TSTP Solution File: SET004^4 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET004^4 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.guozOz5wQz true

% Computer : n002.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 16:11:35 EDT 2023

% Result   : Theorem 54.90s 7.87s
% Output   : Refutation 54.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   56 (  21 unt;  14 typ;   0 def)
%            Number of atoms       :  107 (  15 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  361 (  15   ~;  18   |;   5   &; 313   @)
%                                         (   6 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   61 (  61   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   99 (  46   ^;  53   !;   0   ?;  99   :)

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

thf(subset_type,type,
    subset: $i > $i > mworld > $o ).

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

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

thf(equal_set_type,type,
    equal_set: $i > $i > mworld > $o ).

thf(mactual_type,type,
    mactual: mworld ).

thf(sk__2_type,type,
    sk__2: $i ).

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

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

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

thf(sk__1_type,type,
    sk__1: $i > $i > $i ).

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

thf(intersection_type,type,
    intersection: $i > $i > $i ).

thf(sk__3_type,type,
    sk__3: $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(mand_def,axiom,
    ( mand
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
          & ( B @ W ) ) ) ) ).

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

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

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

thf('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(equal_set_0,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ) ).

thf(zf_stmt_0,axiom,
    ! [X4: $i,X6: $i] :
      ( ( equal_set @ X4 @ X6 @ mactual )
    <=> ( ( subset @ X4 @ X6 @ mactual )
        & ( subset @ X6 @ X4 @ mactual ) ) ) ).

thf(zip_derived_cl16,plain,
    ! [X0: $i,X1: $i] :
      ( ( equal_set @ X0 @ X1 @ mactual )
      | ~ ( subset @ X1 @ X0 @ mactual )
      | ~ ( subset @ X0 @ X1 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(thI06,conjecture,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] : ( equal_set @ ( intersection @ A @ B ) @ ( intersection @ B @ A ) ) ) ) ) ).

thf(zf_stmt_1,conjecture,
    ! [X4: $i,X6: $i] : ( equal_set @ ( intersection @ X4 @ X6 ) @ ( intersection @ X6 @ X4 ) @ mactual ) ).

thf(zf_stmt_2,negated_conjecture,
    ~ ! [X4: $i,X6: $i] : ( equal_set @ ( intersection @ X4 @ X6 ) @ ( intersection @ X6 @ X4 ) @ mactual ),
    inference('cnf.neg',[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl20,plain,
    ~ ( equal_set @ ( intersection @ sk__2 @ sk__3 ) @ ( intersection @ sk__3 @ sk__2 ) @ mactual ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl85,plain,
    ( ~ ( subset @ ( intersection @ sk__2 @ sk__3 ) @ ( intersection @ sk__3 @ sk__2 ) @ mactual )
    | ~ ( subset @ ( intersection @ sk__3 @ sk__2 ) @ ( intersection @ sk__2 @ sk__3 ) @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl20]) ).

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

thf('8',plain,
    ( mimplies
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
         => ( B @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies_def]) ).

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

thf(subset_0,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [A: $i] :
          ( mforall_di
          @ ^ [B: $i] :
              ( mequiv @ ( subset @ A @ B )
              @ ( mforall_di
                @ ^ [X: $i] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).

thf(zf_stmt_3,axiom,
    ! [X4: $i,X6: $i] :
      ( ( subset @ X4 @ X6 @ mactual )
    <=> ! [X8: $i] :
          ( ( member @ X8 @ X4 @ mactual )
         => ( member @ X8 @ X6 @ mactual ) ) ) ).

thf(zip_derived_cl13,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ X0 @ X1 @ mactual )
      | ( member @ ( sk__1 @ X1 @ X0 ) @ X0 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(intersection_0,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [X: $i] :
          ( mforall_di
          @ ^ [A: $i] :
              ( mforall_di
              @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).

thf(zf_stmt_4,axiom,
    ! [X4: $i,X6: $i,X8: $i] :
      ( ( member @ X4 @ ( intersection @ X6 @ X8 ) @ mactual )
    <=> ( ( member @ X4 @ X6 @ mactual )
        & ( member @ X4 @ X8 @ mactual ) ) ) ).

thf(zip_derived_cl18,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( member @ X0 @ X1 @ mactual )
      | ~ ( member @ X0 @ ( intersection @ X2 @ X1 ) @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl23,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( subset @ ( intersection @ X1 @ X0 ) @ X2 @ mactual )
      | ( member @ ( sk__1 @ X2 @ ( intersection @ X1 @ X0 ) ) @ X0 @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl18]) ).

thf(zip_derived_cl13_001,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ X0 @ X1 @ mactual )
      | ( member @ ( sk__1 @ X1 @ X0 ) @ X0 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl17,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( member @ X0 @ X1 @ mactual )
      | ~ ( member @ X0 @ ( intersection @ X1 @ X2 ) @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl21,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( subset @ ( intersection @ X1 @ X0 ) @ X2 @ mactual )
      | ( member @ ( sk__1 @ X2 @ ( intersection @ X1 @ X0 ) ) @ X1 @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl17]) ).

thf(zip_derived_cl12,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ X0 @ X1 @ mactual )
      | ~ ( member @ ( sk__1 @ X1 @ X0 ) @ X1 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl19,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( member @ X0 @ ( intersection @ X1 @ X2 ) @ mactual )
      | ~ ( member @ X0 @ X2 @ mactual )
      | ~ ( member @ X0 @ X1 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl100,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( subset @ X2 @ ( intersection @ X1 @ X0 ) @ mactual )
      | ~ ( member @ ( sk__1 @ ( intersection @ X1 @ X0 ) @ X2 ) @ X1 @ mactual )
      | ~ ( member @ ( sk__1 @ ( intersection @ X1 @ X0 ) @ X2 ) @ X0 @ mactual ) ),
    inference('sup+',[status(thm)],[zip_derived_cl12,zip_derived_cl19]) ).

thf(zip_derived_cl455,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( subset @ ( intersection @ X0 @ X1 ) @ ( intersection @ X2 @ X0 ) @ mactual )
      | ~ ( member @ ( sk__1 @ ( intersection @ X2 @ X0 ) @ ( intersection @ X0 @ X1 ) ) @ X2 @ mactual )
      | ( subset @ ( intersection @ X0 @ X1 ) @ ( intersection @ X2 @ X0 ) @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl100]) ).

thf(zip_derived_cl507,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ ( sk__1 @ ( intersection @ X2 @ X0 ) @ ( intersection @ X0 @ X1 ) ) @ X2 @ mactual )
      | ( subset @ ( intersection @ X0 @ X1 ) @ ( intersection @ X2 @ X0 ) @ mactual ) ),
    inference(simplify,[status(thm)],[zip_derived_cl455]) ).

thf(zip_derived_cl17645,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ ( intersection @ X1 @ X0 ) @ ( intersection @ X0 @ X1 ) @ mactual )
      | ( subset @ ( intersection @ X1 @ X0 ) @ ( intersection @ X0 @ X1 ) @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl507]) ).

thf(zip_derived_cl17732,plain,
    ! [X0: $i,X1: $i] : ( subset @ ( intersection @ X1 @ X0 ) @ ( intersection @ X0 @ X1 ) @ mactual ),
    inference(simplify,[status(thm)],[zip_derived_cl17645]) ).

thf(zip_derived_cl17732_002,plain,
    ! [X0: $i,X1: $i] : ( subset @ ( intersection @ X1 @ X0 ) @ ( intersection @ X0 @ X1 ) @ mactual ),
    inference(simplify,[status(thm)],[zip_derived_cl17645]) ).

thf(zip_derived_cl17810,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl85,zip_derived_cl17732,zip_derived_cl17732]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET004^4 : TPTP v8.1.2. Released v8.1.0.
% 0.13/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.guozOz5wQz true
% 0.13/0.34  % Computer : n002.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 08:42:03 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in HO mode
% 0.20/0.65  % Total configuration time : 828
% 0.20/0.65  % Estimated wc time : 1656
% 0.20/0.65  % Estimated cpu time (8 cpus) : 207.0
% 0.52/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.52/0.75  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.52/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.52/0.75  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.52/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.52/0.76  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.52/0.76  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.56/0.86  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 9.20/1.85  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 54.90/7.87  % Solved by lams/40_c.s.sh.
% 54.90/7.87  % done 2983 iterations in 7.087s
% 54.90/7.87  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 54.90/7.87  % SZS output start Refutation
% See solution above
% 54.90/7.87  
% 54.90/7.87  
% 54.90/7.87  % Terminating...
% 55.86/7.97  % Runner terminated.
% 55.86/7.98  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------