TSTP Solution File: NUM668^4 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM668^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.IcberyJZIn true

% Computer : n025.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 12:43:16 EDT 2023

% Result   : Theorem 2.28s 1.00s
% Output   : Refutation 2.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   40
% Syntax   : Number of formulae    :   56 (  36 unt;  16 typ;   0 def)
%            Number of atoms       :  126 (  40 equ;   0 cnn)
%            Maximal formula atoms :    5 (   3 avg)
%            Number of connectives :  137 (   8   ~;   1   |;   0   &; 116   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   48 (  48   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  16 usr;   4 con; 0-3 aty)
%            Number of variables   :   77 (  67   ^;  10   !;   0   ?;  77   :)

% Comments : 
%------------------------------------------------------------------------------
thf(d_29_ii_type,type,
    d_29_ii: $i > $i > $o ).

thf(nat_type,type,
    nat: $i ).

thf(sk__75_type,type,
    sk__75: $i ).

thf(is_of_type,type,
    is_of: $i > ( $i > $o ) > $o ).

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

thf(non_type,type,
    non: $i > ( $i > $o ) > $i > $o ).

thf(l_some_type,type,
    l_some: $i > ( $i > $o ) > $o ).

thf(n_is_type,type,
    n_is: $i > $i > $o ).

thf(imp_type,type,
    imp: $o > $o > $o ).

thf(all_of_type,type,
    all_of: ( $i > $o ) > ( $i > $o ) > $o ).

thf(diffprop_type,type,
    diffprop: $i > $i > $i > $o ).

thf(n_some_type,type,
    n_some: ( $i > $o ) > $o ).

thf(sk__76_type,type,
    sk__76: $i ).

thf(d_not_type,type,
    d_not: $o > $o ).

thf(e_is_type,type,
    e_is: $i > $i > $i > $o ).

thf(n_pl_type,type,
    n_pl: $i > $i > $i ).

thf(def_d_29_ii,axiom,
    ( d_29_ii
    = ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ) ).

thf(def_diffprop,axiom,
    ( diffprop
    = ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ).

thf(def_n_is,axiom,
    ( n_is
    = ( e_is @ nat ) ) ).

thf(def_e_is,axiom,
    ( e_is
    = ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ) ).

thf('0',plain,
    ( e_is
    = ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_e_is]) ).

thf('1',plain,
    ( e_is
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( V_2 = V_3 ) ) ),
    define([status(thm)]) ).

thf('2',plain,
    ( n_is
    = ( e_is @ nat ) ),
    inference(simplify_rw_rule,[status(thm)],[def_n_is,'1']) ).

thf('3',plain,
    ( n_is
    = ( e_is @ nat ) ),
    define([status(thm)]) ).

thf('4',plain,
    ( diffprop
    = ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_diffprop,'3','1']) ).

thf('5',plain,
    ( diffprop
    = ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( n_is @ V_1 @ ( n_pl @ V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(def_n_some,axiom,
    ( n_some
    = ( l_some @ nat ) ) ).

thf(def_l_some,axiom,
    ( l_some
    = ( ^ [X0: $i,X1: $i > $o] :
          ( d_not
          @ ( all_of
            @ ^ [X2: $i] : ( in @ X2 @ X0 )
            @ ( non @ X0 @ X1 ) ) ) ) ) ).

thf(def_non,axiom,
    ( non
    = ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ) ).

thf(def_d_not,axiom,
    ( d_not
    = ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ) ).

thf(def_imp,axiom,
    ( imp
    = ( ^ [X0: $o,X1: $o] :
          ( X0
         => X1 ) ) ) ).

thf('6',plain,
    ( imp
    = ( ^ [X0: $o,X1: $o] :
          ( X0
         => X1 ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_imp]) ).

thf('7',plain,
    ( imp
    = ( ^ [V_1: $o,V_2: $o] :
          ( V_1
         => V_2 ) ) ),
    define([status(thm)]) ).

thf('8',plain,
    ( d_not
    = ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_d_not,'7']) ).

thf('9',plain,
    ( d_not
    = ( ^ [V_1: $o] : ( imp @ V_1 @ $false ) ) ),
    define([status(thm)]) ).

thf('10',plain,
    ( non
    = ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_non,'9','7']) ).

thf('11',plain,
    ( non
    = ( ^ [V_1: $i,V_2: $i > $o,V_3: $i] : ( d_not @ ( V_2 @ V_3 ) ) ) ),
    define([status(thm)]) ).

thf(def_all_of,axiom,
    ( all_of
    = ( ^ [X0: $i > $o,X1: $i > $o] :
        ! [X2: $i] :
          ( ( is_of @ X2 @ X0 )
         => ( X1 @ X2 ) ) ) ) ).

thf(def_is_of,axiom,
    ( is_of
    = ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ) ).

thf('12',plain,
    ( is_of
    = ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_is_of]) ).

thf('13',plain,
    ( is_of
    = ( ^ [V_1: $i,V_2: $i > $o] : ( V_2 @ V_1 ) ) ),
    define([status(thm)]) ).

thf('14',plain,
    ( all_of
    = ( ^ [X0: $i > $o,X1: $i > $o] :
        ! [X2: $i] :
          ( ( is_of @ X2 @ X0 )
         => ( X1 @ X2 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_all_of,'13']) ).

thf('15',plain,
    ( all_of
    = ( ^ [V_1: $i > $o,V_2: $i > $o] :
        ! [X4: $i] :
          ( ( is_of @ X4 @ V_1 )
         => ( V_2 @ X4 ) ) ) ),
    define([status(thm)]) ).

thf('16',plain,
    ( l_some
    = ( ^ [X0: $i,X1: $i > $o] :
          ( d_not
          @ ( all_of
            @ ^ [X2: $i] : ( in @ X2 @ X0 )
            @ ( non @ X0 @ X1 ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_l_some,'11','9','7','15','13']) ).

thf('17',plain,
    ( l_some
    = ( ^ [V_1: $i,V_2: $i > $o] :
          ( d_not
          @ ( all_of
            @ ^ [V_3: $i] : ( in @ V_3 @ V_1 )
            @ ( non @ V_1 @ V_2 ) ) ) ) ),
    define([status(thm)]) ).

thf('18',plain,
    ( n_some
    = ( l_some @ nat ) ),
    inference(simplify_rw_rule,[status(thm)],[def_n_some,'17','11','9','7','15','13']) ).

thf('19',plain,
    ( n_some
    = ( l_some @ nat ) ),
    define([status(thm)]) ).

thf('20',plain,
    ( d_29_ii
    = ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_d_29_ii,'5','19','3','1','17','11','9','7','15','13']) ).

thf('21',plain,
    ( d_29_ii
    = ( ^ [V_1: $i,V_2: $i] : ( n_some @ ( diffprop @ V_1 @ V_2 ) ) ) ),
    define([status(thm)]) ).

thf(satz18,conjecture,
    ( all_of
    @ ^ [X0: $i] : ( in @ X0 @ nat )
    @ ^ [X0: $i] :
        ( all_of
        @ ^ [X1: $i] : ( in @ X1 @ nat )
        @ ^ [X1: $i] : ( d_29_ii @ ( n_pl @ X0 @ X1 ) @ X0 ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i] :
      ( ( in @ X4 @ nat )
     => ! [X6: $i] :
          ( ( in @ X6 @ nat )
         => ~ ! [X8: $i] :
                ( ( in @ X8 @ nat )
               => ( ( n_pl @ X4 @ X6 )
                 != ( n_pl @ X4 @ X8 ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i] :
        ( ( in @ X4 @ nat )
       => ! [X6: $i] :
            ( ( in @ X6 @ nat )
           => ~ ! [X8: $i] :
                  ( ( in @ X8 @ nat )
                 => ( ( n_pl @ X4 @ X6 )
                   != ( n_pl @ X4 @ X8 ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl317,plain,
    in @ sk__76 @ nat,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl316,plain,
    ! [X0: $i] :
      ( ( ( n_pl @ sk__75 @ sk__76 )
       != ( n_pl @ sk__75 @ X0 ) )
      | ~ ( in @ X0 @ nat ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl340,plain,
    ( ( n_pl @ sk__75 @ sk__76 )
   != ( n_pl @ sk__75 @ sk__76 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl317,zip_derived_cl316]) ).

thf(zip_derived_cl344,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl340]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM668^4 : TPTP v8.1.2. Released v7.1.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.IcberyJZIn true
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Aug 25 17:10:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % 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
% 0.21/0.71  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.73  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.75  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.76  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 2.28/1.00  % Solved by lams/40_noforms.sh.
% 2.28/1.00  % done 17 iterations in 0.170s
% 2.28/1.00  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 2.28/1.00  % SZS output start Refutation
% See solution above
% 2.28/1.00  
% 2.28/1.00  
% 2.28/1.00  % Terminating...
% 2.78/1.06  % Runner terminated.
% 2.78/1.07  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------