TSTP Solution File: SEU640^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU640^2 : 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.zkzw9rak7b true

% Computer : n022.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 19:15:16 EDT 2023

% Result   : Theorem 0.16s 0.74s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   21 (   9 unt;   7 typ;   0 def)
%            Number of atoms       :  114 (  30 equ;   0 cnn)
%            Maximal formula atoms :   24 (   8 avg)
%            Number of connectives :  354 (   3   ~;   0   |;  22   &; 234   @)
%                                         (   0 <=>;  71  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  25   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   7 usr;   5 con; 0-2 aty)
%                                         (  16  !!;   8  ??;   0 @@+;   0 @@-)
%            Number of variables   :   93 (  51   ^;  28   !;  14   ?;  93   :)

% Comments : 
%------------------------------------------------------------------------------
thf(singleton_type,type,
    singleton: $i > $o ).

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

thf(setadjoin_type,type,
    setadjoin: $i > $i > $i ).

thf(singletonprop_type,type,
    singletonprop: $o ).

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

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

thf(ex1_type,type,
    ex1: $i > ( $i > $o ) > $o ).

thf(ex1,axiom,
    ( ex1
    = ( ^ [A: $i,Xphi: $i > $o] :
          ( singleton
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).

thf(singleton,axiom,
    ( singleton
    = ( ^ [A: $i] :
        ? [Xx: $i] :
          ( ( A
            = ( setadjoin @ Xx @ emptyset ) )
          & ( in @ Xx @ A ) ) ) ) ).

thf('0',plain,
    ( singleton
    = ( ^ [A: $i] :
        ? [Xx: $i] :
          ( ( A
            = ( setadjoin @ Xx @ emptyset ) )
          & ( in @ Xx @ A ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[singleton]) ).

thf('1',plain,
    ( singleton
    = ( ^ [V_1: $i] :
        ? [X4: $i] :
          ( ( V_1
            = ( setadjoin @ X4 @ emptyset ) )
          & ( in @ X4 @ V_1 ) ) ) ),
    define([status(thm)]) ).

thf('2',plain,
    ( ex1
    = ( ^ [A: $i,Xphi: $i > $o] :
          ( singleton
          @ ( dsetconstr @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[ex1,'1']) ).

thf('3',plain,
    ( ex1
    = ( ^ [V_1: $i,V_2: $i > $o] :
          ( singleton
          @ ( dsetconstr @ V_1
            @ ^ [V_3: $i] : ( V_2 @ V_3 ) ) ) ) ),
    define([status(thm)]) ).

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

thf('4',plain,
    ( singletonprop
    = ( ! [X4: $i,X6: $i > $o] :
          ( ! [X8: $i] :
              ( ( in @ X8 @ X4 )
             => ! [X10: $i] :
                  ( ( in @ X10 @ X4 )
                 => ( ( X6 @ X8 )
                   => ( ( X6 @ X10 )
                     => ( X8 = X10 ) ) ) ) )
         => ( ? [X12: $i] :
                ( ( X6 @ X12 )
                & ( in @ X12 @ X4 ) )
           => ( singleton
              @ ( dsetconstr @ X4
                @ ^ [V_1: $i] : ( X6 @ V_1 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(ex1I2,conjecture,
    ( singletonprop
   => ! [A: $i,Xphi: $i > $o] :
        ( ! [Xx: $i] :
            ( ( in @ Xx @ A )
           => ! [Xy: $i] :
                ( ( in @ Xy @ A )
               => ( ( Xphi @ Xx )
                 => ( ( Xphi @ Xy )
                   => ( Xx = Xy ) ) ) ) )
       => ( ? [Xx: $i] :
              ( ( Xphi @ Xx )
              & ( in @ Xx @ A ) )
         => ( ex1 @ A
            @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i,X6: $i > $o] :
        ( ! [X8: $i] :
            ( ( in @ X8 @ X4 )
           => ! [X10: $i] :
                ( ( in @ X10 @ X4 )
               => ( ( X6 @ X8 )
                 => ( ( X6 @ X10 )
                   => ( X8 = X10 ) ) ) ) )
       => ( ? [X12: $i] :
              ( ( in @ X12 @ X4 )
              & ( X6 @ X12 ) )
         => ? [X14: $i] :
              ( ( in @ X14
                @ ( dsetconstr @ X4
                  @ ^ [V_2: $i] : ( X6 @ V_2 ) ) )
              & ( ( dsetconstr @ X4
                  @ ^ [V_1: $i] : ( X6 @ V_1 ) )
                = ( setadjoin @ X14 @ emptyset ) ) ) ) )
   => ! [X16: $i,X18: $i > $o] :
        ( ! [X20: $i] :
            ( ( in @ X20 @ X16 )
           => ! [X22: $i] :
                ( ( in @ X22 @ X16 )
               => ( ( X18 @ X20 )
                 => ( ( X18 @ X22 )
                   => ( X20 = X22 ) ) ) ) )
       => ( ? [X24: $i] :
              ( ( in @ X24 @ X16 )
              & ( X18 @ X24 ) )
         => ? [X26: $i] :
              ( ( in @ X26
                @ ( dsetconstr @ X16
                  @ ^ [V_4: $i] : ( X18 @ V_4 ) ) )
              & ( ( dsetconstr @ X16
                  @ ^ [V_3: $i] : ( X18 @ V_3 ) )
                = ( setadjoin @ X26 @ emptyset ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i,X6: $i > $o] :
          ( ! [X8: $i] :
              ( ( in @ X8 @ X4 )
             => ! [X10: $i] :
                  ( ( in @ X10 @ X4 )
                 => ( ( X6 @ X8 )
                   => ( ( X6 @ X10 )
                     => ( X8 = X10 ) ) ) ) )
         => ( ? [X12: $i] :
                ( ( in @ X12 @ X4 )
                & ( X6 @ X12 ) )
           => ? [X14: $i] :
                ( ( in @ X14
                  @ ( dsetconstr @ X4
                    @ ^ [V_2: $i] : ( X6 @ V_2 ) ) )
                & ( ( dsetconstr @ X4
                    @ ^ [V_1: $i] : ( X6 @ V_1 ) )
                  = ( setadjoin @ X14 @ emptyset ) ) ) ) )
     => ! [X16: $i,X18: $i > $o] :
          ( ! [X20: $i] :
              ( ( in @ X20 @ X16 )
             => ! [X22: $i] :
                  ( ( in @ X22 @ X16 )
                 => ( ( X18 @ X20 )
                   => ( ( X18 @ X22 )
                     => ( X20 = X22 ) ) ) ) )
         => ( ? [X24: $i] :
                ( ( in @ X24 @ X16 )
                & ( X18 @ X24 ) )
           => ? [X26: $i] :
                ( ( in @ X26
                  @ ( dsetconstr @ X16
                    @ ^ [V_4: $i] : ( X18 @ V_4 ) ) )
                & ( ( dsetconstr @ X16
                    @ ^ [V_3: $i] : ( X18 @ V_3 ) )
                  = ( setadjoin @ X26 @ emptyset ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

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

thf(zip_derived_cl3,plain,
    ~ ( ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ Y0 )
                     => ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ Y0 )
                           => ( ( Y1 @ Y2 )
                             => ( ( Y1 @ Y3 )
                               => ( Y2 = Y3 ) ) ) ) ) ) )
               => ( ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ Y0 )
                        & ( Y1 @ Y2 ) ) )
                 => ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
                        & ( ( dsetconstr @ Y0 @ Y1 )
                          = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) ) ) )
     => ( !!
        @ ^ [Y0: $i] :
            ( !!
            @ ^ [Y1: $i > $o] :
                ( ( !!
                  @ ^ [Y2: $i] :
                      ( ( in @ Y2 @ Y0 )
                     => ( !!
                        @ ^ [Y3: $i] :
                            ( ( in @ Y3 @ Y0 )
                           => ( ( Y1 @ Y2 )
                             => ( ( Y1 @ Y3 )
                               => ( Y2 = Y3 ) ) ) ) ) ) )
               => ( ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ Y0 )
                        & ( Y1 @ Y2 ) ) )
                 => ( ??
                    @ ^ [Y2: $i] :
                        ( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
                        & ( ( dsetconstr @ Y0 @ Y1 )
                          = ( setadjoin @ Y2 @ emptyset ) ) ) ) ) ) ) ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl4,plain,
    $false,
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl3]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SEU640^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.11  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.zkzw9rak7b true
% 0.10/0.31  % Computer : n022.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Wed Aug 23 18:20:11 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.10/0.31  % Running portfolio for 300 s
% 0.10/0.31  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.31  % Number of cores: 8
% 0.10/0.31  % Python version: Python 3.6.8
% 0.10/0.32  % Running in HO mode
% 0.16/0.60  % Total configuration time : 828
% 0.16/0.60  % Estimated wc time : 1656
% 0.16/0.60  % Estimated cpu time (8 cpus) : 207.0
% 0.16/0.69  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.16/0.69  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.16/0.69  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.16/0.69  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.16/0.69  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.16/0.70  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.16/0.70  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.16/0.70  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.16/0.74  % Solved by lams/15_e_short1.sh.
% 0.16/0.74  % done 0 iterations in 0.011s
% 0.16/0.74  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.16/0.74  % SZS output start Refutation
% See solution above
% 0.16/0.74  
% 0.16/0.74  
% 0.16/0.75  % Terminating...
% 1.84/0.84  % Runner terminated.
% 1.84/0.86  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------