TSTP Solution File: SEU523^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU523^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YbtmXTH6s9 true

% Computer : n028.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 19:13:32 EDT 2023

% Result   : Theorem 1.10s 0.80s
% Output   : Refutation 1.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   42 (  15 unt;   7 typ;   0 def)
%            Number of atoms       :  134 (   8 equ;   0 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  364 (  15   ~;   6   |;  15   &; 250   @)
%                                         (   8 <=>;  43  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   7 usr;   8 con; 0-2 aty)
%                                         (  22  !!;   5  ??;   0 @@+;   0 @@-)
%            Number of variables   :   71 (  28   ^;  39   !;   4   ?;  71   :)

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

thf('#sk1_type',type,
    '#sk1': $i ).

thf(setunionAx_type,type,
    setunionAx: $o ).

thf('#sk4_type',type,
    '#sk4': $o ).

thf('#sk2_type',type,
    '#sk2': $i ).

thf(setunion_type,type,
    setunion: $i > $i ).

thf('#sk3_type',type,
    '#sk3': $i > $i > $i ).

thf(setunionAx,axiom,
    ( setunionAx
    = ( ! [A: $i,Xx: $i] :
          ( ( in @ Xx @ ( setunion @ A ) )
        <=> ? [B: $i] :
              ( ( in @ B @ A )
              & ( in @ Xx @ B ) ) ) ) ) ).

thf('0',plain,
    ( setunionAx
    = ( ! [X4: $i,X6: $i] :
          ( ( in @ X6 @ ( setunion @ X4 ) )
        <=> ? [X8: $i] :
              ( ( in @ X8 @ X4 )
              & ( in @ X6 @ X8 ) ) ) ) ),
    define([status(thm)]) ).

thf(setunionE,conjecture,
    ( setunionAx
   => ! [A: $i,Xx: $i] :
        ( ( in @ Xx @ ( setunion @ A ) )
       => ! [Xphi: $o] :
            ( ! [B: $i] :
                ( ( in @ Xx @ B )
               => ( ( in @ B @ A )
                 => Xphi ) )
           => Xphi ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i] :
        ( ( in @ X6 @ ( setunion @ X4 ) )
      <=> ? [X8: $i] :
            ( ( in @ X6 @ X8 )
            & ( in @ X8 @ X4 ) ) )
   => ! [X10: $i,X12: $i] :
        ( ( in @ X12 @ ( setunion @ X10 ) )
       => ! [X14: $o] :
            ( ! [X16: $i] :
                ( ( in @ X12 @ X16 )
               => ( ( in @ X16 @ X10 )
                 => X14 ) )
           => X14 ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i] :
          ( ( in @ X6 @ ( setunion @ X4 ) )
        <=> ? [X8: $i] :
              ( ( in @ X6 @ X8 )
              & ( in @ X8 @ X4 ) ) )
     => ! [X10: $i,X12: $i] :
          ( ( in @ X12 @ ( setunion @ X10 ) )
         => ! [X14: $o] :
              ( ! [X16: $i] :
                  ( ( in @ X12 @ X16 )
                 => ( ( in @ X16 @ X10 )
                   => X14 ) )
             => X14 ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl0,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ ( setunion @ Y0 ) )
              <=> ( ??
                  @ ^ [Y2: $i] :
                      ( ( in @ Y1 @ Y2 )
                      & ( in @ Y2 @ Y0 ) ) ) ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ ( setunion @ Y0 ) )
               => ( !!
                  @ ^ [Y2: $o] :
                      ( ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y1 @ Y3 )
                           => ( ( in @ Y3 @ Y0 )
                             => Y2 ) ) )
                     => Y2 ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl2,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( !!
          @ ^ [Y1: $i] :
              ( ( in @ Y1 @ ( setunion @ Y0 ) )
             => ( !!
                @ ^ [Y2: $o] :
                    ( ( !!
                      @ ^ [Y3: $i] :
                          ( ( in @ Y1 @ Y3 )
                         => ( ( in @ Y3 @ Y0 )
                           => Y2 ) ) )
                   => Y2 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl4,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ ( setunion @ '#sk1' ) )
         => ( !!
            @ ^ [Y1: $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y0 @ Y2 )
                     => ( ( in @ Y2 @ '#sk1' )
                       => Y1 ) ) )
               => Y1 ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl6,plain,
    ~ ( ( in @ '#sk2' @ ( setunion @ '#sk1' ) )
     => ( !!
        @ ^ [Y0: $o] :
            ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ '#sk2' @ Y1 )
                 => ( ( in @ Y1 @ '#sk1' )
                   => Y0 ) ) )
           => Y0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl10,plain,
    in @ '#sk2' @ ( setunion @ '#sk1' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( in @ Y1 @ ( setunion @ Y0 ) )
          <=> ( ??
              @ ^ [Y2: $i] :
                  ( ( in @ Y1 @ Y2 )
                  & ( in @ Y2 @ Y0 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl3,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( in @ Y0 @ ( setunion @ X2 ) )
        <=> ( ??
            @ ^ [Y1: $i] :
                ( ( in @ Y0 @ Y1 )
                & ( in @ Y1 @ X2 ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl5,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ X4 @ ( setunion @ X2 ) )
    <=> ( ??
        @ ^ [Y0: $i] :
            ( ( in @ X4 @ Y0 )
            & ( in @ Y0 @ X2 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl7,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ X4 @ ( setunion @ X2 ) )
      = ( ??
        @ ^ [Y0: $i] :
            ( ( in @ X4 @ Y0 )
            & ( in @ Y0 @ X2 ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl9,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ X4 @ ( setunion @ X2 ) )
      = ( ^ [Y0: $i] :
            ( ( in @ X4 @ Y0 )
            & ( in @ Y0 @ X2 ) )
        @ ( '#sk3' @ X2 @ X4 ) ) ),
    inference(quantifier_rw,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl12,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ X4 @ ( setunion @ X2 ) )
      = ( ( in @ X4 @ ( '#sk3' @ X2 @ X4 ) )
        & ( in @ ( '#sk3' @ X2 @ X4 ) @ X2 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl25,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ( ( in @ X4 @ ( setunion @ X2 ) )
        = ( $false
          & ( in @ ( '#sk3' @ X2 @ X4 ) @ X2 ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl26,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ X4 @ ( '#sk3' @ X2 @ X4 ) )
      | ~ ( in @ X4 @ ( setunion @ X2 ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl25]) ).

thf(zip_derived_cl27,plain,
    in @ '#sk2' @ ( '#sk3' @ '#sk1' @ '#sk2' ),
    inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl26]) ).

thf(zip_derived_cl12_001,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ X4 @ ( setunion @ X2 ) )
      = ( ( in @ X4 @ ( '#sk3' @ X2 @ X4 ) )
        & ( in @ ( '#sk3' @ X2 @ X4 ) @ X2 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl29,plain,
    ( ( in @ '#sk2' @ ( setunion @ '#sk1' ) )
    = ( $true
      & ( in @ ( '#sk3' @ '#sk1' @ '#sk2' ) @ '#sk1' ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl27,zip_derived_cl12]) ).

thf(zip_derived_cl10_002,plain,
    in @ '#sk2' @ ( setunion @ '#sk1' ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl31,plain,
    ( $true
    & ( in @ ( '#sk3' @ '#sk1' @ '#sk2' ) @ '#sk1' ) ),
    inference(demod,[status(thm)],[zip_derived_cl29,zip_derived_cl10]) ).

thf(zip_derived_cl32,plain,
    in @ ( '#sk3' @ '#sk1' @ '#sk2' ) @ '#sk1',
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl31]) ).

thf(zip_derived_cl11,plain,
    ~ ( !!
      @ ^ [Y0: $o] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( in @ '#sk2' @ Y1 )
               => ( ( in @ Y1 @ '#sk1' )
                 => Y0 ) ) )
         => Y0 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl16,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( ( in @ '#sk2' @ Y0 )
           => ( ( in @ Y0 @ '#sk1' )
             => '#sk4' ) ) )
     => '#sk4' ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl17,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( in @ '#sk2' @ Y0 )
       => ( ( in @ Y0 @ '#sk1' )
         => '#sk4' ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl19,plain,
    ! [X2: $i] :
      ( ( in @ '#sk2' @ X2 )
     => ( ( in @ X2 @ '#sk1' )
       => '#sk4' ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl20,plain,
    ! [X2: $i] :
      ( ~ ( in @ '#sk2' @ X2 )
      | ( ( in @ X2 @ '#sk1' )
       => '#sk4' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl21,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ '#sk1' )
      | '#sk4'
      | ~ ( in @ '#sk2' @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).

thf(zip_derived_cl18,plain,
    ~ '#sk4',
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl22,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ '#sk1' )
      | ~ ( in @ '#sk2' @ X2 ) ),
    inference(demod,[status(thm)],[zip_derived_cl21,zip_derived_cl18]) ).

thf(zip_derived_cl35,plain,
    ~ ( in @ '#sk2' @ ( '#sk3' @ '#sk1' @ '#sk2' ) ),
    inference('sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl22]) ).

thf(zip_derived_cl27_003,plain,
    in @ '#sk2' @ ( '#sk3' @ '#sk1' @ '#sk2' ),
    inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl26]) ).

thf(zip_derived_cl37,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl35,zip_derived_cl27]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU523^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.YbtmXTH6s9 true
% 0.14/0.35  % Computer : n028.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
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Wed Aug 23 19:57:04 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  % Running portfolio for 300 s
% 0.14/0.36  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36  % Number of cores: 8
% 0.14/0.36  % Python version: Python 3.6.8
% 0.14/0.36  % Running in HO mode
% 0.22/0.65  % Total configuration time : 828
% 0.22/0.65  % Estimated wc time : 1656
% 0.22/0.65  % Estimated cpu time (8 cpus) : 207.0
% 1.10/0.77  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.10/0.77  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.10/0.77  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.10/0.77  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.10/0.77  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.10/0.77  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.10/0.78  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.10/0.80  % Solved by lams/35_full_unif4.sh.
% 1.10/0.80  % done 6 iterations in 0.013s
% 1.10/0.80  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.10/0.80  % SZS output start Refutation
% See solution above
% 1.10/0.80  
% 1.10/0.80  
% 1.10/0.80  % Terminating...
% 1.53/0.86  % Runner terminated.
% 1.83/0.87  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------