EDT 2023

% Result   : Theorem 1.74s 1.02s
% Output   : Refutation 1.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   57
% Syntax   : Number of formulae    :  128 (  46 unt;  23 typ;   0 def)
%            Number of atoms       :  364 (  36 equ;  10 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives : 1023 (  51   ~;  49   |;   7   &; 771   @)
%                                         (   0 <=>;  68  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   7 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  269 ( 269   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   27 (  22 usr;   6 con; 0-4 aty)
%                                         (  59  !!;  18  ??;   0 @@+;   0 @@-)
%            Number of variables   :  321 ( 200   ^; 110   !;  11   ?; 321   :)

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

thf(mdia_type,type,
    mdia: ( $i > $o ) > $i > $o ).

thf(mexists_ind_type,type,
    mexists_ind: ( mu > $i > $o ) > $i > $o ).

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

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

thf(necessary_existence_type,type,
    necessary_existence: mu > $i > $o ).

thf(msymmetric_type,type,
    msymmetric: ( $i > $i > $o ) > $o ).

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

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

thf('#sk35_type',type,
    '#sk35': ( mu > $i > $o ) > $i > mu ).

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

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

thf(mdia_generic_type,type,
    mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).

thf(essence_type,type,
    essence: ( mu > $i > $o ) > mu > $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('#sk3_type',type,
    '#sk3': mu > mu > $i > $o ).

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

thf('#sk4_type',type,
    '#sk4': $i > $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(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(mexists_ind,axiom,
    ( mexists_ind
    = ( ^ [Phi: mu > $i > $o,W: $i] :
        ? [X: mu] : ( Phi @ X @ W ) ) ) ).

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

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

thf(thmT3,conjecture,
    ( mvalid
    @ ( mbox
      @ ( mexists_ind
        @ ^ [X: mu] : ( god @ X ) ) ) ) ).

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

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

thf(zip_derived_cl4,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( (~) @ ( rel @ Y0 @ Y1 ) )
              | ( ??
                @ ^ [Y2: mu] :
                    ( !!
                    @ ^ [Y3: mu > $i > $o] :
                        ( ( positive @ Y3 @ Y1 )
                       => ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl10,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( (~) @ ( rel @ '#sk1' @ Y0 ) )
          | ( ??
            @ ^ [Y1: mu] :
                ( !!
                @ ^ [Y2: mu > $i > $o] :
                    ( ( positive @ Y2 @ Y0 )
                   => ( Y2 @ Y1 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl11,plain,
    ~ ( ( (~) @ ( rel @ '#sk1' @ '#sk2' ) )
      | ( ??
        @ ^ [Y0: mu] :
            ( !!
            @ ^ [Y1: mu > $i > $o] :
                ( ( positive @ Y1 @ '#sk2' )
               => ( Y1 @ Y0 @ '#sk2' ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl13,plain,
    ~ ( ??
      @ ^ [Y0: mu] :
          ( !!
          @ ^ [Y1: mu > $i > $o] :
              ( ( positive @ Y1 @ '#sk2' )
             => ( Y1 @ Y0 @ '#sk2' ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl14,plain,
    ! [X2: mu] :
      ~ ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ '#sk2' )
           => ( Y0 @ X2 @ '#sk2' ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl15,plain,
    ! [X2: mu] :
      ~ ( ( positive @ ( '#sk3' @ X2 ) @ '#sk2' )
       => ( '#sk3' @ X2 @ X2 @ '#sk2' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).

thf(zip_derived_cl16,plain,
    ! [X2: mu] : ( positive @ ( '#sk3' @ X2 ) @ '#sk2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl16_001,plain,
    ! [X2: mu] : ( positive @ ( '#sk3' @ X2 ) @ '#sk2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).

thf(mdia,axiom,
    ( mdia
    = ( mdia_generic @ rel ) ) ).

thf(mdia_generic,axiom,
    ( mdia_generic
    = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
        ? [V: $i] :
          ( ( Phi @ V )
          & ( R @ W @ V ) ) ) ) ).

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

thf('15',plain,
    ( mdia_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('16',plain,
    ( mdia
    = ( mdia_generic @ rel ) ),
    inference(simplify_rw_rule,[status(thm)],[mdia,'15']) ).

thf('17',plain,
    ( mdia
    = ( mdia_generic @ rel ) ),
    define([status(thm)]) ).

thf(corC,axiom,
    ( mvalid
    @ ( mdia
      @ ( mexists_ind
        @ ^ [X: mu] : ( god @ X ) ) ) ) ).

thf(zf_stmt_2,axiom,
    ! [X4: $i] :
    ? [X6: $i] :
      ( ( rel @ X4 @ X6 )
      & ? [X8: mu] :
        ! [X10: mu > $i > $o] :
          ( ( positive @ X10 @ X6 )
         => ( X10 @ X8 @ X6 ) ) ) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ??
        @ ^ [Y1: $i] :
            ( ( rel @ Y0 @ Y1 )
            & ( ??
              @ ^ [Y2: mu] :
                  ( !!
                  @ ^ [Y3: mu > $i > $o] :
                      ( ( positive @ Y3 @ Y1 )
                     => ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl22,plain,
    ! [X2: $i] :
      ( ??
      @ ^ [Y0: $i] :
          ( ( rel @ X2 @ Y0 )
          & ( ??
            @ ^ [Y1: mu] :
                ( !!
                @ ^ [Y2: mu > $i > $o] :
                    ( ( positive @ Y2 @ Y0 )
                   => ( Y2 @ Y1 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl23,plain,
    ! [X2: $i] :
      ( ( rel @ X2 @ ( '#sk4' @ X2 ) )
      & ( ??
        @ ^ [Y0: mu] :
            ( !!
            @ ^ [Y1: mu > $i > $o] :
                ( ( positive @ Y1 @ ( '#sk4' @ X2 ) )
               => ( Y1 @ Y0 @ ( '#sk4' @ X2 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl24,plain,
    ! [X2: $i] : ( rel @ X2 @ ( '#sk4' @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).

thf(msymmetric,axiom,
    ( msymmetric
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i] :
          ( ( R @ S @ T )
         => ( R @ T @ S ) ) ) ) ).

thf('18',plain,
    ( msymmetric
    = ( ^ [R: $i > $i > $o] :
        ! [S: $i,T: $i] :
          ( ( R @ S @ T )
         => ( R @ T @ S ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[msymmetric]) ).

thf('19',plain,
    ( msymmetric
    = ( ^ [V_1: $i > $i > $o] :
        ! [X4: $i,X6: $i] :
          ( ( V_1 @ X4 @ X6 )
         => ( V_1 @ X6 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(sym,axiom,
    msymmetric @ rel ).

thf(zf_stmt_3,axiom,
    ! [X4: $i,X6: $i] :
      ( ( rel @ X4 @ X6 )
     => ( rel @ X6 @ X4 ) ) ).

thf(zip_derived_cl0,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( rel @ Y0 @ Y1 )
           => ( rel @ Y1 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl5,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( rel @ X2 @ Y0 )
         => ( rel @ Y0 @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl6,plain,
    ! [X2: $i,X4: $i] :
      ( ( rel @ X2 @ X4 )
     => ( rel @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl7,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( rel @ X2 @ X4 )
      | ( rel @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl30,plain,
    ! [X0: $i] : ( rel @ ( '#sk4' @ X0 ) @ X0 ),
    inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl7]) ).

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

thf('20',plain,
    ( mforall_ind
    = ( ^ [Phi: mu > $i > $o,W: $i] :
        ! [X: mu] : ( Phi @ X @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mforall_ind]) ).

thf('21',plain,
    ( mforall_ind
    = ( ^ [V_1: mu > $i > $o,V_2: $i] :
        ! [X4: mu] : ( V_1 @ X4 @ V_2 ) ) ),
    define([status(thm)]) ).

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

thf(zf_stmt_4,axiom,
    ! [X4: $i,X6: mu] :
      ( ! [X8: mu > $i > $o] :
          ( ( positive @ X8 @ X4 )
         => ( X8 @ X6 @ X4 ) )
     => ( essence
        @ ^ [V_1: mu,V_2: $i] :
          ! [X10: mu > $i > $o] :
            ( ( positive @ X10 @ V_2 )
           => ( X10 @ V_1 @ V_2 ) )
        @ X6
        @ X4 ) ) ).

thf(zip_derived_cl3,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu] :
            ( ( !!
              @ ^ [Y2: mu > $i > $o] :
                  ( ( positive @ Y2 @ Y0 )
                 => ( Y2 @ Y1 @ Y0 ) ) )
           => ( essence
              @ ^ [Y2: mu,Y3: $i] :
                  ( !!
                  @ ^ [Y4: mu > $i > $o] :
                      ( ( positive @ Y4 @ Y3 )
                     => ( Y4 @ Y2 @ Y3 ) ) )
              @ Y1
              @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl34,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu] :
          ( ( !!
            @ ^ [Y1: mu > $i > $o] :
                ( ( positive @ Y1 @ X2 )
               => ( Y1 @ Y0 @ X2 ) ) )
         => ( essence
            @ ^ [Y1: mu,Y2: $i] :
                ( !!
                @ ^ [Y3: mu > $i > $o] :
                    ( ( positive @ Y3 @ Y2 )
                   => ( Y3 @ Y1 @ Y2 ) ) )
            @ Y0
            @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl35,plain,
    ! [X2: $i,X4: mu] :
      ( ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ X2 )
           => ( Y0 @ X4 @ X2 ) ) )
     => ( essence
        @ ^ [Y0: mu,Y1: $i] :
            ( !!
            @ ^ [Y2: mu > $i > $o] :
                ( ( positive @ Y2 @ Y1 )
               => ( Y2 @ Y0 @ Y1 ) ) )
        @ X4
        @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl36,plain,
    ! [X2: $i,X4: mu] :
      ( ~ ( !!
          @ ^ [Y0: mu > $i > $o] :
              ( ( positive @ Y0 @ X2 )
             => ( Y0 @ X4 @ X2 ) ) )
      | ( essence
        @ ^ [Y0: mu,Y1: $i] :
            ( !!
            @ ^ [Y2: mu > $i > $o] :
                ( ( positive @ Y2 @ Y1 )
               => ( Y2 @ Y0 @ Y1 ) ) )
        @ X4
        @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).

thf(zip_derived_cl38,plain,
    ! [X2: $i,X4: mu] :
      ( ~ ( ( positive @ ( '#sk10' @ X2 @ X4 ) @ X2 )
         => ( '#sk10' @ X2 @ X4 @ X4 @ X2 ) )
      | ( essence
        @ ^ [Y0: mu,Y1: $i] :
            ( !!
            @ ^ [Y2: mu > $i > $o] :
                ( ( positive @ Y2 @ Y1 )
               => ( Y2 @ Y0 @ Y1 ) ) )
        @ X4
        @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl39,plain,
    ! [X2: $i,X4: mu] :
      ( ( positive @ ( '#sk10' @ X2 @ X4 ) @ X2 )
      | ( essence
        @ ^ [Y0: mu,Y1: $i] :
            ( !!
            @ ^ [Y2: mu > $i > $o] :
                ( ( positive @ Y2 @ Y1 )
               => ( Y2 @ Y0 @ Y1 ) ) )
        @ X4
        @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).

thf(defD3,axiom,
    ( necessary_existence
    = ( ^ [X: mu] :
          ( mforall_indset
          @ ^ [Phi: mu > $i > $o] :
              ( mimplies @ ( essence @ Phi @ X )
              @ ( mbox
                @ ( mexists_ind
                  @ ^ [Y: mu] : ( Phi @ Y ) ) ) ) ) ) ) ).

thf('22',plain,
    ( necessary_existence
    = ( ^ [X: mu] :
          ( mforall_indset
          @ ^ [Phi: mu > $i > $o] :
              ( mimplies @ ( essence @ Phi @ X )
              @ ( mbox
                @ ( mexists_ind
                  @ ^ [Y: mu] : ( Phi @ Y ) ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[defD3,'11','9','13','1','3']) ).

thf('23',plain,
    ( necessary_existence
    = ( ^ [V_1: mu] :
          ( mforall_indset
          @ ^ [V_2: mu > $i > $o] :
              ( mimplies @ ( essence @ V_2 @ V_1 )
              @ ( mbox
                @ ( mexists_ind
                  @ ^ [V_3: mu] : ( V_2 @ V_3 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(axA5,axiom,
    mvalid @ ( positive @ necessary_existence ) ).

thf(zf_stmt_5,axiom,
    ! [X4: $i] :
      ( positive
      @ ^ [V_1: mu,V_2: $i] :
        ! [X6: mu > $i > $o] :
          ( ( essence @ X6 @ V_1 @ V_2 )
         => ! [X8: $i] :
              ( ~ ( rel @ V_2 @ X8 )
              | ? [X10: mu] : ( X6 @ X10 @ X8 ) ) )
      @ X4 ) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( positive
        @ ^ [Y1: mu,Y2: $i] :
            ( !!
            @ ^ [Y3: mu > $i > $o] :
                ( ( essence @ Y3 @ Y1 @ Y2 )
               => ( !!
                  @ ^ [Y4: $i] :
                      ( ( (~) @ ( rel @ Y2 @ Y4 ) )
                      | ( ??
                        @ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
        @ Y0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_5]) ).

thf(zip_derived_cl32,plain,
    ! [X2: $i] :
      ( positive
      @ ^ [Y0: mu,Y1: $i] :
          ( !!
          @ ^ [Y2: mu > $i > $o] :
              ( ( essence @ Y2 @ Y0 @ Y1 )
             => ( !!
                @ ^ [Y3: $i] :
                    ( ( (~) @ ( rel @ Y1 @ Y3 ) )
                    | ( ??
                      @ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
      @ X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl25,plain,
    ! [X2: $i] :
      ( ??
      @ ^ [Y0: mu] :
          ( !!
          @ ^ [Y1: mu > $i > $o] :
              ( ( positive @ Y1 @ ( '#sk4' @ X2 ) )
             => ( Y1 @ Y0 @ ( '#sk4' @ X2 ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).

thf(zip_derived_cl26,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu > $i > $o] :
          ( ( positive @ Y0 @ ( '#sk4' @ X2 ) )
         => ( Y0 @ ( '#sk5' @ X2 ) @ ( '#sk4' @ X2 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl27,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ( positive @ X4 @ ( '#sk4' @ X2 ) )
     => ( X4 @ ( '#sk5' @ X2 ) @ ( '#sk4' @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).

thf(zip_derived_cl29,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ~ ( positive @ X4 @ ( '#sk4' @ X2 ) )
      | ( X4 @ ( '#sk5' @ X2 ) @ ( '#sk4' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl58,plain,
    ! [X0: $i] :
      ( ^ [Y0: mu,Y1: $i] :
          ( !!
          @ ^ [Y2: mu > $i > $o] :
              ( ( essence @ Y2 @ Y0 @ Y1 )
             => ( !!
                @ ^ [Y3: $i] :
                    ( ( (~) @ ( rel @ Y1 @ Y3 ) )
                    | ( ??
                      @ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
      @ ( '#sk5' @ X0 )
      @ ( '#sk4' @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl29]) ).

thf(zip_derived_cl68,plain,
    ! [X0: $i] :
      ( !!
      @ ^ [Y0: mu > $i > $o] :
          ( ( essence @ Y0 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) )
         => ( !!
            @ ^ [Y1: $i] :
                ( ( (~) @ ( rel @ ( '#sk4' @ X0 ) @ Y1 ) )
                | ( ??
                  @ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl76,plain,
    ! [X0: $i,X2: mu > $i > $o] :
      ( ( essence @ X2 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel @ ( '#sk4' @ X0 ) @ Y0 ) )
            | ( ??
              @ ^ [Y1: mu] : ( X2 @ Y1 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl68]) ).

thf(zip_derived_cl81,plain,
    ! [X0: $i,X2: mu > $i > $o] :
      ( ~ ( essence @ X2 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) )
      | ( !!
        @ ^ [Y0: $i] :
            ( ( (~) @ ( rel @ ( '#sk4' @ X0 ) @ Y0 ) )
            | ( ??
              @ ^ [Y1: mu] : ( X2 @ Y1 @ Y0 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl82,plain,
    ! [X0: $i,X2: mu > $i > $o,X4: $i] :
      ( ( (~) @ ( rel @ ( '#sk4' @ X0 ) @ X4 ) )
      | ( ??
        @ ^ [Y0: mu] : ( X2 @ Y0 @ X4 ) )
      | ~ ( essence @ X2 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl81]) ).

thf(zip_derived_cl83,plain,
    ! [X0: $i,X2: mu > $i > $o,X4: $i] :
      ( ~ ( rel @ ( '#sk4' @ X0 ) @ X4 )
      | ( ??
        @ ^ [Y0: mu] : ( X2 @ Y0 @ X4 ) )
      | ~ ( essence @ X2 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl82]) ).

thf(zip_derived_cl84,plain,
    ! [X0: $i,X2: mu > $i > $o,X4: $i] :
      ( ( X2 @ ( '#sk35' @ X2 @ X4 ) @ X4 )
      | ~ ( essence @ X2 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) )
      | ~ ( rel @ ( '#sk4' @ X0 ) @ X4 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl83]) ).

thf(zip_derived_cl85,plain,
    ! [X0: $i,X1: $i] :
      ( ( positive @ ( '#sk10' @ ( '#sk4' @ X0 ) @ ( '#sk5' @ X0 ) ) @ ( '#sk4' @ X0 ) )
      | ~ ( rel @ ( '#sk4' @ X0 ) @ X1 )
      | ( ^ [Y0: mu,Y1: $i] :
            ( !!
            @ ^ [Y2: mu > $i > $o] :
                ( ( positive @ Y2 @ Y1 )
               => ( Y2 @ Y0 @ Y1 ) ) )
        @ ( '#sk35'
          @ ^ [Y0: mu,Y1: $i] :
              ( !!
              @ ^ [Y2: mu > $i > $o] :
                  ( ( positive @ Y2 @ Y1 )
                 => ( Y2 @ Y0 @ Y1 ) ) )
          @ X1 )
        @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl84]) ).

thf(zip_derived_cl93,plain,
    ! [X0: $i,X1: $i] :
      ( ( positive @ ( '#sk10' @ ( '#sk4' @ X0 ) @ ( '#sk5' @ X0 ) ) @ ( '#sk4' @ X0 ) )
      | ~ ( rel @ ( '#sk4' @ X0 ) @ X1 )
      | ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ X1 )
           => ( Y0
              @ ( '#sk35'
                @ ^ [Y1: mu,Y2: $i] :
                    ( !!
                    @ ^ [Y3: mu > $i > $o] :
                        ( ( positive @ Y3 @ Y2 )
                       => ( Y3 @ Y1 @ Y2 ) ) )
                @ X1 )
              @ X1 ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl85]) ).

thf(zip_derived_cl109,plain,
    ! [X0: $i,X1: $i,X3: mu > $i > $o] :
      ( ( ( positive @ X3 @ X1 )
       => ( X3
          @ ( '#sk35'
            @ ^ [Y0: mu,Y1: $i] :
                ( !!
                @ ^ [Y2: mu > $i > $o] :
                    ( ( positive @ Y2 @ Y1 )
                   => ( Y2 @ Y0 @ Y1 ) ) )
            @ X1 )
          @ X1 ) )
      | ~ ( rel @ ( '#sk4' @ X0 ) @ X1 )
      | ( positive @ ( '#sk10' @ ( '#sk4' @ X0 ) @ ( '#sk5' @ X0 ) ) @ ( '#sk4' @ X0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl93]) ).

thf(zip_derived_cl114,plain,
    ! [X0: $i,X1: $i,X3: mu > $i > $o] :
      ( ~ ( positive @ X3 @ X1 )
      | ( X3
        @ ( '#sk35'
          @ ^ [Y0: mu,Y1: $i] :
              ( !!
              @ ^ [Y2: mu > $i > $o] :
                  ( ( positive @ Y2 @ Y1 )
                 => ( Y2 @ Y0 @ Y1 ) ) )
          @ X1 )
        @ X1 )
      | ( positive @ ( '#sk10' @ ( '#sk4' @ X0 ) @ ( '#sk5' @ X0 ) ) @ ( '#sk4' @ X0 ) )
      | ~ ( rel @ ( '#sk4' @ X0 ) @ X1 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl109]) ).

thf(zip_derived_cl115,plain,
    ! [X0: $i,X1: mu > $i > $o] :
      ( ( positive @ ( '#sk10' @ ( '#sk4' @ X0 ) @ ( '#sk5' @ X0 ) ) @ ( '#sk4' @ X0 ) )
      | ( X1
        @ ( '#sk35'
          @ ^ [Y0: mu,Y1: $i] :
              ( !!
              @ ^ [Y2: mu > $i > $o] :
                  ( ( positive @ Y2 @ Y1 )
                 => ( Y2 @ Y0 @ Y1 ) ) )
          @ X0 )
        @ X0 )
      | ~ ( positive @ X1 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl114]) ).

thf(zip_derived_cl123,plain,
    ! [X0: mu] :
      ( ( '#sk3' @ X0
        @ ( '#sk35'
          @ ^ [Y0: mu,Y1: $i] :
              ( !!
              @ ^ [Y2: mu > $i > $o] :
                  ( ( positive @ Y2 @ Y1 )
                 => ( Y2 @ Y0 @ Y1 ) ) )
          @ '#sk2' )
        @ '#sk2' )
      | ( positive @ ( '#sk10' @ ( '#sk4' @ '#sk2' ) @ ( '#sk5' @ '#sk2' ) ) @ ( '#sk4' @ '#sk2' ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl115]) ).

thf(zip_derived_cl17,plain,
    ! [X2: mu] :
      ~ ( '#sk3' @ X2 @ X2 @ '#sk2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl127,plain,
    positive @ ( '#sk10' @ ( '#sk4' @ '#sk2' ) @ ( '#sk5' @ '#sk2' ) ) @ ( '#sk4' @ '#sk2' ),
    inference('sup-',[status(thm)],[zip_derived_cl123,zip_derived_cl17]) ).

thf(zip_derived_cl29_002,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ~ ( positive @ X4 @ ( '#sk4' @ X2 ) )
      | ( X4 @ ( '#sk5' @ X2 ) @ ( '#sk4' @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).

thf(zip_derived_cl129,plain,
    '#sk10' @ ( '#sk4' @ '#sk2' ) @ ( '#sk5' @ '#sk2' ) @ ( '#sk5' @ '#sk2' ) @ ( '#sk4' @ '#sk2' ),
    inference('sup-',[status(thm)],[zip_derived_cl127,zip_derived_cl29]) ).

thf(zip_derived_cl40,plain,
    ! [X2: $i,X4: mu] :
      ( ~ ( '#sk10' @ X2 @ X4 @ X4 @ X2 )
      | ( essence
        @ ^ [Y0: mu,Y1: $i] :
            ( !!
            @ ^ [Y2: mu > $i > $o] :
                ( ( positive @ Y2 @ Y1 )
               => ( Y2 @ Y0 @ Y1 ) ) )
        @ X4
        @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).

thf(zip_derived_cl133,plain,
    ( essence
    @ ^ [Y0: mu,Y1: $i] :
        ( !!
        @ ^ [Y2: mu > $i > $o] :
            ( ( positive @ Y2 @ Y1 )
           => ( Y2 @ Y0 @ Y1 ) ) )
    @ ( '#sk5' @ '#sk2' )
    @ ( '#sk4' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl129,zip_derived_cl40]) ).

thf(zip_derived_cl84_003,plain,
    ! [X0: $i,X2: mu > $i > $o,X4: $i] :
      ( ( X2 @ ( '#sk35' @ X2 @ X4 ) @ X4 )
      | ~ ( essence @ X2 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) )
      | ~ ( rel @ ( '#sk4' @ X0 ) @ X4 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl83]) ).

thf(zip_derived_cl135,plain,
    ! [X0: $i] :
      ( ~ ( rel @ ( '#sk4' @ '#sk2' ) @ X0 )
      | ( ^ [Y0: mu,Y1: $i] :
            ( !!
            @ ^ [Y2: mu > $i > $o] :
                ( ( positive @ Y2 @ Y1 )
               => ( Y2 @ Y0 @ Y1 ) ) )
        @ ( '#sk35'
          @ ^ [Y0: mu,Y1: $i] :
              ( !!
              @ ^ [Y2: mu > $i > $o] :
                  ( ( positive @ Y2 @ Y1 )
                 => ( Y2 @ Y0 @ Y1 ) ) )
          @ X0 )
        @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl133,zip_derived_cl84]) ).

thf(zip_derived_cl136,plain,
    ! [X0: $i] :
      ( ~ ( rel @ ( '#sk4' @ '#sk2' ) @ X0 )
      | ( !!
        @ ^ [Y0: mu > $i > $o] :
            ( ( positive @ Y0 @ X0 )
           => ( Y0
              @ ( '#sk35'
                @ ^ [Y1: mu,Y2: $i] :
                    ( !!
                    @ ^ [Y3: mu > $i > $o] :
                        ( ( positive @ Y3 @ Y2 )
                       => ( Y3 @ Y1 @ Y2 ) ) )
                @ X0 )
              @ X0 ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl135]) ).

thf(zip_derived_cl162,plain,
    ! [X0: $i,X2: mu > $i > $o] :
      ( ( ( positive @ X2 @ X0 )
       => ( X2
          @ ( '#sk35'
            @ ^ [Y0: mu,Y1: $i] :
                ( !!
                @ ^ [Y2: mu > $i > $o] :
                    ( ( positive @ Y2 @ Y1 )
                   => ( Y2 @ Y0 @ Y1 ) ) )
            @ X0 )
          @ X0 ) )
      | ~ ( rel @ ( '#sk4' @ '#sk2' ) @ X0 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl136]) ).

thf(zip_derived_cl167,plain,
    ! [X0: $i,X2: mu > $i > $o] :
      ( ~ ( positive @ X2 @ X0 )
      | ( X2
        @ ( '#sk35'
          @ ^ [Y0: mu,Y1: $i] :
              ( !!
              @ ^ [Y2: mu > $i > $o] :
                  ( ( positive @ Y2 @ Y1 )
                 => ( Y2 @ Y0 @ Y1 ) ) )
          @ X0 )
        @ X0 )
      | ~ ( rel @ ( '#sk4' @ '#sk2' ) @ X0 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl162]) ).

thf(zip_derived_cl171,plain,
    ! [X0: mu] :
      ( ~ ( rel @ ( '#sk4' @ '#sk2' ) @ '#sk2' )
      | ( '#sk3' @ X0
        @ ( '#sk35'
          @ ^ [Y0: mu,Y1: $i] :
              ( !!
              @ ^ [Y2: mu > $i > $o] :
                  ( ( positive @ Y2 @ Y1 )
                 => ( Y2 @ Y0 @ Y1 ) ) )
          @ '#sk2' )
        @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl167]) ).

thf(zip_derived_cl30_004,plain,
    ! [X0: $i] : ( rel @ ( '#sk4' @ X0 ) @ X0 ),
    inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl7]) ).

thf(zip_derived_cl176,plain,
    ! [X0: mu] :
      ( '#sk3' @ X0
      @ ( '#sk35'
        @ ^ [Y0: mu,Y1: $i] :
            ( !!
            @ ^ [Y2: mu > $i > $o] :
                ( ( positive @ Y2 @ Y1 )
               => ( Y2 @ Y0 @ Y1 ) ) )
        @ '#sk2' )
      @ '#sk2' ),
    inference(demod,[status(thm)],[zip_derived_cl171,zip_derived_cl30]) ).

thf(zip_derived_cl17_005,plain,
    ! [X2: mu] :
      ~ ( '#sk3' @ X2 @ X2 @ '#sk2' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl178,plain,
    $false,
    inference('sup-',[status(thm)],[zip_derived_cl176,zip_derived_cl17]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : PHI005^2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.EGtArhmBNu true
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun Aug 27 09:14:08 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.36  % Python version: Python 3.6.8
% 0.14/0.36  % Running in HO mode
% 0.22/0.68  % Total configuration time : 828
% 0.22/0.68  % Estimated wc time : 1656
% 0.22/0.68  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.72  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.74  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.78  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.81  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.49/0.92  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 1.74/1.02  % Solved by lams/35_full_unif4.sh.
% 1.74/1.02  % done 44 iterations in 0.216s
% 1.74/1.02  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.74/1.02  % SZS output start Refutation
% See solution above
% 1.74/1.02  
% 1.74/1.02  
% 1.74/1.02  % Terminating...
% 1.75/1.14  % Runner terminated.
% 1.89/1.15  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------