TSTP Solution File: SET576^7 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET576^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.g4Tn4RxGuP true

% Computer : n029.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 16:14:39 EDT 2023

% Result   : Theorem 1.58s 0.87s
% Output   : Refutation 1.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   98 (  38 unt;  17 typ;   0 def)
%            Number of atoms       :  517 (  24 equ; 116 cnn)
%            Maximal formula atoms :   24 (   6 avg)
%            Number of connectives : 1391 ( 207   ~; 136   |;   0   &; 944   @)
%                                         (   0 <=>;  62  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   8 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   89 (  89   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   20 (  16 usr;   6 con; 0-3 aty)
%                                         (  42  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  174 (  98   ^;  76   !;   0   ?; 174   :)

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

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

thf(intersect_type,type,
    intersect: mu > mu > $i > $o ).

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

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

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

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

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

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

thf(member_type,type,
    member: mu > mu > $i > $o ).

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

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

thf('#sk3_type',type,
    '#sk3': mu ).

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

thf('#sk4_type',type,
    '#sk4': mu ).

thf(disjoint_type,type,
    disjoint: mu > mu > $i > $o ).

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

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

thf('0',plain,
    ( mvalid
    = ( ^ [Phi: $i > $o] :
        ! [W: $i] : ( Phi @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mvalid]) ).

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

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

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

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

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

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

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

thf('5',plain,
    ( mnot
    = ( ^ [V_1: $i > $o,V_2: $i] :
          ~ ( V_1 @ V_2 ) ) ),
    define([status(thm)]) ).

thf('6',plain,
    ( mexists_ind
    = ( ^ [Phi: mu > $i > $o] :
          ( mnot
          @ ( mforall_ind
            @ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mexists_ind,'3','5']) ).

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

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

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

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

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

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

thf('10',plain,
    ( mimplies
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies,'9','5']) ).

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

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

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

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

thf('14',plain,
    ( mequiv
    = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mequiv,'11','13','9','5']) ).

thf('15',plain,
    ( mequiv
    = ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ ( mimplies @ V_1 @ V_2 ) @ ( mimplies @ V_2 @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf(intersect_defn,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [B: mu] :
          ( mforall_ind
          @ ^ [C: mu] :
              ( mequiv @ ( intersect @ B @ C )
              @ ( mexists_ind
                @ ^ [D: mu] : ( mand @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).

thf(zf_stmt_0,axiom,
    ! [X4: $i,X6: mu] :
      ( ( exists_in_world @ X6 @ X4 )
     => ! [X8: mu] :
          ( ( exists_in_world @ X8 @ X4 )
         => ~ ( ~ ( ( intersect @ X6 @ X8 @ X4 )
                  | ! [X12: mu] :
                      ( ( exists_in_world @ X12 @ X4 )
                     => ( ~ ( member @ X12 @ X8 @ X4 )
                        | ~ ( member @ X12 @ X6 @ X4 ) ) ) )
              | ~ ( ~ ! [X10: mu] :
                        ( ( exists_in_world @ X10 @ X4 )
                       => ( ~ ( member @ X10 @ X8 @ X4 )
                          | ~ ( member @ X10 @ X6 @ X4 ) ) )
                  | ~ ( intersect @ X6 @ X8 @ X4 ) ) ) ) ) ).

thf(zip_derived_cl4,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu] :
            ( ( exists_in_world @ Y1 @ Y0 )
           => ( !!
              @ ^ [Y2: mu] :
                  ( ( exists_in_world @ Y2 @ Y0 )
                 => ( (~)
                    @ ( ( (~)
                        @ ( ( intersect @ Y1 @ Y2 @ Y0 )
                          | ( !!
                            @ ^ [Y3: mu] :
                                ( ( exists_in_world @ Y3 @ Y0 )
                               => ( ( (~) @ ( member @ Y3 @ Y2 @ Y0 ) )
                                  | ( (~) @ ( member @ Y3 @ Y1 @ Y0 ) ) ) ) ) ) )
                      | ( (~)
                        @ ( ( (~)
                            @ ( !!
                              @ ^ [Y3: mu] :
                                  ( ( exists_in_world @ Y3 @ Y0 )
                                 => ( ( (~) @ ( member @ Y3 @ Y2 @ Y0 ) )
                                    | ( (~) @ ( member @ Y3 @ Y1 @ Y0 ) ) ) ) ) )
                          | ( (~) @ ( intersect @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl74,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu] :
          ( ( exists_in_world @ Y0 @ X2 )
         => ( !!
            @ ^ [Y1: mu] :
                ( ( exists_in_world @ Y1 @ X2 )
               => ( (~)
                  @ ( ( (~)
                      @ ( ( intersect @ Y0 @ Y1 @ X2 )
                        | ( !!
                          @ ^ [Y2: mu] :
                              ( ( exists_in_world @ Y2 @ X2 )
                             => ( ( (~) @ ( member @ Y2 @ Y1 @ X2 ) )
                                | ( (~) @ ( member @ Y2 @ Y0 @ X2 ) ) ) ) ) ) )
                    | ( (~)
                      @ ( ( (~)
                          @ ( !!
                            @ ^ [Y2: mu] :
                                ( ( exists_in_world @ Y2 @ X2 )
                               => ( ( (~) @ ( member @ Y2 @ Y1 @ X2 ) )
                                  | ( (~) @ ( member @ Y2 @ Y0 @ X2 ) ) ) ) ) )
                        | ( (~) @ ( intersect @ Y0 @ Y1 @ X2 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl75,plain,
    ! [X2: $i,X4: mu] :
      ( ( exists_in_world @ X4 @ X2 )
     => ( !!
        @ ^ [Y0: mu] :
            ( ( exists_in_world @ Y0 @ X2 )
           => ( (~)
              @ ( ( (~)
                  @ ( ( intersect @ X4 @ Y0 @ X2 )
                    | ( !!
                      @ ^ [Y1: mu] :
                          ( ( exists_in_world @ Y1 @ X2 )
                         => ( ( (~) @ ( member @ Y1 @ Y0 @ X2 ) )
                            | ( (~) @ ( member @ Y1 @ X4 @ X2 ) ) ) ) ) ) )
                | ( (~)
                  @ ( ( (~)
                      @ ( !!
                        @ ^ [Y1: mu] :
                            ( ( exists_in_world @ Y1 @ X2 )
                           => ( ( (~) @ ( member @ Y1 @ Y0 @ X2 ) )
                              | ( (~) @ ( member @ Y1 @ X4 @ X2 ) ) ) ) ) )
                    | ( (~) @ ( intersect @ X4 @ Y0 @ X2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl74]) ).

thf(zip_derived_cl76,plain,
    ! [X2: $i,X4: mu] :
      ( ~ ( exists_in_world @ X4 @ X2 )
      | ( !!
        @ ^ [Y0: mu] :
            ( ( exists_in_world @ Y0 @ X2 )
           => ( (~)
              @ ( ( (~)
                  @ ( ( intersect @ X4 @ Y0 @ X2 )
                    | ( !!
                      @ ^ [Y1: mu] :
                          ( ( exists_in_world @ Y1 @ X2 )
                         => ( ( (~) @ ( member @ Y1 @ Y0 @ X2 ) )
                            | ( (~) @ ( member @ Y1 @ X4 @ X2 ) ) ) ) ) ) )
                | ( (~)
                  @ ( ( (~)
                      @ ( !!
                        @ ^ [Y1: mu] :
                            ( ( exists_in_world @ Y1 @ X2 )
                           => ( ( (~) @ ( member @ Y1 @ Y0 @ X2 ) )
                              | ( (~) @ ( member @ Y1 @ X4 @ X2 ) ) ) ) ) )
                    | ( (~) @ ( intersect @ X4 @ Y0 @ X2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl75]) ).

thf(zip_derived_cl77,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( ( exists_in_world @ X6 @ X2 )
       => ( (~)
          @ ( ( (~)
              @ ( ( intersect @ X4 @ X6 @ X2 )
                | ( !!
                  @ ^ [Y0: mu] :
                      ( ( exists_in_world @ Y0 @ X2 )
                     => ( ( (~) @ ( member @ Y0 @ X6 @ X2 ) )
                        | ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) ) ) )
            | ( (~)
              @ ( ( (~)
                  @ ( !!
                    @ ^ [Y0: mu] :
                        ( ( exists_in_world @ Y0 @ X2 )
                       => ( ( (~) @ ( member @ Y0 @ X6 @ X2 ) )
                          | ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) ) )
                | ( (~) @ ( intersect @ X4 @ X6 @ X2 ) ) ) ) ) ) )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl78,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( ( (~)
            @ ( ( intersect @ X4 @ X6 @ X2 )
              | ( !!
                @ ^ [Y0: mu] :
                    ( ( exists_in_world @ Y0 @ X2 )
                   => ( ( (~) @ ( member @ Y0 @ X6 @ X2 ) )
                      | ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) ) ) )
          | ( (~)
            @ ( ( (~)
                @ ( !!
                  @ ^ [Y0: mu] :
                      ( ( exists_in_world @ Y0 @ X2 )
                     => ( ( (~) @ ( member @ Y0 @ X6 @ X2 ) )
                        | ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) ) )
              | ( (~) @ ( intersect @ X4 @ X6 @ X2 ) ) ) ) )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl77]) ).

thf(zip_derived_cl80,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( (~)
        @ ( !!
          @ ^ [Y0: mu] :
              ( ( exists_in_world @ Y0 @ X2 )
             => ( ( (~) @ ( member @ Y0 @ X6 @ X2 ) )
                | ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) ) )
      | ( (~) @ ( intersect @ X4 @ X6 @ X2 ) )
      | ~ ( exists_in_world @ X4 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl78]) ).

thf(zip_derived_cl82,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ~ ( !!
          @ ^ [Y0: mu] :
              ( ( exists_in_world @ Y0 @ X2 )
             => ( ( (~) @ ( member @ Y0 @ X6 @ X2 ) )
                | ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) )
      | ~ ( intersect @ X4 @ X6 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl80]) ).

thf(zip_derived_cl84,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ~ ( ( exists_in_world @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X2 )
         => ( ( (~) @ ( member @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X6 @ X2 ) )
            | ( (~) @ ( member @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X4 @ X2 ) ) ) )
      | ~ ( exists_in_world @ X4 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( intersect @ X4 @ X6 @ X2 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl82]) ).

thf(zip_derived_cl87,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ~ ( ( (~) @ ( member @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X6 @ X2 ) )
          | ( (~) @ ( member @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X4 @ X2 ) ) )
      | ~ ( intersect @ X4 @ X6 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl84]) ).

thf(zip_derived_cl89,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( member @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X6 @ X2 )
      | ~ ( exists_in_world @ X4 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( intersect @ X4 @ X6 @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl87]) ).

thf(prove_th17,conjecture,
    ( mvalid
    @ ( mforall_ind
      @ ^ [B: mu] :
          ( mforall_ind
          @ ^ [C: mu] :
              ( mimplies
              @ ( mforall_ind
                @ ^ [D: mu] : ( mimplies @ ( member @ D @ B ) @ ( mnot @ ( member @ D @ C ) ) ) )
              @ ( disjoint @ B @ C ) ) ) ) ) ).

thf(zf_stmt_1,conjecture,
    ! [X4: $i,X6: mu] :
      ( ( exists_in_world @ X6 @ X4 )
     => ! [X8: mu] :
          ( ( exists_in_world @ X8 @ X4 )
         => ( ( disjoint @ X6 @ X8 @ X4 )
            | ~ ! [X10: mu] :
                  ( ( exists_in_world @ X10 @ X4 )
                 => ( ~ ( member @ X10 @ X8 @ X4 )
                    | ~ ( member @ X10 @ X6 @ X4 ) ) ) ) ) ) ).

thf(zf_stmt_2,negated_conjecture,
    ~ ! [X4: $i,X6: mu] :
        ( ( exists_in_world @ X6 @ X4 )
       => ! [X8: mu] :
            ( ( exists_in_world @ X8 @ X4 )
           => ( ( disjoint @ X6 @ X8 @ X4 )
              | ~ ! [X10: mu] :
                    ( ( exists_in_world @ X10 @ X4 )
                   => ( ~ ( member @ X10 @ X8 @ X4 )
                      | ~ ( member @ X10 @ X6 @ X4 ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: mu] :
              ( ( exists_in_world @ Y1 @ Y0 )
             => ( !!
                @ ^ [Y2: mu] :
                    ( ( exists_in_world @ Y2 @ Y0 )
                   => ( ( disjoint @ Y1 @ Y2 @ Y0 )
                      | ( (~)
                        @ ( !!
                          @ ^ [Y3: mu] :
                              ( ( exists_in_world @ Y3 @ Y0 )
                             => ( ( (~) @ ( member @ Y3 @ Y2 @ Y0 ) )
                                | ( (~) @ ( member @ Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl50,plain,
    ~ ( !!
      @ ^ [Y0: mu] :
          ( ( exists_in_world @ Y0 @ '#sk2' )
         => ( !!
            @ ^ [Y1: mu] :
                ( ( exists_in_world @ Y1 @ '#sk2' )
               => ( ( disjoint @ Y0 @ Y1 @ '#sk2' )
                  | ( (~)
                    @ ( !!
                      @ ^ [Y2: mu] :
                          ( ( exists_in_world @ Y2 @ '#sk2' )
                         => ( ( (~) @ ( member @ Y2 @ Y1 @ '#sk2' ) )
                            | ( (~) @ ( member @ Y2 @ Y0 @ '#sk2' ) ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl51,plain,
    ~ ( ( exists_in_world @ '#sk3' @ '#sk2' )
     => ( !!
        @ ^ [Y0: mu] :
            ( ( exists_in_world @ Y0 @ '#sk2' )
           => ( ( disjoint @ '#sk3' @ Y0 @ '#sk2' )
              | ( (~)
                @ ( !!
                  @ ^ [Y1: mu] :
                      ( ( exists_in_world @ Y1 @ '#sk2' )
                     => ( ( (~) @ ( member @ Y1 @ Y0 @ '#sk2' ) )
                        | ( (~) @ ( member @ Y1 @ '#sk3' @ '#sk2' ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).

thf(zip_derived_cl53,plain,
    ~ ( !!
      @ ^ [Y0: mu] :
          ( ( exists_in_world @ Y0 @ '#sk2' )
         => ( ( disjoint @ '#sk3' @ Y0 @ '#sk2' )
            | ( (~)
              @ ( !!
                @ ^ [Y1: mu] :
                    ( ( exists_in_world @ Y1 @ '#sk2' )
                   => ( ( (~) @ ( member @ Y1 @ Y0 @ '#sk2' ) )
                      | ( (~) @ ( member @ Y1 @ '#sk3' @ '#sk2' ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl54,plain,
    ~ ( ( exists_in_world @ '#sk4' @ '#sk2' )
     => ( ( disjoint @ '#sk3' @ '#sk4' @ '#sk2' )
        | ( (~)
          @ ( !!
            @ ^ [Y0: mu] :
                ( ( exists_in_world @ Y0 @ '#sk2' )
               => ( ( (~) @ ( member @ Y0 @ '#sk4' @ '#sk2' ) )
                  | ( (~) @ ( member @ Y0 @ '#sk3' @ '#sk2' ) ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).

thf(zip_derived_cl56,plain,
    ~ ( ( disjoint @ '#sk3' @ '#sk4' @ '#sk2' )
      | ( (~)
        @ ( !!
          @ ^ [Y0: mu] :
              ( ( exists_in_world @ Y0 @ '#sk2' )
             => ( ( (~) @ ( member @ Y0 @ '#sk4' @ '#sk2' ) )
                | ( (~) @ ( member @ Y0 @ '#sk3' @ '#sk2' ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl58,plain,
    ( !!
    @ ^ [Y0: mu] :
        ( ( exists_in_world @ Y0 @ '#sk2' )
       => ( ( (~) @ ( member @ Y0 @ '#sk4' @ '#sk2' ) )
          | ( (~) @ ( member @ Y0 @ '#sk3' @ '#sk2' ) ) ) ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).

thf(zip_derived_cl59,plain,
    ! [X2: mu] :
      ( ( exists_in_world @ X2 @ '#sk2' )
     => ( ( (~) @ ( member @ X2 @ '#sk4' @ '#sk2' ) )
        | ( (~) @ ( member @ X2 @ '#sk3' @ '#sk2' ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl58]) ).

thf(zip_derived_cl60,plain,
    ! [X2: mu] :
      ( ~ ( exists_in_world @ X2 @ '#sk2' )
      | ( (~) @ ( member @ X2 @ '#sk4' @ '#sk2' ) )
      | ( (~) @ ( member @ X2 @ '#sk3' @ '#sk2' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl59]) ).

thf(zip_derived_cl61,plain,
    ! [X2: mu] :
      ( ~ ( member @ X2 @ '#sk4' @ '#sk2' )
      | ~ ( member @ X2 @ '#sk3' @ '#sk2' )
      | ~ ( exists_in_world @ X2 @ '#sk2' ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl60]) ).

thf(zip_derived_cl111,plain,
    ! [X0: mu] :
      ( ~ ( intersect @ X0 @ '#sk4' @ '#sk2' )
      | ~ ( exists_in_world @ '#sk4' @ '#sk2' )
      | ~ ( exists_in_world @ X0 @ '#sk2' )
      | ~ ( exists_in_world @ ( '#sk5' @ '#sk2' @ X0 @ '#sk4' ) @ '#sk2' )
      | ~ ( member @ ( '#sk5' @ '#sk2' @ X0 @ '#sk4' ) @ '#sk3' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl61]) ).

thf(zip_derived_cl55,plain,
    exists_in_world @ '#sk4' @ '#sk2',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl113,plain,
    ! [X0: mu] :
      ( ~ ( intersect @ X0 @ '#sk4' @ '#sk2' )
      | ~ ( exists_in_world @ X0 @ '#sk2' )
      | ~ ( exists_in_world @ ( '#sk5' @ '#sk2' @ X0 @ '#sk4' ) @ '#sk2' )
      | ~ ( member @ ( '#sk5' @ '#sk2' @ X0 @ '#sk4' ) @ '#sk3' @ '#sk2' ) ),
    inference(demod,[status(thm)],[zip_derived_cl111,zip_derived_cl55]) ).

thf(zip_derived_cl90,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( member @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X4 @ X2 )
      | ~ ( exists_in_world @ X4 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( intersect @ X4 @ X6 @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl87]) ).

thf(zip_derived_cl131,plain,
    ( ~ ( exists_in_world @ ( '#sk5' @ '#sk2' @ '#sk3' @ '#sk4' ) @ '#sk2' )
    | ~ ( exists_in_world @ '#sk3' @ '#sk2' )
    | ~ ( intersect @ '#sk3' @ '#sk4' @ '#sk2' )
    | ~ ( intersect @ '#sk3' @ '#sk4' @ '#sk2' )
    | ~ ( exists_in_world @ '#sk4' @ '#sk2' )
    | ~ ( exists_in_world @ '#sk3' @ '#sk2' ) ),
    inference('sup+',[status(thm)],[zip_derived_cl113,zip_derived_cl90]) ).

thf(disjoint_defn,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [B: mu] :
          ( mforall_ind
          @ ^ [C: mu] : ( mequiv @ ( disjoint @ B @ C ) @ ( mnot @ ( intersect @ B @ C ) ) ) ) ) ) ).

thf(zf_stmt_3,axiom,
    ! [X4: $i,X6: mu] :
      ( ( exists_in_world @ X6 @ X4 )
     => ! [X8: mu] :
          ( ( exists_in_world @ X8 @ X4 )
         => ~ ( ~ ( ( disjoint @ X6 @ X8 @ X4 )
                  | ( intersect @ X6 @ X8 @ X4 ) )
              | ~ ( ~ ( intersect @ X6 @ X8 @ X4 )
                  | ~ ( disjoint @ X6 @ X8 @ X4 ) ) ) ) ) ).

thf(zip_derived_cl5,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: mu] :
            ( ( exists_in_world @ Y1 @ Y0 )
           => ( !!
              @ ^ [Y2: mu] :
                  ( ( exists_in_world @ Y2 @ Y0 )
                 => ( (~)
                    @ ( ( (~)
                        @ ( ( disjoint @ Y1 @ Y2 @ Y0 )
                          | ( intersect @ Y1 @ Y2 @ Y0 ) ) )
                      | ( (~)
                        @ ( ( (~) @ ( intersect @ Y1 @ Y2 @ Y0 ) )
                          | ( (~) @ ( disjoint @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl41,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: mu] :
          ( ( exists_in_world @ Y0 @ X2 )
         => ( !!
            @ ^ [Y1: mu] :
                ( ( exists_in_world @ Y1 @ X2 )
               => ( (~)
                  @ ( ( (~)
                      @ ( ( disjoint @ Y0 @ Y1 @ X2 )
                        | ( intersect @ Y0 @ Y1 @ X2 ) ) )
                    | ( (~)
                      @ ( ( (~) @ ( intersect @ Y0 @ Y1 @ X2 ) )
                        | ( (~) @ ( disjoint @ Y0 @ Y1 @ X2 ) ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl42,plain,
    ! [X2: $i,X4: mu] :
      ( ( exists_in_world @ X4 @ X2 )
     => ( !!
        @ ^ [Y0: mu] :
            ( ( exists_in_world @ Y0 @ X2 )
           => ( (~)
              @ ( ( (~)
                  @ ( ( disjoint @ X4 @ Y0 @ X2 )
                    | ( intersect @ X4 @ Y0 @ X2 ) ) )
                | ( (~)
                  @ ( ( (~) @ ( intersect @ X4 @ Y0 @ X2 ) )
                    | ( (~) @ ( disjoint @ X4 @ Y0 @ X2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).

thf(zip_derived_cl43,plain,
    ! [X2: $i,X4: mu] :
      ( ~ ( exists_in_world @ X4 @ X2 )
      | ( !!
        @ ^ [Y0: mu] :
            ( ( exists_in_world @ Y0 @ X2 )
           => ( (~)
              @ ( ( (~)
                  @ ( ( disjoint @ X4 @ Y0 @ X2 )
                    | ( intersect @ X4 @ Y0 @ X2 ) ) )
                | ( (~)
                  @ ( ( (~) @ ( intersect @ X4 @ Y0 @ X2 ) )
                    | ( (~) @ ( disjoint @ X4 @ Y0 @ X2 ) ) ) ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl42]) ).

thf(zip_derived_cl44,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( ( exists_in_world @ X6 @ X2 )
       => ( (~)
          @ ( ( (~)
              @ ( ( disjoint @ X4 @ X6 @ X2 )
                | ( intersect @ X4 @ X6 @ X2 ) ) )
            | ( (~)
              @ ( ( (~) @ ( intersect @ X4 @ X6 @ X2 ) )
                | ( (~) @ ( disjoint @ X4 @ X6 @ X2 ) ) ) ) ) ) )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).

thf(zip_derived_cl45,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( ( (~)
            @ ( ( disjoint @ X4 @ X6 @ X2 )
              | ( intersect @ X4 @ X6 @ X2 ) ) )
          | ( (~)
            @ ( ( (~) @ ( intersect @ X4 @ X6 @ X2 ) )
              | ( (~) @ ( disjoint @ X4 @ X6 @ X2 ) ) ) ) )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).

thf(zip_derived_cl46,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( disjoint @ X4 @ X6 @ X2 )
      | ( intersect @ X4 @ X6 @ X2 )
      | ~ ( exists_in_world @ X4 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).

thf(zip_derived_cl48,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( disjoint @ X4 @ X6 @ X2 )
      | ( intersect @ X4 @ X6 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl46]) ).

thf(zip_derived_cl57,plain,
    ~ ( disjoint @ '#sk3' @ '#sk4' @ '#sk2' ),
    inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).

thf(zip_derived_cl63,plain,
    ( ~ ( exists_in_world @ '#sk3' @ '#sk2' )
    | ~ ( exists_in_world @ '#sk4' @ '#sk2' )
    | ( intersect @ '#sk3' @ '#sk4' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl48,zip_derived_cl57]) ).

thf(zip_derived_cl52,plain,
    exists_in_world @ '#sk3' @ '#sk2',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl55_001,plain,
    exists_in_world @ '#sk4' @ '#sk2',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl66,plain,
    intersect @ '#sk3' @ '#sk4' @ '#sk2',
    inference(demod,[status(thm)],[zip_derived_cl63,zip_derived_cl52,zip_derived_cl55]) ).

thf(zip_derived_cl86,plain,
    ! [X2: $i,X4: mu,X6: mu] :
      ( ( exists_in_world @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X2 )
      | ~ ( intersect @ X4 @ X6 @ X2 )
      | ~ ( exists_in_world @ X6 @ X2 )
      | ~ ( exists_in_world @ X4 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl84]) ).

thf(zip_derived_cl91,plain,
    ( ~ ( exists_in_world @ '#sk3' @ '#sk2' )
    | ~ ( exists_in_world @ '#sk4' @ '#sk2' )
    | ( exists_in_world @ ( '#sk5' @ '#sk2' @ '#sk3' @ '#sk4' ) @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl86]) ).

thf(zip_derived_cl52_002,plain,
    exists_in_world @ '#sk3' @ '#sk2',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl55_003,plain,
    exists_in_world @ '#sk4' @ '#sk2',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl93,plain,
    exists_in_world @ ( '#sk5' @ '#sk2' @ '#sk3' @ '#sk4' ) @ '#sk2',
    inference(demod,[status(thm)],[zip_derived_cl91,zip_derived_cl52,zip_derived_cl55]) ).

thf(zip_derived_cl52_004,plain,
    exists_in_world @ '#sk3' @ '#sk2',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl66_005,plain,
    intersect @ '#sk3' @ '#sk4' @ '#sk2',
    inference(demod,[status(thm)],[zip_derived_cl63,zip_derived_cl52,zip_derived_cl55]) ).

thf(zip_derived_cl66_006,plain,
    intersect @ '#sk3' @ '#sk4' @ '#sk2',
    inference(demod,[status(thm)],[zip_derived_cl63,zip_derived_cl52,zip_derived_cl55]) ).

thf(zip_derived_cl55_007,plain,
    exists_in_world @ '#sk4' @ '#sk2',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl52_008,plain,
    exists_in_world @ '#sk3' @ '#sk2',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl137,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl131,zip_derived_cl93,zip_derived_cl52,zip_derived_cl66,zip_derived_cl66,zip_derived_cl55,zip_derived_cl52]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET576^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.g4Tn4RxGuP true
% 0.14/0.35  % Computer : n029.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 : Sat Aug 26 13:09:24 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36  % 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
% 0.22/0.75  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.75  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.77  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.77  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.77  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.78  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.82  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.83  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.58/0.87  % Solved by lams/35_full_unif4.sh.
% 1.58/0.87  % done 29 iterations in 0.070s
% 1.58/0.87  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.58/0.87  % SZS output start Refutation
% See solution above
% 1.58/0.87  
% 1.58/0.87  
% 1.58/0.87  % Terminating...
% 2.29/0.96  % Runner terminated.
% 2.29/0.97  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------