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Zipperpin---2.1.9999.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : PHI006^5 : TPTP v9.2.0. Released v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.T74dWGJj8N true

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Oct  2 04:49:04 PM UTC 2025

% Result   : Theorem 34.80s 5.37s
% Output   : Refutation 34.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   61 (  32 unt;   0 typ;   0 def)
%            Number of atoms       :  221 (  32 equ;  11 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  501 (  34   ~;  19   |;  10   &; 371   @)
%                                         (   0 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  149 ( 149   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  13 usr;   5 con; 0-3 aty)
%                                         (  35  !!;   1  ??;   0 @@+;   0 @@-)
%            Number of variables   :  228 ( 159   ^;  65   !;   4   ?; 228   :)

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

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

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

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

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

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

thf('#sk1279_type',type,
    '#sk1279': ( mu > $i > $o ) > ( mu > $i > $o ) > $i ).

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

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

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

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

thf('#sk1294_type',type,
    '#sk1294': ( mu > $i > $o ) > ( mu > $i > $o ) > mu ).

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

thf(positive_type,type,
    positive: ( mu > $i > $o ) > $i > $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(mbox,axiom,
    ( mbox
    = ( ^ [Phi: $i > $o,W: $i] :
        ! [V: $i] : ( Phi @ V ) ) ) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(axA2,axiom,
    ( mvalid
    @ ( mforall_indset
      @ ^ [Phi: mu > $i > $o] :
          ( mforall_indset
          @ ^ [Psi: mu > $i > $o] :
              ( mimplies
              @ ( mand @ ( positive @ Phi )
                @ ( mbox
                  @ ( mforall_ind
                    @ ^ [X: mu] : ( mimplies @ ( Phi @ X ) @ ( Psi @ X ) ) ) ) )
              @ ( positive @ Psi ) ) ) ) ) ).

thf(zf_stmt_0,axiom,
    ! [X4: $i,X6: mu > $i > $o,X8: mu > $i > $o] :
      ( ( ! [X10: $i,X12: mu] :
            ( ( X6 @ X12 @ X10 )
           => ( X8 @ X12 @ X10 ) )
        & ( positive @ X6 @ X4 ) )
     => ( positive @ X8 @ X4 ) ) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu > $i > $o] :
            ( !!
            @ ^ [Y2: mu > $i > $o] :
                ( ( ( !!
                    @ ^ [Y3: $i] :
                        ( !!
                        @ ^ [Y4: mu] :
                            ( ( Y1 @ Y4 @ Y3 )
                           => ( Y2 @ Y4 @ Y3 ) ) ) )
                  & ( positive @ Y1 @ Y0 ) )
               => ( positive @ Y2 @ Y0 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

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

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

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

thf(axA1b,axiom,
    ( mvalid
    @ ( mforall_indset
      @ ^ [Phi: mu > $i > $o] :
          ( mimplies @ ( mnot @ ( positive @ Phi ) )
          @ ( positive
            @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).

thf(zf_stmt_1,axiom,
    ! [X4: $i,X6: mu > $i > $o] :
      ( ~ ( positive @ X6 @ X4 )
     => ( positive
        @ ^ [V_1: mu,V_2: $i] :
            ~ ( X6 @ V_1 @ V_2 )
        @ X4 ) ) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu > $i > $o] :
            ( ( (~) @ ( positive @ Y1 @ Y0 ) )
           => ( positive
              @ ^ [Y2: mu,Y3: $i] : ( (~) @ ( Y1 @ Y2 @ Y3 ) )
              @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl64,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu > $i > $o] :
          ( ( (~) @ ( positive @ Y0 @ X2 ) )
         => ( positive
            @ ^ [Y1: mu,Y2: $i] : ( (~) @ ( Y0 @ Y1 @ Y2 ) )
            @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl65,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ( (~) @ ( positive @ X4 @ X2 ) )
     => ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
        @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl64]) ).

thf(zip_derived_cl66,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( ( positive @ X4 @ X2 )
      | ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
        @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).

thf(zip_derived_cl78,plain,
    ! [X0: $o,X1: $i] :
      ( ~ X0
      | ( positive
        @ ^ [Y0: mu,Y1: $i] : X0
        @ X1 )
      | ( positive
        @ ( ^ [Y0: $o,Y1: mu,Y2: $i] :
              ( (~)
              @ ( ^ [Y3: $o,Y4: mu,Y5: $i] : Y3
                @ Y0
                @ Y1
                @ Y2 ) )
          @ $true )
        @ X1 ) ),
    inference(fluid_loob_hoist,[status(thm)],[zip_derived_cl66]) ).

thf(zip_derived_cl121,plain,
    ! [X0: $o,X1: $i] :
      ( ~ X0
      | ( positive
        @ ^ [Y0: mu,Y1: $i] : X0
        @ X1 )
      | ( positive
        @ ^ [Y0: mu,Y1: $i] : ( (~) @ $true )
        @ X1 ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl78]) ).

thf(zip_derived_cl122,plain,
    ! [X0: $o,X1: $i] :
      ( ~ X0
      | ( positive
        @ ^ [Y0: mu,Y1: $i] : X0
        @ X1 )
      | ( positive
        @ ^ [Y0: mu,Y1: $i] : $false
        @ X1 ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl121]) ).

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

thf('14',plain,
    ( essence
    = ( ^ [Phi: mu > $i > $o,X: mu] :
          ( mforall_indset
          @ ^ [Psi: mu > $i > $o] :
              ( mimplies @ ( Psi @ X )
              @ ( mbox
                @ ( mforall_ind
                  @ ^ [Y: mu] : ( mimplies @ ( Phi @ Y ) @ ( Psi @ Y ) ) ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[defD2,'3','5','7','9']) ).

thf('15',plain,
    ( essence
    = ( ^ [V_1: mu > $i > $o,V_2: mu] :
          ( mforall_indset
          @ ^ [V_3: mu > $i > $o] :
              ( mimplies @ ( V_3 @ V_2 )
              @ ( mbox
                @ ( mforall_ind
                  @ ^ [V_4: mu] : ( mimplies @ ( V_1 @ V_4 ) @ ( V_3 @ V_4 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

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

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

thf('17',plain,
    ( mexists_ind
    = ( ^ [V_1: mu > $i > $o,V_2: $i] :
        ? [X4: mu] : ( V_1 @ X4 @ V_2 ) ) ),
    define([status(thm)]) ).

thf('18',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,'15','3','17','5','7','9']) ).

thf('19',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_2,axiom,
    ! [X4: $i] :
      ( positive
      @ ^ [V_1: mu,V_2: $i] :
        ! [X6: mu > $i > $o] :
          ( ! [X8: mu > $i > $o] :
              ( ( X8 @ V_1 @ V_2 )
             => ! [X10: $i,X12: mu] :
                  ( ( X6 @ X12 @ X10 )
                 => ( X8 @ X12 @ X10 ) ) )
         => ! [X14: $i] :
            ? [X16: mu] : ( X6 @ X16 @ X14 ) )
      @ X4 ) ).

thf(zip_derived_cl3,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( positive
        @ ^ [Y1: mu,Y2: $i] :
            ( !!
            @ ^ [Y3: mu > $i > $o] :
                ( ( !!
                  @ ^ [Y4: mu > $i > $o] :
                      ( ( Y4 @ Y1 @ Y2 )
                     => ( !!
                        @ ^ [Y5: $i] :
                            ( !!
                            @ ^ [Y6: mu] :
                                ( ( Y3 @ Y6 @ Y5 )
                               => ( Y4 @ Y6 @ Y5 ) ) ) ) ) )
               => ( !!
                  @ ^ [Y4: $i] :
                      ( ??
                      @ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) ) ) ) )
        @ Y0 ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(axA1a,axiom,
    ( mvalid
    @ ( mforall_indset
      @ ^ [Phi: mu > $i > $o] :
          ( mimplies
          @ ( positive
            @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) )
          @ ( mnot @ ( positive @ Phi ) ) ) ) ) ).

thf(zf_stmt_3,axiom,
    ! [X4: $i,X6: mu > $i > $o] :
      ( ( positive
        @ ^ [V_1: mu,V_2: $i] :
            ~ ( X6 @ V_1 @ V_2 )
        @ X4 )
     => ~ ( positive @ X6 @ X4 ) ) ).

thf(zip_derived_cl0,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu > $i > $o] :
            ( ( positive
              @ ^ [Y2: mu,Y3: $i] : ( (~) @ ( Y1 @ Y2 @ Y3 ) )
              @ Y0 )
           => ( (~) @ ( positive @ Y1 @ Y0 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl2_001,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu > $i > $o] :
            ( !!
            @ ^ [Y2: mu > $i > $o] :
                ( ( ( !!
                    @ ^ [Y3: $i] :
                        ( !!
                        @ ^ [Y4: mu] :
                            ( ( Y1 @ Y4 @ Y3 )
                           => ( Y2 @ Y4 @ Y3 ) ) ) )
                  & ( positive @ Y1 @ Y0 ) )
               => ( positive @ Y2 @ Y0 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl332,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu > $i > $o] :
          ( !!
          @ ^ [Y1: mu > $i > $o] :
              ( ( ( !!
                  @ ^ [Y2: $i] :
                      ( !!
                      @ ^ [Y3: mu] :
                          ( ( Y0 @ Y3 @ Y2 )
                         => ( Y1 @ Y3 @ Y2 ) ) ) )
                & ( positive @ Y0 @ X2 ) )
             => ( positive @ Y1 @ X2 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl333,plain,
    ! [X2: $i,X4: mu > $i > $o] :
      ( !!
      @ ^ [Y0: mu > $i > $o] :
          ( ( ( !!
              @ ^ [Y1: $i] :
                  ( !!
                  @ ^ [Y2: mu] :
                      ( ( X4 @ Y2 @ Y1 )
                     => ( Y0 @ Y2 @ Y1 ) ) ) )
            & ( positive @ X4 @ X2 ) )
         => ( positive @ Y0 @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl332]) ).

thf(zip_derived_cl334,plain,
    ! [X2: $i,X4: mu > $i > $o,X6: mu > $i > $o] :
      ( ( ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: mu] :
                  ( ( X4 @ Y1 @ Y0 )
                 => ( X6 @ Y1 @ Y0 ) ) ) )
        & ( positive @ X4 @ X2 ) )
     => ( positive @ X6 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl333]) ).

thf(zip_derived_cl335,plain,
    ! [X2: $i,X4: mu > $i > $o,X6: mu > $i > $o] :
      ( ~ ( ( !!
            @ ^ [Y0: $i] :
                ( !!
                @ ^ [Y1: mu] :
                    ( ( X4 @ Y1 @ Y0 )
                   => ( X6 @ Y1 @ Y0 ) ) ) )
          & ( positive @ X4 @ X2 ) )
      | ( positive @ X6 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl334]) ).

thf(zip_derived_cl336,plain,
    ! [X2: $i,X4: mu > $i > $o,X6: mu > $i > $o] :
      ( ~ ( !!
          @ ^ [Y0: $i] :
              ( !!
              @ ^ [Y1: mu] :
                  ( ( X4 @ Y1 @ Y0 )
                 => ( X6 @ Y1 @ Y0 ) ) ) )
      | ~ ( positive @ X4 @ X2 )
      | ( positive @ X6 @ X2 ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl335]) ).

thf(zip_derived_cl337,plain,
    ! [X2: $i,X4: mu > $i > $o,X6: mu > $i > $o] :
      ( ~ ( !!
          @ ^ [Y0: mu] :
              ( ( X4 @ Y0 @ ( '#sk1279' @ X4 @ X6 ) )
             => ( X6 @ Y0 @ ( '#sk1279' @ X4 @ X6 ) ) ) )
      | ( positive @ X6 @ X2 )
      | ~ ( positive @ X4 @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl336]) ).

thf(zip_derived_cl338,plain,
    ! [X2: $i,X4: mu > $i > $o,X6: mu > $i > $o] :
      ( ~ ( ( X4 @ ( '#sk1294' @ X4 @ X6 ) @ ( '#sk1279' @ X4 @ X6 ) )
         => ( X6 @ ( '#sk1294' @ X4 @ X6 ) @ ( '#sk1279' @ X4 @ X6 ) ) )
      | ~ ( positive @ X4 @ X2 )
      | ( positive @ X6 @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl337]) ).

thf(zip_derived_cl339,plain,
    ! [X2: $i,X4: mu > $i > $o,X6: mu > $i > $o] :
      ( ( X4 @ ( '#sk1294' @ X4 @ X6 ) @ ( '#sk1279' @ X4 @ X6 ) )
      | ( positive @ X6 @ X2 )
      | ~ ( positive @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl338]) ).

thf(zip_derived_cl393,plain,
    ! [X0: mu > $i > $o,X1: $i] :
      ( ( positive @ X0 @ X1 )
      | ~ ( positive
          @ ^ [Y0: mu,Y1: $i] :
              ( ( ^ [Y2: mu,Y3: $i] : Y2
                @ Y0
                @ Y1 )
             != ( ^ [Y2: mu,Y3: $i] : Y2
                @ Y0
                @ Y1 ) )
          @ X1 ) ),
    inference(fluid_log_symbol_hoist,[status(thm)],[zip_derived_cl339]) ).

thf(zip_derived_cl507,plain,
    ! [X0: mu > $i > $o,X1: $i] :
      ( ( positive @ X0 @ X1 )
      | ~ ( positive
          @ ^ [Y0: mu,Y1: $i] : ( Y0 != Y0 )
          @ X1 ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl393]) ).

thf(zip_derived_cl508,plain,
    ! [X0: mu > $i > $o,X1: $i] :
      ( ( positive @ X0 @ X1 )
      | ~ ( positive
          @ ^ [Y0: mu,Y1: $i] : $false
          @ X1 ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl507]) ).

thf(zip_derived_cl1027,plain,
    $false,
    inference(eprover,[status(thm)],[zip_derived_cl2,zip_derived_cl122,zip_derived_cl3,zip_derived_cl0,zip_derived_cl508]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : PHI006^5 : TPTP v9.2.0. Released v6.4.0.
% 0.03/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.T74dWGJj8N true
% 0.14/0.35  % Computer : n004.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 : Wed Oct  1 16:56:23 EDT 2025
% 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
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.35  % Running in HO mode
% 0.65/0.69  % Total configuration time : 828
% 0.65/0.69  % Estimated wc time : 1656
% 0.65/0.69  % Estimated cpu time (8 cpus) : 207.0
% 0.65/0.80  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.65/0.80  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.65/0.81  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.65/0.82  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.65/0.82  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.66/0.83  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.66/0.83  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.66/0.85  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.66/0.86  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 0.66/0.86  % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s
% 0.66/0.86  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.66/0.86  % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s
% 34.80/5.37  % Solved by lams/15_e_short1.sh.
% 34.80/5.37  % done 23 iterations in 4.496s
% 34.80/5.37  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 34.80/5.37  % SZS output start Refutation
% See solution above
% 34.80/5.38  
% 34.80/5.38  
% 34.80/5.38  % Terminating...
% 34.80/5.46  % Runner terminated.
% 34.80/5.47  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------