TSTP Solution File: ALG261^1 by E---3.1.00

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%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ALG261^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n024.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 : Mon May 20 18:05:55 EDT 2024

% Result   : Theorem 0.18s 0.50s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :  115
% Syntax   : Number of formulae    :  132 (  15 unt;  77 typ;   0 def)
%            Number of atoms       :  327 ( 166 equ;   0 cnn)
%            Maximal formula atoms :   69 (   5 avg)
%            Number of connectives : 2270 ( 113   ~; 147   |;  81   &;1654   @)
%                                         (  38 <=>; 237  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  161 (  10 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  160 ( 160   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   77 (  75 usr;  41 con; 0-4 aty)
%            Number of variables   :  485 (  36   ^ 449   !;   0   ?; 485   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    term: $tType ).

thf(decl_sort2,type,
    subst: $tType ).

thf(decl_22,type,
    one: term ).

thf(decl_23,type,
    ap: term > term > term ).

thf(decl_24,type,
    lam: term > term ).

thf(decl_25,type,
    sub: term > subst > term ).

thf(decl_26,type,
    id: subst ).

thf(decl_27,type,
    sh: subst ).

thf(decl_28,type,
    push: term > subst > subst ).

thf(decl_29,type,
    comp: subst > subst > subst ).

thf(decl_30,type,
    var: term > $o ).

thf(decl_33,type,
    axmap: $o ).

thf(decl_35,type,
    shinj: $o ).

thf(decl_38,type,
    hoasap: subst > term > subst > term > term ).

thf(decl_39,type,
    induction2lem: $o ).

thf(decl_41,type,
    axvarshift: $o ).

thf(decl_42,type,
    hoasapinj2: $o ).

thf(decl_43,type,
    hoasapnotvar_gthm: $o ).

thf(decl_44,type,
    hoasapinj1: $o ).

thf(decl_45,type,
    ulamvar1: $o ).

thf(decl_48,type,
    apnotvar: $o ).

thf(decl_53,type,
    hoaslaminj: $o ).

thf(decl_63,type,
    hoasapnotvar: $o ).

thf(decl_67,type,
    axapp: $o ).

thf(decl_71,type,
    ulamvarind: $o ).

thf(decl_72,type,
    induction: $o ).

thf(decl_82,type,
    axclos: $o ).

thf(decl_83,type,
    axassoc: $o ).

thf(decl_86,type,
    apinj2: $o ).

thf(decl_87,type,
    apinj1: $o ).

thf(decl_92,type,
    axvarcons: $o ).

thf(decl_93,type,
    hoaslam: subst > ( subst > term > term ) > term ).

thf(decl_94,type,
    axscons: $o ).

thf(decl_96,type,
    axidr: $o ).

thf(decl_98,type,
    laminj: $o ).

thf(decl_102,type,
    axabs: $o ).

thf(decl_108,type,
    lamnotap: $o ).

thf(decl_110,type,
    hoaslamnotvar: $o ).

thf(decl_111,type,
    axidl: $o ).

thf(decl_116,type,
    pushprop: $o ).

thf(decl_120,type,
    substmonoid: $o ).

thf(decl_121,type,
    lamnotvar: $o ).

thf(decl_127,type,
    hoasvar: subst > term > subst > $o ).

thf(decl_128,type,
    hoaslamnotap: $o ).

thf(decl_130,type,
    ulamvarsh: $o ).

thf(decl_131,type,
    induction2: $o ).

thf(decl_136,type,
    axshiftcons: $o ).

thf(decl_137,type,
    termmset: $o ).

thf(decl_142,type,
    axvarid: $o ).

thf(decl_144,type,
    esk1_1: ( term > $o ) > term ).

thf(decl_145,type,
    esk2_1: ( term > $o ) > term ).

thf(decl_146,type,
    esk3_1: ( term > $o ) > term ).

thf(decl_147,type,
    esk4_1: ( term > $o ) > term ).

thf(decl_148,type,
    esk5_1: ( term > $o ) > term ).

thf(decl_149,type,
    esk6_3: ( term > $o ) > term > subst > term ).

thf(decl_150,type,
    esk7_1: ( term > $o ) > term ).

thf(decl_151,type,
    esk8_1: ( term > $o ) > term ).

thf(decl_152,type,
    esk9_1: ( term > $o ) > term ).

thf(decl_153,type,
    esk10_3: ( term > $o ) > term > subst > term ).

thf(decl_154,type,
    esk11_1: ( term > $o ) > term ).

thf(decl_155,type,
    esk12_1: ( term > $o ) > term ).

thf(decl_156,type,
    esk13_1: ( term > $o ) > term ).

thf(decl_157,type,
    esk14_1: ( term > $o ) > term ).

thf(decl_158,type,
    esk15_1: ( subst > term > term ) > subst ).

thf(decl_159,type,
    esk16_1: ( subst > term > term ) > term ).

thf(decl_160,type,
    esk17_1: ( subst > term > term ) > subst ).

thf(decl_161,type,
    esk18_2: ( subst > term > term ) > ( subst > term > term ) > subst ).

thf(decl_162,type,
    esk19_2: ( subst > term > term ) > ( subst > term > term ) > term ).

thf(decl_163,type,
    esk20_2: ( subst > term > term ) > ( subst > term > term ) > subst ).

thf(decl_164,type,
    esk21_1: ( subst > term > term ) > subst ).

thf(decl_165,type,
    esk22_1: ( subst > term > term ) > term ).

thf(decl_166,type,
    esk23_1: ( subst > term > term ) > subst ).

thf(decl_167,type,
    esk24_1: ( subst > term > term ) > subst ).

thf(decl_168,type,
    esk25_1: ( subst > term > term ) > term ).

thf(decl_169,type,
    esk26_1: ( subst > term > term ) > subst ).

thf(decl_170,type,
    esk27_0: term ).

thf(decl_171,type,
    esk28_0: term ).

thf(hoaslamnotvar,axiom,
    ( hoaslamnotvar
  <=> ! [X12: subst > term > term] :
        ( ! [X3: subst,X1: term,X4: subst] :
            ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
            = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
       => ~ ( hoasvar @ id
            @ ( hoaslam @ id
              @ ^ [X3: subst,X1: term] : ( X12 @ X3 @ X1 ) )
            @ id ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoaslamnotvar) ).

thf(hoasvar,axiom,
    ( hoasvar
    = ( ^ [X3: subst,X1: term,X4: subst] : ( var @ ( sub @ X1 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasvar) ).

thf(hoaslaminj,axiom,
    ( hoaslaminj
  <=> ! [X12: subst > term > term] :
        ( ! [X3: subst,X1: term,X4: subst] :
            ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
            = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
       => ! [X13: subst > term > term] :
            ( ! [X3: subst,X1: term,X4: subst] :
                ( ( sub @ ( X13 @ X3 @ X1 ) @ X4 )
                = ( X13 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
           => ( ( ( hoaslam @ id
                  @ ^ [X3: subst,X1: term] : ( X12 @ X3 @ X1 ) )
                = ( hoaslam @ id
                  @ ^ [X3: subst,X1: term] : ( X13 @ X3 @ X1 ) ) )
             => ! [X3: subst,X1: term] :
                  ( ( X12 @ X3 @ X1 )
                  = ( X13 @ X3 @ X1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoaslaminj) ).

thf(hoaslamnotap,axiom,
    ( hoaslamnotap
  <=> ! [X12: subst > term > term] :
        ( ! [X3: subst,X1: term,X4: subst] :
            ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
            = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
       => ! [X1: term,X2: term] :
            ( ( hoaslam @ id
              @ ^ [X3: subst,X7: term] : ( X12 @ X3 @ X7 ) )
           != ( hoasap @ id @ X1 @ id @ X2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoaslamnotap) ).

thf(hoasapnotvar,axiom,
    ( hoasapnotvar
  <=> ! [X1: term,X2: term] :
        ~ ( hoasvar @ id @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasapnotvar) ).

thf(hoasapnotvar_gthm,axiom,
    ( hoasapnotvar_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
                                                           => ( hoasapinj1
                                                             => ( hoasapinj2
                                                               => ( hoaslaminj
                                                                 => ( hoaslamnotap
                                                                   => ( hoaslamnotvar
                                                                     => hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasapnotvar_gthm) ).

thf(axapp,axiom,
    ( axapp
  <=> ! [X1: term,X2: term,X3: subst] :
        ( ( sub @ ( ap @ X1 @ X2 ) @ X3 )
        = ( ap @ ( sub @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axapp) ).

thf(axvarcons,axiom,
    ( axvarcons
  <=> ! [X1: term,X3: subst] :
        ( ( sub @ one @ ( push @ X1 @ X3 ) )
        = X1 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarcons) ).

thf(axvarid,axiom,
    ( axvarid
  <=> ! [X1: term] :
        ( ( sub @ X1 @ id )
        = X1 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarid) ).

thf(axabs,axiom,
    ( axabs
  <=> ! [X1: term,X3: subst] :
        ( ( sub @ ( lam @ X1 ) @ X3 )
        = ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X3 @ sh ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axabs) ).

thf(axclos,axiom,
    ( axclos
  <=> ! [X1: term,X3: subst,X4: subst] :
        ( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
        = ( sub @ X1 @ ( comp @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axclos) ).

thf(axidl,axiom,
    ( axidl
  <=> ! [X3: subst] :
        ( ( comp @ id @ X3 )
        = X3 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axidl) ).

thf(axshiftcons,axiom,
    ( axshiftcons
  <=> ! [X1: term,X3: subst] :
        ( ( comp @ sh @ ( push @ X1 @ X3 ) )
        = X3 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axshiftcons) ).

thf(axassoc,axiom,
    ( axassoc
  <=> ! [X3: subst,X4: subst,X5: subst] :
        ( ( comp @ ( comp @ X3 @ X4 ) @ X5 )
        = ( comp @ X3 @ ( comp @ X4 @ X5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axassoc) ).

thf(axmap,axiom,
    ( axmap
  <=> ! [X1: term,X3: subst,X4: subst] :
        ( ( comp @ ( push @ X1 @ X3 ) @ X4 )
        = ( push @ ( sub @ X1 @ X4 ) @ ( comp @ X3 @ X4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axmap) ).

thf(axidr,axiom,
    ( axidr
  <=> ! [X3: subst] :
        ( ( comp @ X3 @ id )
        = X3 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axidr) ).

thf(axvarshift,axiom,
    ( axvarshift
  <=> ( ( push @ one @ sh )
      = id ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarshift) ).

thf(axscons,axiom,
    ( axscons
  <=> ! [X3: subst] :
        ( ( push @ ( sub @ one @ X3 ) @ ( comp @ sh @ X3 ) )
        = X3 ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axscons) ).

thf(ulamvar1,axiom,
    ( ulamvar1
  <=> ( var @ one ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',ulamvar1) ).

thf(ulamvarsh,axiom,
    ( ulamvarsh
  <=> ! [X1: term] :
        ( ( var @ X1 )
       => ( var @ ( sub @ X1 @ sh ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',ulamvarsh) ).

thf(ulamvarind,axiom,
    ( ulamvarind
  <=> ! [X6: term > $o] :
        ( ( X6 @ one )
       => ( ! [X1: term] :
              ( ( var @ X1 )
             => ( ( X6 @ X1 )
               => ( X6 @ ( sub @ X1 @ sh ) ) ) )
         => ! [X1: term] :
              ( ( var @ X1 )
             => ( X6 @ X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',ulamvarind) ).

thf(apinj1,axiom,
    ( apinj1
  <=> ! [X1: term,X2: term,X7: term,X8: term] :
        ( ( ( ap @ X1 @ X7 )
          = ( ap @ X2 @ X8 ) )
       => ( X1 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',apinj1) ).

thf(apinj2,axiom,
    ( apinj2
  <=> ! [X1: term,X2: term,X7: term,X8: term] :
        ( ( ( ap @ X1 @ X7 )
          = ( ap @ X2 @ X8 ) )
       => ( X7 = X8 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',apinj2) ).

thf(laminj,axiom,
    ( laminj
  <=> ! [X1: term,X2: term] :
        ( ( ( lam @ X1 )
          = ( lam @ X2 ) )
       => ( X1 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',laminj) ).

thf(shinj,axiom,
    ( shinj
  <=> ! [X1: term,X2: term] :
        ( ( ( sub @ X1 @ sh )
          = ( sub @ X2 @ sh ) )
       => ( X1 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',shinj) ).

thf(lamnotap,axiom,
    ( lamnotap
  <=> ! [X1: term,X2: term,X7: term] :
        ( ( lam @ X1 )
       != ( ap @ X2 @ X7 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',lamnotap) ).

thf(apnotvar,axiom,
    ( apnotvar
  <=> ! [X1: term,X2: term] :
        ~ ( var @ ( ap @ X1 @ X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',apnotvar) ).

thf(lamnotvar,axiom,
    ( lamnotvar
  <=> ! [X1: term] :
        ~ ( var @ ( lam @ X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',lamnotvar) ).

thf(induction,axiom,
    ( induction
  <=> ! [X6: term > $o] :
        ( ! [X1: term] :
            ( ( var @ X1 )
           => ( X6 @ X1 ) )
       => ( ! [X1: term,X2: term] :
              ( ( X6 @ X1 )
             => ( ( X6 @ X2 )
               => ( X6 @ ( ap @ X1 @ X2 ) ) ) )
         => ( ! [X1: term] :
                ( ( X6 @ X1 )
               => ( X6 @ ( lam @ X1 ) ) )
           => ! [X1: term] : ( X6 @ X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',induction) ).

thf(pushprop,axiom,
    ( pushprop
  <=> ! [X6: term > $o,X1: term,X3: subst] :
        ( ! [X2: term] :
            ( ( var @ X2 )
           => ( X6 @ ( sub @ X2 @ X3 ) ) )
       => ( ( X6 @ X1 )
         => ! [X2: term] :
              ( ( var @ X2 )
             => ( X6 @ ( sub @ X2 @ ( push @ X1 @ X3 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',pushprop) ).

thf(induction2lem,axiom,
    ( induction2lem
  <=> ! [X6: term > $o] :
        ( ! [X1: term,X2: term] :
            ( ( X6 @ X1 )
           => ( ( X6 @ X2 )
             => ( X6 @ ( ap @ X1 @ X2 ) ) ) )
       => ( ! [X1: term] :
              ( ! [X2: term] :
                  ( ( X6 @ X2 )
                 => ( X6 @ ( sub @ X1 @ ( push @ X2 @ id ) ) ) )
             => ( X6 @ ( lam @ X1 ) ) )
         => ! [X1: term,X3: subst] :
              ( ! [X2: term] :
                  ( ( var @ X2 )
                 => ( X6 @ ( sub @ X2 @ X3 ) ) )
             => ( X6 @ ( sub @ X1 @ X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',induction2lem) ).

thf(induction2,axiom,
    ( induction2
  <=> ! [X6: term > $o] :
        ( ! [X1: term] :
            ( ( var @ X1 )
           => ( X6 @ X1 ) )
       => ( ! [X1: term,X2: term] :
              ( ( X6 @ X1 )
             => ( ( X6 @ X2 )
               => ( X6 @ ( ap @ X1 @ X2 ) ) ) )
         => ( ! [X1: term] :
                ( ! [X2: term] :
                    ( ( X6 @ X2 )
                   => ( X6 @ ( sub @ X1 @ ( push @ X2 @ id ) ) ) )
               => ( X6 @ ( lam @ X1 ) ) )
           => ! [X1: term] : ( X6 @ X1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',induction2) ).

thf(substmonoid,axiom,
    ( substmonoid
  <=> ( ! [X3: subst,X4: subst,X5: subst] :
          ( ( comp @ ( comp @ X3 @ X4 ) @ X5 )
          = ( comp @ X3 @ ( comp @ X4 @ X5 ) ) )
      & ! [X3: subst] :
          ( ( comp @ id @ X3 )
          = X3 )
      & ! [X3: subst] :
          ( ( comp @ X3 @ id )
          = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',substmonoid) ).

thf(termmset,axiom,
    ( termmset
  <=> ( ! [X1: term,X3: subst,X4: subst] :
          ( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
          = ( sub @ X1 @ ( comp @ X3 @ X4 ) ) )
      & ! [X1: term] :
          ( ( sub @ X1 @ id )
          = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',termmset) ).

thf(hoasapinj1,axiom,
    ( hoasapinj1
  <=> ! [X1: term,X2: term,X7: term,X8: term] :
        ( ( ( hoasap @ id @ X1 @ id @ X7 )
          = ( hoasap @ id @ X2 @ id @ X8 ) )
       => ( X1 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasapinj1) ).

thf(hoasapinj2,axiom,
    ( hoasapinj2
  <=> ! [X1: term,X2: term,X7: term,X8: term] :
        ( ( ( hoasap @ id @ X1 @ id @ X7 )
          = ( hoasap @ id @ X2 @ id @ X8 ) )
       => ( X7 = X8 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasapinj2) ).

thf(thm,conjecture,
    hoasapnotvar_gthm,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(hoasap,axiom,
    ( hoasap
    = ( ^ [X3: subst,X1: term,X4: subst,X2: term] : ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasap) ).

thf(c_0_38,plain,
    ( hoaslamnotvar
  <=> ! [X12: subst > term > term] :
        ( ! [X3: subst,X1: term,X4: subst] :
            ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
            = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
       => ~ ( hoasvar @ id
            @ ( hoaslam @ id
              @ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
            @ id ) ) ),
    inference(fof_simplification,[status(thm)],[hoaslamnotvar]) ).

thf(c_0_39,plain,
    ( hoasvar
    = ( ^ [Z0: subst,Z1: term,Z2: subst] : ( var @ ( sub @ Z1 @ Z2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[hoasvar]) ).

thf(c_0_40,plain,
    ( hoaslaminj
  <=> ! [X12: subst > term > term] :
        ( ! [X3: subst,X1: term,X4: subst] :
            ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
            = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
       => ! [X13: subst > term > term] :
            ( ! [X3: subst,X1: term,X4: subst] :
                ( ( sub @ ( X13 @ X3 @ X1 ) @ X4 )
                = ( X13 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
           => ( ( ( hoaslam @ id
                  @ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
                = ( hoaslam @ id
                  @ ^ [Z0: subst,Z1: term] : ( X13 @ Z0 @ Z1 ) ) )
             => ! [X3: subst,X1: term] :
                  ( ( X12 @ X3 @ X1 )
                  = ( X13 @ X3 @ X1 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[hoaslaminj]) ).

thf(c_0_41,plain,
    ( hoaslamnotap
  <=> ! [X12: subst > term > term] :
        ( ! [X3: subst,X1: term,X4: subst] :
            ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
            = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
       => ! [X1: term,X2: term] :
            ( ( hoaslam @ id
              @ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
           != ( hoasap @ id @ X1 @ id @ X2 ) ) ) ),
    inference(fof_simplification,[status(thm)],[hoaslamnotap]) ).

thf(c_0_42,plain,
    ( hoaslamnotvar
    = ( ! [X12: subst > term > term] :
          ( ! [X3: subst,X1: term,X4: subst] :
              ( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
              = ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
         => ~ ( var
              @ ( sub
                @ ( hoaslam @ id
                  @ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
                @ id ) ) ) ) ),
    inference(apply_def,[status(thm)],[c_0_38,c_0_39]) ).

thf(c_0_43,axiom,
    ( hoasapnotvar
    = ( ! [X1: term,X2: term] :
          ~ ( var @ ( sub @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ) ) ),
    inference(apply_def,[status(thm)],[hoasapnotvar,c_0_39]) ).

thf(c_0_44,axiom,
    ( hoasapnotvar_gthm
    = ( ! [X548: term,X549: term,X550: subst] :
          ( ( sub @ ( ap @ X548 @ X549 ) @ X550 )
          = ( ap @ ( sub @ X548 @ X550 ) @ ( sub @ X549 @ X550 ) ) )
     => ( ! [X551: term,X552: subst] :
            ( ( sub @ one @ ( push @ X551 @ X552 ) )
            = X551 )
       => ( ! [X553: term] :
              ( ( sub @ X553 @ id )
              = X553 )
         => ( ! [X554: term,X555: subst] :
                ( ( sub @ ( lam @ X554 ) @ X555 )
                = ( lam @ ( sub @ X554 @ ( push @ one @ ( comp @ X555 @ sh ) ) ) ) )
           => ( ! [X556: term,X557: subst,X558: subst] :
                  ( ( sub @ ( sub @ X556 @ X557 ) @ X558 )
                  = ( sub @ X556 @ ( comp @ X557 @ X558 ) ) )
             => ( ! [X559: subst] :
                    ( ( comp @ id @ X559 )
                    = X559 )
               => ( ! [X560: term,X561: subst] :
                      ( ( comp @ sh @ ( push @ X560 @ X561 ) )
                      = X561 )
                 => ( ! [X562: subst,X563: subst,X564: subst] :
                        ( ( comp @ ( comp @ X562 @ X563 ) @ X564 )
                        = ( comp @ X562 @ ( comp @ X563 @ X564 ) ) )
                   => ( ! [X565: term,X566: subst,X567: subst] :
                          ( ( comp @ ( push @ X565 @ X566 ) @ X567 )
                          = ( push @ ( sub @ X565 @ X567 ) @ ( comp @ X566 @ X567 ) ) )
                     => ( ! [X568: subst] :
                            ( ( comp @ X568 @ id )
                            = X568 )
                       => ( ( ( push @ one @ sh )
                            = id )
                         => ( ! [X569: subst] :
                                ( ( push @ ( sub @ one @ X569 ) @ ( comp @ sh @ X569 ) )
                                = X569 )
                           => ( ( var @ one )
                             => ( ! [X570: term] :
                                    ( ( var @ X570 )
                                   => ( var @ ( sub @ X570 @ sh ) ) )
                               => ( ! [X571: term > $o] :
                                      ( ( X571 @ one )
                                     => ( ! [X572: term] :
                                            ( ( var @ X572 )
                                           => ( ( X571 @ X572 )
                                             => ( X571 @ ( sub @ X572 @ sh ) ) ) )
                                       => ! [X573: term] :
                                            ( ( var @ X573 )
                                           => ( X571 @ X573 ) ) ) )
                                 => ( ! [X574: term,X575: term,X576: term,X577: term] :
                                        ( ( ( ap @ X574 @ X576 )
                                          = ( ap @ X575 @ X577 ) )
                                       => ( X574 = X575 ) )
                                   => ( ! [X578: term,X579: term,X580: term,X581: term] :
                                          ( ( ( ap @ X578 @ X580 )
                                            = ( ap @ X579 @ X581 ) )
                                         => ( X580 = X581 ) )
                                     => ( ! [X582: term,X583: term] :
                                            ( ( ( lam @ X582 )
                                              = ( lam @ X583 ) )
                                           => ( X582 = X583 ) )
                                       => ( ! [X584: term,X585: term] :
                                              ( ( ( sub @ X584 @ sh )
                                                = ( sub @ X585 @ sh ) )
                                             => ( X584 = X585 ) )
                                         => ( ! [X586: term,X587: term,X588: term] :
                                                ( ( lam @ X586 )
                                               != ( ap @ X587 @ X588 ) )
                                           => ( ! [X589: term,X590: term] :
                                                  ~ ( var @ ( ap @ X589 @ X590 ) )
                                             => ( ! [X591: term] :
                                                    ~ ( var @ ( lam @ X591 ) )
                                               => ( ! [X592: term > $o] :
                                                      ( ! [X593: term] :
                                                          ( ( var @ X593 )
                                                         => ( X592 @ X593 ) )
                                                     => ( ! [X594: term,X595: term] :
                                                            ( ( X592 @ X594 )
                                                           => ( ( X592 @ X595 )
                                                             => ( X592 @ ( ap @ X594 @ X595 ) ) ) )
                                                       => ( ! [X596: term] :
                                                              ( ( X592 @ X596 )
                                                             => ( X592 @ ( lam @ X596 ) ) )
                                                         => ! [X597: term] : ( X592 @ X597 ) ) ) )
                                                 => ( ! [X598: term > $o,X599: term,X600: subst] :
                                                        ( ! [X601: term] :
                                                            ( ( var @ X601 )
                                                           => ( X598 @ ( sub @ X601 @ X600 ) ) )
                                                       => ( ( X598 @ X599 )
                                                         => ! [X602: term] :
                                                              ( ( var @ X602 )
                                                             => ( X598 @ ( sub @ X602 @ ( push @ X599 @ X600 ) ) ) ) ) )
                                                   => ( ! [X603: term > $o] :
                                                          ( ! [X604: term,X605: term] :
                                                              ( ( X603 @ X604 )
                                                             => ( ( X603 @ X605 )
                                                               => ( X603 @ ( ap @ X604 @ X605 ) ) ) )
                                                         => ( ! [X606: term] :
                                                                ( ! [X607: term] :
                                                                    ( ( X603 @ X607 )
                                                                   => ( X603 @ ( sub @ X606 @ ( push @ X607 @ id ) ) ) )
                                                               => ( X603 @ ( lam @ X606 ) ) )
                                                           => ! [X608: term,X609: subst] :
                                                                ( ! [X610: term] :
                                                                    ( ( var @ X610 )
                                                                   => ( X603 @ ( sub @ X610 @ X609 ) ) )
                                                               => ( X603 @ ( sub @ X608 @ X609 ) ) ) ) )
                                                     => ( ! [X611: term > $o] :
                                                            ( ! [X612: term] :
                                                                ( ( var @ X612 )
                                                               => ( X611 @ X612 ) )
                                                           => ( ! [X613: term,X614: term] :
                                                                  ( ( X611 @ X613 )
                                                                 => ( ( X611 @ X614 )
                                                                   => ( X611 @ ( ap @ X613 @ X614 ) ) ) )
                                                             => ( ! [X615: term] :
                                                                    ( ! [X616: term] :
                                                                        ( ( X611 @ X616 )
                                                                       => ( X611 @ ( sub @ X615 @ ( push @ X616 @ id ) ) ) )
                                                                   => ( X611 @ ( lam @ X615 ) ) )
                                                               => ! [X617: term] : ( X611 @ X617 ) ) ) )
                                                       => ( ( ! [X618: subst,X619: subst,X620: subst] :
                                                                ( ( comp @ ( comp @ X618 @ X619 ) @ X620 )
                                                                = ( comp @ X618 @ ( comp @ X619 @ X620 ) ) )
                                                            & ! [X621: subst] :
                                                                ( ( comp @ id @ X621 )
                                                                = X621 )
                                                            & ! [X622: subst] :
                                                                ( ( comp @ X622 @ id )
                                                                = X622 ) )
                                                         => ( ( ! [X623: term,X624: subst,X625: subst] :
                                                                  ( ( sub @ ( sub @ X623 @ X624 ) @ X625 )
                                                                  = ( sub @ X623 @ ( comp @ X624 @ X625 ) ) )
                                                              & ! [X626: term] :
                                                                  ( ( sub @ X626 @ id )
                                                                  = X626 ) )
                                                           => ( ! [X627: term,X628: term,X629: term,X630: term] :
                                                                  ( ( ( hoasap @ id @ X627 @ id @ X629 )
                                                                    = ( hoasap @ id @ X628 @ id @ X630 ) )
                                                                 => ( X627 = X628 ) )
                                                             => ( ! [X631: term,X632: term,X633: term,X634: term] :
                                                                    ( ( ( hoasap @ id @ X631 @ id @ X633 )
                                                                      = ( hoasap @ id @ X632 @ id @ X634 ) )
                                                                   => ( X633 = X634 ) )
                                                               => ( ! [X635: subst > term > term] :
                                                                      ( ! [X636: subst,X637: term,X638: subst] :
                                                                          ( ( sub @ ( X635 @ X636 @ X637 ) @ X638 )
                                                                          = ( X635 @ ( comp @ X636 @ X638 ) @ ( sub @ X637 @ X638 ) ) )
                                                                     => ! [X639: subst > term > term] :
                                                                          ( ! [X640: subst,X641: term,X642: subst] :
                                                                              ( ( sub @ ( X639 @ X640 @ X641 ) @ X642 )
                                                                              = ( X639 @ ( comp @ X640 @ X642 ) @ ( sub @ X641 @ X642 ) ) )
                                                                         => ( ( ( hoaslam @ id
                                                                                @ ^ [Z0: subst,Z1: term] : ( X635 @ Z0 @ Z1 ) )
                                                                              = ( hoaslam @ id
                                                                                @ ^ [Z0: subst,Z1: term] : ( X639 @ Z0 @ Z1 ) ) )
                                                                           => ! [X643: subst,X644: term] :
                                                                                ( ( X635 @ X643 @ X644 )
                                                                                = ( X639 @ X643 @ X644 ) ) ) ) )
                                                                 => ( ! [X645: subst > term > term] :
                                                                        ( ! [X646: subst,X647: term,X648: subst] :
                                                                            ( ( sub @ ( X645 @ X646 @ X647 ) @ X648 )
                                                                            = ( X645 @ ( comp @ X646 @ X648 ) @ ( sub @ X647 @ X648 ) ) )
                                                                       => ! [X649: term,X650: term] :
                                                                            ( ( hoaslam @ id
                                                                              @ ^ [Z0: subst,Z1: term] : ( X645 @ Z0 @ Z1 ) )
                                                                           != ( hoasap @ id @ X649 @ id @ X650 ) ) )
                                                                   => ( ! [X651: subst > term > term] :
                                                                          ( ! [X652: subst,X653: term,X654: subst] :
                                                                              ( ( sub @ ( X651 @ X652 @ X653 ) @ X654 )
                                                                              = ( X651 @ ( comp @ X652 @ X654 ) @ ( sub @ X653 @ X654 ) ) )
                                                                         => ~ ( var
                                                                              @ ( sub
                                                                                @ ( hoaslam @ id
                                                                                  @ ^ [Z0: subst,Z1: term] : ( X651 @ Z0 @ Z1 ) )
                                                                                @ id ) ) )
                                                                     => ! [X655: term,X656: term] :
                                                                          ~ ( var @ ( sub @ ( hoasap @ id @ X655 @ id @ X656 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoasapnotvar_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]),c_0_39]),hoasapinj1]),hoasapinj2]),c_0_40]),c_0_41]),c_0_42]),c_0_43]) ).

thf(c_0_45,negated_conjecture,
    ~ ( ! [X3373: term,X3374: term,X3375: subst] :
          ( ( sub @ ( ap @ X3373 @ X3374 ) @ X3375 )
          = ( ap @ ( sub @ X3373 @ X3375 ) @ ( sub @ X3374 @ X3375 ) ) )
     => ( ! [X3376: term,X3377: subst] :
            ( ( sub @ one @ ( push @ X3376 @ X3377 ) )
            = X3376 )
       => ( ! [X3378: term] :
              ( ( sub @ X3378 @ id )
              = X3378 )
         => ( ! [X3379: term,X3380: subst] :
                ( ( sub @ ( lam @ X3379 ) @ X3380 )
                = ( lam @ ( sub @ X3379 @ ( push @ one @ ( comp @ X3380 @ sh ) ) ) ) )
           => ( ! [X3381: term,X3382: subst,X3383: subst] :
                  ( ( sub @ ( sub @ X3381 @ X3382 ) @ X3383 )
                  = ( sub @ X3381 @ ( comp @ X3382 @ X3383 ) ) )
             => ( ! [X3384: subst] :
                    ( ( comp @ id @ X3384 )
                    = X3384 )
               => ( ! [X3385: term,X3386: subst] :
                      ( ( comp @ sh @ ( push @ X3385 @ X3386 ) )
                      = X3386 )
                 => ( ! [X3387: subst,X3388: subst,X3389: subst] :
                        ( ( comp @ ( comp @ X3387 @ X3388 ) @ X3389 )
                        = ( comp @ X3387 @ ( comp @ X3388 @ X3389 ) ) )
                   => ( ! [X3390: term,X3391: subst,X3392: subst] :
                          ( ( comp @ ( push @ X3390 @ X3391 ) @ X3392 )
                          = ( push @ ( sub @ X3390 @ X3392 ) @ ( comp @ X3391 @ X3392 ) ) )
                     => ( ! [X3393: subst] :
                            ( ( comp @ X3393 @ id )
                            = X3393 )
                       => ( ( ( push @ one @ sh )
                            = id )
                         => ( ! [X3394: subst] :
                                ( ( push @ ( sub @ one @ X3394 ) @ ( comp @ sh @ X3394 ) )
                                = X3394 )
                           => ( ( var @ one )
                             => ( ! [X3395: term] :
                                    ( ( var @ X3395 )
                                   => ( var @ ( sub @ X3395 @ sh ) ) )
                               => ( ! [X3396: term > $o] :
                                      ( ( X3396 @ one )
                                     => ( ! [X3397: term] :
                                            ( ( var @ X3397 )
                                           => ( ( X3396 @ X3397 )
                                             => ( X3396 @ ( sub @ X3397 @ sh ) ) ) )
                                       => ! [X3398: term] :
                                            ( ( var @ X3398 )
                                           => ( X3396 @ X3398 ) ) ) )
                                 => ( ! [X3399: term,X3400: term,X3401: term,X3402: term] :
                                        ( ( ( ap @ X3399 @ X3401 )
                                          = ( ap @ X3400 @ X3402 ) )
                                       => ( X3399 = X3400 ) )
                                   => ( ! [X3403: term,X3404: term,X3405: term,X3406: term] :
                                          ( ( ( ap @ X3403 @ X3405 )
                                            = ( ap @ X3404 @ X3406 ) )
                                         => ( X3405 = X3406 ) )
                                     => ( ! [X3407: term,X3408: term] :
                                            ( ( ( lam @ X3407 )
                                              = ( lam @ X3408 ) )
                                           => ( X3407 = X3408 ) )
                                       => ( ! [X3409: term,X3410: term] :
                                              ( ( ( sub @ X3409 @ sh )
                                                = ( sub @ X3410 @ sh ) )
                                             => ( X3409 = X3410 ) )
                                         => ( ! [X3411: term,X3412: term,X3413: term] :
                                                ( ( lam @ X3411 )
                                               != ( ap @ X3412 @ X3413 ) )
                                           => ( ! [X3414: term,X3415: term] :
                                                  ~ ( var @ ( ap @ X3414 @ X3415 ) )
                                             => ( ! [X3416: term] :
                                                    ~ ( var @ ( lam @ X3416 ) )
                                               => ( ! [X3417: term > $o] :
                                                      ( ! [X3418: term] :
                                                          ( ( var @ X3418 )
                                                         => ( X3417 @ X3418 ) )
                                                     => ( ! [X3419: term,X3420: term] :
                                                            ( ( X3417 @ X3419 )
                                                           => ( ( X3417 @ X3420 )
                                                             => ( X3417 @ ( ap @ X3419 @ X3420 ) ) ) )
                                                       => ( ! [X3421: term] :
                                                              ( ( X3417 @ X3421 )
                                                             => ( X3417 @ ( lam @ X3421 ) ) )
                                                         => ! [X3422: term] : ( X3417 @ X3422 ) ) ) )
                                                 => ( ! [X3423: term > $o,X3424: term,X3425: subst] :
                                                        ( ! [X3426: term] :
                                                            ( ( var @ X3426 )
                                                           => ( X3423 @ ( sub @ X3426 @ X3425 ) ) )
                                                       => ( ( X3423 @ X3424 )
                                                         => ! [X3427: term] :
                                                              ( ( var @ X3427 )
                                                             => ( X3423 @ ( sub @ X3427 @ ( push @ X3424 @ X3425 ) ) ) ) ) )
                                                   => ( ! [X3428: term > $o] :
                                                          ( ! [X3429: term,X3430: term] :
                                                              ( ( X3428 @ X3429 )
                                                             => ( ( X3428 @ X3430 )
                                                               => ( X3428 @ ( ap @ X3429 @ X3430 ) ) ) )
                                                         => ( ! [X3431: term] :
                                                                ( ! [X3432: term] :
                                                                    ( ( X3428 @ X3432 )
                                                                   => ( X3428 @ ( sub @ X3431 @ ( push @ X3432 @ id ) ) ) )
                                                               => ( X3428 @ ( lam @ X3431 ) ) )
                                                           => ! [X3433: term,X3434: subst] :
                                                                ( ! [X3435: term] :
                                                                    ( ( var @ X3435 )
                                                                   => ( X3428 @ ( sub @ X3435 @ X3434 ) ) )
                                                               => ( X3428 @ ( sub @ X3433 @ X3434 ) ) ) ) )
                                                     => ( ! [X3436: term > $o] :
                                                            ( ! [X3437: term] :
                                                                ( ( var @ X3437 )
                                                               => ( X3436 @ X3437 ) )
                                                           => ( ! [X3438: term,X3439: term] :
                                                                  ( ( X3436 @ X3438 )
                                                                 => ( ( X3436 @ X3439 )
                                                                   => ( X3436 @ ( ap @ X3438 @ X3439 ) ) ) )
                                                             => ( ! [X3440: term] :
                                                                    ( ! [X3441: term] :
                                                                        ( ( X3436 @ X3441 )
                                                                       => ( X3436 @ ( sub @ X3440 @ ( push @ X3441 @ id ) ) ) )
                                                                   => ( X3436 @ ( lam @ X3440 ) ) )
                                                               => ! [X3442: term] : ( X3436 @ X3442 ) ) ) )
                                                       => ( ( ! [X3443: subst,X3444: subst,X3445: subst] :
                                                                ( ( comp @ ( comp @ X3443 @ X3444 ) @ X3445 )
                                                                = ( comp @ X3443 @ ( comp @ X3444 @ X3445 ) ) )
                                                            & ! [X3446: subst] :
                                                                ( ( comp @ id @ X3446 )
                                                                = X3446 )
                                                            & ! [X3447: subst] :
                                                                ( ( comp @ X3447 @ id )
                                                                = X3447 ) )
                                                         => ( ( ! [X3448: term,X3449: subst,X3450: subst] :
                                                                  ( ( sub @ ( sub @ X3448 @ X3449 ) @ X3450 )
                                                                  = ( sub @ X3448 @ ( comp @ X3449 @ X3450 ) ) )
                                                              & ! [X3451: term] :
                                                                  ( ( sub @ X3451 @ id )
                                                                  = X3451 ) )
                                                           => ( ! [X3452: term,X3453: term,X3454: term,X3455: term] :
                                                                  ( ( ( hoasap @ id @ X3452 @ id @ X3454 )
                                                                    = ( hoasap @ id @ X3453 @ id @ X3455 ) )
                                                                 => ( X3452 = X3453 ) )
                                                             => ( ! [X3456: term,X3457: term,X3458: term,X3459: term] :
                                                                    ( ( ( hoasap @ id @ X3456 @ id @ X3458 )
                                                                      = ( hoasap @ id @ X3457 @ id @ X3459 ) )
                                                                   => ( X3458 = X3459 ) )
                                                               => ( ! [X3460: subst > term > term] :
                                                                      ( ! [X3461: subst,X3462: term,X3463: subst] :
                                                                          ( ( sub @ ( X3460 @ X3461 @ X3462 ) @ X3463 )
                                                                          = ( X3460 @ ( comp @ X3461 @ X3463 ) @ ( sub @ X3462 @ X3463 ) ) )
                                                                     => ! [X3464: subst > term > term] :
                                                                          ( ! [X3465: subst,X3466: term,X3467: subst] :
                                                                              ( ( sub @ ( X3464 @ X3465 @ X3466 ) @ X3467 )
                                                                              = ( X3464 @ ( comp @ X3465 @ X3467 ) @ ( sub @ X3466 @ X3467 ) ) )
                                                                         => ( ( ( hoaslam @ id @ X3460 )
                                                                              = ( hoaslam @ id @ X3464 ) )
                                                                           => ! [X3468: subst,X3469: term] :
                                                                                ( ( X3460 @ X3468 @ X3469 )
                                                                                = ( X3464 @ X3468 @ X3469 ) ) ) ) )
                                                                 => ( ! [X3470: subst > term > term] :
                                                                        ( ! [X3471: subst,X3472: term,X3473: subst] :
                                                                            ( ( sub @ ( X3470 @ X3471 @ X3472 ) @ X3473 )
                                                                            = ( X3470 @ ( comp @ X3471 @ X3473 ) @ ( sub @ X3472 @ X3473 ) ) )
                                                                       => ! [X3474: term,X3475: term] :
                                                                            ( ( hoaslam @ id @ X3470 )
                                                                           != ( hoasap @ id @ X3474 @ id @ X3475 ) ) )
                                                                   => ( ! [X3476: subst > term > term] :
                                                                          ( ! [X3477: subst,X3478: term,X3479: subst] :
                                                                              ( ( sub @ ( X3476 @ X3477 @ X3478 ) @ X3479 )
                                                                              = ( X3476 @ ( comp @ X3477 @ X3479 ) @ ( sub @ X3478 @ X3479 ) ) )
                                                                         => ~ ( var @ ( sub @ ( hoaslam @ id @ X3476 ) @ id ) ) )
                                                                     => ! [X3480: term,X3481: term] :
                                                                          ~ ( var @ ( sub @ ( hoasap @ id @ X3480 @ id @ X3481 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_44])])]) ).

thf(c_0_46,negated_conjecture,
    ! [X3494: term,X3495: term,X3496: subst,X3497: term,X3498: subst,X3499: term,X3500: term,X3501: subst,X3502: term,X3503: subst,X3504: subst,X3505: subst,X3506: term,X3507: subst,X3508: subst,X3509: subst,X3510: subst,X3511: term,X3512: subst,X3513: subst,X3514: subst,X3515: subst,X3516: term,X3517: term > $o,X3519: term,X3520: term,X3521: term,X3522: term,X3523: term,X3524: term,X3525: term,X3526: term,X3527: term,X3528: term,X3529: term,X3530: term,X3531: term,X3532: term,X3533: term,X3534: term,X3535: term,X3536: term,X3537: term,X3538: term > $o,X3543: term,X3544: term > $o,X3545: term,X3546: subst,X3548: term,X3549: term > $o,X3553: term,X3554: term,X3555: subst,X3557: term > $o,X3562: term,X3563: term,X3564: subst,X3565: subst,X3566: subst,X3567: subst,X3568: subst,X3569: term,X3570: subst,X3571: subst,X3572: term,X3573: term,X3574: term,X3575: term,X3576: term,X3577: term,X3578: term,X3579: term,X3580: term,X3581: subst > term > term,X3585: subst > term > term,X3589: subst,X3590: term,X3591: subst > term > term,X3595: term,X3596: term,X3597: subst > term > term] :
      ( ( ( sub @ ( ap @ X3494 @ X3495 ) @ X3496 )
        = ( ap @ ( sub @ X3494 @ X3496 ) @ ( sub @ X3495 @ X3496 ) ) )
      & ( ( sub @ one @ ( push @ X3497 @ X3498 ) )
        = X3497 )
      & ( ( sub @ X3499 @ id )
        = X3499 )
      & ( ( sub @ ( lam @ X3500 ) @ X3501 )
        = ( lam @ ( sub @ X3500 @ ( push @ one @ ( comp @ X3501 @ sh ) ) ) ) )
      & ( ( sub @ ( sub @ X3502 @ X3503 ) @ X3504 )
        = ( sub @ X3502 @ ( comp @ X3503 @ X3504 ) ) )
      & ( ( comp @ id @ X3505 )
        = X3505 )
      & ( ( comp @ sh @ ( push @ X3506 @ X3507 ) )
        = X3507 )
      & ( ( comp @ ( comp @ X3508 @ X3509 ) @ X3510 )
        = ( comp @ X3508 @ ( comp @ X3509 @ X3510 ) ) )
      & ( ( comp @ ( push @ X3511 @ X3512 ) @ X3513 )
        = ( push @ ( sub @ X3511 @ X3513 ) @ ( comp @ X3512 @ X3513 ) ) )
      & ( ( comp @ X3514 @ id )
        = X3514 )
      & ( ( push @ one @ sh )
        = id )
      & ( ( push @ ( sub @ one @ X3515 ) @ ( comp @ sh @ X3515 ) )
        = X3515 )
      & ( var @ one )
      & ( ~ ( var @ X3516 )
        | ( var @ ( sub @ X3516 @ sh ) ) )
      & ( ( var @ ( esk1_1 @ X3517 ) )
        | ~ ( var @ X3519 )
        | ( X3517 @ X3519 )
        | ~ ( X3517 @ one ) )
      & ( ( X3517 @ ( esk1_1 @ X3517 ) )
        | ~ ( var @ X3519 )
        | ( X3517 @ X3519 )
        | ~ ( X3517 @ one ) )
      & ( ~ ( X3517 @ ( sub @ ( esk1_1 @ X3517 ) @ sh ) )
        | ~ ( var @ X3519 )
        | ( X3517 @ X3519 )
        | ~ ( X3517 @ one ) )
      & ( ( ( ap @ X3520 @ X3522 )
         != ( ap @ X3521 @ X3523 ) )
        | ( X3520 = X3521 ) )
      & ( ( ( ap @ X3524 @ X3526 )
         != ( ap @ X3525 @ X3527 ) )
        | ( X3526 = X3527 ) )
      & ( ( ( lam @ X3528 )
         != ( lam @ X3529 ) )
        | ( X3528 = X3529 ) )
      & ( ( ( sub @ X3530 @ sh )
         != ( sub @ X3531 @ sh ) )
        | ( X3530 = X3531 ) )
      & ( ( lam @ X3532 )
       != ( ap @ X3533 @ X3534 ) )
      & ~ ( var @ ( ap @ X3535 @ X3536 ) )
      & ~ ( var @ ( lam @ X3537 ) )
      & ( ( X3538 @ ( esk5_1 @ X3538 ) )
        | ( X3538 @ X3543 )
        | ( X3538 @ ( esk3_1 @ X3538 ) )
        | ( var @ ( esk2_1 @ X3538 ) ) )
      & ( ~ ( X3538 @ ( lam @ ( esk5_1 @ X3538 ) ) )
        | ( X3538 @ X3543 )
        | ( X3538 @ ( esk3_1 @ X3538 ) )
        | ( var @ ( esk2_1 @ X3538 ) ) )
      & ( ( X3538 @ ( esk5_1 @ X3538 ) )
        | ( X3538 @ X3543 )
        | ( X3538 @ ( esk4_1 @ X3538 ) )
        | ( var @ ( esk2_1 @ X3538 ) ) )
      & ( ~ ( X3538 @ ( lam @ ( esk5_1 @ X3538 ) ) )
        | ( X3538 @ X3543 )
        | ( X3538 @ ( esk4_1 @ X3538 ) )
        | ( var @ ( esk2_1 @ X3538 ) ) )
      & ( ( X3538 @ ( esk5_1 @ X3538 ) )
        | ( X3538 @ X3543 )
        | ~ ( X3538 @ ( ap @ ( esk3_1 @ X3538 ) @ ( esk4_1 @ X3538 ) ) )
        | ( var @ ( esk2_1 @ X3538 ) ) )
      & ( ~ ( X3538 @ ( lam @ ( esk5_1 @ X3538 ) ) )
        | ( X3538 @ X3543 )
        | ~ ( X3538 @ ( ap @ ( esk3_1 @ X3538 ) @ ( esk4_1 @ X3538 ) ) )
        | ( var @ ( esk2_1 @ X3538 ) ) )
      & ( ( X3538 @ ( esk5_1 @ X3538 ) )
        | ( X3538 @ X3543 )
        | ( X3538 @ ( esk3_1 @ X3538 ) )
        | ~ ( X3538 @ ( esk2_1 @ X3538 ) ) )
      & ( ~ ( X3538 @ ( lam @ ( esk5_1 @ X3538 ) ) )
        | ( X3538 @ X3543 )
        | ( X3538 @ ( esk3_1 @ X3538 ) )
        | ~ ( X3538 @ ( esk2_1 @ X3538 ) ) )
      & ( ( X3538 @ ( esk5_1 @ X3538 ) )
        | ( X3538 @ X3543 )
        | ( X3538 @ ( esk4_1 @ X3538 ) )
        | ~ ( X3538 @ ( esk2_1 @ X3538 ) ) )
      & ( ~ ( X3538 @ ( lam @ ( esk5_1 @ X3538 ) ) )
        | ( X3538 @ X3543 )
        | ( X3538 @ ( esk4_1 @ X3538 ) )
        | ~ ( X3538 @ ( esk2_1 @ X3538 ) ) )
      & ( ( X3538 @ ( esk5_1 @ X3538 ) )
        | ( X3538 @ X3543 )
        | ~ ( X3538 @ ( ap @ ( esk3_1 @ X3538 ) @ ( esk4_1 @ X3538 ) ) )
        | ~ ( X3538 @ ( esk2_1 @ X3538 ) ) )
      & ( ~ ( X3538 @ ( lam @ ( esk5_1 @ X3538 ) ) )
        | ( X3538 @ X3543 )
        | ~ ( X3538 @ ( ap @ ( esk3_1 @ X3538 ) @ ( esk4_1 @ X3538 ) ) )
        | ~ ( X3538 @ ( esk2_1 @ X3538 ) ) )
      & ( ( var @ ( esk6_3 @ X3544 @ X3545 @ X3546 ) )
        | ~ ( X3544 @ X3545 )
        | ~ ( var @ X3548 )
        | ( X3544 @ ( sub @ X3548 @ ( push @ X3545 @ X3546 ) ) ) )
      & ( ~ ( X3544 @ ( sub @ ( esk6_3 @ X3544 @ X3545 @ X3546 ) @ X3546 ) )
        | ~ ( X3544 @ X3545 )
        | ~ ( var @ X3548 )
        | ( X3544 @ ( sub @ X3548 @ ( push @ X3545 @ X3546 ) ) ) )
      & ( ( var @ ( esk10_3 @ X3549 @ X3554 @ X3555 ) )
        | ( X3549 @ ( sub @ X3554 @ X3555 ) )
        | ~ ( X3549 @ X3553 )
        | ( X3549 @ ( sub @ ( esk9_1 @ X3549 ) @ ( push @ X3553 @ id ) ) )
        | ( X3549 @ ( esk7_1 @ X3549 ) ) )
      & ( ~ ( X3549 @ ( sub @ ( esk10_3 @ X3549 @ X3554 @ X3555 ) @ X3555 ) )
        | ( X3549 @ ( sub @ X3554 @ X3555 ) )
        | ~ ( X3549 @ X3553 )
        | ( X3549 @ ( sub @ ( esk9_1 @ X3549 ) @ ( push @ X3553 @ id ) ) )
        | ( X3549 @ ( esk7_1 @ X3549 ) ) )
      & ( ( var @ ( esk10_3 @ X3549 @ X3554 @ X3555 ) )
        | ( X3549 @ ( sub @ X3554 @ X3555 ) )
        | ~ ( X3549 @ ( lam @ ( esk9_1 @ X3549 ) ) )
        | ( X3549 @ ( esk7_1 @ X3549 ) ) )
      & ( ~ ( X3549 @ ( sub @ ( esk10_3 @ X3549 @ X3554 @ X3555 ) @ X3555 ) )
        | ( X3549 @ ( sub @ X3554 @ X3555 ) )
        | ~ ( X3549 @ ( lam @ ( esk9_1 @ X3549 ) ) )
        | ( X3549 @ ( esk7_1 @ X3549 ) ) )
      & ( ( var @ ( esk10_3 @ X3549 @ X3554 @ X3555 ) )
        | ( X3549 @ ( sub @ X3554 @ X3555 ) )
        | ~ ( X3549 @ X3553 )
        | ( X3549 @ ( sub @ ( esk9_1 @ X3549 ) @ ( push @ X3553 @ id ) ) )
        | ( X3549 @ ( esk8_1 @ X3549 ) ) )
      & ( ~ ( X3549 @ ( sub @ ( esk10_3 @ X3549 @ X3554 @ X3555 ) @ X3555 ) )
        | ( X3549 @ ( sub @ X3554 @ X3555 ) )
        | ~ ( X3549 @ X3553 )
        | ( X3549 @ ( sub @ ( esk9_1 @ X3549 ) @ ( push @ X3553 @ id ) ) )
        | ( X3549 @ ( esk8_1 @ X3549 ) ) )
      & ( ( var @ ( esk10_3 @ X3549 @ X3554 @ X3555 ) )
        | ( X3549 @ ( sub @ X3554 @ X3555 ) )
        | ~ ( X3549 @ ( lam @ ( esk9_1 @ X3549 ) ) )
        | ( X3549 @ ( esk8_1 @ X3549 ) ) )
      & ( ~ ( X3549 @ ( sub @ ( esk10_3 @ X3549 @ X3554 @ X3555 ) @ X3555 ) )
        | ( X3549 @ ( sub @ X3554 @ X3555 ) )
        | ~ ( X3549 @ ( lam @ ( esk9_1 @ X3549 ) ) )
        | ( X3549 @ ( esk8_1 @ X3549 ) ) )
      & ( ( var @ ( esk10_3 @ X3549 @ X3554 @ X3555 ) )
        | ( X3549 @ ( sub @ X3554 @ X3555 ) )
        | ~ ( X3549 @ X3553 )
        | ( X3549 @ ( sub @ ( esk9_1 @ X3549 ) @ ( push @ X3553 @ id ) ) )
        | ~ ( X3549 @ ( ap @ ( esk7_1 @ X3549 ) @ ( esk8_1 @ X3549 ) ) ) )
      & ( ~ ( X3549 @ ( sub @ ( esk10_3 @ X3549 @ X3554 @ X3555 ) @ X3555 ) )
        | ( X3549 @ ( sub @ X3554 @ X3555 ) )
        | ~ ( X3549 @ X3553 )
        | ( X3549 @ ( sub @ ( esk9_1 @ X3549 ) @ ( push @ X3553 @ id ) ) )
        | ~ ( X3549 @ ( ap @ ( esk7_1 @ X3549 ) @ ( esk8_1 @ X3549 ) ) ) )
      & ( ( var @ ( esk10_3 @ X3549 @ X3554 @ X3555 ) )
        | ( X3549 @ ( sub @ X3554 @ X3555 ) )
        | ~ ( X3549 @ ( lam @ ( esk9_1 @ X3549 ) ) )
        | ~ ( X3549 @ ( ap @ ( esk7_1 @ X3549 ) @ ( esk8_1 @ X3549 ) ) ) )
      & ( ~ ( X3549 @ ( sub @ ( esk10_3 @ X3549 @ X3554 @ X3555 ) @ X3555 ) )
        | ( X3549 @ ( sub @ X3554 @ X3555 ) )
        | ~ ( X3549 @ ( lam @ ( esk9_1 @ X3549 ) ) )
        | ~ ( X3549 @ ( ap @ ( esk7_1 @ X3549 ) @ ( esk8_1 @ X3549 ) ) ) )
      & ( ~ ( X3557 @ X3562 )
        | ( X3557 @ ( sub @ ( esk14_1 @ X3557 ) @ ( push @ X3562 @ id ) ) )
        | ( X3557 @ X3563 )
        | ( X3557 @ ( esk12_1 @ X3557 ) )
        | ( var @ ( esk11_1 @ X3557 ) ) )
      & ( ~ ( X3557 @ ( lam @ ( esk14_1 @ X3557 ) ) )
        | ( X3557 @ X3563 )
        | ( X3557 @ ( esk12_1 @ X3557 ) )
        | ( var @ ( esk11_1 @ X3557 ) ) )
      & ( ~ ( X3557 @ X3562 )
        | ( X3557 @ ( sub @ ( esk14_1 @ X3557 ) @ ( push @ X3562 @ id ) ) )
        | ( X3557 @ X3563 )
        | ( X3557 @ ( esk13_1 @ X3557 ) )
        | ( var @ ( esk11_1 @ X3557 ) ) )
      & ( ~ ( X3557 @ ( lam @ ( esk14_1 @ X3557 ) ) )
        | ( X3557 @ X3563 )
        | ( X3557 @ ( esk13_1 @ X3557 ) )
        | ( var @ ( esk11_1 @ X3557 ) ) )
      & ( ~ ( X3557 @ X3562 )
        | ( X3557 @ ( sub @ ( esk14_1 @ X3557 ) @ ( push @ X3562 @ id ) ) )
        | ( X3557 @ X3563 )
        | ~ ( X3557 @ ( ap @ ( esk12_1 @ X3557 ) @ ( esk13_1 @ X3557 ) ) )
        | ( var @ ( esk11_1 @ X3557 ) ) )
      & ( ~ ( X3557 @ ( lam @ ( esk14_1 @ X3557 ) ) )
        | ( X3557 @ X3563 )
        | ~ ( X3557 @ ( ap @ ( esk12_1 @ X3557 ) @ ( esk13_1 @ X3557 ) ) )
        | ( var @ ( esk11_1 @ X3557 ) ) )
      & ( ~ ( X3557 @ X3562 )
        | ( X3557 @ ( sub @ ( esk14_1 @ X3557 ) @ ( push @ X3562 @ id ) ) )
        | ( X3557 @ X3563 )
        | ( X3557 @ ( esk12_1 @ X3557 ) )
        | ~ ( X3557 @ ( esk11_1 @ X3557 ) ) )
      & ( ~ ( X3557 @ ( lam @ ( esk14_1 @ X3557 ) ) )
        | ( X3557 @ X3563 )
        | ( X3557 @ ( esk12_1 @ X3557 ) )
        | ~ ( X3557 @ ( esk11_1 @ X3557 ) ) )
      & ( ~ ( X3557 @ X3562 )
        | ( X3557 @ ( sub @ ( esk14_1 @ X3557 ) @ ( push @ X3562 @ id ) ) )
        | ( X3557 @ X3563 )
        | ( X3557 @ ( esk13_1 @ X3557 ) )
        | ~ ( X3557 @ ( esk11_1 @ X3557 ) ) )
      & ( ~ ( X3557 @ ( lam @ ( esk14_1 @ X3557 ) ) )
        | ( X3557 @ X3563 )
        | ( X3557 @ ( esk13_1 @ X3557 ) )
        | ~ ( X3557 @ ( esk11_1 @ X3557 ) ) )
      & ( ~ ( X3557 @ X3562 )
        | ( X3557 @ ( sub @ ( esk14_1 @ X3557 ) @ ( push @ X3562 @ id ) ) )
        | ( X3557 @ X3563 )
        | ~ ( X3557 @ ( ap @ ( esk12_1 @ X3557 ) @ ( esk13_1 @ X3557 ) ) )
        | ~ ( X3557 @ ( esk11_1 @ X3557 ) ) )
      & ( ~ ( X3557 @ ( lam @ ( esk14_1 @ X3557 ) ) )
        | ( X3557 @ X3563 )
        | ~ ( X3557 @ ( ap @ ( esk12_1 @ X3557 ) @ ( esk13_1 @ X3557 ) ) )
        | ~ ( X3557 @ ( esk11_1 @ X3557 ) ) )
      & ( ( comp @ ( comp @ X3564 @ X3565 ) @ X3566 )
        = ( comp @ X3564 @ ( comp @ X3565 @ X3566 ) ) )
      & ( ( comp @ id @ X3567 )
        = X3567 )
      & ( ( comp @ X3568 @ id )
        = X3568 )
      & ( ( sub @ ( sub @ X3569 @ X3570 ) @ X3571 )
        = ( sub @ X3569 @ ( comp @ X3570 @ X3571 ) ) )
      & ( ( sub @ X3572 @ id )
        = X3572 )
      & ( ( ( hoasap @ id @ X3573 @ id @ X3575 )
         != ( hoasap @ id @ X3574 @ id @ X3576 ) )
        | ( X3573 = X3574 ) )
      & ( ( ( hoasap @ id @ X3577 @ id @ X3579 )
         != ( hoasap @ id @ X3578 @ id @ X3580 ) )
        | ( X3579 = X3580 ) )
      & ( ( ( sub @ ( X3581 @ ( esk15_1 @ X3581 ) @ ( esk16_1 @ X3581 ) ) @ ( esk17_1 @ X3581 ) )
         != ( X3581 @ ( comp @ ( esk15_1 @ X3581 ) @ ( esk17_1 @ X3581 ) ) @ ( sub @ ( esk16_1 @ X3581 ) @ ( esk17_1 @ X3581 ) ) ) )
        | ( ( sub @ ( X3585 @ ( esk18_2 @ X3581 @ X3585 ) @ ( esk19_2 @ X3581 @ X3585 ) ) @ ( esk20_2 @ X3581 @ X3585 ) )
         != ( X3585 @ ( comp @ ( esk18_2 @ X3581 @ X3585 ) @ ( esk20_2 @ X3581 @ X3585 ) ) @ ( sub @ ( esk19_2 @ X3581 @ X3585 ) @ ( esk20_2 @ X3581 @ X3585 ) ) ) )
        | ( ( hoaslam @ id @ X3581 )
         != ( hoaslam @ id @ X3585 ) )
        | ( ( X3581 @ X3589 @ X3590 )
          = ( X3585 @ X3589 @ X3590 ) ) )
      & ( ( ( sub @ ( X3591 @ ( esk21_1 @ X3591 ) @ ( esk22_1 @ X3591 ) ) @ ( esk23_1 @ X3591 ) )
         != ( X3591 @ ( comp @ ( esk21_1 @ X3591 ) @ ( esk23_1 @ X3591 ) ) @ ( sub @ ( esk22_1 @ X3591 ) @ ( esk23_1 @ X3591 ) ) ) )
        | ( ( hoaslam @ id @ X3591 )
         != ( hoasap @ id @ X3595 @ id @ X3596 ) ) )
      & ( ( ( sub @ ( X3597 @ ( esk24_1 @ X3597 ) @ ( esk25_1 @ X3597 ) ) @ ( esk26_1 @ X3597 ) )
         != ( X3597 @ ( comp @ ( esk24_1 @ X3597 ) @ ( esk26_1 @ X3597 ) ) @ ( sub @ ( esk25_1 @ X3597 ) @ ( esk26_1 @ X3597 ) ) ) )
        | ~ ( var @ ( sub @ ( hoaslam @ id @ X3597 ) @ id ) ) )
      & ( var @ ( sub @ ( hoasap @ id @ esk27_0 @ id @ esk28_0 ) @ id ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])])])]) ).

thf(c_0_47,plain,
    ! [X3482: subst,X3483: term,X3484: subst,X3485: term] :
      ( ( hoasap @ X3482 @ X3483 @ X3484 @ X3485 )
      = ( ap @ ( sub @ X3483 @ X3484 ) @ X3485 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoasap])]) ).

thf(c_0_48,negated_conjecture,
    var @ ( sub @ ( hoasap @ id @ esk27_0 @ id @ esk28_0 ) @ id ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

thf(c_0_49,negated_conjecture,
    ! [X1: term] :
      ( ( sub @ X1 @ id )
      = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

thf(c_0_50,plain,
    ! [X3488: subst,X3489: term,X3490: subst,X3491: term] :
      ( ( hoasap @ X3488 @ X3489 @ X3490 @ X3491 )
      = ( ap @ ( sub @ X3489 @ X3490 ) @ X3491 ) ),
    inference(variable_rename,[status(thm)],[c_0_47]) ).

thf(c_0_51,negated_conjecture,
    var @ ( hoasap @ id @ esk27_0 @ id @ esk28_0 ),
    inference(rw,[status(thm)],[c_0_48,c_0_49]) ).

thf(c_0_52,plain,
    ! [X1: term,X3: subst,X4: subst,X2: term] :
      ( ( hoasap @ X3 @ X1 @ X4 @ X2 )
      = ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

thf(c_0_53,negated_conjecture,
    ! [X1: term,X2: term] :
      ~ ( var @ ( ap @ X1 @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

thf(c_0_54,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_49]),c_0_53]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : ALG261^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.10/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sat May 18 23:00:08 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.18/0.45  Running higher-order theorem proving
% 0.18/0.45  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.50  # Version: 3.1.0-ho
% 0.18/0.50  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.50  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.50  # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.50  # Starting post_as_ho5 with 300s (1) cores
% 0.18/0.50  # Starting post_as_ho10 with 300s (1) cores
% 0.18/0.50  # post_as_ho1 with pid 20566 completed with status 0
% 0.18/0.50  # Result found by post_as_ho1
% 0.18/0.50  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.50  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.50  # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.50  # No SInE strategy applied
% 0.18/0.50  # Search class: HGHSM-FFMS31-MHFMMMBN
% 0.18/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.18/0.50  # new_ho_10 with pid 20575 completed with status 0
% 0.18/0.50  # Result found by new_ho_10
% 0.18/0.50  # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.50  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.50  # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.50  # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.50  # No SInE strategy applied
% 0.18/0.50  # Search class: HGHSM-FFMS31-MHFMMMBN
% 0.18/0.50  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.50  # Starting new_ho_10 with 163s (1) cores
% 0.18/0.50  # Preprocessing time       : 0.002 s
% 0.18/0.50  # Presaturation interreduction done
% 0.18/0.50  
% 0.18/0.50  # Proof found!
% 0.18/0.50  # SZS status Theorem
% 0.18/0.50  # SZS output start CNFRefutation
% See solution above
% 0.18/0.50  # Parsed axioms                        : 238
% 0.18/0.50  # Removed by relevancy pruning/SinE    : 0
% 0.18/0.50  # Initial clauses                      : 199
% 0.18/0.50  # Removed in clause preprocessing      : 124
% 0.18/0.50  # Initial clauses in saturation        : 75
% 0.18/0.50  # Processed clauses                    : 38
% 0.18/0.50  # ...of these trivial                  : 5
% 0.18/0.50  # ...subsumed                          : 1
% 0.18/0.50  # ...remaining for further processing  : 32
% 0.18/0.50  # Other redundant clauses eliminated   : 0
% 0.18/0.50  # Clauses deleted for lack of memory   : 0
% 0.18/0.50  # Backward-subsumed                    : 0
% 0.18/0.50  # Backward-rewritten                   : 6
% 0.18/0.50  # Generated clauses                    : 0
% 0.18/0.50  # ...of the previous two non-redundant : 5
% 0.18/0.50  # ...aggressively subsumed             : 0
% 0.18/0.50  # Contextual simplify-reflections      : 0
% 0.18/0.50  # Paramodulations                      : 0
% 0.18/0.50  # Factorizations                       : 0
% 0.18/0.50  # NegExts                              : 0
% 0.18/0.50  # Equation resolutions                 : 0
% 0.18/0.50  # Disequality decompositions           : 0
% 0.18/0.50  # Total rewrite steps                  : 21
% 0.18/0.50  # ...of those cached                   : 3
% 0.18/0.50  # Propositional unsat checks           : 0
% 0.18/0.50  #    Propositional check models        : 0
% 0.18/0.50  #    Propositional check unsatisfiable : 0
% 0.18/0.50  #    Propositional clauses             : 0
% 0.18/0.50  #    Propositional clauses after purity: 0
% 0.18/0.50  #    Propositional unsat core size     : 0
% 0.18/0.50  #    Propositional preprocessing time  : 0.000
% 0.18/0.50  #    Propositional encoding time       : 0.000
% 0.18/0.50  #    Propositional solver time         : 0.000
% 0.18/0.50  #    Success case prop preproc time    : 0.000
% 0.18/0.50  #    Success case prop encoding time   : 0.000
% 0.18/0.50  #    Success case prop solver time     : 0.000
% 0.18/0.50  # Current number of processed clauses  : 26
% 0.18/0.50  #    Positive orientable unit clauses  : 13
% 0.18/0.50  #    Positive unorientable unit clauses: 0
% 0.18/0.50  #    Negative unit clauses             : 3
% 0.18/0.50  #    Non-unit-clauses                  : 10
% 0.18/0.50  # Current number of unprocessed clauses: 39
% 0.18/0.50  # ...number of literals in the above   : 162
% 0.18/0.50  # Current number of archived formulas  : 0
% 0.18/0.50  # Current number of archived clauses   : 6
% 0.18/0.50  # Clause-clause subsumption calls (NU) : 14
% 0.18/0.50  # Rec. Clause-clause subsumption calls : 9
% 0.18/0.50  # Non-unit clause-clause subsumptions  : 0
% 0.18/0.50  # Unit Clause-clause subsumption calls : 4
% 0.18/0.50  # Rewrite failures with RHS unbound    : 0
% 0.18/0.50  # BW rewrite match attempts            : 8
% 0.18/0.50  # BW rewrite match successes           : 8
% 0.18/0.50  # Condensation attempts                : 38
% 0.18/0.50  # Condensation successes               : 0
% 0.18/0.50  # Termbank termtop insertions          : 32755
% 0.18/0.50  # Search garbage collected termcells   : 4195
% 0.18/0.50  
% 0.18/0.50  # -------------------------------------------------
% 0.18/0.50  # User time                : 0.022 s
% 0.18/0.50  # System time              : 0.009 s
% 0.18/0.50  # Total time               : 0.031 s
% 0.18/0.50  # Maximum resident set size: 6072 pages
% 0.18/0.50  
% 0.18/0.50  # -------------------------------------------------
% 0.18/0.50  # User time                : 0.029 s
% 0.18/0.50  # System time              : 0.013 s
% 0.18/0.50  # Total time               : 0.042 s
% 0.18/0.50  # Maximum resident set size: 2080 pages
% 0.18/0.50  % E---3.1 exiting
% 0.18/0.50  % E exiting
%------------------------------------------------------------------------------