%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG257^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:08:39 AM UTC 2026
% Result : Theorem 1.58s 0.55s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 114
% Syntax : Number of formulae : 569 ( 270 unt; 0 typ; 113 def)
% Number of atoms : 4151 (1584 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 9127 ( 726 ~;1375 |; 7 &;5856 @)
% ( 2 <=>;1161 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 409 ( 409 >; 0 *; 0 +; 0 <<)
% Number of symbols : 164 ( 161 usr; 117 con; 0-4 aty)
% Number of variables : 1919 ( 39 ^;1875 !; 5 ?;1919 :)
% 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_SY235,type,
sK10_SY235: ( term > $o ) > term ).
thf(tp_sK11_SY219,type,
sK11_SY219: ( term > $o ) > term ).
thf(tp_sK12_SY225,type,
sK12_SY225: ( term > $o ) > term ).
thf(tp_sK13_SY219,type,
sK13_SY219: ( term > $o ) > term ).
thf(tp_sK14_SY279,type,
sK14_SY279: ( term > $o ) > term ).
thf(tp_sK15_SY225,type,
sK15_SY225: ( term > $o ) > term ).
thf(tp_sK16_SY280,type,
sK16_SY280: ( term > $o ) > term ).
thf(tp_sK17_SY281,type,
sK17_SY281: ( term > $o ) > term ).
thf(tp_sK18_SY282,type,
sK18_SY282: ( term > $o ) > term ).
thf(tp_sK19_SY243,type,
sK19_SY243: ( term > $o ) > term ).
thf(tp_sK1_SX0,type,
sK1_SX0: term ).
thf(tp_sK20_SY243,type,
sK20_SY243: ( term > $o ) > term ).
thf(tp_sK21_SY243,type,
sK21_SY243: ( term > $o ) > term ).
thf(tp_sK22_SY221,type,
sK22_SY221: ( term > $o ) > term ).
thf(tp_sK23_SY221,type,
sK23_SY221: ( term > $o ) > term ).
thf(tp_sK24_SY227,type,
sK24_SY227: ( term > $o ) > term ).
thf(tp_sK25_SY227,type,
sK25_SY227: ( term > $o ) > term ).
thf(tp_sK26_SY221,type,
sK26_SY221: ( term > $o ) > term ).
thf(tp_sK27_SY221,type,
sK27_SY221: ( term > $o ) > term ).
thf(tp_sK28_SY221,type,
sK28_SY221: ( term > $o ) > term ).
thf(tp_sK29_SY227,type,
sK29_SY227: ( term > $o ) > term ).
thf(tp_sK2_SY264,type,
sK2_SY264: term ).
thf(tp_sK30_SY227,type,
sK30_SY227: ( term > $o ) > term ).
thf(tp_sK31_SY227,type,
sK31_SY227: ( term > $o ) > term ).
thf(tp_sK32_SY221,type,
sK32_SY221: ( term > $o ) > term ).
thf(tp_sK33_SY227,type,
sK33_SY227: ( term > $o ) > term ).
thf(tp_sK34_SY290,type,
sK34_SY290: term > subst > ( term > $o ) > term ).
thf(tp_sK35_SY293,type,
sK35_SY293: term > subst > ( term > $o ) > term ).
thf(tp_sK36_SY296,type,
sK36_SY296: term > subst > ( term > $o ) > term ).
thf(tp_sK37_SY305,type,
sK37_SY305: term > term > subst > ( term > $o ) > term ).
thf(tp_sK38_SY308,type,
sK38_SY308: term > term > subst > ( term > $o ) > term ).
thf(tp_sK39_SY309,type,
sK39_SY309: term > term > subst > ( term > $o ) > term ).
thf(tp_sK3_SY218,type,
sK3_SY218: ( term > $o ) > term ).
thf(tp_sK4_SY224,type,
sK4_SY224: ( term > $o ) > term ).
thf(tp_sK5_SY274,type,
sK5_SY274: term ).
thf(tp_sK6_SY241,type,
sK6_SY241: ( term > $o ) > term ).
thf(tp_sK7_SY277,type,
sK7_SY277: term ).
thf(tp_sK8_SY278,type,
sK8_SY278: ( term > $o ) > term ).
thf(tp_sK9_SY270,type,
sK9_SY270: term > subst > ( term > $o ) > 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,
hoasapinj2_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
hoasapinj2_gthm = $false,
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) )
=> ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A )
=> ( ! [A: term] :
( ( sub @ A @ id )
= A )
=> ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) )
=> ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) )
=> ( ! [M: subst] :
( ( comp @ id @ M )
= M )
=> ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M )
=> ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) )
=> ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
=> ( ! [M: subst] :
( ( comp @ M @ id )
= M )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M )
=> ( ( var @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) )
=> ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) )
=> ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) )
=> ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) )
=> ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) )
=> ( ! [A: term] :
~ ( var @ ( lam @ A ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ( ! [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 ) )
=> ( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) )
=> ( ! [SY79: term,SY80: term,SY81: term,SY82: term] :
( ( ( ap @ ( sub @ SY79 @ id ) @ SY81 )
= ( ap @ ( sub @ SY80 @ id ) @ SY82 ) )
=> ( SY79 = SY80 ) )
=> ! [SY95: term,SY96: term,SY97: term,SY98: term] :
( ( ( ap @ ( sub @ SY95 @ id ) @ SY97 )
= ( ap @ ( sub @ SY96 @ id ) @ SY98 ) )
=> ( SY97 = SY98 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,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(4,plain,
( ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( var @ one )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: term] :
~ ( var @ ( lam @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(33,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [SY79: term,SY80: term,SY81: term,SY82: term] :
( ( ( ap @ ( sub @ SY79 @ id ) @ SY81 )
= ( ap @ ( sub @ SY80 @ id ) @ SY82 ) )
=> ( SY79 = SY80 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [SY95: term,SY96: term,SY97: term,SY98: term] :
( ( ( ap @ ( sub @ SY95 @ id ) @ SY97 )
= ( ap @ ( sub @ SY96 @ id ) @ SY98 ) )
=> ( SY97 = SY98 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(37,plain,
( ( ~ ! [SY95: term,SY96: term,SY97: term,SY98: term] :
( ( ( ap @ ( sub @ SY95 @ id ) @ SY97 )
= ( ap @ ( sub @ SY96 @ id ) @ SY98 ) )
=> ( SY97 = SY98 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[36]) ).
thf(38,plain,
( ( ! [SY79: term,SY80: term,SY81: term,SY82: term] :
( ( ( ap @ ( sub @ SY79 @ id ) @ SY81 )
= ( ap @ ( sub @ SY80 @ id ) @ SY82 ) )
=> ( SY79 = SY80 ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(39,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(40,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(41,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(42,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(43,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(44,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(45,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(46,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(47,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(48,plain,
( ( ! [A: term] :
~ ( var @ ( lam @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(49,plain,
( ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(50,plain,
( ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(51,plain,
( ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(52,plain,
( ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(53,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(54,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(55,plain,
( ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(56,plain,
( ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(57,plain,
( ( var @ one )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(58,plain,
( ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(59,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(60,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(61,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(62,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(63,plain,
( ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(64,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(65,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(66,plain,
( ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(67,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(68,plain,
( ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(69,plain,
( ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(70,plain,
( ( ~ ! [SY95: term,SY96: term,SY97: term,SY98: term] :
( ( ( ap @ ( sub @ SY95 @ id ) @ SY97 )
= ( ap @ ( sub @ SY96 @ id ) @ SY98 ) )
=> ( SY97 = SY98 ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(71,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(unfold_def,[status(thm)],[46,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(72,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(unfold_def,[status(thm)],[44,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(73,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(unfold_def,[status(thm)],[47,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(74,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53,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(75,plain,
( ( ! [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)],[38,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(76,plain,
( ( ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55,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(77,plain,
( ( ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51,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(78,plain,
( ( ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70,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(79,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54,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(80,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(unfold_def,[status(thm)],[45,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(81,plain,
( ( ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56,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(82,plain,
( ( ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52,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(83,plain,
( ( ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50,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(84,plain,
! [SV1: term] :
( ( ( sub @ SV1 @ id )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(85,plain,
! [SV2: term] :
( ( ! [SY198: subst,SY199: subst] :
( ( sub @ ( sub @ SV2 @ SY198 ) @ SY199 )
= ( sub @ SV2 @ ( comp @ SY198 @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(86,plain,
! [SV3: subst] :
( ( ( comp @ SV3 @ id )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(87,plain,
! [SV4: subst] :
( ( ( comp @ id @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(88,plain,
! [SV5: subst] :
( ( ! [SY200: subst,SY201: subst] :
( ( comp @ ( comp @ SV5 @ SY200 ) @ SY201 )
= ( comp @ SV5 @ ( comp @ SY200 @ SY201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(89,plain,
! [SV6: term] :
( ( ~ ( var @ ( lam @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(90,plain,
! [SV7: term] :
( ( ! [SY202: term] :
~ ( var @ ( ap @ SV7 @ SY202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(91,plain,
! [SV8: subst] :
( ( ( push @ ( sub @ one @ SV8 ) @ ( comp @ sh @ SV8 ) )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(92,plain,
! [SV9: subst] :
( ( ( comp @ SV9 @ id )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(93,plain,
! [SV10: term] :
( ( ! [SY203: subst,SY204: subst] :
( ( comp @ ( push @ SV10 @ SY203 ) @ SY204 )
= ( push @ ( sub @ SV10 @ SY204 ) @ ( comp @ SY203 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(94,plain,
! [SV11: subst] :
( ( ! [SY205: subst,SY206: subst] :
( ( comp @ ( comp @ SV11 @ SY205 ) @ SY206 )
= ( comp @ SV11 @ ( comp @ SY205 @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(95,plain,
! [SV12: term] :
( ( ! [SY207: subst] :
( ( comp @ sh @ ( push @ SV12 @ SY207 ) )
= SY207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(96,plain,
! [SV13: subst] :
( ( ( comp @ id @ SV13 )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(97,plain,
! [SV14: term] :
( ( ! [SY208: subst,SY209: subst] :
( ( sub @ ( sub @ SV14 @ SY208 ) @ SY209 )
= ( sub @ SV14 @ ( comp @ SY208 @ SY209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(98,plain,
! [SV15: term] :
( ( ! [SY210: subst] :
( ( sub @ ( lam @ SV15 ) @ SY210 )
= ( lam @ ( sub @ SV15 @ ( push @ one @ ( comp @ SY210 @ sh ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(99,plain,
! [SV16: term] :
( ( ( sub @ SV16 @ id )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(100,plain,
! [SV17: term] :
( ( ! [SY211: subst] :
( ( sub @ one @ ( push @ SV17 @ SY211 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(101,plain,
! [SV18: term] :
( ( ! [SY212: term,SY213: subst] :
( ( sub @ ( ap @ SV18 @ SY212 ) @ SY213 )
= ( ap @ ( sub @ SV18 @ SY213 ) @ ( sub @ SY212 @ SY213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(102,plain,
! [SV19: term > $o] :
( ( ! [SY214: term,SY215: subst] :
( ~ ! [SY216: term] :
( ~ ( var @ SY216 )
| ( SV19 @ ( sub @ SY216 @ SY215 ) ) )
| ~ ( SV19 @ SY214 )
| ! [SY217: term] :
( ~ ( var @ SY217 )
| ( SV19 @ ( sub @ SY217 @ ( push @ SY214 @ SY215 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(103,plain,
! [SV20: term > $o] :
( ( ~ ! [SY218: term] :
( ~ ( var @ SY218 )
| ( SV20 @ SY218 ) )
| ~ ! [SY219: term,SY220: term] :
( ~ ( SV20 @ SY219 )
| ~ ( SV20 @ SY220 )
| ( SV20 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(104,plain,
! [SV21: term > $o] :
( ( ~ ! [SY224: term] :
( ~ ( var @ SY224 )
| ( SV21 @ SY224 ) )
| ~ ! [SY225: term,SY226: term] :
( ~ ( SV21 @ SY225 )
| ~ ( SV21 @ SY226 )
| ( SV21 @ ( ap @ SY225 @ SY226 ) ) )
| ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(105,plain,
! [SV22: term] :
( ( ! [SY229: term,SY230: term,SY231: term] :
( ( ( ap @ SV22 @ SY230 )
!= ( ap @ SY229 @ SY231 ) )
| ( SY230 = SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(106,plain,
! [SV23: term] :
( ( ! [SY232: term,SY233: term,SY234: term] :
( ( ( ap @ ( sub @ SV23 @ id ) @ SY233 )
!= ( ap @ ( sub @ SY232 @ id ) @ SY234 ) )
| ( SV23 = SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(107,plain,
! [SV24: term > $o] :
( ( ~ ( SV24 @ one )
| ~ ! [SY235: term] :
( ~ ( var @ SY235 )
| ~ ( SV24 @ SY235 )
| ( SV24 @ ( sub @ SY235 @ sh ) ) )
| ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV24 @ SY236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(108,plain,
! [SV25: term] :
( ( ! [SY237: term] :
( ( ( sub @ SV25 @ sh )
!= ( sub @ SY237 @ sh ) )
| ( SV25 = SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(109,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(110,plain,
! [SV26: term] :
( ( ! [SY238: term,SY239: term,SY240: term] :
( ( ( ap @ SV26 @ SY239 )
!= ( ap @ SY238 @ SY240 ) )
| ( SV26 = SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(111,plain,
! [SV27: term > $o] :
( ( ~ ! [SY241: term,SY242: term] :
( ~ ( SV27 @ SY241 )
| ~ ( SV27 @ SY242 )
| ( SV27 @ ( ap @ SY241 @ SY242 ) ) )
| ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) )
| ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(112,plain,
! [SV28: term] :
( ( ~ ( var @ SV28 )
| ( var @ ( sub @ SV28 @ sh ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(113,plain,
! [SV29: term] :
( ( ! [SY248: term] :
( ( ( lam @ SV29 )
!= ( lam @ SY248 ) )
| ( SV29 = SY248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(114,plain,
! [SV30: term] :
( ( ! [SY249: term,SY250: term] :
( ( lam @ SV30 )
!= ( ap @ SY249 @ SY250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(115,plain,
! [SV31: subst,SV2: term] :
( ( ! [SY251: subst] :
( ( sub @ ( sub @ SV2 @ SV31 ) @ SY251 )
= ( sub @ SV2 @ ( comp @ SV31 @ SY251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(116,plain,
! [SV32: subst,SV5: subst] :
( ( ! [SY252: subst] :
( ( comp @ ( comp @ SV5 @ SV32 ) @ SY252 )
= ( comp @ SV5 @ ( comp @ SV32 @ SY252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(117,plain,
! [SV6: term] :
( ( var @ ( lam @ SV6 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(118,plain,
! [SV33: term,SV7: term] :
( ( ~ ( var @ ( ap @ SV7 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(119,plain,
! [SV34: subst,SV10: term] :
( ( ! [SY253: subst] :
( ( comp @ ( push @ SV10 @ SV34 ) @ SY253 )
= ( push @ ( sub @ SV10 @ SY253 ) @ ( comp @ SV34 @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(120,plain,
! [SV35: subst,SV11: subst] :
( ( ! [SY254: subst] :
( ( comp @ ( comp @ SV11 @ SV35 ) @ SY254 )
= ( comp @ SV11 @ ( comp @ SV35 @ SY254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(121,plain,
! [SV36: subst,SV12: term] :
( ( ( comp @ sh @ ( push @ SV12 @ SV36 ) )
= SV36 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(122,plain,
! [SV37: subst,SV14: term] :
( ( ! [SY255: subst] :
( ( sub @ ( sub @ SV14 @ SV37 ) @ SY255 )
= ( sub @ SV14 @ ( comp @ SV37 @ SY255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(123,plain,
! [SV38: subst,SV15: term] :
( ( ( sub @ ( lam @ SV15 ) @ SV38 )
= ( lam @ ( sub @ SV15 @ ( push @ one @ ( comp @ SV38 @ sh ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(124,plain,
! [SV39: subst,SV17: term] :
( ( ( sub @ one @ ( push @ SV17 @ SV39 ) )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(125,plain,
! [SV40: term,SV18: term] :
( ( ! [SY256: subst] :
( ( sub @ ( ap @ SV18 @ SV40 ) @ SY256 )
= ( ap @ ( sub @ SV18 @ SY256 ) @ ( sub @ SV40 @ SY256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(126,plain,
! [SV41: term,SV19: term > $o] :
( ( ! [SY257: subst] :
( ~ ! [SY216: term] :
( ~ ( var @ SY216 )
| ( SV19 @ ( sub @ SY216 @ SY257 ) ) )
| ~ ( SV19 @ SV41 )
| ! [SY259: term] :
( ~ ( var @ SY259 )
| ( SV19 @ ( sub @ SY259 @ ( push @ SV41 @ SY257 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(127,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY218: term] :
( ~ ( var @ SY218 )
| ( SV20 @ SY218 ) ) )
= $true )
| ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV20 @ SY219 )
| ~ ( SV20 @ SY220 )
| ( SV20 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(128,plain,
! [SV21: term > $o] :
( ( ( ~ ! [SY224: term] :
( ~ ( var @ SY224 )
| ( SV21 @ SY224 ) ) )
= $true )
| ( ( ~ ! [SY225: term,SY226: term] :
( ~ ( SV21 @ SY225 )
| ~ ( SV21 @ SY226 )
| ( SV21 @ ( ap @ SY225 @ SY226 ) ) )
| ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(129,plain,
! [SV42: term,SV22: term] :
( ( ! [SY260: term,SY261: term] :
( ( ( ap @ SV22 @ SY260 )
!= ( ap @ SV42 @ SY261 ) )
| ( SY260 = SY261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(130,plain,
! [SV43: term,SV23: term] :
( ( ! [SY262: term,SY263: term] :
( ( ( ap @ ( sub @ SV23 @ id ) @ SY262 )
!= ( ap @ ( sub @ SV43 @ id ) @ SY263 ) )
| ( SV23 = SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(131,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ one ) )
= $true )
| ( ( ~ ! [SY235: term] :
( ~ ( var @ SY235 )
| ~ ( SV24 @ SY235 )
| ( SV24 @ ( sub @ SY235 @ sh ) ) )
| ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV24 @ SY236 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(132,plain,
! [SV44: term,SV25: term] :
( ( ( ( sub @ SV25 @ sh )
!= ( sub @ SV44 @ sh ) )
| ( SV25 = SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(133,plain,
( ( ! [SY264: term,SY265: term,SY266: term] :
( ( ( ap @ ( sub @ sK1_SX0 @ id ) @ SY265 )
!= ( ap @ ( sub @ SY264 @ id ) @ SY266 ) )
| ( SY265 = SY266 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[109]) ).
thf(134,plain,
! [SV45: term,SV26: term] :
( ( ! [SY267: term,SY268: term] :
( ( ( ap @ SV26 @ SY267 )
!= ( ap @ SV45 @ SY268 ) )
| ( SV26 = SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(135,plain,
! [SV27: term > $o] :
( ( ( ~ ! [SY241: term,SY242: term] :
( ~ ( SV27 @ SY241 )
| ~ ( SV27 @ SY242 )
| ( SV27 @ ( ap @ SY241 @ SY242 ) ) ) )
= $true )
| ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) )
| ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(136,plain,
! [SV28: term] :
( ( ( ~ ( var @ SV28 ) )
= $true )
| ( ( var @ ( sub @ SV28 @ sh ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(137,plain,
! [SV46: term,SV29: term] :
( ( ( ( lam @ SV29 )
!= ( lam @ SV46 ) )
| ( SV29 = SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(138,plain,
! [SV47: term,SV30: term] :
( ( ! [SY269: term] :
( ( lam @ SV30 )
!= ( ap @ SV47 @ SY269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(139,plain,
! [SV48: subst,SV31: subst,SV2: term] :
( ( ( sub @ ( sub @ SV2 @ SV31 ) @ SV48 )
= ( sub @ SV2 @ ( comp @ SV31 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(140,plain,
! [SV49: subst,SV32: subst,SV5: subst] :
( ( ( comp @ ( comp @ SV5 @ SV32 ) @ SV49 )
= ( comp @ SV5 @ ( comp @ SV32 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(141,plain,
! [SV33: term,SV7: term] :
( ( var @ ( ap @ SV7 @ SV33 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(142,plain,
! [SV50: subst,SV34: subst,SV10: term] :
( ( ( comp @ ( push @ SV10 @ SV34 ) @ SV50 )
= ( push @ ( sub @ SV10 @ SV50 ) @ ( comp @ SV34 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(143,plain,
! [SV51: subst,SV35: subst,SV11: subst] :
( ( ( comp @ ( comp @ SV11 @ SV35 ) @ SV51 )
= ( comp @ SV11 @ ( comp @ SV35 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(144,plain,
! [SV52: subst,SV37: subst,SV14: term] :
( ( ( sub @ ( sub @ SV14 @ SV37 ) @ SV52 )
= ( sub @ SV14 @ ( comp @ SV37 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(145,plain,
! [SV53: subst,SV40: term,SV18: term] :
( ( ( sub @ ( ap @ SV18 @ SV40 ) @ SV53 )
= ( ap @ ( sub @ SV18 @ SV53 ) @ ( sub @ SV40 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(146,plain,
! [SV41: term,SV54: subst,SV19: term > $o] :
( ( ~ ! [SY270: term] :
( ~ ( var @ SY270 )
| ( SV19 @ ( sub @ SY270 @ SV54 ) ) )
| ~ ( SV19 @ SV41 )
| ! [SY271: term] :
( ~ ( var @ SY271 )
| ( SV19 @ ( sub @ SY271 @ ( push @ SV41 @ SV54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(147,plain,
! [SV20: term > $o] :
( ( ( ! [SY218: term] :
( ~ ( var @ SY218 )
| ( SV20 @ SY218 ) ) )
= $false )
| ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV20 @ SY219 )
| ~ ( SV20 @ SY220 )
| ( SV20 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(148,plain,
! [SV21: term > $o] :
( ( ( ! [SY224: term] :
( ~ ( var @ SY224 )
| ( SV21 @ SY224 ) ) )
= $false )
| ( ( ~ ! [SY225: term,SY226: term] :
( ~ ( SV21 @ SY225 )
| ~ ( SV21 @ SY226 )
| ( SV21 @ ( ap @ SY225 @ SY226 ) ) )
| ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(149,plain,
! [SV42: term,SV55: term,SV22: term] :
( ( ! [SY272: term] :
( ( ( ap @ SV22 @ SV55 )
!= ( ap @ SV42 @ SY272 ) )
| ( SV55 = SY272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(150,plain,
! [SV43: term,SV56: term,SV23: term] :
( ( ! [SY273: term] :
( ( ( ap @ ( sub @ SV23 @ id ) @ SV56 )
!= ( ap @ ( sub @ SV43 @ id ) @ SY273 ) )
| ( SV23 = SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(151,plain,
! [SV24: term > $o] :
( ( ( SV24 @ one )
= $false )
| ( ( ~ ! [SY235: term] :
( ~ ( var @ SY235 )
| ~ ( SV24 @ SY235 )
| ( SV24 @ ( sub @ SY235 @ sh ) ) )
| ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV24 @ SY236 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(152,plain,
! [SV44: term,SV25: term] :
( ( ( ( sub @ SV25 @ sh )
!= ( sub @ SV44 @ sh ) )
= $true )
| ( ( SV25 = SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(153,plain,
( ( ! [SY274: term,SY275: term] :
( ( ( ap @ ( sub @ sK1_SX0 @ id ) @ SY274 )
!= ( ap @ ( sub @ sK2_SY264 @ id ) @ SY275 ) )
| ( SY274 = SY275 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[133]) ).
thf(154,plain,
! [SV45: term,SV57: term,SV26: term] :
( ( ! [SY276: term] :
( ( ( ap @ SV26 @ SV57 )
!= ( ap @ SV45 @ SY276 ) )
| ( SV26 = SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(155,plain,
! [SV27: term > $o] :
( ( ( ! [SY241: term,SY242: term] :
( ~ ( SV27 @ SY241 )
| ~ ( SV27 @ SY242 )
| ( SV27 @ ( ap @ SY241 @ SY242 ) ) ) )
= $false )
| ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) )
| ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(156,plain,
! [SV28: term] :
( ( ( var @ SV28 )
= $false )
| ( ( var @ ( sub @ SV28 @ sh ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(157,plain,
! [SV46: term,SV29: term] :
( ( ( ( lam @ SV29 )
!= ( lam @ SV46 ) )
= $true )
| ( ( SV29 = SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(158,plain,
! [SV58: term,SV47: term,SV30: term] :
( ( ( lam @ SV30 )
!= ( ap @ SV47 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(159,plain,
! [SV41: term,SV54: subst,SV19: term > $o] :
( ( ( ~ ! [SY270: term] :
( ~ ( var @ SY270 )
| ( SV19 @ ( sub @ SY270 @ SV54 ) ) ) )
= $true )
| ( ( ~ ( SV19 @ SV41 )
| ! [SY271: term] :
( ~ ( var @ SY271 )
| ( SV19 @ ( sub @ SY271 @ ( push @ SV41 @ SV54 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(160,plain,
! [SV20: term > $o] :
( ( ( ~ ( var @ ( sK3_SY218 @ SV20 ) )
| ( SV20 @ ( sK3_SY218 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV20 @ SY219 )
| ~ ( SV20 @ SY220 )
| ( SV20 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[147]) ).
thf(161,plain,
! [SV21: term > $o] :
( ( ( ~ ( var @ ( sK4_SY224 @ SV21 ) )
| ( SV21 @ ( sK4_SY224 @ SV21 ) ) )
= $false )
| ( ( ~ ! [SY225: term,SY226: term] :
( ~ ( SV21 @ SY225 )
| ~ ( SV21 @ SY226 )
| ( SV21 @ ( ap @ SY225 @ SY226 ) ) )
| ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[148]) ).
thf(162,plain,
! [SV59: term,SV42: term,SV55: term,SV22: term] :
( ( ( ( ap @ SV22 @ SV55 )
!= ( ap @ SV42 @ SV59 ) )
| ( SV55 = SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(163,plain,
! [SV60: term,SV43: term,SV56: term,SV23: term] :
( ( ( ( ap @ ( sub @ SV23 @ id ) @ SV56 )
!= ( ap @ ( sub @ SV43 @ id ) @ SV60 ) )
| ( SV23 = SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(164,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY235: term] :
( ~ ( var @ SY235 )
| ~ ( SV24 @ SY235 )
| ( SV24 @ ( sub @ SY235 @ sh ) ) ) )
= $true )
| ( ( ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV24 @ SY236 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(165,plain,
! [SV44: term,SV25: term] :
( ( ( ( sub @ SV25 @ sh )
= ( sub @ SV44 @ sh ) )
= $false )
| ( ( SV25 = SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(166,plain,
( ( ! [SY277: term] :
( ( ( ap @ ( sub @ sK1_SX0 @ id ) @ sK5_SY274 )
!= ( ap @ ( sub @ sK2_SY264 @ id ) @ SY277 ) )
| ( sK5_SY274 = SY277 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[153]) ).
thf(167,plain,
! [SV61: term,SV45: term,SV57: term,SV26: term] :
( ( ( ( ap @ SV26 @ SV57 )
!= ( ap @ SV45 @ SV61 ) )
| ( SV26 = SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(168,plain,
! [SV27: term > $o] :
( ( ( ! [SY278: term] :
( ~ ( SV27 @ ( sK6_SY241 @ SV27 ) )
| ~ ( SV27 @ SY278 )
| ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ SY278 ) ) ) )
= $false )
| ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) )
| ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[155]) ).
thf(169,plain,
! [SV46: term,SV29: term] :
( ( ( ( lam @ SV29 )
= ( lam @ SV46 ) )
= $false )
| ( ( SV29 = SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(170,plain,
! [SV58: term,SV47: term,SV30: term] :
( ( ( lam @ SV30 )
= ( ap @ SV47 @ SV58 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(171,plain,
! [SV41: term,SV54: subst,SV19: term > $o] :
( ( ( ! [SY270: term] :
( ~ ( var @ SY270 )
| ( SV19 @ ( sub @ SY270 @ SV54 ) ) ) )
= $false )
| ( ( ~ ( SV19 @ SV41 )
| ! [SY271: term] :
( ~ ( var @ SY271 )
| ( SV19 @ ( sub @ SY271 @ ( push @ SV41 @ SV54 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(172,plain,
! [SV20: term > $o] :
( ( ( ~ ( var @ ( sK3_SY218 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV20 @ SY219 )
| ~ ( SV20 @ SY220 )
| ( SV20 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(173,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false )
| ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV20 @ SY219 )
| ~ ( SV20 @ SY220 )
| ( SV20 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(174,plain,
! [SV21: term > $o] :
( ( ( ~ ( var @ ( sK4_SY224 @ SV21 ) ) )
= $false )
| ( ( ~ ! [SY225: term,SY226: term] :
( ~ ( SV21 @ SY225 )
| ~ ( SV21 @ SY226 )
| ( SV21 @ ( ap @ SY225 @ SY226 ) ) )
| ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(175,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false )
| ( ( ~ ! [SY225: term,SY226: term] :
( ~ ( SV21 @ SY225 )
| ~ ( SV21 @ SY226 )
| ( SV21 @ ( ap @ SY225 @ SY226 ) ) )
| ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(176,plain,
! [SV59: term,SV42: term,SV55: term,SV22: term] :
( ( ( ( ap @ SV22 @ SV55 )
!= ( ap @ SV42 @ SV59 ) )
= $true )
| ( ( SV55 = SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(177,plain,
! [SV60: term,SV43: term,SV56: term,SV23: term] :
( ( ( ( ap @ ( sub @ SV23 @ id ) @ SV56 )
!= ( ap @ ( sub @ SV43 @ id ) @ SV60 ) )
= $true )
| ( ( SV23 = SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(178,plain,
! [SV24: term > $o] :
( ( ( ! [SY235: term] :
( ~ ( var @ SY235 )
| ~ ( SV24 @ SY235 )
| ( SV24 @ ( sub @ SY235 @ sh ) ) ) )
= $false )
| ( ( ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV24 @ SY236 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(179,plain,
( ( ( ( ap @ ( sub @ sK1_SX0 @ id ) @ sK5_SY274 )
!= ( ap @ ( sub @ sK2_SY264 @ id ) @ sK7_SY277 ) )
| ( sK5_SY274 = sK7_SY277 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[166]) ).
thf(180,plain,
! [SV61: term,SV45: term,SV57: term,SV26: term] :
( ( ( ( ap @ SV26 @ SV57 )
!= ( ap @ SV45 @ SV61 ) )
= $true )
| ( ( SV26 = SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(181,plain,
! [SV27: term > $o] :
( ( ( ~ ( SV27 @ ( sK6_SY241 @ SV27 ) )
| ~ ( SV27 @ ( sK8_SY278 @ SV27 ) )
| ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) ) )
= $false )
| ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) )
| ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[168]) ).
thf(182,plain,
! [SV19: term > $o,SV54: subst,SV41: term] :
( ( ( ~ ( var @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) )
| ( SV19 @ ( sub @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) @ SV54 ) ) )
= $false )
| ( ( ~ ( SV19 @ SV41 )
| ! [SY271: term] :
( ~ ( var @ SY271 )
| ( SV19 @ ( sub @ SY271 @ ( push @ SV41 @ SV54 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[171]) ).
thf(183,plain,
! [SV20: term > $o] :
( ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true )
| ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV20 @ SY219 )
| ~ ( SV20 @ SY220 )
| ( SV20 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(184,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV20 @ SY219 )
| ~ ( SV20 @ SY220 )
| ( SV20 @ ( ap @ SY219 @ SY220 ) ) ) )
= $true )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(185,plain,
! [SV21: term > $o] :
( ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true )
| ( ( ~ ! [SY225: term,SY226: term] :
( ~ ( SV21 @ SY225 )
| ~ ( SV21 @ SY226 )
| ( SV21 @ ( ap @ SY225 @ SY226 ) ) )
| ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(186,plain,
! [SV21: term > $o] :
( ( ( ~ ! [SY225: term,SY226: term] :
( ~ ( SV21 @ SY225 )
| ~ ( SV21 @ SY226 )
| ( SV21 @ ( ap @ SY225 @ SY226 ) ) ) )
= $true )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(187,plain,
! [SV59: term,SV42: term,SV55: term,SV22: term] :
( ( ( ( ap @ SV22 @ SV55 )
= ( ap @ SV42 @ SV59 ) )
= $false )
| ( ( SV55 = SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(188,plain,
! [SV60: term,SV43: term,SV56: term,SV23: term] :
( ( ( ( ap @ ( sub @ SV23 @ id ) @ SV56 )
= ( ap @ ( sub @ SV43 @ id ) @ SV60 ) )
= $false )
| ( ( SV23 = SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(189,plain,
! [SV24: term > $o] :
( ( ( ~ ( var @ ( sK10_SY235 @ SV24 ) )
| ~ ( SV24 @ ( sK10_SY235 @ SV24 ) )
| ( SV24 @ ( sub @ ( sK10_SY235 @ SV24 ) @ sh ) ) )
= $false )
| ( ( ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV24 @ SY236 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[178]) ).
thf(190,plain,
( ( ( ap @ ( sub @ sK1_SX0 @ id ) @ sK5_SY274 )
!= ( ap @ ( sub @ sK2_SY264 @ id ) @ sK7_SY277 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(191,plain,
( ( sK5_SY274 = sK7_SY277 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(192,plain,
! [SV61: term,SV45: term,SV57: term,SV26: term] :
( ( ( ( ap @ SV26 @ SV57 )
= ( ap @ SV45 @ SV61 ) )
= $false )
| ( ( SV26 = SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(193,plain,
! [SV27: term > $o] :
( ( ( ~ ( SV27 @ ( sK6_SY241 @ SV27 ) ) )
= $false )
| ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) )
| ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(194,plain,
! [SV27: term > $o] :
( ( ( ~ ( SV27 @ ( sK8_SY278 @ SV27 ) )
| ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) ) )
= $false )
| ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) )
| ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[181]) ).
thf(195,plain,
! [SV19: term > $o,SV54: subst,SV41: term] :
( ( ( ~ ( var @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) ) )
= $false )
| ( ( ~ ( SV19 @ SV41 )
| ! [SY271: term] :
( ~ ( var @ SY271 )
| ( SV19 @ ( sub @ SY271 @ ( push @ SV41 @ SV54 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(196,plain,
! [SV54: subst,SV41: term,SV19: term > $o] :
( ( ( SV19 @ ( sub @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) @ SV54 ) )
= $false )
| ( ( ~ ( SV19 @ SV41 )
| ! [SY271: term] :
( ~ ( var @ SY271 )
| ( SV19 @ ( sub @ SY271 @ ( push @ SV41 @ SV54 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(197,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV20 @ SY219 )
| ~ ( SV20 @ SY220 )
| ( SV20 @ ( ap @ SY219 @ SY220 ) ) ) )
= $true )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(198,plain,
! [SV20: term > $o] :
( ( ( ! [SY219: term,SY220: term] :
( ~ ( SV20 @ SY219 )
| ~ ( SV20 @ SY220 )
| ( SV20 @ ( ap @ SY219 @ SY220 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(199,plain,
! [SV21: term > $o] :
( ( ( ~ ! [SY225: term,SY226: term] :
( ~ ( SV21 @ SY225 )
| ~ ( SV21 @ SY226 )
| ( SV21 @ ( ap @ SY225 @ SY226 ) ) ) )
= $true )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(200,plain,
! [SV21: term > $o] :
( ( ( ! [SY225: term,SY226: term] :
( ~ ( SV21 @ SY225 )
| ~ ( SV21 @ SY226 )
| ( SV21 @ ( ap @ SY225 @ SY226 ) ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(201,plain,
! [SV24: term > $o] :
( ( ( ~ ( var @ ( sK10_SY235 @ SV24 ) ) )
= $false )
| ( ( ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV24 @ SY236 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(202,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sK10_SY235 @ SV24 ) )
| ( SV24 @ ( sub @ ( sK10_SY235 @ SV24 ) @ sh ) ) )
= $false )
| ( ( ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV24 @ SY236 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(203,plain,
( ( ( ap @ ( sub @ sK1_SX0 @ id ) @ sK5_SY274 )
= ( ap @ ( sub @ sK2_SY264 @ id ) @ sK7_SY277 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(204,plain,
! [SV27: term > $o] :
( ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true )
| ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) )
| ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(205,plain,
! [SV27: term > $o] :
( ( ( ~ ( SV27 @ ( sK8_SY278 @ SV27 ) ) )
= $false )
| ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) )
| ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(206,plain,
! [SV27: term > $o] :
( ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false )
| ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) )
| ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(207,plain,
! [SV19: term > $o,SV54: subst,SV41: term] :
( ( ( var @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) )
= $true )
| ( ( ~ ( SV19 @ SV41 )
| ! [SY271: term] :
( ~ ( var @ SY271 )
| ( SV19 @ ( sub @ SY271 @ ( push @ SV41 @ SV54 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(208,plain,
! [SV54: subst,SV41: term,SV19: term > $o] :
( ( ( ~ ( SV19 @ SV41 ) )
= $true )
| ( ( ! [SY271: term] :
( ~ ( var @ SY271 )
| ( SV19 @ ( sub @ SY271 @ ( push @ SV41 @ SV54 ) ) ) ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(209,plain,
! [SV20: term > $o] :
( ( ( ! [SY219: term,SY220: term] :
( ~ ( SV20 @ SY219 )
| ~ ( SV20 @ SY220 )
| ( SV20 @ ( ap @ SY219 @ SY220 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(210,plain,
! [SV20: term > $o] :
( ( ( ! [SY279: term] :
( ~ ( SV20 @ ( sK11_SY219 @ SV20 ) )
| ~ ( SV20 @ SY279 )
| ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ SY279 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[198]) ).
thf(211,plain,
! [SV21: term > $o] :
( ( ( ! [SY225: term,SY226: term] :
( ~ ( SV21 @ SY225 )
| ~ ( SV21 @ SY226 )
| ( SV21 @ ( ap @ SY225 @ SY226 ) ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(212,plain,
! [SV21: term > $o] :
( ( ( ! [SY280: term] :
( ~ ( SV21 @ ( sK12_SY225 @ SV21 ) )
| ~ ( SV21 @ SY280 )
| ( SV21 @ ( ap @ ( sK12_SY225 @ SV21 ) @ SY280 ) ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[200]) ).
thf(213,plain,
! [SV24: term > $o] :
( ( ( var @ ( sK10_SY235 @ SV24 ) )
= $true )
| ( ( ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV24 @ SY236 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(214,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sK10_SY235 @ SV24 ) ) )
= $false )
| ( ( ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV24 @ SY236 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(215,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK10_SY235 @ SV24 ) @ sh ) )
= $false )
| ( ( ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV24 @ SY236 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[202]) ).
thf(216,plain,
! [SV27: term > $o] :
( ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(217,plain,
! [SV27: term > $o] :
( ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true )
| ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) )
| ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(218,plain,
! [SV27: term > $o] :
( ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(219,plain,
! [SV54: subst,SV41: term,SV19: term > $o] :
( ( ( ~ ( SV19 @ SV41 ) )
= $true )
| ( ( ! [SY271: term] :
( ~ ( var @ SY271 )
| ( SV19 @ ( sub @ SY271 @ ( push @ SV41 @ SV54 ) ) ) ) )
= $true )
| ( ( var @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(220,plain,
! [SV54: subst,SV41: term,SV19: term > $o] :
( ( ( SV19 @ SV41 )
= $false )
| ( ( ! [SY271: term] :
( ~ ( var @ SY271 )
| ( SV19 @ ( sub @ SY271 @ ( push @ SV41 @ SV54 ) ) ) ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(221,plain,
! [SV20: term > $o] :
( ( ( ! [SY281: term] :
( ~ ( SV20 @ ( sK13_SY219 @ SV20 ) )
| ~ ( SV20 @ SY281 )
| ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ SY281 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[209]) ).
thf(222,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK11_SY219 @ SV20 ) )
| ~ ( SV20 @ ( sK14_SY279 @ SV20 ) )
| ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[210]) ).
thf(223,plain,
! [SV21: term > $o] :
( ( ( ! [SY282: term] :
( ~ ( SV21 @ ( sK15_SY225 @ SV21 ) )
| ~ ( SV21 @ SY282 )
| ( SV21 @ ( ap @ ( sK15_SY225 @ SV21 ) @ SY282 ) ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[211]) ).
thf(224,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK12_SY225 @ SV21 ) )
| ~ ( SV21 @ ( sK16_SY280 @ SV21 ) )
| ( SV21 @ ( ap @ ( sK12_SY225 @ SV21 ) @ ( sK16_SY280 @ SV21 ) ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[212]) ).
thf(225,plain,
! [SV24: term > $o,SV62: term] :
( ( ( ~ ( var @ SV62 )
| ( SV24 @ SV62 ) )
= $true )
| ( ( var @ ( sK10_SY235 @ SV24 ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(226,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( sK10_SY235 @ SV24 ) )
= $true )
| ( ( ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV24 @ SY236 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(227,plain,
! [SV24: term > $o,SV63: term] :
( ( ( ~ ( var @ SV63 )
| ( SV24 @ SV63 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK10_SY235 @ SV24 ) @ sh ) )
= $false )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(228,plain,
! [SV27: term > $o] :
( ( ( ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) ) )
= $false )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(229,plain,
! [SV27: term > $o] :
( ( ( ~ ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(230,plain,
! [SV27: term > $o] :
( ( ( ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) ) )
= $false )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(231,plain,
! [SV54: subst,SV41: term,SV19: term > $o] :
( ( ( SV19 @ SV41 )
= $false )
| ( ( ! [SY271: term] :
( ~ ( var @ SY271 )
| ( SV19 @ ( sub @ SY271 @ ( push @ SV41 @ SV54 ) ) ) ) )
= $true )
| ( ( var @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(232,plain,
! [SV54: subst,SV41: term,SV19: term > $o,SV64: term] :
( ( ( ~ ( var @ SV64 )
| ( SV19 @ ( sub @ SV64 @ ( push @ SV41 @ SV54 ) ) ) )
= $true )
| ( ( SV19 @ SV41 )
= $false )
| ( ( SV19 @ ( sub @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(233,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK13_SY219 @ SV20 ) )
| ~ ( SV20 @ ( sK17_SY281 @ SV20 ) )
| ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[221]) ).
thf(234,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK11_SY219 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(235,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK14_SY279 @ SV20 ) )
| ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(236,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK15_SY225 @ SV21 ) )
| ~ ( SV21 @ ( sK18_SY282 @ SV21 ) )
| ( SV21 @ ( ap @ ( sK15_SY225 @ SV21 ) @ ( sK18_SY282 @ SV21 ) ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[223]) ).
thf(237,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK12_SY225 @ SV21 ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(238,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK16_SY280 @ SV21 ) )
| ( SV21 @ ( ap @ ( sK12_SY225 @ SV21 ) @ ( sK16_SY280 @ SV21 ) ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(239,plain,
! [SV24: term > $o,SV62: term] :
( ( ( ~ ( var @ SV62 ) )
= $true )
| ( ( SV24 @ SV62 )
= $true )
| ( ( var @ ( sK10_SY235 @ SV24 ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[225]) ).
thf(240,plain,
! [SV24: term > $o,SV65: term] :
( ( ( ~ ( var @ SV65 )
| ( SV24 @ SV65 ) )
= $true )
| ( ( SV24 @ ( sK10_SY235 @ SV24 ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(241,plain,
! [SV24: term > $o,SV63: term] :
( ( ( ~ ( var @ SV63 ) )
= $true )
| ( ( SV24 @ SV63 )
= $true )
| ( ( SV24 @ ( sub @ ( sK10_SY235 @ SV24 ) @ sh ) )
= $false )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(242,plain,
! [SV27: term > $o] :
( ( ( ~ ! [SY283: term] :
( ~ ( SV27 @ SY283 )
| ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SY283 @ id ) ) ) )
| ( SV27 @ ( lam @ ( sK19_SY243 @ SV27 ) ) ) )
= $false )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[228]) ).
thf(243,plain,
! [SV27: term > $o] :
( ( ( ! [SY243: term] :
( ~ ! [SY244: term] :
( ~ ( SV27 @ SY244 )
| ( SV27 @ ( sub @ SY243 @ ( push @ SY244 @ id ) ) ) )
| ( SV27 @ ( lam @ SY243 ) ) ) )
= $false )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(244,plain,
! [SV27: term > $o] :
( ( ( ~ ! [SY284: term] :
( ~ ( SV27 @ SY284 )
| ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SY284 @ id ) ) ) )
| ( SV27 @ ( lam @ ( sK20_SY243 @ SV27 ) ) ) )
= $false )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[230]) ).
thf(245,plain,
! [SV54: subst,SV41: term,SV19: term > $o,SV66: term] :
( ( ( ~ ( var @ SV66 )
| ( SV19 @ ( sub @ SV66 @ ( push @ SV41 @ SV54 ) ) ) )
= $true )
| ( ( SV19 @ SV41 )
= $false )
| ( ( var @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(246,plain,
! [SV54: subst,SV41: term,SV19: term > $o,SV64: term] :
( ( ( ~ ( var @ SV64 ) )
= $true )
| ( ( SV19 @ ( sub @ SV64 @ ( push @ SV41 @ SV54 ) ) )
= $true )
| ( ( SV19 @ SV41 )
= $false )
| ( ( SV19 @ ( sub @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(247,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK13_SY219 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(248,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK17_SY281 @ SV20 ) )
| ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(249,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( sK11_SY219 @ SV20 ) )
= $true )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(250,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(251,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(252,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK15_SY225 @ SV21 ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(253,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK18_SY282 @ SV21 ) )
| ( SV21 @ ( ap @ ( sK15_SY225 @ SV21 ) @ ( sK18_SY282 @ SV21 ) ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(254,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( sK12_SY225 @ SV21 ) )
= $true )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(255,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK16_SY280 @ SV21 ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(256,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( ap @ ( sK12_SY225 @ SV21 ) @ ( sK16_SY280 @ SV21 ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(257,plain,
! [SV24: term > $o,SV62: term] :
( ( ( var @ SV62 )
= $false )
| ( ( SV24 @ SV62 )
= $true )
| ( ( var @ ( sK10_SY235 @ SV24 ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(258,plain,
! [SV24: term > $o,SV65: term] :
( ( ( ~ ( var @ SV65 ) )
= $true )
| ( ( SV24 @ SV65 )
= $true )
| ( ( SV24 @ ( sK10_SY235 @ SV24 ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(259,plain,
! [SV24: term > $o,SV63: term] :
( ( ( var @ SV63 )
= $false )
| ( ( SV24 @ SV63 )
= $true )
| ( ( SV24 @ ( sub @ ( sK10_SY235 @ SV24 ) @ sh ) )
= $false )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(260,plain,
! [SV27: term > $o] :
( ( ( ~ ! [SY283: term] :
( ~ ( SV27 @ SY283 )
| ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SY283 @ id ) ) ) ) )
= $false )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(261,plain,
! [SV27: term > $o] :
( ( ( SV27 @ ( lam @ ( sK19_SY243 @ SV27 ) ) )
= $false )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(262,plain,
! [SV27: term > $o] :
( ( ( ~ ! [SY285: term] :
( ~ ( SV27 @ SY285 )
| ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SY285 @ id ) ) ) )
| ( SV27 @ ( lam @ ( sK21_SY243 @ SV27 ) ) ) )
= $false )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[243]) ).
thf(263,plain,
! [SV27: term > $o] :
( ( ( ~ ! [SY284: term] :
( ~ ( SV27 @ SY284 )
| ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SY284 @ id ) ) ) ) )
= $false )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(264,plain,
! [SV27: term > $o] :
( ( ( SV27 @ ( lam @ ( sK20_SY243 @ SV27 ) ) )
= $false )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(265,plain,
! [SV54: subst,SV41: term,SV19: term > $o,SV66: term] :
( ( ( ~ ( var @ SV66 ) )
= $true )
| ( ( SV19 @ ( sub @ SV66 @ ( push @ SV41 @ SV54 ) ) )
= $true )
| ( ( SV19 @ SV41 )
= $false )
| ( ( var @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(266,plain,
! [SV54: subst,SV41: term,SV19: term > $o,SV64: term] :
( ( ( var @ SV64 )
= $false )
| ( ( SV19 @ ( sub @ SV64 @ ( push @ SV41 @ SV54 ) ) )
= $true )
| ( ( SV19 @ SV41 )
= $false )
| ( ( SV19 @ ( sub @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(267,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( sK13_SY219 @ SV20 ) )
= $true )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(268,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(269,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(270,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK11_SY219 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(271,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( sK14_SY279 @ SV20 ) )
= $true )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(272,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(273,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( sK15_SY225 @ SV21 ) )
= $true )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[252]) ).
thf(274,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK18_SY282 @ SV21 ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(275,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( ap @ ( sK15_SY225 @ SV21 ) @ ( sK18_SY282 @ SV21 ) ) )
= $false )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(276,plain,
! [SV21: term > $o] :
( ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) ) )
= $true )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK12_SY225 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(277,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( sK16_SY280 @ SV21 ) )
= $true )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(278,plain,
! [SV21: term > $o] :
( ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) ) )
= $true )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK12_SY225 @ SV21 ) @ ( sK16_SY280 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(279,plain,
! [SV24: term > $o,SV65: term] :
( ( ( var @ SV65 )
= $false )
| ( ( SV24 @ SV65 )
= $true )
| ( ( SV24 @ ( sK10_SY235 @ SV24 ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(280,plain,
! [SV27: term > $o] :
( ( ( ! [SY283: term] :
( ~ ( SV27 @ SY283 )
| ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SY283 @ id ) ) ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(281,plain,
! [SV67: term,SV27: term > $o] :
( ( ( ! [SY286: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY286 ) ) )
| ( SV27 @ ( sub @ SV67 @ SY286 ) ) ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK19_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(282,plain,
! [SV27: term > $o] :
( ( ( ~ ! [SY285: term] :
( ~ ( SV27 @ SY285 )
| ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SY285 @ id ) ) ) ) )
= $false )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(283,plain,
! [SV27: term > $o] :
( ( ( SV27 @ ( lam @ ( sK21_SY243 @ SV27 ) ) )
= $false )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(284,plain,
! [SV27: term > $o] :
( ( ( ! [SY284: term] :
( ~ ( SV27 @ SY284 )
| ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SY284 @ id ) ) ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(285,plain,
! [SV68: term,SV27: term > $o] :
( ( ( ! [SY288: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY288 ) ) )
| ( SV27 @ ( sub @ SV68 @ SY288 ) ) ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK20_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(286,plain,
! [SV54: subst,SV41: term,SV19: term > $o,SV66: term] :
( ( ( var @ SV66 )
= $false )
| ( ( SV19 @ ( sub @ SV66 @ ( push @ SV41 @ SV54 ) ) )
= $true )
| ( ( SV19 @ SV41 )
= $false )
| ( ( var @ ( sK9_SY270 @ SV41 @ SV54 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(287,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK13_SY219 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(288,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( sK17_SY281 @ SV20 ) )
= $true )
| ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) )
| ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(289,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(290,plain,
! [SV20: term > $o] :
( ( ( ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK11_SY219 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(291,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK14_SY279 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(292,plain,
! [SV20: term > $o] :
( ( ( ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(293,plain,
! [SV21: term > $o] :
( ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) ) )
= $true )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK15_SY225 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(294,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( sK18_SY282 @ SV21 ) )
= $true )
| ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) )
| ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(295,plain,
! [SV21: term > $o] :
( ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) ) )
= $true )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK15_SY225 @ SV21 ) @ ( sK18_SY282 @ SV21 ) ) )
= $false )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(296,plain,
! [SV21: term > $o] :
( ( ( ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK12_SY225 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(297,plain,
! [SV21: term > $o] :
( ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) ) )
= $true )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK16_SY280 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(298,plain,
! [SV21: term > $o] :
( ( ( ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK12_SY225 @ SV21 ) @ ( sK16_SY280 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(299,plain,
! [SV69: term,SV27: term > $o] :
( ( ( ~ ( SV27 @ SV69 )
| ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SV69 @ id ) ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(300,plain,
! [SV67: term,SV70: subst,SV27: term > $o] :
( ( ( ~ ! [SY290: term] :
( ~ ( var @ SY290 )
| ( SV27 @ ( sub @ SY290 @ SV70 ) ) )
| ( SV27 @ ( sub @ SV67 @ SV70 ) ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK19_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(301,plain,
! [SV27: term > $o] :
( ( ( ! [SY285: term] :
( ~ ( SV27 @ SY285 )
| ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SY285 @ id ) ) ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(302,plain,
! [SV71: term,SV27: term > $o] :
( ( ( ! [SY291: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY291 ) ) )
| ( SV27 @ ( sub @ SV71 @ SY291 ) ) ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK21_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(303,plain,
! [SV72: term,SV27: term > $o] :
( ( ( ~ ( SV27 @ SV72 )
| ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SV72 @ id ) ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(304,plain,
! [SV68: term,SV73: subst,SV27: term > $o] :
( ( ( ~ ! [SY293: term] :
( ~ ( var @ SY293 )
| ( SV27 @ ( sub @ SY293 @ SV73 ) ) )
| ( SV27 @ ( sub @ SV68 @ SV73 ) ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK20_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(305,plain,
! [SV20: term > $o] :
( ( ( ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK13_SY219 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(306,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK17_SY281 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(307,plain,
! [SV20: term > $o] :
( ( ( ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(308,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY294: term] :
( ~ ( SV20 @ SY294 )
| ( SV20 @ ( sub @ ( sK22_SY221 @ SV20 ) @ ( push @ SY294 @ id ) ) ) )
| ( SV20 @ ( lam @ ( sK22_SY221 @ SV20 ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK11_SY219 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[290]) ).
thf(309,plain,
! [SV20: term > $o] :
( ( ( ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK14_SY279 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(310,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY295: term] :
( ~ ( SV20 @ SY295 )
| ( SV20 @ ( sub @ ( sK23_SY221 @ SV20 ) @ ( push @ SY295 @ id ) ) ) )
| ( SV20 @ ( lam @ ( sK23_SY221 @ SV20 ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[292]) ).
thf(311,plain,
! [SV21: term > $o] :
( ( ( ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK15_SY225 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(312,plain,
! [SV21: term > $o] :
( ( ( ~ ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) ) )
= $true )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK18_SY282 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(313,plain,
! [SV21: term > $o] :
( ( ( ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK15_SY225 @ SV21 ) @ ( sK18_SY282 @ SV21 ) ) )
= $false )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(314,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK24_SY227 @ SV21 ) )
| ( SV21 @ ( lam @ ( sK24_SY227 @ SV21 ) ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK12_SY225 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[296]) ).
thf(315,plain,
! [SV21: term > $o] :
( ( ( ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK16_SY280 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(316,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK25_SY227 @ SV21 ) )
| ( SV21 @ ( lam @ ( sK25_SY227 @ SV21 ) ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK12_SY225 @ SV21 ) @ ( sK16_SY280 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[298]) ).
thf(317,plain,
! [SV69: term,SV27: term > $o] :
( ( ( ~ ( SV27 @ SV69 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SV69 @ id ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(318,plain,
! [SV67: term,SV70: subst,SV27: term > $o] :
( ( ( ~ ! [SY290: term] :
( ~ ( var @ SY290 )
| ( SV27 @ ( sub @ SY290 @ SV70 ) ) ) )
= $true )
| ( ( SV27 @ ( sub @ SV67 @ SV70 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK19_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(319,plain,
! [SV74: term,SV27: term > $o] :
( ( ( ~ ( SV27 @ SV74 )
| ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SV74 @ id ) ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(320,plain,
! [SV71: term,SV75: subst,SV27: term > $o] :
( ( ( ~ ! [SY296: term] :
( ~ ( var @ SY296 )
| ( SV27 @ ( sub @ SY296 @ SV75 ) ) )
| ( SV27 @ ( sub @ SV71 @ SV75 ) ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK21_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(321,plain,
! [SV72: term,SV27: term > $o] :
( ( ( ~ ( SV27 @ SV72 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(322,plain,
! [SV68: term,SV73: subst,SV27: term > $o] :
( ( ( ~ ! [SY293: term] :
( ~ ( var @ SY293 )
| ( SV27 @ ( sub @ SY293 @ SV73 ) ) ) )
= $true )
| ( ( SV27 @ ( sub @ SV68 @ SV73 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK20_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(323,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY297: term] :
( ~ ( SV20 @ SY297 )
| ( SV20 @ ( sub @ ( sK26_SY221 @ SV20 ) @ ( push @ SY297 @ id ) ) ) )
| ( SV20 @ ( lam @ ( sK26_SY221 @ SV20 ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK13_SY219 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[305]) ).
thf(324,plain,
! [SV20: term > $o] :
( ( ( ! [SY221: term] :
( ~ ! [SY222: term] :
( ~ ( SV20 @ SY222 )
| ( SV20 @ ( sub @ SY221 @ ( push @ SY222 @ id ) ) ) )
| ( SV20 @ ( lam @ SY221 ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK17_SY281 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(325,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY298: term] :
( ~ ( SV20 @ SY298 )
| ( SV20 @ ( sub @ ( sK27_SY221 @ SV20 ) @ ( push @ SY298 @ id ) ) ) )
| ( SV20 @ ( lam @ ( sK27_SY221 @ SV20 ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[307]) ).
thf(326,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY294: term] :
( ~ ( SV20 @ SY294 )
| ( SV20 @ ( sub @ ( sK22_SY221 @ SV20 ) @ ( push @ SY294 @ id ) ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK11_SY219 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(327,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( lam @ ( sK22_SY221 @ SV20 ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK11_SY219 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(328,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY299: term] :
( ~ ( SV20 @ SY299 )
| ( SV20 @ ( sub @ ( sK28_SY221 @ SV20 ) @ ( push @ SY299 @ id ) ) ) )
| ( SV20 @ ( lam @ ( sK28_SY221 @ SV20 ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK14_SY279 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[309]) ).
thf(329,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY295: term] :
( ~ ( SV20 @ SY295 )
| ( SV20 @ ( sub @ ( sK23_SY221 @ SV20 ) @ ( push @ SY295 @ id ) ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(330,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( lam @ ( sK23_SY221 @ SV20 ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(331,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK29_SY227 @ SV21 ) )
| ( SV21 @ ( lam @ ( sK29_SY227 @ SV21 ) ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK15_SY225 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[311]) ).
thf(332,plain,
! [SV21: term > $o] :
( ( ( ! [SY227: term] :
( ~ ( SV21 @ SY227 )
| ( SV21 @ ( lam @ SY227 ) ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK18_SY282 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(333,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK30_SY227 @ SV21 ) )
| ( SV21 @ ( lam @ ( sK30_SY227 @ SV21 ) ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK15_SY225 @ SV21 ) @ ( sK18_SY282 @ SV21 ) ) )
= $false )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[313]) ).
thf(334,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK24_SY227 @ SV21 ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK12_SY225 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(335,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( lam @ ( sK24_SY227 @ SV21 ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK12_SY225 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[314]) ).
thf(336,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK31_SY227 @ SV21 ) )
| ( SV21 @ ( lam @ ( sK31_SY227 @ SV21 ) ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK16_SY280 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[315]) ).
thf(337,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK25_SY227 @ SV21 ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK12_SY225 @ SV21 ) @ ( sK16_SY280 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[316]) ).
thf(338,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( lam @ ( sK25_SY227 @ SV21 ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK12_SY225 @ SV21 ) @ ( sK16_SY280 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[316]) ).
thf(339,plain,
! [SV69: term,SV27: term > $o] :
( ( ( SV27 @ SV69 )
= $false )
| ( ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SV69 @ id ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(340,plain,
! [SV67: term,SV70: subst,SV27: term > $o] :
( ( ( ! [SY290: term] :
( ~ ( var @ SY290 )
| ( SV27 @ ( sub @ SY290 @ SV70 ) ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV67 @ SV70 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK19_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(341,plain,
! [SV74: term,SV27: term > $o] :
( ( ( ~ ( SV27 @ SV74 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(342,plain,
! [SV71: term,SV75: subst,SV27: term > $o] :
( ( ( ~ ! [SY296: term] :
( ~ ( var @ SY296 )
| ( SV27 @ ( sub @ SY296 @ SV75 ) ) ) )
= $true )
| ( ( SV27 @ ( sub @ SV71 @ SV75 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK21_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(343,plain,
! [SV72: term,SV27: term > $o] :
( ( ( SV27 @ SV72 )
= $false )
| ( ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(344,plain,
! [SV68: term,SV73: subst,SV27: term > $o] :
( ( ( ! [SY293: term] :
( ~ ( var @ SY293 )
| ( SV27 @ ( sub @ SY293 @ SV73 ) ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV68 @ SV73 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK20_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(345,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY297: term] :
( ~ ( SV20 @ SY297 )
| ( SV20 @ ( sub @ ( sK26_SY221 @ SV20 ) @ ( push @ SY297 @ id ) ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK13_SY219 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(346,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( lam @ ( sK26_SY221 @ SV20 ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK13_SY219 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(347,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY300: term] :
( ~ ( SV20 @ SY300 )
| ( SV20 @ ( sub @ ( sK32_SY221 @ SV20 ) @ ( push @ SY300 @ id ) ) ) )
| ( SV20 @ ( lam @ ( sK32_SY221 @ SV20 ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK17_SY281 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[324]) ).
thf(348,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY298: term] :
( ~ ( SV20 @ SY298 )
| ( SV20 @ ( sub @ ( sK27_SY221 @ SV20 ) @ ( push @ SY298 @ id ) ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(349,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( lam @ ( sK27_SY221 @ SV20 ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(350,plain,
! [SV20: term > $o] :
( ( ( ! [SY294: term] :
( ~ ( SV20 @ SY294 )
| ( SV20 @ ( sub @ ( sK22_SY221 @ SV20 ) @ ( push @ SY294 @ id ) ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK11_SY219 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(351,plain,
! [SV76: term,SV20: term > $o] :
( ( ( SV20 @ SV76 )
= $true )
| ( ( SV20 @ ( lam @ ( sK22_SY221 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK11_SY219 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(352,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY299: term] :
( ~ ( SV20 @ SY299 )
| ( SV20 @ ( sub @ ( sK28_SY221 @ SV20 ) @ ( push @ SY299 @ id ) ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK14_SY279 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(353,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( lam @ ( sK28_SY221 @ SV20 ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK14_SY279 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(354,plain,
! [SV20: term > $o] :
( ( ( ! [SY295: term] :
( ~ ( SV20 @ SY295 )
| ( SV20 @ ( sub @ ( sK23_SY221 @ SV20 ) @ ( push @ SY295 @ id ) ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(355,plain,
! [SV77: term,SV20: term > $o] :
( ( ( SV20 @ SV77 )
= $true )
| ( ( SV20 @ ( lam @ ( sK23_SY221 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(356,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK29_SY227 @ SV21 ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK15_SY225 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(357,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( lam @ ( sK29_SY227 @ SV21 ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK15_SY225 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(358,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK33_SY227 @ SV21 ) )
| ( SV21 @ ( lam @ ( sK33_SY227 @ SV21 ) ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK18_SY282 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[332]) ).
thf(359,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK30_SY227 @ SV21 ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK15_SY225 @ SV21 ) @ ( sK18_SY282 @ SV21 ) ) )
= $false )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(360,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( lam @ ( sK30_SY227 @ SV21 ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK15_SY225 @ SV21 ) @ ( sK18_SY282 @ SV21 ) ) )
= $false )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(361,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( sK24_SY227 @ SV21 ) )
= $true )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK12_SY225 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(362,plain,
! [SV78: term,SV21: term > $o] :
( ( ( SV21 @ SV78 )
= $true )
| ( ( SV21 @ ( lam @ ( sK24_SY227 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK12_SY225 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(363,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK31_SY227 @ SV21 ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK16_SY280 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(364,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( lam @ ( sK31_SY227 @ SV21 ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK16_SY280 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(365,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( sK25_SY227 @ SV21 ) )
= $true )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK12_SY225 @ SV21 ) @ ( sK16_SY280 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(366,plain,
! [SV79: term,SV21: term > $o] :
( ( ( SV21 @ SV79 )
= $true )
| ( ( SV21 @ ( lam @ ( sK25_SY227 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( ap @ ( sK12_SY225 @ SV21 ) @ ( sK16_SY280 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(367,plain,
! [SV69: term,SV80: term,SV27: term > $o] :
( ( ( ! [SY301: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY301 ) ) )
| ( SV27 @ ( sub @ SV80 @ SY301 ) ) ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SV69 @ id ) ) )
= $true )
| ( ( SV27 @ SV69 )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(368,plain,
! [SV27: term > $o,SV70: subst,SV67: term] :
( ( ( ~ ( var @ ( sK34_SY290 @ SV67 @ SV70 @ SV27 ) )
| ( SV27 @ ( sub @ ( sK34_SY290 @ SV67 @ SV70 @ SV27 ) @ SV70 ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV67 @ SV70 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK19_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[340]) ).
thf(369,plain,
! [SV74: term,SV27: term > $o] :
( ( ( SV27 @ SV74 )
= $false )
| ( ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( ! [SY245: term,SY246: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY246 ) ) )
| ( SV27 @ ( sub @ SY245 @ SY246 ) ) ) )
= $true )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(370,plain,
! [SV71: term,SV75: subst,SV27: term > $o] :
( ( ( ! [SY296: term] :
( ~ ( var @ SY296 )
| ( SV27 @ ( sub @ SY296 @ SV75 ) ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV71 @ SV75 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK21_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(371,plain,
! [SV72: term,SV81: term,SV27: term > $o] :
( ( ( ! [SY303: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY303 ) ) )
| ( SV27 @ ( sub @ SV81 @ SY303 ) ) ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV27 @ SV72 )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(372,plain,
! [SV27: term > $o,SV73: subst,SV68: term] :
( ( ( ~ ( var @ ( sK35_SY293 @ SV68 @ SV73 @ SV27 ) )
| ( SV27 @ ( sub @ ( sK35_SY293 @ SV68 @ SV73 @ SV27 ) @ SV73 ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV68 @ SV73 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK20_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[344]) ).
thf(373,plain,
! [SV20: term > $o] :
( ( ( ! [SY297: term] :
( ~ ( SV20 @ SY297 )
| ( SV20 @ ( sub @ ( sK26_SY221 @ SV20 ) @ ( push @ SY297 @ id ) ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK13_SY219 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(374,plain,
! [SV82: term,SV20: term > $o] :
( ( ( SV20 @ SV82 )
= $true )
| ( ( SV20 @ ( lam @ ( sK26_SY221 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK13_SY219 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(375,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY300: term] :
( ~ ( SV20 @ SY300 )
| ( SV20 @ ( sub @ ( sK32_SY221 @ SV20 ) @ ( push @ SY300 @ id ) ) ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK17_SY281 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(376,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( lam @ ( sK32_SY221 @ SV20 ) ) )
= $false )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK17_SY281 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(377,plain,
! [SV20: term > $o] :
( ( ( ! [SY298: term] :
( ~ ( SV20 @ SY298 )
| ( SV20 @ ( sub @ ( sK27_SY221 @ SV20 ) @ ( push @ SY298 @ id ) ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[348]) ).
thf(378,plain,
! [SV83: term,SV20: term > $o] :
( ( ( SV20 @ SV83 )
= $true )
| ( ( SV20 @ ( lam @ ( sK27_SY221 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(379,plain,
! [SV84: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV84 )
| ( SV20 @ ( sub @ ( sK22_SY221 @ SV20 ) @ ( push @ SV84 @ id ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK11_SY219 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(380,plain,
! [SV20: term > $o] :
( ( ( ! [SY299: term] :
( ~ ( SV20 @ SY299 )
| ( SV20 @ ( sub @ ( sK28_SY221 @ SV20 ) @ ( push @ SY299 @ id ) ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK14_SY279 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(381,plain,
! [SV85: term,SV20: term > $o] :
( ( ( SV20 @ SV85 )
= $true )
| ( ( SV20 @ ( lam @ ( sK28_SY221 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK14_SY279 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(382,plain,
! [SV86: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV86 )
| ( SV20 @ ( sub @ ( sK23_SY221 @ SV20 ) @ ( push @ SV86 @ id ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(383,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( sK29_SY227 @ SV21 ) )
= $true )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK15_SY225 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(384,plain,
! [SV87: term,SV21: term > $o] :
( ( ( SV21 @ SV87 )
= $true )
| ( ( SV21 @ ( lam @ ( sK29_SY227 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK15_SY225 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(385,plain,
! [SV21: term > $o] :
( ( ( ~ ( SV21 @ ( sK33_SY227 @ SV21 ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK18_SY282 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(386,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( lam @ ( sK33_SY227 @ SV21 ) ) )
= $false )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK18_SY282 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(387,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( sK30_SY227 @ SV21 ) )
= $true )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK15_SY225 @ SV21 ) @ ( sK18_SY282 @ SV21 ) ) )
= $false )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(388,plain,
! [SV88: term,SV21: term > $o] :
( ( ( SV21 @ SV88 )
= $true )
| ( ( SV21 @ ( lam @ ( sK30_SY227 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( ap @ ( sK15_SY225 @ SV21 ) @ ( sK18_SY282 @ SV21 ) ) )
= $false )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(389,plain,
! [SV89: term,SV21: term > $o] :
( ( ( SV21 @ SV89 )
= $true )
| ( ( SV21 @ ( sK24_SY227 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK12_SY225 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(390,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( sK31_SY227 @ SV21 ) )
= $true )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK16_SY280 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[363]) ).
thf(391,plain,
! [SV90: term,SV21: term > $o] :
( ( ( SV21 @ SV90 )
= $true )
| ( ( SV21 @ ( lam @ ( sK31_SY227 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK16_SY280 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(392,plain,
! [SV91: term,SV21: term > $o] :
( ( ( SV21 @ SV91 )
= $true )
| ( ( SV21 @ ( sK25_SY227 @ SV21 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK12_SY225 @ SV21 ) @ ( sK16_SY280 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(393,plain,
! [SV69: term,SV80: term,SV92: subst,SV27: term > $o] :
( ( ( ~ ! [SY305: term] :
( ~ ( var @ SY305 )
| ( SV27 @ ( sub @ SY305 @ SV92 ) ) )
| ( SV27 @ ( sub @ SV80 @ SV92 ) ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SV69 @ id ) ) )
= $true )
| ( ( SV27 @ SV69 )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(394,plain,
! [SV27: term > $o,SV70: subst,SV67: term] :
( ( ( ~ ( var @ ( sK34_SY290 @ SV67 @ SV70 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV67 @ SV70 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK19_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(395,plain,
! [SV70: subst,SV67: term,SV27: term > $o] :
( ( ( SV27 @ ( sub @ ( sK34_SY290 @ SV67 @ SV70 @ SV27 ) @ SV70 ) )
= $false )
| ( ( SV27 @ ( sub @ SV67 @ SV70 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK19_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(396,plain,
! [SV74: term,SV93: term,SV27: term > $o] :
( ( ( ! [SY306: subst] :
( ~ ! [SY247: term] :
( ~ ( var @ SY247 )
| ( SV27 @ ( sub @ SY247 @ SY306 ) ) )
| ( SV27 @ ( sub @ SV93 @ SY306 ) ) ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( SV27 @ SV74 )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(397,plain,
! [SV27: term > $o,SV75: subst,SV71: term] :
( ( ( ~ ( var @ ( sK36_SY296 @ SV71 @ SV75 @ SV27 ) )
| ( SV27 @ ( sub @ ( sK36_SY296 @ SV71 @ SV75 @ SV27 ) @ SV75 ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV71 @ SV75 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK21_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[370]) ).
thf(398,plain,
! [SV72: term,SV81: term,SV94: subst,SV27: term > $o] :
( ( ( ~ ! [SY308: term] :
( ~ ( var @ SY308 )
| ( SV27 @ ( sub @ SY308 @ SV94 ) ) )
| ( SV27 @ ( sub @ SV81 @ SV94 ) ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV27 @ SV72 )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(399,plain,
! [SV27: term > $o,SV73: subst,SV68: term] :
( ( ( ~ ( var @ ( sK35_SY293 @ SV68 @ SV73 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV68 @ SV73 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK20_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(400,plain,
! [SV73: subst,SV68: term,SV27: term > $o] :
( ( ( SV27 @ ( sub @ ( sK35_SY293 @ SV68 @ SV73 @ SV27 ) @ SV73 ) )
= $false )
| ( ( SV27 @ ( sub @ SV68 @ SV73 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK20_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(401,plain,
! [SV95: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV95 )
| ( SV20 @ ( sub @ ( sK26_SY221 @ SV20 ) @ ( push @ SV95 @ id ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK13_SY219 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(402,plain,
! [SV20: term > $o] :
( ( ( ! [SY300: term] :
( ~ ( SV20 @ SY300 )
| ( SV20 @ ( sub @ ( sK32_SY221 @ SV20 ) @ ( push @ SY300 @ id ) ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK17_SY281 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[375]) ).
thf(403,plain,
! [SV96: term,SV20: term > $o] :
( ( ( SV20 @ SV96 )
= $true )
| ( ( SV20 @ ( lam @ ( sK32_SY221 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK17_SY281 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(404,plain,
! [SV97: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV97 )
| ( SV20 @ ( sub @ ( sK27_SY221 @ SV20 ) @ ( push @ SV97 @ id ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(405,plain,
! [SV84: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV84 ) )
= $true )
| ( ( SV20 @ ( sub @ ( sK22_SY221 @ SV20 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK11_SY219 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(406,plain,
! [SV98: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV98 )
| ( SV20 @ ( sub @ ( sK28_SY221 @ SV20 ) @ ( push @ SV98 @ id ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK14_SY279 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(407,plain,
! [SV86: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV86 ) )
= $true )
| ( ( SV20 @ ( sub @ ( sK23_SY221 @ SV20 ) @ ( push @ SV86 @ id ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(408,plain,
! [SV99: term,SV21: term > $o] :
( ( ( SV21 @ SV99 )
= $true )
| ( ( SV21 @ ( sK29_SY227 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK15_SY225 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(409,plain,
! [SV21: term > $o] :
( ( ( SV21 @ ( sK33_SY227 @ SV21 ) )
= $true )
| ( ( ! [SY228: term] : ( SV21 @ SY228 ) )
= $true )
| ( ( SV21 @ ( sK18_SY282 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[385]) ).
thf(410,plain,
! [SV100: term,SV21: term > $o] :
( ( ( SV21 @ SV100 )
= $true )
| ( ( SV21 @ ( lam @ ( sK33_SY227 @ SV21 ) ) )
= $false )
| ( ( SV21 @ ( sK18_SY282 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(411,plain,
! [SV101: term,SV21: term > $o] :
( ( ( SV21 @ SV101 )
= $true )
| ( ( SV21 @ ( sK30_SY227 @ SV21 ) )
= $true )
| ( ( SV21 @ ( ap @ ( sK15_SY225 @ SV21 ) @ ( sK18_SY282 @ SV21 ) ) )
= $false )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(412,plain,
! [SV102: term,SV21: term > $o] :
( ( ( SV21 @ SV102 )
= $true )
| ( ( SV21 @ ( sK31_SY227 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK16_SY280 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK4_SY224 @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(413,plain,
! [SV69: term,SV80: term,SV92: subst,SV27: term > $o] :
( ( ( ~ ! [SY305: term] :
( ~ ( var @ SY305 )
| ( SV27 @ ( sub @ SY305 @ SV92 ) ) ) )
= $true )
| ( ( SV27 @ ( sub @ SV80 @ SV92 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SV69 @ id ) ) )
= $true )
| ( ( SV27 @ SV69 )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(414,plain,
! [SV27: term > $o,SV70: subst,SV67: term] :
( ( ( var @ ( sK34_SY290 @ SV67 @ SV70 @ SV27 ) )
= $true )
| ( ( SV27 @ ( sub @ SV67 @ SV70 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK19_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(415,plain,
! [SV74: term,SV93: term,SV103: subst,SV27: term > $o] :
( ( ( ~ ! [SY309: term] :
( ~ ( var @ SY309 )
| ( SV27 @ ( sub @ SY309 @ SV103 ) ) )
| ( SV27 @ ( sub @ SV93 @ SV103 ) ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( SV27 @ SV74 )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(416,plain,
! [SV27: term > $o,SV75: subst,SV71: term] :
( ( ( ~ ( var @ ( sK36_SY296 @ SV71 @ SV75 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV71 @ SV75 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK21_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(417,plain,
! [SV75: subst,SV71: term,SV27: term > $o] :
( ( ( SV27 @ ( sub @ ( sK36_SY296 @ SV71 @ SV75 @ SV27 ) @ SV75 ) )
= $false )
| ( ( SV27 @ ( sub @ SV71 @ SV75 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK21_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(418,plain,
! [SV72: term,SV81: term,SV94: subst,SV27: term > $o] :
( ( ( ~ ! [SY308: term] :
( ~ ( var @ SY308 )
| ( SV27 @ ( sub @ SY308 @ SV94 ) ) ) )
= $true )
| ( ( SV27 @ ( sub @ SV81 @ SV94 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV27 @ SV72 )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(419,plain,
! [SV27: term > $o,SV73: subst,SV68: term] :
( ( ( var @ ( sK35_SY293 @ SV68 @ SV73 @ SV27 ) )
= $true )
| ( ( SV27 @ ( sub @ SV68 @ SV73 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK20_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(420,plain,
! [SV95: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV95 ) )
= $true )
| ( ( SV20 @ ( sub @ ( sK26_SY221 @ SV20 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK13_SY219 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(421,plain,
! [SV104: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV104 )
| ( SV20 @ ( sub @ ( sK32_SY221 @ SV20 ) @ ( push @ SV104 @ id ) ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK17_SY281 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(422,plain,
! [SV97: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV97 ) )
= $true )
| ( ( SV20 @ ( sub @ ( sK27_SY221 @ SV20 ) @ ( push @ SV97 @ id ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(423,plain,
! [SV84: term,SV20: term > $o] :
( ( ( SV20 @ SV84 )
= $false )
| ( ( SV20 @ ( sub @ ( sK22_SY221 @ SV20 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK11_SY219 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(424,plain,
! [SV98: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV98 ) )
= $true )
| ( ( SV20 @ ( sub @ ( sK28_SY221 @ SV20 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK14_SY279 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(425,plain,
! [SV86: term,SV20: term > $o] :
( ( ( SV20 @ SV86 )
= $false )
| ( ( SV20 @ ( sub @ ( sK23_SY221 @ SV20 ) @ ( push @ SV86 @ id ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(426,plain,
! [SV105: term,SV21: term > $o] :
( ( ( SV21 @ SV105 )
= $true )
| ( ( SV21 @ ( sK33_SY227 @ SV21 ) )
= $true )
| ( ( SV21 @ ( sK18_SY282 @ SV21 ) )
= $true )
| ( ( var @ ( sK4_SY224 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(427,plain,
! [SV69: term,SV80: term,SV92: subst,SV27: term > $o] :
( ( ( ! [SY305: term] :
( ~ ( var @ SY305 )
| ( SV27 @ ( sub @ SY305 @ SV92 ) ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV80 @ SV92 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SV69 @ id ) ) )
= $true )
| ( ( SV27 @ SV69 )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(428,plain,
! [SV74: term,SV93: term,SV103: subst,SV27: term > $o] :
( ( ( ~ ! [SY309: term] :
( ~ ( var @ SY309 )
| ( SV27 @ ( sub @ SY309 @ SV103 ) ) ) )
= $true )
| ( ( SV27 @ ( sub @ SV93 @ SV103 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( SV27 @ SV74 )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(429,plain,
! [SV27: term > $o,SV75: subst,SV71: term] :
( ( ( var @ ( sK36_SY296 @ SV71 @ SV75 @ SV27 ) )
= $true )
| ( ( SV27 @ ( sub @ SV71 @ SV75 ) )
= $true )
| ( ( SV27 @ ( lam @ ( sK21_SY243 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(430,plain,
! [SV72: term,SV81: term,SV94: subst,SV27: term > $o] :
( ( ( ! [SY308: term] :
( ~ ( var @ SY308 )
| ( SV27 @ ( sub @ SY308 @ SV94 ) ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV81 @ SV94 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV27 @ SV72 )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(431,plain,
! [SV95: term,SV20: term > $o] :
( ( ( SV20 @ SV95 )
= $false )
| ( ( SV20 @ ( sub @ ( sK26_SY221 @ SV20 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK13_SY219 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(432,plain,
! [SV104: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV104 ) )
= $true )
| ( ( SV20 @ ( sub @ ( sK32_SY221 @ SV20 ) @ ( push @ SV104 @ id ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK17_SY281 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(433,plain,
! [SV97: term,SV20: term > $o] :
( ( ( SV20 @ SV97 )
= $false )
| ( ( SV20 @ ( sub @ ( sK27_SY221 @ SV20 ) @ ( push @ SV97 @ id ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(434,plain,
! [SV84: term,SV106: term,SV20: term > $o] :
( ( ( SV20 @ SV106 )
= $true )
| ( ( SV20 @ ( sub @ ( sK22_SY221 @ SV20 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV20 @ SV84 )
= $false )
| ( ( SV20 @ ( sK11_SY219 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(435,plain,
! [SV98: term,SV20: term > $o] :
( ( ( SV20 @ SV98 )
= $false )
| ( ( SV20 @ ( sub @ ( sK28_SY221 @ SV20 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK14_SY279 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(436,plain,
! [SV86: term,SV107: term,SV20: term > $o] :
( ( ( SV20 @ SV107 )
= $true )
| ( ( SV20 @ ( sub @ ( sK23_SY221 @ SV20 ) @ ( push @ SV86 @ id ) ) )
= $true )
| ( ( SV20 @ SV86 )
= $false )
| ( ( SV20 @ ( ap @ ( sK11_SY219 @ SV20 ) @ ( sK14_SY279 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(437,plain,
! [SV27: term > $o,SV92: subst,SV80: term,SV69: term] :
( ( ( ~ ( var @ ( sK37_SY305 @ SV69 @ SV80 @ SV92 @ SV27 ) )
| ( SV27 @ ( sub @ ( sK37_SY305 @ SV69 @ SV80 @ SV92 @ SV27 ) @ SV92 ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV80 @ SV92 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SV69 @ id ) ) )
= $true )
| ( ( SV27 @ SV69 )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[427]) ).
thf(438,plain,
! [SV74: term,SV93: term,SV103: subst,SV27: term > $o] :
( ( ( ! [SY309: term] :
( ~ ( var @ SY309 )
| ( SV27 @ ( sub @ SY309 @ SV103 ) ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV93 @ SV103 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( SV27 @ SV74 )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(439,plain,
! [SV27: term > $o,SV94: subst,SV81: term,SV72: term] :
( ( ( ~ ( var @ ( sK38_SY308 @ SV72 @ SV81 @ SV94 @ SV27 ) )
| ( SV27 @ ( sub @ ( sK38_SY308 @ SV72 @ SV81 @ SV94 @ SV27 ) @ SV94 ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV81 @ SV94 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV27 @ SV72 )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[430]) ).
thf(440,plain,
! [SV95: term,SV108: term,SV20: term > $o] :
( ( ( SV20 @ SV108 )
= $true )
| ( ( SV20 @ ( sub @ ( sK26_SY221 @ SV20 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( SV20 @ SV95 )
= $false )
| ( ( SV20 @ ( sK13_SY219 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(441,plain,
! [SV104: term,SV20: term > $o] :
( ( ( SV20 @ SV104 )
= $false )
| ( ( SV20 @ ( sub @ ( sK32_SY221 @ SV20 ) @ ( push @ SV104 @ id ) ) )
= $true )
| ( ( ! [SY223: term] : ( SV20 @ SY223 ) )
= $true )
| ( ( SV20 @ ( sK17_SY281 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(442,plain,
! [SV97: term,SV109: term,SV20: term > $o] :
( ( ( SV20 @ SV109 )
= $true )
| ( ( SV20 @ ( sub @ ( sK27_SY221 @ SV20 ) @ ( push @ SV97 @ id ) ) )
= $true )
| ( ( SV20 @ SV97 )
= $false )
| ( ( SV20 @ ( ap @ ( sK13_SY219 @ SV20 ) @ ( sK17_SY281 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(443,plain,
! [SV98: term,SV110: term,SV20: term > $o] :
( ( ( SV20 @ SV110 )
= $true )
| ( ( SV20 @ ( sub @ ( sK28_SY221 @ SV20 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( SV20 @ SV98 )
= $false )
| ( ( SV20 @ ( sK14_SY279 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK3_SY218 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(444,plain,
! [SV27: term > $o,SV92: subst,SV80: term,SV69: term] :
( ( ( ~ ( var @ ( sK37_SY305 @ SV69 @ SV80 @ SV92 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV80 @ SV92 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SV69 @ id ) ) )
= $true )
| ( ( SV27 @ SV69 )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(445,plain,
! [SV92: subst,SV80: term,SV69: term,SV27: term > $o] :
( ( ( SV27 @ ( sub @ ( sK37_SY305 @ SV69 @ SV80 @ SV92 @ SV27 ) @ SV92 ) )
= $false )
| ( ( SV27 @ ( sub @ SV80 @ SV92 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SV69 @ id ) ) )
= $true )
| ( ( SV27 @ SV69 )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[437]) ).
thf(446,plain,
! [SV27: term > $o,SV103: subst,SV93: term,SV74: term] :
( ( ( ~ ( var @ ( sK39_SY309 @ SV74 @ SV93 @ SV103 @ SV27 ) )
| ( SV27 @ ( sub @ ( sK39_SY309 @ SV74 @ SV93 @ SV103 @ SV27 ) @ SV103 ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV93 @ SV103 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( SV27 @ SV74 )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[438]) ).
thf(447,plain,
! [SV27: term > $o,SV94: subst,SV81: term,SV72: term] :
( ( ( ~ ( var @ ( sK38_SY308 @ SV72 @ SV81 @ SV94 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV81 @ SV94 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV27 @ SV72 )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(448,plain,
! [SV94: subst,SV81: term,SV72: term,SV27: term > $o] :
( ( ( SV27 @ ( sub @ ( sK38_SY308 @ SV72 @ SV81 @ SV94 @ SV27 ) @ SV94 ) )
= $false )
| ( ( SV27 @ ( sub @ SV81 @ SV94 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV27 @ SV72 )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[439]) ).
thf(449,plain,
! [SV104: term,SV111: term,SV20: term > $o] :
( ( ( SV20 @ SV111 )
= $true )
| ( ( SV20 @ ( sub @ ( sK32_SY221 @ SV20 ) @ ( push @ SV104 @ id ) ) )
= $true )
| ( ( SV20 @ SV104 )
= $false )
| ( ( SV20 @ ( sK17_SY281 @ SV20 ) )
= $true )
| ( ( var @ ( sK3_SY218 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(450,plain,
! [SV27: term > $o,SV92: subst,SV80: term,SV69: term] :
( ( ( var @ ( sK37_SY305 @ SV69 @ SV80 @ SV92 @ SV27 ) )
= $true )
| ( ( SV27 @ ( sub @ SV80 @ SV92 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK19_SY243 @ SV27 ) @ ( push @ SV69 @ id ) ) )
= $true )
| ( ( SV27 @ SV69 )
= $false )
| ( ( SV27 @ ( sK6_SY241 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[444]) ).
thf(451,plain,
! [SV27: term > $o,SV103: subst,SV93: term,SV74: term] :
( ( ( ~ ( var @ ( sK39_SY309 @ SV74 @ SV93 @ SV103 @ SV27 ) ) )
= $false )
| ( ( SV27 @ ( sub @ SV93 @ SV103 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( SV27 @ SV74 )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[446]) ).
thf(452,plain,
! [SV103: subst,SV93: term,SV74: term,SV27: term > $o] :
( ( ( SV27 @ ( sub @ ( sK39_SY309 @ SV74 @ SV93 @ SV103 @ SV27 ) @ SV103 ) )
= $false )
| ( ( SV27 @ ( sub @ SV93 @ SV103 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( SV27 @ SV74 )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[446]) ).
thf(453,plain,
! [SV27: term > $o,SV94: subst,SV81: term,SV72: term] :
( ( ( var @ ( sK38_SY308 @ SV72 @ SV81 @ SV94 @ SV27 ) )
= $true )
| ( ( SV27 @ ( sub @ SV81 @ SV94 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK20_SY243 @ SV27 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV27 @ SV72 )
= $false )
| ( ( SV27 @ ( ap @ ( sK6_SY241 @ SV27 ) @ ( sK8_SY278 @ SV27 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(454,plain,
! [SV27: term > $o,SV103: subst,SV93: term,SV74: term] :
( ( ( var @ ( sK39_SY309 @ SV74 @ SV93 @ SV103 @ SV27 ) )
= $true )
| ( ( SV27 @ ( sub @ SV93 @ SV103 ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK21_SY243 @ SV27 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( SV27 @ SV74 )
= $false )
| ( ( SV27 @ ( sK8_SY278 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(455,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[57,454,453,452,450,449,448,445,443,442,440,436,434,429,426,419,417,414,412,411,410,408,403,400,395,392,391,389,388,384,381,378,374,366,362,355,351,286,279,266,259,257,203,192,191,188,187,170,169,165,156,145,144,143,142,141,140,139,124,123,121,117,99,96,92,91,87,86,84,59]) ).
thf(456,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG257^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 18:13:13 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.58/0.55
% 1.58/0.55 No.of.Axioms: 0
% 1.58/0.55
% 1.58/0.55 Length.of.Defs: 38092
% 1.58/0.55
% 1.58/0.55 Contains.Choice.Funs: false
% 1.58/0.55 ................
% 1.58/0.55
% 1.58/0.55 ********************************
% 1.58/0.55 * All subproblems solved! *
% 1.58/0.55 ********************************
% 1.58/0.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:32,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:455,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.58/0.55
% 1.58/0.55 %**** Beginning of derivation protocol ****
% 1.58/0.55 % SZS output start CNFRefutation
% See solution above
% 1.58/0.56
% 1.58/0.56 %**** End of derivation protocol ****
% 1.58/0.56 %**** no. of clauses in derivation: 456 ****
% 1.58/0.56 %**** clause counter: 455 ****
% 1.58/0.56
% 1.58/0.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:32,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:455,loop_count:0,foatp_calls:1,translation:fof_full)
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