TSTP Solution File: SET666+3 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.nE42JTuGia 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 16:15:24 EDT 2023

% Result   : Theorem 1.47s 0.81s
% Output   : Refutation 1.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   71 (  25 unt;  14 typ;   0 def)
%            Number of atoms       :  134 (   0 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  491 (  47   ~;  46   |;   2   &; 367   @)
%                                         (   6 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  18   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  14 usr;   3 con; 0-2 aty)
%            Number of variables   :   89 (   0   ^;  89   !;   0   ?;  89   :)

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

thf(sk__11_type,type,
    sk__11: $i ).

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

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

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

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

thf(identity_relation_of_type_type,type,
    identity_relation_of_type: $i > $i ).

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

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

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

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

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

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

thf(identity_relation_of_type,type,
    identity_relation_of: $i > $i ).

thf(prove_relset_1_29,conjecture,
    ! [B: $i] :
      ( ( ilf_type @ B @ set_type )
     => ( ilf_type @ ( identity_relation_of @ B ) @ ( identity_relation_of_type @ B ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ! [B: $i] :
        ( ( ilf_type @ B @ set_type )
       => ( ilf_type @ ( identity_relation_of @ B ) @ ( identity_relation_of_type @ B ) ) ),
    inference('cnf.neg',[status(esa)],[prove_relset_1_29]) ).

thf(zip_derived_cl47,plain,
    ~ ( ilf_type @ ( identity_relation_of @ sk__11 ) @ ( identity_relation_of_type @ sk__11 ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(p16,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_cl26,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ( member @ ( sk__5 @ X0 @ X1 ) @ X1 )
      | ( member @ X1 @ ( power_set @ X0 ) )
      | ~ ( ilf_type @ X1 @ set_type ) ),
    inference(cnf,[status(esa)],[p16]) ).

thf(p24,axiom,
    ! [B: $i] : ( ilf_type @ B @ set_type ) ).

thf(zip_derived_cl45,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl45_001,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl480,plain,
    ! [X0: $i,X1: $i] :
      ( ( member @ ( sk__5 @ X0 @ X1 ) @ X1 )
      | ( member @ X1 @ ( power_set @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl45,zip_derived_cl45]) ).

thf(p3,axiom,
    ! [B: $i] :
      ( ( ilf_type @ B @ set_type )
     => ( subset @ ( identity_relation_of @ B ) @ ( cross_product @ B @ B ) ) ) ).

thf(zip_derived_cl3,plain,
    ! [X0: $i] :
      ( ( subset @ ( identity_relation_of @ X0 ) @ ( cross_product @ X0 @ X0 ) )
      | ~ ( ilf_type @ X0 @ set_type ) ),
    inference(cnf,[status(esa)],[p3]) ).

thf(p14,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_cl20,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ~ ( subset @ X1 @ X0 )
      | ~ ( member @ X2 @ X1 )
      | ( member @ X2 @ X0 )
      | ~ ( ilf_type @ X2 @ set_type )
      | ~ ( ilf_type @ X1 @ set_type ) ),
    inference(cnf,[status(esa)],[p14]) ).

thf(zip_derived_cl378,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ~ ( ilf_type @ ( identity_relation_of @ X0 ) @ set_type )
      | ~ ( ilf_type @ X1 @ set_type )
      | ( member @ X1 @ ( cross_product @ X0 @ X0 ) )
      | ~ ( member @ X1 @ ( identity_relation_of @ X0 ) )
      | ~ ( ilf_type @ ( cross_product @ X0 @ X0 ) @ set_type ) ),
    inference('dp-resolution',[status(thm)],[zip_derived_cl3,zip_derived_cl20]) ).

thf(zip_derived_cl45_002,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl45_003,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl45_004,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl45_005,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl538,plain,
    ! [X0: $i,X1: $i] :
      ( ( member @ X1 @ ( cross_product @ X0 @ X0 ) )
      | ~ ( member @ X1 @ ( identity_relation_of @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl378,zip_derived_cl45,zip_derived_cl45,zip_derived_cl45,zip_derived_cl45]) ).

thf(zip_derived_cl27,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ~ ( member @ ( sk__5 @ X0 @ X1 ) @ X0 )
      | ( member @ X1 @ ( power_set @ X0 ) )
      | ~ ( ilf_type @ X1 @ set_type ) ),
    inference(cnf,[status(esa)],[p16]) ).

thf(zip_derived_cl45_006,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl45_007,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl464,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ ( sk__5 @ X0 @ X1 ) @ X0 )
      | ( member @ X1 @ ( power_set @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl27,zip_derived_cl45,zip_derived_cl45]) ).

thf(zip_derived_cl541,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ ( sk__5 @ ( cross_product @ X0 @ X0 ) @ X1 ) @ ( identity_relation_of @ X0 ) )
      | ( member @ X1 @ ( power_set @ ( cross_product @ X0 @ X0 ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl538,zip_derived_cl464]) ).

thf(zip_derived_cl681,plain,
    ! [X0: $i] :
      ( ( member @ ( identity_relation_of @ X0 ) @ ( power_set @ ( cross_product @ X0 @ X0 ) ) )
      | ( member @ ( identity_relation_of @ X0 ) @ ( power_set @ ( cross_product @ X0 @ X0 ) ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl480,zip_derived_cl541]) ).

thf(zip_derived_cl682,plain,
    ! [X0: $i] : ( member @ ( identity_relation_of @ X0 ) @ ( power_set @ ( cross_product @ X0 @ X0 ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl681]) ).

thf(p18,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_cl31,plain,
    ! [X0: $i,X1: $i] :
      ( ( empty @ X0 )
      | ~ ( ilf_type @ X0 @ set_type )
      | ~ ( member @ X1 @ X0 )
      | ( ilf_type @ X1 @ ( member_type @ X0 ) )
      | ~ ( ilf_type @ X1 @ set_type ) ),
    inference(cnf,[status(esa)],[p18]) ).

thf(zip_derived_cl45_008,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl45_009,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl497,plain,
    ! [X0: $i,X1: $i] :
      ( ( empty @ X0 )
      | ~ ( member @ X1 @ X0 )
      | ( ilf_type @ X1 @ ( member_type @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl31,zip_derived_cl45,zip_derived_cl45]) ).

thf(p22,axiom,
    ! [B: $i] :
      ( ( ilf_type @ B @ set_type )
     => ( ( empty @ B )
      <=> ! [C: $i] :
            ( ( ilf_type @ C @ set_type )
           => ~ ( member @ C @ B ) ) ) ) ).

thf(zip_derived_cl43,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( empty @ X0 )
      | ~ ( member @ X1 @ X0 )
      | ~ ( ilf_type @ X1 @ set_type )
      | ~ ( ilf_type @ X0 @ set_type ) ),
    inference(cnf,[status(esa)],[p22]) ).

thf(zip_derived_cl45_010,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl45_011,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl428,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( empty @ X0 )
      | ~ ( member @ X1 @ X0 ) ),
    inference(demod,[status(thm)],[zip_derived_cl43,zip_derived_cl45,zip_derived_cl45]) ).

thf(zip_derived_cl498,plain,
    ! [X0: $i,X1: $i] :
      ( ( ilf_type @ X1 @ ( member_type @ X0 ) )
      | ~ ( member @ X1 @ X0 ) ),
    inference(clc,[status(thm)],[zip_derived_cl497,zip_derived_cl428]) ).

thf(p12,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_cl18,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ~ ( ilf_type @ X0 @ ( member_type @ ( power_set @ X1 ) ) )
      | ( ilf_type @ X0 @ ( subset_type @ X1 ) )
      | ~ ( ilf_type @ X1 @ set_type ) ),
    inference(cnf,[status(esa)],[p12]) ).

thf(zip_derived_cl45_012,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl45_013,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl466,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ilf_type @ X0 @ ( member_type @ ( power_set @ X1 ) ) )
      | ( ilf_type @ X0 @ ( subset_type @ X1 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl18,zip_derived_cl45,zip_derived_cl45]) ).

thf(zip_derived_cl499,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X1 @ ( power_set @ X0 ) )
      | ( ilf_type @ X1 @ ( subset_type @ X0 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl498,zip_derived_cl466]) ).

thf(zip_derived_cl697,plain,
    ! [X0: $i] : ( ilf_type @ ( identity_relation_of @ X0 ) @ ( subset_type @ ( cross_product @ X0 @ X0 ) ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl682,zip_derived_cl499]) ).

thf(p1,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_cl1,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ~ ( ilf_type @ X1 @ ( subset_type @ ( cross_product @ X2 @ X0 ) ) )
      | ( ilf_type @ X1 @ ( relation_type @ X2 @ X0 ) )
      | ~ ( ilf_type @ X2 @ set_type ) ),
    inference(cnf,[status(esa)],[p1]) ).

thf(zip_derived_cl45_014,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl45_015,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl425,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( ilf_type @ X1 @ ( subset_type @ ( cross_product @ X2 @ X0 ) ) )
      | ( ilf_type @ X1 @ ( relation_type @ X2 @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl1,zip_derived_cl45,zip_derived_cl45]) ).

thf(zip_derived_cl740,plain,
    ! [X0: $i] : ( ilf_type @ ( identity_relation_of @ X0 ) @ ( relation_type @ X0 @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl697,zip_derived_cl425]) ).

thf(p6,axiom,
    ! [B: $i] :
      ( ( ilf_type @ B @ set_type )
     => ! [C: $i] :
          ( ( ilf_type @ C @ set_type )
         => ( ( ilf_type @ C @ ( identity_relation_of_type @ B ) )
          <=> ( ilf_type @ C @ ( relation_type @ B @ B ) ) ) ) ) ).

thf(zip_derived_cl9,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ilf_type @ X0 @ set_type )
      | ~ ( ilf_type @ X0 @ ( relation_type @ X1 @ X1 ) )
      | ( ilf_type @ X0 @ ( identity_relation_of_type @ X1 ) )
      | ~ ( ilf_type @ X1 @ set_type ) ),
    inference(cnf,[status(esa)],[p6]) ).

thf(zip_derived_cl45_016,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl45_017,plain,
    ! [X0: $i] : ( ilf_type @ X0 @ set_type ),
    inference(cnf,[status(esa)],[p24]) ).

thf(zip_derived_cl448,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( ilf_type @ X0 @ ( relation_type @ X1 @ X1 ) )
      | ( ilf_type @ X0 @ ( identity_relation_of_type @ X1 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl9,zip_derived_cl45,zip_derived_cl45]) ).

thf(zip_derived_cl750,plain,
    ! [X0: $i] : ( ilf_type @ ( identity_relation_of @ X0 ) @ ( identity_relation_of_type @ X0 ) ),
    inference('s_sup-',[status(thm)],[zip_derived_cl740,zip_derived_cl448]) ).

thf(zip_derived_cl783,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl47,zip_derived_cl750]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET666+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.nE42JTuGia 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 13:28:03 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
% 0.20/0.62  % Total configuration time : 435
% 0.20/0.62  % Estimated wc time : 1092
% 0.20/0.62  % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.70  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.73  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.73  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.75  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.75  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.75  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.77  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 1.47/0.81  % Solved by fo/fo6_bce.sh.
% 1.47/0.81  % BCE start: 48
% 1.47/0.81  % BCE eliminated: 0
% 1.47/0.81  % PE start: 48
% 1.47/0.81  logic: eq
% 1.47/0.81  % PE eliminated: 2
% 1.47/0.81  % done 157 iterations in 0.089s
% 1.47/0.81  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.47/0.81  % SZS output start Refutation
% See solution above
% 1.51/0.81  
% 1.51/0.81  
% 1.51/0.81  % Terminating...
% 1.51/0.87  % Runner terminated.
% 1.51/0.88  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------