TSTP Solution File: NUM637^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM637^1 : 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.7iCKayuWGk true

% Computer : n016.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 12:42:57 EDT 2023

% Result   : Theorem 1.59s 1.54s
% Output   : Refutation 1.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   44 (  16 unt;   8 typ;   0 def)
%            Number of atoms       :   87 (  24 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  283 (  41   ~;  25   |;   0   &; 178   @)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   6 usr;   4 con; 0-2 aty)
%                                         (  18  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   63 (  22   ^;  41   !;   0   ?;  63   :)

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

thf(set_type,type,
    set: $tType ).

thf(n_1_type,type,
    n_1: nat ).

thf(setof_type,type,
    setof: ( nat > $o ) > set ).

thf(esti_type,type,
    esti: nat > set > $o ).

thf(suc_type,type,
    suc: nat > nat ).

thf(x_type,type,
    x: nat ).

thf('#sk9_type',type,
    '#sk9': set > nat ).

thf(ax5,axiom,
    ! [Xs: set] :
      ( ( esti @ n_1 @ Xs )
     => ( ! [Xx: nat] :
            ( ( esti @ Xx @ Xs )
           => ( esti @ ( suc @ Xx ) @ Xs ) )
       => ! [Xx: nat] : ( esti @ Xx @ Xs ) ) ) ).

thf(zip_derived_cl2,plain,
    ( !!
    @ ^ [Y0: set] :
        ( ( esti @ n_1 @ Y0 )
       => ( ( !!
            @ ^ [Y1: nat] :
                ( ( esti @ Y1 @ Y0 )
               => ( esti @ ( suc @ Y1 ) @ Y0 ) ) )
         => ( !!
            @ ^ [Y1: nat] : ( esti @ Y1 @ Y0 ) ) ) ) ),
    inference(cnf,[status(esa)],[ax5]) ).

thf(zip_derived_cl15,plain,
    ! [X2: set] :
      ( ( esti @ n_1 @ X2 )
     => ( ( !!
          @ ^ [Y0: nat] :
              ( ( esti @ Y0 @ X2 )
             => ( esti @ ( suc @ Y0 ) @ X2 ) ) )
       => ( !!
          @ ^ [Y0: nat] : ( esti @ Y0 @ X2 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).

thf(zip_derived_cl16,plain,
    ! [X2: set] :
      ( ~ ( esti @ n_1 @ X2 )
      | ( ( !!
          @ ^ [Y0: nat] :
              ( ( esti @ Y0 @ X2 )
             => ( esti @ ( suc @ Y0 ) @ X2 ) ) )
       => ( !!
          @ ^ [Y0: nat] : ( esti @ Y0 @ X2 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl17,plain,
    ! [X2: set] :
      ( ~ ( !!
          @ ^ [Y0: nat] :
              ( ( esti @ Y0 @ X2 )
             => ( esti @ ( suc @ Y0 ) @ X2 ) ) )
      | ( !!
        @ ^ [Y0: nat] : ( esti @ Y0 @ X2 ) )
      | ~ ( esti @ n_1 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).

thf(zip_derived_cl18,plain,
    ! [X2: set] :
      ( ~ ( ( esti @ ( '#sk9' @ X2 ) @ X2 )
         => ( esti @ ( suc @ ( '#sk9' @ X2 ) ) @ X2 ) )
      | ~ ( esti @ n_1 @ X2 )
      | ( !!
        @ ^ [Y0: nat] : ( esti @ Y0 @ X2 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).

thf(zip_derived_cl20,plain,
    ! [X2: set] :
      ( ~ ( esti @ ( suc @ ( '#sk9' @ X2 ) ) @ X2 )
      | ( !!
        @ ^ [Y0: nat] : ( esti @ Y0 @ X2 ) )
      | ~ ( esti @ n_1 @ X2 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).

thf(zip_derived_cl22,plain,
    ! [X2: set,X4: nat] :
      ( ( esti @ X4 @ X2 )
      | ~ ( esti @ n_1 @ X2 )
      | ~ ( esti @ ( suc @ ( '#sk9' @ X2 ) ) @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).

thf(estie,axiom,
    ! [Xp: nat > $o,Xs: nat] :
      ( ( esti @ Xs @ ( setof @ Xp ) )
     => ( Xp @ Xs ) ) ).

thf(zip_derived_cl1,plain,
    ( !!
    @ ^ [Y0: nat > $o] :
        ( !!
        @ ^ [Y1: nat] :
            ( ( esti @ Y1 @ ( setof @ Y0 ) )
           => ( Y0 @ Y1 ) ) ) ),
    inference(cnf,[status(esa)],[estie]) ).

thf(zip_derived_cl9,plain,
    ! [X2: nat > $o] :
      ( !!
      @ ^ [Y0: nat] :
          ( ( esti @ Y0 @ ( setof @ X2 ) )
         => ( X2 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).

thf(zip_derived_cl10,plain,
    ! [X2: nat > $o,X4: nat] :
      ( ( esti @ X4 @ ( setof @ X2 ) )
     => ( X2 @ X4 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl11,plain,
    ! [X2: nat > $o,X4: nat] :
      ( ~ ( esti @ X4 @ ( setof @ X2 ) )
      | ( X2 @ X4 ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl88,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ~ ( esti @ ( suc @ ( '#sk9' @ ( setof @ X0 ) ) ) @ ( setof @ X0 ) )
      | ~ ( esti @ n_1 @ ( setof @ X0 ) )
      | ( X0 @ X1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl11]) ).

thf(estii,axiom,
    ! [Xp: nat > $o,Xs: nat] :
      ( ( Xp @ Xs )
     => ( esti @ Xs @ ( setof @ Xp ) ) ) ).

thf(zip_derived_cl3,plain,
    ( !!
    @ ^ [Y0: nat > $o] :
        ( !!
        @ ^ [Y1: nat] :
            ( ( Y0 @ Y1 )
           => ( esti @ Y1 @ ( setof @ Y0 ) ) ) ) ),
    inference(cnf,[status(esa)],[estii]) ).

thf(zip_derived_cl12,plain,
    ! [X2: nat > $o] :
      ( !!
      @ ^ [Y0: nat] :
          ( ( X2 @ Y0 )
         => ( esti @ Y0 @ ( setof @ X2 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl13,plain,
    ! [X2: nat > $o,X4: nat] :
      ( ( X2 @ X4 )
     => ( esti @ X4 @ ( setof @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl14,plain,
    ! [X2: nat > $o,X4: nat] :
      ( ~ ( X2 @ X4 )
      | ( esti @ X4 @ ( setof @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl680,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ( X0 @ X1 )
      | ~ ( esti @ n_1 @ ( setof @ X0 ) )
      | ~ ( X0 @ ( suc @ ( '#sk9' @ ( setof @ X0 ) ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl88,zip_derived_cl14]) ).

thf(zip_derived_cl14_001,plain,
    ! [X2: nat > $o,X4: nat] :
      ( ~ ( X2 @ X4 )
      | ( esti @ X4 @ ( setof @ X2 ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).

thf(zip_derived_cl757,plain,
    ! [X0: nat > $o,X1: nat] :
      ( ~ ( X0 @ ( suc @ ( '#sk9' @ ( setof @ X0 ) ) ) )
      | ( X0 @ X1 )
      | ~ ( X0 @ n_1 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl680,zip_derived_cl14]) ).

thf(zip_derived_cl1043,plain,
    ! [X0: nat] :
      ( ~ ( ^ [Y0: nat] : ( X0 != Y0 )
          @ ( suc
            @ ( '#sk9'
              @ ( setof
                @ ^ [Y0: nat] : ( X0 != Y0 ) ) ) ) )
      | ( ^ [Y0: nat] : ( X0 != Y0 )
        @ X0 )
      | ~ ( ^ [Y0: nat] : ( X0 != Y0 )
          @ n_1 ) ),
    inference('elim_leibniz_eq_+',[status(thm)],[zip_derived_cl757]) ).

thf(zip_derived_cl1076,plain,
    ! [X0: nat] :
      ( ( X0
       != ( suc @ ( '#sk9' @ ( setof @ ( nat != X0 ) ) ) ) )
      | ( X0 != X0 )
      | ( X0 != n_1 ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl1043]) ).

thf(zip_derived_cl1077,plain,
    ! [X0: nat] :
      ( ( X0
       != ( suc @ ( '#sk9' @ ( setof @ ( nat != X0 ) ) ) ) )
      | ( X0 != n_1 ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl1076]) ).

thf(zip_derived_cl1078,plain,
    ! [X0: nat] :
      ( ( X0
        = ( suc @ ( '#sk9' @ ( setof @ ( nat != X0 ) ) ) ) )
      | ( X0 = n_1 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl1077]) ).

thf(satz3,conjecture,
    ~ ! [Xx_0: nat] :
        ( x
       != ( suc @ Xx_0 ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ! [Xx_0: nat] :
      ( x
     != ( suc @ Xx_0 ) ),
    inference('cnf.neg',[status(esa)],[satz3]) ).

thf(zip_derived_cl5,plain,
    ( !!
    @ ^ [Y0: nat] :
        ( x
       != ( suc @ Y0 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl7,plain,
    ! [X2: nat] :
      ( x
     != ( suc @ X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl8,plain,
    ! [X2: nat] :
      ( x
     != ( suc @ X2 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl1259,plain,
    ! [X0: nat] :
      ( ( x != X0 )
      | ( X0 = n_1 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl1078,zip_derived_cl8]) ).

thf(zip_derived_cl1293,plain,
    x = n_1,
    inference(simplify,[status(thm)],[zip_derived_cl1259]) ).

thf(n,axiom,
    x != n_1 ).

thf(zip_derived_cl0,plain,
    x != n_1,
    inference(cnf,[status(esa)],[n]) ).

thf(zip_derived_cl1294,plain,
    $false,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1293,zip_derived_cl0]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM637^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.15  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.7iCKayuWGk true
% 0.14/0.36  % Computer : n016.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Fri Aug 25 16:56:41 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  % Running portfolio for 300 s
% 0.14/0.36  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36  % Number of cores: 8
% 0.22/0.37  % Python version: Python 3.6.8
% 0.22/0.37  % Running in HO mode
% 0.22/0.69  % Total configuration time : 828
% 0.22/0.69  % Estimated wc time : 1656
% 0.22/0.69  % Estimated cpu time (8 cpus) : 207.0
% 1.03/0.77  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.03/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.03/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 1.03/0.77  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.03/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.03/0.78  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.03/0.78  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.43/0.81  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.44/0.95  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.59/1.54  % Solved by lams/30_b.l.sh.
% 1.59/1.54  % done 51 iterations in 0.515s
% 1.59/1.54  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.59/1.54  % SZS output start Refutation
% See solution above
% 1.59/1.54  
% 1.59/1.54  
% 1.59/1.54  % Terminating...
% 7.88/1.66  % Runner terminated.
% 7.88/1.66  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------