TSTP Solution File: SEU805^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU805^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZQigE8K5K6 true

% Computer : n017.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 19:18:02 EDT 2023

% Result   : Theorem 0.22s 0.79s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   39 (  14 unt;  11 typ;   0 def)
%            Number of atoms       :   97 (  35 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  221 (  29   ~;  12   |;  15   &; 141   @)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   63 (   3   ^;  37   !;  23   ?;  63   :)

% Comments : 
%------------------------------------------------------------------------------
thf(disjointsetsI1_type,type,
    disjointsetsI1: $o ).

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

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

thf(foundationAx_type,type,
    foundationAx: $o ).

thf(nonemptyE1_type,type,
    nonemptyE1: $o ).

thf(sk__12_type,type,
    sk__12: $i > $i ).

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

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

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

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

thf(binintersect_type,type,
    binintersect: $i > $i > $i ).

thf(disjointsetsI1,axiom,
    ( disjointsetsI1
    = ( ! [A: $i,B: $i] :
          ( ~ ? [Xx: $i] :
                ( ( in @ Xx @ B )
                & ( in @ Xx @ A ) )
         => ( ( binintersect @ A @ B )
            = emptyset ) ) ) ) ).

thf('0',plain,
    ( disjointsetsI1
    = ( ! [X4: $i,X6: $i] :
          ( ~ ? [X8: $i] :
                ( ( in @ X8 @ X6 )
                & ( in @ X8 @ X4 ) )
         => ( ( binintersect @ X4 @ X6 )
            = emptyset ) ) ) ),
    define([status(thm)]) ).

thf(nonemptyE1,axiom,
    ( nonemptyE1
    = ( ! [A: $i] :
          ( ( nonempty @ A )
         => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).

thf('1',plain,
    ( nonemptyE1
    = ( ! [X4: $i] :
          ( ( nonempty @ X4 )
         => ? [X6: $i] : ( in @ X6 @ X4 ) ) ) ),
    define([status(thm)]) ).

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

thf('2',plain,
    ( nonempty
    = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
    inference(simplify_rw_rule,[status(thm)],[nonempty]) ).

thf('3',plain,
    ( nonempty
    = ( ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
    define([status(thm)]) ).

thf(foundationAx,axiom,
    ( foundationAx
    = ( ! [A: $i] :
          ( ? [Xx: $i] : ( in @ Xx @ A )
         => ? [B: $i] :
              ( ~ ? [Xx: $i] :
                    ( ( in @ Xx @ A )
                    & ( in @ Xx @ B ) )
              & ( in @ B @ A ) ) ) ) ) ).

thf('4',plain,
    ( foundationAx
    = ( ! [X4: $i] :
          ( ? [X6: $i] : ( in @ X6 @ X4 )
         => ? [X8: $i] :
              ( ~ ? [X10: $i] :
                    ( ( in @ X10 @ X4 )
                    & ( in @ X10 @ X8 ) )
              & ( in @ X8 @ X4 ) ) ) ) ),
    define([status(thm)]) ).

thf(foundation2,conjecture,
    ( foundationAx
   => ( nonemptyE1
     => ( disjointsetsI1
       => ! [A: $i] :
            ( ( nonempty @ A )
           => ? [X: $i] :
                ( ( ( binintersect @ X @ A )
                  = emptyset )
                & ( in @ X @ A ) ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: $i] :
        ( ? [X6: $i] : ( in @ X6 @ X4 )
       => ? [X8: $i] :
            ( ~ ? [X10: $i] :
                  ( ( in @ X10 @ X4 )
                  & ( in @ X10 @ X8 ) )
            & ( in @ X8 @ X4 ) ) )
   => ( ! [X12: $i] :
          ( ( X12 != emptyset )
         => ? [X14: $i] : ( in @ X14 @ X12 ) )
     => ( ! [X16: $i,X18: $i] :
            ( ~ ? [X20: $i] :
                  ( ( in @ X20 @ X18 )
                  & ( in @ X20 @ X16 ) )
           => ( ( binintersect @ X16 @ X18 )
              = emptyset ) )
       => ! [X22: $i] :
            ( ( X22 != emptyset )
           => ? [X24: $i] :
                ( ( ( binintersect @ X24 @ X22 )
                  = emptyset )
                & ( in @ X24 @ X22 ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: $i] :
          ( ? [X6: $i] : ( in @ X6 @ X4 )
         => ? [X8: $i] :
              ( ~ ? [X10: $i] :
                    ( ( in @ X10 @ X4 )
                    & ( in @ X10 @ X8 ) )
              & ( in @ X8 @ X4 ) ) )
     => ( ! [X12: $i] :
            ( ( X12 != emptyset )
           => ? [X14: $i] : ( in @ X14 @ X12 ) )
       => ( ! [X16: $i,X18: $i] :
              ( ~ ? [X20: $i] :
                    ( ( in @ X20 @ X18 )
                    & ( in @ X20 @ X16 ) )
             => ( ( binintersect @ X16 @ X18 )
                = emptyset ) )
         => ! [X22: $i] :
              ( ( X22 != emptyset )
             => ? [X24: $i] :
                  ( ( ( binintersect @ X24 @ X22 )
                    = emptyset )
                  & ( in @ X24 @ X22 ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl6,plain,
    ! [X6: $i] :
      ( ( in @ ( sk__9 @ X6 ) @ X6 )
      | ( X6 = emptyset ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ! [X1: $i,X2: $i] :
      ( ( in @ ( sk__12 @ X1 ) @ X1 )
      | ~ ( in @ X2 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl9,plain,
    ! [X0: $i] :
      ( ( X0 = emptyset )
      | ( in @ ( sk__12 @ X0 ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl1]) ).

thf(zip_derived_cl2,plain,
    ! [X3: $i,X4: $i] :
      ( ( ( binintersect @ X3 @ X4 )
        = emptyset )
      | ( in @ ( sk__11 @ X4 @ X3 ) @ X4 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl3,plain,
    ! [X3: $i,X4: $i] :
      ( ( ( binintersect @ X3 @ X4 )
        = emptyset )
      | ( in @ ( sk__11 @ X4 @ X3 ) @ X3 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl0,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( in @ X0 @ ( sk__12 @ X1 ) )
      | ~ ( in @ X0 @ X1 )
      | ~ ( in @ X2 @ X1 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl17,plain,
    ! [X0: $i,X1: $i] :
      ( ~ ( in @ X1 @ ( sk__12 @ X0 ) )
      | ~ ( in @ X1 @ X0 ) ),
    inference(condensation,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl19,plain,
    ! [X0: $i,X1: $i] :
      ( ( ( binintersect @ ( sk__12 @ X0 ) @ X1 )
        = emptyset )
      | ~ ( in @ ( sk__11 @ X1 @ ( sk__12 @ X0 ) ) @ X0 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl17]) ).

thf(zip_derived_cl47,plain,
    ! [X0: $i] :
      ( ( ( binintersect @ ( sk__12 @ X0 ) @ X0 )
        = emptyset )
      | ( ( binintersect @ ( sk__12 @ X0 ) @ X0 )
        = emptyset ) ),
    inference('sup-',[status(thm)],[zip_derived_cl2,zip_derived_cl19]) ).

thf(zip_derived_cl50,plain,
    ! [X0: $i] :
      ( ( binintersect @ ( sk__12 @ X0 ) @ X0 )
      = emptyset ),
    inference(simplify,[status(thm)],[zip_derived_cl47]) ).

thf(zip_derived_cl4,plain,
    ! [X5: $i] :
      ( ( ( binintersect @ X5 @ sk__10 )
       != emptyset )
      | ~ ( in @ X5 @ sk__10 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl54,plain,
    ( ( emptyset != emptyset )
    | ~ ( in @ ( sk__12 @ sk__10 ) @ sk__10 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl4]) ).

thf(zip_derived_cl56,plain,
    ~ ( in @ ( sk__12 @ sk__10 ) @ sk__10 ),
    inference(simplify,[status(thm)],[zip_derived_cl54]) ).

thf(zip_derived_cl59,plain,
    sk__10 = emptyset,
    inference('sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl56]) ).

thf(zip_derived_cl5,plain,
    sk__10 != emptyset,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl66,plain,
    $false,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl59,zip_derived_cl5]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU805^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ZQigE8K5K6 true
% 0.14/0.35  % Computer : n017.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 : Thu Aug 24 00:59:39 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36  % Number of cores: 8
% 0.14/0.36  % Python version: Python 3.6.8
% 0.14/0.36  % Running in HO mode
% 0.22/0.62  % Total configuration time : 828
% 0.22/0.62  % Estimated wc time : 1656
% 0.22/0.62  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.72  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.73  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.75  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.75  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.75  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.75  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.76  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.79  % Solved by lams/40_c.s.sh.
% 0.22/0.79  % done 32 iterations in 0.022s
% 0.22/0.79  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.22/0.79  % SZS output start Refutation
% See solution above
% 0.22/0.79  
% 0.22/0.79  
% 0.22/0.79  % Terminating...
% 0.22/0.84  % Runner terminated.
% 0.22/0.85  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------