TSTP Solution File: SEU526^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU526^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.H4gKy3yQur true

% Computer : n027.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 19:13:34 EDT 2023

% Result   : Theorem 1.29s 0.77s
% Output   : Refutation 1.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   43 (  14 unt;   7 typ;   0 def)
%            Number of atoms       :  162 (  36 equ;   0 cnn)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  363 (  26   ~;  14   |;   0   &; 216   @)
%                                         (   0 <=>;  70  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   7 usr;   7 con; 0-2 aty)
%                                         (  32  !!;   5  ??;   0 @@+;   0 @@-)
%            Number of variables   :   94 (  40   ^;  51   !;   3   ?;  94   :)

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

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

thf(emptysetE_type,type,
    emptysetE: $o ).

thf(setext_type,type,
    setext: $o ).

thf(nonempty_type,type,
    nonempty: $i > $o ).

thf(emptyset_type,type,
    emptyset: $i ).

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

thf(nonempty,axiom,
    ( nonempty
    = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).

thf('0',plain,
    ( nonempty
    = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
    inference(simplify_rw_rule,[status(thm)],[nonempty]) ).

thf('1',plain,
    ( nonempty
    = ( ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
    define([status(thm)]) ).

thf(setext,axiom,
    ( setext
    = ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( ! [Xx: $i] :
                ( ( in @ Xx @ B )
               => ( in @ Xx @ A ) )
           => ( A = B ) ) ) ) ) ).

thf('2',plain,
    ( setext
    = ( ! [X4: $i,X6: $i] :
          ( ! [X8: $i] :
              ( ( in @ X8 @ X4 )
             => ( in @ X8 @ X6 ) )
         => ( ! [X10: $i] :
                ( ( in @ X10 @ X6 )
               => ( in @ X10 @ X4 ) )
           => ( X4 = X6 ) ) ) ) ),
    define([status(thm)]) ).

thf(emptysetE,axiom,
    ( emptysetE
    = ( ! [Xx: $i] :
          ( ( in @ Xx @ emptyset )
         => ! [Xphi: $o] : Xphi ) ) ) ).

thf('3',plain,
    ( emptysetE
    = ( ! [X4: $i] :
          ( ( in @ X4 @ emptyset )
         => ! [X6: $o] : X6 ) ) ),
    define([status(thm)]) ).

thf(nonemptyImpWitness,conjecture,
    ( emptysetE
   => ( setext
     => ! [A: $i] :
          ( ( nonempty @ A )
         => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i] :
        ( ( in @ X4 @ emptyset )
       => ! [X6: $o] : X6 )
   => ( ! [X8: $i,X10: $i] :
          ( ! [X12: $i] :
              ( ( in @ X12 @ X8 )
             => ( in @ X12 @ X10 ) )
         => ( ! [X14: $i] :
                ( ( in @ X14 @ X10 )
               => ( in @ X14 @ X8 ) )
           => ( X8 = X10 ) ) )
     => ! [X16: $i] :
          ( ( X16 != emptyset )
         => ? [X18: $i] : ( in @ X18 @ X16 ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i] :
          ( ( in @ X4 @ emptyset )
         => ! [X6: $o] : X6 )
     => ( ! [X8: $i,X10: $i] :
            ( ! [X12: $i] :
                ( ( in @ X12 @ X8 )
               => ( in @ X12 @ X10 ) )
           => ( ! [X14: $i] :
                  ( ( in @ X14 @ X10 )
                 => ( in @ X14 @ X8 ) )
             => ( X8 = X10 ) ) )
       => ! [X16: $i] :
            ( ( X16 != emptyset )
           => ? [X18: $i] : ( in @ X18 @ X16 ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

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

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( ( in @ Y0 @ emptyset )
       => ( !!
          @ ^ [Y1: $o] : Y1 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl3,plain,
    ! [X2: $i] :
      ( ( in @ X2 @ emptyset )
     => ( !!
        @ ^ [Y0: $o] : Y0 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl6,plain,
    ! [X2: $i] :
      ( ~ ( in @ X2 @ emptyset )
      | ( !!
        @ ^ [Y0: $o] : Y0 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl9,plain,
    ! [X2: $i,X4: $o] :
      ( X4
      | ~ ( in @ X2 @ emptyset ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl30,plain,
    ! [X0: $i] :
      ~ ( in @ X0 @ emptyset ),
    inference('ho.refine',[status(thm)],[zip_derived_cl9]) ).

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

thf(zip_derived_cl4,plain,
    ( !!
    @ ^ [Y0: $i] :
        ( !!
        @ ^ [Y1: $i] :
            ( ( !!
              @ ^ [Y2: $i] :
                  ( ( in @ Y2 @ Y0 )
                 => ( in @ Y2 @ Y1 ) ) )
           => ( ( !!
                @ ^ [Y2: $i] :
                    ( ( in @ Y2 @ Y1 )
                   => ( in @ Y2 @ Y0 ) ) )
             => ( Y0 = Y1 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl7,plain,
    ! [X2: $i] :
      ( !!
      @ ^ [Y0: $i] :
          ( ( !!
            @ ^ [Y1: $i] :
                ( ( in @ Y1 @ X2 )
               => ( in @ Y1 @ Y0 ) ) )
         => ( ( !!
              @ ^ [Y1: $i] :
                  ( ( in @ Y1 @ Y0 )
                 => ( in @ Y1 @ X2 ) ) )
           => ( X2 = Y0 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl10,plain,
    ! [X2: $i,X4: $i] :
      ( ( !!
        @ ^ [Y0: $i] :
            ( ( in @ Y0 @ X2 )
           => ( in @ Y0 @ X4 ) ) )
     => ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X4 )
             => ( in @ Y0 @ X2 ) ) )
       => ( X2 = X4 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl13,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X2 )
             => ( in @ Y0 @ X4 ) ) )
      | ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X4 )
             => ( in @ Y0 @ X2 ) ) )
       => ( X2 = X4 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl16,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( ( in @ ( '#sk2' @ X2 @ X4 ) @ X2 )
         => ( in @ ( '#sk2' @ X2 @ X4 ) @ X4 ) )
      | ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X4 )
             => ( in @ Y0 @ X2 ) ) )
       => ( X2 = X4 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl17,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ ( '#sk2' @ X2 @ X4 ) @ X2 )
      | ( ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X4 )
             => ( in @ Y0 @ X2 ) ) )
       => ( X2 = X4 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl19,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X4 )
             => ( in @ Y0 @ X2 ) ) )
      | ( X2 = X4 )
      | ( in @ ( '#sk2' @ X2 @ X4 ) @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl21,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( !!
          @ ^ [Y0: $i] :
              ( ( in @ Y0 @ X4 )
             => ( in @ Y0 @ X2 ) ) )
      | ( X2 = X4 )
      | ( in @ ( '#sk2' @ X2 @ X4 ) @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl19]) ).

thf(zip_derived_cl22,plain,
    ! [X2: $i,X4: $i] :
      ( ~ ( ( in @ ( '#sk2' @ X4 @ X2 ) @ X4 )
         => ( in @ ( '#sk2' @ X4 @ X2 ) @ X2 ) )
      | ( in @ ( '#sk2' @ X2 @ X4 ) @ X2 )
      | ( X2 = X4 ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl21]) ).

thf(zip_derived_cl25,plain,
    ! [X2: $i,X4: $i] :
      ( ( in @ ( '#sk2' @ X4 @ X2 ) @ X4 )
      | ( X2 = X4 )
      | ( in @ ( '#sk2' @ X2 @ X4 ) @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl5,plain,
    ~ ( !!
      @ ^ [Y0: $i] :
          ( ( Y0 != emptyset )
         => ( ??
            @ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl8,plain,
    ~ ( ( '#sk1' != emptyset )
     => ( ??
        @ ^ [Y0: $i] : ( in @ Y0 @ '#sk1' ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl12,plain,
    ~ ( ??
      @ ^ [Y0: $i] : ( in @ Y0 @ '#sk1' ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl15,plain,
    ! [X2: $i] :
      ~ ( in @ X2 @ '#sk1' ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl35,plain,
    ! [X0: $i] :
      ( ( '#sk1' = X0 )
      | ( in @ ( '#sk2' @ X0 @ '#sk1' ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl15]) ).

thf(zip_derived_cl58,plain,
    '#sk1' = emptyset,
    inference('sup+',[status(thm)],[zip_derived_cl30,zip_derived_cl35]) ).

thf(zip_derived_cl11,plain,
    '#sk1' != emptyset,
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl14,plain,
    '#sk1' != emptyset,
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl63,plain,
    $false,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl58,zip_derived_cl14]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU526^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.H4gKy3yQur true
% 0.13/0.34  % Computer : n027.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 : Wed Aug 23 21:36:47 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in HO mode
% 0.20/0.65  % Total configuration time : 828
% 0.20/0.65  % Estimated wc time : 1656
% 0.20/0.65  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.72  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.72  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.73  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.74  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.74  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.29/0.75  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.29/0.77  % Solved by lams/35_full_unif4.sh.
% 1.29/0.77  % done 5 iterations in 0.018s
% 1.29/0.77  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.29/0.77  % SZS output start Refutation
% See solution above
% 1.29/0.77  
% 1.29/0.77  
% 1.29/0.77  % Terminating...
% 1.62/0.85  % Runner terminated.
% 1.62/0.86  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------