TSTP Solution File: SET924^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET924^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.MMQNwQhwiu 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 16:16:50 EDT 2023

% Result   : Theorem 0.21s 0.79s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   39 (  16 unt;  12 typ;   0 def)
%            Number of atoms       :   78 (  15 equ;   6 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  210 (  18   ~;   0   |;   0   &; 174   @)
%                                         (  12 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   41 (  41   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  11 usr;   6 con; 0-3 aty)
%                                         (   6  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   48 (  34   ^;  14   !;   0   ?;  48   :)

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

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

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

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

thf(mactual_type,type,
    mactual: mworld ).

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

thf('#sk3_type',type,
    '#sk3': $i ).

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

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

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

thf(singleton_type,type,
    singleton: $i > $i ).

thf(set_difference_type,type,
    set_difference: $i > $i > $i ).

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

thf('0',plain,
    ( mforall_di
    = ( ^ [A: $i > mworld > $o,W: mworld] :
        ! [X: $i] : ( 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] : ( V_1 @ X4 @ V_2 ) ) ),
    define([status(thm)]) ).

thf(mequiv_def,axiom,
    ( mequiv
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
        <=> ( B @ W ) ) ) ) ).

thf('2',plain,
    ( mequiv
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
        <=> ( B @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mequiv_def]) ).

thf('3',plain,
    ( mequiv
    = ( ^ [V_1: mworld > $o,V_2: mworld > $o,V_3: mworld] :
          ( ( V_1 @ V_3 )
        <=> ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(mnot_def,axiom,
    ( mnot
    = ( ^ [A: mworld > $o,W: mworld] :
          ~ ( A @ W ) ) ) ).

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

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

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

thf('6',plain,
    ( mlocal
    = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mlocal_def]) ).

thf('7',plain,
    ( mlocal
    = ( ^ [V_1: mworld > $o] : ( V_1 @ mactual ) ) ),
    define([status(thm)]) ).

thf(t67_zfmisc_1,conjecture,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i,X6: $i] :
      ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ ( singleton @ X4 ) @ mactual )
    <=> ~ ( in @ X4 @ X6 @ mactual ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i,X6: $i] :
        ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ ( singleton @ X4 ) @ mactual )
      <=> ~ ( in @ X4 @ X6 @ mactual ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl12,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
            <=> ( (~) @ ( in @ Y0 @ Y1 @ mactual ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl34,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( qmltpeq @ ( set_difference @ ( singleton @ '#sk3' ) @ Y0 ) @ ( singleton @ '#sk3' ) @ mactual )
        <=> ( (~) @ ( in @ '#sk3' @ Y0 @ mactual ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl35,plain,
    ~ ( ( qmltpeq @ ( set_difference @ ( singleton @ '#sk3' ) @ '#sk4' ) @ ( singleton @ '#sk3' ) @ mactual )
    <=> ( (~) @ ( in @ '#sk3' @ '#sk4' @ mactual ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).

thf(zip_derived_cl36,plain,
    ( ( qmltpeq @ ( set_difference @ ( singleton @ '#sk3' ) @ '#sk4' ) @ ( singleton @ '#sk3' ) @ mactual )
    = ( in @ '#sk3' @ '#sk4' @ mactual ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl35]) ).

thf(l34_zfmisc_1,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).

thf(zf_stmt_2,axiom,
    ! [X4: $i,X6: $i] :
      ( ( qmltpeq @ ( set_difference @ ( singleton @ X4 ) @ X6 ) @ ( singleton @ X4 ) @ mactual )
    <=> ~ ( in @ X4 @ X6 @ mactual ) ) ).

thf(zip_derived_cl13,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
          <=> ( (~) @ ( in @ Y0 @ Y1 @ mactual ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl51,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ Y0 ) @ ( singleton @ X2 ) @ mactual )
        <=> ( (~) @ ( in @ X2 @ Y0 @ mactual ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl52,plain,
    ! [X2: $i,X4: $i] :
      ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X4 ) @ ( singleton @ X2 ) @ mactual )
    <=> ( (~) @ ( in @ X2 @ X4 @ mactual ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).

thf(zip_derived_cl53,plain,
    ! [X2: $i,X4: $i] :
      ( ( qmltpeq @ ( set_difference @ ( singleton @ X2 ) @ X4 ) @ ( singleton @ X2 ) @ mactual )
     != ( in @ X2 @ X4 @ mactual ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl52]) ).

thf(zip_derived_cl54,plain,
    ( ( in @ '#sk3' @ '#sk4' @ mactual )
   != ( in @ '#sk3' @ '#sk4' @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl53]) ).

thf(zip_derived_cl59,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl54]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET924^1 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.MMQNwQhwiu true
% 0.14/0.36  % Computer : n029.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sat Aug 26 12:24:54 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  % Running portfolio for 300 s
% 0.14/0.36  % 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
% 0.21/0.66  % Total configuration time : 828
% 0.21/0.66  % Estimated wc time : 1656
% 0.21/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.72  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.79  % Solved by lams/35_full_unif4.sh.
% 0.21/0.79  % done 8 iterations in 0.025s
% 0.21/0.79  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.21/0.79  % SZS output start Refutation
% See solution above
% 0.21/0.79  
% 0.21/0.79  
% 0.21/0.79  % Terminating...
% 0.21/0.85  % Runner terminated.
% 0.21/0.86  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------