TSTP Solution File: ALG259^2 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : ALG259^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.pkQTRShOA7 true

% Computer : n013.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 : Wed Aug 30 17:12:33 EDT 2023

% Result   : Theorem 1.81s 0.92s
% Output   : Refutation 1.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   45 (  18 unt;  17 typ;   0 def)
%            Number of atoms       :   81 (  40 equ;   0 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  296 (  26   ~;   0   |;   0   &; 229   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   35 (  35   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;  10 con; 0-4 aty)
%                                         (  29  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   96 (  51   ^;  45   !;   0   ?;  96   :)

% Comments : 
%------------------------------------------------------------------------------
thf(term_type,type,
    term: $tType ).

thf(subst_type,type,
    subst: $tType ).

thf(lam_type,type,
    lam: term > term ).

thf(lamnotap_type,type,
    lamnotap: $o ).

thf(hoaslamnotap_lthm_type,type,
    hoaslamnotap_lthm: $o ).

thf('#sk2_type',type,
    '#sk2': term ).

thf(hoasap_type,type,
    hoasap: subst > term > subst > term > term ).

thf(one_type,type,
    one: term ).

thf(id_type,type,
    id: subst ).

thf(comp_type,type,
    comp: subst > subst > subst ).

thf(hoaslamnotap_type,type,
    hoaslamnotap: $o ).

thf(sh_type,type,
    sh: subst ).

thf('#sk1_type',type,
    '#sk1': subst > term > term ).

thf('#sk3_type',type,
    '#sk3': term ).

thf(sub_type,type,
    sub: term > subst > term ).

thf(ap_type,type,
    ap: term > term > term ).

thf(hoaslam_type,type,
    hoaslam: subst > ( subst > term > term ) > term ).

thf(hoaslamnotap_lthm,axiom,
    ( hoaslamnotap_lthm
    = ( lamnotap
     => hoaslamnotap ) ) ).

thf('0',plain,
    ( hoaslamnotap_lthm
    = ( lamnotap
     => hoaslamnotap ) ),
    define([status(thm)]) ).

thf(hoaslamnotap,axiom,
    ( hoaslamnotap
    = ( ! [F: subst > term > term] :
          ( ! [M: subst,A: term,N: subst] :
              ( ( sub @ ( F @ M @ A ) @ N )
              = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
         => ! [A: term,B: term] :
              ( ( hoaslam @ id
                @ ^ [M: subst,C: term] : ( F @ M @ C ) )
             != ( hoasap @ id @ A @ id @ B ) ) ) ) ) ).

thf('1',plain,
    ( hoaslamnotap
    = ( ! [X4: subst > term > term] :
          ( ! [X6: subst,X8: term,X10: subst] :
              ( ( sub @ ( X4 @ X6 @ X8 ) @ X10 )
              = ( X4 @ ( comp @ X6 @ X10 ) @ ( sub @ X8 @ X10 ) ) )
         => ! [X12: term,X14: term] :
              ( ( hoaslam @ id
                @ ^ [V_1: subst,V_2: term] : ( X4 @ V_1 @ V_2 ) )
             != ( hoasap @ id @ X12 @ id @ X14 ) ) ) ) ),
    define([status(thm)]) ).

thf(hoaslam,axiom,
    ( hoaslam
    = ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ) ).

thf('2',plain,
    ( hoaslam
    = ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[hoaslam]) ).

thf('3',plain,
    ( hoaslam
    = ( ^ [V_1: subst,V_2: subst > term > term] : ( lam @ ( V_2 @ sh @ one ) ) ) ),
    define([status(thm)]) ).

thf(hoasap,axiom,
    ( hoasap
    = ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ) ).

thf('4',plain,
    ( hoasap
    = ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ),
    inference(simplify_rw_rule,[status(thm)],[hoasap]) ).

thf('5',plain,
    ( hoasap
    = ( ^ [V_1: subst,V_2: term,V_3: subst,V_4: term] : ( ap @ ( sub @ V_2 @ V_3 ) @ V_4 ) ) ),
    define([status(thm)]) ).

thf(lamnotap,axiom,
    ( lamnotap
    = ( ! [A: term,B: term,C: term] :
          ( ( lam @ A )
         != ( ap @ B @ C ) ) ) ) ).

thf('6',plain,
    ( lamnotap
    = ( ! [X4: term,X6: term,X8: term] :
          ( ( lam @ X4 )
         != ( ap @ X6 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(thm,conjecture,
    hoaslamnotap_lthm ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: term,X6: term,X8: term] :
        ( ( lam @ X4 )
       != ( ap @ X6 @ X8 ) )
   => ! [X10: subst > term > term] :
        ( ! [X12: subst,X14: term,X16: subst] :
            ( ( sub @ ( X10 @ X12 @ X14 ) @ X16 )
            = ( X10 @ ( comp @ X12 @ X16 ) @ ( sub @ X14 @ X16 ) ) )
       => ! [X18: term,X20: term] :
            ( ( lam @ ( X10 @ sh @ one ) )
           != ( ap @ ( sub @ X18 @ id ) @ X20 ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: term,X6: term,X8: term] :
          ( ( lam @ X4 )
         != ( ap @ X6 @ X8 ) )
     => ! [X10: subst > term > term] :
          ( ! [X12: subst,X14: term,X16: subst] :
              ( ( sub @ ( X10 @ X12 @ X14 ) @ X16 )
              = ( X10 @ ( comp @ X12 @ X16 ) @ ( sub @ X14 @ X16 ) ) )
         => ! [X18: term,X20: term] :
              ( ( lam @ ( X10 @ sh @ one ) )
             != ( ap @ ( sub @ X18 @ id ) @ X20 ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl0,plain,
    ~ ( ( !!
        @ ^ [Y0: term] :
            ( !!
            @ ^ [Y1: term] :
                ( !!
                @ ^ [Y2: term] :
                    ( ( lam @ Y0 )
                   != ( ap @ Y1 @ Y2 ) ) ) ) )
     => ( !!
        @ ^ [Y0: subst > term > term] :
            ( ( !!
              @ ^ [Y1: subst] :
                  ( !!
                  @ ^ [Y2: term] :
                      ( !!
                      @ ^ [Y3: subst] :
                          ( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
                          = ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
           => ( !!
              @ ^ [Y1: term] :
                  ( !!
                  @ ^ [Y2: term] :
                      ( ( lam @ ( Y0 @ sh @ one ) )
                     != ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl4,plain,
    ~ ( !!
      @ ^ [Y0: subst > term > term] :
          ( ( !!
            @ ^ [Y1: subst] :
                ( !!
                @ ^ [Y2: term] :
                    ( !!
                    @ ^ [Y3: subst] :
                        ( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
                        = ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
         => ( !!
            @ ^ [Y1: term] :
                ( !!
                @ ^ [Y2: term] :
                    ( ( lam @ ( Y0 @ sh @ one ) )
                   != ( ap @ ( sub @ Y1 @ id ) @ Y2 ) ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl6,plain,
    ~ ( ( !!
        @ ^ [Y0: subst] :
            ( !!
            @ ^ [Y1: term] :
                ( !!
                @ ^ [Y2: subst] :
                    ( ( sub @ ( '#sk1' @ Y0 @ Y1 ) @ Y2 )
                    = ( '#sk1' @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
     => ( !!
        @ ^ [Y0: term] :
            ( !!
            @ ^ [Y1: term] :
                ( ( lam @ ( '#sk1' @ sh @ one ) )
               != ( ap @ ( sub @ Y0 @ id ) @ Y1 ) ) ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl9,plain,
    ~ ( !!
      @ ^ [Y0: term] :
          ( !!
          @ ^ [Y1: term] :
              ( ( lam @ ( '#sk1' @ sh @ one ) )
             != ( ap @ ( sub @ Y0 @ id ) @ Y1 ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).

thf(zip_derived_cl12,plain,
    ~ ( !!
      @ ^ [Y0: term] :
          ( ( lam @ ( '#sk1' @ sh @ one ) )
         != ( ap @ ( sub @ '#sk2' @ id ) @ Y0 ) ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).

thf(zip_derived_cl15,plain,
    ( ( lam @ ( '#sk1' @ sh @ one ) )
   != ( ap @ ( sub @ '#sk2' @ id ) @ '#sk3' ) ),
    inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl17,plain,
    ( ( lam @ ( '#sk1' @ sh @ one ) )
    = ( ap @ ( sub @ '#sk2' @ id ) @ '#sk3' ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl15]) ).

thf(zip_derived_cl3,plain,
    ( !!
    @ ^ [Y0: term] :
        ( !!
        @ ^ [Y1: term] :
            ( !!
            @ ^ [Y2: term] :
                ( ( lam @ Y0 )
               != ( ap @ Y1 @ Y2 ) ) ) ) ),
    inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl5,plain,
    ! [X2: term] :
      ( !!
      @ ^ [Y0: term] :
          ( !!
          @ ^ [Y1: term] :
              ( ( lam @ X2 )
             != ( ap @ Y0 @ Y1 ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl7,plain,
    ! [X2: term,X4: term] :
      ( !!
      @ ^ [Y0: term] :
          ( ( lam @ X2 )
         != ( ap @ X4 @ Y0 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl10,plain,
    ! [X2: term,X4: term,X6: term] :
      ( ( lam @ X2 )
     != ( ap @ X4 @ X6 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).

thf(zip_derived_cl13,plain,
    ! [X2: term,X4: term,X6: term] :
      ( ( lam @ X2 )
     != ( ap @ X4 @ X6 ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl10]) ).

thf(zip_derived_cl37,plain,
    $false,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl17,zip_derived_cl13]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ALG259^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.12/0.13  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.pkQTRShOA7 true
% 0.13/0.34  % Computer : n013.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 : Mon Aug 28 03:33:32 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in HO mode
% 0.20/0.69  % Total configuration time : 828
% 0.20/0.69  % Estimated wc time : 1656
% 0.20/0.69  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.79  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.80  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.80  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.80  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.80  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.55/0.83  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.55/0.85  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.55/0.85  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.55/0.86  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.76/0.86  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 1.81/0.91  % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s
% 1.81/0.92  % Solved by lams/15_e_short1.sh.
% 1.81/0.92  % done 3 iterations in 0.088s
% 1.81/0.92  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.81/0.92  % SZS output start Refutation
% See solution above
% 1.81/0.92  
% 1.81/0.92  
% 1.81/0.93  % Terminating...
% 2.09/0.99  % Runner terminated.
% 2.09/1.01  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------