TSTP Solution File: SEU324+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU324+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.gEu0hbnNk8 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 19:12:09 EDT 2023

% Result   : Theorem 1.22s 0.82s
% Output   : Refutation 1.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   65 (  10 unt;  14 typ;   0 def)
%            Number of atoms       :  148 (  39 equ;   0 cnn)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  567 (  70   ~;  59   |;   8   &; 400   @)
%                                         (   1 <=>;  23  =>;   6  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   5 con; 0-2 aty)
%            Number of variables   :   52 (   0   ^;  52   !;   0   ?;  52   :)

% Comments : 
%------------------------------------------------------------------------------
thf(powerset_type,type,
    powerset: $i > $i ).

thf(sk__9_type,type,
    sk__9: $i ).

thf(top_str_type,type,
    top_str: $i > $o ).

thf(open_subset_type,type,
    open_subset: $i > $i > $o ).

thf(sk__8_type,type,
    sk__8: $i ).

thf(the_carrier_type,type,
    the_carrier: $i > $i ).

thf(subset_complement_type,type,
    subset_complement: $i > $i > $i ).

thf(closed_subset_type,type,
    closed_subset: $i > $i > $o ).

thf(topological_space_type,type,
    topological_space: $i > $o ).

thf(topstr_closure_type,type,
    topstr_closure: $i > $i > $i ).

thf(sk__6_type,type,
    sk__6: $i ).

thf(element_type,type,
    element: $i > $i > $o ).

thf(sk__7_type,type,
    sk__7: $i ).

thf(interior_type,type,
    interior: $i > $i > $i ).

thf(t55_tops_1,conjecture,
    ! [A: $i] :
      ( ( ( topological_space @ A )
        & ( top_str @ A ) )
     => ! [B: $i] :
          ( ( top_str @ B )
         => ! [C: $i] :
              ( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
             => ! [D: $i] :
                  ( ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
                 => ( ( ( open_subset @ D @ B )
                     => ( ( interior @ B @ D )
                        = D ) )
                    & ( ( ( interior @ A @ C )
                        = C )
                     => ( open_subset @ C @ A ) ) ) ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [A: $i] :
        ( ( ( topological_space @ A )
          & ( top_str @ A ) )
       => ! [B: $i] :
            ( ( top_str @ B )
           => ! [C: $i] :
                ( ( element @ C @ ( powerset @ ( the_carrier @ A ) ) )
               => ! [D: $i] :
                    ( ( element @ D @ ( powerset @ ( the_carrier @ B ) ) )
                   => ( ( ( open_subset @ D @ B )
                       => ( ( interior @ B @ D )
                          = D ) )
                      & ( ( ( interior @ A @ C )
                          = C )
                       => ( open_subset @ C @ A ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[t55_tops_1]) ).

thf(zip_derived_cl37,plain,
    ( ( open_subset @ sk__9 @ sk__7 )
    | ( ( interior @ sk__6 @ sk__8 )
      = sk__8 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf('0',plain,
    ( ( ( interior @ sk__6 @ sk__8 )
      = sk__8 )
    | ( open_subset @ sk__9 @ sk__7 ) ),
    inference(split,[status(esa)],[zip_derived_cl37]) ).

thf(t30_tops_1,axiom,
    ! [A: $i] :
      ( ( top_str @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
         => ( ( open_subset @ B @ A )
          <=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) ) ) ).

thf(zip_derived_cl25,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( the_carrier @ X1 ) ) )
      | ~ ( open_subset @ X0 @ X1 )
      | ( closed_subset @ ( subset_complement @ ( the_carrier @ X1 ) @ X0 ) @ X1 )
      | ~ ( top_str @ X1 ) ),
    inference(cnf,[status(esa)],[t30_tops_1]) ).

thf(involutiveness_k3_subset_1,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ B @ ( powerset @ A ) )
     => ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
        = B ) ) ).

thf(zip_derived_cl16,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( subset_complement @ X1 @ ( subset_complement @ X1 @ X0 ) )
        = X0 )
      | ~ ( element @ X0 @ ( powerset @ X1 ) ) ),
    inference(cnf,[status(esa)],[involutiveness_k3_subset_1]) ).

thf(t52_pre_topc,axiom,
    ! [A: $i] :
      ( ( top_str @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
         => ( ( ( closed_subset @ B @ A )
             => ( ( topstr_closure @ A @ B )
                = B ) )
            & ( ( ( topological_space @ A )
                & ( ( topstr_closure @ A @ B )
                  = B ) )
             => ( closed_subset @ B @ A ) ) ) ) ) ).

thf(zip_derived_cl30,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( the_carrier @ X1 ) ) )
      | ~ ( closed_subset @ X0 @ X1 )
      | ( ( topstr_closure @ X1 @ X0 )
        = X0 )
      | ~ ( top_str @ X1 ) ),
    inference(cnf,[status(esa)],[t52_pre_topc]) ).

thf(zip_derived_cl16_001,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( subset_complement @ X1 @ ( subset_complement @ X1 @ X0 ) )
        = X0 )
      | ~ ( element @ X0 @ ( powerset @ X1 ) ) ),
    inference(cnf,[status(esa)],[involutiveness_k3_subset_1]) ).

thf(d1_tops_1,axiom,
    ! [A: $i] :
      ( ( top_str @ A )
     => ! [B: $i] :
          ( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
         => ( ( interior @ A @ B )
            = ( subset_complement @ ( the_carrier @ A ) @ ( topstr_closure @ A @ ( subset_complement @ ( the_carrier @ A ) @ B ) ) ) ) ) ) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( the_carrier @ X1 ) ) )
      | ( ( interior @ X1 @ X0 )
        = ( subset_complement @ ( the_carrier @ X1 ) @ ( topstr_closure @ X1 @ ( subset_complement @ ( the_carrier @ X1 ) @ X0 ) ) ) )
      | ~ ( top_str @ X1 ) ),
    inference(cnf,[status(esa)],[d1_tops_1]) ).

thf(zip_derived_cl65,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( the_carrier @ X1 ) ) )
      | ~ ( element @ ( subset_complement @ ( the_carrier @ X1 ) @ X0 ) @ ( powerset @ ( the_carrier @ X1 ) ) )
      | ( ( interior @ X1 @ ( subset_complement @ ( the_carrier @ X1 ) @ X0 ) )
        = ( subset_complement @ ( the_carrier @ X1 ) @ ( topstr_closure @ X1 @ X0 ) ) )
      | ~ ( top_str @ X1 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl16,zip_derived_cl0]) ).

thf(dt_k3_subset_1,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ B @ ( powerset @ A ) )
     => ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ) ).

thf(zip_derived_cl3,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ ( subset_complement @ X0 @ X1 ) @ ( powerset @ X0 ) )
      | ~ ( element @ X1 @ ( powerset @ X0 ) ) ),
    inference(cnf,[status(esa)],[dt_k3_subset_1]) ).

thf(zip_derived_cl110,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( top_str @ X1 )
      | ( ( interior @ X1 @ ( subset_complement @ ( the_carrier @ X1 ) @ X0 ) )
        = ( subset_complement @ ( the_carrier @ X1 ) @ ( topstr_closure @ X1 @ X0 ) ) )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ X1 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl65,zip_derived_cl3]) ).

thf(zip_derived_cl120,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( top_str @ X1 )
      | ~ ( closed_subset @ X0 @ X1 )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ X1 ) ) )
      | ~ ( top_str @ X1 )
      | ( ( interior @ X1 @ ( subset_complement @ ( the_carrier @ X1 ) @ X0 ) )
        = ( subset_complement @ ( the_carrier @ X1 ) @ X0 ) )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ X1 ) ) ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl30,zip_derived_cl110]) ).

thf(zip_derived_cl121,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( interior @ X1 @ ( subset_complement @ ( the_carrier @ X1 ) @ X0 ) )
        = ( subset_complement @ ( the_carrier @ X1 ) @ X0 ) )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ X1 ) ) )
      | ~ ( closed_subset @ X0 @ X1 )
      | ~ ( top_str @ X1 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl120]) ).

thf(zip_derived_cl131,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( the_carrier @ X1 ) ) )
      | ( ( interior @ X1 @ X0 )
        = X0 )
      | ~ ( element @ ( subset_complement @ ( the_carrier @ X1 ) @ X0 ) @ ( powerset @ ( the_carrier @ X1 ) ) )
      | ~ ( closed_subset @ ( subset_complement @ ( the_carrier @ X1 ) @ X0 ) @ X1 )
      | ~ ( top_str @ X1 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl16,zip_derived_cl121]) ).

thf(zip_derived_cl3_002,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ ( subset_complement @ X0 @ X1 ) @ ( powerset @ X0 ) )
      | ~ ( element @ X1 @ ( powerset @ X0 ) ) ),
    inference(cnf,[status(esa)],[dt_k3_subset_1]) ).

thf(zip_derived_cl138,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( top_str @ X1 )
      | ~ ( closed_subset @ ( subset_complement @ ( the_carrier @ X1 ) @ X0 ) @ X1 )
      | ( ( interior @ X1 @ X0 )
        = X0 )
      | ~ ( element @ X0 @ ( powerset @ ( the_carrier @ X1 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl131,zip_derived_cl3]) ).

thf(zip_derived_cl140,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( top_str @ X0 )
      | ~ ( open_subset @ X1 @ X0 )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ X0 ) ) )
      | ~ ( top_str @ X0 )
      | ( ( interior @ X0 @ X1 )
        = X1 )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ X0 ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl138]) ).

thf(zip_derived_cl144,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( interior @ X0 @ X1 )
        = X1 )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ X0 ) ) )
      | ~ ( open_subset @ X1 @ X0 )
      | ~ ( top_str @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl140]) ).

thf(zip_derived_cl34,plain,
    ( ( ( interior @ sk__7 @ sk__9 )
     != sk__9 )
    | ~ ( open_subset @ sk__8 @ sk__6 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl41,plain,
    ( ( ( interior @ sk__7 @ sk__9 )
     != sk__9 )
   <= ( ( interior @ sk__7 @ sk__9 )
     != sk__9 ) ),
    inference(split,[status(esa)],[zip_derived_cl34]) ).

thf('1',plain,
    ( ( ( interior @ sk__7 @ sk__9 )
     != sk__9 )
    | ~ ( open_subset @ sk__8 @ sk__6 ) ),
    inference(split,[status(esa)],[zip_derived_cl34]) ).

thf(zip_derived_cl35,plain,
    ( ( ( interior @ sk__7 @ sk__9 )
     != sk__9 )
    | ( ( interior @ sk__6 @ sk__8 )
      = sk__8 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf('2',plain,
    ( ( ( interior @ sk__6 @ sk__8 )
      = sk__8 )
    | ( ( interior @ sk__7 @ sk__9 )
     != sk__9 ) ),
    inference(split,[status(esa)],[zip_derived_cl35]) ).

thf(zip_derived_cl42,plain,
    ( ( ( interior @ sk__6 @ sk__8 )
      = sk__8 )
   <= ( ( interior @ sk__6 @ sk__8 )
      = sk__8 ) ),
    inference(split,[status(esa)],[zip_derived_cl35]) ).

thf(fc6_tops_1,axiom,
    ! [A: $i,B: $i] :
      ( ( ( topological_space @ A )
        & ( top_str @ A )
        & ( element @ B @ ( powerset @ ( the_carrier @ A ) ) ) )
     => ( open_subset @ ( interior @ A @ B ) @ A ) ) ).

thf(zip_derived_cl15,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( top_str @ X0 )
      | ~ ( topological_space @ X0 )
      | ~ ( element @ X1 @ ( powerset @ ( the_carrier @ X0 ) ) )
      | ( open_subset @ ( interior @ X0 @ X1 ) @ X0 ) ),
    inference(cnf,[status(esa)],[fc6_tops_1]) ).

thf(zip_derived_cl59,plain,
    ( ( ~ ( top_str @ sk__6 )
      | ~ ( topological_space @ sk__6 )
      | ~ ( element @ sk__8 @ ( powerset @ ( the_carrier @ sk__6 ) ) )
      | ( open_subset @ sk__8 @ sk__6 ) )
   <= ( ( interior @ sk__6 @ sk__8 )
      = sk__8 ) ),
    inference('s_sup+',[status(thm)],[zip_derived_cl42,zip_derived_cl15]) ).

thf(zip_derived_cl32,plain,
    top_str @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl31,plain,
    topological_space @ sk__6,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl33,plain,
    element @ sk__8 @ ( powerset @ ( the_carrier @ sk__6 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl60,plain,
    ( ( open_subset @ sk__8 @ sk__6 )
   <= ( ( interior @ sk__6 @ sk__8 )
      = sk__8 ) ),
    inference(demod,[status(thm)],[zip_derived_cl59,zip_derived_cl32,zip_derived_cl31,zip_derived_cl33]) ).

thf(zip_derived_cl40,plain,
    ( ~ ( open_subset @ sk__8 @ sk__6 )
   <= ~ ( open_subset @ sk__8 @ sk__6 ) ),
    inference(split,[status(esa)],[zip_derived_cl34]) ).

thf('3',plain,
    ( ( open_subset @ sk__8 @ sk__6 )
    | ( ( interior @ sk__6 @ sk__8 )
     != sk__8 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl60,zip_derived_cl40]) ).

thf('4',plain,
    ( ( interior @ sk__7 @ sk__9 )
   != sk__9 ),
    inference('sat_resolution*',[status(thm)],['1','2','3']) ).

thf(zip_derived_cl62,plain,
    ( ( interior @ sk__7 @ sk__9 )
   != sk__9 ),
    inference(simpl_trail,[status(thm)],[zip_derived_cl41,'4']) ).

thf(zip_derived_cl150,plain,
    ( ~ ( top_str @ sk__7 )
    | ~ ( open_subset @ sk__9 @ sk__7 )
    | ~ ( element @ sk__9 @ ( powerset @ ( the_carrier @ sk__7 ) ) )
    | ( sk__9 != sk__9 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl144,zip_derived_cl62]) ).

thf(zip_derived_cl39,plain,
    top_str @ sk__7,
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl38,plain,
    element @ sk__9 @ ( powerset @ ( the_carrier @ sk__7 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl153,plain,
    ( ~ ( open_subset @ sk__9 @ sk__7 )
    | ( sk__9 != sk__9 ) ),
    inference(demod,[status(thm)],[zip_derived_cl150,zip_derived_cl39,zip_derived_cl38]) ).

thf(zip_derived_cl154,plain,
    ~ ( open_subset @ sk__9 @ sk__7 ),
    inference(simplify,[status(thm)],[zip_derived_cl153]) ).

thf(zip_derived_cl36,plain,
    ( ( open_subset @ sk__9 @ sk__7 )
    | ~ ( open_subset @ sk__8 @ sk__6 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl44,plain,
    ( ( open_subset @ sk__9 @ sk__7 )
   <= ( open_subset @ sk__9 @ sk__7 ) ),
    inference(split,[status(esa)],[zip_derived_cl36]) ).

thf('5',plain,
    ~ ( open_subset @ sk__9 @ sk__7 ),
    inference('s_sup+',[status(thm)],[zip_derived_cl154,zip_derived_cl44]) ).

thf('6',plain,
    ( ~ ( open_subset @ sk__8 @ sk__6 )
    | ( open_subset @ sk__9 @ sk__7 ) ),
    inference(split,[status(esa)],[zip_derived_cl36]) ).

thf(zip_derived_cl185,plain,
    $false,
    inference('sat_resolution*',[status(thm)],['0','5','6','3']) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SEU324+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.gEu0hbnNk8 true
% 0.16/0.36  % Computer : n002.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Wed Aug 23 15:15:01 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.16/0.36  % Running portfolio for 300 s
% 0.16/0.36  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.36  % Number of cores: 8
% 0.16/0.37  % Python version: Python 3.6.8
% 0.16/0.37  % Running in FO mode
% 0.23/0.68  % Total configuration time : 435
% 0.23/0.68  % Estimated wc time : 1092
% 0.23/0.68  % Estimated cpu time (7 cpus) : 156.0
% 0.23/0.73  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.23/0.75  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.23/0.75  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.23/0.77  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.23/0.78  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.23/0.79  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.23/0.81  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.22/0.82  % Solved by fo/fo1_av.sh.
% 1.22/0.82  % done 61 iterations in 0.044s
% 1.22/0.82  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.22/0.82  % SZS output start Refutation
% See solution above
% 1.22/0.82  
% 1.22/0.82  
% 1.22/0.82  % Terminating...
% 1.62/0.89  % Runner terminated.
% 1.65/0.90  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------