TSTP Solution File: SEU326+2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU326+2 : 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.IIo6Vd1tza true

% Computer : n022.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 19:12:10 EDT 2023

% Result   : Theorem 1.62s 0.98s
% Output   : Refutation 1.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   75 (  17 unt;  11 typ;   0 def)
%            Number of atoms       :  130 (  58 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  415 (  69   ~;  45   |;   9   &; 280   @)
%                                         (   4 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (  13   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :   89 (   0   ^;  89   !;   0   ?;  89   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sk__9_type,type,
    sk__9: $i ).

thf(sk__10_type,type,
    sk__10: $i ).

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

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

thf(sk__4_type,type,
    sk__4: $i > $i > $i ).

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

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

thf(complements_of_subsets_type,type,
    complements_of_subsets: $i > $i > $i ).

thf(sk__type,type,
    sk_: $i > $i ).

thf(empty_type,type,
    empty: $i > $o ).

thf(empty_set_type,type,
    empty_set: $i ).

thf(involutiveness_k7_setfam_1,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
     => ( ( complements_of_subsets @ A @ ( complements_of_subsets @ A @ B ) )
        = B ) ) ).

thf(zip_derived_cl17,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( complements_of_subsets @ X1 @ ( complements_of_subsets @ X1 @ X0 ) )
        = X0 )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ X1 ) ) ) ),
    inference(cnf,[status(esa)],[involutiveness_k7_setfam_1]) ).

thf(t2_xboole_1,axiom,
    ! [A: $i] : ( subset @ empty_set @ A ) ).

thf(zip_derived_cl26,plain,
    ! [X0: $i] : ( subset @ empty_set @ X0 ),
    inference(cnf,[status(esa)],[t2_xboole_1]) ).

thf(d1_zfmisc_1,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( powerset @ A ) )
    <=> ! [C: $i] :
          ( ( in @ C @ B )
        <=> ( subset @ C @ A ) ) ) ).

thf(zip_derived_cl2,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( subset @ X0 @ X1 )
      | ( in @ X0 @ X2 )
      | ( X2
       != ( powerset @ X1 ) ) ),
    inference(cnf,[status(esa)],[d1_zfmisc_1]) ).

thf(zip_derived_cl82,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1
       != ( powerset @ X0 ) )
      | ( in @ empty_set @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl26,zip_derived_cl2]) ).

thf(zip_derived_cl101,plain,
    ! [X0: $i] : ( in @ empty_set @ ( powerset @ X0 ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl82]) ).

thf(t1_subset,axiom,
    ! [A: $i,B: $i] :
      ( ( in @ A @ B )
     => ( element @ A @ B ) ) ).

thf(zip_derived_cl25,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ X1 )
      | ~ ( in @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[t1_subset]) ).

thf(zip_derived_cl104,plain,
    ! [X0: $i] : ( element @ empty_set @ ( powerset @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl101,zip_derived_cl25]) ).

thf(dt_k7_setfam_1,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
     => ( element @ ( complements_of_subsets @ A @ B ) @ ( powerset @ ( powerset @ A ) ) ) ) ).

thf(zip_derived_cl11,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ ( complements_of_subsets @ X0 @ X1 ) @ ( powerset @ ( powerset @ X0 ) ) )
      | ~ ( element @ X1 @ ( powerset @ ( powerset @ X0 ) ) ) ),
    inference(cnf,[status(esa)],[dt_k7_setfam_1]) ).

thf(zip_derived_cl17_001,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( complements_of_subsets @ X1 @ ( complements_of_subsets @ X1 @ X0 ) )
        = X0 )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ X1 ) ) ) ),
    inference(cnf,[status(esa)],[involutiveness_k7_setfam_1]) ).

thf(zip_derived_cl17_002,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( complements_of_subsets @ X1 @ ( complements_of_subsets @ X1 @ X0 ) )
        = X0 )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ X1 ) ) ) ),
    inference(cnf,[status(esa)],[involutiveness_k7_setfam_1]) ).

thf(fc1_xboole_0,axiom,
    empty @ empty_set ).

thf(zip_derived_cl14,plain,
    empty @ empty_set,
    inference(cnf,[status(esa)],[fc1_xboole_0]) ).

thf(d1_xboole_0,axiom,
    ! [A: $i] :
      ( ( A = empty_set )
    <=> ! [B: $i] :
          ~ ( in @ B @ A ) ) ).

thf(zip_derived_cl1,plain,
    ! [X0: $i] :
      ( ( X0 = empty_set )
      | ( in @ ( sk_ @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[d1_xboole_0]) ).

thf(l71_subset_1,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( in @ C @ A )
         => ( in @ C @ B ) )
     => ( element @ A @ ( powerset @ B ) ) ) ).

thf(zip_derived_cl19,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ ( powerset @ X1 ) )
      | ~ ( in @ ( sk__4 @ X1 @ X0 ) @ X1 ) ),
    inference(cnf,[status(esa)],[l71_subset_1]) ).

thf(zip_derived_cl20,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ ( powerset @ X1 ) )
      | ( in @ ( sk__4 @ X1 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[l71_subset_1]) ).

thf(zip_derived_cl336,plain,
    ! [X0: $i] :
      ( ( element @ X0 @ ( powerset @ X0 ) )
      | ( element @ X0 @ ( powerset @ X0 ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl19,zip_derived_cl20]) ).

thf(zip_derived_cl337,plain,
    ! [X0: $i] : ( element @ X0 @ ( powerset @ X0 ) ),
    inference(simplify,[status(thm)],[zip_derived_cl336]) ).

thf(t3_subset,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ A @ ( powerset @ B ) )
    <=> ( subset @ A @ B ) ) ).

thf(zip_derived_cl27,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ X0 @ X1 )
      | ~ ( element @ X0 @ ( powerset @ X1 ) ) ),
    inference(cnf,[status(esa)],[t3_subset]) ).

thf(zip_derived_cl453,plain,
    ! [X0: $i] : ( subset @ X0 @ X0 ),
    inference('sup-',[status(thm)],[zip_derived_cl337,zip_derived_cl27]) ).

thf(zip_derived_cl2_003,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( subset @ X0 @ X1 )
      | ( in @ X0 @ X2 )
      | ( X2
       != ( powerset @ X1 ) ) ),
    inference(cnf,[status(esa)],[d1_zfmisc_1]) ).

thf(zip_derived_cl559,plain,
    ! [X0: $i,X1: $i] :
      ( ( X1
       != ( powerset @ X0 ) )
      | ( in @ X0 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl453,zip_derived_cl2]) ).

thf(zip_derived_cl25_004,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ X1 )
      | ~ ( in @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[t1_subset]) ).

thf(zip_derived_cl789,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0
       != ( powerset @ X1 ) )
      | ( element @ X1 @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl559,zip_derived_cl25]) ).

thf(t5_subset,axiom,
    ! [A: $i,B: $i,C: $i] :
      ~ ( ( in @ A @ B )
        & ( element @ B @ ( powerset @ C ) )
        & ( empty @ C ) ) ).

thf(zip_derived_cl35,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ~ ( empty @ X2 )
      | ~ ( element @ X1 @ ( powerset @ X2 ) ) ),
    inference(cnf,[status(esa)],[t5_subset]) ).

thf(zip_derived_cl921,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ( powerset @ X0 )
       != ( powerset @ X1 ) )
      | ~ ( empty @ X0 )
      | ~ ( in @ X2 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl789,zip_derived_cl35]) ).

thf(zip_derived_cl927,plain,
    ! [X0: $i,X1: $i] :
      ( ( X0 = empty_set )
      | ~ ( empty @ X1 )
      | ( ( powerset @ X1 )
       != ( powerset @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl921]) ).

thf(zip_derived_cl968,plain,
    ! [X0: $i] :
      ( ( ( powerset @ empty_set )
       != ( powerset @ X0 ) )
      | ( X0 = empty_set ) ),
    inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl927]) ).

thf(t10_tops_2,conjecture,
    ! [A: $i,B: $i] :
      ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
     => ( ~ ( ( B != empty_set )
            & ( ( complements_of_subsets @ A @ B )
              = empty_set ) )
        & ~ ( ( ( complements_of_subsets @ A @ B )
             != empty_set )
            & ( B = empty_set ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [A: $i,B: $i] :
        ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
       => ( ~ ( ( B != empty_set )
              & ( ( complements_of_subsets @ A @ B )
                = empty_set ) )
          & ~ ( ( ( complements_of_subsets @ A @ B )
               != empty_set )
              & ( B = empty_set ) ) ) ),
    inference('cnf.neg',[status(esa)],[t10_tops_2]) ).

thf(zip_derived_cl43,plain,
    element @ sk__10 @ ( powerset @ ( powerset @ sk__9 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(t46_setfam_1,axiom,
    ! [A: $i,B: $i] :
      ( ( element @ B @ ( powerset @ ( powerset @ A ) ) )
     => ~ ( ( B != empty_set )
          & ( ( complements_of_subsets @ A @ B )
            = empty_set ) ) ) ).

thf(zip_derived_cl30,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( complements_of_subsets @ X0 @ X1 )
       != empty_set )
      | ( X1 = empty_set )
      | ~ ( element @ X1 @ ( powerset @ ( powerset @ X0 ) ) ) ),
    inference(cnf,[status(esa)],[t46_setfam_1]) ).

thf(zip_derived_cl117,plain,
    ( ( sk__10 = empty_set )
    | ( ( complements_of_subsets @ sk__9 @ sk__10 )
     != empty_set ) ),
    inference('sup-',[status(thm)],[zip_derived_cl43,zip_derived_cl30]) ).

thf(zip_derived_cl44,plain,
    ( ( sk__10 != empty_set )
    | ( ( complements_of_subsets @ sk__9 @ sk__10 )
     != empty_set ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl118,plain,
    ( ( complements_of_subsets @ sk__9 @ sk__10 )
   != empty_set ),
    inference(clc,[status(thm)],[zip_derived_cl117,zip_derived_cl44]) ).

thf(zip_derived_cl47,plain,
    ( ( ( complements_of_subsets @ sk__9 @ sk__10 )
      = empty_set )
    | ( sk__10 = empty_set ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl118_005,plain,
    ( ( complements_of_subsets @ sk__9 @ sk__10 )
   != empty_set ),
    inference(clc,[status(thm)],[zip_derived_cl117,zip_derived_cl44]) ).

thf(zip_derived_cl119,plain,
    ( ( empty_set != empty_set )
    | ( sk__10 = empty_set ) ),
    inference('sup-',[status(thm)],[zip_derived_cl47,zip_derived_cl118]) ).

thf(zip_derived_cl120,plain,
    sk__10 = empty_set,
    inference(simplify,[status(thm)],[zip_derived_cl119]) ).

thf(zip_derived_cl125,plain,
    ( ( complements_of_subsets @ sk__9 @ empty_set )
   != empty_set ),
    inference(demod,[status(thm)],[zip_derived_cl118,zip_derived_cl120]) ).

thf(zip_derived_cl980,plain,
    ! [X0: $i] :
      ( ( ( complements_of_subsets @ sk__9 @ X0 )
       != empty_set )
      | ( ( powerset @ empty_set )
       != ( powerset @ X0 ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl968,zip_derived_cl125]) ).

thf(zip_derived_cl1096,plain,
    ! [X0: $i] :
      ( ( X0 != empty_set )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ sk__9 ) ) )
      | ( ( powerset @ empty_set )
       != ( powerset @ ( complements_of_subsets @ sk__9 @ X0 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl980]) ).

thf(zip_derived_cl20_006,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ ( powerset @ X1 ) )
      | ( in @ ( sk__4 @ X1 @ X0 ) @ X0 ) ),
    inference(cnf,[status(esa)],[l71_subset_1]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X0 @ X1 )
      | ( X1 != empty_set ) ),
    inference(cnf,[status(esa)],[d1_xboole_0]) ).

thf(zip_derived_cl326,plain,
    ! [X0: $i,X1: $i] :
      ( ( element @ X0 @ ( powerset @ X1 ) )
      | ( X0 != empty_set ) ),
    inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl0]) ).

thf(zip_derived_cl1097,plain,
    ! [X0: $i] :
      ( ( ( powerset @ empty_set )
       != ( powerset @ ( complements_of_subsets @ sk__9 @ X0 ) ) )
      | ( X0 != empty_set ) ),
    inference(clc,[status(thm)],[zip_derived_cl1096,zip_derived_cl326]) ).

thf(zip_derived_cl1098,plain,
    ! [X0: $i] :
      ( ( ( powerset @ empty_set )
       != ( powerset @ X0 ) )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ sk__9 ) ) )
      | ( ( complements_of_subsets @ sk__9 @ X0 )
       != empty_set ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl1097]) ).

thf(zip_derived_cl30_007,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( complements_of_subsets @ X0 @ X1 )
       != empty_set )
      | ( X1 = empty_set )
      | ~ ( element @ X1 @ ( powerset @ ( powerset @ X0 ) ) ) ),
    inference(cnf,[status(esa)],[t46_setfam_1]) ).

thf(zip_derived_cl1099,plain,
    ! [X0: $i] :
      ( ( ( complements_of_subsets @ sk__9 @ X0 )
       != empty_set )
      | ~ ( element @ X0 @ ( powerset @ ( powerset @ sk__9 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl1098,zip_derived_cl30]) ).

thf(zip_derived_cl1106,plain,
    ! [X0: $i] :
      ( ~ ( element @ X0 @ ( powerset @ ( powerset @ sk__9 ) ) )
      | ( ( complements_of_subsets @ sk__9 @ ( complements_of_subsets @ sk__9 @ X0 ) )
       != empty_set ) ),
    inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl1099]) ).

thf(zip_derived_cl1187,plain,
    ( ( complements_of_subsets @ sk__9 @ ( complements_of_subsets @ sk__9 @ empty_set ) )
   != empty_set ),
    inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl1106]) ).

thf(zip_derived_cl1195,plain,
    ( ( empty_set != empty_set )
    | ~ ( element @ empty_set @ ( powerset @ ( powerset @ sk__9 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl1187]) ).

thf(zip_derived_cl104_008,plain,
    ! [X0: $i] : ( element @ empty_set @ ( powerset @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl101,zip_derived_cl25]) ).

thf(zip_derived_cl1198,plain,
    empty_set != empty_set,
    inference(demod,[status(thm)],[zip_derived_cl1195,zip_derived_cl104]) ).

thf(zip_derived_cl1199,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl1198]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU326+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.IIo6Vd1tza true
% 0.13/0.34  % Computer : n022.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.19/0.35  % DateTime : Wed Aug 23 15:36:26 EDT 2023
% 0.19/0.35  % CPUTime  : 
% 0.19/0.35  % Running portfolio for 300 s
% 0.19/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.35  % Number of cores: 8
% 0.19/0.35  % Python version: Python 3.6.8
% 0.19/0.35  % Running in FO mode
% 0.21/0.64  % Total configuration time : 435
% 0.21/0.64  % Estimated wc time : 1092
% 0.21/0.64  % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.71  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.77  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.62/0.98  % Solved by fo/fo4.sh.
% 1.62/0.98  % done 426 iterations in 0.193s
% 1.62/0.98  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.62/0.98  % SZS output start Refutation
% See solution above
% 1.62/0.98  
% 1.62/0.98  
% 1.62/0.98  % Terminating...
% 1.71/1.05  % Runner terminated.
% 1.71/1.06  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------