TSTP Solution File: SET579^3 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET579^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8Hi6old4GK true

% Computer : n003.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 16:14:40 EDT 2023

% Result   : Theorem 1.41s 0.92s
% Output   : Refutation 1.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   72 (  22 unt;  16 typ;   0 def)
%            Number of atoms       :  155 (  18 equ;   0 cnn)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :  510 (  24   ~;  33   |;   7   &; 432   @)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   67 (  67   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   5 con; 0-3 aty)
%            Number of variables   :  115 (  54   ^;  61   !;   0   ?; 115   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mworld_type,type,
    mworld: $tType ).

thf(mimplies_type,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

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

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

thf(mactual_type,type,
    mactual: mworld ).

thf(mand_type,type,
    mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mequiv_type,type,
    mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mnot_type,type,
    mnot: ( mworld > $o ) > mworld > $o ).

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

thf(difference_type,type,
    difference: $i > $i > $i ).

thf(mlocal_type,type,
    mlocal: ( mworld > $o ) > $o ).

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

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

thf(mforall_di_type,type,
    mforall_di: ( $i > mworld > $o ) > mworld > $o ).

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

thf(qmltpeq_type,type,
    qmltpeq: $i > $i > mworld > $o ).

thf(mforall_di_def,axiom,
    ( mforall_di
    = ( ^ [A: $i > mworld > $o,W: mworld] :
        ! [X: $i] : ( A @ X @ W ) ) ) ).

thf('0',plain,
    ( mforall_di
    = ( ^ [A: $i > mworld > $o,W: mworld] :
        ! [X: $i] : ( A @ X @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mforall_di_def]) ).

thf('1',plain,
    ( mforall_di
    = ( ^ [V_1: $i > mworld > $o,V_2: mworld] :
        ! [X4: $i] : ( V_1 @ X4 @ V_2 ) ) ),
    define([status(thm)]) ).

thf(mequiv_def,axiom,
    ( mequiv
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
        <=> ( B @ W ) ) ) ) ).

thf('2',plain,
    ( mequiv
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
        <=> ( B @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mequiv_def]) ).

thf('3',plain,
    ( mequiv
    = ( ^ [V_1: mworld > $o,V_2: mworld > $o,V_3: mworld] :
          ( ( V_1 @ V_3 )
        <=> ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(mand_def,axiom,
    ( mand
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
          & ( B @ W ) ) ) ) ).

thf('4',plain,
    ( mand
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
          & ( B @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mand_def]) ).

thf('5',plain,
    ( mand
    = ( ^ [V_1: mworld > $o,V_2: mworld > $o,V_3: mworld] :
          ( ( V_1 @ V_3 )
          & ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(mlocal_def,axiom,
    ( mlocal
    = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).

thf('6',plain,
    ( mlocal
    = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mlocal_def]) ).

thf('7',plain,
    ( mlocal
    = ( ^ [V_1: mworld > $o] : ( V_1 @ mactual ) ) ),
    define([status(thm)]) ).

thf(equal_defn,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [B: $i] :
          ( mforall_di
          @ ^ [C: $i] : ( mequiv @ ( qmltpeq @ B @ C ) @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) ) ) ) ) ).

thf(zf_stmt_0,axiom,
    ! [X4: $i,X6: $i] :
      ( ( qmltpeq @ X4 @ X6 @ mactual )
    <=> ( ( subset @ X4 @ X6 @ mactual )
        & ( subset @ X6 @ X4 @ mactual ) ) ) ).

thf(zip_derived_cl15,plain,
    ! [X0: $i,X1: $i] :
      ( ( qmltpeq @ X0 @ X1 @ mactual )
      | ~ ( subset @ X1 @ X0 @ mactual )
      | ~ ( subset @ X0 @ X1 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(mimplies_def,axiom,
    ( mimplies
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
         => ( B @ W ) ) ) ) ).

thf('8',plain,
    ( mimplies
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
         => ( B @ W ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mimplies_def]) ).

thf('9',plain,
    ( mimplies
    = ( ^ [V_1: mworld > $o,V_2: mworld > $o,V_3: mworld] :
          ( ( V_1 @ V_3 )
         => ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(subset_defn,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [B: $i] :
          ( mforall_di
          @ ^ [C: $i] :
              ( mequiv @ ( subset @ B @ C )
              @ ( mforall_di
                @ ^ [D: $i] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).

thf(zf_stmt_1,axiom,
    ! [X4: $i,X6: $i] :
      ( ( subset @ X4 @ X6 @ mactual )
    <=> ! [X8: $i] :
          ( ( member @ X8 @ X4 @ mactual )
         => ( member @ X8 @ X6 @ mactual ) ) ) ).

thf(zip_derived_cl17,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ X0 @ X1 @ mactual )
      | ~ ( member @ ( sk__5 @ X1 @ X0 ) @ X1 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl18,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ X0 @ X1 @ mactual )
      | ( member @ ( sk__5 @ X1 @ X0 ) @ X0 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(mnot_def,axiom,
    ( mnot
    = ( ^ [A: mworld > $o,W: mworld] :
          ~ ( A @ W ) ) ) ).

thf('10',plain,
    ( mnot
    = ( ^ [A: mworld > $o,W: mworld] :
          ~ ( A @ W ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mnot_def]) ).

thf('11',plain,
    ( mnot
    = ( ^ [V_1: mworld > $o,V_2: mworld] :
          ~ ( V_1 @ V_2 ) ) ),
    define([status(thm)]) ).

thf(difference_defn,axiom,
    ( mlocal
    @ ( mforall_di
      @ ^ [B: $i] :
          ( mforall_di
          @ ^ [C: $i] :
              ( mforall_di
              @ ^ [D: $i] : ( mequiv @ ( member @ D @ ( difference @ B @ C ) ) @ ( mand @ ( member @ D @ B ) @ ( mnot @ ( member @ D @ C ) ) ) ) ) ) ) ) ).

thf(zf_stmt_2,axiom,
    ! [X4: $i,X6: $i,X8: $i] :
      ( ( member @ X8 @ ( difference @ X4 @ X6 ) @ mactual )
    <=> ( ( member @ X8 @ X4 @ mactual )
        & ~ ( member @ X8 @ X6 @ mactual ) ) ) ).

thf(zip_derived_cl11,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( member @ X0 @ X1 @ mactual )
      | ~ ( member @ X0 @ ( difference @ X2 @ X1 ) @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl26,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( subset @ ( difference @ X1 @ X0 ) @ X2 @ mactual )
      | ~ ( member @ ( sk__5 @ X2 @ ( difference @ X1 @ X0 ) ) @ X0 @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl11]) ).

thf(zip_derived_cl18_001,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ X0 @ X1 @ mactual )
      | ( member @ ( sk__5 @ X1 @ X0 ) @ X0 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl10,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( member @ X0 @ X1 @ mactual )
      | ~ ( member @ X0 @ ( difference @ X1 @ X2 ) @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl28,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( subset @ ( difference @ X1 @ X0 ) @ X2 @ mactual )
      | ( member @ ( sk__5 @ X2 @ ( difference @ X1 @ X0 ) ) @ X1 @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl10]) ).

thf(prove_th20,conjecture,
    ( mlocal
    @ ( mforall_di
      @ ^ [B: $i] :
          ( mforall_di
          @ ^ [C: $i] :
              ( mforall_di
              @ ^ [D: $i] :
                  ( mimplies
                  @ ( mforall_di
                    @ ^ [E: $i] : ( mequiv @ ( member @ E @ B ) @ ( mand @ ( member @ E @ C ) @ ( mnot @ ( member @ E @ D ) ) ) ) )
                  @ ( qmltpeq @ B @ ( difference @ C @ D ) ) ) ) ) ) ) ).

thf(zf_stmt_3,conjecture,
    ! [X4: $i,X6: $i,X8: $i] :
      ( ! [X10: $i] :
          ( ( member @ X10 @ X4 @ mactual )
        <=> ( ( member @ X10 @ X6 @ mactual )
            & ~ ( member @ X10 @ X8 @ mactual ) ) )
     => ( qmltpeq @ X4 @ ( difference @ X6 @ X8 ) @ mactual ) ) ).

thf(zf_stmt_4,negated_conjecture,
    ~ ! [X4: $i,X6: $i,X8: $i] :
        ( ! [X10: $i] :
            ( ( member @ X10 @ X4 @ mactual )
          <=> ( ( member @ X10 @ X6 @ mactual )
              & ~ ( member @ X10 @ X8 @ mactual ) ) )
       => ( qmltpeq @ X4 @ ( difference @ X6 @ X8 ) @ mactual ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_3]) ).

thf(zip_derived_cl20,plain,
    ! [X0: $i] :
      ( ( member @ X0 @ sk__6 @ mactual )
      | ( member @ X0 @ sk__8 @ mactual )
      | ~ ( member @ X0 @ sk__7 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl397,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ ( difference @ sk__7 @ X0 ) @ X1 @ mactual )
      | ( member @ ( sk__5 @ X1 @ ( difference @ sk__7 @ X0 ) ) @ sk__8 @ mactual )
      | ( member @ ( sk__5 @ X1 @ ( difference @ sk__7 @ X0 ) ) @ sk__6 @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl28,zip_derived_cl20]) ).

thf(zip_derived_cl512,plain,
    ! [X0: $i] :
      ( ( subset @ ( difference @ sk__7 @ sk__8 ) @ X0 @ mactual )
      | ( member @ ( sk__5 @ X0 @ ( difference @ sk__7 @ sk__8 ) ) @ sk__6 @ mactual )
      | ( subset @ ( difference @ sk__7 @ sk__8 ) @ X0 @ mactual ) ),
    inference('sup+',[status(thm)],[zip_derived_cl26,zip_derived_cl397]) ).

thf(zip_derived_cl521,plain,
    ! [X0: $i] :
      ( ( member @ ( sk__5 @ X0 @ ( difference @ sk__7 @ sk__8 ) ) @ sk__6 @ mactual )
      | ( subset @ ( difference @ sk__7 @ sk__8 ) @ X0 @ mactual ) ),
    inference(simplify,[status(thm)],[zip_derived_cl512]) ).

thf(zip_derived_cl535,plain,
    ( ( subset @ ( difference @ sk__7 @ sk__8 ) @ sk__6 @ mactual )
    | ( subset @ ( difference @ sk__7 @ sk__8 ) @ sk__6 @ mactual ) ),
    inference('sup+',[status(thm)],[zip_derived_cl17,zip_derived_cl521]) ).

thf(zip_derived_cl544,plain,
    subset @ ( difference @ sk__7 @ sk__8 ) @ sk__6 @ mactual,
    inference(simplify,[status(thm)],[zip_derived_cl535]) ).

thf(zip_derived_cl553,plain,
    ( ~ ( subset @ sk__6 @ ( difference @ sk__7 @ sk__8 ) @ mactual )
    | ( qmltpeq @ sk__6 @ ( difference @ sk__7 @ sk__8 ) @ mactual ) ),
    inference('sup+',[status(thm)],[zip_derived_cl15,zip_derived_cl544]) ).

thf(zip_derived_cl17_002,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ X0 @ X1 @ mactual )
      | ~ ( member @ ( sk__5 @ X1 @ X0 ) @ X1 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl18_003,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ X0 @ X1 @ mactual )
      | ( member @ ( sk__5 @ X1 @ X0 ) @ X0 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl21,plain,
    ! [X1: $i] :
      ( ( member @ X1 @ sk__7 @ mactual )
      | ~ ( member @ X1 @ sk__6 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl12,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( member @ X0 @ ( difference @ X1 @ X2 ) @ mactual )
      | ( member @ X0 @ X2 @ mactual )
      | ~ ( member @ X0 @ X1 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl159,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( member @ X0 @ sk__6 @ mactual )
      | ( member @ X0 @ X1 @ mactual )
      | ( member @ X0 @ ( difference @ sk__7 @ X1 ) @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl12]) ).

thf(zip_derived_cl173,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ sk__6 @ X0 @ mactual )
      | ( member @ ( sk__5 @ X0 @ sk__6 ) @ ( difference @ sk__7 @ X1 ) @ mactual )
      | ( member @ ( sk__5 @ X0 @ sk__6 ) @ X1 @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl18,zip_derived_cl159]) ).

thf(zip_derived_cl255,plain,
    ! [X0: $i] :
      ( ( subset @ sk__6 @ ( difference @ sk__7 @ X0 ) @ mactual )
      | ( member @ ( sk__5 @ ( difference @ sk__7 @ X0 ) @ sk__6 ) @ X0 @ mactual )
      | ( subset @ sk__6 @ ( difference @ sk__7 @ X0 ) @ mactual ) ),
    inference('sup+',[status(thm)],[zip_derived_cl17,zip_derived_cl173]) ).

thf(zip_derived_cl262,plain,
    ! [X0: $i] :
      ( ( member @ ( sk__5 @ ( difference @ sk__7 @ X0 ) @ sk__6 ) @ X0 @ mactual )
      | ( subset @ sk__6 @ ( difference @ sk__7 @ X0 ) @ mactual ) ),
    inference(simplify,[status(thm)],[zip_derived_cl255]) ).

thf(zip_derived_cl22,plain,
    ! [X1: $i] :
      ( ~ ( member @ X1 @ sk__8 @ mactual )
      | ~ ( member @ X1 @ sk__6 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl266,plain,
    ( ( subset @ sk__6 @ ( difference @ sk__7 @ sk__8 ) @ mactual )
    | ~ ( member @ ( sk__5 @ ( difference @ sk__7 @ sk__8 ) @ sk__6 ) @ sk__6 @ mactual ) ),
    inference('sup-',[status(thm)],[zip_derived_cl262,zip_derived_cl22]) ).

thf(zip_derived_cl18_004,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset @ X0 @ X1 @ mactual )
      | ( member @ ( sk__5 @ X1 @ X0 ) @ X0 @ mactual ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl319,plain,
    subset @ sk__6 @ ( difference @ sk__7 @ sk__8 ) @ mactual,
    inference(clc,[status(thm)],[zip_derived_cl266,zip_derived_cl18]) ).

thf(zip_derived_cl23,plain,
    ~ ( qmltpeq @ sk__6 @ ( difference @ sk__7 @ sk__8 ) @ mactual ),
    inference(cnf,[status(esa)],[zf_stmt_4]) ).

thf(zip_derived_cl559,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl553,zip_derived_cl319,zip_derived_cl23]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET579^3 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.8Hi6old4GK true
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.20/0.35  % CPULimit : 300
% 0.20/0.35  % WCLimit  : 300
% 0.20/0.35  % DateTime : Sat Aug 26 16:02:24 EDT 2023
% 0.20/0.35  % CPUTime  : 
% 0.20/0.35  % Running portfolio for 300 s
% 0.20/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35  % Number of cores: 8
% 0.20/0.35  % Python version: Python 3.6.8
% 0.20/0.35  % Running in HO mode
% 0.21/0.66  % Total configuration time : 828
% 0.21/0.66  % Estimated wc time : 1656
% 0.21/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.79  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.35/0.80  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.35/0.80  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.35/0.81  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.41/0.86  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.41/0.92  % Solved by lams/40_c_ic.sh.
% 1.41/0.92  % done 150 iterations in 0.140s
% 1.41/0.92  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.41/0.92  % SZS output start Refutation
% See solution above
% 1.41/0.92  
% 1.41/0.92  
% 1.41/0.92  % Terminating...
% 1.88/0.96  % Runner terminated.
% 1.88/0.97  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------