TSTP Solution File: ALG256^1 by LEO-II---1.7.0

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%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : ALG256^1 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n032.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  : 600s
% DateTime : Thu Jul 14 17:25:28 EDT 2022

% Result   : Theorem 1.46s 1.64s
% Output   : CNFRefutation 1.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   56
%            Number of leaves      :  277
% Syntax   : Number of formulae    :  747 ( 287 unt; 163 typ; 113 def)
%            Number of atoms       : 4821 (2012 equ;   0 cnn)
%            Maximal formula atoms :    5 (   8 avg)
%            Number of connectives : 15335 (2464   ~;2825   |;   4   &;9026   @)
%                                         (   2 <=>;1014  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :  637 ( 637   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  164 ( 161 usr; 117 con; 0-4 aty)
%            Number of variables   : 3371 (  39   ^3327   !;   5   ?;3371   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_subst,type,
    subst: $tType ).

thf(tp_term,type,
    term: $tType ).

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

thf(tp_apinj1,type,
    apinj1: $o ).

thf(tp_apinj2,type,
    apinj2: $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(tp_hoasapinj1,type,
    hoasapinj1: $o ).

thf(tp_hoasapinj1_gthm,type,
    hoasapinj1_gthm: $o ).

thf(tp_hoasapinj1_lthm,type,
    hoasapinj1_lthm: $o ).

thf(tp_hoasapinj2,type,
    hoasapinj2: $o ).

thf(tp_hoasapinj2_gthm,type,
    hoasapinj2_gthm: $o ).

thf(tp_hoasapinj2_lthm,type,
    hoasapinj2_lthm: $o ).

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

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

thf(tp_hoasapnotvar_lthm,type,
    hoasapnotvar_lthm: $o ).

thf(tp_hoasinduction,type,
    hoasinduction: $o ).

thf(tp_hoasinduction_gthm,type,
    hoasinduction_gthm: $o ).

thf(tp_hoasinduction_lem0,type,
    hoasinduction_lem0: $o ).

thf(tp_hoasinduction_lem0_lthm,type,
    hoasinduction_lem0_lthm: $o ).

thf(tp_hoasinduction_lem1,type,
    hoasinduction_lem1: $o ).

thf(tp_hoasinduction_lem1_gthm,type,
    hoasinduction_lem1_gthm: $o ).

thf(tp_hoasinduction_lem1_lthm,type,
    hoasinduction_lem1_lthm: $o ).

thf(tp_hoasinduction_lem1v2,type,
    hoasinduction_lem1v2: $o ).

thf(tp_hoasinduction_lem1v2_gthm,type,
    hoasinduction_lem1v2_gthm: $o ).

thf(tp_hoasinduction_lem2,type,
    hoasinduction_lem2: $o ).

thf(tp_hoasinduction_lem2_gthm,type,
    hoasinduction_lem2_gthm: $o ).

thf(tp_hoasinduction_lem2_lthm,type,
    hoasinduction_lem2_lthm: $o ).

thf(tp_hoasinduction_lem2v2,type,
    hoasinduction_lem2v2: $o ).

thf(tp_hoasinduction_lem2v2_gthm,type,
    hoasinduction_lem2v2_gthm: $o ).

thf(tp_hoasinduction_lem3,type,
    hoasinduction_lem3: $o ).

thf(tp_hoasinduction_lem3_gthm,type,
    hoasinduction_lem3_gthm: $o ).

thf(tp_hoasinduction_lem3_lthm,type,
    hoasinduction_lem3_lthm: $o ).

thf(tp_hoasinduction_lem3a,type,
    hoasinduction_lem3a: $o ).

thf(tp_hoasinduction_lem3a_gthm,type,
    hoasinduction_lem3a_gthm: $o ).

thf(tp_hoasinduction_lem3a_lthm,type,
    hoasinduction_lem3a_lthm: $o ).

thf(tp_hoasinduction_lem3aa,type,
    hoasinduction_lem3aa: $o ).

thf(tp_hoasinduction_lem3aa_lthm,type,
    hoasinduction_lem3aa_lthm: $o ).

thf(tp_hoasinduction_lem3aaa,type,
    hoasinduction_lem3aaa: $o ).

thf(tp_hoasinduction_lem3b,type,
    hoasinduction_lem3b: $o ).

thf(tp_hoasinduction_lem3b_gthm,type,
    hoasinduction_lem3b_gthm: $o ).

thf(tp_hoasinduction_lem3b_lthm,type,
    hoasinduction_lem3b_lthm: $o ).

thf(tp_hoasinduction_lem3v2,type,
    hoasinduction_lem3v2: $o ).

thf(tp_hoasinduction_lem3v2_f,type,
    hoasinduction_lem3v2_f: $o ).

thf(tp_hoasinduction_lem3v2_f_lthm,type,
    hoasinduction_lem3v2_f_lthm: $o ).

thf(tp_hoasinduction_lem3v2_gthm,type,
    hoasinduction_lem3v2_gthm: $o ).

thf(tp_hoasinduction_lem3v2_lthm,type,
    hoasinduction_lem3v2_lthm: $o ).

thf(tp_hoasinduction_lem3v2a,type,
    hoasinduction_lem3v2a: $o ).

thf(tp_hoasinduction_lem3v2a_lthm,type,
    hoasinduction_lem3v2a_lthm: $o ).

thf(tp_hoasinduction_lthm,type,
    hoasinduction_lthm: $o ).

thf(tp_hoasinduction_lthm_3,type,
    hoasinduction_lthm_3: $o ).

thf(tp_hoasinduction_no_psi_cond,type,
    hoasinduction_no_psi_cond: $o ).

thf(tp_hoasinduction_no_psi_cond_lthm,type,
    hoasinduction_no_psi_cond_lthm: $o ).

thf(tp_hoasinduction_p_and_p_prime,type,
    hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).

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

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

thf(tp_hoaslaminj_gthm,type,
    hoaslaminj_gthm: $o ).

thf(tp_hoaslaminj_lthm,type,
    hoaslaminj_lthm: $o ).

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

thf(tp_hoaslamnotap_gthm,type,
    hoaslamnotap_gthm: $o ).

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

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

thf(tp_hoaslamnotvar_gthm,type,
    hoaslamnotvar_gthm: $o ).

thf(tp_hoaslamnotvar_lthm,type,
    hoaslamnotvar_lthm: $o ).

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

thf(tp_id,type,
    id: subst ).

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

thf(tp_induction2,type,
    induction2: $o ).

thf(tp_induction2_gthm,type,
    induction2_gthm: $o ).

thf(tp_induction2_lthm,type,
    induction2_lthm: $o ).

thf(tp_induction2lem,type,
    induction2lem: $o ).

thf(tp_induction2lem_gthm,type,
    induction2lem_gthm: $o ).

thf(tp_induction2lem_lthm,type,
    induction2lem_lthm: $o ).

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

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

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

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

thf(tp_one,type,
    one: term ).

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

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

thf(tp_pushprop_gthm,type,
    pushprop_gthm: $o ).

thf(tp_pushprop_lem0,type,
    pushprop_lem0: $o ).

thf(tp_pushprop_lem0_gthm,type,
    pushprop_lem0_gthm: $o ).

thf(tp_pushprop_lem0_lthm,type,
    pushprop_lem0_lthm: $o ).

thf(tp_pushprop_lem1,type,
    pushprop_lem1: $o ).

thf(tp_pushprop_lem1_gthm,type,
    pushprop_lem1_gthm: $o ).

thf(tp_pushprop_lem1_lthm,type,
    pushprop_lem1_lthm: $o ).

thf(tp_pushprop_lem1v2,type,
    pushprop_lem1v2: $o ).

thf(tp_pushprop_lem1v2_gthm,type,
    pushprop_lem1v2_gthm: $o ).

thf(tp_pushprop_lem1v2_lthm,type,
    pushprop_lem1v2_lthm: $o ).

thf(tp_pushprop_lem2v2,type,
    pushprop_lem2v2: $o ).

thf(tp_pushprop_lem2v2_gthm,type,
    pushprop_lem2v2_gthm: $o ).

thf(tp_pushprop_lem2v2_lthm,type,
    pushprop_lem2v2_lthm: $o ).

thf(tp_pushprop_lem3v2,type,
    pushprop_lem3v2: $o ).

thf(tp_pushprop_lem3v2_lthm,type,
    pushprop_lem3v2_lthm: $o ).

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

thf(tp_pushprop_lthm_orig,type,
    pushprop_lthm_orig: $o ).

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

thf(tp_sK10_SY36,type,
    sK10_SY36: ( term > $o ) > term ).

thf(tp_sK11_SY68,type,
    sK11_SY68: term ).

thf(tp_sK12_SY36,type,
    sK12_SY36: ( term > $o ) > term ).

thf(tp_sK13_SY69,type,
    sK13_SY69: ( term > $o ) > term ).

thf(tp_sK14_SY70,type,
    sK14_SY70: ( term > $o ) > term ).

thf(tp_sK15_SY57,type,
    sK15_SY57: ( term > $o ) > term ).

thf(tp_sK16_SY49,type,
    sK16_SY49: ( term > $o ) > term ).

thf(tp_sK17_SY49,type,
    sK17_SY49: ( term > $o ) > term ).

thf(tp_sK18_SY57,type,
    sK18_SY57: ( term > $o ) > term ).

thf(tp_sK19_SY74,type,
    sK19_SY74: ( term > $o ) > term ).

thf(tp_sK1_SY15,type,
    sK1_SY15: ( term > $o ) > term ).

thf(tp_sK20_SY49,type,
    sK20_SY49: ( term > $o ) > term ).

thf(tp_sK21_SY79,type,
    sK21_SY79: ( term > $o ) > term ).

thf(tp_sK22_SY38,type,
    sK22_SY38: ( term > $o ) > term ).

thf(tp_sK23_SY38,type,
    sK23_SY38: ( term > $o ) > term ).

thf(tp_sK24_SY38,type,
    sK24_SY38: ( term > $o ) > term ).

thf(tp_sK25_SY38,type,
    sK25_SY38: ( term > $o ) > term ).

thf(tp_sK26_SY38,type,
    sK26_SY38: ( term > $o ) > term ).

thf(tp_sK27_SY38,type,
    sK27_SY38: ( term > $o ) > term ).

thf(tp_sK28_SY59,type,
    sK28_SY59: ( term > $o ) > term ).

thf(tp_sK29_SY59,type,
    sK29_SY59: ( term > $o ) > term ).

thf(tp_sK2_SY35,type,
    sK2_SY35: ( term > $o ) > term ).

thf(tp_sK30_SY86,type,
    sK30_SY86: term > subst > ( term > $o ) > term ).

thf(tp_sK31_SY89,type,
    sK31_SY89: term > subst > ( term > $o ) > term ).

thf(tp_sK32_SY59,type,
    sK32_SY59: ( term > $o ) > term ).

thf(tp_sK33_SY59,type,
    sK33_SY59: ( term > $o ) > term ).

thf(tp_sK34_SY59,type,
    sK34_SY59: ( term > $o ) > term ).

thf(tp_sK35_SY90,type,
    sK35_SY90: term > subst > ( term > $o ) > term ).

thf(tp_sK36_SY59,type,
    sK36_SY59: ( term > $o ) > term ).

thf(tp_sK37_SY100,type,
    sK37_SY100: term > term > subst > ( term > $o ) > term ).

thf(tp_sK38_SY103,type,
    sK38_SY103: term > term > subst > ( term > $o ) > term ).

thf(tp_sK39_SY105,type,
    sK39_SY105: term > term > subst > ( term > $o ) > term ).

thf(tp_sK3_SX0,type,
    sK3_SX0: term ).

thf(tp_sK4_SY47,type,
    sK4_SY47: ( term > $o ) > term ).

thf(tp_sK5_SY62,type,
    sK5_SY62: term ).

thf(tp_sK6_SY54,type,
    sK6_SY54: term > subst > ( term > $o ) > term ).

thf(tp_sK7_SY65,type,
    sK7_SY65: ( term > $o ) > term ).

thf(tp_sK8_SY56,type,
    sK8_SY56: ( term > $o ) > term ).

thf(tp_sK9_SY66,type,
    sK9_SY66: term ).

thf(tp_sh,type,
    sh: subst ).

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

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

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

thf(tp_substmonoid_gthm,type,
    substmonoid_gthm: $o ).

thf(tp_substmonoid_lthm,type,
    substmonoid_lthm: $o ).

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

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

thf(tp_termmset_lthm,type,
    termmset_lthm: $o ).

thf(tp_ulamvar1,type,
    ulamvar1: $o ).

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

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

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

thf(apinj1,definition,
    ( apinj1
    = ( ! [A: term,B: term,C: term,D: term] :
          ( ( ( ap @ A @ C )
            = ( ap @ B @ D ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apinj1) ).

thf(apinj2,definition,
    ( apinj2
    = ( ! [A: term,B: term,C: term,D: term] :
          ( ( ( ap @ A @ C )
            = ( ap @ B @ D ) )
         => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apinj2) ).

thf(apnotvar,definition,
    ( apnotvar
    = ( ! [A: term,B: term] :
          ~ ( var @ ( ap @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apnotvar) ).

thf(axabs,definition,
    ( axabs
    = ( ! [A: term,M: subst] :
          ( ( sub @ ( lam @ A ) @ M )
          = ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axabs) ).

thf(axapp,definition,
    ( axapp
    = ( ! [A: term,B: term,M: subst] :
          ( ( sub @ ( ap @ A @ B ) @ M )
          = ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axapp) ).

thf(axassoc,definition,
    ( axassoc
    = ( ! [M: subst,N: subst,K: subst] :
          ( ( comp @ ( comp @ M @ N ) @ K )
          = ( comp @ M @ ( comp @ N @ K ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axassoc) ).

thf(axclos,definition,
    ( axclos
    = ( ! [A: term,M: subst,N: subst] :
          ( ( sub @ ( sub @ A @ M ) @ N )
          = ( sub @ A @ ( comp @ M @ N ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axclos) ).

thf(axidl,definition,
    ( axidl
    = ( ! [M: subst] :
          ( ( comp @ id @ M )
          = M ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axidl) ).

thf(axidr,definition,
    ( axidr
    = ( ! [M: subst] :
          ( ( comp @ M @ id )
          = M ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axidr) ).

thf(axmap,definition,
    ( axmap
    = ( ! [A: term,M: subst,N: subst] :
          ( ( comp @ ( push @ A @ M ) @ N )
          = ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axmap) ).

thf(axscons,definition,
    ( axscons
    = ( ! [M: subst] :
          ( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
          = M ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axscons) ).

thf(axshiftcons,definition,
    ( axshiftcons
    = ( ! [A: term,M: subst] :
          ( ( comp @ sh @ ( push @ A @ M ) )
          = M ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axshiftcons) ).

thf(axvarcons,definition,
    ( axvarcons
    = ( ! [A: term,M: subst] :
          ( ( sub @ one @ ( push @ A @ M ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarcons) ).

thf(axvarid,definition,
    ( axvarid
    = ( ! [A: term] :
          ( ( sub @ A @ id )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarid) ).

thf(axvarshift,definition,
    ( axvarshift
    = ( ( push @ one @ sh )
      = id ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarshift) ).

thf(hoasap,definition,
    ( hoasap
    = ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasap) ).

thf(hoasapinj1,definition,
    ( hoasapinj1
    = ( ! [A: term,B: term,C: term,D: term] :
          ( ( ( hoasap @ id @ A @ id @ C )
            = ( hoasap @ id @ B @ id @ D ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj1) ).

thf(hoasapinj1_gthm,definition,
    ( hoasapinj1_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj1_gthm) ).

thf(hoasapinj1_lthm,definition,
    ( hoasapinj1_lthm
    = ( axvarid
     => ( apinj1
       => hoasapinj1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj1_lthm) ).

thf(hoasapinj2,definition,
    ( hoasapinj2
    = ( ! [A: term,B: term,C: term,D: term] :
          ( ( ( hoasap @ id @ A @ id @ C )
            = ( hoasap @ id @ B @ id @ D ) )
         => ( C = D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj2) ).

thf(hoasapinj2_gthm,definition,
    ( hoasapinj2_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj2_gthm) ).

thf(hoasapinj2_lthm,definition,
    ( hoasapinj2_lthm
    = ( apinj2
     => hoasapinj2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj2_lthm) ).

thf(hoasapnotvar,definition,
    ( hoasapnotvar
    = ( ! [A: term,B: term] :
          ~ ( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapnotvar) ).

thf(hoasapnotvar_gthm,definition,
    ( 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/theBenchmark.p',hoasapnotvar_gthm) ).

thf(hoasapnotvar_lthm,definition,
    ( hoasapnotvar_lthm
    = ( axvarid
     => ( apnotvar
       => hoasapnotvar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapnotvar_lthm) ).

thf(hoasinduction,definition,
    ( hoasinduction
    = ( ! [P: subst > term > subst > $o] :
          ( ! [M: subst,A: term,N: subst,K: subst] :
              ( ( P @ M @ A @ ( comp @ K @ N ) )
             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
         => ( ! [M: subst,A: term,N: subst,K: subst] :
                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
               => ( P @ M @ A @ ( comp @ K @ N ) ) )
           => ( ! [A: term] :
                  ( ( hoasvar @ id @ A @ id )
                 => ( P @ id @ A @ id ) )
             => ( ! [A: term,B: term] :
                    ( ( P @ id @ A @ id )
                   => ( ( P @ id @ B @ id )
                     => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
               => ( ! [F: subst > term > term] :
                      ( ! [M: subst,A: term,N: subst] :
                          ( ( sub @ ( F @ M @ A ) @ N )
                          = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
                     => ( ! [A: term] :
                            ( ( P @ id @ A @ id )
                           => ( P @ id @ ( F @ id @ A ) @ id ) )
                       => ( P @ id
                          @ ( hoaslam @ id
                            @ ^ [M: subst,A: term] : ( F @ M @ A ) )
                          @ id ) ) )
                 => ! [A: term] : ( P @ id @ A @ id ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction) ).

thf(hoasinduction_gthm,definition,
    ( hoasinduction_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
                                                                       => ( hoasinduction_lem1
                                                                         => ( hoasinduction_lem2
                                                                           => ( hoasinduction_lem3
                                                                             => hoasinduction ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_gthm) ).

thf(hoasinduction_lem0,definition,
    ( hoasinduction_lem0
    = ( ! [P: subst > term > subst > $o] :
        ? [Q: term > $o] : ( hoasinduction_p_and_p_prime @ P @ Q ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem0) ).

thf(hoasinduction_lem0_lthm,definition,
    hoasinduction_lem0_lthm = hoasinduction_lem0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem0_lthm) ).

thf(hoasinduction_lem1,definition,
    ( hoasinduction_lem1
    = ( ! [P: subst > term > subst > $o] :
          ( ! [M: subst,A: term,N: subst,K: subst] :
              ( ( P @ M @ A @ ( comp @ K @ N ) )
             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
         => ( ! [M: subst,A: term,N: subst,K: subst] :
                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
               => ( P @ M @ A @ ( comp @ K @ N ) ) )
           => ( ! [A: term] :
                  ( ( hoasvar @ id @ A @ id )
                 => ( P @ id @ A @ id ) )
             => ! [A: term] :
                  ( ( var @ A )
                 => ( P @ id @ A @ id ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1) ).

thf(hoasinduction_lem1_gthm,definition,
    ( hoasinduction_lem1_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
                                                                       => hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1_gthm) ).

thf(hoasinduction_lem1_lthm,definition,
    ( hoasinduction_lem1_lthm
    = ( 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
                                                                       => hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1_lthm) ).

thf(hoasinduction_lem1v2,definition,
    ( hoasinduction_lem1v2
    = ( ! [P: subst > term > subst > $o,Q: term > $o] :
          ( ! [M: subst,A: term,N: subst,K: subst] :
              ( ( P @ M @ A @ ( comp @ K @ N ) )
             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
         => ( ! [M: subst,A: term,N: subst,K: subst] :
                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
               => ( P @ M @ A @ ( comp @ K @ N ) ) )
           => ( ! [A: term] :
                  ( ( hoasvar @ id @ A @ id )
                 => ( P @ id @ A @ id ) )
             => ( ( hoasinduction_p_and_p_prime @ P @ Q )
               => ! [A: term] :
                    ( ( var @ A )
                   => ( Q @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1v2) ).

thf(hoasinduction_lem1v2_gthm,definition,
    ( hoasinduction_lem1v2_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
                                                                       => hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1v2_gthm) ).

thf(hoasinduction_lem2,definition,
    ( hoasinduction_lem2
    = ( ! [P: subst > term > subst > $o] :
          ( ! [M: subst,A: term,N: subst,K: subst] :
              ( ( P @ M @ A @ ( comp @ K @ N ) )
             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
         => ( ! [M: subst,A: term,N: subst,K: subst] :
                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
               => ( P @ M @ A @ ( comp @ K @ N ) ) )
           => ( ! [A: term,B: term] :
                  ( ( P @ id @ A @ id )
                 => ( ( P @ id @ B @ id )
                   => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
             => ! [A: term,B: term] :
                  ( ( P @ id @ A @ id )
                 => ( ( P @ id @ B @ id )
                   => ( P @ id @ ( ap @ A @ B ) @ id ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2) ).

thf(hoasinduction_lem2_gthm,definition,
    ( hoasinduction_lem2_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
                                                                       => hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2_gthm) ).

thf(hoasinduction_lem2_lthm,definition,
    ( hoasinduction_lem2_lthm
    = ( 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
                                                                       => hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2_lthm) ).

thf(hoasinduction_lem2v2,definition,
    ( hoasinduction_lem2v2
    = ( ! [P: subst > term > subst > $o,Q: term > $o] :
          ( ! [M: subst,A: term,N: subst,K: subst] :
              ( ( P @ M @ A @ ( comp @ K @ N ) )
             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
         => ( ! [M: subst,A: term,N: subst,K: subst] :
                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
               => ( P @ M @ A @ ( comp @ K @ N ) ) )
           => ( ! [A: term,B: term] :
                  ( ( P @ id @ A @ id )
                 => ( ( P @ id @ B @ id )
                   => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
             => ( ( hoasinduction_p_and_p_prime @ P @ Q )
               => ! [A: term,B: term] :
                    ( ( Q @ A )
                   => ( ( Q @ B )
                     => ( Q @ ( ap @ A @ B ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2v2) ).

thf(hoasinduction_lem2v2_gthm,definition,
    ( hoasinduction_lem2v2_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
                                                                       => hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2v2_gthm) ).

thf(hoasinduction_lem3,definition,
    ( hoasinduction_lem3
    = ( ! [P: subst > term > subst > $o] :
          ( ! [M: subst,A: term,N: subst,K: subst] :
              ( ( P @ M @ A @ ( comp @ K @ N ) )
             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
         => ( ! [M: subst,A: term,N: subst,K: subst] :
                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
               => ( P @ M @ A @ ( comp @ K @ N ) ) )
           => ( ! [F: subst > term > term] :
                  ( ! [M: subst,A: term,N: subst] :
                      ( ( sub @ ( F @ M @ A ) @ N )
                      = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
                 => ( ! [A: term] :
                        ( ( P @ id @ A @ id )
                       => ( P @ id @ ( F @ id @ A ) @ id ) )
                   => ( P @ id
                      @ ( hoaslam @ id
                        @ ^ [M: subst,A: term] : ( F @ M @ A ) )
                      @ id ) ) )
             => ! [A: term] :
                  ( ! [B: term] :
                      ( ( P @ id @ B @ id )
                     => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
                 => ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3) ).

thf(hoasinduction_lem3_gthm,definition,
    ( hoasinduction_lem3_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
                                                                       => ( hoasinduction_lem1
                                                                         => ( hoasinduction_lem2
                                                                           => hoasinduction_lem3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3_gthm) ).

thf(hoasinduction_lem3_lthm,definition,
    ( hoasinduction_lem3_lthm
    = ( axvarid
     => ( axvarshift
       => ( hoasinduction_lem3aa
         => hoasinduction_lem3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3_lthm) ).

thf(hoasinduction_lem3a,definition,
    ( hoasinduction_lem3a
    = ( ! [P: subst > term > subst > $o] :
          ( ! [F: subst > term > term] :
              ( ! [M: subst,A: term,N: subst] :
                  ( ( sub @ ( F @ M @ A ) @ N )
                  = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
             => ( ! [A: term] :
                    ( ( P @ id @ A @ id )
                   => ( P @ id @ ( F @ id @ A ) @ id ) )
               => ( P @ id
                  @ ( hoaslam @ id
                    @ ^ [M: subst,A: term] : ( F @ M @ A ) )
                  @ id ) ) )
         => ! [A: term] :
              ( ! [B: term] :
                  ( ( P @ id @ B @ id )
                 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
             => ( P @ id @ ( lam @ A ) @ id ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3a) ).

thf(hoasinduction_lem3a_gthm,definition,
    ( hoasinduction_lem3a_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
                                                                       => ( hoasinduction_lem1
                                                                         => ( hoasinduction_lem2
                                                                           => hoasinduction_lem3a ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3a_gthm) ).

thf(hoasinduction_lem3a_lthm,definition,
    ( hoasinduction_lem3a_lthm
    = ( axvarid
     => ( axvarshift
       => ( hoasinduction_lem3aa
         => hoasinduction_lem3a ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3a_lthm) ).

thf(hoasinduction_lem3aa,definition,
    ( hoasinduction_lem3aa
    = ( ! [P: subst > term > subst > $o] :
          ( ! [F: subst > term > term] :
              ( ! [M: subst,A: term,N: subst] :
                  ( ( sub @ ( F @ M @ A ) @ N )
                  = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
             => ( ! [A: term] :
                    ( ( P @ id @ A @ id )
                   => ( P @ id @ ( F @ id @ A ) @ id ) )
               => ( P @ id
                  @ ( hoaslam @ id
                    @ ^ [M: subst,A: term] : ( F @ M @ A ) )
                  @ id ) ) )
         => ! [A: term] :
              ( ! [B: term] :
                  ( ( P @ id @ B @ id )
                 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
             => ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3aa) ).

thf(hoasinduction_lem3aa_lthm,definition,
    ( hoasinduction_lem3aa_lthm
    = ( axclos
     => ( axmap
       => hoasinduction_lem3aa ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3aa_lthm) ).

thf(hoasinduction_lem3aaa,definition,
    ( hoasinduction_lem3aaa
    = ( ! [P: subst > term > subst > $o] :
          ( ! [F: subst > term > term] :
              ( ? [C: term] :
                ! [M: subst,A: term,N: subst] :
                  ( ( ( sub @ ( F @ M @ A ) @ N )
                    = ( sub @ ( sub @ C @ ( push @ A @ M ) ) @ N ) )
                  & ( ( sub @ C @ ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
                    = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) )
             => ( ! [A: term] :
                    ( ( P @ id @ A @ id )
                   => ( P @ id @ ( F @ id @ A ) @ id ) )
               => ( P @ id
                  @ ( hoaslam @ id
                    @ ^ [M: subst,A: term] : ( F @ M @ A ) )
                  @ id ) ) )
         => ! [A: term] :
              ( ! [B: term] :
                  ( ( P @ id @ B @ id )
                 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
             => ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3aaa) ).

thf(hoasinduction_lem3b,definition,
    ( hoasinduction_lem3b
    = ( ! [B: term] :
        ? [F: subst > term > term] :
          ( ( sub @ B @ ( push @ one @ sh ) )
          = ( F @ sh @ one ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3b) ).

thf(hoasinduction_lem3b_gthm,definition,
    ( hoasinduction_lem3b_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
                                                                       => ( hoasinduction_lem1
                                                                         => ( hoasinduction_lem2
                                                                           => hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3b_gthm) ).

thf(hoasinduction_lem3b_lthm,definition,
    hoasinduction_lem3b_lthm = hoasinduction_lem3b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3b_lthm) ).

thf(hoasinduction_lem3v2,definition,
    ( hoasinduction_lem3v2
    = ( ! [P: subst > term > subst > $o,Q: term > $o] :
          ( ! [M: subst,A: term,N: subst,K: subst] :
              ( ( P @ M @ A @ ( comp @ K @ N ) )
             => ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
         => ( ! [M: subst,A: term,N: subst,K: subst] :
                ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
               => ( P @ M @ A @ ( comp @ K @ N ) ) )
           => ( ! [F: subst > term > term] :
                  ( ! [M: subst,A: term,N: subst] :
                      ( ( sub @ ( F @ M @ A ) @ N )
                      = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
                 => ( ! [A: term] :
                        ( ( P @ id @ A @ id )
                       => ( P @ id @ ( F @ id @ A ) @ id ) )
                   => ( P @ id
                      @ ( hoaslam @ id
                        @ ^ [M: subst,A: term] : ( F @ M @ A ) )
                      @ id ) ) )
             => ( ( hoasinduction_p_and_p_prime @ P @ Q )
               => ! [A: term] :
                    ( ! [B: term] :
                        ( ( Q @ B )
                       => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
                   => ( Q @ ( lam @ A ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2) ).

thf(hoasinduction_lem3v2_f,definition,
    ( hoasinduction_lem3v2_f
    = ( ! [B: term] :
        ? [F: subst > term > term] :
        ! [A: term,M: subst] :
          ( ( F @ M @ A )
          = ( sub @ B @ ( push @ A @ M ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2_f) ).

thf(hoasinduction_lem3v2_f_lthm,definition,
    hoasinduction_lem3v2_f_lthm = hoasinduction_lem3v2_f,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2_f_lthm) ).

thf(hoasinduction_lem3v2_gthm,definition,
    ( hoasinduction_lem3v2_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
                                                                       => hoasinduction_lem3v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2_gthm) ).

thf(hoasinduction_lem3v2_lthm,definition,
    ( hoasinduction_lem3v2_lthm
    = ( axvarid
     => ( axvarshift
       => ( axclos
         => ( axmap
           => hoasinduction_lem3v2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2_lthm) ).

thf(hoasinduction_lem3v2a,definition,
    ( hoasinduction_lem3v2a
    = ( ! [P: subst > term > subst > $o,Q: term > $o] :
          ( ! [F: subst > term > term] :
              ( ! [M: subst,A: term,N: subst] :
                  ( ( sub @ ( F @ M @ A ) @ N )
                  = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
             => ( ! [A: term] :
                    ( ( P @ id @ A @ id )
                   => ( P @ id @ ( F @ id @ A ) @ id ) )
               => ( P @ id
                  @ ( hoaslam @ id
                    @ ^ [M: subst,A: term] : ( F @ M @ A ) )
                  @ id ) ) )
         => ( ( hoasinduction_p_and_p_prime @ P @ Q )
           => ! [A: term] :
                ( ! [B: term] :
                    ( ( Q @ B )
                   => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
               => ( Q @ ( lam @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2a) ).

thf(hoasinduction_lem3v2a_lthm,definition,
    ( hoasinduction_lem3v2a_lthm
    = ( hoasinduction_lem3v2_f
     => ( axvarid
       => ( axvarshift
         => ( axclos
           => ( axmap
             => hoasinduction_lem3v2a ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2a_lthm) ).

thf(hoasinduction_lthm,definition,
    ( hoasinduction_lthm
    = ( induction2
     => ( hoasinduction_lem1
       => ( hoasinduction_lem2
         => ( hoasinduction_lem3
           => hoasinduction ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lthm) ).

thf(hoasinduction_lthm_3,definition,
    ( hoasinduction_lthm_3
    = ( hoasinduction_lem0
     => ( induction2
       => ( axvarid
         => ( hoasinduction_lem3v2a
           => hoasinduction ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lthm_3) ).

thf(hoasinduction_no_psi_cond,definition,
    ( hoasinduction_no_psi_cond
    = ( ! [P: subst > term > subst > $o] :
          ( ! [A: term,B: term] :
              ( ( P @ id @ A @ id )
             => ( ( P @ id @ B @ id )
               => ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
         => ( ! [F: subst > term > term] :
                ( ! [M: subst,A: term,N: subst] :
                    ( ( sub @ ( F @ M @ A ) @ N )
                    = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
               => ( ! [A: term] :
                      ( ( P @ id @ A @ id )
                     => ( P @ id @ ( F @ id @ A ) @ id ) )
                 => ( P @ id
                    @ ( hoaslam @ id
                      @ ^ [M: subst,A: term] : ( F @ M @ A ) )
                    @ id ) ) )
           => ! [A: term] : ( P @ id @ A @ id ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_no_psi_cond) ).

thf(hoasinduction_no_psi_cond_lthm,definition,
    ( hoasinduction_no_psi_cond_lthm
    = ( hoasinduction_lem0
     => ( induction2
       => ( axvarid
         => ( hoasinduction_lem3v2a
           => hoasinduction_no_psi_cond ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_no_psi_cond_lthm) ).

thf(hoasinduction_p_and_p_prime,definition,
    ( hoasinduction_p_and_p_prime
    = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
        ! [X: term] :
          ( ( Q @ X )
        <=> ( P @ id @ X @ id ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_p_and_p_prime) ).

thf(hoaslam,definition,
    ( hoaslam
    = ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslam) ).

thf(hoaslaminj,definition,
    ( hoaslaminj
    = ( ! [F: subst > term > term] :
          ( ! [M: subst,A: term,N: subst] :
              ( ( sub @ ( F @ M @ A ) @ N )
              = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
         => ! [G: subst > term > term] :
              ( ! [M: subst,A: term,N: subst] :
                  ( ( sub @ ( G @ M @ A ) @ N )
                  = ( G @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
             => ( ( ( hoaslam @ id
                    @ ^ [M: subst,A: term] : ( F @ M @ A ) )
                  = ( hoaslam @ id
                    @ ^ [M: subst,A: term] : ( G @ M @ A ) ) )
               => ! [M: subst,A: term] :
                    ( ( F @ M @ A )
                    = ( G @ M @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj) ).

thf(hoaslaminj_gthm,definition,
    ( hoaslaminj_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj_gthm) ).

thf(hoaslaminj_lthm,definition,
    ( hoaslaminj_lthm
    = ( axvarcons
     => ( axshiftcons
       => ( laminj
         => hoaslaminj ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj_lthm) ).

thf(hoaslamnotap,definition,
    ( hoaslamnotap
    = ( ! [F: subst > term > term] :
          ( ! [M: subst,A: term,N: subst] :
              ( ( sub @ ( F @ M @ A ) @ N )
              = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
         => ! [A: term,B: term] :
              ( ( hoaslam @ id
                @ ^ [M: subst,C: term] : ( F @ M @ C ) )
             != ( hoasap @ id @ A @ id @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotap) ).

thf(hoaslamnotap_gthm,definition,
    ( hoaslamnotap_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotap_gthm) ).

thf(hoaslamnotap_lthm,definition,
    ( hoaslamnotap_lthm
    = ( lamnotap
     => hoaslamnotap ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotap_lthm) ).

thf(hoaslamnotvar,definition,
    ( hoaslamnotvar
    = ( ! [F: subst > term > term] :
          ( ! [M: subst,A: term,N: subst] :
              ( ( sub @ ( F @ M @ A ) @ N )
              = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
         => ~ ( hoasvar @ id
              @ ( hoaslam @ id
                @ ^ [M: subst,A: term] : ( F @ M @ A ) )
              @ id ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotvar) ).

thf(hoaslamnotvar_gthm,definition,
    ( hoaslamnotvar_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotvar_gthm) ).

thf(hoaslamnotvar_lthm,definition,
    ( hoaslamnotvar_lthm
    = ( axvarid
     => ( lamnotvar
       => hoaslamnotvar ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotvar_lthm) ).

thf(hoasvar,definition,
    ( hoasvar
    = ( ^ [M: subst,A: term,N: subst] : ( var @ ( sub @ A @ N ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasvar) ).

thf(induction,definition,
    ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction) ).

thf(induction2,definition,
    ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2) ).

thf(induction2_gthm,definition,
    ( induction2_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2_gthm) ).

thf(induction2_lthm,definition,
    ( induction2_lthm
    = ( axvarid
     => ( induction2lem
       => induction2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2_lthm) ).

thf(induction2lem,definition,
    ( 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 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2lem) ).

thf(induction2lem_gthm,definition,
    ( induction2lem_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2lem_gthm) ).

thf(induction2lem_lthm,definition,
    ( induction2lem_lthm
    = ( axapp
     => ( axvarcons
       => ( axabs
         => ( axclos
           => ( axshiftcons
             => ( axassoc
               => ( axmap
                 => ( axidr
                   => ( induction
                     => ( pushprop
                       => induction2lem ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2lem_lthm) ).

thf(laminj,definition,
    ( laminj
    = ( ! [A: term,B: term] :
          ( ( ( lam @ A )
            = ( lam @ B ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',laminj) ).

thf(lamnotap,definition,
    ( lamnotap
    = ( ! [A: term,B: term,C: term] :
          ( ( lam @ A )
         != ( ap @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamnotap) ).

thf(lamnotvar,definition,
    ( lamnotvar
    = ( ! [A: term] :
          ~ ( var @ ( lam @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamnotvar) ).

thf(pushprop,definition,
    ( 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 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop) ).

thf(pushprop_gthm,definition,
    ( pushprop_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_gthm) ).

thf(pushprop_lem0,definition,
    ( pushprop_lem0
    = ( ! [P: term > $o,A: term,M: subst] :
        ? [Q: term > $o] : ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem0) ).

thf(pushprop_lem0_gthm,definition,
    ( pushprop_lem0_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_lem0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem0_gthm) ).

thf(pushprop_lem0_lthm,definition,
    pushprop_lem0_lthm = pushprop_lem0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem0_lthm) ).

thf(pushprop_lem1,definition,
    ( pushprop_lem1
    = ( ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
          ( ( P @ A )
         => ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1) ).

thf(pushprop_lem1_gthm,definition,
    ( pushprop_lem1_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_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1_gthm) ).

thf(pushprop_lem1_lthm,definition,
    ( pushprop_lem1_lthm
    = ( axvarcons
     => ( axclos
       => ( axshiftcons
         => ( ulamvarind
           => pushprop_lem1 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1_lthm) ).

thf(pushprop_lem1v2,definition,
    ( pushprop_lem1v2
    = ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
          ( ( P @ A )
         => ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
           => ( Q @ one ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1v2) ).

thf(pushprop_lem1v2_gthm,definition,
    ( pushprop_lem1v2_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_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1v2_gthm) ).

thf(pushprop_lem1v2_lthm,definition,
    ( pushprop_lem1v2_lthm
    = ( axvarcons
     => pushprop_lem1v2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1v2_lthm) ).

thf(pushprop_lem2v2,definition,
    ( pushprop_lem2v2
    = ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
          ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
         => ( ! [B: term] :
                ( ( var @ B )
               => ( P @ ( sub @ B @ M ) ) )
           => ! [C: term] :
                ( ( var @ C )
               => ( ( Q @ C )
                 => ( Q @ ( sub @ C @ sh ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem2v2) ).

thf(pushprop_lem2v2_gthm,definition,
    ( pushprop_lem2v2_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_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem2v2_gthm) ).

thf(pushprop_lem2v2_lthm,definition,
    ( pushprop_lem2v2_lthm
    = ( axclos
     => ( axshiftcons
       => pushprop_lem2v2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem2v2_lthm) ).

thf(pushprop_lem3v2,definition,
    ( pushprop_lem3v2
    = ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
          ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
         => ( ! [B: term] :
                ( ( var @ B )
               => ( Q @ B ) )
           => ! [B: term] :
                ( ( var @ B )
               => ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem3v2) ).

thf(pushprop_lem3v2_lthm,definition,
    pushprop_lem3v2_lthm = pushprop_lem3v2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem3v2_lthm) ).

thf(pushprop_lthm,definition,
    ( pushprop_lthm
    = ( pushprop_lem0
     => ( ulamvar1
       => ( axvarcons
         => ( axclos
           => ( axshiftcons
             => ( ulamvarind
               => pushprop ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lthm) ).

thf(pushprop_lthm_orig,definition,
    ( pushprop_lthm_orig
    = ( ulamvar1
     => ( axvarcons
       => ( axclos
         => ( axshiftcons
           => ( ulamvarind
             => pushprop ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lthm_orig) ).

thf(pushprop_p_and_p_prime,definition,
    ( pushprop_p_and_p_prime
    = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
        ! [X: term] :
          ( ( Q @ X )
        <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_p_and_p_prime) ).

thf(shinj,definition,
    ( shinj
    = ( ! [A: term,B: term] :
          ( ( ( sub @ A @ sh )
            = ( sub @ B @ sh ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',shinj) ).

thf(substmonoid,definition,
    ( substmonoid
    = ( ! [M: subst,N: subst,K: subst] :
          ( ( comp @ ( comp @ M @ N ) @ K )
          = ( comp @ M @ ( comp @ N @ K ) ) )
      & ! [M: subst] :
          ( ( comp @ id @ M )
          = M )
      & ! [M: subst] :
          ( ( comp @ M @ id )
          = M ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',substmonoid) ).

thf(substmonoid_gthm,definition,
    ( substmonoid_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',substmonoid_gthm) ).

thf(substmonoid_lthm,definition,
    ( substmonoid_lthm
    = ( axidl
     => ( axassoc
       => ( axidr
         => substmonoid ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',substmonoid_lthm) ).

thf(termmset,definition,
    ( termmset
    = ( ! [A: term,M: subst,N: subst] :
          ( ( sub @ ( sub @ A @ M ) @ N )
          = ( sub @ A @ ( comp @ M @ N ) ) )
      & ! [A: term] :
          ( ( sub @ A @ id )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',termmset) ).

thf(termmset_gthm,definition,
    ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',termmset_gthm) ).

thf(termmset_lthm,definition,
    ( termmset_lthm
    = ( axvarid
     => ( axclos
       => termmset ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',termmset_lthm) ).

thf(ulamvar1,definition,
    ( ulamvar1
    = ( var @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvar1) ).

thf(ulamvarind,definition,
    ( ulamvarind
    = ( ! [P: term > $o] :
          ( ( P @ one )
         => ( ! [A: term] :
                ( ( var @ A )
               => ( ( P @ A )
                 => ( P @ ( sub @ A @ sh ) ) ) )
           => ! [A: term] :
                ( ( var @ A )
               => ( P @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvarind) ).

thf(ulamvarsh,definition,
    ( ulamvarsh
    = ( ! [A: term] :
          ( ( var @ A )
         => ( var @ ( sub @ A @ sh ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvarsh) ).

thf(1,conjecture,
    hoasapinj1_gthm,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

thf(2,negated_conjecture,
    hoasapinj1_gthm = $false,
    inference(negate_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ( ( ~ hoasapinj1_gthm )
    = $true ),
    inference(polarity_switch,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ~ hoasapinj1_gthm )
    = $true ),
    inference(copy,[status(thm)],[3]) ).

thf(5,plain,
    ( ( ~ ( ~ ! [SX0: term,SX1: term,SX2: subst] :
                ( ( sub @ ( ap @ SX0 @ SX1 ) @ SX2 )
                = ( ap @ ( sub @ SX0 @ SX2 ) @ ( sub @ SX1 @ SX2 ) ) )
          | ~ ! [SX0: term,SX1: subst] :
                ( ( sub @ one @ ( push @ SX0 @ SX1 ) )
                = SX0 )
          | ~ ! [SX0: term] :
                ( ( sub @ SX0 @ id )
                = SX0 )
          | ~ ! [SX0: term,SX1: subst] :
                ( ( sub @ ( lam @ SX0 ) @ SX1 )
                = ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) )
          | ~ ! [SX0: term,SX1: subst,SX2: subst] :
                ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
          | ~ ! [SX0: subst] :
                ( ( comp @ id @ SX0 )
                = SX0 )
          | ~ ! [SX0: term,SX1: subst] :
                ( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
                = SX1 )
          | ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
          | ~ ! [SX0: term,SX1: subst,SX2: subst] :
                ( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
                = ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
          | ~ ! [SX0: subst] :
                ( ( comp @ SX0 @ id )
                = SX0 )
          | ( ( push @ one @ sh )
           != id )
          | ~ ! [SX0: subst] :
                ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
                = SX0 )
          | ~ ( var @ one )
          | ~ ! [SX0: term] :
                ( ~ ( var @ SX0 )
                | ( var @ ( sub @ SX0 @ sh ) ) )
          | ~ ! [SX0: term > $o] :
                ( ~ ( SX0 @ one )
                | ~ ! [SX1: term] :
                      ( ~ ( var @ SX1 )
                      | ~ ( SX0 @ SX1 )
                      | ( SX0 @ ( sub @ SX1 @ sh ) ) )
                | ! [SX1: term] :
                    ( ~ ( var @ SX1 )
                    | ( SX0 @ SX1 ) ) )
          | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
                ( ( ( ap @ SX0 @ SX2 )
                 != ( ap @ SX1 @ SX3 ) )
                | ( SX0 = SX1 ) )
          | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
                ( ( ( ap @ SX0 @ SX2 )
                 != ( ap @ SX1 @ SX3 ) )
                | ( SX2 = SX3 ) )
          | ~ ! [SX0: term,SX1: term] :
                ( ( ( lam @ SX0 )
                 != ( lam @ SX1 ) )
                | ( SX0 = SX1 ) )
          | ~ ! [SX0: term,SX1: term] :
                ( ( ( sub @ SX0 @ sh )
                 != ( sub @ SX1 @ sh ) )
                | ( SX0 = SX1 ) )
          | ~ ! [SX0: term,SX1: term,SX2: term] :
                ( ( lam @ SX0 )
               != ( ap @ SX1 @ SX2 ) )
          | ~ ! [SX0: term,SX1: term] :
                ~ ( var @ ( ap @ SX0 @ SX1 ) )
          | ~ ! [SX0: term] :
                ~ ( var @ ( lam @ SX0 ) )
          | ~ ! [SX0: term > $o] :
                ( ~ ! [SX1: term] :
                      ( ~ ( var @ SX1 )
                      | ( SX0 @ SX1 ) )
                | ~ ! [SX1: term,SX2: term] :
                      ( ~ ( SX0 @ SX1 )
                      | ~ ( SX0 @ SX2 )
                      | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
                | ~ ! [SX1: term] :
                      ( ~ ( SX0 @ SX1 )
                      | ( SX0 @ ( lam @ SX1 ) ) )
                | ! [SX1: term] : ( SX0 @ SX1 ) )
          | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ~ ( SX0 @ SX1 )
                | ! [SX3: term] :
                    ( ~ ( var @ SX3 )
                    | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
          | ~ ! [SX0: term > $o] :
                ( ~ ! [SX1: term,SX2: term] :
                      ( ~ ( SX0 @ SX1 )
                      | ~ ( SX0 @ SX2 )
                      | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
                | ~ ! [SX1: term] :
                      ( ~ ! [SX2: term] :
                            ( ~ ( SX0 @ SX2 )
                            | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                      | ( SX0 @ ( lam @ SX1 ) ) )
                | ! [SX1: term,SX2: subst] :
                    ( ~ ! [SX3: term] :
                          ( ~ ( var @ SX3 )
                          | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                    | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
          | ~ ! [SX0: term > $o] :
                ( ~ ! [SX1: term] :
                      ( ~ ( var @ SX1 )
                      | ( SX0 @ SX1 ) )
                | ~ ! [SX1: term,SX2: term] :
                      ( ~ ( SX0 @ SX1 )
                      | ~ ( SX0 @ SX2 )
                      | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
                | ~ ! [SX1: term] :
                      ( ~ ! [SX2: term] :
                            ( ~ ( SX0 @ SX2 )
                            | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                      | ( SX0 @ ( lam @ SX1 ) ) )
                | ! [SX1: term] : ( SX0 @ SX1 ) )
          | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                            ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                            = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                      | ~ ! [SX0: subst] :
                            ( ( comp @ id @ SX0 )
                            = SX0 ) )
                | ~ ! [SX0: subst] :
                      ( ( comp @ SX0 @ id )
                      = SX0 ) )
          | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                      ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                      = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                | ~ ! [SX0: term] :
                      ( ( sub @ SX0 @ id )
                      = SX0 ) )
          | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
              ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
               != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
              | ( SX0 = SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).

thf(6,plain,
    ( ( ~ ! [SX0: term,SX1: term,SX2: subst] :
            ( ( sub @ ( ap @ SX0 @ SX1 ) @ SX2 )
            = ( ap @ ( sub @ SX0 @ SX2 ) @ ( sub @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: term,SX1: subst] :
            ( ( sub @ one @ ( push @ SX0 @ SX1 ) )
            = SX0 )
      | ~ ! [SX0: term] :
            ( ( sub @ SX0 @ id )
            = SX0 )
      | ~ ! [SX0: term,SX1: subst] :
            ( ( sub @ ( lam @ SX0 ) @ SX1 )
            = ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) )
      | ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
            = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ id @ SX0 )
            = SX0 )
      | ~ ! [SX0: term,SX1: subst] :
            ( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
            = SX1 )
      | ~ ! [SX0: subst,SX1: subst,SX2: subst] :
            ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
            = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
            = ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 )
      | ( ( push @ one @ sh )
       != id )
      | ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 )
      | ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[5]) ).

thf(7,plain,
    ( ( ~ ! [SX0: term,SX1: term,SX2: subst] :
            ( ( sub @ ( ap @ SX0 @ SX1 ) @ SX2 )
            = ( ap @ ( sub @ SX0 @ SX2 ) @ ( sub @ SX1 @ SX2 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6]) ).

thf(8,plain,
    ( ( ~ ! [SX0: term,SX1: subst] :
            ( ( sub @ one @ ( push @ SX0 @ SX1 ) )
            = SX0 )
      | ~ ! [SX0: term] :
            ( ( sub @ SX0 @ id )
            = SX0 )
      | ~ ! [SX0: term,SX1: subst] :
            ( ( sub @ ( lam @ SX0 ) @ SX1 )
            = ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) )
      | ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
            = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ id @ SX0 )
            = SX0 )
      | ~ ! [SX0: term,SX1: subst] :
            ( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
            = SX1 )
      | ~ ! [SX0: subst,SX1: subst,SX2: subst] :
            ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
            = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
            = ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 )
      | ( ( push @ one @ sh )
       != id )
      | ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 )
      | ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6]) ).

thf(9,plain,
    ( ( ! [SX0: term,SX1: term,SX2: subst] :
          ( ( sub @ ( ap @ SX0 @ SX1 ) @ SX2 )
          = ( ap @ ( sub @ SX0 @ SX2 ) @ ( sub @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7]) ).

thf(10,plain,
    ( ( ~ ! [SX0: term,SX1: subst] :
            ( ( sub @ one @ ( push @ SX0 @ SX1 ) )
            = SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[8]) ).

thf(11,plain,
    ( ( ~ ! [SX0: term] :
            ( ( sub @ SX0 @ id )
            = SX0 )
      | ~ ! [SX0: term,SX1: subst] :
            ( ( sub @ ( lam @ SX0 ) @ SX1 )
            = ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) )
      | ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
            = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ id @ SX0 )
            = SX0 )
      | ~ ! [SX0: term,SX1: subst] :
            ( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
            = SX1 )
      | ~ ! [SX0: subst,SX1: subst,SX2: subst] :
            ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
            = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
            = ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 )
      | ( ( push @ one @ sh )
       != id )
      | ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 )
      | ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[8]) ).

thf(12,plain,
    ! [SV1: term] :
      ( ( ! [SY0: term,SY1: subst] :
            ( ( sub @ ( ap @ SV1 @ SY0 ) @ SY1 )
            = ( ap @ ( sub @ SV1 @ SY1 ) @ ( sub @ SY0 @ SY1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[9]) ).

thf(13,plain,
    ( ( ! [SX0: term,SX1: subst] :
          ( ( sub @ one @ ( push @ SX0 @ SX1 ) )
          = SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[10]) ).

thf(14,plain,
    ( ( ~ ! [SX0: term] :
            ( ( sub @ SX0 @ id )
            = SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[11]) ).

thf(15,plain,
    ( ( ~ ! [SX0: term,SX1: subst] :
            ( ( sub @ ( lam @ SX0 ) @ SX1 )
            = ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) )
      | ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
            = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ id @ SX0 )
            = SX0 )
      | ~ ! [SX0: term,SX1: subst] :
            ( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
            = SX1 )
      | ~ ! [SX0: subst,SX1: subst,SX2: subst] :
            ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
            = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
            = ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 )
      | ( ( push @ one @ sh )
       != id )
      | ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 )
      | ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[11]) ).

thf(16,plain,
    ! [SV2: term,SV1: term] :
      ( ( ! [SY2: subst] :
            ( ( sub @ ( ap @ SV1 @ SV2 ) @ SY2 )
            = ( ap @ ( sub @ SV1 @ SY2 ) @ ( sub @ SV2 @ SY2 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12]) ).

thf(17,plain,
    ! [SV3: term] :
      ( ( ! [SY3: subst] :
            ( ( sub @ one @ ( push @ SV3 @ SY3 ) )
            = SV3 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[13]) ).

thf(18,plain,
    ( ( ! [SX0: term] :
          ( ( sub @ SX0 @ id )
          = SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[14]) ).

thf(19,plain,
    ( ( ~ ! [SX0: term,SX1: subst] :
            ( ( sub @ ( lam @ SX0 ) @ SX1 )
            = ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(20,plain,
    ( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
            = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ id @ SX0 )
            = SX0 )
      | ~ ! [SX0: term,SX1: subst] :
            ( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
            = SX1 )
      | ~ ! [SX0: subst,SX1: subst,SX2: subst] :
            ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
            = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
            = ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 )
      | ( ( push @ one @ sh )
       != id )
      | ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 )
      | ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[15]) ).

thf(21,plain,
    ! [SV4: subst,SV2: term,SV1: term] :
      ( ( ( sub @ ( ap @ SV1 @ SV2 ) @ SV4 )
        = ( ap @ ( sub @ SV1 @ SV4 ) @ ( sub @ SV2 @ SV4 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[16]) ).

thf(22,plain,
    ! [SV5: subst,SV3: term] :
      ( ( ( sub @ one @ ( push @ SV3 @ SV5 ) )
        = SV3 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[17]) ).

thf(23,plain,
    ! [SV6: term] :
      ( ( ( sub @ SV6 @ id )
        = SV6 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[18]) ).

thf(24,plain,
    ( ( ! [SX0: term,SX1: subst] :
          ( ( sub @ ( lam @ SX0 ) @ SX1 )
          = ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[19]) ).

thf(25,plain,
    ( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
            = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(26,plain,
    ( ( ~ ! [SX0: subst] :
            ( ( comp @ id @ SX0 )
            = SX0 )
      | ~ ! [SX0: term,SX1: subst] :
            ( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
            = SX1 )
      | ~ ! [SX0: subst,SX1: subst,SX2: subst] :
            ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
            = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
            = ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 )
      | ( ( push @ one @ sh )
       != id )
      | ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 )
      | ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[20]) ).

thf(27,plain,
    ! [SV7: term] :
      ( ( ! [SY4: subst] :
            ( ( sub @ ( lam @ SV7 ) @ SY4 )
            = ( lam @ ( sub @ SV7 @ ( push @ one @ ( comp @ SY4 @ sh ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[24]) ).

thf(28,plain,
    ( ( ! [SX0: term,SX1: subst,SX2: subst] :
          ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
          = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[25]) ).

thf(29,plain,
    ( ( ~ ! [SX0: subst] :
            ( ( comp @ id @ SX0 )
            = SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[26]) ).

thf(30,plain,
    ( ( ~ ! [SX0: term,SX1: subst] :
            ( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
            = SX1 )
      | ~ ! [SX0: subst,SX1: subst,SX2: subst] :
            ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
            = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
            = ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 )
      | ( ( push @ one @ sh )
       != id )
      | ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 )
      | ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[26]) ).

thf(31,plain,
    ! [SV8: subst,SV7: term] :
      ( ( ( sub @ ( lam @ SV7 ) @ SV8 )
        = ( lam @ ( sub @ SV7 @ ( push @ one @ ( comp @ SV8 @ sh ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(32,plain,
    ! [SV9: term] :
      ( ( ! [SY5: subst,SY6: subst] :
            ( ( sub @ ( sub @ SV9 @ SY5 ) @ SY6 )
            = ( sub @ SV9 @ ( comp @ SY5 @ SY6 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(33,plain,
    ( ( ! [SX0: subst] :
          ( ( comp @ id @ SX0 )
          = SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[29]) ).

thf(34,plain,
    ( ( ~ ! [SX0: term,SX1: subst] :
            ( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
            = SX1 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(35,plain,
    ( ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
            ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
            = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
            = ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 )
      | ( ( push @ one @ sh )
       != id )
      | ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 )
      | ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[30]) ).

thf(36,plain,
    ! [SV10: subst,SV9: term] :
      ( ( ! [SY7: subst] :
            ( ( sub @ ( sub @ SV9 @ SV10 ) @ SY7 )
            = ( sub @ SV9 @ ( comp @ SV10 @ SY7 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[32]) ).

thf(37,plain,
    ! [SV11: subst] :
      ( ( ( comp @ id @ SV11 )
        = SV11 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[33]) ).

thf(38,plain,
    ( ( ! [SX0: term,SX1: subst] :
          ( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
          = SX1 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[34]) ).

thf(39,plain,
    ( ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
            ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
            = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(40,plain,
    ( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
            = ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 )
      | ( ( push @ one @ sh )
       != id )
      | ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 )
      | ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[35]) ).

thf(41,plain,
    ! [SV12: subst,SV10: subst,SV9: term] :
      ( ( ( sub @ ( sub @ SV9 @ SV10 ) @ SV12 )
        = ( sub @ SV9 @ ( comp @ SV10 @ SV12 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[36]) ).

thf(42,plain,
    ! [SV13: term] :
      ( ( ! [SY8: subst] :
            ( ( comp @ sh @ ( push @ SV13 @ SY8 ) )
            = SY8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[38]) ).

thf(43,plain,
    ( ( ! [SX0: subst,SX1: subst,SX2: subst] :
          ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
          = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[39]) ).

thf(44,plain,
    ( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
            = ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[40]) ).

thf(45,plain,
    ( ( ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 )
      | ( ( push @ one @ sh )
       != id )
      | ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 )
      | ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[40]) ).

thf(46,plain,
    ! [SV14: subst,SV13: term] :
      ( ( ( comp @ sh @ ( push @ SV13 @ SV14 ) )
        = SV14 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[42]) ).

thf(47,plain,
    ! [SV15: subst] :
      ( ( ! [SY9: subst,SY10: subst] :
            ( ( comp @ ( comp @ SV15 @ SY9 ) @ SY10 )
            = ( comp @ SV15 @ ( comp @ SY9 @ SY10 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[43]) ).

thf(48,plain,
    ( ( ! [SX0: term,SX1: subst,SX2: subst] :
          ( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
          = ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[44]) ).

thf(49,plain,
    ( ( ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[45]) ).

thf(50,plain,
    ( ( ( ( push @ one @ sh )
       != id )
      | ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 )
      | ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[45]) ).

thf(51,plain,
    ! [SV16: subst,SV15: subst] :
      ( ( ! [SY11: subst] :
            ( ( comp @ ( comp @ SV15 @ SV16 ) @ SY11 )
            = ( comp @ SV15 @ ( comp @ SV16 @ SY11 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[47]) ).

thf(52,plain,
    ! [SV17: term] :
      ( ( ! [SY12: subst,SY13: subst] :
            ( ( comp @ ( push @ SV17 @ SY12 ) @ SY13 )
            = ( push @ ( sub @ SV17 @ SY13 ) @ ( comp @ SY12 @ SY13 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[48]) ).

thf(53,plain,
    ( ( ! [SX0: subst] :
          ( ( comp @ SX0 @ id )
          = SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[49]) ).

thf(54,plain,
    ( ( ( ( push @ one @ sh )
       != id ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(55,plain,
    ( ( ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 )
      | ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[50]) ).

thf(56,plain,
    ! [SV18: subst,SV16: subst,SV15: subst] :
      ( ( ( comp @ ( comp @ SV15 @ SV16 ) @ SV18 )
        = ( comp @ SV15 @ ( comp @ SV16 @ SV18 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[51]) ).

thf(57,plain,
    ! [SV19: subst,SV17: term] :
      ( ( ! [SY14: subst] :
            ( ( comp @ ( push @ SV17 @ SV19 ) @ SY14 )
            = ( push @ ( sub @ SV17 @ SY14 ) @ ( comp @ SV19 @ SY14 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[52]) ).

thf(58,plain,
    ! [SV20: subst] :
      ( ( ( comp @ SV20 @ id )
        = SV20 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[53]) ).

thf(59,plain,
    ( ( ( push @ one @ sh )
      = id )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[54]) ).

thf(60,plain,
    ( ( ~ ! [SX0: subst] :
            ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
            = SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[55]) ).

thf(61,plain,
    ( ( ~ ( var @ one )
      | ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[55]) ).

thf(62,plain,
    ! [SV21: subst,SV19: subst,SV17: term] :
      ( ( ( comp @ ( push @ SV17 @ SV19 ) @ SV21 )
        = ( push @ ( sub @ SV17 @ SV21 ) @ ( comp @ SV19 @ SV21 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[57]) ).

thf(63,plain,
    ( ( ! [SX0: subst] :
          ( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
          = SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[60]) ).

thf(64,plain,
    ( ( ~ ( var @ one ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[61]) ).

thf(65,plain,
    ( ( ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[61]) ).

thf(66,plain,
    ! [SV22: subst] :
      ( ( ( push @ ( sub @ one @ SV22 ) @ ( comp @ sh @ SV22 ) )
        = SV22 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[63]) ).

thf(67,plain,
    ( ( var @ one )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[64]) ).

thf(68,plain,
    ( ( ~ ! [SX0: term] :
            ( ~ ( var @ SX0 )
            | ( var @ ( sub @ SX0 @ sh ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[65]) ).

thf(69,plain,
    ( ( ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[65]) ).

thf(70,plain,
    ( ( ! [SX0: term] :
          ( ~ ( var @ SX0 )
          | ( var @ ( sub @ SX0 @ sh ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[68]) ).

thf(71,plain,
    ( ( ~ ! [SX0: term > $o] :
            ( ~ ( SX0 @ one )
            | ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( sub @ SX1 @ sh ) ) )
            | ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[69]) ).

thf(72,plain,
    ( ( ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[69]) ).

thf(73,plain,
    ! [SV23: term] :
      ( ( ~ ( var @ SV23 )
        | ( var @ ( sub @ SV23 @ sh ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[70]) ).

thf(74,plain,
    ( ( ! [SX0: term > $o] :
          ( ~ ( SX0 @ one )
          | ~ ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ~ ( SX0 @ SX1 )
                | ( SX0 @ ( sub @ SX1 @ sh ) ) )
          | ! [SX1: term] :
              ( ~ ( var @ SX1 )
              | ( SX0 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[71]) ).

thf(75,plain,
    ( ( ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[72]) ).

thf(76,plain,
    ( ( ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[72]) ).

thf(77,plain,
    ! [SV23: term] :
      ( ( ( ~ ( var @ SV23 ) )
        = $true )
      | ( ( var @ ( sub @ SV23 @ sh ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[73]) ).

thf(78,plain,
    ! [SV24: term > $o] :
      ( ( ~ ( SV24 @ one )
        | ~ ! [SY15: term] :
              ( ~ ( var @ SY15 )
              | ~ ( SV24 @ SY15 )
              | ( SV24 @ ( sub @ SY15 @ sh ) ) )
        | ! [SY16: term] :
            ( ~ ( var @ SY16 )
            | ( SV24 @ SY16 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[74]) ).

thf(79,plain,
    ( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ SX0 @ SX2 )
           != ( ap @ SX1 @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[75]) ).

thf(80,plain,
    ( ( ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
            ( ( ( ap @ SX0 @ SX2 )
             != ( ap @ SX1 @ SX3 ) )
            | ( SX2 = SX3 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[76]) ).

thf(81,plain,
    ( ( ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[76]) ).

thf(82,plain,
    ! [SV23: term] :
      ( ( ( var @ SV23 )
        = $false )
      | ( ( var @ ( sub @ SV23 @ sh ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[77]) ).

thf(83,plain,
    ! [SV24: term > $o] :
      ( ( ( ~ ( SV24 @ one ) )
        = $true )
      | ( ( ~ ! [SY15: term] :
                ( ~ ( var @ SY15 )
                | ~ ( SV24 @ SY15 )
                | ( SV24 @ ( sub @ SY15 @ sh ) ) )
          | ! [SY16: term] :
              ( ~ ( var @ SY16 )
              | ( SV24 @ SY16 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[78]) ).

thf(84,plain,
    ! [SV25: term] :
      ( ( ! [SY17: term,SY18: term,SY19: term] :
            ( ( ( ap @ SV25 @ SY18 )
             != ( ap @ SY17 @ SY19 ) )
            | ( SV25 = SY17 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[79]) ).

thf(85,plain,
    ( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ SX0 @ SX2 )
           != ( ap @ SX1 @ SX3 ) )
          | ( SX2 = SX3 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[80]) ).

thf(86,plain,
    ( ( ~ ! [SX0: term,SX1: term] :
            ( ( ( lam @ SX0 )
             != ( lam @ SX1 ) )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[81]) ).

thf(87,plain,
    ( ( ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[81]) ).

thf(88,plain,
    ! [SV24: term > $o] :
      ( ( ( SV24 @ one )
        = $false )
      | ( ( ~ ! [SY15: term] :
                ( ~ ( var @ SY15 )
                | ~ ( SV24 @ SY15 )
                | ( SV24 @ ( sub @ SY15 @ sh ) ) )
          | ! [SY16: term] :
              ( ~ ( var @ SY16 )
              | ( SV24 @ SY16 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[83]) ).

thf(89,plain,
    ! [SV26: term,SV25: term] :
      ( ( ! [SY20: term,SY21: term] :
            ( ( ( ap @ SV25 @ SY20 )
             != ( ap @ SV26 @ SY21 ) )
            | ( SV25 = SV26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[84]) ).

thf(90,plain,
    ! [SV27: term] :
      ( ( ! [SY22: term,SY23: term,SY24: term] :
            ( ( ( ap @ SV27 @ SY23 )
             != ( ap @ SY22 @ SY24 ) )
            | ( SY23 = SY24 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[85]) ).

thf(91,plain,
    ( ( ! [SX0: term,SX1: term] :
          ( ( ( lam @ SX0 )
           != ( lam @ SX1 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[86]) ).

thf(92,plain,
    ( ( ~ ! [SX0: term,SX1: term] :
            ( ( ( sub @ SX0 @ sh )
             != ( sub @ SX1 @ sh ) )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[87]) ).

thf(93,plain,
    ( ( ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) )
      | ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[87]) ).

thf(94,plain,
    ! [SV24: term > $o] :
      ( ( ( ~ ! [SY15: term] :
                ( ~ ( var @ SY15 )
                | ~ ( SV24 @ SY15 )
                | ( SV24 @ ( sub @ SY15 @ sh ) ) ) )
        = $true )
      | ( ( ! [SY16: term] :
              ( ~ ( var @ SY16 )
              | ( SV24 @ SY16 ) ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[88]) ).

thf(95,plain,
    ! [SV26: term,SV28: term,SV25: term] :
      ( ( ! [SY25: term] :
            ( ( ( ap @ SV25 @ SV28 )
             != ( ap @ SV26 @ SY25 ) )
            | ( SV25 = SV26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[89]) ).

thf(96,plain,
    ! [SV29: term,SV27: term] :
      ( ( ! [SY26: term,SY27: term] :
            ( ( ( ap @ SV27 @ SY26 )
             != ( ap @ SV29 @ SY27 ) )
            | ( SY26 = SY27 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[90]) ).

thf(97,plain,
    ! [SV30: term] :
      ( ( ! [SY28: term] :
            ( ( ( lam @ SV30 )
             != ( lam @ SY28 ) )
            | ( SV30 = SY28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[91]) ).

thf(98,plain,
    ( ( ! [SX0: term,SX1: term] :
          ( ( ( sub @ SX0 @ sh )
           != ( sub @ SX1 @ sh ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[92]) ).

thf(99,plain,
    ( ( ~ ! [SX0: term,SX1: term,SX2: term] :
            ( ( lam @ SX0 )
           != ( ap @ SX1 @ SX2 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[93]) ).

thf(100,plain,
    ( ( ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) )
      | ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[93]) ).

thf(101,plain,
    ! [SV24: term > $o] :
      ( ( ( ! [SY15: term] :
              ( ~ ( var @ SY15 )
              | ~ ( SV24 @ SY15 )
              | ( SV24 @ ( sub @ SY15 @ sh ) ) ) )
        = $false )
      | ( ( ! [SY16: term] :
              ( ~ ( var @ SY16 )
              | ( SV24 @ SY16 ) ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[94]) ).

thf(102,plain,
    ! [SV31: term,SV26: term,SV28: term,SV25: term] :
      ( ( ( ( ap @ SV25 @ SV28 )
         != ( ap @ SV26 @ SV31 ) )
        | ( SV25 = SV26 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[95]) ).

thf(103,plain,
    ! [SV29: term,SV32: term,SV27: term] :
      ( ( ! [SY29: term] :
            ( ( ( ap @ SV27 @ SV32 )
             != ( ap @ SV29 @ SY29 ) )
            | ( SV32 = SY29 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[96]) ).

thf(104,plain,
    ! [SV33: term,SV30: term] :
      ( ( ( ( lam @ SV30 )
         != ( lam @ SV33 ) )
        | ( SV30 = SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[97]) ).

thf(105,plain,
    ! [SV34: term] :
      ( ( ! [SY30: term] :
            ( ( ( sub @ SV34 @ sh )
             != ( sub @ SY30 @ sh ) )
            | ( SV34 = SY30 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[98]) ).

thf(106,plain,
    ( ( ! [SX0: term,SX1: term,SX2: term] :
          ( ( lam @ SX0 )
         != ( ap @ SX1 @ SX2 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[99]) ).

thf(107,plain,
    ( ( ~ ! [SX0: term,SX1: term] :
            ~ ( var @ ( ap @ SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[100]) ).

thf(108,plain,
    ( ( ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[100]) ).

thf(109,plain,
    ! [SV24: term > $o] :
      ( ( ( ~ ( var @ ( sK1_SY15 @ SV24 ) )
          | ~ ( SV24 @ ( sK1_SY15 @ SV24 ) )
          | ( SV24 @ ( sub @ ( sK1_SY15 @ SV24 ) @ sh ) ) )
        = $false )
      | ( ( ! [SY16: term] :
              ( ~ ( var @ SY16 )
              | ( SV24 @ SY16 ) ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[101]) ).

thf(110,plain,
    ! [SV31: term,SV26: term,SV28: term,SV25: term] :
      ( ( ( ( ( ap @ SV25 @ SV28 )
           != ( ap @ SV26 @ SV31 ) ) )
        = $true )
      | ( ( SV25 = SV26 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[102]) ).

thf(111,plain,
    ! [SV35: term,SV29: term,SV32: term,SV27: term] :
      ( ( ( ( ap @ SV27 @ SV32 )
         != ( ap @ SV29 @ SV35 ) )
        | ( SV32 = SV35 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[103]) ).

thf(112,plain,
    ! [SV33: term,SV30: term] :
      ( ( ( ( ( lam @ SV30 )
           != ( lam @ SV33 ) ) )
        = $true )
      | ( ( SV30 = SV33 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[104]) ).

thf(113,plain,
    ! [SV36: term,SV34: term] :
      ( ( ( ( sub @ SV34 @ sh )
         != ( sub @ SV36 @ sh ) )
        | ( SV34 = SV36 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[105]) ).

thf(114,plain,
    ! [SV37: term] :
      ( ( ! [SY31: term,SY32: term] :
            ( ( lam @ SV37 )
           != ( ap @ SY31 @ SY32 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[106]) ).

thf(115,plain,
    ( ( ! [SX0: term,SX1: term] :
          ~ ( var @ ( ap @ SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[107]) ).

thf(116,plain,
    ( ( ~ ! [SX0: term] :
            ~ ( var @ ( lam @ SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[108]) ).

thf(117,plain,
    ( ( ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[108]) ).

thf(118,plain,
    ! [SV24: term > $o] :
      ( ( ( ~ ( var @ ( sK1_SY15 @ SV24 ) ) )
        = $false )
      | ( ( ! [SY16: term] :
              ( ~ ( var @ SY16 )
              | ( SV24 @ SY16 ) ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[109]) ).

thf(119,plain,
    ! [SV24: term > $o] :
      ( ( ( ~ ( SV24 @ ( sK1_SY15 @ SV24 ) )
          | ( SV24 @ ( sub @ ( sK1_SY15 @ SV24 ) @ sh ) ) )
        = $false )
      | ( ( ! [SY16: term] :
              ( ~ ( var @ SY16 )
              | ( SV24 @ SY16 ) ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[109]) ).

thf(120,plain,
    ! [SV31: term,SV26: term,SV28: term,SV25: term] :
      ( ( ( ( ap @ SV25 @ SV28 )
          = ( ap @ SV26 @ SV31 ) )
        = $false )
      | ( ( SV25 = SV26 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[110]) ).

thf(121,plain,
    ! [SV35: term,SV29: term,SV32: term,SV27: term] :
      ( ( ( ( ( ap @ SV27 @ SV32 )
           != ( ap @ SV29 @ SV35 ) ) )
        = $true )
      | ( ( SV32 = SV35 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[111]) ).

thf(122,plain,
    ! [SV33: term,SV30: term] :
      ( ( ( ( lam @ SV30 )
          = ( lam @ SV33 ) )
        = $false )
      | ( ( SV30 = SV33 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[112]) ).

thf(123,plain,
    ! [SV36: term,SV34: term] :
      ( ( ( ( ( sub @ SV34 @ sh )
           != ( sub @ SV36 @ sh ) ) )
        = $true )
      | ( ( SV34 = SV36 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[113]) ).

thf(124,plain,
    ! [SV38: term,SV37: term] :
      ( ( ! [SY33: term] :
            ( ( lam @ SV37 )
           != ( ap @ SV38 @ SY33 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[114]) ).

thf(125,plain,
    ! [SV39: term] :
      ( ( ! [SY34: term] :
            ~ ( var @ ( ap @ SV39 @ SY34 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[115]) ).

thf(126,plain,
    ( ( ! [SX0: term] :
          ~ ( var @ ( lam @ SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[116]) ).

thf(127,plain,
    ( ( ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[117]) ).

thf(128,plain,
    ( ( ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[117]) ).

thf(129,plain,
    ! [SV24: term > $o] :
      ( ( ( var @ ( sK1_SY15 @ SV24 ) )
        = $true )
      | ( ( ! [SY16: term] :
              ( ~ ( var @ SY16 )
              | ( SV24 @ SY16 ) ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[118]) ).

thf(130,plain,
    ! [SV24: term > $o] :
      ( ( ( ~ ( SV24 @ ( sK1_SY15 @ SV24 ) ) )
        = $false )
      | ( ( ! [SY16: term] :
              ( ~ ( var @ SY16 )
              | ( SV24 @ SY16 ) ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[119]) ).

thf(131,plain,
    ! [SV24: term > $o] :
      ( ( ( SV24 @ ( sub @ ( sK1_SY15 @ SV24 ) @ sh ) )
        = $false )
      | ( ( ! [SY16: term] :
              ( ~ ( var @ SY16 )
              | ( SV24 @ SY16 ) ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[119]) ).

thf(132,plain,
    ! [SV35: term,SV29: term,SV32: term,SV27: term] :
      ( ( ( ( ap @ SV27 @ SV32 )
          = ( ap @ SV29 @ SV35 ) )
        = $false )
      | ( ( SV32 = SV35 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[121]) ).

thf(133,plain,
    ! [SV36: term,SV34: term] :
      ( ( ( ( sub @ SV34 @ sh )
          = ( sub @ SV36 @ sh ) )
        = $false )
      | ( ( SV34 = SV36 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[123]) ).

thf(134,plain,
    ! [SV40: term,SV38: term,SV37: term] :
      ( ( ( ( lam @ SV37 )
         != ( ap @ SV38 @ SV40 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[124]) ).

thf(135,plain,
    ! [SV41: term,SV39: term] :
      ( ( ~ ( var @ ( ap @ SV39 @ SV41 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[125]) ).

thf(136,plain,
    ! [SV42: term] :
      ( ( ~ ( var @ ( lam @ SV42 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[126]) ).

thf(137,plain,
    ( ( ! [SX0: term > $o] :
          ( ~ ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) )
          | ~ ! [SX1: term,SX2: term] :
                ( ~ ( SX0 @ SX1 )
                | ~ ( SX0 @ SX2 )
                | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
          | ~ ! [SX1: term] :
                ( ~ ( SX0 @ SX1 )
                | ( SX0 @ ( lam @ SX1 ) ) )
          | ! [SX1: term] : ( SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[127]) ).

thf(138,plain,
    ( ( ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
            ( ~ ! [SX3: term] :
                  ( ~ ( var @ SX3 )
                  | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
            | ~ ( SX0 @ SX1 )
            | ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[128]) ).

thf(139,plain,
    ( ( ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
      | ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[128]) ).

thf(140,plain,
    ! [SV24: term > $o,SV43: term] :
      ( ( ( ~ ( var @ SV43 )
          | ( SV24 @ SV43 ) )
        = $true )
      | ( ( var @ ( sK1_SY15 @ SV24 ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[129]) ).

thf(141,plain,
    ! [SV24: term > $o] :
      ( ( ( SV24 @ ( sK1_SY15 @ SV24 ) )
        = $true )
      | ( ( ! [SY16: term] :
              ( ~ ( var @ SY16 )
              | ( SV24 @ SY16 ) ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[130]) ).

thf(142,plain,
    ! [SV24: term > $o,SV44: term] :
      ( ( ( ~ ( var @ SV44 )
          | ( SV24 @ SV44 ) )
        = $true )
      | ( ( SV24 @ ( sub @ ( sK1_SY15 @ SV24 ) @ sh ) )
        = $false )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[131]) ).

thf(143,plain,
    ! [SV40: term,SV38: term,SV37: term] :
      ( ( ( lam @ SV37 )
        = ( ap @ SV38 @ SV40 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[134]) ).

thf(144,plain,
    ! [SV41: term,SV39: term] :
      ( ( var @ ( ap @ SV39 @ SV41 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[135]) ).

thf(145,plain,
    ! [SV42: term] :
      ( ( var @ ( lam @ SV42 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[136]) ).

thf(146,plain,
    ! [SV45: term > $o] :
      ( ( ~ ! [SY35: term] :
              ( ~ ( var @ SY35 )
              | ( SV45 @ SY35 ) )
        | ~ ! [SY36: term,SY37: term] :
              ( ~ ( SV45 @ SY36 )
              | ~ ( SV45 @ SY37 )
              | ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
        | ~ ! [SY38: term] :
              ( ~ ( SV45 @ SY38 )
              | ( SV45 @ ( lam @ SY38 ) ) )
        | ! [SY39: term] : ( SV45 @ SY39 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[137]) ).

thf(147,plain,
    ( ( ! [SX0: term > $o,SX1: term,SX2: subst] :
          ( ~ ! [SX3: term] :
                ( ~ ( var @ SX3 )
                | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
          | ~ ( SX0 @ SX1 )
          | ! [SX3: term] :
              ( ~ ( var @ SX3 )
              | ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[138]) ).

thf(148,plain,
    ( ( ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term,SX2: subst] :
                ( ~ ! [SX3: term] :
                      ( ~ ( var @ SX3 )
                      | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
                | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[139]) ).

thf(149,plain,
    ( ( ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) )
      | ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[139]) ).

thf(150,plain,
    ! [SV24: term > $o,SV43: term] :
      ( ( ( ~ ( var @ SV43 ) )
        = $true )
      | ( ( SV24 @ SV43 )
        = $true )
      | ( ( var @ ( sK1_SY15 @ SV24 ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[140]) ).

thf(151,plain,
    ! [SV24: term > $o,SV46: term] :
      ( ( ( ~ ( var @ SV46 )
          | ( SV24 @ SV46 ) )
        = $true )
      | ( ( SV24 @ ( sK1_SY15 @ SV24 ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[141]) ).

thf(152,plain,
    ! [SV24: term > $o,SV44: term] :
      ( ( ( ~ ( var @ SV44 ) )
        = $true )
      | ( ( SV24 @ SV44 )
        = $true )
      | ( ( SV24 @ ( sub @ ( sK1_SY15 @ SV24 ) @ sh ) )
        = $false )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[142]) ).

thf(153,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ! [SY35: term] :
                ( ~ ( var @ SY35 )
                | ( SV45 @ SY35 ) ) )
        = $true )
      | ( ( ~ ! [SY36: term,SY37: term] :
                ( ~ ( SV45 @ SY36 )
                | ~ ( SV45 @ SY37 )
                | ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
          | ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[146]) ).

thf(154,plain,
    ! [SV47: term > $o] :
      ( ( ! [SY40: term,SY41: subst] :
            ( ~ ! [SY42: term] :
                  ( ~ ( var @ SY42 )
                  | ( SV47 @ ( sub @ SY42 @ SY41 ) ) )
            | ~ ( SV47 @ SY40 )
            | ! [SY43: term] :
                ( ~ ( var @ SY43 )
                | ( SV47 @ ( sub @ SY43 @ ( push @ SY40 @ SY41 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[147]) ).

thf(155,plain,
    ( ( ! [SX0: term > $o] :
          ( ~ ! [SX1: term,SX2: term] :
                ( ~ ( SX0 @ SX1 )
                | ~ ( SX0 @ SX2 )
                | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
          | ~ ! [SX1: term] :
                ( ~ ! [SX2: term] :
                      ( ~ ( SX0 @ SX2 )
                      | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                | ( SX0 @ ( lam @ SX1 ) ) )
          | ! [SX1: term,SX2: subst] :
              ( ~ ! [SX3: term] :
                    ( ~ ( var @ SX3 )
                    | ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
              | ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[148]) ).

thf(156,plain,
    ( ( ~ ! [SX0: term > $o] :
            ( ~ ! [SX1: term] :
                  ( ~ ( var @ SX1 )
                  | ( SX0 @ SX1 ) )
            | ~ ! [SX1: term,SX2: term] :
                  ( ~ ( SX0 @ SX1 )
                  | ~ ( SX0 @ SX2 )
                  | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
            | ~ ! [SX1: term] :
                  ( ~ ! [SX2: term] :
                        ( ~ ( SX0 @ SX2 )
                        | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                  | ( SX0 @ ( lam @ SX1 ) ) )
            | ! [SX1: term] : ( SX0 @ SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[149]) ).

thf(157,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) )
      | ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[149]) ).

thf(158,plain,
    ! [SV24: term > $o,SV43: term] :
      ( ( ( var @ SV43 )
        = $false )
      | ( ( SV24 @ SV43 )
        = $true )
      | ( ( var @ ( sK1_SY15 @ SV24 ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[150]) ).

thf(159,plain,
    ! [SV24: term > $o,SV46: term] :
      ( ( ( ~ ( var @ SV46 ) )
        = $true )
      | ( ( SV24 @ SV46 )
        = $true )
      | ( ( SV24 @ ( sK1_SY15 @ SV24 ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[151]) ).

thf(160,plain,
    ! [SV24: term > $o,SV44: term] :
      ( ( ( var @ SV44 )
        = $false )
      | ( ( SV24 @ SV44 )
        = $true )
      | ( ( SV24 @ ( sub @ ( sK1_SY15 @ SV24 ) @ sh ) )
        = $false )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[152]) ).

thf(161,plain,
    ! [SV45: term > $o] :
      ( ( ( ! [SY35: term] :
              ( ~ ( var @ SY35 )
              | ( SV45 @ SY35 ) ) )
        = $false )
      | ( ( ~ ! [SY36: term,SY37: term] :
                ( ~ ( SV45 @ SY36 )
                | ~ ( SV45 @ SY37 )
                | ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
          | ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[153]) ).

thf(162,plain,
    ! [SV48: term,SV47: term > $o] :
      ( ( ! [SY44: subst] :
            ( ~ ! [SY42: term] :
                  ( ~ ( var @ SY42 )
                  | ( SV47 @ ( sub @ SY42 @ SY44 ) ) )
            | ~ ( SV47 @ SV48 )
            | ! [SY46: term] :
                ( ~ ( var @ SY46 )
                | ( SV47 @ ( sub @ SY46 @ ( push @ SV48 @ SY44 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[154]) ).

thf(163,plain,
    ! [SV49: term > $o] :
      ( ( ~ ! [SY47: term,SY48: term] :
              ( ~ ( SV49 @ SY47 )
              | ~ ( SV49 @ SY48 )
              | ( SV49 @ ( ap @ SY47 @ SY48 ) ) )
        | ~ ! [SY49: term] :
              ( ~ ! [SY50: term] :
                    ( ~ ( SV49 @ SY50 )
                    | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
              | ( SV49 @ ( lam @ SY49 ) ) )
        | ! [SY51: term,SY52: subst] :
            ( ~ ! [SY53: term] :
                  ( ~ ( var @ SY53 )
                  | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
            | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[155]) ).

thf(164,plain,
    ( ( ! [SX0: term > $o] :
          ( ~ ! [SX1: term] :
                ( ~ ( var @ SX1 )
                | ( SX0 @ SX1 ) )
          | ~ ! [SX1: term,SX2: term] :
                ( ~ ( SX0 @ SX1 )
                | ~ ( SX0 @ SX2 )
                | ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
          | ~ ! [SX1: term] :
                ( ~ ! [SX2: term] :
                      ( ~ ( SX0 @ SX2 )
                      | ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
                | ( SX0 @ ( lam @ SX1 ) ) )
          | ! [SX1: term] : ( SX0 @ SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[156]) ).

thf(165,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                        ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                        = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                  | ~ ! [SX0: subst] :
                        ( ( comp @ id @ SX0 )
                        = SX0 ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ SX0 @ id )
                  = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[157]) ).

thf(166,plain,
    ( ( ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) )
      | ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[157]) ).

thf(167,plain,
    ! [SV24: term > $o,SV46: term] :
      ( ( ( var @ SV46 )
        = $false )
      | ( ( SV24 @ SV46 )
        = $true )
      | ( ( SV24 @ ( sK1_SY15 @ SV24 ) )
        = $true )
      | ( ( SV24 @ one )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[159]) ).

thf(168,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( var @ ( sK2_SY35 @ SV45 ) )
          | ( SV45 @ ( sK2_SY35 @ SV45 ) ) )
        = $false )
      | ( ( ~ ! [SY36: term,SY37: term] :
                ( ~ ( SV45 @ SY36 )
                | ~ ( SV45 @ SY37 )
                | ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
          | ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[161]) ).

thf(169,plain,
    ! [SV48: term,SV50: subst,SV47: term > $o] :
      ( ( ~ ! [SY54: term] :
              ( ~ ( var @ SY54 )
              | ( SV47 @ ( sub @ SY54 @ SV50 ) ) )
        | ~ ( SV47 @ SV48 )
        | ! [SY55: term] :
            ( ~ ( var @ SY55 )
            | ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[162]) ).

thf(170,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ! [SY47: term,SY48: term] :
                ( ~ ( SV49 @ SY47 )
                | ~ ( SV49 @ SY48 )
                | ( SV49 @ ( ap @ SY47 @ SY48 ) ) ) )
        = $true )
      | ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) )
          | ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[163]) ).

thf(171,plain,
    ! [SV51: term > $o] :
      ( ( ~ ! [SY56: term] :
              ( ~ ( var @ SY56 )
              | ( SV51 @ SY56 ) )
        | ~ ! [SY57: term,SY58: term] :
              ( ~ ( SV51 @ SY57 )
              | ~ ( SV51 @ SY58 )
              | ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
        | ~ ! [SY59: term] :
              ( ~ ! [SY60: term] :
                    ( ~ ( SV51 @ SY60 )
                    | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
              | ( SV51 @ ( lam @ SY59 ) ) )
        | ! [SY61: term] : ( SV51 @ SY61 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[164]) ).

thf(172,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                      ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                      = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
                | ~ ! [SX0: subst] :
                      ( ( comp @ id @ SX0 )
                      = SX0 ) )
          | ~ ! [SX0: subst] :
                ( ( comp @ SX0 @ id )
                = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[165]) ).

thf(173,plain,
    ( ( ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                  ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                  = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: term] :
                  ( ( sub @ SX0 @ id )
                  = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[166]) ).

thf(174,plain,
    ( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
          ( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
           != ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
          | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[166]) ).

thf(175,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( var @ ( sK2_SY35 @ SV45 ) ) )
        = $false )
      | ( ( ~ ! [SY36: term,SY37: term] :
                ( ~ ( SV45 @ SY36 )
                | ~ ( SV45 @ SY37 )
                | ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
          | ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[168]) ).

thf(176,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false )
      | ( ( ~ ! [SY36: term,SY37: term] :
                ( ~ ( SV45 @ SY36 )
                | ~ ( SV45 @ SY37 )
                | ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
          | ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[168]) ).

thf(177,plain,
    ! [SV48: term,SV50: subst,SV47: term > $o] :
      ( ( ( ~ ! [SY54: term] :
                ( ~ ( var @ SY54 )
                | ( SV47 @ ( sub @ SY54 @ SV50 ) ) ) )
        = $true )
      | ( ( ~ ( SV47 @ SV48 )
          | ! [SY55: term] :
              ( ~ ( var @ SY55 )
              | ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[169]) ).

thf(178,plain,
    ! [SV49: term > $o] :
      ( ( ( ! [SY47: term,SY48: term] :
              ( ~ ( SV49 @ SY47 )
              | ~ ( SV49 @ SY48 )
              | ( SV49 @ ( ap @ SY47 @ SY48 ) ) ) )
        = $false )
      | ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) )
          | ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[170]) ).

thf(179,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY56: term] :
                ( ~ ( var @ SY56 )
                | ( SV51 @ SY56 ) ) )
        = $true )
      | ( ( ~ ! [SY57: term,SY58: term] :
                ( ~ ( SV51 @ SY57 )
                | ~ ( SV51 @ SY58 )
                | ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
          | ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[171]) ).

thf(180,plain,
    ( ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                  ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                  = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ id @ SX0 )
                  = SX0 ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[172]) ).

thf(181,plain,
    ( ( ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
                ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
                = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
          | ~ ! [SX0: term] :
                ( ( sub @ SX0 @ id )
                = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[173]) ).

thf(182,plain,
    ( ( ! [SY62: term,SY63: term,SY64: term] :
          ( ( ( ap @ ( sub @ sK3_SX0 @ id ) @ SY63 )
           != ( ap @ ( sub @ SY62 @ id ) @ SY64 ) )
          | ( sK3_SX0 = SY62 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[174]) ).

thf(183,plain,
    ! [SV45: term > $o] :
      ( ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true )
      | ( ( ~ ! [SY36: term,SY37: term] :
                ( ~ ( SV45 @ SY36 )
                | ~ ( SV45 @ SY37 )
                | ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
          | ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[175]) ).

thf(184,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ! [SY36: term,SY37: term] :
                ( ~ ( SV45 @ SY36 )
                | ~ ( SV45 @ SY37 )
                | ( SV45 @ ( ap @ SY36 @ SY37 ) ) ) )
        = $true )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[176]) ).

thf(185,plain,
    ! [SV48: term,SV50: subst,SV47: term > $o] :
      ( ( ( ! [SY54: term] :
              ( ~ ( var @ SY54 )
              | ( SV47 @ ( sub @ SY54 @ SV50 ) ) ) )
        = $false )
      | ( ( ~ ( SV47 @ SV48 )
          | ! [SY55: term] :
              ( ~ ( var @ SY55 )
              | ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[177]) ).

thf(186,plain,
    ! [SV49: term > $o] :
      ( ( ( ! [SY65: term] :
              ( ~ ( SV49 @ ( sK4_SY47 @ SV49 ) )
              | ~ ( SV49 @ SY65 )
              | ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ SY65 ) ) ) )
        = $false )
      | ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) )
          | ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[178]) ).

thf(187,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY56: term] :
              ( ~ ( var @ SY56 )
              | ( SV51 @ SY56 ) ) )
        = $false )
      | ( ( ~ ! [SY57: term,SY58: term] :
                ( ~ ( SV51 @ SY57 )
                | ~ ( SV51 @ SY58 )
                | ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
          | ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[179]) ).

thf(188,plain,
    ( ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                  ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                  = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
            | ~ ! [SX0: subst] :
                  ( ( comp @ id @ SX0 )
                  = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[180]) ).

thf(189,plain,
    ( ( ~ ! [SX0: subst] :
            ( ( comp @ SX0 @ id )
            = SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[180]) ).

thf(190,plain,
    ( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
            = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: term] :
            ( ( sub @ SX0 @ id )
            = SX0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[181]) ).

thf(191,plain,
    ( ( ! [SY66: term,SY67: term] :
          ( ( ( ap @ ( sub @ sK3_SX0 @ id ) @ SY66 )
           != ( ap @ ( sub @ sK5_SY62 @ id ) @ SY67 ) )
          | ( sK3_SX0 = sK5_SY62 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[182]) ).

thf(192,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ! [SY36: term,SY37: term] :
                ( ~ ( SV45 @ SY36 )
                | ~ ( SV45 @ SY37 )
                | ( SV45 @ ( ap @ SY36 @ SY37 ) ) ) )
        = $true )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[183]) ).

thf(193,plain,
    ! [SV45: term > $o] :
      ( ( ( ! [SY36: term,SY37: term] :
              ( ~ ( SV45 @ SY36 )
              | ~ ( SV45 @ SY37 )
              | ( SV45 @ ( ap @ SY36 @ SY37 ) ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[184]) ).

thf(194,plain,
    ! [SV47: term > $o,SV50: subst,SV48: term] :
      ( ( ( ~ ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
          | ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) ) )
        = $false )
      | ( ( ~ ( SV47 @ SV48 )
          | ! [SY55: term] :
              ( ~ ( var @ SY55 )
              | ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[185]) ).

thf(195,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ( SV49 @ ( sK4_SY47 @ SV49 ) )
          | ~ ( SV49 @ ( sK7_SY65 @ SV49 ) )
          | ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) ) )
        = $false )
      | ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) )
          | ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[186]) ).

thf(196,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ( var @ ( sK8_SY56 @ SV51 ) )
          | ( SV51 @ ( sK8_SY56 @ SV51 ) ) )
        = $false )
      | ( ( ~ ! [SY57: term,SY58: term] :
                ( ~ ( SV51 @ SY57 )
                | ~ ( SV51 @ SY58 )
                | ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
          | ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[187]) ).

thf(197,plain,
    ( ( ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
                ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
                = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
          | ~ ! [SX0: subst] :
                ( ( comp @ id @ SX0 )
                = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[188]) ).

thf(198,plain,
    ( ( ! [SX0: subst] :
          ( ( comp @ SX0 @ id )
          = SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[189]) ).

thf(199,plain,
    ( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
            ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
            = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[190]) ).

thf(200,plain,
    ( ( ~ ! [SX0: term] :
            ( ( sub @ SX0 @ id )
            = SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[190]) ).

thf(201,plain,
    ( ( ! [SY68: term] :
          ( ( ( ap @ ( sub @ sK3_SX0 @ id ) @ sK9_SY66 )
           != ( ap @ ( sub @ sK5_SY62 @ id ) @ SY68 ) )
          | ( sK3_SX0 = sK5_SY62 ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[191]) ).

thf(202,plain,
    ! [SV45: term > $o] :
      ( ( ( ! [SY36: term,SY37: term] :
              ( ~ ( SV45 @ SY36 )
              | ~ ( SV45 @ SY37 )
              | ( SV45 @ ( ap @ SY36 @ SY37 ) ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[192]) ).

thf(203,plain,
    ! [SV45: term > $o] :
      ( ( ( ! [SY69: term] :
              ( ~ ( SV45 @ ( sK10_SY36 @ SV45 ) )
              | ~ ( SV45 @ SY69 )
              | ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ SY69 ) ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[193]) ).

thf(204,plain,
    ! [SV47: term > $o,SV50: subst,SV48: term] :
      ( ( ( ~ ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) ) )
        = $false )
      | ( ( ~ ( SV47 @ SV48 )
          | ! [SY55: term] :
              ( ~ ( var @ SY55 )
              | ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[194]) ).

thf(205,plain,
    ! [SV50: subst,SV48: term,SV47: term > $o] :
      ( ( ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
        = $false )
      | ( ( ~ ( SV47 @ SV48 )
          | ! [SY55: term] :
              ( ~ ( var @ SY55 )
              | ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[194]) ).

thf(206,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ( SV49 @ ( sK4_SY47 @ SV49 ) ) )
        = $false )
      | ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) )
          | ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[195]) ).

thf(207,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ( SV49 @ ( sK7_SY65 @ SV49 ) )
          | ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) ) )
        = $false )
      | ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) )
          | ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[195]) ).

thf(208,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ( var @ ( sK8_SY56 @ SV51 ) ) )
        = $false )
      | ( ( ~ ! [SY57: term,SY58: term] :
                ( ~ ( SV51 @ SY57 )
                | ~ ( SV51 @ SY58 )
                | ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
          | ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[196]) ).

thf(209,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false )
      | ( ( ~ ! [SY57: term,SY58: term] :
                ( ~ ( SV51 @ SY57 )
                | ~ ( SV51 @ SY58 )
                | ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
          | ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[196]) ).

thf(210,plain,
    ( ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
            ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
            = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
      | ~ ! [SX0: subst] :
            ( ( comp @ id @ SX0 )
            = SX0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[197]) ).

thf(211,plain,
    ! [SV52: subst] :
      ( ( ( comp @ SV52 @ id )
        = SV52 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[198]) ).

thf(212,plain,
    ( ( ! [SX0: term,SX1: subst,SX2: subst] :
          ( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
          = ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[199]) ).

thf(213,plain,
    ( ( ! [SX0: term] :
          ( ( sub @ SX0 @ id )
          = SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[200]) ).

thf(214,plain,
    ( ( ( ( ap @ ( sub @ sK3_SX0 @ id ) @ sK9_SY66 )
       != ( ap @ ( sub @ sK5_SY62 @ id ) @ sK11_SY68 ) )
      | ( sK3_SX0 = sK5_SY62 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[201]) ).

thf(215,plain,
    ! [SV45: term > $o] :
      ( ( ( ! [SY70: term] :
              ( ~ ( SV45 @ ( sK12_SY36 @ SV45 ) )
              | ~ ( SV45 @ SY70 )
              | ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ SY70 ) ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[202]) ).

thf(216,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK10_SY36 @ SV45 ) )
          | ~ ( SV45 @ ( sK13_SY69 @ SV45 ) )
          | ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[203]) ).

thf(217,plain,
    ! [SV47: term > $o,SV50: subst,SV48: term] :
      ( ( ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
        = $true )
      | ( ( ~ ( SV47 @ SV48 )
          | ! [SY55: term] :
              ( ~ ( var @ SY55 )
              | ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[204]) ).

thf(218,plain,
    ! [SV50: subst,SV48: term,SV47: term > $o] :
      ( ( ( ~ ( SV47 @ SV48 ) )
        = $true )
      | ( ( ! [SY55: term] :
              ( ~ ( var @ SY55 )
              | ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
        = $true )
      | ( ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[205]) ).

thf(219,plain,
    ! [SV49: term > $o] :
      ( ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true )
      | ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) )
          | ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[206]) ).

thf(220,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ( SV49 @ ( sK7_SY65 @ SV49 ) ) )
        = $false )
      | ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) )
          | ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[207]) ).

thf(221,plain,
    ! [SV49: term > $o] :
      ( ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false )
      | ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) )
          | ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[207]) ).

thf(222,plain,
    ! [SV51: term > $o] :
      ( ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true )
      | ( ( ~ ! [SY57: term,SY58: term] :
                ( ~ ( SV51 @ SY57 )
                | ~ ( SV51 @ SY58 )
                | ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
          | ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[208]) ).

thf(223,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY57: term,SY58: term] :
                ( ~ ( SV51 @ SY57 )
                | ~ ( SV51 @ SY58 )
                | ( SV51 @ ( ap @ SY57 @ SY58 ) ) ) )
        = $true )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[209]) ).

thf(224,plain,
    ( ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
            ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
            = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[210]) ).

thf(225,plain,
    ( ( ~ ! [SX0: subst] :
            ( ( comp @ id @ SX0 )
            = SX0 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[210]) ).

thf(226,plain,
    ! [SV53: term] :
      ( ( ! [SY71: subst,SY72: subst] :
            ( ( sub @ ( sub @ SV53 @ SY71 ) @ SY72 )
            = ( sub @ SV53 @ ( comp @ SY71 @ SY72 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[212]) ).

thf(227,plain,
    ! [SV54: term] :
      ( ( ( sub @ SV54 @ id )
        = SV54 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[213]) ).

thf(228,plain,
    ( ( ( ( ap @ ( sub @ sK3_SX0 @ id ) @ sK9_SY66 )
       != ( ap @ ( sub @ sK5_SY62 @ id ) @ sK11_SY68 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[214]) ).

thf(229,plain,
    ( ( sK3_SX0 = sK5_SY62 )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[214]) ).

thf(230,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK12_SY36 @ SV45 ) )
          | ~ ( SV45 @ ( sK14_SY70 @ SV45 ) )
          | ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[215]) ).

thf(231,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK10_SY36 @ SV45 ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[216]) ).

thf(232,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK13_SY69 @ SV45 ) )
          | ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[216]) ).

thf(233,plain,
    ! [SV50: subst,SV48: term,SV47: term > $o] :
      ( ( ( ~ ( SV47 @ SV48 ) )
        = $true )
      | ( ( ! [SY55: term] :
              ( ~ ( var @ SY55 )
              | ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
        = $true )
      | ( ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[217]) ).

thf(234,plain,
    ! [SV50: subst,SV48: term,SV47: term > $o] :
      ( ( ( SV47 @ SV48 )
        = $false )
      | ( ( ! [SY55: term] :
              ( ~ ( var @ SY55 )
              | ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
        = $true )
      | ( ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[218]) ).

thf(235,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[219]) ).

thf(236,plain,
    ! [SV49: term > $o] :
      ( ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true )
      | ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) )
          | ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[220]) ).

thf(237,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[221]) ).

thf(238,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY57: term,SY58: term] :
                ( ~ ( SV51 @ SY57 )
                | ~ ( SV51 @ SY58 )
                | ( SV51 @ ( ap @ SY57 @ SY58 ) ) ) )
        = $true )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[222]) ).

thf(239,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY57: term,SY58: term] :
              ( ~ ( SV51 @ SY57 )
              | ~ ( SV51 @ SY58 )
              | ( SV51 @ ( ap @ SY57 @ SY58 ) ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[223]) ).

thf(240,plain,
    ( ( ! [SX0: subst,SX1: subst,SX2: subst] :
          ( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
          = ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[224]) ).

thf(241,plain,
    ( ( ! [SX0: subst] :
          ( ( comp @ id @ SX0 )
          = SX0 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[225]) ).

thf(242,plain,
    ! [SV55: subst,SV53: term] :
      ( ( ! [SY73: subst] :
            ( ( sub @ ( sub @ SV53 @ SV55 ) @ SY73 )
            = ( sub @ SV53 @ ( comp @ SV55 @ SY73 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[226]) ).

thf(243,plain,
    ( ( ( ap @ ( sub @ sK3_SX0 @ id ) @ sK9_SY66 )
      = ( ap @ ( sub @ sK5_SY62 @ id ) @ sK11_SY68 ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[228]) ).

thf(244,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK12_SY36 @ SV45 ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[230]) ).

thf(245,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK14_SY70 @ SV45 ) )
          | ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[230]) ).

thf(246,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
        = $true )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[231]) ).

thf(247,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK13_SY69 @ SV45 ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[232]) ).

thf(248,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[232]) ).

thf(249,plain,
    ! [SV50: subst,SV48: term,SV47: term > $o] :
      ( ( ( SV47 @ SV48 )
        = $false )
      | ( ( ! [SY55: term] :
              ( ~ ( var @ SY55 )
              | ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
        = $true )
      | ( ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[233]) ).

thf(250,plain,
    ! [SV50: subst,SV48: term,SV47: term > $o,SV56: term] :
      ( ( ( ~ ( var @ SV56 )
          | ( SV47 @ ( sub @ SV56 @ ( push @ SV48 @ SV50 ) ) ) )
        = $true )
      | ( ( SV47 @ SV48 )
        = $false )
      | ( ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[234]) ).

thf(251,plain,
    ! [SV49: term > $o] :
      ( ( ( ! [SY49: term] :
              ( ~ ! [SY50: term] :
                    ( ~ ( SV49 @ SY50 )
                    | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
              | ( SV49 @ ( lam @ SY49 ) ) ) )
        = $false )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[235]) ).

thf(252,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ! [SY49: term] :
                ( ~ ! [SY50: term] :
                      ( ~ ( SV49 @ SY50 )
                      | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
                | ( SV49 @ ( lam @ SY49 ) ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[236]) ).

thf(253,plain,
    ! [SV49: term > $o] :
      ( ( ( ! [SY49: term] :
              ( ~ ! [SY50: term] :
                    ( ~ ( SV49 @ SY50 )
                    | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
              | ( SV49 @ ( lam @ SY49 ) ) ) )
        = $false )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[237]) ).

thf(254,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY57: term,SY58: term] :
              ( ~ ( SV51 @ SY57 )
              | ~ ( SV51 @ SY58 )
              | ( SV51 @ ( ap @ SY57 @ SY58 ) ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[238]) ).

thf(255,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY74: term] :
              ( ~ ( SV51 @ ( sK15_SY57 @ SV51 ) )
              | ~ ( SV51 @ SY74 )
              | ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ SY74 ) ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[239]) ).

thf(256,plain,
    ! [SV57: subst] :
      ( ( ! [SY75: subst,SY76: subst] :
            ( ( comp @ ( comp @ SV57 @ SY75 ) @ SY76 )
            = ( comp @ SV57 @ ( comp @ SY75 @ SY76 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[240]) ).

thf(257,plain,
    ! [SV58: subst] :
      ( ( ( comp @ id @ SV58 )
        = SV58 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[241]) ).

thf(258,plain,
    ! [SV59: subst,SV55: subst,SV53: term] :
      ( ( ( sub @ ( sub @ SV53 @ SV55 ) @ SV59 )
        = ( sub @ SV53 @ ( comp @ SV55 @ SV59 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[242]) ).

thf(259,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
        = $true )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[244]) ).

thf(260,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK14_SY70 @ SV45 ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[245]) ).

thf(261,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
        = $false )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[245]) ).

thf(262,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) ) )
        = $true )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[246]) ).

thf(263,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
        = $true )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[247]) ).

thf(264,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) ) )
        = $true )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[248]) ).

thf(265,plain,
    ! [SV50: subst,SV48: term,SV47: term > $o,SV60: term] :
      ( ( ( ~ ( var @ SV60 )
          | ( SV47 @ ( sub @ SV60 @ ( push @ SV48 @ SV50 ) ) ) )
        = $true )
      | ( ( SV47 @ SV48 )
        = $false )
      | ( ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[249]) ).

thf(266,plain,
    ! [SV50: subst,SV48: term,SV47: term > $o,SV56: term] :
      ( ( ( ~ ( var @ SV56 ) )
        = $true )
      | ( ( SV47 @ ( sub @ SV56 @ ( push @ SV48 @ SV50 ) ) )
        = $true )
      | ( ( SV47 @ SV48 )
        = $false )
      | ( ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[250]) ).

thf(267,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ! [SY77: term] :
                ( ~ ( SV49 @ SY77 )
                | ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SY77 @ id ) ) ) )
          | ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) ) )
        = $false )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[251]) ).

thf(268,plain,
    ! [SV49: term > $o] :
      ( ( ( ! [SY49: term] :
              ( ~ ! [SY50: term] :
                    ( ~ ( SV49 @ SY50 )
                    | ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
              | ( SV49 @ ( lam @ SY49 ) ) ) )
        = $false )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[252]) ).

thf(269,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ! [SY78: term] :
                ( ~ ( SV49 @ SY78 )
                | ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SY78 @ id ) ) ) )
          | ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) ) )
        = $false )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[253]) ).

thf(270,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY79: term] :
              ( ~ ( SV51 @ ( sK18_SY57 @ SV51 ) )
              | ~ ( SV51 @ SY79 )
              | ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ SY79 ) ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[254]) ).

thf(271,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ( SV51 @ ( sK15_SY57 @ SV51 ) )
          | ~ ( SV51 @ ( sK19_SY74 @ SV51 ) )
          | ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[255]) ).

thf(272,plain,
    ! [SV61: subst,SV57: subst] :
      ( ( ! [SY80: subst] :
            ( ( comp @ ( comp @ SV57 @ SV61 ) @ SY80 )
            = ( comp @ SV57 @ ( comp @ SV61 @ SY80 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[256]) ).

thf(273,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) ) )
        = $true )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[259]) ).

thf(274,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
        = $true )
      | ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) )
          | ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[260]) ).

thf(275,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) ) )
        = $true )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
        = $false )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[261]) ).

thf(276,plain,
    ! [SV45: term > $o] :
      ( ( ( ! [SY38: term] :
              ( ~ ( SV45 @ SY38 )
              | ( SV45 @ ( lam @ SY38 ) ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[262]) ).

thf(277,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) ) )
        = $true )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[263]) ).

thf(278,plain,
    ! [SV45: term > $o] :
      ( ( ( ! [SY38: term] :
              ( ~ ( SV45 @ SY38 )
              | ( SV45 @ ( lam @ SY38 ) ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[264]) ).

thf(279,plain,
    ! [SV50: subst,SV48: term,SV47: term > $o,SV60: term] :
      ( ( ( ~ ( var @ SV60 ) )
        = $true )
      | ( ( SV47 @ ( sub @ SV60 @ ( push @ SV48 @ SV50 ) ) )
        = $true )
      | ( ( SV47 @ SV48 )
        = $false )
      | ( ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[265]) ).

thf(280,plain,
    ! [SV50: subst,SV48: term,SV47: term > $o,SV56: term] :
      ( ( ( var @ SV56 )
        = $false )
      | ( ( SV47 @ ( sub @ SV56 @ ( push @ SV48 @ SV50 ) ) )
        = $true )
      | ( ( SV47 @ SV48 )
        = $false )
      | ( ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[266]) ).

thf(281,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ! [SY77: term] :
                ( ~ ( SV49 @ SY77 )
                | ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SY77 @ id ) ) ) ) )
        = $false )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[267]) ).

thf(282,plain,
    ! [SV49: term > $o] :
      ( ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
        = $false )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[267]) ).

thf(283,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ! [SY81: term] :
                ( ~ ( SV49 @ SY81 )
                | ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SY81 @ id ) ) ) )
          | ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) ) )
        = $false )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[268]) ).

thf(284,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ! [SY78: term] :
                ( ~ ( SV49 @ SY78 )
                | ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SY78 @ id ) ) ) ) )
        = $false )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[269]) ).

thf(285,plain,
    ! [SV49: term > $o] :
      ( ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
        = $false )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[269]) ).

thf(286,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ( SV51 @ ( sK18_SY57 @ SV51 ) )
          | ~ ( SV51 @ ( sK21_SY79 @ SV51 ) )
          | ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[270]) ).

thf(287,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ( SV51 @ ( sK15_SY57 @ SV51 ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[271]) ).

thf(288,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ( SV51 @ ( sK19_SY74 @ SV51 ) )
          | ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[271]) ).

thf(289,plain,
    ! [SV62: subst,SV61: subst,SV57: subst] :
      ( ( ( comp @ ( comp @ SV57 @ SV61 ) @ SV62 )
        = ( comp @ SV57 @ ( comp @ SV61 @ SV62 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[272]) ).

thf(290,plain,
    ! [SV45: term > $o] :
      ( ( ( ! [SY38: term] :
              ( ~ ( SV45 @ SY38 )
              | ( SV45 @ ( lam @ SY38 ) ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[273]) ).

thf(291,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ! [SY38: term] :
                ( ~ ( SV45 @ SY38 )
                | ( SV45 @ ( lam @ SY38 ) ) ) )
        = $true )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[274]) ).

thf(292,plain,
    ! [SV45: term > $o] :
      ( ( ( ! [SY38: term] :
              ( ~ ( SV45 @ SY38 )
              | ( SV45 @ ( lam @ SY38 ) ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
        = $false )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[275]) ).

thf(293,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK22_SY38 @ SV45 ) )
          | ( SV45 @ ( lam @ ( sK22_SY38 @ SV45 ) ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[276]) ).

thf(294,plain,
    ! [SV45: term > $o] :
      ( ( ( ! [SY38: term] :
              ( ~ ( SV45 @ SY38 )
              | ( SV45 @ ( lam @ SY38 ) ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[277]) ).

thf(295,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK23_SY38 @ SV45 ) )
          | ( SV45 @ ( lam @ ( sK23_SY38 @ SV45 ) ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[278]) ).

thf(296,plain,
    ! [SV50: subst,SV48: term,SV47: term > $o,SV60: term] :
      ( ( ( var @ SV60 )
        = $false )
      | ( ( SV47 @ ( sub @ SV60 @ ( push @ SV48 @ SV50 ) ) )
        = $true )
      | ( ( SV47 @ SV48 )
        = $false )
      | ( ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[279]) ).

thf(297,plain,
    ! [SV49: term > $o] :
      ( ( ( ! [SY77: term] :
              ( ~ ( SV49 @ SY77 )
              | ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SY77 @ id ) ) ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[281]) ).

thf(298,plain,
    ! [SV63: term,SV49: term > $o] :
      ( ( ( ! [SY82: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY82 ) ) )
              | ( SV49 @ ( sub @ SV63 @ SY82 ) ) ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[282]) ).

thf(299,plain,
    ! [SV49: term > $o] :
      ( ( ( ~ ! [SY81: term] :
                ( ~ ( SV49 @ SY81 )
                | ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SY81 @ id ) ) ) ) )
        = $false )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[283]) ).

thf(300,plain,
    ! [SV49: term > $o] :
      ( ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
        = $false )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[283]) ).

thf(301,plain,
    ! [SV49: term > $o] :
      ( ( ( ! [SY78: term] :
              ( ~ ( SV49 @ SY78 )
              | ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SY78 @ id ) ) ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[284]) ).

thf(302,plain,
    ! [SV64: term,SV49: term > $o] :
      ( ( ( ! [SY84: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY84 ) ) )
              | ( SV49 @ ( sub @ SV64 @ SY84 ) ) ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[285]) ).

thf(303,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ( SV51 @ ( sK18_SY57 @ SV51 ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[286]) ).

thf(304,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ( SV51 @ ( sK21_SY79 @ SV51 ) )
          | ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[286]) ).

thf(305,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
        = $true )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[287]) ).

thf(306,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ( SV51 @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[288]) ).

thf(307,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[288]) ).

thf(308,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK24_SY38 @ SV45 ) )
          | ( SV45 @ ( lam @ ( sK24_SY38 @ SV45 ) ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[290]) ).

thf(309,plain,
    ! [SV45: term > $o] :
      ( ( ( ! [SY38: term] :
              ( ~ ( SV45 @ SY38 )
              | ( SV45 @ ( lam @ SY38 ) ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[291]) ).

thf(310,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK25_SY38 @ SV45 ) )
          | ( SV45 @ ( lam @ ( sK25_SY38 @ SV45 ) ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
        = $false )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[292]) ).

thf(311,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK22_SY38 @ SV45 ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[293]) ).

thf(312,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( lam @ ( sK22_SY38 @ SV45 ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[293]) ).

thf(313,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK26_SY38 @ SV45 ) )
          | ( SV45 @ ( lam @ ( sK26_SY38 @ SV45 ) ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[294]) ).

thf(314,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK23_SY38 @ SV45 ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[295]) ).

thf(315,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( lam @ ( sK23_SY38 @ SV45 ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[295]) ).

thf(316,plain,
    ! [SV65: term,SV49: term > $o] :
      ( ( ( ~ ( SV49 @ SV65 )
          | ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[297]) ).

thf(317,plain,
    ! [SV63: term,SV66: subst,SV49: term > $o] :
      ( ( ( ~ ! [SY86: term] :
                ( ~ ( var @ SY86 )
                | ( SV49 @ ( sub @ SY86 @ SV66 ) ) )
          | ( SV49 @ ( sub @ SV63 @ SV66 ) ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[298]) ).

thf(318,plain,
    ! [SV49: term > $o] :
      ( ( ( ! [SY81: term] :
              ( ~ ( SV49 @ SY81 )
              | ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SY81 @ id ) ) ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[299]) ).

thf(319,plain,
    ! [SV67: term,SV49: term > $o] :
      ( ( ( ! [SY87: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY87 ) ) )
              | ( SV49 @ ( sub @ SV67 @ SY87 ) ) ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[300]) ).

thf(320,plain,
    ! [SV68: term,SV49: term > $o] :
      ( ( ( ~ ( SV49 @ SV68 )
          | ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[301]) ).

thf(321,plain,
    ! [SV64: term,SV69: subst,SV49: term > $o] :
      ( ( ( ~ ! [SY89: term] :
                ( ~ ( var @ SY89 )
                | ( SV49 @ ( sub @ SY89 @ SV69 ) ) )
          | ( SV49 @ ( sub @ SV64 @ SV69 ) ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[302]) ).

thf(322,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
        = $true )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[303]) ).

thf(323,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ( SV51 @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[304]) ).

thf(324,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[304]) ).

thf(325,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[305]) ).

thf(326,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
        = $true )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[306]) ).

thf(327,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[307]) ).

thf(328,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK24_SY38 @ SV45 ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[308]) ).

thf(329,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( lam @ ( sK24_SY38 @ SV45 ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[308]) ).

thf(330,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK27_SY38 @ SV45 ) )
          | ( SV45 @ ( lam @ ( sK27_SY38 @ SV45 ) ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[309]) ).

thf(331,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK25_SY38 @ SV45 ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
        = $false )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[310]) ).

thf(332,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( lam @ ( sK25_SY38 @ SV45 ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
        = $false )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[310]) ).

thf(333,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( sK22_SY38 @ SV45 ) )
        = $true )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[311]) ).

thf(334,plain,
    ! [SV70: term,SV45: term > $o] :
      ( ( ( SV45 @ SV70 )
        = $true )
      | ( ( SV45 @ ( lam @ ( sK22_SY38 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[312]) ).

thf(335,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK26_SY38 @ SV45 ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[313]) ).

thf(336,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( lam @ ( sK26_SY38 @ SV45 ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[313]) ).

thf(337,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( sK23_SY38 @ SV45 ) )
        = $true )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[314]) ).

thf(338,plain,
    ! [SV71: term,SV45: term > $o] :
      ( ( ( SV45 @ SV71 )
        = $true )
      | ( ( SV45 @ ( lam @ ( sK23_SY38 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[315]) ).

thf(339,plain,
    ! [SV65: term,SV49: term > $o] :
      ( ( ( ~ ( SV49 @ SV65 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[316]) ).

thf(340,plain,
    ! [SV63: term,SV66: subst,SV49: term > $o] :
      ( ( ( ~ ! [SY86: term] :
                ( ~ ( var @ SY86 )
                | ( SV49 @ ( sub @ SY86 @ SV66 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sub @ SV63 @ SV66 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[317]) ).

thf(341,plain,
    ! [SV72: term,SV49: term > $o] :
      ( ( ( ~ ( SV49 @ SV72 )
          | ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[318]) ).

thf(342,plain,
    ! [SV67: term,SV73: subst,SV49: term > $o] :
      ( ( ( ~ ! [SY90: term] :
                ( ~ ( var @ SY90 )
                | ( SV49 @ ( sub @ SY90 @ SV73 ) ) )
          | ( SV49 @ ( sub @ SV67 @ SV73 ) ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[319]) ).

thf(343,plain,
    ! [SV68: term,SV49: term > $o] :
      ( ( ( ~ ( SV49 @ SV68 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[320]) ).

thf(344,plain,
    ! [SV64: term,SV69: subst,SV49: term > $o] :
      ( ( ( ~ ! [SY89: term] :
                ( ~ ( var @ SY89 )
                | ( SV49 @ ( sub @ SY89 @ SV69 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sub @ SV64 @ SV69 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[321]) ).

thf(345,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[322]) ).

thf(346,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
        = $true )
      | ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) )
          | ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[323]) ).

thf(347,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[324]) ).

thf(348,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY59: term] :
              ( ~ ! [SY60: term] :
                    ( ~ ( SV51 @ SY60 )
                    | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
              | ( SV51 @ ( lam @ SY59 ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[325]) ).

thf(349,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[326]) ).

thf(350,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY59: term] :
              ( ~ ! [SY60: term] :
                    ( ~ ( SV51 @ SY60 )
                    | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
              | ( SV51 @ ( lam @ SY59 ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[327]) ).

thf(351,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( sK24_SY38 @ SV45 ) )
        = $true )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[328]) ).

thf(352,plain,
    ! [SV74: term,SV45: term > $o] :
      ( ( ( SV45 @ SV74 )
        = $true )
      | ( ( SV45 @ ( lam @ ( sK24_SY38 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[329]) ).

thf(353,plain,
    ! [SV45: term > $o] :
      ( ( ( ~ ( SV45 @ ( sK27_SY38 @ SV45 ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[330]) ).

thf(354,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( lam @ ( sK27_SY38 @ SV45 ) ) )
        = $false )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[330]) ).

thf(355,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( sK25_SY38 @ SV45 ) )
        = $true )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
        = $false )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[331]) ).

thf(356,plain,
    ! [SV75: term,SV45: term > $o] :
      ( ( ( SV45 @ SV75 )
        = $true )
      | ( ( SV45 @ ( lam @ ( sK25_SY38 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
        = $false )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[332]) ).

thf(357,plain,
    ! [SV76: term,SV45: term > $o] :
      ( ( ( SV45 @ SV76 )
        = $true )
      | ( ( SV45 @ ( sK22_SY38 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[333]) ).

thf(358,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( sK26_SY38 @ SV45 ) )
        = $true )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[335]) ).

thf(359,plain,
    ! [SV77: term,SV45: term > $o] :
      ( ( ( SV45 @ SV77 )
        = $true )
      | ( ( SV45 @ ( lam @ ( sK26_SY38 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[336]) ).

thf(360,plain,
    ! [SV78: term,SV45: term > $o] :
      ( ( ( SV45 @ SV78 )
        = $true )
      | ( ( SV45 @ ( sK23_SY38 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[337]) ).

thf(361,plain,
    ! [SV65: term,SV49: term > $o] :
      ( ( ( SV49 @ SV65 )
        = $false )
      | ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[339]) ).

thf(362,plain,
    ! [SV63: term,SV66: subst,SV49: term > $o] :
      ( ( ( ! [SY86: term] :
              ( ~ ( var @ SY86 )
              | ( SV49 @ ( sub @ SY86 @ SV66 ) ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV63 @ SV66 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[340]) ).

thf(363,plain,
    ! [SV72: term,SV49: term > $o] :
      ( ( ( ~ ( SV49 @ SV72 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[341]) ).

thf(364,plain,
    ! [SV67: term,SV73: subst,SV49: term > $o] :
      ( ( ( ~ ! [SY90: term] :
                ( ~ ( var @ SY90 )
                | ( SV49 @ ( sub @ SY90 @ SV73 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sub @ SV67 @ SV73 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[342]) ).

thf(365,plain,
    ! [SV68: term,SV49: term > $o] :
      ( ( ( SV49 @ SV68 )
        = $false )
      | ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[343]) ).

thf(366,plain,
    ! [SV64: term,SV69: subst,SV49: term > $o] :
      ( ( ( ! [SY89: term] :
              ( ~ ( var @ SY89 )
              | ( SV49 @ ( sub @ SY89 @ SV69 ) ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV64 @ SV69 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[344]) ).

thf(367,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY59: term] :
              ( ~ ! [SY60: term] :
                    ( ~ ( SV51 @ SY60 )
                    | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
              | ( SV51 @ ( lam @ SY59 ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[345]) ).

thf(368,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY59: term] :
                ( ~ ! [SY60: term] :
                      ( ~ ( SV51 @ SY60 )
                      | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
                | ( SV51 @ ( lam @ SY59 ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[346]) ).

thf(369,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY59: term] :
              ( ~ ! [SY60: term] :
                    ( ~ ( SV51 @ SY60 )
                    | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
              | ( SV51 @ ( lam @ SY59 ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[347]) ).

thf(370,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY91: term] :
                ( ~ ( SV51 @ SY91 )
                | ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SY91 @ id ) ) ) )
          | ( SV51 @ ( lam @ ( sK28_SY59 @ SV51 ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[348]) ).

thf(371,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY59: term] :
              ( ~ ! [SY60: term] :
                    ( ~ ( SV51 @ SY60 )
                    | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
              | ( SV51 @ ( lam @ SY59 ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[349]) ).

thf(372,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY92: term] :
                ( ~ ( SV51 @ SY92 )
                | ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SY92 @ id ) ) ) )
          | ( SV51 @ ( lam @ ( sK29_SY59 @ SV51 ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[350]) ).

thf(373,plain,
    ! [SV79: term,SV45: term > $o] :
      ( ( ( SV45 @ SV79 )
        = $true )
      | ( ( SV45 @ ( sK24_SY38 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[351]) ).

thf(374,plain,
    ! [SV45: term > $o] :
      ( ( ( SV45 @ ( sK27_SY38 @ SV45 ) )
        = $true )
      | ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
        = $true )
      | ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[353]) ).

thf(375,plain,
    ! [SV80: term,SV45: term > $o] :
      ( ( ( SV45 @ SV80 )
        = $true )
      | ( ( SV45 @ ( lam @ ( sK27_SY38 @ SV45 ) ) )
        = $false )
      | ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[354]) ).

thf(376,plain,
    ! [SV81: term,SV45: term > $o] :
      ( ( ( SV45 @ SV81 )
        = $true )
      | ( ( SV45 @ ( sK25_SY38 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
        = $false )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[355]) ).

thf(377,plain,
    ! [SV82: term,SV45: term > $o] :
      ( ( ( SV45 @ SV82 )
        = $true )
      | ( ( SV45 @ ( sK26_SY38 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[358]) ).

thf(378,plain,
    ! [SV65: term,SV83: term,SV49: term > $o] :
      ( ( ( ! [SY93: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY93 ) ) )
              | ( SV49 @ ( sub @ SV83 @ SY93 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV65 )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[361]) ).

thf(379,plain,
    ! [SV49: term > $o,SV66: subst,SV63: term] :
      ( ( ( ~ ( var @ ( sK30_SY86 @ SV63 @ SV66 @ SV49 ) )
          | ( SV49 @ ( sub @ ( sK30_SY86 @ SV63 @ SV66 @ SV49 ) @ SV66 ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV63 @ SV66 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[362]) ).

thf(380,plain,
    ! [SV72: term,SV49: term > $o] :
      ( ( ( SV49 @ SV72 )
        = $false )
      | ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
        = $true )
      | ( ( ! [SY51: term,SY52: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
              | ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[363]) ).

thf(381,plain,
    ! [SV67: term,SV73: subst,SV49: term > $o] :
      ( ( ( ! [SY90: term] :
              ( ~ ( var @ SY90 )
              | ( SV49 @ ( sub @ SY90 @ SV73 ) ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV67 @ SV73 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[364]) ).

thf(382,plain,
    ! [SV68: term,SV84: term,SV49: term > $o] :
      ( ( ( ! [SY95: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY95 ) ) )
              | ( SV49 @ ( sub @ SV84 @ SY95 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV68 )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[365]) ).

thf(383,plain,
    ! [SV49: term > $o,SV69: subst,SV64: term] :
      ( ( ( ~ ( var @ ( sK31_SY89 @ SV64 @ SV69 @ SV49 ) )
          | ( SV49 @ ( sub @ ( sK31_SY89 @ SV64 @ SV69 @ SV49 ) @ SV69 ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV64 @ SV69 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[366]) ).

thf(384,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY97: term] :
                ( ~ ( SV51 @ SY97 )
                | ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SY97 @ id ) ) ) )
          | ( SV51 @ ( lam @ ( sK32_SY59 @ SV51 ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[367]) ).

thf(385,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY59: term] :
              ( ~ ! [SY60: term] :
                    ( ~ ( SV51 @ SY60 )
                    | ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
              | ( SV51 @ ( lam @ SY59 ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[368]) ).

thf(386,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY98: term] :
                ( ~ ( SV51 @ SY98 )
                | ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SY98 @ id ) ) ) )
          | ( SV51 @ ( lam @ ( sK33_SY59 @ SV51 ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[369]) ).

thf(387,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY91: term] :
                ( ~ ( SV51 @ SY91 )
                | ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SY91 @ id ) ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[370]) ).

thf(388,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( lam @ ( sK28_SY59 @ SV51 ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[370]) ).

thf(389,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY99: term] :
                ( ~ ( SV51 @ SY99 )
                | ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SY99 @ id ) ) ) )
          | ( SV51 @ ( lam @ ( sK34_SY59 @ SV51 ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[371]) ).

thf(390,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY92: term] :
                ( ~ ( SV51 @ SY92 )
                | ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SY92 @ id ) ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[372]) ).

thf(391,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( lam @ ( sK29_SY59 @ SV51 ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[372]) ).

thf(392,plain,
    ! [SV85: term,SV45: term > $o] :
      ( ( ( SV45 @ SV85 )
        = $true )
      | ( ( SV45 @ ( sK27_SY38 @ SV45 ) )
        = $true )
      | ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
        = $true )
      | ( ( var @ ( sK2_SY35 @ SV45 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[374]) ).

thf(393,plain,
    ! [SV65: term,SV83: term,SV86: subst,SV49: term > $o] :
      ( ( ( ~ ! [SY100: term] :
                ( ~ ( var @ SY100 )
                | ( SV49 @ ( sub @ SY100 @ SV86 ) ) )
          | ( SV49 @ ( sub @ SV83 @ SV86 ) ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV65 )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[378]) ).

thf(394,plain,
    ! [SV49: term > $o,SV66: subst,SV63: term] :
      ( ( ( ~ ( var @ ( sK30_SY86 @ SV63 @ SV66 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV63 @ SV66 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[379]) ).

thf(395,plain,
    ! [SV66: subst,SV63: term,SV49: term > $o] :
      ( ( ( SV49 @ ( sub @ ( sK30_SY86 @ SV63 @ SV66 @ SV49 ) @ SV66 ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV63 @ SV66 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[379]) ).

thf(396,plain,
    ! [SV72: term,SV87: term,SV49: term > $o] :
      ( ( ( ! [SY101: subst] :
              ( ~ ! [SY53: term] :
                    ( ~ ( var @ SY53 )
                    | ( SV49 @ ( sub @ SY53 @ SY101 ) ) )
              | ( SV49 @ ( sub @ SV87 @ SY101 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV72 )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[380]) ).

thf(397,plain,
    ! [SV49: term > $o,SV73: subst,SV67: term] :
      ( ( ( ~ ( var @ ( sK35_SY90 @ SV67 @ SV73 @ SV49 ) )
          | ( SV49 @ ( sub @ ( sK35_SY90 @ SV67 @ SV73 @ SV49 ) @ SV73 ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV67 @ SV73 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[381]) ).

thf(398,plain,
    ! [SV68: term,SV84: term,SV88: subst,SV49: term > $o] :
      ( ( ( ~ ! [SY103: term] :
                ( ~ ( var @ SY103 )
                | ( SV49 @ ( sub @ SY103 @ SV88 ) ) )
          | ( SV49 @ ( sub @ SV84 @ SV88 ) ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV68 )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[382]) ).

thf(399,plain,
    ! [SV49: term > $o,SV69: subst,SV64: term] :
      ( ( ( ~ ( var @ ( sK31_SY89 @ SV64 @ SV69 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV64 @ SV69 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[383]) ).

thf(400,plain,
    ! [SV69: subst,SV64: term,SV49: term > $o] :
      ( ( ( SV49 @ ( sub @ ( sK31_SY89 @ SV64 @ SV69 @ SV49 ) @ SV69 ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV64 @ SV69 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[383]) ).

thf(401,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY97: term] :
                ( ~ ( SV51 @ SY97 )
                | ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SY97 @ id ) ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[384]) ).

thf(402,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( lam @ ( sK32_SY59 @ SV51 ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[384]) ).

thf(403,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY104: term] :
                ( ~ ( SV51 @ SY104 )
                | ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SY104 @ id ) ) ) )
          | ( SV51 @ ( lam @ ( sK36_SY59 @ SV51 ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[385]) ).

thf(404,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY98: term] :
                ( ~ ( SV51 @ SY98 )
                | ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SY98 @ id ) ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[386]) ).

thf(405,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( lam @ ( sK33_SY59 @ SV51 ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[386]) ).

thf(406,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY91: term] :
              ( ~ ( SV51 @ SY91 )
              | ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SY91 @ id ) ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[387]) ).

thf(407,plain,
    ! [SV89: term,SV51: term > $o] :
      ( ( ( SV51 @ SV89 )
        = $true )
      | ( ( SV51 @ ( lam @ ( sK28_SY59 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[388]) ).

thf(408,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY99: term] :
                ( ~ ( SV51 @ SY99 )
                | ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SY99 @ id ) ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[389]) ).

thf(409,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( lam @ ( sK34_SY59 @ SV51 ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[389]) ).

thf(410,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY92: term] :
              ( ~ ( SV51 @ SY92 )
              | ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SY92 @ id ) ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[390]) ).

thf(411,plain,
    ! [SV90: term,SV51: term > $o] :
      ( ( ( SV51 @ SV90 )
        = $true )
      | ( ( SV51 @ ( lam @ ( sK29_SY59 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[391]) ).

thf(412,plain,
    ! [SV65: term,SV83: term,SV86: subst,SV49: term > $o] :
      ( ( ( ~ ! [SY100: term] :
                ( ~ ( var @ SY100 )
                | ( SV49 @ ( sub @ SY100 @ SV86 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sub @ SV83 @ SV86 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV65 )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[393]) ).

thf(413,plain,
    ! [SV49: term > $o,SV66: subst,SV63: term] :
      ( ( ( var @ ( sK30_SY86 @ SV63 @ SV66 @ SV49 ) )
        = $true )
      | ( ( SV49 @ ( sub @ SV63 @ SV66 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[394]) ).

thf(414,plain,
    ! [SV72: term,SV87: term,SV91: subst,SV49: term > $o] :
      ( ( ( ~ ! [SY105: term] :
                ( ~ ( var @ SY105 )
                | ( SV49 @ ( sub @ SY105 @ SV91 ) ) )
          | ( SV49 @ ( sub @ SV87 @ SV91 ) ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV72 )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[396]) ).

thf(415,plain,
    ! [SV49: term > $o,SV73: subst,SV67: term] :
      ( ( ( ~ ( var @ ( sK35_SY90 @ SV67 @ SV73 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV67 @ SV73 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[397]) ).

thf(416,plain,
    ! [SV73: subst,SV67: term,SV49: term > $o] :
      ( ( ( SV49 @ ( sub @ ( sK35_SY90 @ SV67 @ SV73 @ SV49 ) @ SV73 ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV67 @ SV73 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[397]) ).

thf(417,plain,
    ! [SV68: term,SV84: term,SV88: subst,SV49: term > $o] :
      ( ( ( ~ ! [SY103: term] :
                ( ~ ( var @ SY103 )
                | ( SV49 @ ( sub @ SY103 @ SV88 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sub @ SV84 @ SV88 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV68 )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[398]) ).

thf(418,plain,
    ! [SV49: term > $o,SV69: subst,SV64: term] :
      ( ( ( var @ ( sK31_SY89 @ SV64 @ SV69 @ SV49 ) )
        = $true )
      | ( ( SV49 @ ( sub @ SV64 @ SV69 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[399]) ).

thf(419,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY97: term] :
              ( ~ ( SV51 @ SY97 )
              | ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SY97 @ id ) ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[401]) ).

thf(420,plain,
    ! [SV92: term,SV51: term > $o] :
      ( ( ( SV51 @ SV92 )
        = $true )
      | ( ( SV51 @ ( lam @ ( sK32_SY59 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[402]) ).

thf(421,plain,
    ! [SV51: term > $o] :
      ( ( ( ~ ! [SY104: term] :
                ( ~ ( SV51 @ SY104 )
                | ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SY104 @ id ) ) ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[403]) ).

thf(422,plain,
    ! [SV51: term > $o] :
      ( ( ( SV51 @ ( lam @ ( sK36_SY59 @ SV51 ) ) )
        = $false )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[403]) ).

thf(423,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY98: term] :
              ( ~ ( SV51 @ SY98 )
              | ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SY98 @ id ) ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[404]) ).

thf(424,plain,
    ! [SV93: term,SV51: term > $o] :
      ( ( ( SV51 @ SV93 )
        = $true )
      | ( ( SV51 @ ( lam @ ( sK33_SY59 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[405]) ).

thf(425,plain,
    ! [SV94: term,SV51: term > $o] :
      ( ( ( ~ ( SV51 @ SV94 )
          | ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SV94 @ id ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[406]) ).

thf(426,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY99: term] :
              ( ~ ( SV51 @ SY99 )
              | ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SY99 @ id ) ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[408]) ).

thf(427,plain,
    ! [SV95: term,SV51: term > $o] :
      ( ( ( SV51 @ SV95 )
        = $true )
      | ( ( SV51 @ ( lam @ ( sK34_SY59 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[409]) ).

thf(428,plain,
    ! [SV96: term,SV51: term > $o] :
      ( ( ( ~ ( SV51 @ SV96 )
          | ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SV96 @ id ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[410]) ).

thf(429,plain,
    ! [SV65: term,SV83: term,SV86: subst,SV49: term > $o] :
      ( ( ( ! [SY100: term] :
              ( ~ ( var @ SY100 )
              | ( SV49 @ ( sub @ SY100 @ SV86 ) ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV83 @ SV86 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV65 )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[412]) ).

thf(430,plain,
    ! [SV72: term,SV87: term,SV91: subst,SV49: term > $o] :
      ( ( ( ~ ! [SY105: term] :
                ( ~ ( var @ SY105 )
                | ( SV49 @ ( sub @ SY105 @ SV91 ) ) ) )
        = $true )
      | ( ( SV49 @ ( sub @ SV87 @ SV91 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV72 )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[414]) ).

thf(431,plain,
    ! [SV49: term > $o,SV73: subst,SV67: term] :
      ( ( ( var @ ( sK35_SY90 @ SV67 @ SV73 @ SV49 ) )
        = $true )
      | ( ( SV49 @ ( sub @ SV67 @ SV73 ) )
        = $true )
      | ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[415]) ).

thf(432,plain,
    ! [SV68: term,SV84: term,SV88: subst,SV49: term > $o] :
      ( ( ( ! [SY103: term] :
              ( ~ ( var @ SY103 )
              | ( SV49 @ ( sub @ SY103 @ SV88 ) ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV84 @ SV88 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV68 )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[417]) ).

thf(433,plain,
    ! [SV97: term,SV51: term > $o] :
      ( ( ( ~ ( SV51 @ SV97 )
          | ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SV97 @ id ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[419]) ).

thf(434,plain,
    ! [SV51: term > $o] :
      ( ( ( ! [SY104: term] :
              ( ~ ( SV51 @ SY104 )
              | ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SY104 @ id ) ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[421]) ).

thf(435,plain,
    ! [SV98: term,SV51: term > $o] :
      ( ( ( SV51 @ SV98 )
        = $true )
      | ( ( SV51 @ ( lam @ ( sK36_SY59 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[422]) ).

thf(436,plain,
    ! [SV99: term,SV51: term > $o] :
      ( ( ( ~ ( SV51 @ SV99 )
          | ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SV99 @ id ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[423]) ).

thf(437,plain,
    ! [SV94: term,SV51: term > $o] :
      ( ( ( ~ ( SV51 @ SV94 ) )
        = $true )
      | ( ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SV94 @ id ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[425]) ).

thf(438,plain,
    ! [SV100: term,SV51: term > $o] :
      ( ( ( ~ ( SV51 @ SV100 )
          | ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SV100 @ id ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[426]) ).

thf(439,plain,
    ! [SV96: term,SV51: term > $o] :
      ( ( ( ~ ( SV51 @ SV96 ) )
        = $true )
      | ( ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SV96 @ id ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[428]) ).

thf(440,plain,
    ! [SV49: term > $o,SV86: subst,SV83: term,SV65: term] :
      ( ( ( ~ ( var @ ( sK37_SY100 @ SV65 @ SV83 @ SV86 @ SV49 ) )
          | ( SV49 @ ( sub @ ( sK37_SY100 @ SV65 @ SV83 @ SV86 @ SV49 ) @ SV86 ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV83 @ SV86 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV65 )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[429]) ).

thf(441,plain,
    ! [SV72: term,SV87: term,SV91: subst,SV49: term > $o] :
      ( ( ( ! [SY105: term] :
              ( ~ ( var @ SY105 )
              | ( SV49 @ ( sub @ SY105 @ SV91 ) ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV87 @ SV91 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV72 )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[430]) ).

thf(442,plain,
    ! [SV49: term > $o,SV88: subst,SV84: term,SV68: term] :
      ( ( ( ~ ( var @ ( sK38_SY103 @ SV68 @ SV84 @ SV88 @ SV49 ) )
          | ( SV49 @ ( sub @ ( sK38_SY103 @ SV68 @ SV84 @ SV88 @ SV49 ) @ SV88 ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV84 @ SV88 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV68 )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[432]) ).

thf(443,plain,
    ! [SV97: term,SV51: term > $o] :
      ( ( ( ~ ( SV51 @ SV97 ) )
        = $true )
      | ( ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SV97 @ id ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[433]) ).

thf(444,plain,
    ! [SV101: term,SV51: term > $o] :
      ( ( ( ~ ( SV51 @ SV101 )
          | ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SV101 @ id ) ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[434]) ).

thf(445,plain,
    ! [SV99: term,SV51: term > $o] :
      ( ( ( ~ ( SV51 @ SV99 ) )
        = $true )
      | ( ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SV99 @ id ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[436]) ).

thf(446,plain,
    ! [SV94: term,SV51: term > $o] :
      ( ( ( SV51 @ SV94 )
        = $false )
      | ( ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SV94 @ id ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[437]) ).

thf(447,plain,
    ! [SV100: term,SV51: term > $o] :
      ( ( ( ~ ( SV51 @ SV100 ) )
        = $true )
      | ( ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SV100 @ id ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[438]) ).

thf(448,plain,
    ! [SV96: term,SV51: term > $o] :
      ( ( ( SV51 @ SV96 )
        = $false )
      | ( ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SV96 @ id ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[439]) ).

thf(449,plain,
    ! [SV49: term > $o,SV86: subst,SV83: term,SV65: term] :
      ( ( ( ~ ( var @ ( sK37_SY100 @ SV65 @ SV83 @ SV86 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV83 @ SV86 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV65 )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[440]) ).

thf(450,plain,
    ! [SV86: subst,SV83: term,SV65: term,SV49: term > $o] :
      ( ( ( SV49 @ ( sub @ ( sK37_SY100 @ SV65 @ SV83 @ SV86 @ SV49 ) @ SV86 ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV83 @ SV86 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV65 )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[440]) ).

thf(451,plain,
    ! [SV49: term > $o,SV91: subst,SV87: term,SV72: term] :
      ( ( ( ~ ( var @ ( sK39_SY105 @ SV72 @ SV87 @ SV91 @ SV49 ) )
          | ( SV49 @ ( sub @ ( sK39_SY105 @ SV72 @ SV87 @ SV91 @ SV49 ) @ SV91 ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV87 @ SV91 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV72 )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[441]) ).

thf(452,plain,
    ! [SV49: term > $o,SV88: subst,SV84: term,SV68: term] :
      ( ( ( ~ ( var @ ( sK38_SY103 @ SV68 @ SV84 @ SV88 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV84 @ SV88 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV68 )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[442]) ).

thf(453,plain,
    ! [SV88: subst,SV84: term,SV68: term,SV49: term > $o] :
      ( ( ( SV49 @ ( sub @ ( sK38_SY103 @ SV68 @ SV84 @ SV88 @ SV49 ) @ SV88 ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV84 @ SV88 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV68 )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[442]) ).

thf(454,plain,
    ! [SV97: term,SV51: term > $o] :
      ( ( ( SV51 @ SV97 )
        = $false )
      | ( ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SV97 @ id ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[443]) ).

thf(455,plain,
    ! [SV101: term,SV51: term > $o] :
      ( ( ( ~ ( SV51 @ SV101 ) )
        = $true )
      | ( ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SV101 @ id ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[444]) ).

thf(456,plain,
    ! [SV99: term,SV51: term > $o] :
      ( ( ( SV51 @ SV99 )
        = $false )
      | ( ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SV99 @ id ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[445]) ).

thf(457,plain,
    ! [SV94: term,SV102: term,SV51: term > $o] :
      ( ( ( SV51 @ SV102 )
        = $true )
      | ( ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SV94 @ id ) ) )
        = $true )
      | ( ( SV51 @ SV94 )
        = $false )
      | ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[446]) ).

thf(458,plain,
    ! [SV100: term,SV51: term > $o] :
      ( ( ( SV51 @ SV100 )
        = $false )
      | ( ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SV100 @ id ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[447]) ).

thf(459,plain,
    ! [SV96: term,SV103: term,SV51: term > $o] :
      ( ( ( SV51 @ SV103 )
        = $true )
      | ( ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SV96 @ id ) ) )
        = $true )
      | ( ( SV51 @ SV96 )
        = $false )
      | ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
        = $false )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[448]) ).

thf(460,plain,
    ! [SV49: term > $o,SV86: subst,SV83: term,SV65: term] :
      ( ( ( var @ ( sK37_SY100 @ SV65 @ SV83 @ SV86 @ SV49 ) )
        = $true )
      | ( ( SV49 @ ( sub @ SV83 @ SV86 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV65 )
        = $false )
      | ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[449]) ).

thf(461,plain,
    ! [SV49: term > $o,SV91: subst,SV87: term,SV72: term] :
      ( ( ( ~ ( var @ ( sK39_SY105 @ SV72 @ SV87 @ SV91 @ SV49 ) ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV87 @ SV91 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV72 )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[451]) ).

thf(462,plain,
    ! [SV91: subst,SV87: term,SV72: term,SV49: term > $o] :
      ( ( ( SV49 @ ( sub @ ( sK39_SY105 @ SV72 @ SV87 @ SV91 @ SV49 ) @ SV91 ) )
        = $false )
      | ( ( SV49 @ ( sub @ SV87 @ SV91 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV72 )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[451]) ).

thf(463,plain,
    ! [SV49: term > $o,SV88: subst,SV84: term,SV68: term] :
      ( ( ( var @ ( sK38_SY103 @ SV68 @ SV84 @ SV88 @ SV49 ) )
        = $true )
      | ( ( SV49 @ ( sub @ SV84 @ SV88 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV68 )
        = $false )
      | ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[452]) ).

thf(464,plain,
    ! [SV97: term,SV104: term,SV51: term > $o] :
      ( ( ( SV51 @ SV104 )
        = $true )
      | ( ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SV97 @ id ) ) )
        = $true )
      | ( ( SV51 @ SV97 )
        = $false )
      | ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[454]) ).

thf(465,plain,
    ! [SV101: term,SV51: term > $o] :
      ( ( ( SV51 @ SV101 )
        = $false )
      | ( ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SV101 @ id ) ) )
        = $true )
      | ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
        = $true )
      | ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[455]) ).

thf(466,plain,
    ! [SV99: term,SV105: term,SV51: term > $o] :
      ( ( ( SV51 @ SV105 )
        = $true )
      | ( ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SV99 @ id ) ) )
        = $true )
      | ( ( SV51 @ SV99 )
        = $false )
      | ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
        = $false )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[456]) ).

thf(467,plain,
    ! [SV100: term,SV106: term,SV51: term > $o] :
      ( ( ( SV51 @ SV106 )
        = $true )
      | ( ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SV100 @ id ) ) )
        = $true )
      | ( ( SV51 @ SV100 )
        = $false )
      | ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
        = $true )
      | ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[458]) ).

thf(468,plain,
    ! [SV49: term > $o,SV91: subst,SV87: term,SV72: term] :
      ( ( ( var @ ( sK39_SY105 @ SV72 @ SV87 @ SV91 @ SV49 ) )
        = $true )
      | ( ( SV49 @ ( sub @ SV87 @ SV91 ) )
        = $true )
      | ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
        = $true )
      | ( ( SV49 @ SV72 )
        = $false )
      | ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[461]) ).

thf(469,plain,
    ! [SV101: term,SV107: term,SV51: term > $o] :
      ( ( ( SV51 @ SV107 )
        = $true )
      | ( ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SV101 @ id ) ) )
        = $true )
      | ( ( SV51 @ SV101 )
        = $false )
      | ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
        = $true )
      | ( ( var @ ( sK8_SY56 @ SV51 ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[465]) ).

thf(470,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[21,469,468,467,466,464,463,462,460,459,457,453,450,435,431,427,424,420,418,416,413,411,407,400,395,392,377,376,375,373,360,359,357,356,352,338,334,296,289,280,258,257,243,229,227,211,167,160,158,145,144,143,133,132,122,120,82,67,66,62,59,58,56,46,41,37,31,23,22]) ).

thf(471,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[470]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10  % Problem  : ALG256^1 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.06/0.11  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 600
% 0.10/0.30  % DateTime : Thu Jun  9 00:52:22 EDT 2022
% 0.10/0.30  % CPUTime  : 
% 0.15/0.32  .
% 0.15/0.33  
% 0.15/0.33   No.of.Axioms: 0
% 0.15/0.33  
% 0.15/0.33   Length.of.Defs: 38092
% 0.15/0.33  
% 0.15/0.33   Contains.Choice.Funs: false
% 0.15/0.34  .
% 0.15/0.34  (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)........................................................
% 1.46/1.64  
% 1.46/1.64  ********************************
% 1.46/1.64  *   All subproblems solved!    *
% 1.46/1.64  ********************************
% 1.46/1.64  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:470,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.64/1.82  
% 1.64/1.82  %**** Beginning of derivation protocol ****
% 1.64/1.82  % SZS output start CNFRefutation
% See solution above
% 1.64/1.82  
% 1.64/1.82  %**** End of derivation protocol ****
% 1.64/1.82  %**** no. of clauses in derivation: 471 ****
% 1.64/1.82  %**** clause counter: 470 ****
% 1.64/1.82  
% 1.64/1.82  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:470,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------