TSTP Solution File: SEU620^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU620^2 : 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.lDYbgnSyda 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 19:14:47 EDT 2023

% Result   : Theorem 0.23s 0.84s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   20 (   9 unt;   7 typ;   0 def)
%            Number of atoms       :   53 (  17 equ;   0 cnn)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  419 (   2   ~;   0   |;  18   &; 387   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   7 usr;   5 con; 0-2 aty)
%                                         (   4  !!;   4  ??;   0 @@+;   0 @@-)
%            Number of variables   :   45 (  17   ^;  14   !;  14   ?;  45   :)

% Comments : 
%------------------------------------------------------------------------------
thf(iskpair_type,type,
    iskpair: $i > $o ).

thf(kpair_type,type,
    kpair: $i > $i > $i ).

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

thf(kpairiskpair_type,type,
    kpairiskpair: $o ).

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

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

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

thf(kpair,axiom,
    ( kpair
    = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).

thf('0',plain,
    ( kpair
    = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[kpair]) ).

thf('1',plain,
    ( kpair
    = ( ^ [V_1: $i,V_2: $i] : ( setadjoin @ ( setadjoin @ V_1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ V_1 @ ( setadjoin @ V_2 @ emptyset ) ) @ emptyset ) ) ) ),
    define([status(thm)]) ).

thf(kpairiskpair,axiom,
    ( kpairiskpair
    = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).

thf('2',plain,
    ( kpairiskpair
    = ( ! [X4: $i,X6: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) ),
    define([status(thm)]) ).

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

thf('3',plain,
    ( iskpair
    = ( ^ [A: $i] :
        ? [Xx: $i] :
          ( ? [Xy: $i] :
              ( ( A
                = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
              & ( in @ Xy @ ( setunion @ A ) ) )
          & ( in @ Xx @ ( setunion @ A ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[iskpair]) ).

thf('4',plain,
    ( iskpair
    = ( ^ [V_1: $i] :
        ? [X4: $i] :
          ( ? [X6: $i] :
              ( ( V_1
                = ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) )
              & ( in @ X6 @ ( setunion @ V_1 ) ) )
          & ( in @ X4 @ ( setunion @ V_1 ) ) ) ) ),
    define([status(thm)]) ).

thf(kpairp,conjecture,
    ( kpairiskpair
   => ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ).

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

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

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

thf(zip_derived_cl1,plain,
    $false,
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl0]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU620^2 : 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.lDYbgnSyda true
% 0.13/0.37  % Computer : n022.cluster.edu
% 0.13/0.37  % Model    : x86_64 x86_64
% 0.13/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37  % Memory   : 8042.1875MB
% 0.13/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37  % CPULimit : 300
% 0.13/0.37  % WCLimit  : 300
% 0.13/0.37  % DateTime : Wed Aug 23 21:26:56 EDT 2023
% 0.13/0.37  % CPUTime  : 
% 0.13/0.37  % Running portfolio for 300 s
% 0.13/0.37  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37  % Number of cores: 8
% 0.13/0.37  % Python version: Python 3.6.8
% 0.13/0.38  % Running in HO mode
% 0.23/0.66  % Total configuration time : 828
% 0.23/0.66  % Estimated wc time : 1656
% 0.23/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.23/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.23/0.80  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.23/0.80  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.23/0.84  % Solved by lams/20_acsne_simpl.sh.
% 0.23/0.84  % done 0 iterations in 0.010s
% 0.23/0.84  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.23/0.84  % SZS output start Refutation
% See solution above
% 0.23/0.84  
% 0.23/0.84  
% 0.23/0.84  % Terminating...
% 0.23/0.87  % Runner terminated.
% 1.54/0.89  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------