TSTP Solution File: NUM684^4 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM684^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.X6VKFK5VWv true

% Computer : n031.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 12:43:25 EDT 2023

% Result   : Theorem 20.34s 4.46s
% Output   : Refutation 20.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   40 (  13 unt;  15 typ;   0 def)
%            Number of atoms       :  120 (  44 equ;   0 cnn)
%            Maximal formula atoms :   13 (   4 avg)
%            Number of connectives :  322 (  41   ~;   7   |;   0   &; 257   @)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   28 (  28   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;   7 con; 0-3 aty)
%            Number of variables   :   86 (  71   ^;  15   !;   0   ?;  86   :)

% Comments : 
%------------------------------------------------------------------------------
thf(nat_type,type,
    nat: $i ).

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

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

thf(d_Sep_type,type,
    d_Sep: $i > ( $i > $o ) > $i ).

thf(ap_type,type,
    ap: $i > $i > $i ).

thf(sk__3_type,type,
    sk__3: $i ).

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

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

thf(omega_type,type,
    omega: $i ).

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

thf(sk__4_type,type,
    sk__4: $i ).

thf(plus_type,type,
    plus: $i > $i ).

thf(sk__2_type,type,
    sk__2: $i ).

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

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

thf(def_n_pl,axiom,
    ( n_pl
    = ( ^ [X0: $i] : ( ap @ ( plus @ X0 ) ) ) ) ).

thf('0',plain,
    ( n_pl
    = ( ^ [X0: $i] : ( ap @ ( plus @ X0 ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_n_pl]) ).

thf('1',plain,
    ( n_pl
    = ( ^ [V_1: $i] : ( ap @ ( plus @ V_1 ) ) ) ),
    define([status(thm)]) ).

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

thf(def_nat,axiom,
    ( nat
    = ( d_Sep @ omega
      @ ^ [X0: $i] : ( X0 != emptyset ) ) ) ).

thf('2',plain,
    ( nat
    = ( d_Sep @ omega
      @ ^ [X0: $i] : ( X0 != emptyset ) ) ),
    inference(simplify_rw_rule,[status(thm)],[def_nat]) ).

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

thf('4',plain,
    ( n_is
    = ( e_is @ nat ) ),
    inference(simplify_rw_rule,[status(thm)],[def_n_is,'3']) ).

thf('5',plain,
    ( n_is
    = ( e_is @ nat ) ),
    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('6',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]) ).

thf('7',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(satz20e,conjecture,
    ( all_of
    @ ^ [X0: $i] : ( in @ X0 @ nat )
    @ ^ [X0: $i] :
        ( all_of
        @ ^ [X1: $i] : ( in @ X1 @ nat )
        @ ^ [X1: $i] :
            ( all_of
            @ ^ [X2: $i] : ( in @ X2 @ nat )
            @ ^ [X2: $i] :
                ( ( n_is @ ( n_pl @ X2 @ X0 ) @ ( n_pl @ X2 @ X1 ) )
               => ( n_is @ X0 @ X1 ) ) ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [X4: $i] :
      ( ( is_of @ X4
        @ ^ [V_1: $i] :
            ( in @ V_1
            @ ( d_Sep @ omega
              @ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
     => ! [X6: $i] :
          ( ( is_of @ X6
            @ ^ [V_3: $i] :
                ( in @ V_3
                @ ( d_Sep @ omega
                  @ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
         => ! [X8: $i] :
              ( ( is_of @ X8
                @ ^ [V_5: $i] :
                    ( in @ V_5
                    @ ( d_Sep @ omega
                      @ ^ [V_6: $i] : ( V_6 != emptyset ) ) ) )
             => ( ( e_is
                  @ ( d_Sep @ omega
                    @ ^ [V_7: $i] : ( V_7 != emptyset ) )
                  @ ( ap @ ( plus @ X8 ) @ X4 )
                  @ ( ap @ ( plus @ X8 ) @ X6 ) )
               => ( e_is
                  @ ( d_Sep @ omega
                    @ ^ [V_8: $i] : ( V_8 != emptyset ) )
                  @ X4
                  @ X6 ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [X4: $i] :
        ( ( is_of @ X4
          @ ^ [V_1: $i] :
              ( in @ V_1
              @ ( d_Sep @ omega
                @ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
       => ! [X6: $i] :
            ( ( is_of @ X6
              @ ^ [V_3: $i] :
                  ( in @ V_3
                  @ ( d_Sep @ omega
                    @ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
           => ! [X8: $i] :
                ( ( is_of @ X8
                  @ ^ [V_5: $i] :
                      ( in @ V_5
                      @ ( d_Sep @ omega
                        @ ^ [V_6: $i] : ( V_6 != emptyset ) ) ) )
               => ( ( e_is
                    @ ( d_Sep @ omega
                      @ ^ [V_7: $i] : ( V_7 != emptyset ) )
                    @ ( ap @ ( plus @ X8 ) @ X4 )
                    @ ( ap @ ( plus @ X8 ) @ X6 ) )
                 => ( e_is
                    @ ( d_Sep @ omega
                      @ ^ [V_8: $i] : ( V_8 != emptyset ) )
                    @ X4
                    @ X6 ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl53,plain,
    ( e_is
    @ ( d_Sep @ omega
      @ ^ [Y0: $i] : ( Y0 != emptyset ) )
    @ ( ap @ ( plus @ sk__4 ) @ sk__2 )
    @ ( ap @ ( plus @ sk__4 ) @ sk__3 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(satz8a,axiom,
    ( all_of
    @ ^ [X0: $i] : ( in @ X0 @ nat )
    @ ^ [X0: $i] :
        ( all_of
        @ ^ [X1: $i] : ( in @ X1 @ nat )
        @ ^ [X1: $i] :
            ( all_of
            @ ^ [X2: $i] : ( in @ X2 @ nat )
            @ ^ [X2: $i] :
                ( ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X0 @ X2 ) )
               => ( n_is @ X1 @ X2 ) ) ) ) ) ).

thf(zf_stmt_2,axiom,
    ! [X4: $i] :
      ( ( is_of @ X4
        @ ^ [V_1: $i] :
            ( in @ V_1
            @ ( d_Sep @ omega
              @ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
     => ! [X6: $i] :
          ( ( is_of @ X6
            @ ^ [V_3: $i] :
                ( in @ V_3
                @ ( d_Sep @ omega
                  @ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
         => ! [X8: $i] :
              ( ( is_of @ X8
                @ ^ [V_5: $i] :
                    ( in @ V_5
                    @ ( d_Sep @ omega
                      @ ^ [V_6: $i] : ( V_6 != emptyset ) ) ) )
             => ( ( e_is
                  @ ( d_Sep @ omega
                    @ ^ [V_7: $i] : ( V_7 != emptyset ) )
                  @ ( ap @ ( plus @ X4 ) @ X6 )
                  @ ( ap @ ( plus @ X4 ) @ X8 ) )
               => ( e_is
                  @ ( d_Sep @ omega
                    @ ^ [V_8: $i] : ( V_8 != emptyset ) )
                  @ X6
                  @ X8 ) ) ) ) ) ).

thf(zip_derived_cl10,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ~ ( is_of @ X0
          @ ^ [Y0: $i] :
              ( in @ Y0
              @ ( d_Sep @ omega
                @ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
      | ~ ( e_is
          @ ( d_Sep @ omega
            @ ^ [Y0: $i] : ( Y0 != emptyset ) )
          @ ( ap @ ( plus @ X1 ) @ X0 )
          @ ( ap @ ( plus @ X1 ) @ X2 ) )
      | ( e_is
        @ ( d_Sep @ omega
          @ ^ [Y0: $i] : ( Y0 != emptyset ) )
        @ X0
        @ X2 )
      | ~ ( is_of @ X2
          @ ^ [Y0: $i] :
              ( in @ Y0
              @ ( d_Sep @ omega
                @ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
      | ~ ( is_of @ X1
          @ ^ [Y0: $i] :
              ( in @ Y0
              @ ( d_Sep @ omega
                @ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_2]) ).

thf(zip_derived_cl1368,plain,
    ( ~ ( is_of @ sk__4
        @ ^ [Y0: $i] :
            ( in @ Y0
            @ ( d_Sep @ omega
              @ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
    | ~ ( is_of @ sk__3
        @ ^ [Y0: $i] :
            ( in @ Y0
            @ ( d_Sep @ omega
              @ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
    | ( e_is
      @ ( d_Sep @ omega
        @ ^ [Y0: $i] : ( Y0 != emptyset ) )
      @ sk__2
      @ sk__3 )
    | ~ ( is_of @ sk__2
        @ ^ [Y0: $i] :
            ( in @ Y0
            @ ( d_Sep @ omega
              @ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl53,zip_derived_cl10]) ).

thf(zip_derived_cl52,plain,
    ( is_of @ sk__4
    @ ^ [Y0: $i] :
        ( in @ Y0
        @ ( d_Sep @ omega
          @ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl55,plain,
    ( is_of @ sk__3
    @ ^ [Y0: $i] :
        ( in @ Y0
        @ ( d_Sep @ omega
          @ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl54,plain,
    ~ ( e_is
      @ ( d_Sep @ omega
        @ ^ [Y0: $i] : ( Y0 != emptyset ) )
      @ sk__2
      @ sk__3 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl51,plain,
    ( is_of @ sk__2
    @ ^ [Y0: $i] :
        ( in @ Y0
        @ ( d_Sep @ omega
          @ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1377,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl1368,zip_derived_cl52,zip_derived_cl55,zip_derived_cl54,zip_derived_cl51]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM684^4 : TPTP v8.1.2. Released v7.1.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.X6VKFK5VWv true
% 0.11/0.32  % Computer : n031.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Fri Aug 25 13:39:52 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.11/0.32  % Running portfolio for 300 s
% 0.16/0.32  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.32  % Number of cores: 8
% 0.16/0.33  % Python version: Python 3.6.8
% 0.16/0.33  % Running in HO mode
% 0.16/0.61  % Total configuration time : 828
% 0.16/0.61  % Estimated wc time : 1656
% 0.16/0.61  % Estimated cpu time (8 cpus) : 207.0
% 0.16/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.16/0.71  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.16/0.71  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.16/0.71  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.16/0.75  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.85/0.88  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.85/0.91  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.85/0.92  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 20.34/4.46  % Solved by lams/40_c.s.sh.
% 20.34/4.46  % done 138 iterations in 3.696s
% 20.34/4.46  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 20.34/4.46  % SZS output start Refutation
% See solution above
% 20.34/4.46  
% 20.34/4.46  
% 20.34/4.46  % Terminating...
% 20.66/4.63  % Runner terminated.
% 20.66/4.63  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------