%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : ALG251^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.PG3SeLs4VL true

% Computer : n007.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 17:12:27 EDT 2023

% Result   : Theorem 22.35s 3.46s
% Output   : Refutation 22.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   72 (  33 unt;  22 typ;   0 def)
%            Number of atoms       :  157 (  72 equ;   0 cnn)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  437 (  46   ~;  33   |;   0   &; 293   @)
%                                         (   5 <=>;  60  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   4 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   40 (  40   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  20 usr;  14 con; 0-4 aty)
%            Number of variables   :  127 (  19   ^; 104   !;   4   ?; 127   :)

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

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

thf(axclos_type,type,
    axclos: $o ).

thf(axvarcons_type,type,
    axvarcons: $o ).

thf(push_type,type,
    push: term > subst > subst ).

thf(axshiftcons_type,type,
    axshiftcons: $o ).

thf(one_type,type,
    one: term ).

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

thf(sk__282_type,type,
    sk__282: subst ).

thf(sh_type,type,
    sh: subst ).

thf(ulamvarind_type,type,
    ulamvarind: $o ).

thf(sk__280_type,type,
    sk__280: term > $o ).

thf(pushprop_lthm_type,type,
    pushprop_lthm: $o ).

thf(pushprop_p_and_p_prime_type,type,
    pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).

thf(pushprop_type,type,
    pushprop: $o ).

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

thf(sk__279_type,type,
    sk__279: ( term > $o ) > term ).

thf(sk__283_type,type,
    sk__283: term ).

thf(var_type,type,
    var: term > $o ).

thf(pushprop_lem0_type,type,
    pushprop_lem0: $o ).

thf(sk__281_type,type,
    sk__281: term ).

thf(ulamvar1_type,type,
    ulamvar1: $o ).

thf(pushprop_lthm,axiom,
    ( pushprop_lthm
    = ( pushprop_lem0
     => ( ulamvar1
       => ( axvarcons
         => ( axclos
           => ( axshiftcons
             => ( ulamvarind
               => pushprop ) ) ) ) ) ) ) ).

thf('0',plain,
    ( pushprop_lthm
    = ( pushprop_lem0
     => ( ulamvar1
       => ( axvarcons
         => ( axclos
           => ( axshiftcons
             => ( ulamvarind
               => pushprop ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(pushprop,axiom,
    ( pushprop
    = ( ! [P: term > $o,A: term,M: subst] :
          ( ! [B: term] :
              ( ( var @ B )
             => ( P @ ( sub @ B @ M ) ) )
         => ( ( P @ A )
           => ! [B: term] :
                ( ( var @ B )
               => ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ) ).

thf('1',plain,
    ( pushprop
    = ( ! [X4: term > $o,X6: term,X8: subst] :
          ( ! [X10: term] :
              ( ( var @ X10 )
             => ( X4 @ ( sub @ X10 @ X8 ) ) )
         => ( ( X4 @ X6 )
           => ! [X12: term] :
                ( ( var @ X12 )
               => ( X4 @ ( sub @ X12 @ ( push @ X6 @ X8 ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(pushprop_lem0,axiom,
    ( pushprop_lem0
    = ( ! [P: term > $o,A: term,M: subst] :
        ? [Q: term > $o] : ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) ) ) ).

thf('2',plain,
    ( pushprop_lem0
    = ( ! [X4: term > $o,X6: term,X8: subst] :
        ? [X10: term > $o] : ( pushprop_p_and_p_prime @ X6 @ X8 @ X4 @ X10 ) ) ),
    define([status(thm)]) ).

thf(pushprop_p_and_p_prime,axiom,
    ( pushprop_p_and_p_prime
    = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
        ! [X: term] :
          ( ( Q @ X )
        <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ).

thf('3',plain,
    ( pushprop_p_and_p_prime
    = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
        ! [X: term] :
          ( ( Q @ X )
        <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[pushprop_p_and_p_prime]) ).

thf('4',plain,
    ( pushprop_p_and_p_prime
    = ( ^ [V_1: term,V_2: subst,V_3: term > $o,V_4: term > $o] :
        ! [X4: term] :
          ( ( V_4 @ X4 )
        <=> ( V_3 @ ( sub @ X4 @ ( push @ V_1 @ V_2 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(ulamvarind,axiom,
    ( ulamvarind
    = ( ! [P: term > $o] :
          ( ( P @ one )
         => ( ! [A: term] :
                ( ( var @ A )
               => ( ( P @ A )
                 => ( P @ ( sub @ A @ sh ) ) ) )
           => ! [A: term] :
                ( ( var @ A )
               => ( P @ A ) ) ) ) ) ) ).

thf('5',plain,
    ( ulamvarind
    = ( ! [X4: term > $o] :
          ( ( X4 @ one )
         => ( ! [X6: term] :
                ( ( var @ X6 )
               => ( ( X4 @ X6 )
                 => ( X4 @ ( sub @ X6 @ sh ) ) ) )
           => ! [X8: term] :
                ( ( var @ X8 )
               => ( X4 @ X8 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(ulamvar1,axiom,
    ( ulamvar1
    = ( var @ one ) ) ).

thf('6',plain,
    ( ulamvar1
    = ( var @ one ) ),
    inference(simplify_rw_rule,[status(thm)],[ulamvar1]) ).

thf('7',plain,
    ( ulamvar1
    = ( var @ one ) ),
    define([status(thm)]) ).

thf(axshiftcons,axiom,
    ( axshiftcons
    = ( ! [A: term,M: subst] :
          ( ( comp @ sh @ ( push @ A @ M ) )
          = M ) ) ) ).

thf('8',plain,
    ( axshiftcons
    = ( ! [X4: term,X6: subst] :
          ( ( comp @ sh @ ( push @ X4 @ X6 ) )
          = X6 ) ) ),
    define([status(thm)]) ).

thf(axclos,axiom,
    ( axclos
    = ( ! [A: term,M: subst,N: subst] :
          ( ( sub @ ( sub @ A @ M ) @ N )
          = ( sub @ A @ ( comp @ M @ N ) ) ) ) ) ).

thf('9',plain,
    ( axclos
    = ( ! [X4: term,X6: subst,X8: subst] :
          ( ( sub @ ( sub @ X4 @ X6 ) @ X8 )
          = ( sub @ X4 @ ( comp @ X6 @ X8 ) ) ) ) ),
    define([status(thm)]) ).

thf(axvarcons,axiom,
    ( axvarcons
    = ( ! [A: term,M: subst] :
          ( ( sub @ one @ ( push @ A @ M ) )
          = A ) ) ) ).

thf('10',plain,
    ( axvarcons
    = ( ! [X4: term,X6: subst] :
          ( ( sub @ one @ ( push @ X4 @ X6 ) )
          = X4 ) ) ),
    define([status(thm)]) ).

thf(thm,conjecture,
    pushprop_lthm ).

thf(zf_stmt_0,conjecture,
    ( ! [X4: term > $o,X6: term,X8: subst] :
      ? [X10: term > $o] :
      ! [X12: term] :
        ( ( X10 @ X12 )
      <=> ( X4 @ ( sub @ X12 @ ( push @ X6 @ X8 ) ) ) )
   => ( ( var @ one )
     => ( ! [X14: term,X16: subst] :
            ( ( sub @ one @ ( push @ X14 @ X16 ) )
            = X14 )
       => ( ! [X18: term,X20: subst,X22: subst] :
              ( ( sub @ ( sub @ X18 @ X20 ) @ X22 )
              = ( sub @ X18 @ ( comp @ X20 @ X22 ) ) )
         => ( ! [X24: term,X26: subst] :
                ( ( comp @ sh @ ( push @ X24 @ X26 ) )
                = X26 )
           => ( ! [X28: term > $o] :
                  ( ( X28 @ one )
                 => ( ! [X30: term] :
                        ( ( var @ X30 )
                       => ( ( X28 @ X30 )
                         => ( X28 @ ( sub @ X30 @ sh ) ) ) )
                   => ! [X32: term] :
                        ( ( var @ X32 )
                       => ( X28 @ X32 ) ) ) )
             => ! [X34: term > $o,X36: term,X38: subst] :
                  ( ! [X40: term] :
                      ( ( var @ X40 )
                     => ( X34 @ ( sub @ X40 @ X38 ) ) )
                 => ( ( X34 @ X36 )
                   => ! [X42: term] :
                        ( ( var @ X42 )
                       => ( X34 @ ( sub @ X42 @ ( push @ X36 @ X38 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( ! [X4: term > $o,X6: term,X8: subst] :
        ? [X10: term > $o] :
        ! [X12: term] :
          ( ( X10 @ X12 )
        <=> ( X4 @ ( sub @ X12 @ ( push @ X6 @ X8 ) ) ) )
     => ( ( var @ one )
       => ( ! [X14: term,X16: subst] :
              ( ( sub @ one @ ( push @ X14 @ X16 ) )
              = X14 )
         => ( ! [X18: term,X20: subst,X22: subst] :
                ( ( sub @ ( sub @ X18 @ X20 ) @ X22 )
                = ( sub @ X18 @ ( comp @ X20 @ X22 ) ) )
           => ( ! [X24: term,X26: subst] :
                  ( ( comp @ sh @ ( push @ X24 @ X26 ) )
                  = X26 )
             => ( ! [X28: term > $o] :
                    ( ( X28 @ one )
                   => ( ! [X30: term] :
                          ( ( var @ X30 )
                         => ( ( X28 @ X30 )
                           => ( X28 @ ( sub @ X30 @ sh ) ) ) )
                     => ! [X32: term] :
                          ( ( var @ X32 )
                         => ( X28 @ X32 ) ) ) )
               => ! [X34: term > $o,X36: term,X38: subst] :
                    ( ! [X40: term] :
                        ( ( var @ X40 )
                       => ( X34 @ ( sub @ X40 @ X38 ) ) )
                   => ( ( X34 @ X36 )
                     => ! [X42: term] :
                          ( ( var @ X42 )
                         => ( X34 @ ( sub @ X42 @ ( push @ X36 @ X38 ) ) ) ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl8,plain,
    ~ ( sk__280 @ ( sub @ sk__283 @ ( push @ sk__281 @ sk__282 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl9,plain,
    var @ sk__283,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl11,plain,
    ! [X10: term > $o,X11: term] :
      ( ~ ( X10 @ ( sub @ ( sk__279 @ X10 ) @ sh ) )
      | ~ ( var @ X11 )
      | ( X10 @ X11 )
      | ~ ( X10 @ one ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl149,plain,
    ! [X0: term] :
      ( ~ ( ^ [Y0: term] : ( X0 != Y0 )
          @ ( sub
            @ ( sk__279
              @ ^ [Y0: term] : ( X0 != Y0 ) )
            @ sh ) )
      | ~ ( var @ X0 )
      | ( ^ [Y0: term] : ( X0 != Y0 )
        @ X0 )
      | ~ ( ^ [Y0: term] : ( X0 != Y0 )
          @ one ) ),
    inference('elim_leibniz_eq_+',[status(thm)],[zip_derived_cl11]) ).

thf(zip_derived_cl172,plain,
    ! [X0: term] :
      ( ( X0
       != ( sub @ ( sk__279 @ ( term != X0 ) ) @ sh ) )
      | ~ ( var @ X0 )
      | ( X0 != X0 )
      | ( X0 != one ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl149]) ).

thf(zip_derived_cl173,plain,
    ! [X0: term] :
      ( ( X0
       != ( sub @ ( sk__279 @ ( term != X0 ) ) @ sh ) )
      | ~ ( var @ X0 )
      | ( X0 != one ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl172]) ).

thf(zip_derived_cl174,plain,
    ! [X0: term] :
      ( ( X0
        = ( sub @ ( sk__279 @ ( term != X0 ) ) @ sh ) )
      | ~ ( var @ X0 )
      | ( X0 = one ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl173]) ).

thf(zip_derived_cl261,plain,
    ( ( sk__283 = one )
    | ( sk__283
      = ( sub @ ( sk__279 @ ( term != sk__283 ) ) @ sh ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl174]) ).

thf(zip_derived_cl5,plain,
    ! [X7: subst,X8: term] :
      ( ( comp @ sh @ ( push @ X8 @ X7 ) )
      = X7 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl13,plain,
    ! [X12: term,X13: subst,X14: subst] :
      ( ( sub @ ( sub @ X12 @ X13 ) @ X14 )
      = ( sub @ X12 @ ( comp @ X13 @ X14 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl469,plain,
    ! [X0: subst,X1: term,X2: term] :
      ( ( sub @ ( sub @ X2 @ sh ) @ ( push @ X1 @ X0 ) )
      = ( sub @ X2 @ X0 ) ),
    inference('sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl13]) ).

thf(zip_derived_cl2814,plain,
    ! [X0: subst,X1: term] :
      ( ( ( sub @ sk__283 @ ( push @ X1 @ X0 ) )
        = ( sub @ ( sk__279 @ ( term != sk__283 ) ) @ X0 ) )
      | ( sk__283 = one ) ),
    inference('sup+',[status(thm)],[zip_derived_cl261,zip_derived_cl469]) ).

thf(zip_derived_cl7,plain,
    ! [X9: term] :
      ( ( sk__280 @ ( sub @ X9 @ sk__282 ) )
      | ~ ( var @ X9 ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl5133,plain,
    ! [X0: term] :
      ( ( sk__280 @ ( sub @ sk__283 @ ( push @ X0 @ sk__282 ) ) )
      | ( sk__283 = one )
      | ~ ( var @ ( sk__279 @ ( term != sk__283 ) ) ) ),
    inference('sup+',[status(thm)],[zip_derived_cl2814,zip_derived_cl7]) ).

thf(zip_derived_cl9_001,plain,
    var @ sk__283,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl12,plain,
    ! [X10: term > $o,X11: term] :
      ( ( var @ ( sk__279 @ X10 ) )
      | ~ ( var @ X11 )
      | ( X10 @ X11 )
      | ~ ( X10 @ one ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl71,plain,
    ! [X0: term] :
      ( ( var
        @ ( sk__279
          @ ^ [Y0: term] : ( X0 != Y0 ) ) )
      | ~ ( var @ X0 )
      | ( ^ [Y0: term] : ( X0 != Y0 )
        @ X0 )
      | ~ ( ^ [Y0: term] : ( X0 != Y0 )
          @ one ) ),
    inference('elim_leibniz_eq_+',[status(thm)],[zip_derived_cl12]) ).

thf(zip_derived_cl75,plain,
    ! [X0: term] :
      ( ( var @ ( sk__279 @ ( term != X0 ) ) )
      | ~ ( var @ X0 )
      | ( X0 != X0 )
      | ( X0 != one ) ),
    inference(ho_norm,[status(thm)],[zip_derived_cl71]) ).

thf(zip_derived_cl76,plain,
    ! [X0: term] :
      ( ( var @ ( sk__279 @ ( term != X0 ) ) )
      | ~ ( var @ X0 )
      | ( X0 != one ) ),
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl75]) ).

thf(zip_derived_cl77,plain,
    ! [X0: term] :
      ( ( var @ ( sk__279 @ ( term != X0 ) ) )
      | ~ ( var @ X0 )
      | ( X0 = one ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl76]) ).

thf(zip_derived_cl106,plain,
    ( ( sk__283 = one )
    | ( var @ ( sk__279 @ ( term != sk__283 ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl9,zip_derived_cl77]) ).

thf(zip_derived_cl5153,plain,
    ! [X0: term] :
      ( ( sk__283 = one )
      | ( sk__280 @ ( sub @ sk__283 @ ( push @ X0 @ sk__282 ) ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl5133,zip_derived_cl106]) ).

thf(zip_derived_cl8_002,plain,
    ~ ( sk__280 @ ( sub @ sk__283 @ ( push @ sk__281 @ sk__282 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl5154,plain,
    sk__283 = one,
    inference('sup-',[status(thm)],[zip_derived_cl5153,zip_derived_cl8]) ).

thf(zip_derived_cl4,plain,
    ! [X5: term,X6: subst] :
      ( ( sub @ one @ ( push @ X5 @ X6 ) )
      = X5 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl6,plain,
    sk__280 @ sk__281,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl5162,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl5154,zip_derived_cl4,zip_derived_cl6]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : ALG251^2 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.12/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.PG3SeLs4VL true
% 0.13/0.35  % Computer : n007.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Aug 28 03:57:12 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % 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
% 0.20/0.67  % Total configuration time : 828
% 0.20/0.67  % Estimated wc time : 1656
% 0.20/0.67  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.73  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.74  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.37/0.77  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.37/0.77  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.37/0.77  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.37/0.77  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.41/0.78  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.41/0.78  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 22.35/3.46  % Solved by lams/40_noforms.sh.
% 22.35/3.46  % done 653 iterations in 2.666s
% 22.35/3.46  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 22.35/3.46  % SZS output start Refutation
% See solution above
% 22.35/3.46  
% 22.35/3.46  
% 22.35/3.46  % Terminating...
% 23.01/3.58  % Runner terminated.
% 23.01/3.59  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------