TSTP Solution File: SEU611^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU611^2 : 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.Ac5F14zQrD true

% Computer : n001.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 19:14:41 EDT 2023

% Result   : Theorem 0.21s 0.76s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   45 (  18 unt;  11 typ;   0 def)
%            Number of atoms       :  117 (   9 equ;  10 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  364 (  38   ~;  27   |;   0   &; 257   @)
%                                         (   0 <=>;  42  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  11 usr;  10 con; 0-2 aty)
%            Number of variables   :   87 (  24   ^;  63   !;   0   ?;  87   :)

% Comments : 
%------------------------------------------------------------------------------
thf(binunionE_type,type,
    binunionE: $o ).

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

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

thf(sk__9_type,type,
    sk__9: $i ).

thf(dsetconstrEL_type,type,
    dsetconstrEL: $o ).

thf(dsetconstrER_type,type,
    dsetconstrER: $o ).

thf(sk__12_type,type,
    sk__12: $o ).

thf(dsetconstr_type,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(sk__10_type,type,
    sk__10: $i ).

thf(symdiff_type,type,
    symdiff: $i > $i > $i ).

thf(binunion_type,type,
    binunion: $i > $i > $i ).

thf(symdiff,axiom,
    ( symdiff
    = ( ^ [A: $i,B: $i] :
          ( dsetconstr @ ( binunion @ A @ B )
          @ ^ [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ~ ( in @ Xx @ B ) ) ) ) ) ).

thf('0',plain,
    ( symdiff
    = ( ^ [A: $i,B: $i] :
          ( dsetconstr @ ( binunion @ A @ B )
          @ ^ [Xx: $i] :
              ( ~ ( in @ Xx @ A )
              | ~ ( in @ Xx @ B ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[symdiff]) ).

thf('1',plain,
    ( symdiff
    = ( ^ [V_1: $i,V_2: $i] :
          ( dsetconstr @ ( binunion @ V_1 @ V_2 )
          @ ^ [V_3: $i] :
              ( ~ ( in @ V_3 @ V_1 )
              | ~ ( in @ V_3 @ V_2 ) ) ) ) ),
    define([status(thm)]) ).

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

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

thf(dsetconstrER,axiom,
    ( dsetconstrER
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
         => ( Xphi @ Xx ) ) ) ) ).

thf('3',plain,
    ( dsetconstrER
    = ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
         => ( X6 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(dsetconstrEL,axiom,
    ( dsetconstrEL
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
         => ( in @ Xx @ A ) ) ) ) ).

thf('4',plain,
    ( dsetconstrEL
    = ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
         => ( in @ X8 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(symdiffE,conjecture,
    ( dsetconstrEL
   => ( dsetconstrER
     => ( binunionE
       => ! [A: $i,B: $i,Xx: $i] :
            ( ( in @ Xx @ ( symdiff @ A @ B ) )
           => ! [Xphi: $o] :
                ( ( ( in @ Xx @ A )
                 => ( ~ ( in @ Xx @ B )
                   => Xphi ) )
               => ( ( ~ ( in @ Xx @ A )
                   => ( ( in @ Xx @ B )
                     => Xphi ) )
                 => Xphi ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i > $o,X8: $i] :
        ( ( in @ X8
          @ ( dsetconstr @ X4
            @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
       => ( in @ X8 @ X4 ) )
   => ( ! [X10: $i,X12: $i > $o,X14: $i] :
          ( ( in @ X14
            @ ( dsetconstr @ X10
              @ ^ [V_2: $i] : ( X12 @ V_2 ) ) )
         => ( X12 @ X14 ) )
     => ( ! [X16: $i,X18: $i,X20: $i] :
            ( ( in @ X20 @ ( binunion @ X16 @ X18 ) )
           => ( ( in @ X20 @ X16 )
              | ( in @ X20 @ X18 ) ) )
       => ! [X22: $i,X24: $i,X26: $i] :
            ( ( in @ X26
              @ ( dsetconstr @ ( binunion @ X22 @ X24 )
                @ ^ [V_3: $i] :
                    ( ~ ( in @ V_3 @ X24 )
                    | ~ ( in @ V_3 @ X22 ) ) ) )
           => ! [X28: $o] :
                ( ( ( in @ X26 @ X22 )
                 => ( ~ ( in @ X26 @ X24 )
                   => X28 ) )
               => ( ( ~ ( in @ X26 @ X22 )
                   => ( ( in @ X26 @ X24 )
                     => X28 ) )
                 => X28 ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i > $o,X8: $i] :
          ( ( in @ X8
            @ ( dsetconstr @ X4
              @ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
         => ( in @ X8 @ X4 ) )
     => ( ! [X10: $i,X12: $i > $o,X14: $i] :
            ( ( in @ X14
              @ ( dsetconstr @ X10
                @ ^ [V_2: $i] : ( X12 @ V_2 ) ) )
           => ( X12 @ X14 ) )
       => ( ! [X16: $i,X18: $i,X20: $i] :
              ( ( in @ X20 @ ( binunion @ X16 @ X18 ) )
             => ( ( in @ X20 @ X16 )
                | ( in @ X20 @ X18 ) ) )
         => ! [X22: $i,X24: $i,X26: $i] :
              ( ( in @ X26
                @ ( dsetconstr @ ( binunion @ X22 @ X24 )
                  @ ^ [V_3: $i] :
                      ( ~ ( in @ V_3 @ X24 )
                      | ~ ( in @ V_3 @ X22 ) ) ) )
             => ! [X28: $o] :
                  ( ( ( in @ X26 @ X22 )
                   => ( ~ ( in @ X26 @ X24 )
                     => X28 ) )
                 => ( ( ~ ( in @ X26 @ X22 )
                     => ( ( in @ X26 @ X24 )
                       => X28 ) )
                   => X28 ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl5,plain,
    ( in @ sk__11
    @ ( dsetconstr @ ( binunion @ sk__9 @ sk__10 )
      @ ^ [Y0: $i] :
          ( ( (~) @ ( in @ Y0 @ sk__10 ) )
          | ( (~) @ ( in @ Y0 @ sk__9 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl6,plain,
    ! [X6: $i > $o,X7: $i,X8: $i] :
      ( ( X6 @ X7 )
      | ~ ( in @ X7
          @ ( dsetconstr @ X8
            @ ^ [Y0: $i] : ( X6 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl21,plain,
    ! [X6: $i > $o,X7: $i,X8: $i] :
      ( ( X6 @ X7 )
      | ~ ( in @ X7 @ ( dsetconstr @ X8 @ X6 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl28,plain,
    ( ^ [Y0: $i] :
        ( ( (~) @ ( in @ Y0 @ sk__10 ) )
        | ( (~) @ ( in @ Y0 @ sk__9 ) ) )
    @ sk__11 ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl21]) ).

thf(zip_derived_cl55,plain,
    ( ( (~) @ ( in @ sk__11 @ sk__10 ) )
    | ( (~) @ ( in @ sk__11 @ sk__9 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl28]) ).

thf(zip_derived_cl5_001,plain,
    ( in @ sk__11
    @ ( dsetconstr @ ( binunion @ sk__9 @ sk__10 )
      @ ^ [Y0: $i] :
          ( ( (~) @ ( in @ Y0 @ sk__10 ) )
          | ( (~) @ ( in @ Y0 @ sk__9 ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i,X2: $i > $o] :
      ( ( in @ X0 @ X1 )
      | ~ ( in @ X0
          @ ( dsetconstr @ X1
            @ ^ [Y0: $i] : ( X2 @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl13,plain,
    ! [X0: $i,X1: $i,X2: $i > $o] :
      ( ( in @ X0 @ X1 )
      | ~ ( in @ X0 @ ( dsetconstr @ X1 @ X2 ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl14,plain,
    in @ sk__11 @ ( binunion @ sk__9 @ sk__10 ),
    inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl13]) ).

thf(zip_derived_cl1,plain,
    ! [X3: $i,X4: $i,X5: $i] :
      ( ( in @ X3 @ X4 )
      | ( in @ X3 @ X5 )
      | ~ ( in @ X3 @ ( binunion @ X5 @ X4 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl15,plain,
    ( ( in @ sk__11 @ sk__9 )
    | ( in @ sk__11 @ sk__10 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl14,zip_derived_cl1]) ).

thf(zip_derived_cl2,plain,
    ( ( in @ sk__11 @ sk__10 )
    | sk__12
    | ~ ( in @ sk__11 @ sk__9 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl3,plain,
    ~ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl7,plain,
    ( ( in @ sk__11 @ sk__10 )
    | ~ ( in @ sk__11 @ sk__9 ) ),
    inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl3]) ).

thf(zip_derived_cl17,plain,
    in @ sk__11 @ sk__10,
    inference(clc,[status(thm)],[zip_derived_cl15,zip_derived_cl7]) ).

thf(zip_derived_cl4,plain,
    ( ~ ( in @ sk__11 @ sk__10 )
    | sk__12
    | ( in @ sk__11 @ sk__9 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl3_002,plain,
    ~ sk__12,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl8,plain,
    ( ~ ( in @ sk__11 @ sk__10 )
    | ( in @ sk__11 @ sk__9 ) ),
    inference(demod,[status(thm)],[zip_derived_cl4,zip_derived_cl3]) ).

thf(zip_derived_cl17_003,plain,
    in @ sk__11 @ sk__10,
    inference(clc,[status(thm)],[zip_derived_cl15,zip_derived_cl7]) ).

thf(zip_derived_cl18,plain,
    in @ sk__11 @ sk__9,
    inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl17]) ).

thf(zip_derived_cl56,plain,
    ( ( (~) @ $true )
    | ( (~) @ $true ) ),
    inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl17,zip_derived_cl18]) ).

thf(zip_derived_cl57,plain,
    $false,
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl56]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU611^2 : 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.Ac5F14zQrD true
% 0.14/0.34  % Computer : n001.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Wed Aug 23 16:02:54 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
% 0.14/0.35  % Running in HO mode
% 0.21/0.64  % Total configuration time : 828
% 0.21/0.64  % Estimated wc time : 1656
% 0.21/0.64  % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.70  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.71  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.74  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.76  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.76  % Solved by lams/40_c.s.sh.
% 0.21/0.76  % done 10 iterations in 0.028s
% 0.21/0.76  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.21/0.76  % SZS output start Refutation
% See solution above
% 0.21/0.76  
% 0.21/0.76  
% 0.21/0.76  % Terminating...
% 0.62/0.85  % Runner terminated.
% 0.62/0.86  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------