TSTP Solution File: SET609^3 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SET609^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.2t0ox8nFSD 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 16:14:58 EDT 2023

% Result   : Theorem 0.87s 0.78s
% Output   : Refutation 0.87s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   39 (  25 unt;   7 typ;   0 def)
%            Number of atoms       :  163 (  28 equ;  33 cnn)
%            Maximal formula atoms :    4 (   5 avg)
%            Number of connectives :  312 (  59   ~;  22   |;  56   &; 169   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   51 (  51   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   12 (   7 usr;   5 con; 0-3 aty)
%                                         (   6  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   56 (  47   ^;   9   !;   0   ?;  56   :)

% Comments : 
%------------------------------------------------------------------------------
thf(intersection_type,type,
    intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(union_type,type,
    union: ( $i > $o ) > ( $i > $o ) > $i > $o ).

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

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

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

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

thf(setminus_type,type,
    setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).

thf(setminus,axiom,
    ( setminus
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          & ~ ( Y @ U ) ) ) ) ).

thf('0',plain,
    ( setminus
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          & ~ ( Y @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[setminus]) ).

thf('1',plain,
    ( setminus
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
          ( ( V_1 @ V_3 )
          & ~ ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(intersection,axiom,
    ( intersection
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          & ( Y @ U ) ) ) ) ).

thf('2',plain,
    ( intersection
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          & ( Y @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[intersection]) ).

thf('3',plain,
    ( intersection
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
          ( ( V_1 @ V_3 )
          & ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(union,axiom,
    ( union
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          | ( Y @ U ) ) ) ) ).

thf('4',plain,
    ( union
    = ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
          ( ( X @ U )
          | ( Y @ U ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[union]) ).

thf('5',plain,
    ( union
    = ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
          ( ( V_1 @ V_3 )
          | ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(thm,conjecture,
    ! [X: $i > $o,Y: $i > $o,Z: $i > $o] :
      ( ( setminus @ X @ ( setminus @ Y @ Z ) )
      = ( union @ ( setminus @ X @ Y ) @ ( intersection @ X @ Z ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i > $o,X6: $i > $o,X8: $i > $o] :
      ( ( ^ [V_1: $i] :
            ( ~ ( ~ ( X8 @ V_1 )
                & ( X6 @ V_1 ) )
            & ( X4 @ V_1 ) ) )
      = ( ^ [V_2: $i] :
            ( ( ( X8 @ V_2 )
              & ( X4 @ V_2 ) )
            | ( ~ ( X6 @ V_2 )
              & ( X4 @ V_2 ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i > $o,X6: $i > $o,X8: $i > $o] :
        ( ( ^ [V_1: $i] :
              ( ~ ( ~ ( X8 @ V_1 )
                  & ( X6 @ V_1 ) )
              & ( X4 @ V_1 ) ) )
        = ( ^ [V_2: $i] :
              ( ( ( X8 @ V_2 )
                & ( X4 @ V_2 ) )
              | ( ~ ( X6 @ V_2 )
                & ( X4 @ V_2 ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

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

thf(zip_derived_cl1,plain,
    ~ ( !!
      @ ^ [Y0: $i > $o] :
          ( !!
          @ ^ [Y1: $i > $o] :
              ( ( ^ [Y2: $i] :
                    ( ( (~)
                      @ ( ( (~) @ ( Y1 @ Y2 ) )
                        & ( Y0 @ Y2 ) ) )
                    & ( '#sk1' @ Y2 ) ) )
              = ( ^ [Y2: $i] :
                    ( ( ( Y1 @ Y2 )
                      & ( '#sk1' @ Y2 ) )
                    | ( ( (~) @ ( Y0 @ Y2 ) )
                      & ( '#sk1' @ Y2 ) ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl2,plain,
    ~ ( !!
      @ ^ [Y0: $i > $o] :
          ( ( ^ [Y1: $i] :
                ( ( (~)
                  @ ( ( (~) @ ( Y0 @ Y1 ) )
                    & ( '#sk2' @ Y1 ) ) )
                & ( '#sk1' @ Y1 ) ) )
          = ( ^ [Y1: $i] :
                ( ( ( Y0 @ Y1 )
                  & ( '#sk1' @ Y1 ) )
                | ( ( (~) @ ( '#sk2' @ Y1 ) )
                  & ( '#sk1' @ Y1 ) ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl3,plain,
    ( ( ^ [Y0: $i] :
          ( ( (~)
            @ ( ( (~) @ ( '#sk3' @ Y0 ) )
              & ( '#sk2' @ Y0 ) ) )
          & ( '#sk1' @ Y0 ) ) )
   != ( ^ [Y0: $i] :
          ( ( ( '#sk3' @ Y0 )
            & ( '#sk1' @ Y0 ) )
          | ( ( (~) @ ( '#sk2' @ Y0 ) )
            & ( '#sk1' @ Y0 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl4,plain,
    ( ( ^ [Y0: $i] :
          ( ( (~)
            @ ( ( (~) @ ( '#sk3' @ Y0 ) )
              & ( '#sk2' @ Y0 ) ) )
          & ( '#sk1' @ Y0 ) ) )
   != ( ^ [Y0: $i] :
          ( ( ( '#sk3' @ Y0 )
            & ( '#sk1' @ Y0 ) )
          | ( ( (~) @ ( '#sk2' @ Y0 ) )
            & ( '#sk1' @ Y0 ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl5,plain,
    ( ( ( (~)
        @ ( ( (~) @ ( '#sk3' @ '#sk4' ) )
          & ( '#sk2' @ '#sk4' ) ) )
      & ( '#sk1' @ '#sk4' ) )
   != ( ( ( '#sk3' @ '#sk4' )
        & ( '#sk1' @ '#sk4' ) )
      | ( ( (~) @ ( '#sk2' @ '#sk4' ) )
        & ( '#sk1' @ '#sk4' ) ) ) ),
    inference(neg_ext,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl5_001,plain,
    ( ( ( (~)
        @ ( ( (~) @ ( '#sk3' @ '#sk4' ) )
          & ( '#sk2' @ '#sk4' ) ) )
      & ( '#sk1' @ '#sk4' ) )
   != ( ( ( '#sk3' @ '#sk4' )
        & ( '#sk1' @ '#sk4' ) )
      | ( ( (~) @ ( '#sk2' @ '#sk4' ) )
        & ( '#sk1' @ '#sk4' ) ) ) ),
    inference(neg_ext,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl8,plain,
    ( ( '#sk3' @ '#sk4' )
    | ( ( ( (~)
          @ ( ( (~) @ $false )
            & ( '#sk2' @ '#sk4' ) ) )
        & ( '#sk1' @ '#sk4' ) )
     != ( ( $false
          & ( '#sk1' @ '#sk4' ) )
        | ( ( (~) @ ( '#sk2' @ '#sk4' ) )
          & ( '#sk1' @ '#sk4' ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl9,plain,
    ( ( '#sk3' @ '#sk4' )
    | ( ( ( (~) @ ( '#sk2' @ '#sk4' ) )
        & ( '#sk1' @ '#sk4' ) )
     != ( ( (~) @ ( '#sk2' @ '#sk4' ) )
        & ( '#sk1' @ '#sk4' ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl8]) ).

thf(zip_derived_cl10,plain,
    '#sk3' @ '#sk4',
    inference(simplify,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl10_002,plain,
    '#sk3' @ '#sk4',
    inference(simplify,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl11,plain,
    ( ( ( (~)
        @ ( ( (~) @ $true )
          & ( '#sk2' @ '#sk4' ) ) )
      & ( '#sk1' @ '#sk4' ) )
   != ( ( $true
        & ( '#sk1' @ '#sk4' ) )
      | ( ( (~) @ ( '#sk2' @ '#sk4' ) )
        & ( '#sk1' @ '#sk4' ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5,zip_derived_cl10,zip_derived_cl10]) ).

thf(zip_derived_cl12,plain,
    ( ( '#sk1' @ '#sk4' )
   != ( ( '#sk1' @ '#sk4' )
      | ( ( (~) @ ( '#sk2' @ '#sk4' ) )
        & ( '#sk1' @ '#sk4' ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl12_003,plain,
    ( ( '#sk1' @ '#sk4' )
   != ( ( '#sk1' @ '#sk4' )
      | ( ( (~) @ ( '#sk2' @ '#sk4' ) )
        & ( '#sk1' @ '#sk4' ) ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl15,plain,
    ( ( '#sk2' @ '#sk4' )
    | ( ( '#sk1' @ '#sk4' )
     != ( ( '#sk1' @ '#sk4' )
        | ( ( (~) @ $false )
          & ( '#sk1' @ '#sk4' ) ) ) ) ),
    inference(bool_hoist,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl16,plain,
    ( ( '#sk2' @ '#sk4' )
    | ( ( '#sk1' @ '#sk4' )
     != ( '#sk1' @ '#sk4' ) ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl17,plain,
    '#sk2' @ '#sk4',
    inference(simplify,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl22,plain,
    ( ( '#sk1' @ '#sk4' )
   != ( ( '#sk1' @ '#sk4' )
      | ( ( (~) @ $true )
        & ( '#sk1' @ '#sk4' ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl12,zip_derived_cl17]) ).

thf(zip_derived_cl23,plain,
    ( ( '#sk1' @ '#sk4' )
   != ( '#sk1' @ '#sk4' ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl22]) ).

thf(zip_derived_cl24,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl23]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET609^3 : TPTP v8.1.2. Released v3.6.0.
% 0.13/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.2t0ox8nFSD 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
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat Aug 26 13:58:54 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.36  % 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/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.75  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.87/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.87/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.87/0.78  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.87/0.78  % Solved by lams/35_full_unif4.sh.
% 0.87/0.78  % done 4 iterations in 0.014s
% 0.87/0.78  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.87/0.78  % SZS output start Refutation
% See solution above
% 0.87/0.78  
% 0.87/0.78  
% 0.87/0.78  % Terminating...
% 1.44/0.86  % Runner terminated.
% 1.44/0.88  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------