%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG263^1 : 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 10:08:42 AM UTC 2026
% Result : Theorem 1.15s 0.43s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 114
% Syntax : Number of formulae : 646 ( 310 unt; 0 typ; 113 def)
% Number of atoms : 4615 (1825 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 11154 ( 837 ~;1497 |; 7 &;7603 @)
% ( 2 <=>;1208 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 555 ( 555 >; 0 *; 0 +; 0 <<)
% Number of symbols : 174 ( 171 usr; 114 con; 0-4 aty)
% Number of variables : 2339 ( 39 ^;2295 !; 5 ?;2339 :)
% 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_SY413,type,
sK10_SY413: ( term > $o ) > term ).
thf(tp_sK11_SY414,type,
sK11_SY414: ( subst > term > term ) > term ).
thf(tp_sK12_SY416,type,
sK12_SY416: ( subst > term > term ) > subst ).
thf(tp_sK13_SY417,type,
sK13_SY417: ( subst > term > term ) > subst ).
thf(tp_sK14_SY336,type,
sK14_SY336: ( term > $o ) > term ).
thf(tp_sK15_SY418,type,
sK15_SY418: ( subst > term > term ) > subst ).
thf(tp_sK16_SY407,type,
sK16_SY407: term > subst > ( term > $o ) > term ).
thf(tp_sK17_SY402,type,
sK17_SY402: term ).
thf(tp_sK18_SY355,type,
sK18_SY355: ( term > $o ) > term ).
thf(tp_sK19_SY360,type,
sK19_SY360: ( term > $o ) > term ).
thf(tp_sK1_SX0,type,
sK1_SX0: subst > term > subst > $o ).
thf(tp_sK20_SY355,type,
sK20_SY355: ( term > $o ) > term ).
thf(tp_sK21_SY436,type,
sK21_SY436: ( term > $o ) > term ).
thf(tp_sK22_SY360,type,
sK22_SY360: ( term > $o ) > term ).
thf(tp_sK23_SY437,type,
sK23_SY437: ( term > $o ) > term ).
thf(tp_sK24_SY427,type,
sK24_SY427: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(tp_sK25_SY346,type,
sK25_SY346: ( term > $o ) > term ).
thf(tp_sK26_SY346,type,
sK26_SY346: ( term > $o ) > term ).
thf(tp_sK27_SY439,type,
sK27_SY439: ( term > $o ) > term ).
thf(tp_sK28_SY440,type,
sK28_SY440: ( term > $o ) > term ).
thf(tp_sK29_SY441,type,
sK29_SY441: ( subst > term > term ) > ( subst > term > term ) > term ).
thf(tp_sK2_SY318,type,
sK2_SY318: ( subst > term > term ) > subst ).
thf(tp_sK30_SY346,type,
sK30_SY346: ( term > $o ) > term ).
thf(tp_sK31_SY445,type,
sK31_SY445: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(tp_sK32_SY357,type,
sK32_SY357: ( term > $o ) > term ).
thf(tp_sK33_SY357,type,
sK33_SY357: ( term > $o ) > term ).
thf(tp_sK34_SY362,type,
sK34_SY362: ( term > $o ) > term ).
thf(tp_sK35_SY362,type,
sK35_SY362: ( term > $o ) > term ).
thf(tp_sK36_SY357,type,
sK36_SY357: ( term > $o ) > term ).
thf(tp_sK37_SY357,type,
sK37_SY357: ( term > $o ) > term ).
thf(tp_sK38_SY357,type,
sK38_SY357: ( term > $o ) > term ).
thf(tp_sK39_SY362,type,
sK39_SY362: ( term > $o ) > term ).
thf(tp_sK3_SY330,type,
sK3_SY330: ( subst > term > term ) > subst ).
thf(tp_sK40_SY362,type,
sK40_SY362: ( term > $o ) > term ).
thf(tp_sK41_SY362,type,
sK41_SY362: ( term > $o ) > term ).
thf(tp_sK42_SY451,type,
sK42_SY451: term > subst > ( term > $o ) > term ).
thf(tp_sK43_SY454,type,
sK43_SY454: term > subst > ( term > $o ) > term ).
thf(tp_sK44_SY357,type,
sK44_SY357: ( term > $o ) > term ).
thf(tp_sK45_SY362,type,
sK45_SY362: ( term > $o ) > term ).
thf(tp_sK46_SY455,type,
sK46_SY455: term > subst > ( term > $o ) > term ).
thf(tp_sK47_SY467,type,
sK47_SY467: term > term > subst > ( term > $o ) > term ).
thf(tp_sK48_SY470,type,
sK48_SY470: term > term > subst > ( term > $o ) > term ).
thf(tp_sK49_SY471,type,
sK49_SY471: term > term > subst > ( term > $o ) > term ).
thf(tp_sK4_SY344,type,
sK4_SY344: ( term > $o ) > term ).
thf(tp_sK5_SY354,type,
sK5_SY354: ( term > $o ) > term ).
thf(tp_sK6_SY359,type,
sK6_SY359: ( term > $o ) > term ).
thf(tp_sK7_SY365,type,
sK7_SY365: ( subst > term > term ) > subst ).
thf(tp_sK8_SY409,type,
sK8_SY409: ( subst > term > term ) > term ).
thf(tp_sK9_SY411,type,
sK9_SY411: ( subst > term > term ) > 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,
hoasinduction_lem1_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
hoasinduction_lem1_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 ) )
=> ( ! [SY111: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY111 @ M @ A ) @ N )
= ( SY111 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY115: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY115 @ M @ A ) @ N )
= ( SY115 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( lam @ ( SY111 @ sh @ one ) )
= ( lam @ ( SY115 @ sh @ one ) ) )
=> ! [M: subst,A: term] :
( ( SY111 @ M @ A )
= ( SY115 @ M @ A ) ) ) ) )
=> ( ! [SY129: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY129 @ M @ A ) @ N )
= ( SY129 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY133: term,SY134: term] :
( ( lam @ ( SY129 @ sh @ one ) )
!= ( ap @ ( sub @ SY133 @ id ) @ SY134 ) ) )
=> ( ! [SY145: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY145 @ M @ A ) @ N )
= ( SY145 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( SY145 @ sh @ one ) ) @ id ) ) )
=> ( ! [SY156: term,SY157: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SY156 @ id ) @ SY157 ) @ id ) )
=> ! [SY167: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ M @ A @ ( comp @ K @ N ) )
=> ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( SY167 @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [SY176: term] :
( ( var @ ( sub @ SY176 @ id ) )
=> ( SY167 @ id @ SY176 @ id ) )
=> ! [A: term] :
( ( var @ A )
=> ( SY167 @ id @ A @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [SY111: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY111 @ M @ A ) @ N )
= ( SY111 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY115: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY115 @ M @ A ) @ N )
= ( SY115 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( lam @ ( SY111 @ sh @ one ) )
= ( lam @ ( SY115 @ sh @ one ) ) )
=> ! [M: subst,A: term] :
( ( SY111 @ M @ A )
= ( SY115 @ M @ A ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [SY129: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY129 @ M @ A ) @ N )
= ( SY129 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY133: term,SY134: term] :
( ( lam @ ( SY129 @ sh @ one ) )
!= ( ap @ ( sub @ SY133 @ id ) @ SY134 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [SY145: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY145 @ M @ A ) @ N )
= ( SY145 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( SY145 @ sh @ one ) ) @ id ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [SY156: term,SY157: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SY156 @ id ) @ SY157 ) @ id ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [SY167: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ M @ A @ ( comp @ K @ N ) )
=> ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( SY167 @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [SY176: term] :
( ( var @ ( sub @ SY176 @ id ) )
=> ( SY167 @ id @ SY176 @ id ) )
=> ! [A: term] :
( ( var @ A )
=> ( SY167 @ id @ A @ id ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(42,plain,
( ( ~ ! [SY167: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ M @ A @ ( comp @ K @ N ) )
=> ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( SY167 @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [SY176: term] :
( ( var @ ( sub @ SY176 @ id ) )
=> ( SY167 @ id @ SY176 @ id ) )
=> ! [A: term] :
( ( var @ A )
=> ( SY167 @ id @ A @ id ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[41]) ).
thf(43,plain,
( ( ! [SY156: term,SY157: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SY156 @ id ) @ SY157 ) @ id ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(44,plain,
( ( ! [SY145: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY145 @ M @ A ) @ N )
= ( SY145 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( SY145 @ sh @ one ) ) @ id ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(45,plain,
( ( ! [SY129: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY129 @ M @ A ) @ N )
= ( SY129 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY133: term,SY134: term] :
( ( lam @ ( SY129 @ sh @ one ) )
!= ( ap @ ( sub @ SY133 @ id ) @ SY134 ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(46,plain,
( ( ! [SY111: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY111 @ M @ A ) @ N )
= ( SY111 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY115: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY115 @ M @ A ) @ N )
= ( SY115 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( lam @ ( SY111 @ sh @ one ) )
= ( lam @ ( SY115 @ sh @ one ) ) )
=> ! [M: subst,A: term] :
( ( SY111 @ M @ A )
= ( SY115 @ M @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(47,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)],[36]) ).
thf(48,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(49,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(50,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(51,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(52,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(53,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(54,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(55,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(56,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(57,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(58,plain,
( ( ! [A: term] :
~ ( var @ ( lam @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(59,plain,
( ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(60,plain,
( ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(61,plain,
( ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(62,plain,
( ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(63,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(64,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(65,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(66,plain,
( ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(67,plain,
( ( var @ one )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(68,plain,
( ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(69,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(70,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(71,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(72,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(73,plain,
( ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(74,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(75,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(76,plain,
( ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(77,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(78,plain,
( ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(79,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(80,plain,
( ( ~ ! [SY167: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ M @ A @ ( comp @ K @ N ) )
=> ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( SY167 @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [SY176: term] :
( ( var @ ( sub @ SY176 @ id ) )
=> ( SY167 @ id @ SY176 @ id ) )
=> ! [A: term] :
( ( var @ A )
=> ( SY167 @ id @ A @ id ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(81,plain,
( ( ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66,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: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) ) )
= $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(83,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64,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,
( ( ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) ) )
= $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(85,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)],[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(86,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)],[65,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(87,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)],[48,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(88,plain,
( ( ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61,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(89,plain,
( ( ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60,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(90,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)],[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(91,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63,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(92,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)],[57,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(93,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)],[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(94,plain,
( ( ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ 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(95,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)],[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(96,plain,
( ( ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62,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(97,plain,
( ( ~ ! [SX0: subst > term > subst > $o] :
( ~ ! [SX1: subst,SX2: term,SX3: subst,SX4: subst] :
( ~ ( SX0 @ SX1 @ SX2 @ ( comp @ SX4 @ SX3 ) )
| ( SX0 @ ( comp @ SX1 @ SX4 ) @ ( sub @ SX2 @ SX4 ) @ SX3 ) )
| ~ ! [SX1: subst,SX2: term,SX3: subst,SX4: subst] :
( ~ ( SX0 @ ( comp @ SX1 @ SX4 ) @ ( sub @ SX2 @ SX4 ) @ SX3 )
| ( SX0 @ SX1 @ SX2 @ ( comp @ SX4 @ SX3 ) ) )
| ~ ! [SX1: term] :
( ~ ( var @ ( sub @ SX1 @ id ) )
| ( SX0 @ id @ SX1 @ id ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ id @ SX1 @ id ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80,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(98,plain,
! [SV1: term] :
( ( ! [SY301: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SV1 @ id ) @ SY301 ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(99,plain,
! [SV2: term] :
( ( ( sub @ SV2 @ id )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(100,plain,
! [SV3: term] :
( ( ! [SY302: subst,SY303: subst] :
( ( sub @ ( sub @ SV3 @ SY302 ) @ SY303 )
= ( sub @ SV3 @ ( comp @ SY302 @ SY303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(101,plain,
! [SV4: subst] :
( ( ( comp @ SV4 @ id )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(102,plain,
! [SV5: subst] :
( ( ( comp @ id @ SV5 )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(103,plain,
! [SV6: subst] :
( ( ! [SY304: subst,SY305: subst] :
( ( comp @ ( comp @ SV6 @ SY304 ) @ SY305 )
= ( comp @ SV6 @ ( comp @ SY304 @ SY305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(104,plain,
! [SV7: term] :
( ( ~ ( var @ ( lam @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(105,plain,
! [SV8: term] :
( ( ! [SY306: term] :
~ ( var @ ( ap @ SV8 @ SY306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(106,plain,
! [SV9: subst] :
( ( ( push @ ( sub @ one @ SV9 ) @ ( comp @ sh @ SV9 ) )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(107,plain,
! [SV10: subst] :
( ( ( comp @ SV10 @ id )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(108,plain,
! [SV11: term] :
( ( ! [SY307: subst,SY308: subst] :
( ( comp @ ( push @ SV11 @ SY307 ) @ SY308 )
= ( push @ ( sub @ SV11 @ SY308 ) @ ( comp @ SY307 @ SY308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(109,plain,
! [SV12: subst] :
( ( ! [SY309: subst,SY310: subst] :
( ( comp @ ( comp @ SV12 @ SY309 ) @ SY310 )
= ( comp @ SV12 @ ( comp @ SY309 @ SY310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(110,plain,
! [SV13: term] :
( ( ! [SY311: subst] :
( ( comp @ sh @ ( push @ SV13 @ SY311 ) )
= SY311 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(111,plain,
! [SV14: subst] :
( ( ( comp @ id @ SV14 )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(112,plain,
! [SV15: term] :
( ( ! [SY312: subst,SY313: subst] :
( ( sub @ ( sub @ SV15 @ SY312 ) @ SY313 )
= ( sub @ SV15 @ ( comp @ SY312 @ SY313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(113,plain,
! [SV16: term] :
( ( ! [SY314: subst] :
( ( sub @ ( lam @ SV16 ) @ SY314 )
= ( lam @ ( sub @ SV16 @ ( push @ one @ ( comp @ SY314 @ sh ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(114,plain,
! [SV17: term] :
( ( ( sub @ SV17 @ id )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(115,plain,
! [SV18: term] :
( ( ! [SY315: subst] :
( ( sub @ one @ ( push @ SV18 @ SY315 ) )
= SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(116,plain,
! [SV19: term] :
( ( ! [SY316: term,SY317: subst] :
( ( sub @ ( ap @ SV19 @ SY316 ) @ SY317 )
= ( ap @ ( sub @ SV19 @ SY317 ) @ ( sub @ SY316 @ SY317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(117,plain,
! [SV20: term] :
( ( ~ ( var @ SV20 )
| ( var @ ( sub @ SV20 @ sh ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(118,plain,
! [SV21: subst > term > term] :
( ( ~ ! [SY318: subst,SY319: term,SY320: subst] :
( ( sub @ ( SV21 @ SY318 @ SY319 ) @ SY320 )
= ( SV21 @ ( comp @ SY318 @ SY320 ) @ ( sub @ SY319 @ SY320 ) ) )
| ! [SY321: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY321 @ SX2 @ SX3 ) @ SX4 )
= ( SY321 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SY321 @ sh @ one ) ) )
| ! [SY325: subst,SY326: term] :
( ( SV21 @ SY325 @ SY326 )
= ( SY321 @ SY325 @ SY326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(119,plain,
! [SV22: term] :
( ( ! [SY327: term,SY328: term,SY329: term] :
( ( ( ap @ SV22 @ SY328 )
!= ( ap @ SY327 @ SY329 ) )
| ( SV22 = SY327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(120,plain,
! [SV23: subst > term > term] :
( ( ~ ! [SY330: subst,SY331: term,SY332: subst] :
( ( sub @ ( SV23 @ SY330 @ SY331 ) @ SY332 )
= ( SV23 @ ( comp @ SY330 @ SY332 ) @ ( sub @ SY331 @ SY332 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SV23 @ sh @ one ) ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(121,plain,
! [SV24: term] :
( ( ! [SY333: term,SY334: term,SY335: term] :
( ( ( ap @ ( sub @ SV24 @ id ) @ SY334 )
!= ( ap @ ( sub @ SY333 @ id ) @ SY335 ) )
| ( SY334 = SY335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(122,plain,
! [SV25: term > $o] :
( ( ~ ( SV25 @ one )
| ~ ! [SY336: term] :
( ~ ( var @ SY336 )
| ~ ( SV25 @ SY336 )
| ( SV25 @ ( sub @ SY336 @ sh ) ) )
| ! [SY337: term] :
( ~ ( var @ SY337 )
| ( SV25 @ SY337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(123,plain,
! [SV26: term] :
( ( ! [SY338: term,SY339: term,SY340: term] :
( ( ( ap @ ( sub @ SV26 @ id ) @ SY339 )
!= ( ap @ ( sub @ SY338 @ id ) @ SY340 ) )
| ( SV26 = SY338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(124,plain,
! [SV27: term] :
( ( ! [SY341: term] :
( ( ( sub @ SV27 @ sh )
!= ( sub @ SY341 @ sh ) )
| ( SV27 = SY341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(125,plain,
! [SV28: term] :
( ( ! [SY342: term,SY343: term] :
( ( lam @ SV28 )
!= ( ap @ SY342 @ SY343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(126,plain,
! [SV29: term > $o] :
( ( ~ ! [SY344: term,SY345: term] :
( ~ ( SV29 @ SY344 )
| ~ ( SV29 @ SY345 )
| ( SV29 @ ( ap @ SY344 @ SY345 ) ) )
| ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) )
| ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(127,plain,
! [SV30: term] :
( ( ! [SY351: term,SY352: term,SY353: term] :
( ( ( ap @ SV30 @ SY352 )
!= ( ap @ SY351 @ SY353 ) )
| ( SY352 = SY353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(128,plain,
! [SV31: term > $o] :
( ( ~ ! [SY354: term] :
( ~ ( var @ SY354 )
| ( SV31 @ SY354 ) )
| ~ ! [SY355: term,SY356: term] :
( ~ ( SV31 @ SY355 )
| ~ ( SV31 @ SY356 )
| ( SV31 @ ( ap @ SY355 @ SY356 ) ) )
| ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(129,plain,
! [SV32: term > $o] :
( ( ~ ! [SY359: term] :
( ~ ( var @ SY359 )
| ( SV32 @ SY359 ) )
| ~ ! [SY360: term,SY361: term] :
( ~ ( SV32 @ SY360 )
| ~ ( SV32 @ SY361 )
| ( SV32 @ ( ap @ SY360 @ SY361 ) ) )
| ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(130,plain,
! [SV33: subst > term > term] :
( ( ~ ! [SY365: subst,SY366: term,SY367: subst] :
( ( sub @ ( SV33 @ SY365 @ SY366 ) @ SY367 )
= ( SV33 @ ( comp @ SY365 @ SY367 ) @ ( sub @ SY366 @ SY367 ) ) )
| ! [SY368: term,SY369: term] :
( ( lam @ ( SV33 @ sh @ one ) )
!= ( ap @ ( sub @ SY368 @ id ) @ SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(131,plain,
! [SV34: term > $o] :
( ( ! [SY370: term,SY371: subst] :
( ~ ! [SY372: term] :
( ~ ( var @ SY372 )
| ( SV34 @ ( sub @ SY372 @ SY371 ) ) )
| ~ ( SV34 @ SY370 )
| ! [SY373: term] :
( ~ ( var @ SY373 )
| ( SV34 @ ( sub @ SY373 @ ( push @ SY370 @ SY371 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(132,plain,
! [SV35: term] :
( ( ! [SY374: term] :
( ( ( lam @ SV35 )
!= ( lam @ SY374 ) )
| ( SV35 = SY374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(133,plain,
( ( ! [SX0: subst > term > subst > $o] :
( ~ ! [SX1: subst,SX2: term,SX3: subst,SX4: subst] :
( ~ ( SX0 @ SX1 @ SX2 @ ( comp @ SX4 @ SX3 ) )
| ( SX0 @ ( comp @ SX1 @ SX4 ) @ ( sub @ SX2 @ SX4 ) @ SX3 ) )
| ~ ! [SX1: subst,SX2: term,SX3: subst,SX4: subst] :
( ~ ( SX0 @ ( comp @ SX1 @ SX4 ) @ ( sub @ SX2 @ SX4 ) @ SX3 )
| ( SX0 @ SX1 @ SX2 @ ( comp @ SX4 @ SX3 ) ) )
| ~ ! [SX1: term] :
( ~ ( var @ ( sub @ SX1 @ id ) )
| ( SX0 @ id @ SX1 @ id ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ id @ SX1 @ id ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(134,plain,
! [SV36: term,SV1: term] :
( ( ~ ( var @ ( sub @ ( ap @ ( sub @ SV1 @ id ) @ SV36 ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(135,plain,
! [SV37: subst,SV3: term] :
( ( ! [SY375: subst] :
( ( sub @ ( sub @ SV3 @ SV37 ) @ SY375 )
= ( sub @ SV3 @ ( comp @ SV37 @ SY375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(136,plain,
! [SV38: subst,SV6: subst] :
( ( ! [SY376: subst] :
( ( comp @ ( comp @ SV6 @ SV38 ) @ SY376 )
= ( comp @ SV6 @ ( comp @ SV38 @ SY376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(137,plain,
! [SV7: term] :
( ( var @ ( lam @ SV7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(138,plain,
! [SV39: term,SV8: term] :
( ( ~ ( var @ ( ap @ SV8 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(139,plain,
! [SV40: subst,SV11: term] :
( ( ! [SY377: subst] :
( ( comp @ ( push @ SV11 @ SV40 ) @ SY377 )
= ( push @ ( sub @ SV11 @ SY377 ) @ ( comp @ SV40 @ SY377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(140,plain,
! [SV41: subst,SV12: subst] :
( ( ! [SY378: subst] :
( ( comp @ ( comp @ SV12 @ SV41 ) @ SY378 )
= ( comp @ SV12 @ ( comp @ SV41 @ SY378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(141,plain,
! [SV42: subst,SV13: term] :
( ( ( comp @ sh @ ( push @ SV13 @ SV42 ) )
= SV42 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(142,plain,
! [SV43: subst,SV15: term] :
( ( ! [SY379: subst] :
( ( sub @ ( sub @ SV15 @ SV43 ) @ SY379 )
= ( sub @ SV15 @ ( comp @ SV43 @ SY379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(143,plain,
! [SV44: subst,SV16: term] :
( ( ( sub @ ( lam @ SV16 ) @ SV44 )
= ( lam @ ( sub @ SV16 @ ( push @ one @ ( comp @ SV44 @ sh ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(144,plain,
! [SV45: subst,SV18: term] :
( ( ( sub @ one @ ( push @ SV18 @ SV45 ) )
= SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(145,plain,
! [SV46: term,SV19: term] :
( ( ! [SY380: subst] :
( ( sub @ ( ap @ SV19 @ SV46 ) @ SY380 )
= ( ap @ ( sub @ SV19 @ SY380 ) @ ( sub @ SV46 @ SY380 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(146,plain,
! [SV20: term] :
( ( ( ~ ( var @ SV20 ) )
= $true )
| ( ( var @ ( sub @ SV20 @ sh ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(147,plain,
! [SV21: subst > term > term] :
( ( ( ~ ! [SY318: subst,SY319: term,SY320: subst] :
( ( sub @ ( SV21 @ SY318 @ SY319 ) @ SY320 )
= ( SV21 @ ( comp @ SY318 @ SY320 ) @ ( sub @ SY319 @ SY320 ) ) ) )
= $true )
| ( ( ! [SY321: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY321 @ SX2 @ SX3 ) @ SX4 )
= ( SY321 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SY321 @ sh @ one ) ) )
| ! [SY325: subst,SY326: term] :
( ( SV21 @ SY325 @ SY326 )
= ( SY321 @ SY325 @ SY326 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(148,plain,
! [SV47: term,SV22: term] :
( ( ! [SY381: term,SY382: term] :
( ( ( ap @ SV22 @ SY381 )
!= ( ap @ SV47 @ SY382 ) )
| ( SV22 = SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(149,plain,
! [SV23: subst > term > term] :
( ( ( ~ ! [SY330: subst,SY331: term,SY332: subst] :
( ( sub @ ( SV23 @ SY330 @ SY331 ) @ SY332 )
= ( SV23 @ ( comp @ SY330 @ SY332 ) @ ( sub @ SY331 @ SY332 ) ) ) )
= $true )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV23 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(150,plain,
! [SV48: term,SV24: term] :
( ( ! [SY383: term,SY384: term] :
( ( ( ap @ ( sub @ SV24 @ id ) @ SY383 )
!= ( ap @ ( sub @ SV48 @ id ) @ SY384 ) )
| ( SY383 = SY384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(151,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ one ) )
= $true )
| ( ( ~ ! [SY336: term] :
( ~ ( var @ SY336 )
| ~ ( SV25 @ SY336 )
| ( SV25 @ ( sub @ SY336 @ sh ) ) )
| ! [SY337: term] :
( ~ ( var @ SY337 )
| ( SV25 @ SY337 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(152,plain,
! [SV49: term,SV26: term] :
( ( ! [SY385: term,SY386: term] :
( ( ( ap @ ( sub @ SV26 @ id ) @ SY385 )
!= ( ap @ ( sub @ SV49 @ id ) @ SY386 ) )
| ( SV26 = SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(153,plain,
! [SV50: term,SV27: term] :
( ( ( ( sub @ SV27 @ sh )
!= ( sub @ SV50 @ sh ) )
| ( SV27 = SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(154,plain,
! [SV51: term,SV28: term] :
( ( ! [SY387: term] :
( ( lam @ SV28 )
!= ( ap @ SV51 @ SY387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(155,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY344: term,SY345: term] :
( ~ ( SV29 @ SY344 )
| ~ ( SV29 @ SY345 )
| ( SV29 @ ( ap @ SY344 @ SY345 ) ) ) )
= $true )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) )
| ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(156,plain,
! [SV52: term,SV30: term] :
( ( ! [SY388: term,SY389: term] :
( ( ( ap @ SV30 @ SY388 )
!= ( ap @ SV52 @ SY389 ) )
| ( SY388 = SY389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(157,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY354: term] :
( ~ ( var @ SY354 )
| ( SV31 @ SY354 ) ) )
= $true )
| ( ( ~ ! [SY355: term,SY356: term] :
( ~ ( SV31 @ SY355 )
| ~ ( SV31 @ SY356 )
| ( SV31 @ ( ap @ SY355 @ SY356 ) ) )
| ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(158,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY359: term] :
( ~ ( var @ SY359 )
| ( SV32 @ SY359 ) ) )
= $true )
| ( ( ~ ! [SY360: term,SY361: term] :
( ~ ( SV32 @ SY360 )
| ~ ( SV32 @ SY361 )
| ( SV32 @ ( ap @ SY360 @ SY361 ) ) )
| ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(159,plain,
! [SV33: subst > term > term] :
( ( ( ~ ! [SY365: subst,SY366: term,SY367: subst] :
( ( sub @ ( SV33 @ SY365 @ SY366 ) @ SY367 )
= ( SV33 @ ( comp @ SY365 @ SY367 ) @ ( sub @ SY366 @ SY367 ) ) ) )
= $true )
| ( ( ! [SY368: term,SY369: term] :
( ( lam @ ( SV33 @ sh @ one ) )
!= ( ap @ ( sub @ SY368 @ id ) @ SY369 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(160,plain,
! [SV53: term,SV34: term > $o] :
( ( ! [SY390: subst] :
( ~ ! [SY372: term] :
( ~ ( var @ SY372 )
| ( SV34 @ ( sub @ SY372 @ SY390 ) ) )
| ~ ( SV34 @ SV53 )
| ! [SY392: term] :
( ~ ( var @ SY392 )
| ( SV34 @ ( sub @ SY392 @ ( push @ SV53 @ SY390 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(161,plain,
! [SV54: term,SV35: term] :
( ( ( ( lam @ SV35 )
!= ( lam @ SV54 ) )
| ( SV35 = SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(162,plain,
( ( ~ ! [SY393: subst,SY394: term,SY395: subst,SY396: subst] :
( ~ ( sK1_SX0 @ SY393 @ SY394 @ ( comp @ SY396 @ SY395 ) )
| ( sK1_SX0 @ ( comp @ SY393 @ SY396 ) @ ( sub @ SY394 @ SY396 ) @ SY395 ) )
| ~ ! [SY397: subst,SY398: term,SY399: subst,SY400: subst] :
( ~ ( sK1_SX0 @ ( comp @ SY397 @ SY400 ) @ ( sub @ SY398 @ SY400 ) @ SY399 )
| ( sK1_SX0 @ SY397 @ SY398 @ ( comp @ SY400 @ SY399 ) ) )
| ~ ! [SY401: term] :
( ~ ( var @ ( sub @ SY401 @ id ) )
| ( sK1_SX0 @ id @ SY401 @ id ) )
| ! [SY402: term] :
( ~ ( var @ SY402 )
| ( sK1_SX0 @ id @ SY402 @ id ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[133]) ).
thf(163,plain,
! [SV36: term,SV1: term] :
( ( var @ ( sub @ ( ap @ ( sub @ SV1 @ id ) @ SV36 ) @ id ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(164,plain,
! [SV55: subst,SV37: subst,SV3: term] :
( ( ( sub @ ( sub @ SV3 @ SV37 ) @ SV55 )
= ( sub @ SV3 @ ( comp @ SV37 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(165,plain,
! [SV56: subst,SV38: subst,SV6: subst] :
( ( ( comp @ ( comp @ SV6 @ SV38 ) @ SV56 )
= ( comp @ SV6 @ ( comp @ SV38 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(166,plain,
! [SV39: term,SV8: term] :
( ( var @ ( ap @ SV8 @ SV39 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(167,plain,
! [SV57: subst,SV40: subst,SV11: term] :
( ( ( comp @ ( push @ SV11 @ SV40 ) @ SV57 )
= ( push @ ( sub @ SV11 @ SV57 ) @ ( comp @ SV40 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(168,plain,
! [SV58: subst,SV41: subst,SV12: subst] :
( ( ( comp @ ( comp @ SV12 @ SV41 ) @ SV58 )
= ( comp @ SV12 @ ( comp @ SV41 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(169,plain,
! [SV59: subst,SV43: subst,SV15: term] :
( ( ( sub @ ( sub @ SV15 @ SV43 ) @ SV59 )
= ( sub @ SV15 @ ( comp @ SV43 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(170,plain,
! [SV60: subst,SV46: term,SV19: term] :
( ( ( sub @ ( ap @ SV19 @ SV46 ) @ SV60 )
= ( ap @ ( sub @ SV19 @ SV60 ) @ ( sub @ SV46 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(171,plain,
! [SV20: term] :
( ( ( var @ SV20 )
= $false )
| ( ( var @ ( sub @ SV20 @ sh ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(172,plain,
! [SV21: subst > term > term] :
( ( ( ! [SY318: subst,SY319: term,SY320: subst] :
( ( sub @ ( SV21 @ SY318 @ SY319 ) @ SY320 )
= ( SV21 @ ( comp @ SY318 @ SY320 ) @ ( sub @ SY319 @ SY320 ) ) ) )
= $false )
| ( ( ! [SY321: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY321 @ SX2 @ SX3 ) @ SX4 )
= ( SY321 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SY321 @ sh @ one ) ) )
| ! [SY325: subst,SY326: term] :
( ( SV21 @ SY325 @ SY326 )
= ( SY321 @ SY325 @ SY326 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(173,plain,
! [SV47: term,SV61: term,SV22: term] :
( ( ! [SY403: term] :
( ( ( ap @ SV22 @ SV61 )
!= ( ap @ SV47 @ SY403 ) )
| ( SV22 = SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(174,plain,
! [SV23: subst > term > term] :
( ( ( ! [SY330: subst,SY331: term,SY332: subst] :
( ( sub @ ( SV23 @ SY330 @ SY331 ) @ SY332 )
= ( SV23 @ ( comp @ SY330 @ SY332 ) @ ( sub @ SY331 @ SY332 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV23 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(175,plain,
! [SV48: term,SV62: term,SV24: term] :
( ( ! [SY404: term] :
( ( ( ap @ ( sub @ SV24 @ id ) @ SV62 )
!= ( ap @ ( sub @ SV48 @ id ) @ SY404 ) )
| ( SV62 = SY404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(176,plain,
! [SV25: term > $o] :
( ( ( SV25 @ one )
= $false )
| ( ( ~ ! [SY336: term] :
( ~ ( var @ SY336 )
| ~ ( SV25 @ SY336 )
| ( SV25 @ ( sub @ SY336 @ sh ) ) )
| ! [SY337: term] :
( ~ ( var @ SY337 )
| ( SV25 @ SY337 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(177,plain,
! [SV49: term,SV63: term,SV26: term] :
( ( ! [SY405: term] :
( ( ( ap @ ( sub @ SV26 @ id ) @ SV63 )
!= ( ap @ ( sub @ SV49 @ id ) @ SY405 ) )
| ( SV26 = SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(178,plain,
! [SV50: term,SV27: term] :
( ( ( ( sub @ SV27 @ sh )
!= ( sub @ SV50 @ sh ) )
= $true )
| ( ( SV27 = SV50 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(179,plain,
! [SV64: term,SV51: term,SV28: term] :
( ( ( lam @ SV28 )
!= ( ap @ SV51 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(180,plain,
! [SV29: term > $o] :
( ( ( ! [SY344: term,SY345: term] :
( ~ ( SV29 @ SY344 )
| ~ ( SV29 @ SY345 )
| ( SV29 @ ( ap @ SY344 @ SY345 ) ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) )
| ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(181,plain,
! [SV52: term,SV65: term,SV30: term] :
( ( ! [SY406: term] :
( ( ( ap @ SV30 @ SV65 )
!= ( ap @ SV52 @ SY406 ) )
| ( SV65 = SY406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(182,plain,
! [SV31: term > $o] :
( ( ( ! [SY354: term] :
( ~ ( var @ SY354 )
| ( SV31 @ SY354 ) ) )
= $false )
| ( ( ~ ! [SY355: term,SY356: term] :
( ~ ( SV31 @ SY355 )
| ~ ( SV31 @ SY356 )
| ( SV31 @ ( ap @ SY355 @ SY356 ) ) )
| ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(183,plain,
! [SV32: term > $o] :
( ( ( ! [SY359: term] :
( ~ ( var @ SY359 )
| ( SV32 @ SY359 ) ) )
= $false )
| ( ( ~ ! [SY360: term,SY361: term] :
( ~ ( SV32 @ SY360 )
| ~ ( SV32 @ SY361 )
| ( SV32 @ ( ap @ SY360 @ SY361 ) ) )
| ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(184,plain,
! [SV33: subst > term > term] :
( ( ( ! [SY365: subst,SY366: term,SY367: subst] :
( ( sub @ ( SV33 @ SY365 @ SY366 ) @ SY367 )
= ( SV33 @ ( comp @ SY365 @ SY367 ) @ ( sub @ SY366 @ SY367 ) ) ) )
= $false )
| ( ( ! [SY368: term,SY369: term] :
( ( lam @ ( SV33 @ sh @ one ) )
!= ( ap @ ( sub @ SY368 @ id ) @ SY369 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(185,plain,
! [SV53: term,SV66: subst,SV34: term > $o] :
( ( ~ ! [SY407: term] :
( ~ ( var @ SY407 )
| ( SV34 @ ( sub @ SY407 @ SV66 ) ) )
| ~ ( SV34 @ SV53 )
| ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV34 @ ( sub @ SY408 @ ( push @ SV53 @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(186,plain,
! [SV54: term,SV35: term] :
( ( ( ( lam @ SV35 )
!= ( lam @ SV54 ) )
= $true )
| ( ( SV35 = SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(187,plain,
( ( ~ ! [SY393: subst,SY394: term,SY395: subst,SY396: subst] :
( ~ ( sK1_SX0 @ SY393 @ SY394 @ ( comp @ SY396 @ SY395 ) )
| ( sK1_SX0 @ ( comp @ SY393 @ SY396 ) @ ( sub @ SY394 @ SY396 ) @ SY395 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(188,plain,
( ( ~ ! [SY397: subst,SY398: term,SY399: subst,SY400: subst] :
( ~ ( sK1_SX0 @ ( comp @ SY397 @ SY400 ) @ ( sub @ SY398 @ SY400 ) @ SY399 )
| ( sK1_SX0 @ SY397 @ SY398 @ ( comp @ SY400 @ SY399 ) ) )
| ~ ! [SY401: term] :
( ~ ( var @ ( sub @ SY401 @ id ) )
| ( sK1_SX0 @ id @ SY401 @ id ) )
| ! [SY402: term] :
( ~ ( var @ SY402 )
| ( sK1_SX0 @ id @ SY402 @ id ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(189,plain,
! [SV21: subst > term > term] :
( ( ( ! [SY409: term,SY410: subst] :
( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ SY409 ) @ SY410 )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ SY410 ) @ ( sub @ SY409 @ SY410 ) ) ) )
= $false )
| ( ( ! [SY321: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY321 @ SX2 @ SX3 ) @ SX4 )
= ( SY321 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SY321 @ sh @ one ) ) )
| ! [SY325: subst,SY326: term] :
( ( SV21 @ SY325 @ SY326 )
= ( SY321 @ SY325 @ SY326 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[172]) ).
thf(190,plain,
! [SV67: term,SV47: term,SV61: term,SV22: term] :
( ( ( ( ap @ SV22 @ SV61 )
!= ( ap @ SV47 @ SV67 ) )
| ( SV22 = SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(191,plain,
! [SV23: subst > term > term] :
( ( ( ! [SY411: term,SY412: subst] :
( ( sub @ ( SV23 @ ( sK3_SY330 @ SV23 ) @ SY411 ) @ SY412 )
= ( SV23 @ ( comp @ ( sK3_SY330 @ SV23 ) @ SY412 ) @ ( sub @ SY411 @ SY412 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV23 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[174]) ).
thf(192,plain,
! [SV68: term,SV48: term,SV62: term,SV24: term] :
( ( ( ( ap @ ( sub @ SV24 @ id ) @ SV62 )
!= ( ap @ ( sub @ SV48 @ id ) @ SV68 ) )
| ( SV62 = SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(193,plain,
! [SV25: term > $o] :
( ( ( ~ ! [SY336: term] :
( ~ ( var @ SY336 )
| ~ ( SV25 @ SY336 )
| ( SV25 @ ( sub @ SY336 @ sh ) ) ) )
= $true )
| ( ( ! [SY337: term] :
( ~ ( var @ SY337 )
| ( SV25 @ SY337 ) ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(194,plain,
! [SV69: term,SV49: term,SV63: term,SV26: term] :
( ( ( ( ap @ ( sub @ SV26 @ id ) @ SV63 )
!= ( ap @ ( sub @ SV49 @ id ) @ SV69 ) )
| ( SV26 = SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(195,plain,
! [SV50: term,SV27: term] :
( ( ( ( sub @ SV27 @ sh )
= ( sub @ SV50 @ sh ) )
= $false )
| ( ( SV27 = SV50 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(196,plain,
! [SV64: term,SV51: term,SV28: term] :
( ( ( lam @ SV28 )
= ( ap @ SV51 @ SV64 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(197,plain,
! [SV29: term > $o] :
( ( ( ! [SY413: term] :
( ~ ( SV29 @ ( sK4_SY344 @ SV29 ) )
| ~ ( SV29 @ SY413 )
| ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ SY413 ) ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) )
| ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[180]) ).
thf(198,plain,
! [SV70: term,SV52: term,SV65: term,SV30: term] :
( ( ( ( ap @ SV30 @ SV65 )
!= ( ap @ SV52 @ SV70 ) )
| ( SV65 = SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(199,plain,
! [SV31: term > $o] :
( ( ( ~ ( var @ ( sK5_SY354 @ SV31 ) )
| ( SV31 @ ( sK5_SY354 @ SV31 ) ) )
= $false )
| ( ( ~ ! [SY355: term,SY356: term] :
( ~ ( SV31 @ SY355 )
| ~ ( SV31 @ SY356 )
| ( SV31 @ ( ap @ SY355 @ SY356 ) ) )
| ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[182]) ).
thf(200,plain,
! [SV32: term > $o] :
( ( ( ~ ( var @ ( sK6_SY359 @ SV32 ) )
| ( SV32 @ ( sK6_SY359 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY360: term,SY361: term] :
( ~ ( SV32 @ SY360 )
| ~ ( SV32 @ SY361 )
| ( SV32 @ ( ap @ SY360 @ SY361 ) ) )
| ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[183]) ).
thf(201,plain,
! [SV33: subst > term > term] :
( ( ( ! [SY414: term,SY415: subst] :
( ( sub @ ( SV33 @ ( sK7_SY365 @ SV33 ) @ SY414 ) @ SY415 )
= ( SV33 @ ( comp @ ( sK7_SY365 @ SV33 ) @ SY415 ) @ ( sub @ SY414 @ SY415 ) ) ) )
= $false )
| ( ( ! [SY368: term,SY369: term] :
( ( lam @ ( SV33 @ sh @ one ) )
!= ( ap @ ( sub @ SY368 @ id ) @ SY369 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[184]) ).
thf(202,plain,
! [SV53: term,SV66: subst,SV34: term > $o] :
( ( ( ~ ! [SY407: term] :
( ~ ( var @ SY407 )
| ( SV34 @ ( sub @ SY407 @ SV66 ) ) ) )
= $true )
| ( ( ~ ( SV34 @ SV53 )
| ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV34 @ ( sub @ SY408 @ ( push @ SV53 @ SV66 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(203,plain,
! [SV54: term,SV35: term] :
( ( ( ( lam @ SV35 )
= ( lam @ SV54 ) )
= $false )
| ( ( SV35 = SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(204,plain,
( ( ! [SY393: subst,SY394: term,SY395: subst,SY396: subst] :
( ~ ( sK1_SX0 @ SY393 @ SY394 @ ( comp @ SY396 @ SY395 ) )
| ( sK1_SX0 @ ( comp @ SY393 @ SY396 ) @ ( sub @ SY394 @ SY396 ) @ SY395 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(205,plain,
( ( ~ ! [SY397: subst,SY398: term,SY399: subst,SY400: subst] :
( ~ ( sK1_SX0 @ ( comp @ SY397 @ SY400 ) @ ( sub @ SY398 @ SY400 ) @ SY399 )
| ( sK1_SX0 @ SY397 @ SY398 @ ( comp @ SY400 @ SY399 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(206,plain,
( ( ~ ! [SY401: term] :
( ~ ( var @ ( sub @ SY401 @ id ) )
| ( sK1_SX0 @ id @ SY401 @ id ) )
| ! [SY402: term] :
( ~ ( var @ SY402 )
| ( sK1_SX0 @ id @ SY402 @ id ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[188]) ).
thf(207,plain,
! [SV21: subst > term > term] :
( ( ( ! [SY416: subst] :
( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ ( sK8_SY409 @ SV21 ) ) @ SY416 )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ SY416 ) @ ( sub @ ( sK8_SY409 @ SV21 ) @ SY416 ) ) ) )
= $false )
| ( ( ! [SY321: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY321 @ SX2 @ SX3 ) @ SX4 )
= ( SY321 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SY321 @ sh @ one ) ) )
| ! [SY325: subst,SY326: term] :
( ( SV21 @ SY325 @ SY326 )
= ( SY321 @ SY325 @ SY326 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[189]) ).
thf(208,plain,
! [SV67: term,SV47: term,SV61: term,SV22: term] :
( ( ( ( ap @ SV22 @ SV61 )
!= ( ap @ SV47 @ SV67 ) )
= $true )
| ( ( SV22 = SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(209,plain,
! [SV23: subst > term > term] :
( ( ( ! [SY417: subst] :
( ( sub @ ( SV23 @ ( sK3_SY330 @ SV23 ) @ ( sK9_SY411 @ SV23 ) ) @ SY417 )
= ( SV23 @ ( comp @ ( sK3_SY330 @ SV23 ) @ SY417 ) @ ( sub @ ( sK9_SY411 @ SV23 ) @ SY417 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV23 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[191]) ).
thf(210,plain,
! [SV68: term,SV48: term,SV62: term,SV24: term] :
( ( ( ( ap @ ( sub @ SV24 @ id ) @ SV62 )
!= ( ap @ ( sub @ SV48 @ id ) @ SV68 ) )
= $true )
| ( ( SV62 = SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(211,plain,
! [SV25: term > $o] :
( ( ( ! [SY336: term] :
( ~ ( var @ SY336 )
| ~ ( SV25 @ SY336 )
| ( SV25 @ ( sub @ SY336 @ sh ) ) ) )
= $false )
| ( ( ! [SY337: term] :
( ~ ( var @ SY337 )
| ( SV25 @ SY337 ) ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(212,plain,
! [SV69: term,SV49: term,SV63: term,SV26: term] :
( ( ( ( ap @ ( sub @ SV26 @ id ) @ SV63 )
!= ( ap @ ( sub @ SV49 @ id ) @ SV69 ) )
= $true )
| ( ( SV26 = SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(213,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK4_SY344 @ SV29 ) )
| ~ ( SV29 @ ( sK10_SY413 @ SV29 ) )
| ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) )
| ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[197]) ).
thf(214,plain,
! [SV70: term,SV52: term,SV65: term,SV30: term] :
( ( ( ( ap @ SV30 @ SV65 )
!= ( ap @ SV52 @ SV70 ) )
= $true )
| ( ( SV65 = SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(215,plain,
! [SV31: term > $o] :
( ( ( ~ ( var @ ( sK5_SY354 @ SV31 ) ) )
= $false )
| ( ( ~ ! [SY355: term,SY356: term] :
( ~ ( SV31 @ SY355 )
| ~ ( SV31 @ SY356 )
| ( SV31 @ ( ap @ SY355 @ SY356 ) ) )
| ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(216,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false )
| ( ( ~ ! [SY355: term,SY356: term] :
( ~ ( SV31 @ SY355 )
| ~ ( SV31 @ SY356 )
| ( SV31 @ ( ap @ SY355 @ SY356 ) ) )
| ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(217,plain,
! [SV32: term > $o] :
( ( ( ~ ( var @ ( sK6_SY359 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY360: term,SY361: term] :
( ~ ( SV32 @ SY360 )
| ~ ( SV32 @ SY361 )
| ( SV32 @ ( ap @ SY360 @ SY361 ) ) )
| ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(218,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false )
| ( ( ~ ! [SY360: term,SY361: term] :
( ~ ( SV32 @ SY360 )
| ~ ( SV32 @ SY361 )
| ( SV32 @ ( ap @ SY360 @ SY361 ) ) )
| ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[200]) ).
thf(219,plain,
! [SV33: subst > term > term] :
( ( ( ! [SY418: subst] :
( ( sub @ ( SV33 @ ( sK7_SY365 @ SV33 ) @ ( sK11_SY414 @ SV33 ) ) @ SY418 )
= ( SV33 @ ( comp @ ( sK7_SY365 @ SV33 ) @ SY418 ) @ ( sub @ ( sK11_SY414 @ SV33 ) @ SY418 ) ) ) )
= $false )
| ( ( ! [SY368: term,SY369: term] :
( ( lam @ ( SV33 @ sh @ one ) )
!= ( ap @ ( sub @ SY368 @ id ) @ SY369 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[201]) ).
thf(220,plain,
! [SV53: term,SV66: subst,SV34: term > $o] :
( ( ( ! [SY407: term] :
( ~ ( var @ SY407 )
| ( SV34 @ ( sub @ SY407 @ SV66 ) ) ) )
= $false )
| ( ( ~ ( SV34 @ SV53 )
| ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV34 @ ( sub @ SY408 @ ( push @ SV53 @ SV66 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(221,plain,
! [SV71: subst] :
( ( ! [SY419: term,SY420: subst,SY421: subst] :
( ~ ( sK1_SX0 @ SV71 @ SY419 @ ( comp @ SY421 @ SY420 ) )
| ( sK1_SX0 @ ( comp @ SV71 @ SY421 ) @ ( sub @ SY419 @ SY421 ) @ SY420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(222,plain,
( ( ! [SY397: subst,SY398: term,SY399: subst,SY400: subst] :
( ~ ( sK1_SX0 @ ( comp @ SY397 @ SY400 ) @ ( sub @ SY398 @ SY400 ) @ SY399 )
| ( sK1_SX0 @ SY397 @ SY398 @ ( comp @ SY400 @ SY399 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(223,plain,
( ( ~ ! [SY401: term] :
( ~ ( var @ ( sub @ SY401 @ id ) )
| ( sK1_SX0 @ id @ SY401 @ id ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(224,plain,
( ( ! [SY402: term] :
( ~ ( var @ SY402 )
| ( sK1_SX0 @ id @ SY402 @ id ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(225,plain,
! [SV21: subst > term > term] :
( ( ( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ ( sK8_SY409 @ SV21 ) ) @ ( sK12_SY416 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) @ ( sub @ ( sK8_SY409 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) ) )
= $false )
| ( ( ! [SY321: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY321 @ SX2 @ SX3 ) @ SX4 )
= ( SY321 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SY321 @ sh @ one ) ) )
| ! [SY325: subst,SY326: term] :
( ( SV21 @ SY325 @ SY326 )
= ( SY321 @ SY325 @ SY326 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[207]) ).
thf(226,plain,
! [SV67: term,SV47: term,SV61: term,SV22: term] :
( ( ( ( ap @ SV22 @ SV61 )
= ( ap @ SV47 @ SV67 ) )
= $false )
| ( ( SV22 = SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(227,plain,
! [SV23: subst > term > term] :
( ( ( ( sub @ ( SV23 @ ( sK3_SY330 @ SV23 ) @ ( sK9_SY411 @ SV23 ) ) @ ( sK13_SY417 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK3_SY330 @ SV23 ) @ ( sK13_SY417 @ SV23 ) ) @ ( sub @ ( sK9_SY411 @ SV23 ) @ ( sK13_SY417 @ SV23 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV23 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[209]) ).
thf(228,plain,
! [SV68: term,SV48: term,SV62: term,SV24: term] :
( ( ( ( ap @ ( sub @ SV24 @ id ) @ SV62 )
= ( ap @ ( sub @ SV48 @ id ) @ SV68 ) )
= $false )
| ( ( SV62 = SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(229,plain,
! [SV25: term > $o] :
( ( ( ~ ( var @ ( sK14_SY336 @ SV25 ) )
| ~ ( SV25 @ ( sK14_SY336 @ SV25 ) )
| ( SV25 @ ( sub @ ( sK14_SY336 @ SV25 ) @ sh ) ) )
= $false )
| ( ( ! [SY337: term] :
( ~ ( var @ SY337 )
| ( SV25 @ SY337 ) ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[211]) ).
thf(230,plain,
! [SV69: term,SV49: term,SV63: term,SV26: term] :
( ( ( ( ap @ ( sub @ SV26 @ id ) @ SV63 )
= ( ap @ ( sub @ SV49 @ id ) @ SV69 ) )
= $false )
| ( ( SV26 = SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(231,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK4_SY344 @ SV29 ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) )
| ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(232,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK10_SY413 @ SV29 ) )
| ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) )
| ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(233,plain,
! [SV70: term,SV52: term,SV65: term,SV30: term] :
( ( ( ( ap @ SV30 @ SV65 )
= ( ap @ SV52 @ SV70 ) )
= $false )
| ( ( SV65 = SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(234,plain,
! [SV31: term > $o] :
( ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true )
| ( ( ~ ! [SY355: term,SY356: term] :
( ~ ( SV31 @ SY355 )
| ~ ( SV31 @ SY356 )
| ( SV31 @ ( ap @ SY355 @ SY356 ) ) )
| ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(235,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY355: term,SY356: term] :
( ~ ( SV31 @ SY355 )
| ~ ( SV31 @ SY356 )
| ( SV31 @ ( ap @ SY355 @ SY356 ) ) ) )
= $true )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(236,plain,
! [SV32: term > $o] :
( ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true )
| ( ( ~ ! [SY360: term,SY361: term] :
( ~ ( SV32 @ SY360 )
| ~ ( SV32 @ SY361 )
| ( SV32 @ ( ap @ SY360 @ SY361 ) ) )
| ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(237,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY360: term,SY361: term] :
( ~ ( SV32 @ SY360 )
| ~ ( SV32 @ SY361 )
| ( SV32 @ ( ap @ SY360 @ SY361 ) ) ) )
= $true )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(238,plain,
! [SV33: subst > term > term] :
( ( ( ( sub @ ( SV33 @ ( sK7_SY365 @ SV33 ) @ ( sK11_SY414 @ SV33 ) ) @ ( sK15_SY418 @ SV33 ) )
= ( SV33 @ ( comp @ ( sK7_SY365 @ SV33 ) @ ( sK15_SY418 @ SV33 ) ) @ ( sub @ ( sK11_SY414 @ SV33 ) @ ( sK15_SY418 @ SV33 ) ) ) )
= $false )
| ( ( ! [SY368: term,SY369: term] :
( ( lam @ ( SV33 @ sh @ one ) )
!= ( ap @ ( sub @ SY368 @ id ) @ SY369 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[219]) ).
thf(239,plain,
! [SV34: term > $o,SV66: subst,SV53: term] :
( ( ( ~ ( var @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) )
| ( SV34 @ ( sub @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) @ SV66 ) ) )
= $false )
| ( ( ~ ( SV34 @ SV53 )
| ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV34 @ ( sub @ SY408 @ ( push @ SV53 @ SV66 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[220]) ).
thf(240,plain,
! [SV72: term,SV71: subst] :
( ( ! [SY422: subst,SY423: subst] :
( ~ ( sK1_SX0 @ SV71 @ SV72 @ ( comp @ SY423 @ SY422 ) )
| ( sK1_SX0 @ ( comp @ SV71 @ SY423 ) @ ( sub @ SV72 @ SY423 ) @ SY422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(241,plain,
! [SV73: subst] :
( ( ! [SY424: term,SY425: subst,SY426: subst] :
( ~ ( sK1_SX0 @ ( comp @ SV73 @ SY426 ) @ ( sub @ SY424 @ SY426 ) @ SY425 )
| ( sK1_SX0 @ SV73 @ SY424 @ ( comp @ SY426 @ SY425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(242,plain,
( ( ! [SY401: term] :
( ~ ( var @ ( sub @ SY401 @ id ) )
| ( sK1_SX0 @ id @ SY401 @ id ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(243,plain,
( ( ~ ( var @ sK17_SY402 )
| ( sK1_SX0 @ id @ sK17_SY402 @ id ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[224]) ).
thf(244,plain,
! [SV21: subst > term > term,SV74: subst > term > term] :
( ( ( ~ ! [SY427: subst,SY428: term,SY429: subst] :
( ( sub @ ( SV74 @ SY427 @ SY428 ) @ SY429 )
= ( SV74 @ ( comp @ SY427 @ SY429 ) @ ( sub @ SY428 @ SY429 ) ) )
| ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SV74 @ sh @ one ) ) )
| ! [SY430: subst,SY431: term] :
( ( SV21 @ SY430 @ SY431 )
= ( SV74 @ SY430 @ SY431 ) ) )
= $true )
| ( ( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ ( sK8_SY409 @ SV21 ) ) @ ( sK12_SY416 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) @ ( sub @ ( sK8_SY409 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(245,plain,
! [SV23: subst > term > term] :
( ( ( var @ ( sub @ ( lam @ ( SV23 @ sh @ one ) ) @ id ) )
= $false )
| ( ( ( sub @ ( SV23 @ ( sK3_SY330 @ SV23 ) @ ( sK9_SY411 @ SV23 ) ) @ ( sK13_SY417 @ SV23 ) )
= ( SV23 @ ( comp @ ( sK3_SY330 @ SV23 ) @ ( sK13_SY417 @ SV23 ) ) @ ( sub @ ( sK9_SY411 @ SV23 ) @ ( sK13_SY417 @ SV23 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(246,plain,
! [SV25: term > $o] :
( ( ( ~ ( var @ ( sK14_SY336 @ SV25 ) ) )
= $false )
| ( ( ! [SY337: term] :
( ~ ( var @ SY337 )
| ( SV25 @ SY337 ) ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(247,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK14_SY336 @ SV25 ) )
| ( SV25 @ ( sub @ ( sK14_SY336 @ SV25 ) @ sh ) ) )
= $false )
| ( ( ! [SY337: term] :
( ~ ( var @ SY337 )
| ( SV25 @ SY337 ) ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(248,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) )
| ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(249,plain,
! [SV29: term > $o] :
( ( ( ~ ( SV29 @ ( sK10_SY413 @ SV29 ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) )
| ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(250,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) )
| ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(251,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY355: term,SY356: term] :
( ~ ( SV31 @ SY355 )
| ~ ( SV31 @ SY356 )
| ( SV31 @ ( ap @ SY355 @ SY356 ) ) ) )
= $true )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(252,plain,
! [SV31: term > $o] :
( ( ( ! [SY355: term,SY356: term] :
( ~ ( SV31 @ SY355 )
| ~ ( SV31 @ SY356 )
| ( SV31 @ ( ap @ SY355 @ SY356 ) ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(253,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY360: term,SY361: term] :
( ~ ( SV32 @ SY360 )
| ~ ( SV32 @ SY361 )
| ( SV32 @ ( ap @ SY360 @ SY361 ) ) ) )
= $true )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(254,plain,
! [SV32: term > $o] :
( ( ( ! [SY360: term,SY361: term] :
( ~ ( SV32 @ SY360 )
| ~ ( SV32 @ SY361 )
| ( SV32 @ ( ap @ SY360 @ SY361 ) ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(255,plain,
! [SV75: term,SV33: subst > term > term] :
( ( ( ! [SY432: term] :
( ( lam @ ( SV33 @ sh @ one ) )
!= ( ap @ ( sub @ SV75 @ id ) @ SY432 ) ) )
= $true )
| ( ( ( sub @ ( SV33 @ ( sK7_SY365 @ SV33 ) @ ( sK11_SY414 @ SV33 ) ) @ ( sK15_SY418 @ SV33 ) )
= ( SV33 @ ( comp @ ( sK7_SY365 @ SV33 ) @ ( sK15_SY418 @ SV33 ) ) @ ( sub @ ( sK11_SY414 @ SV33 ) @ ( sK15_SY418 @ SV33 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(256,plain,
! [SV34: term > $o,SV66: subst,SV53: term] :
( ( ( ~ ( var @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) ) )
= $false )
| ( ( ~ ( SV34 @ SV53 )
| ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV34 @ ( sub @ SY408 @ ( push @ SV53 @ SV66 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(257,plain,
! [SV66: subst,SV53: term,SV34: term > $o] :
( ( ( SV34 @ ( sub @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) @ SV66 ) )
= $false )
| ( ( ~ ( SV34 @ SV53 )
| ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV34 @ ( sub @ SY408 @ ( push @ SV53 @ SV66 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(258,plain,
! [SV76: subst,SV72: term,SV71: subst] :
( ( ! [SY433: subst] :
( ~ ( sK1_SX0 @ SV71 @ SV72 @ ( comp @ SY433 @ SV76 ) )
| ( sK1_SX0 @ ( comp @ SV71 @ SY433 ) @ ( sub @ SV72 @ SY433 ) @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(259,plain,
! [SV77: term,SV73: subst] :
( ( ! [SY434: subst,SY435: subst] :
( ~ ( sK1_SX0 @ ( comp @ SV73 @ SY435 ) @ ( sub @ SV77 @ SY435 ) @ SY434 )
| ( sK1_SX0 @ SV73 @ SV77 @ ( comp @ SY435 @ SY434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(260,plain,
! [SV78: term] :
( ( ~ ( var @ ( sub @ SV78 @ id ) )
| ( sK1_SX0 @ id @ SV78 @ id ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(261,plain,
( ( ~ ( var @ sK17_SY402 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(262,plain,
( ( sK1_SX0 @ id @ sK17_SY402 @ id )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(263,plain,
! [SV21: subst > term > term,SV74: subst > term > term] :
( ( ( ~ ! [SY427: subst,SY428: term,SY429: subst] :
( ( sub @ ( SV74 @ SY427 @ SY428 ) @ SY429 )
= ( SV74 @ ( comp @ SY427 @ SY429 ) @ ( sub @ SY428 @ SY429 ) ) ) )
= $true )
| ( ( ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SV74 @ sh @ one ) ) )
| ! [SY430: subst,SY431: term] :
( ( SV21 @ SY430 @ SY431 )
= ( SV74 @ SY430 @ SY431 ) ) )
= $true )
| ( ( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ ( sK8_SY409 @ SV21 ) ) @ ( sK12_SY416 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) @ ( sub @ ( sK8_SY409 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(264,plain,
! [SV25: term > $o] :
( ( ( var @ ( sK14_SY336 @ SV25 ) )
= $true )
| ( ( ! [SY337: term] :
( ~ ( var @ SY337 )
| ( SV25 @ SY337 ) ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[246]) ).
thf(265,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK14_SY336 @ SV25 ) ) )
= $false )
| ( ( ! [SY337: term] :
( ~ ( var @ SY337 )
| ( SV25 @ SY337 ) ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(266,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sub @ ( sK14_SY336 @ SV25 ) @ sh ) )
= $false )
| ( ( ! [SY337: term] :
( ~ ( var @ SY337 )
| ( SV25 @ SY337 ) ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(267,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(268,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true )
| ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) )
| ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(269,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(270,plain,
! [SV31: term > $o] :
( ( ( ! [SY355: term,SY356: term] :
( ~ ( SV31 @ SY355 )
| ~ ( SV31 @ SY356 )
| ( SV31 @ ( ap @ SY355 @ SY356 ) ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(271,plain,
! [SV31: term > $o] :
( ( ( ! [SY436: term] :
( ~ ( SV31 @ ( sK18_SY355 @ SV31 ) )
| ~ ( SV31 @ SY436 )
| ( SV31 @ ( ap @ ( sK18_SY355 @ SV31 ) @ SY436 ) ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[252]) ).
thf(272,plain,
! [SV32: term > $o] :
( ( ( ! [SY360: term,SY361: term] :
( ~ ( SV32 @ SY360 )
| ~ ( SV32 @ SY361 )
| ( SV32 @ ( ap @ SY360 @ SY361 ) ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(273,plain,
! [SV32: term > $o] :
( ( ( ! [SY437: term] :
( ~ ( SV32 @ ( sK19_SY360 @ SV32 ) )
| ~ ( SV32 @ SY437 )
| ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ SY437 ) ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[254]) ).
thf(274,plain,
! [SV79: term,SV75: term,SV33: subst > term > term] :
( ( ( ( lam @ ( SV33 @ sh @ one ) )
!= ( ap @ ( sub @ SV75 @ id ) @ SV79 ) )
= $true )
| ( ( ( sub @ ( SV33 @ ( sK7_SY365 @ SV33 ) @ ( sK11_SY414 @ SV33 ) ) @ ( sK15_SY418 @ SV33 ) )
= ( SV33 @ ( comp @ ( sK7_SY365 @ SV33 ) @ ( sK15_SY418 @ SV33 ) ) @ ( sub @ ( sK11_SY414 @ SV33 ) @ ( sK15_SY418 @ SV33 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(275,plain,
! [SV34: term > $o,SV66: subst,SV53: term] :
( ( ( var @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) )
= $true )
| ( ( ~ ( SV34 @ SV53 )
| ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV34 @ ( sub @ SY408 @ ( push @ SV53 @ SV66 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(276,plain,
! [SV66: subst,SV53: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV53 ) )
= $true )
| ( ( ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV34 @ ( sub @ SY408 @ ( push @ SV53 @ SV66 ) ) ) ) )
= $true )
| ( ( SV34 @ ( sub @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(277,plain,
! [SV76: subst,SV80: subst,SV72: term,SV71: subst] :
( ( ~ ( sK1_SX0 @ SV71 @ SV72 @ ( comp @ SV80 @ SV76 ) )
| ( sK1_SX0 @ ( comp @ SV71 @ SV80 ) @ ( sub @ SV72 @ SV80 ) @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(278,plain,
! [SV81: subst,SV77: term,SV73: subst] :
( ( ! [SY438: subst] :
( ~ ( sK1_SX0 @ ( comp @ SV73 @ SY438 ) @ ( sub @ SV77 @ SY438 ) @ SV81 )
| ( sK1_SX0 @ SV73 @ SV77 @ ( comp @ SY438 @ SV81 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(279,plain,
! [SV78: term] :
( ( ( ~ ( var @ ( sub @ SV78 @ id ) ) )
= $true )
| ( ( sK1_SX0 @ id @ SV78 @ id )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(280,plain,
( ( var @ sK17_SY402 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(281,plain,
! [SV21: subst > term > term,SV74: subst > term > term] :
( ( ( ! [SY427: subst,SY428: term,SY429: subst] :
( ( sub @ ( SV74 @ SY427 @ SY428 ) @ SY429 )
= ( SV74 @ ( comp @ SY427 @ SY429 ) @ ( sub @ SY428 @ SY429 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SV74 @ sh @ one ) ) )
| ! [SY430: subst,SY431: term] :
( ( SV21 @ SY430 @ SY431 )
= ( SV74 @ SY430 @ SY431 ) ) )
= $true )
| ( ( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ ( sK8_SY409 @ SV21 ) ) @ ( sK12_SY416 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) @ ( sub @ ( sK8_SY409 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(282,plain,
! [SV25: term > $o,SV82: term] :
( ( ( ~ ( var @ SV82 )
| ( SV25 @ SV82 ) )
= $true )
| ( ( var @ ( sK14_SY336 @ SV25 ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(283,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sK14_SY336 @ SV25 ) )
= $true )
| ( ( ! [SY337: term] :
( ~ ( var @ SY337 )
| ( SV25 @ SY337 ) ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[265]) ).
thf(284,plain,
! [SV25: term > $o,SV83: term] :
( ( ( ~ ( var @ SV83 )
| ( SV25 @ SV83 ) )
= $true )
| ( ( SV25 @ ( sub @ ( sK14_SY336 @ SV25 ) @ sh ) )
= $false )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(285,plain,
! [SV29: term > $o] :
( ( ( ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) ) )
= $false )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(286,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(287,plain,
! [SV29: term > $o] :
( ( ( ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) ) )
= $false )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(288,plain,
! [SV31: term > $o] :
( ( ( ! [SY439: term] :
( ~ ( SV31 @ ( sK20_SY355 @ SV31 ) )
| ~ ( SV31 @ SY439 )
| ( SV31 @ ( ap @ ( sK20_SY355 @ SV31 ) @ SY439 ) ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[270]) ).
thf(289,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK18_SY355 @ SV31 ) )
| ~ ( SV31 @ ( sK21_SY436 @ SV31 ) )
| ( SV31 @ ( ap @ ( sK18_SY355 @ SV31 ) @ ( sK21_SY436 @ SV31 ) ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[271]) ).
thf(290,plain,
! [SV32: term > $o] :
( ( ( ! [SY440: term] :
( ~ ( SV32 @ ( sK22_SY360 @ SV32 ) )
| ~ ( SV32 @ SY440 )
| ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ SY440 ) ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[272]) ).
thf(291,plain,
! [SV32: term > $o] :
( ( ( ~ ( SV32 @ ( sK19_SY360 @ SV32 ) )
| ~ ( SV32 @ ( sK23_SY437 @ SV32 ) )
| ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[273]) ).
thf(292,plain,
! [SV79: term,SV75: term,SV33: subst > term > term] :
( ( ( ( lam @ ( SV33 @ sh @ one ) )
= ( ap @ ( sub @ SV75 @ id ) @ SV79 ) )
= $false )
| ( ( ( sub @ ( SV33 @ ( sK7_SY365 @ SV33 ) @ ( sK11_SY414 @ SV33 ) ) @ ( sK15_SY418 @ SV33 ) )
= ( SV33 @ ( comp @ ( sK7_SY365 @ SV33 ) @ ( sK15_SY418 @ SV33 ) ) @ ( sub @ ( sK11_SY414 @ SV33 ) @ ( sK15_SY418 @ SV33 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(293,plain,
! [SV66: subst,SV53: term,SV34: term > $o] :
( ( ( ~ ( SV34 @ SV53 ) )
= $true )
| ( ( ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV34 @ ( sub @ SY408 @ ( push @ SV53 @ SV66 ) ) ) ) )
= $true )
| ( ( var @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(294,plain,
! [SV66: subst,SV53: term,SV34: term > $o] :
( ( ( SV34 @ SV53 )
= $false )
| ( ( ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV34 @ ( sub @ SY408 @ ( push @ SV53 @ SV66 ) ) ) ) )
= $true )
| ( ( SV34 @ ( sub @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(295,plain,
! [SV76: subst,SV80: subst,SV72: term,SV71: subst] :
( ( ( ~ ( sK1_SX0 @ SV71 @ SV72 @ ( comp @ SV80 @ SV76 ) ) )
= $true )
| ( ( sK1_SX0 @ ( comp @ SV71 @ SV80 ) @ ( sub @ SV72 @ SV80 ) @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(296,plain,
! [SV81: subst,SV77: term,SV84: subst,SV73: subst] :
( ( ~ ( sK1_SX0 @ ( comp @ SV73 @ SV84 ) @ ( sub @ SV77 @ SV84 ) @ SV81 )
| ( sK1_SX0 @ SV73 @ SV77 @ ( comp @ SV84 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(297,plain,
! [SV78: term] :
( ( ( var @ ( sub @ SV78 @ id ) )
= $false )
| ( ( sK1_SX0 @ id @ SV78 @ id )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(298,plain,
! [SV21: subst > term > term,SV74: subst > term > term] :
( ( ( ! [SY441: term,SY442: subst] :
( ( sub @ ( SV74 @ ( sK24_SY427 @ SV21 @ SV74 ) @ SY441 ) @ SY442 )
= ( SV74 @ ( comp @ ( sK24_SY427 @ SV21 @ SV74 ) @ SY442 ) @ ( sub @ SY441 @ SY442 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SV74 @ sh @ one ) ) )
| ! [SY430: subst,SY431: term] :
( ( SV21 @ SY430 @ SY431 )
= ( SV74 @ SY430 @ SY431 ) ) )
= $true )
| ( ( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ ( sK8_SY409 @ SV21 ) ) @ ( sK12_SY416 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) @ ( sub @ ( sK8_SY409 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[281]) ).
thf(299,plain,
! [SV25: term > $o,SV82: term] :
( ( ( ~ ( var @ SV82 ) )
= $true )
| ( ( SV25 @ SV82 )
= $true )
| ( ( var @ ( sK14_SY336 @ SV25 ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(300,plain,
! [SV25: term > $o,SV85: term] :
( ( ( ~ ( var @ SV85 )
| ( SV25 @ SV85 ) )
= $true )
| ( ( SV25 @ ( sK14_SY336 @ SV25 ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(301,plain,
! [SV25: term > $o,SV83: term] :
( ( ( ~ ( var @ SV83 ) )
= $true )
| ( ( SV25 @ SV83 )
= $true )
| ( ( SV25 @ ( sub @ ( sK14_SY336 @ SV25 ) @ sh ) )
= $false )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(302,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY443: term] :
( ~ ( SV29 @ SY443 )
| ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SY443 @ id ) ) ) )
| ( SV29 @ ( lam @ ( sK25_SY346 @ SV29 ) ) ) )
= $false )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[285]) ).
thf(303,plain,
! [SV29: term > $o] :
( ( ( ! [SY346: term] :
( ~ ! [SY347: term] :
( ~ ( SV29 @ SY347 )
| ( SV29 @ ( sub @ SY346 @ ( push @ SY347 @ id ) ) ) )
| ( SV29 @ ( lam @ SY346 ) ) ) )
= $false )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[286]) ).
thf(304,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY444: term] :
( ~ ( SV29 @ SY444 )
| ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SY444 @ id ) ) ) )
| ( SV29 @ ( lam @ ( sK26_SY346 @ SV29 ) ) ) )
= $false )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[287]) ).
thf(305,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK20_SY355 @ SV31 ) )
| ~ ( SV31 @ ( sK27_SY439 @ SV31 ) )
| ( SV31 @ ( ap @ ( sK20_SY355 @ SV31 ) @ ( sK27_SY439 @ SV31 ) ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[288]) ).
thf(306,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK18_SY355 @ SV31 ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(307,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK21_SY436 @ SV31 ) )
| ( SV31 @ ( ap @ ( sK18_SY355 @ SV31 ) @ ( sK21_SY436 @ SV31 ) ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[289]) ).
thf(308,plain,
! [SV32: term > $o] :
( ( ( ~ ( SV32 @ ( sK22_SY360 @ SV32 ) )
| ~ ( SV32 @ ( sK28_SY440 @ SV32 ) )
| ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[290]) ).
thf(309,plain,
! [SV32: term > $o] :
( ( ( ~ ( SV32 @ ( sK19_SY360 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(310,plain,
! [SV32: term > $o] :
( ( ( ~ ( SV32 @ ( sK23_SY437 @ SV32 ) )
| ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(311,plain,
! [SV66: subst,SV53: term,SV34: term > $o] :
( ( ( SV34 @ SV53 )
= $false )
| ( ( ! [SY408: term] :
( ~ ( var @ SY408 )
| ( SV34 @ ( sub @ SY408 @ ( push @ SV53 @ SV66 ) ) ) ) )
= $true )
| ( ( var @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(312,plain,
! [SV66: subst,SV53: term,SV34: term > $o,SV86: term] :
( ( ( ~ ( var @ SV86 )
| ( SV34 @ ( sub @ SV86 @ ( push @ SV53 @ SV66 ) ) ) )
= $true )
| ( ( SV34 @ SV53 )
= $false )
| ( ( SV34 @ ( sub @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) @ SV66 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(313,plain,
! [SV76: subst,SV80: subst,SV72: term,SV71: subst] :
( ( ( sK1_SX0 @ SV71 @ SV72 @ ( comp @ SV80 @ SV76 ) )
= $false )
| ( ( sK1_SX0 @ ( comp @ SV71 @ SV80 ) @ ( sub @ SV72 @ SV80 ) @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(314,plain,
! [SV81: subst,SV77: term,SV84: subst,SV73: subst] :
( ( ( ~ ( sK1_SX0 @ ( comp @ SV73 @ SV84 ) @ ( sub @ SV77 @ SV84 ) @ SV81 ) )
= $true )
| ( ( sK1_SX0 @ SV73 @ SV77 @ ( comp @ SV84 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(315,plain,
! [SV21: subst > term > term,SV74: subst > term > term] :
( ( ( ! [SY445: subst] :
( ( sub @ ( SV74 @ ( sK24_SY427 @ SV21 @ SV74 ) @ ( sK29_SY441 @ SV21 @ SV74 ) ) @ SY445 )
= ( SV74 @ ( comp @ ( sK24_SY427 @ SV21 @ SV74 ) @ SY445 ) @ ( sub @ ( sK29_SY441 @ SV21 @ SV74 ) @ SY445 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SV74 @ sh @ one ) ) )
| ! [SY430: subst,SY431: term] :
( ( SV21 @ SY430 @ SY431 )
= ( SV74 @ SY430 @ SY431 ) ) )
= $true )
| ( ( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ ( sK8_SY409 @ SV21 ) ) @ ( sK12_SY416 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) @ ( sub @ ( sK8_SY409 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[298]) ).
thf(316,plain,
! [SV25: term > $o,SV82: term] :
( ( ( var @ SV82 )
= $false )
| ( ( SV25 @ SV82 )
= $true )
| ( ( var @ ( sK14_SY336 @ SV25 ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(317,plain,
! [SV25: term > $o,SV85: term] :
( ( ( ~ ( var @ SV85 ) )
= $true )
| ( ( SV25 @ SV85 )
= $true )
| ( ( SV25 @ ( sK14_SY336 @ SV25 ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(318,plain,
! [SV25: term > $o,SV83: term] :
( ( ( var @ SV83 )
= $false )
| ( ( SV25 @ SV83 )
= $true )
| ( ( SV25 @ ( sub @ ( sK14_SY336 @ SV25 ) @ sh ) )
= $false )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(319,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY443: term] :
( ~ ( SV29 @ SY443 )
| ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SY443 @ id ) ) ) ) )
= $false )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(320,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( lam @ ( sK25_SY346 @ SV29 ) ) )
= $false )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[302]) ).
thf(321,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY446: term] :
( ~ ( SV29 @ SY446 )
| ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SY446 @ id ) ) ) )
| ( SV29 @ ( lam @ ( sK30_SY346 @ SV29 ) ) ) )
= $false )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[303]) ).
thf(322,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY444: term] :
( ~ ( SV29 @ SY444 )
| ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SY444 @ id ) ) ) ) )
= $false )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(323,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( lam @ ( sK26_SY346 @ SV29 ) ) )
= $false )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(324,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK20_SY355 @ SV31 ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(325,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK27_SY439 @ SV31 ) )
| ( SV31 @ ( ap @ ( sK20_SY355 @ SV31 ) @ ( sK27_SY439 @ SV31 ) ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(326,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK18_SY355 @ SV31 ) )
= $true )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(327,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK21_SY436 @ SV31 ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(328,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( ap @ ( sK18_SY355 @ SV31 ) @ ( sK21_SY436 @ SV31 ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(329,plain,
! [SV32: term > $o] :
( ( ( ~ ( SV32 @ ( sK22_SY360 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(330,plain,
! [SV32: term > $o] :
( ( ( ~ ( SV32 @ ( sK28_SY440 @ SV32 ) )
| ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(331,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( sK19_SY360 @ SV32 ) )
= $true )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(332,plain,
! [SV32: term > $o] :
( ( ( ~ ( SV32 @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(333,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(334,plain,
! [SV66: subst,SV53: term,SV34: term > $o,SV87: term] :
( ( ( ~ ( var @ SV87 )
| ( SV34 @ ( sub @ SV87 @ ( push @ SV53 @ SV66 ) ) ) )
= $true )
| ( ( SV34 @ SV53 )
= $false )
| ( ( var @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(335,plain,
! [SV66: subst,SV53: term,SV34: term > $o,SV86: term] :
( ( ( ~ ( var @ SV86 ) )
= $true )
| ( ( SV34 @ ( sub @ SV86 @ ( push @ SV53 @ SV66 ) ) )
= $true )
| ( ( SV34 @ SV53 )
= $false )
| ( ( SV34 @ ( sub @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(336,plain,
! [SV81: subst,SV77: term,SV84: subst,SV73: subst] :
( ( ( sK1_SX0 @ ( comp @ SV73 @ SV84 ) @ ( sub @ SV77 @ SV84 ) @ SV81 )
= $false )
| ( ( sK1_SX0 @ SV73 @ SV77 @ ( comp @ SV84 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(337,plain,
! [SV21: subst > term > term,SV74: subst > term > term] :
( ( ( ( sub @ ( SV74 @ ( sK24_SY427 @ SV21 @ SV74 ) @ ( sK29_SY441 @ SV21 @ SV74 ) ) @ ( sK31_SY445 @ SV21 @ SV74 ) )
= ( SV74 @ ( comp @ ( sK24_SY427 @ SV21 @ SV74 ) @ ( sK31_SY445 @ SV21 @ SV74 ) ) @ ( sub @ ( sK29_SY441 @ SV21 @ SV74 ) @ ( sK31_SY445 @ SV21 @ SV74 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SV74 @ sh @ one ) ) )
| ! [SY430: subst,SY431: term] :
( ( SV21 @ SY430 @ SY431 )
= ( SV74 @ SY430 @ SY431 ) ) )
= $true )
| ( ( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ ( sK8_SY409 @ SV21 ) ) @ ( sK12_SY416 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) @ ( sub @ ( sK8_SY409 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[315]) ).
thf(338,plain,
! [SV25: term > $o,SV85: term] :
( ( ( var @ SV85 )
= $false )
| ( ( SV25 @ SV85 )
= $true )
| ( ( SV25 @ ( sK14_SY336 @ SV25 ) )
= $true )
| ( ( SV25 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(339,plain,
! [SV29: term > $o] :
( ( ( ! [SY443: term] :
( ~ ( SV29 @ SY443 )
| ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SY443 @ id ) ) ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[319]) ).
thf(340,plain,
! [SV88: term,SV29: term > $o] :
( ( ( ! [SY447: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY447 ) ) )
| ( SV29 @ ( sub @ SV88 @ SY447 ) ) ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK25_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(341,plain,
! [SV29: term > $o] :
( ( ( ~ ! [SY446: term] :
( ~ ( SV29 @ SY446 )
| ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SY446 @ id ) ) ) ) )
= $false )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(342,plain,
! [SV29: term > $o] :
( ( ( SV29 @ ( lam @ ( sK30_SY346 @ SV29 ) ) )
= $false )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[321]) ).
thf(343,plain,
! [SV29: term > $o] :
( ( ( ! [SY444: term] :
( ~ ( SV29 @ SY444 )
| ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SY444 @ id ) ) ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[322]) ).
thf(344,plain,
! [SV89: term,SV29: term > $o] :
( ( ( ! [SY449: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY449 ) ) )
| ( SV29 @ ( sub @ SV89 @ SY449 ) ) ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK26_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(345,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK20_SY355 @ SV31 ) )
= $true )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(346,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK27_SY439 @ SV31 ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(347,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( ap @ ( sK20_SY355 @ SV31 ) @ ( sK27_SY439 @ SV31 ) ) )
= $false )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(348,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) ) )
= $true )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK18_SY355 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(349,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK21_SY436 @ SV31 ) )
= $true )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[327]) ).
thf(350,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) ) )
= $true )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK18_SY355 @ SV31 ) @ ( sK21_SY436 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(351,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( sK22_SY360 @ SV32 ) )
= $true )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(352,plain,
! [SV32: term > $o] :
( ( ( ~ ( SV32 @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(353,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(354,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK19_SY360 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(355,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( sK23_SY437 @ SV32 ) )
= $true )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(356,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(357,plain,
! [SV66: subst,SV53: term,SV34: term > $o,SV87: term] :
( ( ( ~ ( var @ SV87 ) )
= $true )
| ( ( SV34 @ ( sub @ SV87 @ ( push @ SV53 @ SV66 ) ) )
= $true )
| ( ( SV34 @ SV53 )
= $false )
| ( ( var @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(358,plain,
! [SV66: subst,SV53: term,SV34: term > $o,SV86: term] :
( ( ( var @ SV86 )
= $false )
| ( ( SV34 @ ( sub @ SV86 @ ( push @ SV53 @ SV66 ) ) )
= $true )
| ( ( SV34 @ SV53 )
= $false )
| ( ( SV34 @ ( sub @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(359,plain,
! [SV74: subst > term > term,SV21: subst > term > term] :
( ( ( ( lam @ ( SV21 @ sh @ one ) )
!= ( lam @ ( SV74 @ sh @ one ) ) )
= $true )
| ( ( ! [SY430: subst,SY431: term] :
( ( SV21 @ SY430 @ SY431 )
= ( SV74 @ SY430 @ SY431 ) ) )
= $true )
| ( ( ( sub @ ( SV74 @ ( sK24_SY427 @ SV21 @ SV74 ) @ ( sK29_SY441 @ SV21 @ SV74 ) ) @ ( sK31_SY445 @ SV21 @ SV74 ) )
= ( SV74 @ ( comp @ ( sK24_SY427 @ SV21 @ SV74 ) @ ( sK31_SY445 @ SV21 @ SV74 ) ) @ ( sub @ ( sK29_SY441 @ SV21 @ SV74 ) @ ( sK31_SY445 @ SV21 @ SV74 ) ) ) )
= $false )
| ( ( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ ( sK8_SY409 @ SV21 ) ) @ ( sK12_SY416 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) @ ( sub @ ( sK8_SY409 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(360,plain,
! [SV90: term,SV29: term > $o] :
( ( ( ~ ( SV29 @ SV90 )
| ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SV90 @ id ) ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(361,plain,
! [SV88: term,SV91: subst,SV29: term > $o] :
( ( ( ~ ! [SY451: term] :
( ~ ( var @ SY451 )
| ( SV29 @ ( sub @ SY451 @ SV91 ) ) )
| ( SV29 @ ( sub @ SV88 @ SV91 ) ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK25_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(362,plain,
! [SV29: term > $o] :
( ( ( ! [SY446: term] :
( ~ ( SV29 @ SY446 )
| ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SY446 @ id ) ) ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(363,plain,
! [SV92: term,SV29: term > $o] :
( ( ( ! [SY452: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY452 ) ) )
| ( SV29 @ ( sub @ SV92 @ SY452 ) ) ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK30_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(364,plain,
! [SV93: term,SV29: term > $o] :
( ( ( ~ ( SV29 @ SV93 )
| ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SV93 @ id ) ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(365,plain,
! [SV89: term,SV94: subst,SV29: term > $o] :
( ( ( ~ ! [SY454: term] :
( ~ ( var @ SY454 )
| ( SV29 @ ( sub @ SY454 @ SV94 ) ) )
| ( SV29 @ ( sub @ SV89 @ SV94 ) ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK26_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(366,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) ) )
= $true )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK20_SY355 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(367,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK27_SY439 @ SV31 ) )
= $true )
| ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) )
| ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(368,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) ) )
= $true )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK20_SY355 @ SV31 ) @ ( sK27_SY439 @ SV31 ) ) )
= $false )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(369,plain,
! [SV31: term > $o] :
( ( ( ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK18_SY355 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(370,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) ) )
= $true )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK21_SY436 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(371,plain,
! [SV31: term > $o] :
( ( ( ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK18_SY355 @ SV31 ) @ ( sK21_SY436 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(372,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK22_SY360 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(373,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( sK28_SY440 @ SV32 ) )
= $true )
| ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) )
| ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[352]) ).
thf(374,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(375,plain,
! [SV32: term > $o] :
( ( ( ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK19_SY360 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(376,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK23_SY437 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[355]) ).
thf(377,plain,
! [SV32: term > $o] :
( ( ( ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(378,plain,
! [SV66: subst,SV53: term,SV34: term > $o,SV87: term] :
( ( ( var @ SV87 )
= $false )
| ( ( SV34 @ ( sub @ SV87 @ ( push @ SV53 @ SV66 ) ) )
= $true )
| ( ( SV34 @ SV53 )
= $false )
| ( ( var @ ( sK16_SY407 @ SV53 @ SV66 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(379,plain,
! [SV74: subst > term > term,SV21: subst > term > term] :
( ( ( ( lam @ ( SV21 @ sh @ one ) )
= ( lam @ ( SV74 @ sh @ one ) ) )
= $false )
| ( ( ! [SY430: subst,SY431: term] :
( ( SV21 @ SY430 @ SY431 )
= ( SV74 @ SY430 @ SY431 ) ) )
= $true )
| ( ( ( sub @ ( SV74 @ ( sK24_SY427 @ SV21 @ SV74 ) @ ( sK29_SY441 @ SV21 @ SV74 ) ) @ ( sK31_SY445 @ SV21 @ SV74 ) )
= ( SV74 @ ( comp @ ( sK24_SY427 @ SV21 @ SV74 ) @ ( sK31_SY445 @ SV21 @ SV74 ) ) @ ( sub @ ( sK29_SY441 @ SV21 @ SV74 ) @ ( sK31_SY445 @ SV21 @ SV74 ) ) ) )
= $false )
| ( ( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ ( sK8_SY409 @ SV21 ) ) @ ( sK12_SY416 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) @ ( sub @ ( sK8_SY409 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(380,plain,
! [SV90: term,SV29: term > $o] :
( ( ( ~ ( SV29 @ SV90 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SV90 @ id ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[360]) ).
thf(381,plain,
! [SV88: term,SV91: subst,SV29: term > $o] :
( ( ( ~ ! [SY451: term] :
( ~ ( var @ SY451 )
| ( SV29 @ ( sub @ SY451 @ SV91 ) ) ) )
= $true )
| ( ( SV29 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK25_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(382,plain,
! [SV95: term,SV29: term > $o] :
( ( ( ~ ( SV29 @ SV95 )
| ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SV95 @ id ) ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(383,plain,
! [SV92: term,SV96: subst,SV29: term > $o] :
( ( ( ~ ! [SY455: term] :
( ~ ( var @ SY455 )
| ( SV29 @ ( sub @ SY455 @ SV96 ) ) )
| ( SV29 @ ( sub @ SV92 @ SV96 ) ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK30_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(384,plain,
! [SV93: term,SV29: term > $o] :
( ( ( ~ ( SV29 @ SV93 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SV93 @ id ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(385,plain,
! [SV89: term,SV94: subst,SV29: term > $o] :
( ( ( ~ ! [SY454: term] :
( ~ ( var @ SY454 )
| ( SV29 @ ( sub @ SY454 @ SV94 ) ) ) )
= $true )
| ( ( SV29 @ ( sub @ SV89 @ SV94 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK26_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(386,plain,
! [SV31: term > $o] :
( ( ( ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK20_SY355 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(387,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) ) )
= $true )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK27_SY439 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(388,plain,
! [SV31: term > $o] :
( ( ( ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK20_SY355 @ SV31 ) @ ( sK27_SY439 @ SV31 ) ) )
= $false )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(389,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK32_SY357 @ SV31 ) )
| ( SV31 @ ( lam @ ( sK32_SY357 @ SV31 ) ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK18_SY355 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[369]) ).
thf(390,plain,
! [SV31: term > $o] :
( ( ( ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK21_SY436 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(391,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK33_SY357 @ SV31 ) )
| ( SV31 @ ( lam @ ( sK33_SY357 @ SV31 ) ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK18_SY355 @ SV31 ) @ ( sK21_SY436 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[371]) ).
thf(392,plain,
! [SV32: term > $o] :
( ( ( ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK22_SY360 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(393,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK28_SY440 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(394,plain,
! [SV32: term > $o] :
( ( ( ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(395,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY456: term] :
( ~ ( SV32 @ SY456 )
| ( SV32 @ ( sub @ ( sK34_SY362 @ SV32 ) @ ( push @ SY456 @ id ) ) ) )
| ( SV32 @ ( lam @ ( sK34_SY362 @ SV32 ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK19_SY360 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[375]) ).
thf(396,plain,
! [SV32: term > $o] :
( ( ( ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK23_SY437 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(397,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY457: term] :
( ~ ( SV32 @ SY457 )
| ( SV32 @ ( sub @ ( sK35_SY362 @ SV32 ) @ ( push @ SY457 @ id ) ) ) )
| ( SV32 @ ( lam @ ( sK35_SY362 @ SV32 ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[377]) ).
thf(398,plain,
! [SV74: subst > term > term,SV97: subst,SV21: subst > term > term] :
( ( ( ! [SY458: term] :
( ( SV21 @ SV97 @ SY458 )
= ( SV74 @ SV97 @ SY458 ) ) )
= $true )
| ( ( ( lam @ ( SV21 @ sh @ one ) )
= ( lam @ ( SV74 @ sh @ one ) ) )
= $false )
| ( ( ( sub @ ( SV74 @ ( sK24_SY427 @ SV21 @ SV74 ) @ ( sK29_SY441 @ SV21 @ SV74 ) ) @ ( sK31_SY445 @ SV21 @ SV74 ) )
= ( SV74 @ ( comp @ ( sK24_SY427 @ SV21 @ SV74 ) @ ( sK31_SY445 @ SV21 @ SV74 ) ) @ ( sub @ ( sK29_SY441 @ SV21 @ SV74 ) @ ( sK31_SY445 @ SV21 @ SV74 ) ) ) )
= $false )
| ( ( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ ( sK8_SY409 @ SV21 ) ) @ ( sK12_SY416 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) @ ( sub @ ( sK8_SY409 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(399,plain,
! [SV90: term,SV29: term > $o] :
( ( ( SV29 @ SV90 )
= $false )
| ( ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SV90 @ id ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(400,plain,
! [SV88: term,SV91: subst,SV29: term > $o] :
( ( ( ! [SY451: term] :
( ~ ( var @ SY451 )
| ( SV29 @ ( sub @ SY451 @ SV91 ) ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK25_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(401,plain,
! [SV95: term,SV29: term > $o] :
( ( ( ~ ( SV29 @ SV95 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(402,plain,
! [SV92: term,SV96: subst,SV29: term > $o] :
( ( ( ~ ! [SY455: term] :
( ~ ( var @ SY455 )
| ( SV29 @ ( sub @ SY455 @ SV96 ) ) ) )
= $true )
| ( ( SV29 @ ( sub @ SV92 @ SV96 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK30_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(403,plain,
! [SV93: term,SV29: term > $o] :
( ( ( SV29 @ SV93 )
= $false )
| ( ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SV93 @ id ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(404,plain,
! [SV89: term,SV94: subst,SV29: term > $o] :
( ( ( ! [SY454: term] :
( ~ ( var @ SY454 )
| ( SV29 @ ( sub @ SY454 @ SV94 ) ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV89 @ SV94 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK26_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(405,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK36_SY357 @ SV31 ) )
| ( SV31 @ ( lam @ ( sK36_SY357 @ SV31 ) ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK20_SY355 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[386]) ).
thf(406,plain,
! [SV31: term > $o] :
( ( ( ! [SY357: term] :
( ~ ( SV31 @ SY357 )
| ( SV31 @ ( lam @ SY357 ) ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK27_SY439 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(407,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK37_SY357 @ SV31 ) )
| ( SV31 @ ( lam @ ( sK37_SY357 @ SV31 ) ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK20_SY355 @ SV31 ) @ ( sK27_SY439 @ SV31 ) ) )
= $false )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[388]) ).
thf(408,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK32_SY357 @ SV31 ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK18_SY355 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(409,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( lam @ ( sK32_SY357 @ SV31 ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK18_SY355 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(410,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK38_SY357 @ SV31 ) )
| ( SV31 @ ( lam @ ( sK38_SY357 @ SV31 ) ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK21_SY436 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[390]) ).
thf(411,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK33_SY357 @ SV31 ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK18_SY355 @ SV31 ) @ ( sK21_SY436 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[391]) ).
thf(412,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( lam @ ( sK33_SY357 @ SV31 ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK18_SY355 @ SV31 ) @ ( sK21_SY436 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[391]) ).
thf(413,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY459: term] :
( ~ ( SV32 @ SY459 )
| ( SV32 @ ( sub @ ( sK39_SY362 @ SV32 ) @ ( push @ SY459 @ id ) ) ) )
| ( SV32 @ ( lam @ ( sK39_SY362 @ SV32 ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK22_SY360 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[392]) ).
thf(414,plain,
! [SV32: term > $o] :
( ( ( ! [SY362: term] :
( ~ ! [SY363: term] :
( ~ ( SV32 @ SY363 )
| ( SV32 @ ( sub @ SY362 @ ( push @ SY363 @ id ) ) ) )
| ( SV32 @ ( lam @ SY362 ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK28_SY440 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[393]) ).
thf(415,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY460: term] :
( ~ ( SV32 @ SY460 )
| ( SV32 @ ( sub @ ( sK40_SY362 @ SV32 ) @ ( push @ SY460 @ id ) ) ) )
| ( SV32 @ ( lam @ ( sK40_SY362 @ SV32 ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[394]) ).
thf(416,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY456: term] :
( ~ ( SV32 @ SY456 )
| ( SV32 @ ( sub @ ( sK34_SY362 @ SV32 ) @ ( push @ SY456 @ id ) ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK19_SY360 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(417,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( lam @ ( sK34_SY362 @ SV32 ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK19_SY360 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(418,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY461: term] :
( ~ ( SV32 @ SY461 )
| ( SV32 @ ( sub @ ( sK41_SY362 @ SV32 ) @ ( push @ SY461 @ id ) ) ) )
| ( SV32 @ ( lam @ ( sK41_SY362 @ SV32 ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK23_SY437 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[396]) ).
thf(419,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY457: term] :
( ~ ( SV32 @ SY457 )
| ( SV32 @ ( sub @ ( sK35_SY362 @ SV32 ) @ ( push @ SY457 @ id ) ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(420,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( lam @ ( sK35_SY362 @ SV32 ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(421,plain,
! [SV74: subst > term > term,SV98: term,SV97: subst,SV21: subst > term > term] :
( ( ( ( SV21 @ SV97 @ SV98 )
= ( SV74 @ SV97 @ SV98 ) )
= $true )
| ( ( ( lam @ ( SV21 @ sh @ one ) )
= ( lam @ ( SV74 @ sh @ one ) ) )
= $false )
| ( ( ( sub @ ( SV74 @ ( sK24_SY427 @ SV21 @ SV74 ) @ ( sK29_SY441 @ SV21 @ SV74 ) ) @ ( sK31_SY445 @ SV21 @ SV74 ) )
= ( SV74 @ ( comp @ ( sK24_SY427 @ SV21 @ SV74 ) @ ( sK31_SY445 @ SV21 @ SV74 ) ) @ ( sub @ ( sK29_SY441 @ SV21 @ SV74 ) @ ( sK31_SY445 @ SV21 @ SV74 ) ) ) )
= $false )
| ( ( ( sub @ ( SV21 @ ( sK2_SY318 @ SV21 ) @ ( sK8_SY409 @ SV21 ) ) @ ( sK12_SY416 @ SV21 ) )
= ( SV21 @ ( comp @ ( sK2_SY318 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) @ ( sub @ ( sK8_SY409 @ SV21 ) @ ( sK12_SY416 @ SV21 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(422,plain,
! [SV90: term,SV99: term,SV29: term > $o] :
( ( ( ! [SY462: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY462 ) ) )
| ( SV29 @ ( sub @ SV99 @ SY462 ) ) ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SV90 @ id ) ) )
= $true )
| ( ( SV29 @ SV90 )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(423,plain,
! [SV29: term > $o,SV91: subst,SV88: term] :
( ( ( ~ ( var @ ( sK42_SY451 @ SV88 @ SV91 @ SV29 ) )
| ( SV29 @ ( sub @ ( sK42_SY451 @ SV88 @ SV91 @ SV29 ) @ SV91 ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK25_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[400]) ).
thf(424,plain,
! [SV95: term,SV29: term > $o] :
( ( ( SV29 @ SV95 )
= $false )
| ( ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( ! [SY348: term,SY349: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY349 ) ) )
| ( SV29 @ ( sub @ SY348 @ SY349 ) ) ) )
= $true )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(425,plain,
! [SV92: term,SV96: subst,SV29: term > $o] :
( ( ( ! [SY455: term] :
( ~ ( var @ SY455 )
| ( SV29 @ ( sub @ SY455 @ SV96 ) ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV92 @ SV96 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK30_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(426,plain,
! [SV93: term,SV100: term,SV29: term > $o] :
( ( ( ! [SY464: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY464 ) ) )
| ( SV29 @ ( sub @ SV100 @ SY464 ) ) ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SV93 @ id ) ) )
= $true )
| ( ( SV29 @ SV93 )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(427,plain,
! [SV29: term > $o,SV94: subst,SV89: term] :
( ( ( ~ ( var @ ( sK43_SY454 @ SV89 @ SV94 @ SV29 ) )
| ( SV29 @ ( sub @ ( sK43_SY454 @ SV89 @ SV94 @ SV29 ) @ SV94 ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV89 @ SV94 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK26_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[404]) ).
thf(428,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK36_SY357 @ SV31 ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK20_SY355 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(429,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( lam @ ( sK36_SY357 @ SV31 ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK20_SY355 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(430,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK44_SY357 @ SV31 ) )
| ( SV31 @ ( lam @ ( sK44_SY357 @ SV31 ) ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK27_SY439 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[406]) ).
thf(431,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK37_SY357 @ SV31 ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK20_SY355 @ SV31 ) @ ( sK27_SY439 @ SV31 ) ) )
= $false )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(432,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( lam @ ( sK37_SY357 @ SV31 ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK20_SY355 @ SV31 ) @ ( sK27_SY439 @ SV31 ) ) )
= $false )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(433,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK32_SY357 @ SV31 ) )
= $true )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK18_SY355 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(434,plain,
! [SV101: term,SV31: term > $o] :
( ( ( SV31 @ SV101 )
= $true )
| ( ( SV31 @ ( lam @ ( sK32_SY357 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK18_SY355 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(435,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK38_SY357 @ SV31 ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK21_SY436 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(436,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( lam @ ( sK38_SY357 @ SV31 ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK21_SY436 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(437,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK33_SY357 @ SV31 ) )
= $true )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK18_SY355 @ SV31 ) @ ( sK21_SY436 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[411]) ).
thf(438,plain,
! [SV102: term,SV31: term > $o] :
( ( ( SV31 @ SV102 )
= $true )
| ( ( SV31 @ ( lam @ ( sK33_SY357 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( ap @ ( sK18_SY355 @ SV31 ) @ ( sK21_SY436 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(439,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY459: term] :
( ~ ( SV32 @ SY459 )
| ( SV32 @ ( sub @ ( sK39_SY362 @ SV32 ) @ ( push @ SY459 @ id ) ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK22_SY360 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(440,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( lam @ ( sK39_SY362 @ SV32 ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK22_SY360 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(441,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY466: term] :
( ~ ( SV32 @ SY466 )
| ( SV32 @ ( sub @ ( sK45_SY362 @ SV32 ) @ ( push @ SY466 @ id ) ) ) )
| ( SV32 @ ( lam @ ( sK45_SY362 @ SV32 ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK28_SY440 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[414]) ).
thf(442,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY460: term] :
( ~ ( SV32 @ SY460 )
| ( SV32 @ ( sub @ ( sK40_SY362 @ SV32 ) @ ( push @ SY460 @ id ) ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(443,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( lam @ ( sK40_SY362 @ SV32 ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(444,plain,
! [SV32: term > $o] :
( ( ( ! [SY456: term] :
( ~ ( SV32 @ SY456 )
| ( SV32 @ ( sub @ ( sK34_SY362 @ SV32 ) @ ( push @ SY456 @ id ) ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK19_SY360 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(445,plain,
! [SV103: term,SV32: term > $o] :
( ( ( SV32 @ SV103 )
= $true )
| ( ( SV32 @ ( lam @ ( sK34_SY362 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK19_SY360 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(446,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY461: term] :
( ~ ( SV32 @ SY461 )
| ( SV32 @ ( sub @ ( sK41_SY362 @ SV32 ) @ ( push @ SY461 @ id ) ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK23_SY437 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(447,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( lam @ ( sK41_SY362 @ SV32 ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK23_SY437 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(448,plain,
! [SV32: term > $o] :
( ( ( ! [SY457: term] :
( ~ ( SV32 @ SY457 )
| ( SV32 @ ( sub @ ( sK35_SY362 @ SV32 ) @ ( push @ SY457 @ id ) ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[419]) ).
thf(449,plain,
! [SV104: term,SV32: term > $o] :
( ( ( SV32 @ SV104 )
= $true )
| ( ( SV32 @ ( lam @ ( sK35_SY362 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(450,plain,
! [SV90: term,SV99: term,SV105: subst,SV29: term > $o] :
( ( ( ~ ! [SY467: term] :
( ~ ( var @ SY467 )
| ( SV29 @ ( sub @ SY467 @ SV105 ) ) )
| ( SV29 @ ( sub @ SV99 @ SV105 ) ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SV90 @ id ) ) )
= $true )
| ( ( SV29 @ SV90 )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(451,plain,
! [SV29: term > $o,SV91: subst,SV88: term] :
( ( ( ~ ( var @ ( sK42_SY451 @ SV88 @ SV91 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK25_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(452,plain,
! [SV91: subst,SV88: term,SV29: term > $o] :
( ( ( SV29 @ ( sub @ ( sK42_SY451 @ SV88 @ SV91 @ SV29 ) @ SV91 ) )
= $false )
| ( ( SV29 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK25_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(453,plain,
! [SV95: term,SV106: term,SV29: term > $o] :
( ( ( ! [SY468: subst] :
( ~ ! [SY350: term] :
( ~ ( var @ SY350 )
| ( SV29 @ ( sub @ SY350 @ SY468 ) ) )
| ( SV29 @ ( sub @ SV106 @ SY468 ) ) ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( SV29 @ SV95 )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(454,plain,
! [SV29: term > $o,SV96: subst,SV92: term] :
( ( ( ~ ( var @ ( sK46_SY455 @ SV92 @ SV96 @ SV29 ) )
| ( SV29 @ ( sub @ ( sK46_SY455 @ SV92 @ SV96 @ SV29 ) @ SV96 ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV92 @ SV96 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK30_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[425]) ).
thf(455,plain,
! [SV93: term,SV100: term,SV107: subst,SV29: term > $o] :
( ( ( ~ ! [SY470: term] :
( ~ ( var @ SY470 )
| ( SV29 @ ( sub @ SY470 @ SV107 ) ) )
| ( SV29 @ ( sub @ SV100 @ SV107 ) ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SV93 @ id ) ) )
= $true )
| ( ( SV29 @ SV93 )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(456,plain,
! [SV29: term > $o,SV94: subst,SV89: term] :
( ( ( ~ ( var @ ( sK43_SY454 @ SV89 @ SV94 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV89 @ SV94 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK26_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(457,plain,
! [SV94: subst,SV89: term,SV29: term > $o] :
( ( ( SV29 @ ( sub @ ( sK43_SY454 @ SV89 @ SV94 @ SV29 ) @ SV94 ) )
= $false )
| ( ( SV29 @ ( sub @ SV89 @ SV94 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK26_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(458,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK36_SY357 @ SV31 ) )
= $true )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK20_SY355 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[428]) ).
thf(459,plain,
! [SV108: term,SV31: term > $o] :
( ( ( SV31 @ SV108 )
= $true )
| ( ( SV31 @ ( lam @ ( sK36_SY357 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK20_SY355 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(460,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK44_SY357 @ SV31 ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK27_SY439 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(461,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( lam @ ( sK44_SY357 @ SV31 ) ) )
= $false )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK27_SY439 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(462,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK37_SY357 @ SV31 ) )
= $true )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK20_SY355 @ SV31 ) @ ( sK27_SY439 @ SV31 ) ) )
= $false )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(463,plain,
! [SV109: term,SV31: term > $o] :
( ( ( SV31 @ SV109 )
= $true )
| ( ( SV31 @ ( lam @ ( sK37_SY357 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( ap @ ( sK20_SY355 @ SV31 ) @ ( sK27_SY439 @ SV31 ) ) )
= $false )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(464,plain,
! [SV110: term,SV31: term > $o] :
( ( ( SV31 @ SV110 )
= $true )
| ( ( SV31 @ ( sK32_SY357 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK18_SY355 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(465,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK38_SY357 @ SV31 ) )
= $true )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK21_SY436 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[435]) ).
thf(466,plain,
! [SV111: term,SV31: term > $o] :
( ( ( SV31 @ SV111 )
= $true )
| ( ( SV31 @ ( lam @ ( sK38_SY357 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK21_SY436 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(467,plain,
! [SV112: term,SV31: term > $o] :
( ( ( SV31 @ SV112 )
= $true )
| ( ( SV31 @ ( sK33_SY357 @ SV31 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK18_SY355 @ SV31 ) @ ( sK21_SY436 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(468,plain,
! [SV32: term > $o] :
( ( ( ! [SY459: term] :
( ~ ( SV32 @ SY459 )
| ( SV32 @ ( sub @ ( sK39_SY362 @ SV32 ) @ ( push @ SY459 @ id ) ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK22_SY360 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(469,plain,
! [SV113: term,SV32: term > $o] :
( ( ( SV32 @ SV113 )
= $true )
| ( ( SV32 @ ( lam @ ( sK39_SY362 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK22_SY360 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(470,plain,
! [SV32: term > $o] :
( ( ( ~ ! [SY466: term] :
( ~ ( SV32 @ SY466 )
| ( SV32 @ ( sub @ ( sK45_SY362 @ SV32 ) @ ( push @ SY466 @ id ) ) ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK28_SY440 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(471,plain,
! [SV32: term > $o] :
( ( ( SV32 @ ( lam @ ( sK45_SY362 @ SV32 ) ) )
= $false )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK28_SY440 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[441]) ).
thf(472,plain,
! [SV32: term > $o] :
( ( ( ! [SY460: term] :
( ~ ( SV32 @ SY460 )
| ( SV32 @ ( sub @ ( sK40_SY362 @ SV32 ) @ ( push @ SY460 @ id ) ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[442]) ).
thf(473,plain,
! [SV114: term,SV32: term > $o] :
( ( ( SV32 @ SV114 )
= $true )
| ( ( SV32 @ ( lam @ ( sK40_SY362 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(474,plain,
! [SV115: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV115 )
| ( SV32 @ ( sub @ ( sK34_SY362 @ SV32 ) @ ( push @ SV115 @ id ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK19_SY360 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(475,plain,
! [SV32: term > $o] :
( ( ( ! [SY461: term] :
( ~ ( SV32 @ SY461 )
| ( SV32 @ ( sub @ ( sK41_SY362 @ SV32 ) @ ( push @ SY461 @ id ) ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK23_SY437 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(476,plain,
! [SV116: term,SV32: term > $o] :
( ( ( SV32 @ SV116 )
= $true )
| ( ( SV32 @ ( lam @ ( sK41_SY362 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK23_SY437 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(477,plain,
! [SV117: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV117 )
| ( SV32 @ ( sub @ ( sK35_SY362 @ SV32 ) @ ( push @ SV117 @ id ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(478,plain,
! [SV90: term,SV99: term,SV105: subst,SV29: term > $o] :
( ( ( ~ ! [SY467: term] :
( ~ ( var @ SY467 )
| ( SV29 @ ( sub @ SY467 @ SV105 ) ) ) )
= $true )
| ( ( SV29 @ ( sub @ SV99 @ SV105 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SV90 @ id ) ) )
= $true )
| ( ( SV29 @ SV90 )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(479,plain,
! [SV29: term > $o,SV91: subst,SV88: term] :
( ( ( var @ ( sK42_SY451 @ SV88 @ SV91 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK25_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(480,plain,
! [SV95: term,SV106: term,SV118: subst,SV29: term > $o] :
( ( ( ~ ! [SY471: term] :
( ~ ( var @ SY471 )
| ( SV29 @ ( sub @ SY471 @ SV118 ) ) )
| ( SV29 @ ( sub @ SV106 @ SV118 ) ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( SV29 @ SV95 )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(481,plain,
! [SV29: term > $o,SV96: subst,SV92: term] :
( ( ( ~ ( var @ ( sK46_SY455 @ SV92 @ SV96 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV92 @ SV96 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK30_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(482,plain,
! [SV96: subst,SV92: term,SV29: term > $o] :
( ( ( SV29 @ ( sub @ ( sK46_SY455 @ SV92 @ SV96 @ SV29 ) @ SV96 ) )
= $false )
| ( ( SV29 @ ( sub @ SV92 @ SV96 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK30_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(483,plain,
! [SV93: term,SV100: term,SV107: subst,SV29: term > $o] :
( ( ( ~ ! [SY470: term] :
( ~ ( var @ SY470 )
| ( SV29 @ ( sub @ SY470 @ SV107 ) ) ) )
= $true )
| ( ( SV29 @ ( sub @ SV100 @ SV107 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SV93 @ id ) ) )
= $true )
| ( ( SV29 @ SV93 )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(484,plain,
! [SV29: term > $o,SV94: subst,SV89: term] :
( ( ( var @ ( sK43_SY454 @ SV89 @ SV94 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sub @ SV89 @ SV94 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK26_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[456]) ).
thf(485,plain,
! [SV119: term,SV31: term > $o] :
( ( ( SV31 @ SV119 )
= $true )
| ( ( SV31 @ ( sK36_SY357 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK20_SY355 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(486,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK44_SY357 @ SV31 ) )
= $true )
| ( ( ! [SY358: term] : ( SV31 @ SY358 ) )
= $true )
| ( ( SV31 @ ( sK27_SY439 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(487,plain,
! [SV120: term,SV31: term > $o] :
( ( ( SV31 @ SV120 )
= $true )
| ( ( SV31 @ ( lam @ ( sK44_SY357 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK27_SY439 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(488,plain,
! [SV121: term,SV31: term > $o] :
( ( ( SV31 @ SV121 )
= $true )
| ( ( SV31 @ ( sK37_SY357 @ SV31 ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK20_SY355 @ SV31 ) @ ( sK27_SY439 @ SV31 ) ) )
= $false )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(489,plain,
! [SV122: term,SV31: term > $o] :
( ( ( SV31 @ SV122 )
= $true )
| ( ( SV31 @ ( sK38_SY357 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK21_SY436 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK5_SY354 @ SV31 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(490,plain,
! [SV123: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV123 )
| ( SV32 @ ( sub @ ( sK39_SY362 @ SV32 ) @ ( push @ SV123 @ id ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK22_SY360 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(491,plain,
! [SV32: term > $o] :
( ( ( ! [SY466: term] :
( ~ ( SV32 @ SY466 )
| ( SV32 @ ( sub @ ( sK45_SY362 @ SV32 ) @ ( push @ SY466 @ id ) ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK28_SY440 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(492,plain,
! [SV124: term,SV32: term > $o] :
( ( ( SV32 @ SV124 )
= $true )
| ( ( SV32 @ ( lam @ ( sK45_SY362 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK28_SY440 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(493,plain,
! [SV125: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV125 )
| ( SV32 @ ( sub @ ( sK40_SY362 @ SV32 ) @ ( push @ SV125 @ id ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(494,plain,
! [SV115: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV115 ) )
= $true )
| ( ( SV32 @ ( sub @ ( sK34_SY362 @ SV32 ) @ ( push @ SV115 @ id ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK19_SY360 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(495,plain,
! [SV126: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV126 )
| ( SV32 @ ( sub @ ( sK41_SY362 @ SV32 ) @ ( push @ SV126 @ id ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK23_SY437 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(496,plain,
! [SV117: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV117 ) )
= $true )
| ( ( SV32 @ ( sub @ ( sK35_SY362 @ SV32 ) @ ( push @ SV117 @ id ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(497,plain,
! [SV90: term,SV99: term,SV105: subst,SV29: term > $o] :
( ( ( ! [SY467: term] :
( ~ ( var @ SY467 )
| ( SV29 @ ( sub @ SY467 @ SV105 ) ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV99 @ SV105 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SV90 @ id ) ) )
= $true )
| ( ( SV29 @ SV90 )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(498,plain,
! [SV95: term,SV106: term,SV118: subst,SV29: term > $o] :
( ( ( ~ ! [SY471: term] :
( ~ ( var @ SY471 )
| ( SV29 @ ( sub @ SY471 @ SV118 ) ) ) )
= $true )
| ( ( SV29 @ ( sub @ SV106 @ SV118 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( SV29 @ SV95 )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(499,plain,
! [SV29: term > $o,SV96: subst,SV92: term] :
( ( ( var @ ( sK46_SY455 @ SV92 @ SV96 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sub @ SV92 @ SV96 ) )
= $true )
| ( ( SV29 @ ( lam @ ( sK30_SY346 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[481]) ).
thf(500,plain,
! [SV93: term,SV100: term,SV107: subst,SV29: term > $o] :
( ( ( ! [SY470: term] :
( ~ ( var @ SY470 )
| ( SV29 @ ( sub @ SY470 @ SV107 ) ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV100 @ SV107 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SV93 @ id ) ) )
= $true )
| ( ( SV29 @ SV93 )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(501,plain,
! [SV127: term,SV31: term > $o] :
( ( ( SV31 @ SV127 )
= $true )
| ( ( SV31 @ ( sK44_SY357 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sK27_SY439 @ SV31 ) )
= $true )
| ( ( var @ ( sK5_SY354 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(502,plain,
! [SV123: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV123 ) )
= $true )
| ( ( SV32 @ ( sub @ ( sK39_SY362 @ SV32 ) @ ( push @ SV123 @ id ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK22_SY360 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(503,plain,
! [SV128: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV128 )
| ( SV32 @ ( sub @ ( sK45_SY362 @ SV32 ) @ ( push @ SV128 @ id ) ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK28_SY440 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(504,plain,
! [SV125: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV125 ) )
= $true )
| ( ( SV32 @ ( sub @ ( sK40_SY362 @ SV32 ) @ ( push @ SV125 @ id ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(505,plain,
! [SV115: term,SV32: term > $o] :
( ( ( SV32 @ SV115 )
= $false )
| ( ( SV32 @ ( sub @ ( sK34_SY362 @ SV32 ) @ ( push @ SV115 @ id ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK19_SY360 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(506,plain,
! [SV126: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV126 ) )
= $true )
| ( ( SV32 @ ( sub @ ( sK41_SY362 @ SV32 ) @ ( push @ SV126 @ id ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK23_SY437 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(507,plain,
! [SV117: term,SV32: term > $o] :
( ( ( SV32 @ SV117 )
= $false )
| ( ( SV32 @ ( sub @ ( sK35_SY362 @ SV32 ) @ ( push @ SV117 @ id ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(508,plain,
! [SV29: term > $o,SV105: subst,SV99: term,SV90: term] :
( ( ( ~ ( var @ ( sK47_SY467 @ SV90 @ SV99 @ SV105 @ SV29 ) )
| ( SV29 @ ( sub @ ( sK47_SY467 @ SV90 @ SV99 @ SV105 @ SV29 ) @ SV105 ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV99 @ SV105 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SV90 @ id ) ) )
= $true )
| ( ( SV29 @ SV90 )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[497]) ).
thf(509,plain,
! [SV95: term,SV106: term,SV118: subst,SV29: term > $o] :
( ( ( ! [SY471: term] :
( ~ ( var @ SY471 )
| ( SV29 @ ( sub @ SY471 @ SV118 ) ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV106 @ SV118 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( SV29 @ SV95 )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(510,plain,
! [SV29: term > $o,SV107: subst,SV100: term,SV93: term] :
( ( ( ~ ( var @ ( sK48_SY470 @ SV93 @ SV100 @ SV107 @ SV29 ) )
| ( SV29 @ ( sub @ ( sK48_SY470 @ SV93 @ SV100 @ SV107 @ SV29 ) @ SV107 ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV100 @ SV107 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SV93 @ id ) ) )
= $true )
| ( ( SV29 @ SV93 )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[500]) ).
thf(511,plain,
! [SV123: term,SV32: term > $o] :
( ( ( SV32 @ SV123 )
= $false )
| ( ( SV32 @ ( sub @ ( sK39_SY362 @ SV32 ) @ ( push @ SV123 @ id ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK22_SY360 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(512,plain,
! [SV128: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV128 ) )
= $true )
| ( ( SV32 @ ( sub @ ( sK45_SY362 @ SV32 ) @ ( push @ SV128 @ id ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK28_SY440 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(513,plain,
! [SV125: term,SV32: term > $o] :
( ( ( SV32 @ SV125 )
= $false )
| ( ( SV32 @ ( sub @ ( sK40_SY362 @ SV32 ) @ ( push @ SV125 @ id ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(514,plain,
! [SV115: term,SV129: term,SV32: term > $o] :
( ( ( SV32 @ SV129 )
= $true )
| ( ( SV32 @ ( sub @ ( sK34_SY362 @ SV32 ) @ ( push @ SV115 @ id ) ) )
= $true )
| ( ( SV32 @ SV115 )
= $false )
| ( ( SV32 @ ( sK19_SY360 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(515,plain,
! [SV126: term,SV32: term > $o] :
( ( ( SV32 @ SV126 )
= $false )
| ( ( SV32 @ ( sub @ ( sK41_SY362 @ SV32 ) @ ( push @ SV126 @ id ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK23_SY437 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(516,plain,
! [SV117: term,SV130: term,SV32: term > $o] :
( ( ( SV32 @ SV130 )
= $true )
| ( ( SV32 @ ( sub @ ( sK35_SY362 @ SV32 ) @ ( push @ SV117 @ id ) ) )
= $true )
| ( ( SV32 @ SV117 )
= $false )
| ( ( SV32 @ ( ap @ ( sK19_SY360 @ SV32 ) @ ( sK23_SY437 @ SV32 ) ) )
= $false )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(517,plain,
! [SV29: term > $o,SV105: subst,SV99: term,SV90: term] :
( ( ( ~ ( var @ ( sK47_SY467 @ SV90 @ SV99 @ SV105 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV99 @ SV105 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SV90 @ id ) ) )
= $true )
| ( ( SV29 @ SV90 )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(518,plain,
! [SV105: subst,SV99: term,SV90: term,SV29: term > $o] :
( ( ( SV29 @ ( sub @ ( sK47_SY467 @ SV90 @ SV99 @ SV105 @ SV29 ) @ SV105 ) )
= $false )
| ( ( SV29 @ ( sub @ SV99 @ SV105 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SV90 @ id ) ) )
= $true )
| ( ( SV29 @ SV90 )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[508]) ).
thf(519,plain,
! [SV29: term > $o,SV118: subst,SV106: term,SV95: term] :
( ( ( ~ ( var @ ( sK49_SY471 @ SV95 @ SV106 @ SV118 @ SV29 ) )
| ( SV29 @ ( sub @ ( sK49_SY471 @ SV95 @ SV106 @ SV118 @ SV29 ) @ SV118 ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV106 @ SV118 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( SV29 @ SV95 )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[509]) ).
thf(520,plain,
! [SV29: term > $o,SV107: subst,SV100: term,SV93: term] :
( ( ( ~ ( var @ ( sK48_SY470 @ SV93 @ SV100 @ SV107 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV100 @ SV107 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SV93 @ id ) ) )
= $true )
| ( ( SV29 @ SV93 )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(521,plain,
! [SV107: subst,SV100: term,SV93: term,SV29: term > $o] :
( ( ( SV29 @ ( sub @ ( sK48_SY470 @ SV93 @ SV100 @ SV107 @ SV29 ) @ SV107 ) )
= $false )
| ( ( SV29 @ ( sub @ SV100 @ SV107 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SV93 @ id ) ) )
= $true )
| ( ( SV29 @ SV93 )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[510]) ).
thf(522,plain,
! [SV123: term,SV131: term,SV32: term > $o] :
( ( ( SV32 @ SV131 )
= $true )
| ( ( SV32 @ ( sub @ ( sK39_SY362 @ SV32 ) @ ( push @ SV123 @ id ) ) )
= $true )
| ( ( SV32 @ SV123 )
= $false )
| ( ( SV32 @ ( sK22_SY360 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(523,plain,
! [SV128: term,SV32: term > $o] :
( ( ( SV32 @ SV128 )
= $false )
| ( ( SV32 @ ( sub @ ( sK45_SY362 @ SV32 ) @ ( push @ SV128 @ id ) ) )
= $true )
| ( ( ! [SY364: term] : ( SV32 @ SY364 ) )
= $true )
| ( ( SV32 @ ( sK28_SY440 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(524,plain,
! [SV125: term,SV132: term,SV32: term > $o] :
( ( ( SV32 @ SV132 )
= $true )
| ( ( SV32 @ ( sub @ ( sK40_SY362 @ SV32 ) @ ( push @ SV125 @ id ) ) )
= $true )
| ( ( SV32 @ SV125 )
= $false )
| ( ( SV32 @ ( ap @ ( sK22_SY360 @ SV32 ) @ ( sK28_SY440 @ SV32 ) ) )
= $false )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(525,plain,
! [SV126: term,SV133: term,SV32: term > $o] :
( ( ( SV32 @ SV133 )
= $true )
| ( ( SV32 @ ( sub @ ( sK41_SY362 @ SV32 ) @ ( push @ SV126 @ id ) ) )
= $true )
| ( ( SV32 @ SV126 )
= $false )
| ( ( SV32 @ ( sK23_SY437 @ SV32 ) )
= $true )
| ( ( SV32 @ ( sK6_SY359 @ SV32 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(526,plain,
! [SV29: term > $o,SV105: subst,SV99: term,SV90: term] :
( ( ( var @ ( sK47_SY467 @ SV90 @ SV99 @ SV105 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sub @ SV99 @ SV105 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK25_SY346 @ SV29 ) @ ( push @ SV90 @ id ) ) )
= $true )
| ( ( SV29 @ SV90 )
= $false )
| ( ( SV29 @ ( sK4_SY344 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(527,plain,
! [SV29: term > $o,SV118: subst,SV106: term,SV95: term] :
( ( ( ~ ( var @ ( sK49_SY471 @ SV95 @ SV106 @ SV118 @ SV29 ) ) )
= $false )
| ( ( SV29 @ ( sub @ SV106 @ SV118 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( SV29 @ SV95 )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(528,plain,
! [SV118: subst,SV106: term,SV95: term,SV29: term > $o] :
( ( ( SV29 @ ( sub @ ( sK49_SY471 @ SV95 @ SV106 @ SV118 @ SV29 ) @ SV118 ) )
= $false )
| ( ( SV29 @ ( sub @ SV106 @ SV118 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( SV29 @ SV95 )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[519]) ).
thf(529,plain,
! [SV29: term > $o,SV107: subst,SV100: term,SV93: term] :
( ( ( var @ ( sK48_SY470 @ SV93 @ SV100 @ SV107 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sub @ SV100 @ SV107 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK26_SY346 @ SV29 ) @ ( push @ SV93 @ id ) ) )
= $true )
| ( ( SV29 @ SV93 )
= $false )
| ( ( SV29 @ ( ap @ ( sK4_SY344 @ SV29 ) @ ( sK10_SY413 @ SV29 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(530,plain,
! [SV128: term,SV134: term,SV32: term > $o] :
( ( ( SV32 @ SV134 )
= $true )
| ( ( SV32 @ ( sub @ ( sK45_SY362 @ SV32 ) @ ( push @ SV128 @ id ) ) )
= $true )
| ( ( SV32 @ SV128 )
= $false )
| ( ( SV32 @ ( sK28_SY440 @ SV32 ) )
= $true )
| ( ( var @ ( sK6_SY359 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(531,plain,
! [SV29: term > $o,SV118: subst,SV106: term,SV95: term] :
( ( ( var @ ( sK49_SY471 @ SV95 @ SV106 @ SV118 @ SV29 ) )
= $true )
| ( ( SV29 @ ( sub @ SV106 @ SV118 ) )
= $true )
| ( ( SV29 @ ( sub @ ( sK30_SY346 @ SV29 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( SV29 @ SV95 )
= $false )
| ( ( SV29 @ ( sK10_SY413 @ SV29 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(532,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[67,531,530,529,528,526,525,524,522,521,518,516,514,501,499,492,489,488,487,485,484,482,479,476,473,469,467,466,464,463,459,457,452,449,445,438,434,421,378,358,338,336,318,316,313,297,292,280,262,245,233,230,228,226,203,196,195,171,170,169,168,167,166,165,164,163,144,143,141,137,114,111,107,106,102,101,99,69]) ).
thf(533,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG263^1 : 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
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 18:13:28 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.15/0.43
% 1.15/0.43 No.of.Axioms: 0
% 1.15/0.43
% 1.15/0.43 Length.of.Defs: 38092
% 1.15/0.43
% 1.15/0.43 Contains.Choice.Funs: false
% 1.15/0.43 .....................
% 1.15/0.43
% 1.15/0.43 ********************************
% 1.15/0.43 * All subproblems solved! *
% 1.15/0.43 ********************************
% 1.15/0.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:37,ps:0,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:532,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.15/0.43
% 1.15/0.43 %**** Beginning of derivation protocol ****
% 1.15/0.43 % SZS output start CNFRefutation
% See solution above
% 1.15/0.44
% 1.15/0.44 %**** End of derivation protocol ****
% 1.15/0.44 %**** no. of clauses in derivation: 533 ****
% 1.15/0.44 %**** clause counter: 532 ****
% 1.15/0.44
% 1.15/0.44 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:37,ps:0,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:532,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------