TSTP Solution File: SET656+3 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET656+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.a3yKRG3YOD true

% Computer : n011.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 16:15:21 EDT 2023

% Result   : Theorem 2.18s 1.16s
% Output   : Refutation 2.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   69 (  26 unt;  15 typ;   0 def)
%            Number of atoms       :  125 (   7 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  438 (  37   ~;  38   |;   3   &; 330   @)
%                                         (   4 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   5 con; 0-2 aty)
%            Number of variables   :   76 (   0   ^;  76   !;   0   ?;  76   :)

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

thf(subset_type_type,type,
    subset_type: $i > $i ).

thf(sk__16_type,type,
    sk__16: $i ).

thf(power_set_type,type,
    power_set: $i > $i ).

thf(member_type_type,type,
    member_type: $i > $i ).

thf(set_type_type,type,
    set_type: $i ).

thf(sk__17_type,type,
    sk__17: $i ).

thf(relation_type_type,type,
    relation_type: $i > $i > $i ).

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

thf(ilf_type_type,type,
    ilf_type: $i > $i > $o ).

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

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

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

thf(sk__15_type,type,
    sk__15: $i ).

thf(cross_product_type,type,
    cross_product: $i > $i > $i ).

thf(p17,axiom,
    ! [B: $i] :
      ( ( ilf_type @ B @ set_type )
     => ! [C: $i] :
          ( ( ilf_type @ C @ set_type )
         => ( ( subset @ B @ C )
          <=> ! [D: $i] :
                ( ( ilf_type @ D @ set_type )
               => ( ( member @ D @ B )
                 => ( member @ D @ C ) ) ) ) ) ) ).

thf(zip_derived_cl33,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ( member @ ( sk__7 @ X0 @ X1 ) @ X1 )
      | ( subset @ X1 @ X0 )
      | ~ ( ilf_type @ X1 @ set_type ) ),
    inference(cnf,[status(esa)],[p17]) ).

thf(p30,axiom,
    ! [B: $i] : ( ilf_type @ B @ set_type ) ).

thf(zip_derived_cl64,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl64_001,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl131,plain,
    ! [X0: $i,X1: $i] :
      ( ( member @ ( sk__7 @ X0 @ X1 ) @ X1 )
      | ( subset @ X1 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl33,zip_derived_cl64,zip_derived_cl64]) ).

thf(prove_relset_1_18,conjecture,
    ! [B: $i] :
      ( ( ilf_type @ B @ set_type )
     => ! [C: $i] :
          ( ( ilf_type @ C @ set_type )
         => ! [D: $i] :
              ( ( ilf_type @ D @ ( relation_type @ B @ C ) )
             => ( ( intersection @ D @ ( cross_product @ B @ C ) )
                = D ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [B: $i] :
        ( ( ilf_type @ B @ set_type )
       => ! [C: $i] :
            ( ( ilf_type @ C @ set_type )
           => ! [D: $i] :
                ( ( ilf_type @ D @ ( relation_type @ B @ C ) )
               => ( ( intersection @ D @ ( cross_product @ B @ C ) )
                  = D ) ) ) ),
    inference('cnf.neg',[status(esa)],[prove_relset_1_18]) ).

thf(zip_derived_cl66,plain,
    ilf_type @ sk__17 @ ( relation_type @ sk__15 @ sk__16 ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(p6,axiom,
    ! [B: $i] :
      ( ( ilf_type @ B @ set_type )
     => ! [C: $i] :
          ( ( ilf_type @ C @ set_type )
         => ( ! [D: $i] :
                ( ( ilf_type @ D @ ( subset_type @ ( cross_product @ B @ C ) ) )
               => ( ilf_type @ D @ ( relation_type @ B @ C ) ) )
            & ! [E: $i] :
                ( ( ilf_type @ E @ ( relation_type @ B @ C ) )
               => ( ilf_type @ E @ ( subset_type @ ( cross_product @ B @ C ) ) ) ) ) ) ) ).

thf(zip_derived_cl12,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ~ ( ilf_type @ X1 @ ( relation_type @ X2 @ X0 ) )
      | ( ilf_type @ X1 @ ( subset_type @ ( cross_product @ X2 @ X0 ) ) )
      | ~ ( ilf_type @ X2 @ set_type ) ),
    inference(cnf,[status(esa)],[p6]) ).

thf(zip_derived_cl64_002,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl64_003,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl122,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ilf_type @ X1 @ ( relation_type @ X2 @ X0 ) )
      | ( ilf_type @ X1 @ ( subset_type @ ( cross_product @ X2 @ X0 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl12,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl224,plain,
    ilf_type @ sk__17 @ ( subset_type @ ( cross_product @ sk__15 @ sk__16 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl122]) ).

thf(p13,axiom,
    ! [B: $i] :
      ( ( ilf_type @ B @ set_type )
     => ! [C: $i] :
          ( ( ilf_type @ C @ set_type )
         => ( ( ilf_type @ C @ ( subset_type @ B ) )
          <=> ( ilf_type @ C @ ( member_type @ ( power_set @ B ) ) ) ) ) ) ).

thf(zip_derived_cl27,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ~ ( ilf_type @ X0 @ ( subset_type @ X1 ) )
      | ( ilf_type @ X0 @ ( member_type @ ( power_set @ X1 ) ) )
      | ~ ( ilf_type @ X1 @ set_type ) ),
    inference(cnf,[status(esa)],[p13]) ).

thf(zip_derived_cl64_004,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl64_005,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl121,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ilf_type @ X0 @ ( subset_type @ X1 ) )
      | ( ilf_type @ X0 @ ( member_type @ ( power_set @ X1 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl27,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl230,plain,
    ilf_type @ sk__17 @ ( member_type @ ( power_set @ ( cross_product @ sk__15 @ sk__16 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl224,zip_derived_cl121]) ).

thf(p21,axiom,
    ! [B: $i] :
      ( ( ilf_type @ B @ set_type )
     => ! [C: $i] :
          ( ( ~ ( empty @ C )
            & ( ilf_type @ C @ set_type ) )
         => ( ( ilf_type @ B @ ( member_type @ C ) )
          <=> ( member @ B @ C ) ) ) ) ).

thf(zip_derived_cl44,plain,
    ! [X0: $i,X1: $i] :
      ( ( empty @ X0 )
      | ~ ( ilf_type @ X0 @ set_type )
      | ~ ( ilf_type @ X1 @ ( member_type @ X0 ) )
      | ( member @ X1 @ X0 )
      | ~ ( ilf_type @ X1 @ set_type ) ),
    inference(cnf,[status(esa)],[p21]) ).

thf(zip_derived_cl64_006,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl64_007,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl128,plain,
    ! [X0: $i,X1: $i] :
      ( ( empty @ X0 )
      | ~ ( ilf_type @ X1 @ ( member_type @ X0 ) )
      | ( member @ X1 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl44,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl262,plain,
    ( ( empty @ ( power_set @ ( cross_product @ sk__15 @ sk__16 ) ) )
    | ( member @ sk__17 @ ( power_set @ ( cross_product @ sk__15 @ sk__16 ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl230,zip_derived_cl128]) ).

thf(p20,axiom,
    ! [B: $i] :
      ( ( ilf_type @ B @ set_type )
     => ( ~ ( empty @ ( power_set @ B ) )
        & ( ilf_type @ ( power_set @ B ) @ set_type ) ) ) ).

thf(zip_derived_cl41,plain,
    ! [X0: $i] :
      ( ~ ( empty @ ( power_set @ X0 ) )
      | ~ ( ilf_type @ X0 @ set_type ) ),
    inference(cnf,[status(esa)],[p20]) ).

thf(zip_derived_cl64_008,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl70,plain,
    ! [X0: $i] :
      ~ ( empty @ ( power_set @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl41,zip_derived_cl64]) ).

thf(zip_derived_cl263,plain,
    member @ sk__17 @ ( power_set @ ( cross_product @ sk__15 @ sk__16 ) ),
    inference(clc,[status(thm)],[zip_derived_cl262,zip_derived_cl70]) ).

thf(p19,axiom,
    ! [B: $i] :
      ( ( ilf_type @ B @ set_type )
     => ! [C: $i] :
          ( ( ilf_type @ C @ set_type )
         => ( ( member @ B @ ( power_set @ C ) )
          <=> ! [D: $i] :
                ( ( ilf_type @ D @ set_type )
               => ( ( member @ D @ B )
                 => ( member @ D @ C ) ) ) ) ) ) ).

thf(zip_derived_cl37,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ~ ( member @ X1 @ ( power_set @ X0 ) )
      | ~ ( member @ X2 @ X1 )
      | ( member @ X2 @ X0 )
      | ~ ( ilf_type @ X2 @ set_type )
      | ~ ( ilf_type @ X1 @ set_type ) ),
    inference(cnf,[status(esa)],[p19]) ).

thf(zip_derived_cl64_009,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl64_010,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl64_011,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl127,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X1 @ ( power_set @ X0 ) )
      | ~ ( member @ X2 @ X1 )
      | ( member @ X2 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl37,zip_derived_cl64,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl268,plain,
    ! [X0: $i] :
      ( ~ ( member @ X0 @ sk__17 )
      | ( member @ X0 @ ( cross_product @ sk__15 @ sk__16 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl263,zip_derived_cl127]) ).

thf(zip_derived_cl287,plain,
    ! [X0: $i] :
      ( ( subset @ sk__17 @ X0 )
      | ( member @ ( sk__7 @ X0 @ sk__17 ) @ ( cross_product @ sk__15 @ sk__16 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl131,zip_derived_cl268]) ).

thf(zip_derived_cl34,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ~ ( member @ ( sk__7 @ X0 @ X1 ) @ X0 )
      | ( subset @ X1 @ X0 )
      | ~ ( ilf_type @ X1 @ set_type ) ),
    inference(cnf,[status(esa)],[p17]) ).

thf(zip_derived_cl64_012,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl64_013,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl84,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ ( sk__7 @ X0 @ X1 ) @ X0 )
      | ( subset @ X1 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl34,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl2695,plain,
    ( ( subset @ sk__17 @ ( cross_product @ sk__15 @ sk__16 ) )
    | ( subset @ sk__17 @ ( cross_product @ sk__15 @ sk__16 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl287,zip_derived_cl84]) ).

thf(zip_derived_cl2704,plain,
    subset @ sk__17 @ ( cross_product @ sk__15 @ sk__16 ),
    inference(simplify,[status(thm)],[zip_derived_cl2695]) ).

thf(p1,axiom,
    ! [B: $i] :
      ( ( ilf_type @ B @ set_type )
     => ! [C: $i] :
          ( ( ilf_type @ C @ set_type )
         => ( ( subset @ B @ C )
           => ( ( intersection @ B @ C )
              = B ) ) ) ) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ( ( intersection @ X1 @ X0 )
        = X1 )
      | ~ ( subset @ X1 @ X0 )
      | ~ ( ilf_type @ X1 @ set_type ) ),
    inference(cnf,[status(esa)],[p1]) ).

thf(zip_derived_cl64_014,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl64_015,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p30]) ).

thf(zip_derived_cl69,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( intersection @ X1 @ X0 )
        = X1 )
      | ~ ( subset @ X1 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl0,zip_derived_cl64,zip_derived_cl64]) ).

thf(zip_derived_cl2705,plain,
    ( ( intersection @ sk__17 @ ( cross_product @ sk__15 @ sk__16 ) )
    = sk__17 ),
    inference('s_sup-',[status(thm)],[zip_derived_cl2704,zip_derived_cl69]) ).

thf(zip_derived_cl67,plain,
    ( ( intersection @ sk__17 @ ( cross_product @ sk__15 @ sk__16 ) )
   != sk__17 ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl2711,plain,
    $false,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl2705,zip_derived_cl67]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : SET656+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.15  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.a3yKRG3YOD true
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sat Aug 26 13:50:09 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 0.16/0.37  % Running portfolio for 300 s
% 0.16/0.37  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.37  % Number of cores: 8
% 0.23/0.38  % Python version: Python 3.6.8
% 0.23/0.38  % Running in FO mode
% 0.24/0.60  % Total configuration time : 435
% 0.24/0.60  % Estimated wc time : 1092
% 0.24/0.60  % Estimated cpu time (7 cpus) : 156.0
% 0.24/0.64  % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.24/0.66  % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.24/0.70  % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.24/0.70  % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.24/0.70  % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.24/0.70  % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.24/0.72  % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 2.18/1.16  % Solved by fo/fo13.sh.
% 2.18/1.16  % done 383 iterations in 0.441s
% 2.18/1.16  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 2.18/1.16  % SZS output start Refutation
% See solution above
% 2.18/1.17  
% 2.18/1.17  
% 2.18/1.17  % Terminating...
% 2.18/1.21  % Runner terminated.
% 2.18/1.22  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------