TSTP Solution File: ALG255^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : ALG255^1 : 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.aEzMqeBvjS 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 17:12:30 EDT 2023

% Result   : Theorem 1.45s 0.85s
% Output   : Refutation 1.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   96
% Syntax   : Number of formulae    :  103 (  55 unt;  44 typ;   0 def)
%            Number of atoms       :  299 ( 133 equ;   0 cnn)
%            Maximal formula atoms :   35 (   5 avg)
%            Number of connectives :  948 (  17   ~;   2   |;  12   &; 673   @)
%                                         (   0 <=>; 244  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   40 (   2 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :   30 (  30   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   44 (  42 usr;  37 con; 0-2 aty)
%            Number of variables   :  268 (   0   ^; 268   !;   0   ?; 268   :)

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

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

thf(axmap_type,type,
    axmap: $o ).

thf(termmset_gthm_type,type,
    termmset_gthm: $o ).

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

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

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

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

thf(substmonoid_type,type,
    substmonoid: $o ).

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

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

thf(axapp_type,type,
    axapp: $o ).

thf(shinj_type,type,
    shinj: $o ).

thf(sk__72_type,type,
    sk__72: term ).

thf(sk__73_type,type,
    sk__73: subst ).

thf(one_type,type,
    one: term ).

thf(id_type,type,
    id: subst ).

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

thf(induction2_type,type,
    induction2: $o ).

thf(axvarid_type,type,
    axvarid: $o ).

thf(axvarshift_type,type,
    axvarshift: $o ).

thf(induction2lem_type,type,
    induction2lem: $o ).

thf(sh_type,type,
    sh: subst ).

thf(laminj_type,type,
    laminj: $o ).

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

thf(apinj2_type,type,
    apinj2: $o ).

thf(ulamvarsh_type,type,
    ulamvarsh: $o ).

thf(lamnotvar_type,type,
    lamnotvar: $o ).

thf(sk__74_type,type,
    sk__74: subst ).

thf(apnotvar_type,type,
    apnotvar: $o ).

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

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

thf(apinj1_type,type,
    apinj1: $o ).

thf(axidl_type,type,
    axidl: $o ).

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

thf(termmset_type,type,
    termmset: $o ).

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

thf(axassoc_type,type,
    axassoc: $o ).

thf(axidr_type,type,
    axidr: $o ).

thf(sk__71_type,type,
    sk__71: term ).

thf(axabs_type,type,
    axabs: $o ).

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

thf(induction_type,type,
    induction: $o ).

thf(axscons_type,type,
    axscons: $o ).

thf(termmset_gthm,axiom,
    ( termmset_gthm
    = ( axapp
     => ( axvarcons
       => ( axvarid
         => ( axabs
           => ( axclos
             => ( axidl
               => ( axshiftcons
                 => ( axassoc
                   => ( axmap
                     => ( axidr
                       => ( axvarshift
                         => ( axscons
                           => ( ulamvar1
                             => ( ulamvarsh
                               => ( ulamvarind
                                 => ( apinj1
                                   => ( apinj2
                                     => ( laminj
                                       => ( shinj
                                         => ( lamnotap
                                           => ( apnotvar
                                             => ( lamnotvar
                                               => ( induction
                                                 => ( pushprop
                                                   => ( induction2lem
                                                     => ( induction2
                                                       => ( substmonoid
                                                         => termmset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf('0',plain,
    ( termmset_gthm
    = ( axapp
     => ( axvarcons
       => ( axvarid
         => ( axabs
           => ( axclos
             => ( axidl
               => ( axshiftcons
                 => ( axassoc
                   => ( axmap
                     => ( axidr
                       => ( axvarshift
                         => ( axscons
                           => ( ulamvar1
                             => ( ulamvarsh
                               => ( ulamvarind
                                 => ( apinj1
                                   => ( apinj2
                                     => ( laminj
                                       => ( shinj
                                         => ( lamnotap
                                           => ( apnotvar
                                             => ( lamnotvar
                                               => ( induction
                                                 => ( pushprop
                                                   => ( induction2lem
                                                     => ( induction2
                                                       => ( substmonoid
                                                         => termmset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

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

thf('1',plain,
    ( termmset
    = ( ! [X4: term] :
          ( ( sub @ X4 @ id )
          = X4 )
      & ! [X6: term,X8: subst,X10: subst] :
          ( ( sub @ ( sub @ X6 @ X8 ) @ X10 )
          = ( sub @ X6 @ ( comp @ X8 @ X10 ) ) ) ) ),
    define([status(thm)]) ).

thf(substmonoid,axiom,
    ( substmonoid
    = ( ! [M: subst] :
          ( ( comp @ M @ id )
          = M )
      & ! [M: subst] :
          ( ( comp @ id @ M )
          = M )
      & ! [M: subst,N: subst,K: subst] :
          ( ( comp @ ( comp @ M @ N ) @ K )
          = ( comp @ M @ ( comp @ N @ K ) ) ) ) ) ).

thf('2',plain,
    ( substmonoid
    = ( ! [X4: subst] :
          ( ( comp @ X4 @ id )
          = X4 )
      & ! [X6: subst] :
          ( ( comp @ id @ X6 )
          = X6 )
      & ! [X8: subst,X10: subst,X12: subst] :
          ( ( comp @ ( comp @ X8 @ X10 ) @ X12 )
          = ( comp @ X8 @ ( comp @ X10 @ X12 ) ) ) ) ),
    define([status(thm)]) ).

thf(induction2,axiom,
    ( induction2
    = ( ! [P: term > $o] :
          ( ! [A: term] :
              ( ( var @ A )
             => ( P @ A ) )
         => ( ! [A: term,B: term] :
                ( ( P @ A )
               => ( ( P @ B )
                 => ( P @ ( ap @ A @ B ) ) ) )
           => ( ! [A: term] :
                  ( ! [B: term] :
                      ( ( P @ B )
                     => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
                 => ( P @ ( lam @ A ) ) )
             => ! [A: term] : ( P @ A ) ) ) ) ) ) ).

thf('3',plain,
    ( induction2
    = ( ! [X4: term > $o] :
          ( ! [X6: term] :
              ( ( var @ X6 )
             => ( X4 @ X6 ) )
         => ( ! [X8: term,X10: term] :
                ( ( X4 @ X8 )
               => ( ( X4 @ X10 )
                 => ( X4 @ ( ap @ X8 @ X10 ) ) ) )
           => ( ! [X12: term] :
                  ( ! [X14: term] :
                      ( ( X4 @ X14 )
                     => ( X4 @ ( sub @ X12 @ ( push @ X14 @ id ) ) ) )
                 => ( X4 @ ( lam @ X12 ) ) )
             => ! [X16: term] : ( X4 @ X16 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(induction2lem,axiom,
    ( induction2lem
    = ( ! [P: term > $o] :
          ( ! [A: term,B: term] :
              ( ( P @ A )
             => ( ( P @ B )
               => ( P @ ( ap @ A @ B ) ) ) )
         => ( ! [A: term] :
                ( ! [B: term] :
                    ( ( P @ B )
                   => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
               => ( P @ ( lam @ A ) ) )
           => ! [A: term,M: subst] :
                ( ! [B: term] :
                    ( ( var @ B )
                   => ( P @ ( sub @ B @ M ) ) )
               => ( P @ ( sub @ A @ M ) ) ) ) ) ) ) ).

thf('4',plain,
    ( induction2lem
    = ( ! [X4: term > $o] :
          ( ! [X6: term,X8: term] :
              ( ( X4 @ X6 )
             => ( ( X4 @ X8 )
               => ( X4 @ ( ap @ X6 @ X8 ) ) ) )
         => ( ! [X10: term] :
                ( ! [X12: term] :
                    ( ( X4 @ X12 )
                   => ( X4 @ ( sub @ X10 @ ( push @ X12 @ id ) ) ) )
               => ( X4 @ ( lam @ X10 ) ) )
           => ! [X14: term,X16: subst] :
                ( ! [X18: term] :
                    ( ( var @ X18 )
                   => ( X4 @ ( sub @ X18 @ X16 ) ) )
               => ( X4 @ ( sub @ X14 @ X16 ) ) ) ) ) ) ),
    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('5',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(induction,axiom,
    ( induction
    = ( ! [P: term > $o] :
          ( ! [A: term] :
              ( ( var @ A )
             => ( P @ A ) )
         => ( ! [A: term,B: term] :
                ( ( P @ A )
               => ( ( P @ B )
                 => ( P @ ( ap @ A @ B ) ) ) )
           => ( ! [A: term] :
                  ( ( P @ A )
                 => ( P @ ( lam @ A ) ) )
             => ! [A: term] : ( P @ A ) ) ) ) ) ) ).

thf('6',plain,
    ( induction
    = ( ! [X4: term > $o] :
          ( ! [X6: term] :
              ( ( var @ X6 )
             => ( X4 @ X6 ) )
         => ( ! [X8: term,X10: term] :
                ( ( X4 @ X8 )
               => ( ( X4 @ X10 )
                 => ( X4 @ ( ap @ X8 @ X10 ) ) ) )
           => ( ! [X12: term] :
                  ( ( X4 @ X12 )
                 => ( X4 @ ( lam @ X12 ) ) )
             => ! [X14: term] : ( X4 @ X14 ) ) ) ) ) ),
    define([status(thm)]) ).

thf(lamnotvar,axiom,
    ( lamnotvar
    = ( ! [A: term] :
          ~ ( var @ ( lam @ A ) ) ) ) ).

thf('7',plain,
    ( lamnotvar
    = ( ! [X4: term] :
          ~ ( var @ ( lam @ X4 ) ) ) ),
    define([status(thm)]) ).

thf(apnotvar,axiom,
    ( apnotvar
    = ( ! [A: term,B: term] :
          ~ ( var @ ( ap @ A @ B ) ) ) ) ).

thf('8',plain,
    ( apnotvar
    = ( ! [X4: term,X6: term] :
          ~ ( var @ ( ap @ X4 @ X6 ) ) ) ),
    define([status(thm)]) ).

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

thf('9',plain,
    ( lamnotap
    = ( ! [X4: term,X6: term,X8: term] :
          ( ( lam @ X4 )
         != ( ap @ X6 @ X8 ) ) ) ),
    define([status(thm)]) ).

thf(laminj,axiom,
    ( laminj
    = ( ! [A: term,B: term] :
          ( ( ( lam @ A )
            = ( lam @ B ) )
         => ( A = B ) ) ) ) ).

thf('10',plain,
    ( laminj
    = ( ! [X4: term,X6: term] :
          ( ( ( lam @ X4 )
            = ( lam @ X6 ) )
         => ( X4 = X6 ) ) ) ),
    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('11',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(ulamvarsh,axiom,
    ( ulamvarsh
    = ( ! [A: term] :
          ( ( var @ A )
         => ( var @ ( sub @ A @ sh ) ) ) ) ) ).

thf('12',plain,
    ( ulamvarsh
    = ( ! [X4: term] :
          ( ( var @ X4 )
         => ( var @ ( sub @ X4 @ sh ) ) ) ) ),
    define([status(thm)]) ).

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

thf('13',plain,
    ( ulamvar1
    = ( var @ one ) ),
    inference(simplify_rw_rule,[status(thm)],[ulamvar1]) ).

thf('14',plain,
    ( ulamvar1
    = ( var @ one ) ),
    define([status(thm)]) ).

thf(axscons,axiom,
    ( axscons
    = ( ! [M: subst] :
          ( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
          = M ) ) ) ).

thf('15',plain,
    ( axscons
    = ( ! [X4: subst] :
          ( ( push @ ( sub @ one @ X4 ) @ ( comp @ sh @ X4 ) )
          = X4 ) ) ),
    define([status(thm)]) ).

thf(axvarshift,axiom,
    ( axvarshift
    = ( ( push @ one @ sh )
      = id ) ) ).

thf('16',plain,
    ( axvarshift
    = ( ( push @ one @ sh )
      = id ) ),
    define([status(thm)]) ).

thf(axidr,axiom,
    ( axidr
    = ( ! [M: subst] :
          ( ( comp @ M @ id )
          = M ) ) ) ).

thf('17',plain,
    ( axidr
    = ( ! [X4: subst] :
          ( ( comp @ X4 @ id )
          = X4 ) ) ),
    define([status(thm)]) ).

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

thf('18',plain,
    ( axmap
    = ( ! [X4: term,X6: subst,X8: subst] :
          ( ( comp @ ( push @ X4 @ X6 ) @ X8 )
          = ( push @ ( sub @ X4 @ X8 ) @ ( comp @ X6 @ X8 ) ) ) ) ),
    define([status(thm)]) ).

thf(axassoc,axiom,
    ( axassoc
    = ( ! [M: subst,N: subst,K: subst] :
          ( ( comp @ ( comp @ M @ N ) @ K )
          = ( comp @ M @ ( comp @ N @ K ) ) ) ) ) ).

thf('19',plain,
    ( axassoc
    = ( ! [X4: subst,X6: subst,X8: subst] :
          ( ( comp @ ( comp @ X4 @ X6 ) @ X8 )
          = ( comp @ X4 @ ( comp @ X6 @ X8 ) ) ) ) ),
    define([status(thm)]) ).

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

thf('20',plain,
    ( axshiftcons
    = ( ! [X4: term,X6: subst] :
          ( ( comp @ sh @ ( push @ X4 @ X6 ) )
          = X6 ) ) ),
    define([status(thm)]) ).

thf(axidl,axiom,
    ( axidl
    = ( ! [M: subst] :
          ( ( comp @ id @ M )
          = M ) ) ) ).

thf('21',plain,
    ( axidl
    = ( ! [X4: subst] :
          ( ( comp @ id @ X4 )
          = X4 ) ) ),
    define([status(thm)]) ).

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

thf('22',plain,
    ( axclos
    = ( ! [X4: term,X6: subst,X8: subst] :
          ( ( sub @ ( sub @ X4 @ X6 ) @ X8 )
          = ( sub @ X4 @ ( comp @ X6 @ X8 ) ) ) ) ),
    define([status(thm)]) ).

thf(axabs,axiom,
    ( axabs
    = ( ! [A: term,M: subst] :
          ( ( sub @ ( lam @ A ) @ M )
          = ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) ) ) ).

thf('23',plain,
    ( axabs
    = ( ! [X4: term,X6: subst] :
          ( ( sub @ ( lam @ X4 ) @ X6 )
          = ( lam @ ( sub @ X4 @ ( push @ one @ ( comp @ X6 @ sh ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(axvarid,axiom,
    ( axvarid
    = ( ! [A: term] :
          ( ( sub @ A @ id )
          = A ) ) ) ).

thf('24',plain,
    ( axvarid
    = ( ! [X4: term] :
          ( ( sub @ X4 @ id )
          = X4 ) ) ),
    define([status(thm)]) ).

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

thf('25',plain,
    ( axvarcons
    = ( ! [X4: term,X6: subst] :
          ( ( sub @ one @ ( push @ X4 @ X6 ) )
          = X4 ) ) ),
    define([status(thm)]) ).

thf(thm,conjecture,
    termmset_gthm ).

thf(zf_stmt_0,conjecture,
    ( axapp
   => ( ! [X4: term,X6: subst] :
          ( ( sub @ one @ ( push @ X4 @ X6 ) )
          = X4 )
     => ( ! [X8: term] :
            ( ( sub @ X8 @ id )
            = X8 )
       => ( ! [X10: term,X12: subst] :
              ( ( sub @ ( lam @ X10 ) @ X12 )
              = ( lam @ ( sub @ X10 @ ( push @ one @ ( comp @ X12 @ sh ) ) ) ) )
         => ( ! [X14: term,X16: subst,X18: subst] :
                ( ( sub @ ( sub @ X14 @ X16 ) @ X18 )
                = ( sub @ X14 @ ( comp @ X16 @ X18 ) ) )
           => ( ! [X20: subst] :
                  ( ( comp @ id @ X20 )
                  = X20 )
             => ( ! [X22: term,X24: subst] :
                    ( ( comp @ sh @ ( push @ X22 @ X24 ) )
                    = X24 )
               => ( ! [X26: subst,X28: subst,X30: subst] :
                      ( ( comp @ ( comp @ X26 @ X28 ) @ X30 )
                      = ( comp @ X26 @ ( comp @ X28 @ X30 ) ) )
                 => ( ! [X32: term,X34: subst,X36: subst] :
                        ( ( comp @ ( push @ X32 @ X34 ) @ X36 )
                        = ( push @ ( sub @ X32 @ X36 ) @ ( comp @ X34 @ X36 ) ) )
                   => ( ! [X38: subst] :
                          ( ( comp @ X38 @ id )
                          = X38 )
                     => ( ( ( push @ one @ sh )
                          = id )
                       => ( ! [X40: subst] :
                              ( ( push @ ( sub @ one @ X40 ) @ ( comp @ sh @ X40 ) )
                              = X40 )
                         => ( ( var @ one )
                           => ( ! [X42: term] :
                                  ( ( var @ X42 )
                                 => ( var @ ( sub @ X42 @ sh ) ) )
                             => ( ! [X44: term > $o] :
                                    ( ( X44 @ one )
                                   => ( ! [X46: term] :
                                          ( ( var @ X46 )
                                         => ( ( X44 @ X46 )
                                           => ( X44 @ ( sub @ X46 @ sh ) ) ) )
                                     => ! [X48: term] :
                                          ( ( var @ X48 )
                                         => ( X44 @ X48 ) ) ) )
                               => ( apinj1
                                 => ( apinj2
                                   => ( ! [X50: term,X52: term] :
                                          ( ( ( lam @ X50 )
                                            = ( lam @ X52 ) )
                                         => ( X50 = X52 ) )
                                     => ( shinj
                                       => ( ! [X54: term,X56: term,X58: term] :
                                              ( ( lam @ X54 )
                                             != ( ap @ X56 @ X58 ) )
                                         => ( ! [X60: term,X62: term] :
                                                ~ ( var @ ( ap @ X60 @ X62 ) )
                                           => ( ! [X64: term] :
                                                  ~ ( var @ ( lam @ X64 ) )
                                             => ( ! [X66: term > $o] :
                                                    ( ! [X68: term] :
                                                        ( ( var @ X68 )
                                                       => ( X66 @ X68 ) )
                                                   => ( ! [X70: term,X72: term] :
                                                          ( ( X66 @ X70 )
                                                         => ( ( X66 @ X72 )
                                                           => ( X66 @ ( ap @ X70 @ X72 ) ) ) )
                                                     => ( ! [X74: term] :
                                                            ( ( X66 @ X74 )
                                                           => ( X66 @ ( lam @ X74 ) ) )
                                                       => ! [X76: term] : ( X66 @ X76 ) ) ) )
                                               => ( ! [X78: term > $o,X80: term,X82: subst] :
                                                      ( ! [X84: term] :
                                                          ( ( var @ X84 )
                                                         => ( X78 @ ( sub @ X84 @ X82 ) ) )
                                                     => ( ( X78 @ X80 )
                                                       => ! [X86: term] :
                                                            ( ( var @ X86 )
                                                           => ( X78 @ ( sub @ X86 @ ( push @ X80 @ X82 ) ) ) ) ) )
                                                 => ( ! [X88: term > $o] :
                                                        ( ! [X90: term,X92: term] :
                                                            ( ( X88 @ X90 )
                                                           => ( ( X88 @ X92 )
                                                             => ( X88 @ ( ap @ X90 @ X92 ) ) ) )
                                                       => ( ! [X94: term] :
                                                              ( ! [X96: term] :
                                                                  ( ( X88 @ X96 )
                                                                 => ( X88 @ ( sub @ X94 @ ( push @ X96 @ id ) ) ) )
                                                             => ( X88 @ ( lam @ X94 ) ) )
                                                         => ! [X98: term,X100: subst] :
                                                              ( ! [X102: term] :
                                                                  ( ( var @ X102 )
                                                                 => ( X88 @ ( sub @ X102 @ X100 ) ) )
                                                             => ( X88 @ ( sub @ X98 @ X100 ) ) ) ) )
                                                   => ( ! [X104: term > $o] :
                                                          ( ! [X106: term] :
                                                              ( ( var @ X106 )
                                                             => ( X104 @ X106 ) )
                                                         => ( ! [X108: term,X110: term] :
                                                                ( ( X104 @ X108 )
                                                               => ( ( X104 @ X110 )
                                                                 => ( X104 @ ( ap @ X108 @ X110 ) ) ) )
                                                           => ( ! [X112: term] :
                                                                  ( ! [X114: term] :
                                                                      ( ( X104 @ X114 )
                                                                     => ( X104 @ ( sub @ X112 @ ( push @ X114 @ id ) ) ) )
                                                                 => ( X104 @ ( lam @ X112 ) ) )
                                                             => ! [X116: term] : ( X104 @ X116 ) ) ) )
                                                     => ( ( ! [X118: subst] :
                                                              ( ( comp @ X118 @ id )
                                                              = X118 )
                                                          & ! [X120: subst] :
                                                              ( ( comp @ id @ X120 )
                                                              = X120 )
                                                          & ! [X122: subst,X124: subst,X126: subst] :
                                                              ( ( comp @ ( comp @ X122 @ X124 ) @ X126 )
                                                              = ( comp @ X122 @ ( comp @ X124 @ X126 ) ) ) )
                                                       => ( ! [X128: term] :
                                                              ( ( sub @ X128 @ id )
                                                              = X128 )
                                                          & ! [X130: term,X132: subst,X134: subst] :
                                                              ( ( sub @ ( sub @ X130 @ X132 ) @ X134 )
                                                              = ( sub @ X130 @ ( comp @ X132 @ X134 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ( axapp
     => ( ! [X4: term,X6: subst] :
            ( ( sub @ one @ ( push @ X4 @ X6 ) )
            = X4 )
       => ( ! [X8: term] :
              ( ( sub @ X8 @ id )
              = X8 )
         => ( ! [X10: term,X12: subst] :
                ( ( sub @ ( lam @ X10 ) @ X12 )
                = ( lam @ ( sub @ X10 @ ( push @ one @ ( comp @ X12 @ sh ) ) ) ) )
           => ( ! [X14: term,X16: subst,X18: subst] :
                  ( ( sub @ ( sub @ X14 @ X16 ) @ X18 )
                  = ( sub @ X14 @ ( comp @ X16 @ X18 ) ) )
             => ( ! [X20: subst] :
                    ( ( comp @ id @ X20 )
                    = X20 )
               => ( ! [X22: term,X24: subst] :
                      ( ( comp @ sh @ ( push @ X22 @ X24 ) )
                      = X24 )
                 => ( ! [X26: subst,X28: subst,X30: subst] :
                        ( ( comp @ ( comp @ X26 @ X28 ) @ X30 )
                        = ( comp @ X26 @ ( comp @ X28 @ X30 ) ) )
                   => ( ! [X32: term,X34: subst,X36: subst] :
                          ( ( comp @ ( push @ X32 @ X34 ) @ X36 )
                          = ( push @ ( sub @ X32 @ X36 ) @ ( comp @ X34 @ X36 ) ) )
                     => ( ! [X38: subst] :
                            ( ( comp @ X38 @ id )
                            = X38 )
                       => ( ( ( push @ one @ sh )
                            = id )
                         => ( ! [X40: subst] :
                                ( ( push @ ( sub @ one @ X40 ) @ ( comp @ sh @ X40 ) )
                                = X40 )
                           => ( ( var @ one )
                             => ( ! [X42: term] :
                                    ( ( var @ X42 )
                                   => ( var @ ( sub @ X42 @ sh ) ) )
                               => ( ! [X44: term > $o] :
                                      ( ( X44 @ one )
                                     => ( ! [X46: term] :
                                            ( ( var @ X46 )
                                           => ( ( X44 @ X46 )
                                             => ( X44 @ ( sub @ X46 @ sh ) ) ) )
                                       => ! [X48: term] :
                                            ( ( var @ X48 )
                                           => ( X44 @ X48 ) ) ) )
                                 => ( apinj1
                                   => ( apinj2
                                     => ( ! [X50: term,X52: term] :
                                            ( ( ( lam @ X50 )
                                              = ( lam @ X52 ) )
                                           => ( X50 = X52 ) )
                                       => ( shinj
                                         => ( ! [X54: term,X56: term,X58: term] :
                                                ( ( lam @ X54 )
                                               != ( ap @ X56 @ X58 ) )
                                           => ( ! [X60: term,X62: term] :
                                                  ~ ( var @ ( ap @ X60 @ X62 ) )
                                             => ( ! [X64: term] :
                                                    ~ ( var @ ( lam @ X64 ) )
                                               => ( ! [X66: term > $o] :
                                                      ( ! [X68: term] :
                                                          ( ( var @ X68 )
                                                         => ( X66 @ X68 ) )
                                                     => ( ! [X70: term,X72: term] :
                                                            ( ( X66 @ X70 )
                                                           => ( ( X66 @ X72 )
                                                             => ( X66 @ ( ap @ X70 @ X72 ) ) ) )
                                                       => ( ! [X74: term] :
                                                              ( ( X66 @ X74 )
                                                             => ( X66 @ ( lam @ X74 ) ) )
                                                         => ! [X76: term] : ( X66 @ X76 ) ) ) )
                                                 => ( ! [X78: term > $o,X80: term,X82: subst] :
                                                        ( ! [X84: term] :
                                                            ( ( var @ X84 )
                                                           => ( X78 @ ( sub @ X84 @ X82 ) ) )
                                                       => ( ( X78 @ X80 )
                                                         => ! [X86: term] :
                                                              ( ( var @ X86 )
                                                             => ( X78 @ ( sub @ X86 @ ( push @ X80 @ X82 ) ) ) ) ) )
                                                   => ( ! [X88: term > $o] :
                                                          ( ! [X90: term,X92: term] :
                                                              ( ( X88 @ X90 )
                                                             => ( ( X88 @ X92 )
                                                               => ( X88 @ ( ap @ X90 @ X92 ) ) ) )
                                                         => ( ! [X94: term] :
                                                                ( ! [X96: term] :
                                                                    ( ( X88 @ X96 )
                                                                   => ( X88 @ ( sub @ X94 @ ( push @ X96 @ id ) ) ) )
                                                               => ( X88 @ ( lam @ X94 ) ) )
                                                           => ! [X98: term,X100: subst] :
                                                                ( ! [X102: term] :
                                                                    ( ( var @ X102 )
                                                                   => ( X88 @ ( sub @ X102 @ X100 ) ) )
                                                               => ( X88 @ ( sub @ X98 @ X100 ) ) ) ) )
                                                     => ( ! [X104: term > $o] :
                                                            ( ! [X106: term] :
                                                                ( ( var @ X106 )
                                                               => ( X104 @ X106 ) )
                                                           => ( ! [X108: term,X110: term] :
                                                                  ( ( X104 @ X108 )
                                                                 => ( ( X104 @ X110 )
                                                                   => ( X104 @ ( ap @ X108 @ X110 ) ) ) )
                                                             => ( ! [X112: term] :
                                                                    ( ! [X114: term] :
                                                                        ( ( X104 @ X114 )
                                                                       => ( X104 @ ( sub @ X112 @ ( push @ X114 @ id ) ) ) )
                                                                   => ( X104 @ ( lam @ X112 ) ) )
                                                               => ! [X116: term] : ( X104 @ X116 ) ) ) )
                                                       => ( ( ! [X118: subst] :
                                                                ( ( comp @ X118 @ id )
                                                                = X118 )
                                                            & ! [X120: subst] :
                                                                ( ( comp @ id @ X120 )
                                                                = X120 )
                                                            & ! [X122: subst,X124: subst,X126: subst] :
                                                                ( ( comp @ ( comp @ X122 @ X124 ) @ X126 )
                                                                = ( comp @ X122 @ ( comp @ X124 @ X126 ) ) ) )
                                                         => ( ! [X128: term] :
                                                                ( ( sub @ X128 @ id )
                                                                = X128 )
                                                            & ! [X130: term,X132: subst,X134: subst] :
                                                                ( ( sub @ ( sub @ X130 @ X132 ) @ X134 )
                                                                = ( sub @ X130 @ ( comp @ X132 @ X134 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl40,plain,
    ( ( ( sub @ sk__71 @ id )
     != sk__71 )
    | ( ( sub @ ( sub @ sk__72 @ sk__73 ) @ sk__74 )
     != ( sub @ sk__72 @ ( comp @ sk__73 @ sk__74 ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl1,plain,
    ! [X0: term] :
      ( ( sub @ X0 @ id )
      = X0 ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl2,plain,
    ! [X1: term,X2: subst,X3: subst] :
      ( ( sub @ ( sub @ X1 @ X2 ) @ X3 )
      = ( sub @ X1 @ ( comp @ X2 @ X3 ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_1]) ).

thf(zip_derived_cl236,plain,
    ( ( sk__71 != sk__71 )
    | ( ( sub @ ( sub @ sk__72 @ sk__73 ) @ sk__74 )
     != ( sub @ ( sub @ sk__72 @ sk__73 ) @ sk__74 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl40,zip_derived_cl1,zip_derived_cl2]) ).

thf(zip_derived_cl237,plain,
    $false,
    inference(simplify,[status(thm)],[zip_derived_cl236]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ALG255^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.aEzMqeBvjS true
% 0.15/0.35  % Computer : n013.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Mon Aug 28 04:10:32 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.15/0.35  % Running portfolio for 300 s
% 0.15/0.35  % File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.35  % Number of cores: 8
% 0.22/0.35  % Python version: Python 3.6.8
% 0.22/0.36  % Running in HO mode
% 0.22/0.68  % Total configuration time : 828
% 0.22/0.68  % Estimated wc time : 1656
% 0.22/0.68  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.74  % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.74  % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.76  % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.77  % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.25/0.80  % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.45/0.85  % Solved by lams/40_c.s.sh.
% 1.45/0.85  % done 28 iterations in 0.066s
% 1.45/0.85  % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.45/0.85  % SZS output start Refutation
% See solution above
% 1.45/0.85  
% 1.45/0.85  
% 1.45/0.85  % Terminating...
% 1.75/0.97  % Runner terminated.
% 1.75/0.98  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------