TSTP Solution File: SET984+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.7og89Lmzha true

% Computer : n006.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 16:17:05 EDT 2023

% Result   : Theorem 1.51s 0.84s
% Output   : Refutation 1.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   49 (  20 unt;   8 typ;   0 def)
%            Number of atoms       :   83 (  65 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  230 (  16   ~;  34   |;   3   &; 172   @)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   56 (   0   ^;  56   !;   0   ?;  56   :)

% Comments : 
%------------------------------------------------------------------------------
thf(sk__2_type,type,
    sk__2: $i ).

thf(set_intersection2_type,type,
    set_intersection2: $i > $i > $i ).

thf(cartesian_product2_type,type,
    cartesian_product2: $i > $i > $i ).

thf(sk__3_type,type,
    sk__3: $i ).

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

thf(sk__5_type,type,
    sk__5: $i ).

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

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

thf(t138_zfmisc_1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
     => ( ( ( cartesian_product2 @ A @ B )
          = empty_set )
        | ( ( subset @ A @ C )
          & ( subset @ B @ D ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
       => ( ( ( cartesian_product2 @ A @ B )
            = empty_set )
          | ( ( subset @ A @ C )
            & ( subset @ B @ D ) ) ) ),
    inference('cnf.neg',[status(esa)],[t138_zfmisc_1]) ).

thf(zip_derived_cl14,plain,
    ( ( cartesian_product2 @ sk__2 @ sk__3 )
   != empty_set ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl13,plain,
    subset @ ( cartesian_product2 @ sk__2 @ sk__3 ) @ ( cartesian_product2 @ sk__4 @ sk__5 ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(t28_xboole_1,axiom,
    ! [A: $i,B: $i] :
      ( ( subset @ A @ B )
     => ( ( set_intersection2 @ A @ B )
        = A ) ) ).

thf(zip_derived_cl16,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( set_intersection2 @ X0 @ X1 )
        = X0 )
      | ~ ( subset @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[t28_xboole_1]) ).

thf(zip_derived_cl32,plain,
    ( ( set_intersection2 @ ( cartesian_product2 @ sk__2 @ sk__3 ) @ ( cartesian_product2 @ sk__4 @ sk__5 ) )
    = ( cartesian_product2 @ sk__2 @ sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl16]) ).

thf(t123_zfmisc_1,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( cartesian_product2 @ ( set_intersection2 @ A @ B ) @ ( set_intersection2 @ C @ D ) )
      = ( set_intersection2 @ ( cartesian_product2 @ A @ C ) @ ( cartesian_product2 @ B @ D ) ) ) ).

thf(zip_derived_cl9,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( cartesian_product2 @ ( set_intersection2 @ X0 @ X2 ) @ ( set_intersection2 @ X1 @ X3 ) )
      = ( set_intersection2 @ ( cartesian_product2 @ X0 @ X1 ) @ ( cartesian_product2 @ X2 @ X3 ) ) ),
    inference(cnf,[status(esa)],[t123_zfmisc_1]) ).

thf(zip_derived_cl56,plain,
    ( ( cartesian_product2 @ ( set_intersection2 @ sk__2 @ sk__4 ) @ ( set_intersection2 @ sk__3 @ sk__5 ) )
    = ( cartesian_product2 @ sk__2 @ sk__3 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl32,zip_derived_cl9]) ).

thf(commutativity_k3_xboole_0,axiom,
    ! [A: $i,B: $i] :
      ( ( set_intersection2 @ A @ B )
      = ( set_intersection2 @ B @ A ) ) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i] :
      ( ( set_intersection2 @ X1 @ X0 )
      = ( set_intersection2 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[commutativity_k3_xboole_0]) ).

thf(zip_derived_cl0_001,plain,
    ! [X0: $i,X1: $i] :
      ( ( set_intersection2 @ X1 @ X0 )
      = ( set_intersection2 @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[commutativity_k3_xboole_0]) ).

thf(zip_derived_cl61,plain,
    ( ( cartesian_product2 @ ( set_intersection2 @ sk__4 @ sk__2 ) @ ( set_intersection2 @ sk__5 @ sk__3 ) )
    = ( cartesian_product2 @ sk__2 @ sk__3 ) ),
    inference(demod,[status(thm)],[zip_derived_cl56,zip_derived_cl0,zip_derived_cl0]) ).

thf(t134_zfmisc_1,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( cartesian_product2 @ A @ B )
        = ( cartesian_product2 @ C @ D ) )
     => ( ( A = empty_set )
        | ( B = empty_set )
        | ( ( A = C )
          & ( B = D ) ) ) ) ).

thf(zip_derived_cl11,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X0 = empty_set )
      | ( X1 = empty_set )
      | ( ( cartesian_product2 @ X1 @ X0 )
       != ( cartesian_product2 @ X2 @ X3 ) )
      | ( X0 = X3 ) ),
    inference(cnf,[status(esa)],[t134_zfmisc_1]) ).

thf(zip_derived_cl230,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( cartesian_product2 @ X1 @ X0 )
       != ( cartesian_product2 @ sk__2 @ sk__3 ) )
      | ( X0
        = ( set_intersection2 @ sk__5 @ sk__3 ) )
      | ( X1 = empty_set )
      | ( X0 = empty_set ) ),
    inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl11]) ).

thf(zip_derived_cl604,plain,
    ( ( sk__3 = empty_set )
    | ( sk__2 = empty_set )
    | ( sk__3
      = ( set_intersection2 @ sk__5 @ sk__3 ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl230]) ).

thf(t17_xboole_1,axiom,
    ! [A: $i,B: $i] : ( subset @ ( set_intersection2 @ A @ B ) @ A ) ).

thf(zip_derived_cl15,plain,
    ! [X0: $i,X1: $i] : ( subset @ ( set_intersection2 @ X0 @ X1 ) @ X0 ),
    inference(cnf,[status(esa)],[t17_xboole_1]) ).

thf(zip_derived_cl606,plain,
    ( ( subset @ sk__3 @ sk__5 )
    | ( sk__2 = empty_set )
    | ( sk__3 = empty_set ) ),
    inference('sup+',[status(thm)],[zip_derived_cl604,zip_derived_cl15]) ).

thf(zip_derived_cl61_002,plain,
    ( ( cartesian_product2 @ ( set_intersection2 @ sk__4 @ sk__2 ) @ ( set_intersection2 @ sk__5 @ sk__3 ) )
    = ( cartesian_product2 @ sk__2 @ sk__3 ) ),
    inference(demod,[status(thm)],[zip_derived_cl56,zip_derived_cl0,zip_derived_cl0]) ).

thf(zip_derived_cl10,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( ( X0 = empty_set )
      | ( X1 = empty_set )
      | ( ( cartesian_product2 @ X1 @ X0 )
       != ( cartesian_product2 @ X2 @ X3 ) )
      | ( X1 = X2 ) ),
    inference(cnf,[status(esa)],[t134_zfmisc_1]) ).

thf(zip_derived_cl229,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( cartesian_product2 @ X1 @ X0 )
       != ( cartesian_product2 @ sk__2 @ sk__3 ) )
      | ( X1
        = ( set_intersection2 @ sk__4 @ sk__2 ) )
      | ( X1 = empty_set )
      | ( X0 = empty_set ) ),
    inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl10]) ).

thf(zip_derived_cl242,plain,
    ( ( sk__3 = empty_set )
    | ( sk__2 = empty_set )
    | ( sk__2
      = ( set_intersection2 @ sk__4 @ sk__2 ) ) ),
    inference(eq_res,[status(thm)],[zip_derived_cl229]) ).

thf(zip_derived_cl15_003,plain,
    ! [X0: $i,X1: $i] : ( subset @ ( set_intersection2 @ X0 @ X1 ) @ X0 ),
    inference(cnf,[status(esa)],[t17_xboole_1]) ).

thf(zip_derived_cl244,plain,
    ( ( subset @ sk__2 @ sk__4 )
    | ( sk__2 = empty_set )
    | ( sk__3 = empty_set ) ),
    inference('sup+',[status(thm)],[zip_derived_cl242,zip_derived_cl15]) ).

thf(zip_derived_cl12,plain,
    ( ~ ( subset @ sk__2 @ sk__4 )
    | ~ ( subset @ sk__3 @ sk__5 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl258,plain,
    ( ( sk__3 = empty_set )
    | ( sk__2 = empty_set )
    | ~ ( subset @ sk__3 @ sk__5 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl244,zip_derived_cl12]) ).

thf(zip_derived_cl628,plain,
    ( ( sk__3 = empty_set )
    | ( sk__2 = empty_set ) ),
    inference(clc,[status(thm)],[zip_derived_cl606,zip_derived_cl258]) ).

thf(zip_derived_cl14_004,plain,
    ( ( cartesian_product2 @ sk__2 @ sk__3 )
   != empty_set ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl630,plain,
    ( ( ( cartesian_product2 @ sk__2 @ empty_set )
     != empty_set )
    | ( sk__2 = empty_set ) ),
    inference('sup-',[status(thm)],[zip_derived_cl628,zip_derived_cl14]) ).

thf(t113_zfmisc_1,axiom,
    ! [A: $i,B: $i] :
      ( ( ( cartesian_product2 @ A @ B )
        = empty_set )
    <=> ( ( A = empty_set )
        | ( B = empty_set ) ) ) ).

thf(zip_derived_cl8,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( cartesian_product2 @ X0 @ X1 )
        = empty_set )
      | ( X1 != empty_set ) ),
    inference(cnf,[status(esa)],[t113_zfmisc_1]) ).

thf(zip_derived_cl28,plain,
    ! [X0: $i] :
      ( ( cartesian_product2 @ X0 @ empty_set )
      = empty_set ),
    inference(eq_res,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl637,plain,
    ( ( empty_set != empty_set )
    | ( sk__2 = empty_set ) ),
    inference(demod,[status(thm)],[zip_derived_cl630,zip_derived_cl28]) ).

thf(zip_derived_cl638,plain,
    sk__2 = empty_set,
    inference(simplify,[status(thm)],[zip_derived_cl637]) ).

thf(zip_derived_cl7,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( cartesian_product2 @ X0 @ X1 )
        = empty_set )
      | ( X0 != empty_set ) ),
    inference(cnf,[status(esa)],[t113_zfmisc_1]) ).

thf(zip_derived_cl22,plain,
    ! [X0: $i] :
      ( ( cartesian_product2 @ empty_set @ X0 )
      = empty_set ),
    inference(eq_res,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl646,plain,
    empty_set != empty_set,
    inference(demod,[status(thm)],[zip_derived_cl14,zip_derived_cl638,zip_derived_cl22]) ).

thf(zip_derived_cl647,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl646]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET984+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.7og89Lmzha true
% 0.13/0.34  % Computer : n006.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 11:03:22 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox/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 FO mode
% 0.19/0.64  % Total configuration time : 435
% 0.19/0.64  % Estimated wc time : 1092
% 0.19/0.64  % Estimated cpu time (7 cpus) : 156.0
% 0.19/0.70  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.19/0.71  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.19/0.73  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.19/0.73  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.19/0.74  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.19/0.75  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.19/0.76  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.51/0.84  % Solved by fo/fo5.sh.
% 1.51/0.84  % done 133 iterations in 0.072s
% 1.51/0.84  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.51/0.84  % SZS output start Refutation
% See solution above
% 1.51/0.84  
% 1.51/0.84  
% 1.51/0.84  % Terminating...
% 2.20/0.94  % Runner terminated.
% 2.20/0.95  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------