%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG256^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 10:08:38 AM UTC 2026
% Result : Theorem 1.59s 0.55s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 114
% Syntax : Number of formulae : 560 ( 263 unt; 0 typ; 113 def)
% Number of atoms : 4109 (1553 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 9030 ( 720 ~;1368 |; 7 &;5776 @)
% ( 2 <=>;1157 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 409 ( 409 >; 0 *; 0 +; 0 <<)
% Number of symbols : 164 ( 161 usr; 117 con; 0-4 aty)
% Number of variables : 1879 ( 39 ^;1835 !; 5 ?;1879 :)
% 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_SY211,type,
sK10_SY211: ( term > $o ) > term ).
thf(tp_sK11_SY202,type,
sK11_SY202: ( term > $o ) > term ).
thf(tp_sK12_SY219,type,
sK12_SY219: ( term > $o ) > term ).
thf(tp_sK13_SY202,type,
sK13_SY202: ( term > $o ) > term ).
thf(tp_sK14_SY253,type,
sK14_SY253: ( term > $o ) > term ).
thf(tp_sK15_SY219,type,
sK15_SY219: ( term > $o ) > term ).
thf(tp_sK16_SY254,type,
sK16_SY254: ( term > $o ) > term ).
thf(tp_sK17_SY196,type,
sK17_SY196: ( term > $o ) > term ).
thf(tp_sK18_SY196,type,
sK18_SY196: ( term > $o ) > term ).
thf(tp_sK19_SY255,type,
sK19_SY255: ( term > $o ) > term ).
thf(tp_sK1_SX0,type,
sK1_SX0: term ).
thf(tp_sK20_SY256,type,
sK20_SY256: ( term > $o ) > term ).
thf(tp_sK21_SY196,type,
sK21_SY196: ( term > $o ) > term ).
thf(tp_sK22_SY204,type,
sK22_SY204: ( term > $o ) > term ).
thf(tp_sK23_SY204,type,
sK23_SY204: ( term > $o ) > term ).
thf(tp_sK24_SY221,type,
sK24_SY221: ( term > $o ) > term ).
thf(tp_sK25_SY221,type,
sK25_SY221: ( term > $o ) > term ).
thf(tp_sK26_SY204,type,
sK26_SY204: ( term > $o ) > term ).
thf(tp_sK27_SY204,type,
sK27_SY204: ( term > $o ) > term ).
thf(tp_sK28_SY204,type,
sK28_SY204: ( term > $o ) > term ).
thf(tp_sK29_SY221,type,
sK29_SY221: ( term > $o ) > term ).
thf(tp_sK2_SY240,type,
sK2_SY240: term ).
thf(tp_sK30_SY221,type,
sK30_SY221: ( term > $o ) > term ).
thf(tp_sK31_SY221,type,
sK31_SY221: ( term > $o ) > term ).
thf(tp_sK32_SY264,type,
sK32_SY264: term > subst > ( term > $o ) > term ).
thf(tp_sK33_SY267,type,
sK33_SY267: term > subst > ( term > $o ) > term ).
thf(tp_sK34_SY204,type,
sK34_SY204: ( term > $o ) > term ).
thf(tp_sK35_SY221,type,
sK35_SY221: ( term > $o ) > term ).
thf(tp_sK36_SY268,type,
sK36_SY268: term > subst > ( term > $o ) > term ).
thf(tp_sK37_SY279,type,
sK37_SY279: term > term > subst > ( term > $o ) > term ).
thf(tp_sK38_SY282,type,
sK38_SY282: term > term > subst > ( term > $o ) > term ).
thf(tp_sK39_SY283,type,
sK39_SY283: term > term > subst > ( term > $o ) > term ).
thf(tp_sK3_SY194,type,
sK3_SY194: ( term > $o ) > term ).
thf(tp_sK4_SY201,type,
sK4_SY201: ( term > $o ) > term ).
thf(tp_sK5_SY248,type,
sK5_SY248: term ).
thf(tp_sK6_SY218,type,
sK6_SY218: ( term > $o ) > term ).
thf(tp_sK7_SY251,type,
sK7_SY251: ( term > $o ) > term ).
thf(tp_sK8_SY252,type,
sK8_SY252: term ).
thf(tp_sK9_SY245,type,
sK9_SY245: term > subst > ( term > $o ) > term ).
thf(tp_sh,type,
sh: subst ).
thf(tp_shinj,type,
shinj: $o ).
thf(tp_sub,type,
sub: term > subst > term ).
thf(tp_substmonoid,type,
substmonoid: $o ).
thf(tp_substmonoid_gthm,type,
substmonoid_gthm: $o ).
thf(tp_substmonoid_lthm,type,
substmonoid_lthm: $o ).
thf(tp_termmset,type,
termmset: $o ).
thf(tp_termmset_gthm,type,
termmset_gthm: $o ).
thf(tp_termmset_lthm,type,
termmset_lthm: $o ).
thf(tp_ulamvar1,type,
ulamvar1: $o ).
thf(tp_ulamvarind,type,
ulamvarind: $o ).
thf(tp_ulamvarsh,type,
ulamvarsh: $o ).
thf(tp_var,type,
var: term > $o ).
thf(apinj1,definition,
( apinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',apinj2) ).
thf(apnotvar,definition,
( apnotvar
= ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axclos) ).
thf(axidl,definition,
( axidl
= ( ! [M: subst] :
( ( comp @ id @ M )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axidl) ).
thf(axidr,definition,
( axidr
= ( ! [M: subst] :
( ( comp @ M @ id )
= M ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axmap) ).
thf(axscons,definition,
( axscons
= ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axscons) ).
thf(axshiftcons,definition,
( axshiftcons
= ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axshiftcons) ).
thf(axvarcons,definition,
( axvarcons
= ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarcons) ).
thf(axvarid,definition,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarid) ).
thf(axvarshift,definition,
( axvarshift
= ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarshift) ).
thf(hoasap,definition,
( hoasap
= ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoasapinj1_gthm) ).
thf(hoasapinj1_lthm,definition,
( hoasapinj1_lthm
= ( axvarid
=> ( apinj1
=> hoasapinj1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoasapinj2_gthm) ).
thf(hoasapinj2_lthm,definition,
( hoasapinj2_lthm
= ( apinj2
=> hoasapinj2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj2_lthm) ).
thf(hoasapnotvar,definition,
( hoasapnotvar
= ( ! [A: term,B: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoasapnotvar_gthm) ).
thf(hoasapnotvar_lthm,definition,
( hoasapnotvar_lthm
= ( axvarid
=> ( apnotvar
=> hoasapnotvar ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem0) ).
thf(hoasinduction_lem0_lthm,definition,
hoasinduction_lem0_lthm = hoasinduction_lem0,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3_gthm) ).
thf(hoasinduction_lem3_lthm,definition,
( hoasinduction_lem3_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3a_gthm) ).
thf(hoasinduction_lem3a_lthm,definition,
( hoasinduction_lem3a_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3a ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3aa) ).
thf(hoasinduction_lem3aa_lthm,definition,
( hoasinduction_lem3aa_lthm
= ( axclos
=> ( axmap
=> hoasinduction_lem3aa ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3b_gthm) ).
thf(hoasinduction_lem3b_lthm,definition,
hoasinduction_lem3b_lthm = hoasinduction_lem3b,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2_f) ).
thf(hoasinduction_lem3v2_f_lthm,definition,
hoasinduction_lem3v2_f_lthm = hoasinduction_lem3v2_f,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2_gthm) ).
thf(hoasinduction_lem3v2_lthm,definition,
( hoasinduction_lem3v2_lthm
= ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2a_lthm) ).
thf(hoasinduction_lthm,definition,
( hoasinduction_lthm
= ( induction2
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lthm) ).
thf(hoasinduction_lthm_3,definition,
( hoasinduction_lthm_3
= ( hoasinduction_lem0
=> ( induction2
=> ( axvarid
=> ( hoasinduction_lem3v2a
=> hoasinduction ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoaslaminj_gthm) ).
thf(hoaslaminj_lthm,definition,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoaslamnotap_gthm) ).
thf(hoaslamnotap_lthm,definition,
( hoaslamnotap_lthm
= ( lamnotap
=> hoaslamnotap ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',hoaslamnotvar_gthm) ).
thf(hoaslamnotvar_lthm,definition,
( hoaslamnotvar_lthm
= ( axvarid
=> ( lamnotvar
=> hoaslamnotvar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotvar_lthm) ).
thf(hoasvar,definition,
( hoasvar
= ( ^ [M: subst,A: term,N: subst] : ( var @ ( sub @ A @ N ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',induction2_gthm) ).
thf(induction2_lthm,definition,
( induction2_lthm
= ( axvarid
=> ( induction2lem
=> induction2 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',induction2lem_lthm) ).
thf(laminj,definition,
( laminj
= ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',laminj) ).
thf(lamnotap,definition,
( lamnotap
= ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotap) ).
thf(lamnotvar,definition,
( lamnotvar
= ( ! [A: term] :
~ ( var @ ( lam @ A ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',pushprop_lem0_gthm) ).
thf(pushprop_lem0_lthm,definition,
pushprop_lem0_lthm = pushprop_lem0,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',pushprop_lem1_gthm) ).
thf(pushprop_lem1_lthm,definition,
( pushprop_lem1_lthm
= ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop_lem1 ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',pushprop_lem1v2_gthm) ).
thf(pushprop_lem1v2_lthm,definition,
( pushprop_lem1v2_lthm
= ( axvarcons
=> pushprop_lem1v2 ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',pushprop_lem2v2_gthm) ).
thf(pushprop_lem2v2_lthm,definition,
( pushprop_lem2v2_lthm
= ( axclos
=> ( axshiftcons
=> pushprop_lem2v2 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',pushprop_lem3v2) ).
thf(pushprop_lem3v2_lthm,definition,
pushprop_lem3v2_lthm = pushprop_lem3v2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem3v2_lthm) ).
thf(pushprop_lthm,definition,
( pushprop_lthm
= ( pushprop_lem0
=> ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lthm) ).
thf(pushprop_lthm_orig,definition,
( pushprop_lthm_orig
= ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',substmonoid_gthm) ).
thf(substmonoid_lthm,definition,
( substmonoid_lthm
= ( axidl
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',termmset_gthm) ).
thf(termmset_lthm,definition,
( termmset_lthm
= ( axvarid
=> ( axclos
=> termmset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',termmset_lthm) ).
thf(ulamvar1,definition,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ulamvarind) ).
thf(ulamvarsh,definition,
( ulamvarsh
= ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvarsh) ).
thf(1,conjecture,
hoasapinj1_gthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
hoasapinj1_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,plain,
( ( ~ ! [SY79: term,SY80: term,SY81: term,SY82: term] :
( ( ( ap @ ( sub @ SY79 @ id ) @ SY81 )
= ( ap @ ( sub @ SY80 @ id ) @ SY82 ) )
=> ( SY79 = SY80 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(38,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(39,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(40,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(41,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(42,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(43,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(44,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(45,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(46,plain,
( ( ! [A: term] :
~ ( var @ ( lam @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(47,plain,
( ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(48,plain,
( ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(49,plain,
( ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(50,plain,
( ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(51,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(52,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(53,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(54,plain,
( ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(55,plain,
( ( var @ one )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(56,plain,
( ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(57,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(58,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(59,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(60,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(61,plain,
( ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(62,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(63,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(64,plain,
( ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(65,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(66,plain,
( ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(67,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(68,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)],[36]) ).
thf(69,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)],[43,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(70,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)],[42,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(71,plain,
( ( ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[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(72,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)],[53,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(73,plain,
( ( ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) ) )
= $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(74,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(75,plain,
( ( ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(76,plain,
( ( ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) ) )
= $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(77,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)],[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(78,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(79,plain,
( ( ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(80,plain,
( ( ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(81,plain,
! [SV1: term] :
( ( ( sub @ SV1 @ id )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(82,plain,
! [SV2: term] :
( ( ! [SY178: subst,SY179: subst] :
( ( sub @ ( sub @ SV2 @ SY178 ) @ SY179 )
= ( sub @ SV2 @ ( comp @ SY178 @ SY179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(83,plain,
! [SV3: subst] :
( ( ( comp @ SV3 @ id )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(84,plain,
! [SV4: subst] :
( ( ( comp @ id @ SV4 )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(85,plain,
! [SV5: subst] :
( ( ! [SY180: subst,SY181: subst] :
( ( comp @ ( comp @ SV5 @ SY180 ) @ SY181 )
= ( comp @ SV5 @ ( comp @ SY180 @ SY181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(86,plain,
! [SV6: term] :
( ( ~ ( var @ ( lam @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(87,plain,
! [SV7: term] :
( ( ! [SY182: term] :
~ ( var @ ( ap @ SV7 @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(88,plain,
! [SV8: subst] :
( ( ( push @ ( sub @ one @ SV8 ) @ ( comp @ sh @ SV8 ) )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(89,plain,
! [SV9: subst] :
( ( ( comp @ SV9 @ id )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(90,plain,
! [SV10: term] :
( ( ! [SY183: subst,SY184: subst] :
( ( comp @ ( push @ SV10 @ SY183 ) @ SY184 )
= ( push @ ( sub @ SV10 @ SY184 ) @ ( comp @ SY183 @ SY184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(91,plain,
! [SV11: subst] :
( ( ! [SY185: subst,SY186: subst] :
( ( comp @ ( comp @ SV11 @ SY185 ) @ SY186 )
= ( comp @ SV11 @ ( comp @ SY185 @ SY186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(92,plain,
! [SV12: term] :
( ( ! [SY187: subst] :
( ( comp @ sh @ ( push @ SV12 @ SY187 ) )
= SY187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(93,plain,
! [SV13: subst] :
( ( ( comp @ id @ SV13 )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(94,plain,
! [SV14: term] :
( ( ! [SY188: subst,SY189: subst] :
( ( sub @ ( sub @ SV14 @ SY188 ) @ SY189 )
= ( sub @ SV14 @ ( comp @ SY188 @ SY189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(95,plain,
! [SV15: term] :
( ( ! [SY190: subst] :
( ( sub @ ( lam @ SV15 ) @ SY190 )
= ( lam @ ( sub @ SV15 @ ( push @ one @ ( comp @ SY190 @ sh ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(96,plain,
! [SV16: term] :
( ( ( sub @ SV16 @ id )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(97,plain,
! [SV17: term] :
( ( ! [SY191: subst] :
( ( sub @ one @ ( push @ SV17 @ SY191 ) )
= SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(98,plain,
! [SV18: term] :
( ( ! [SY192: term,SY193: subst] :
( ( sub @ ( ap @ SV18 @ SY192 ) @ SY193 )
= ( ap @ ( sub @ SV18 @ SY193 ) @ ( sub @ SY192 @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(99,plain,
! [SV19: term > $o] :
( ( ~ ! [SY194: term,SY195: term] :
( ~ ( SV19 @ SY194 )
| ~ ( SV19 @ SY195 )
| ( SV19 @ ( ap @ SY194 @ SY195 ) ) )
| ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) )
| ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(100,plain,
! [SV20: term > $o] :
( ( ~ ! [SY201: term] :
( ~ ( var @ SY201 )
| ( SV20 @ SY201 ) )
| ~ ! [SY202: term,SY203: term] :
( ~ ( SV20 @ SY202 )
| ~ ( SV20 @ SY203 )
| ( SV20 @ ( ap @ SY202 @ SY203 ) ) )
| ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(101,plain,
! [SV21: term > $o] :
( ( ! [SY207: term,SY208: subst] :
( ~ ! [SY209: term] :
( ~ ( var @ SY209 )
| ( SV21 @ ( sub @ SY209 @ SY208 ) ) )
| ~ ( SV21 @ SY207 )
| ! [SY210: term] :
( ~ ( var @ SY210 )
| ( SV21 @ ( sub @ SY210 @ ( push @ SY207 @ SY208 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(102,plain,
! [SV22: term > $o] :
( ( ~ ( SV22 @ one )
| ~ ! [SY211: term] :
( ~ ( var @ SY211 )
| ~ ( SV22 @ SY211 )
| ( SV22 @ ( sub @ SY211 @ sh ) ) )
| ! [SY212: term] :
( ~ ( var @ SY212 )
| ( SV22 @ SY212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(103,plain,
! [SV23: term] :
( ( ! [SY213: term,SY214: term] :
( ( lam @ SV23 )
!= ( ap @ SY213 @ SY214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(104,plain,
! [SV24: term] :
( ( ! [SY215: term,SY216: term,SY217: term] :
( ( ( ap @ SV24 @ SY216 )
!= ( ap @ SY215 @ SY217 ) )
| ( SY216 = SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(105,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(106,plain,
! [SV25: term] :
( ( ~ ( var @ SV25 )
| ( var @ ( sub @ SV25 @ sh ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(107,plain,
! [SV26: term > $o] :
( ( ~ ! [SY218: term] :
( ~ ( var @ SY218 )
| ( SV26 @ SY218 ) )
| ~ ! [SY219: term,SY220: term] :
( ~ ( SV26 @ SY219 )
| ~ ( SV26 @ SY220 )
| ( SV26 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(108,plain,
! [SV27: term] :
( ( ! [SY223: term,SY224: term,SY225: term] :
( ( ( ap @ SV27 @ SY224 )
!= ( ap @ SY223 @ SY225 ) )
| ( SV27 = SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(109,plain,
! [SV28: term] :
( ( ! [SY226: term] :
( ( ( sub @ SV28 @ sh )
!= ( sub @ SY226 @ sh ) )
| ( SV28 = SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(110,plain,
! [SV29: term] :
( ( ! [SY227: term] :
( ( ( lam @ SV29 )
!= ( lam @ SY227 ) )
| ( SV29 = SY227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(111,plain,
! [SV30: subst,SV2: term] :
( ( ! [SY228: subst] :
( ( sub @ ( sub @ SV2 @ SV30 ) @ SY228 )
= ( sub @ SV2 @ ( comp @ SV30 @ SY228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(112,plain,
! [SV31: subst,SV5: subst] :
( ( ! [SY229: subst] :
( ( comp @ ( comp @ SV5 @ SV31 ) @ SY229 )
= ( comp @ SV5 @ ( comp @ SV31 @ SY229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(113,plain,
! [SV6: term] :
( ( var @ ( lam @ SV6 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(114,plain,
! [SV32: term,SV7: term] :
( ( ~ ( var @ ( ap @ SV7 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(115,plain,
! [SV33: subst,SV10: term] :
( ( ! [SY230: subst] :
( ( comp @ ( push @ SV10 @ SV33 ) @ SY230 )
= ( push @ ( sub @ SV10 @ SY230 ) @ ( comp @ SV33 @ SY230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(116,plain,
! [SV34: subst,SV11: subst] :
( ( ! [SY231: subst] :
( ( comp @ ( comp @ SV11 @ SV34 ) @ SY231 )
= ( comp @ SV11 @ ( comp @ SV34 @ SY231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(117,plain,
! [SV35: subst,SV12: term] :
( ( ( comp @ sh @ ( push @ SV12 @ SV35 ) )
= SV35 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(118,plain,
! [SV36: subst,SV14: term] :
( ( ! [SY232: subst] :
( ( sub @ ( sub @ SV14 @ SV36 ) @ SY232 )
= ( sub @ SV14 @ ( comp @ SV36 @ SY232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(119,plain,
! [SV37: subst,SV15: term] :
( ( ( sub @ ( lam @ SV15 ) @ SV37 )
= ( lam @ ( sub @ SV15 @ ( push @ one @ ( comp @ SV37 @ sh ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(120,plain,
! [SV38: subst,SV17: term] :
( ( ( sub @ one @ ( push @ SV17 @ SV38 ) )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(121,plain,
! [SV39: term,SV18: term] :
( ( ! [SY233: subst] :
( ( sub @ ( ap @ SV18 @ SV39 ) @ SY233 )
= ( ap @ ( sub @ SV18 @ SY233 ) @ ( sub @ SV39 @ SY233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(122,plain,
! [SV19: term > $o] :
( ( ( ~ ! [SY194: term,SY195: term] :
( ~ ( SV19 @ SY194 )
| ~ ( SV19 @ SY195 )
| ( SV19 @ ( ap @ SY194 @ SY195 ) ) ) )
= $true )
| ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) )
| ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(123,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY201: term] :
( ~ ( var @ SY201 )
| ( SV20 @ SY201 ) ) )
= $true )
| ( ( ~ ! [SY202: term,SY203: term] :
( ~ ( SV20 @ SY202 )
| ~ ( SV20 @ SY203 )
| ( SV20 @ ( ap @ SY202 @ SY203 ) ) )
| ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(124,plain,
! [SV40: term,SV21: term > $o] :
( ( ! [SY234: subst] :
( ~ ! [SY209: term] :
( ~ ( var @ SY209 )
| ( SV21 @ ( sub @ SY209 @ SY234 ) ) )
| ~ ( SV21 @ SV40 )
| ! [SY236: term] :
( ~ ( var @ SY236 )
| ( SV21 @ ( sub @ SY236 @ ( push @ SV40 @ SY234 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(125,plain,
! [SV22: term > $o] :
( ( ( ~ ( SV22 @ one ) )
= $true )
| ( ( ~ ! [SY211: term] :
( ~ ( var @ SY211 )
| ~ ( SV22 @ SY211 )
| ( SV22 @ ( sub @ SY211 @ sh ) ) )
| ! [SY212: term] :
( ~ ( var @ SY212 )
| ( SV22 @ SY212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(126,plain,
! [SV41: term,SV23: term] :
( ( ! [SY237: term] :
( ( lam @ SV23 )
!= ( ap @ SV41 @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(127,plain,
! [SV42: term,SV24: term] :
( ( ! [SY238: term,SY239: term] :
( ( ( ap @ SV24 @ SY238 )
!= ( ap @ SV42 @ SY239 ) )
| ( SY238 = SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(128,plain,
( ( ! [SY240: term,SY241: term,SY242: term] :
( ( ( ap @ ( sub @ sK1_SX0 @ id ) @ SY241 )
!= ( ap @ ( sub @ SY240 @ id ) @ SY242 ) )
| ( sK1_SX0 = SY240 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[105]) ).
thf(129,plain,
! [SV25: term] :
( ( ( ~ ( var @ SV25 ) )
= $true )
| ( ( var @ ( sub @ SV25 @ sh ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(130,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY218: term] :
( ~ ( var @ SY218 )
| ( SV26 @ SY218 ) ) )
= $true )
| ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV26 @ SY219 )
| ~ ( SV26 @ SY220 )
| ( SV26 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(131,plain,
! [SV43: term,SV27: term] :
( ( ! [SY243: term,SY244: term] :
( ( ( ap @ SV27 @ SY243 )
!= ( ap @ SV43 @ SY244 ) )
| ( SV27 = SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(132,plain,
! [SV44: term,SV28: term] :
( ( ( ( sub @ SV28 @ sh )
!= ( sub @ SV44 @ sh ) )
| ( SV28 = SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(133,plain,
! [SV45: term,SV29: term] :
( ( ( ( lam @ SV29 )
!= ( lam @ SV45 ) )
| ( SV29 = SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(134,plain,
! [SV46: subst,SV30: subst,SV2: term] :
( ( ( sub @ ( sub @ SV2 @ SV30 ) @ SV46 )
= ( sub @ SV2 @ ( comp @ SV30 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(135,plain,
! [SV47: subst,SV31: subst,SV5: subst] :
( ( ( comp @ ( comp @ SV5 @ SV31 ) @ SV47 )
= ( comp @ SV5 @ ( comp @ SV31 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(136,plain,
! [SV32: term,SV7: term] :
( ( var @ ( ap @ SV7 @ SV32 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(137,plain,
! [SV48: subst,SV33: subst,SV10: term] :
( ( ( comp @ ( push @ SV10 @ SV33 ) @ SV48 )
= ( push @ ( sub @ SV10 @ SV48 ) @ ( comp @ SV33 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(138,plain,
! [SV49: subst,SV34: subst,SV11: subst] :
( ( ( comp @ ( comp @ SV11 @ SV34 ) @ SV49 )
= ( comp @ SV11 @ ( comp @ SV34 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(139,plain,
! [SV50: subst,SV36: subst,SV14: term] :
( ( ( sub @ ( sub @ SV14 @ SV36 ) @ SV50 )
= ( sub @ SV14 @ ( comp @ SV36 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(140,plain,
! [SV51: subst,SV39: term,SV18: term] :
( ( ( sub @ ( ap @ SV18 @ SV39 ) @ SV51 )
= ( ap @ ( sub @ SV18 @ SV51 ) @ ( sub @ SV39 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(141,plain,
! [SV19: term > $o] :
( ( ( ! [SY194: term,SY195: term] :
( ~ ( SV19 @ SY194 )
| ~ ( SV19 @ SY195 )
| ( SV19 @ ( ap @ SY194 @ SY195 ) ) ) )
= $false )
| ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) )
| ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(142,plain,
! [SV20: term > $o] :
( ( ( ! [SY201: term] :
( ~ ( var @ SY201 )
| ( SV20 @ SY201 ) ) )
= $false )
| ( ( ~ ! [SY202: term,SY203: term] :
( ~ ( SV20 @ SY202 )
| ~ ( SV20 @ SY203 )
| ( SV20 @ ( ap @ SY202 @ SY203 ) ) )
| ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(143,plain,
! [SV40: term,SV52: subst,SV21: term > $o] :
( ( ~ ! [SY245: term] :
( ~ ( var @ SY245 )
| ( SV21 @ ( sub @ SY245 @ SV52 ) ) )
| ~ ( SV21 @ SV40 )
| ! [SY246: term] :
( ~ ( var @ SY246 )
| ( SV21 @ ( sub @ SY246 @ ( push @ SV40 @ SV52 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(144,plain,
! [SV22: term > $o] :
( ( ( SV22 @ one )
= $false )
| ( ( ~ ! [SY211: term] :
( ~ ( var @ SY211 )
| ~ ( SV22 @ SY211 )
| ( SV22 @ ( sub @ SY211 @ sh ) ) )
| ! [SY212: term] :
( ~ ( var @ SY212 )
| ( SV22 @ SY212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(145,plain,
! [SV53: term,SV41: term,SV23: term] :
( ( ( lam @ SV23 )
!= ( ap @ SV41 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(146,plain,
! [SV42: term,SV54: term,SV24: term] :
( ( ! [SY247: term] :
( ( ( ap @ SV24 @ SV54 )
!= ( ap @ SV42 @ SY247 ) )
| ( SV54 = SY247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(147,plain,
( ( ! [SY248: term,SY249: term] :
( ( ( ap @ ( sub @ sK1_SX0 @ id ) @ SY248 )
!= ( ap @ ( sub @ sK2_SY240 @ id ) @ SY249 ) )
| ( sK1_SX0 = sK2_SY240 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[128]) ).
thf(148,plain,
! [SV25: term] :
( ( ( var @ SV25 )
= $false )
| ( ( var @ ( sub @ SV25 @ sh ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(149,plain,
! [SV26: term > $o] :
( ( ( ! [SY218: term] :
( ~ ( var @ SY218 )
| ( SV26 @ SY218 ) ) )
= $false )
| ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV26 @ SY219 )
| ~ ( SV26 @ SY220 )
| ( SV26 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(150,plain,
! [SV43: term,SV55: term,SV27: term] :
( ( ! [SY250: term] :
( ( ( ap @ SV27 @ SV55 )
!= ( ap @ SV43 @ SY250 ) )
| ( SV27 = SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(151,plain,
! [SV44: term,SV28: term] :
( ( ( ( sub @ SV28 @ sh )
!= ( sub @ SV44 @ sh ) )
= $true )
| ( ( SV28 = SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(152,plain,
! [SV45: term,SV29: term] :
( ( ( ( lam @ SV29 )
!= ( lam @ SV45 ) )
= $true )
| ( ( SV29 = SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(153,plain,
! [SV19: term > $o] :
( ( ( ! [SY251: term] :
( ~ ( SV19 @ ( sK3_SY194 @ SV19 ) )
| ~ ( SV19 @ SY251 )
| ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ SY251 ) ) ) )
= $false )
| ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) )
| ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[141]) ).
thf(154,plain,
! [SV20: term > $o] :
( ( ( ~ ( var @ ( sK4_SY201 @ SV20 ) )
| ( SV20 @ ( sK4_SY201 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY202: term,SY203: term] :
( ~ ( SV20 @ SY202 )
| ~ ( SV20 @ SY203 )
| ( SV20 @ ( ap @ SY202 @ SY203 ) ) )
| ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[142]) ).
thf(155,plain,
! [SV40: term,SV52: subst,SV21: term > $o] :
( ( ( ~ ! [SY245: term] :
( ~ ( var @ SY245 )
| ( SV21 @ ( sub @ SY245 @ SV52 ) ) ) )
= $true )
| ( ( ~ ( SV21 @ SV40 )
| ! [SY246: term] :
( ~ ( var @ SY246 )
| ( SV21 @ ( sub @ SY246 @ ( push @ SV40 @ SV52 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(156,plain,
! [SV22: term > $o] :
( ( ( ~ ! [SY211: term] :
( ~ ( var @ SY211 )
| ~ ( SV22 @ SY211 )
| ( SV22 @ ( sub @ SY211 @ sh ) ) ) )
= $true )
| ( ( ! [SY212: term] :
( ~ ( var @ SY212 )
| ( SV22 @ SY212 ) ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV53: term,SV41: term,SV23: term] :
( ( ( lam @ SV23 )
= ( ap @ SV41 @ SV53 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(158,plain,
! [SV56: term,SV42: term,SV54: term,SV24: term] :
( ( ( ( ap @ SV24 @ SV54 )
!= ( ap @ SV42 @ SV56 ) )
| ( SV54 = SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(159,plain,
( ( ! [SY252: term] :
( ( ( ap @ ( sub @ sK1_SX0 @ id ) @ sK5_SY248 )
!= ( ap @ ( sub @ sK2_SY240 @ id ) @ SY252 ) )
| ( sK1_SX0 = sK2_SY240 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[147]) ).
thf(160,plain,
! [SV26: term > $o] :
( ( ( ~ ( var @ ( sK6_SY218 @ SV26 ) )
| ( SV26 @ ( sK6_SY218 @ SV26 ) ) )
= $false )
| ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV26 @ SY219 )
| ~ ( SV26 @ SY220 )
| ( SV26 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[149]) ).
thf(161,plain,
! [SV57: term,SV43: term,SV55: term,SV27: term] :
( ( ( ( ap @ SV27 @ SV55 )
!= ( ap @ SV43 @ SV57 ) )
| ( SV27 = SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(162,plain,
! [SV44: term,SV28: term] :
( ( ( ( sub @ SV28 @ sh )
= ( sub @ SV44 @ sh ) )
= $false )
| ( ( SV28 = SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(163,plain,
! [SV45: term,SV29: term] :
( ( ( ( lam @ SV29 )
= ( lam @ SV45 ) )
= $false )
| ( ( SV29 = SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(164,plain,
! [SV19: term > $o] :
( ( ( ~ ( SV19 @ ( sK3_SY194 @ SV19 ) )
| ~ ( SV19 @ ( sK7_SY251 @ SV19 ) )
| ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) ) )
= $false )
| ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) )
| ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[153]) ).
thf(165,plain,
! [SV20: term > $o] :
( ( ( ~ ( var @ ( sK4_SY201 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY202: term,SY203: term] :
( ~ ( SV20 @ SY202 )
| ~ ( SV20 @ SY203 )
| ( SV20 @ ( ap @ SY202 @ SY203 ) ) )
| ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(166,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false )
| ( ( ~ ! [SY202: term,SY203: term] :
( ~ ( SV20 @ SY202 )
| ~ ( SV20 @ SY203 )
| ( SV20 @ ( ap @ SY202 @ SY203 ) ) )
| ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[154]) ).
thf(167,plain,
! [SV40: term,SV52: subst,SV21: term > $o] :
( ( ( ! [SY245: term] :
( ~ ( var @ SY245 )
| ( SV21 @ ( sub @ SY245 @ SV52 ) ) ) )
= $false )
| ( ( ~ ( SV21 @ SV40 )
| ! [SY246: term] :
( ~ ( var @ SY246 )
| ( SV21 @ ( sub @ SY246 @ ( push @ SV40 @ SV52 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(168,plain,
! [SV22: term > $o] :
( ( ( ! [SY211: term] :
( ~ ( var @ SY211 )
| ~ ( SV22 @ SY211 )
| ( SV22 @ ( sub @ SY211 @ sh ) ) ) )
= $false )
| ( ( ! [SY212: term] :
( ~ ( var @ SY212 )
| ( SV22 @ SY212 ) ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(169,plain,
! [SV56: term,SV42: term,SV54: term,SV24: term] :
( ( ( ( ap @ SV24 @ SV54 )
!= ( ap @ SV42 @ SV56 ) )
= $true )
| ( ( SV54 = SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(170,plain,
( ( ( ( ap @ ( sub @ sK1_SX0 @ id ) @ sK5_SY248 )
!= ( ap @ ( sub @ sK2_SY240 @ id ) @ sK8_SY252 ) )
| ( sK1_SX0 = sK2_SY240 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[159]) ).
thf(171,plain,
! [SV26: term > $o] :
( ( ( ~ ( var @ ( sK6_SY218 @ SV26 ) ) )
= $false )
| ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV26 @ SY219 )
| ~ ( SV26 @ SY220 )
| ( SV26 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(172,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false )
| ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV26 @ SY219 )
| ~ ( SV26 @ SY220 )
| ( SV26 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(173,plain,
! [SV57: term,SV43: term,SV55: term,SV27: term] :
( ( ( ( ap @ SV27 @ SV55 )
!= ( ap @ SV43 @ SV57 ) )
= $true )
| ( ( SV27 = SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(174,plain,
! [SV19: term > $o] :
( ( ( ~ ( SV19 @ ( sK3_SY194 @ SV19 ) ) )
= $false )
| ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) )
| ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(175,plain,
! [SV19: term > $o] :
( ( ( ~ ( SV19 @ ( sK7_SY251 @ SV19 ) )
| ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) ) )
= $false )
| ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) )
| ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(176,plain,
! [SV20: term > $o] :
( ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true )
| ( ( ~ ! [SY202: term,SY203: term] :
( ~ ( SV20 @ SY202 )
| ~ ( SV20 @ SY203 )
| ( SV20 @ ( ap @ SY202 @ SY203 ) ) )
| ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(177,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY202: term,SY203: term] :
( ~ ( SV20 @ SY202 )
| ~ ( SV20 @ SY203 )
| ( SV20 @ ( ap @ SY202 @ SY203 ) ) ) )
= $true )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(178,plain,
! [SV21: term > $o,SV52: subst,SV40: term] :
( ( ( ~ ( var @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) )
| ( SV21 @ ( sub @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) @ SV52 ) ) )
= $false )
| ( ( ~ ( SV21 @ SV40 )
| ! [SY246: term] :
( ~ ( var @ SY246 )
| ( SV21 @ ( sub @ SY246 @ ( push @ SV40 @ SV52 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[167]) ).
thf(179,plain,
! [SV22: term > $o] :
( ( ( ~ ( var @ ( sK10_SY211 @ SV22 ) )
| ~ ( SV22 @ ( sK10_SY211 @ SV22 ) )
| ( SV22 @ ( sub @ ( sK10_SY211 @ SV22 ) @ sh ) ) )
= $false )
| ( ( ! [SY212: term] :
( ~ ( var @ SY212 )
| ( SV22 @ SY212 ) ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[168]) ).
thf(180,plain,
! [SV56: term,SV42: term,SV54: term,SV24: term] :
( ( ( ( ap @ SV24 @ SV54 )
= ( ap @ SV42 @ SV56 ) )
= $false )
| ( ( SV54 = SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(181,plain,
( ( ( ap @ ( sub @ sK1_SX0 @ id ) @ sK5_SY248 )
!= ( ap @ ( sub @ sK2_SY240 @ id ) @ sK8_SY252 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(182,plain,
( ( sK1_SX0 = sK2_SY240 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[170]) ).
thf(183,plain,
! [SV26: term > $o] :
( ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true )
| ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV26 @ SY219 )
| ~ ( SV26 @ SY220 )
| ( SV26 @ ( ap @ SY219 @ SY220 ) ) )
| ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[171]) ).
thf(184,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV26 @ SY219 )
| ~ ( SV26 @ SY220 )
| ( SV26 @ ( ap @ SY219 @ SY220 ) ) ) )
= $true )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(185,plain,
! [SV57: term,SV43: term,SV55: term,SV27: term] :
( ( ( ( ap @ SV27 @ SV55 )
= ( ap @ SV43 @ SV57 ) )
= $false )
| ( ( SV27 = SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(186,plain,
! [SV19: term > $o] :
( ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true )
| ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) )
| ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[174]) ).
thf(187,plain,
! [SV19: term > $o] :
( ( ( ~ ( SV19 @ ( sK7_SY251 @ SV19 ) ) )
= $false )
| ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) )
| ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(188,plain,
! [SV19: term > $o] :
( ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false )
| ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) )
| ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(189,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY202: term,SY203: term] :
( ~ ( SV20 @ SY202 )
| ~ ( SV20 @ SY203 )
| ( SV20 @ ( ap @ SY202 @ SY203 ) ) ) )
= $true )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(190,plain,
! [SV20: term > $o] :
( ( ( ! [SY202: term,SY203: term] :
( ~ ( SV20 @ SY202 )
| ~ ( SV20 @ SY203 )
| ( SV20 @ ( ap @ SY202 @ SY203 ) ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(191,plain,
! [SV21: term > $o,SV52: subst,SV40: term] :
( ( ( ~ ( var @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) ) )
= $false )
| ( ( ~ ( SV21 @ SV40 )
| ! [SY246: term] :
( ~ ( var @ SY246 )
| ( SV21 @ ( sub @ SY246 @ ( push @ SV40 @ SV52 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(192,plain,
! [SV52: subst,SV40: term,SV21: term > $o] :
( ( ( SV21 @ ( sub @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) @ SV52 ) )
= $false )
| ( ( ~ ( SV21 @ SV40 )
| ! [SY246: term] :
( ~ ( var @ SY246 )
| ( SV21 @ ( sub @ SY246 @ ( push @ SV40 @ SV52 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[178]) ).
thf(193,plain,
! [SV22: term > $o] :
( ( ( ~ ( var @ ( sK10_SY211 @ SV22 ) ) )
= $false )
| ( ( ! [SY212: term] :
( ~ ( var @ SY212 )
| ( SV22 @ SY212 ) ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(194,plain,
! [SV22: term > $o] :
( ( ( ~ ( SV22 @ ( sK10_SY211 @ SV22 ) )
| ( SV22 @ ( sub @ ( sK10_SY211 @ SV22 ) @ sh ) ) )
= $false )
| ( ( ! [SY212: term] :
( ~ ( var @ SY212 )
| ( SV22 @ SY212 ) ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[179]) ).
thf(195,plain,
( ( ( ap @ ( sub @ sK1_SX0 @ id ) @ sK5_SY248 )
= ( ap @ ( sub @ sK2_SY240 @ id ) @ sK8_SY252 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(196,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY219: term,SY220: term] :
( ~ ( SV26 @ SY219 )
| ~ ( SV26 @ SY220 )
| ( SV26 @ ( ap @ SY219 @ SY220 ) ) ) )
= $true )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(197,plain,
! [SV26: term > $o] :
( ( ( ! [SY219: term,SY220: term] :
( ~ ( SV26 @ SY219 )
| ~ ( SV26 @ SY220 )
| ( SV26 @ ( ap @ SY219 @ SY220 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(198,plain,
! [SV19: term > $o] :
( ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(199,plain,
! [SV19: term > $o] :
( ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true )
| ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) )
| ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(200,plain,
! [SV19: term > $o] :
( ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(201,plain,
! [SV20: term > $o] :
( ( ( ! [SY202: term,SY203: term] :
( ~ ( SV20 @ SY202 )
| ~ ( SV20 @ SY203 )
| ( SV20 @ ( ap @ SY202 @ SY203 ) ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(202,plain,
! [SV20: term > $o] :
( ( ( ! [SY253: term] :
( ~ ( SV20 @ ( sK11_SY202 @ SV20 ) )
| ~ ( SV20 @ SY253 )
| ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ SY253 ) ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[190]) ).
thf(203,plain,
! [SV21: term > $o,SV52: subst,SV40: term] :
( ( ( var @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) )
= $true )
| ( ( ~ ( SV21 @ SV40 )
| ! [SY246: term] :
( ~ ( var @ SY246 )
| ( SV21 @ ( sub @ SY246 @ ( push @ SV40 @ SV52 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(204,plain,
! [SV52: subst,SV40: term,SV21: term > $o] :
( ( ( ~ ( SV21 @ SV40 ) )
= $true )
| ( ( ! [SY246: term] :
( ~ ( var @ SY246 )
| ( SV21 @ ( sub @ SY246 @ ( push @ SV40 @ SV52 ) ) ) ) )
= $true )
| ( ( SV21 @ ( sub @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) @ SV52 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(205,plain,
! [SV22: term > $o] :
( ( ( var @ ( sK10_SY211 @ SV22 ) )
= $true )
| ( ( ! [SY212: term] :
( ~ ( var @ SY212 )
| ( SV22 @ SY212 ) ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(206,plain,
! [SV22: term > $o] :
( ( ( ~ ( SV22 @ ( sK10_SY211 @ SV22 ) ) )
= $false )
| ( ( ! [SY212: term] :
( ~ ( var @ SY212 )
| ( SV22 @ SY212 ) ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(207,plain,
! [SV22: term > $o] :
( ( ( SV22 @ ( sub @ ( sK10_SY211 @ SV22 ) @ sh ) )
= $false )
| ( ( ! [SY212: term] :
( ~ ( var @ SY212 )
| ( SV22 @ SY212 ) ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(208,plain,
! [SV26: term > $o] :
( ( ( ! [SY219: term,SY220: term] :
( ~ ( SV26 @ SY219 )
| ~ ( SV26 @ SY220 )
| ( SV26 @ ( ap @ SY219 @ SY220 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(209,plain,
! [SV26: term > $o] :
( ( ( ! [SY254: term] :
( ~ ( SV26 @ ( sK12_SY219 @ SV26 ) )
| ~ ( SV26 @ SY254 )
| ( SV26 @ ( ap @ ( sK12_SY219 @ SV26 ) @ SY254 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[197]) ).
thf(210,plain,
! [SV19: term > $o] :
( ( ( ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) ) )
= $false )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(211,plain,
! [SV19: term > $o] :
( ( ( ~ ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(212,plain,
! [SV19: term > $o] :
( ( ( ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) ) )
= $false )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(213,plain,
! [SV20: term > $o] :
( ( ( ! [SY255: term] :
( ~ ( SV20 @ ( sK13_SY202 @ SV20 ) )
| ~ ( SV20 @ SY255 )
| ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ SY255 ) ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[201]) ).
thf(214,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK11_SY202 @ SV20 ) )
| ~ ( SV20 @ ( sK14_SY253 @ SV20 ) )
| ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[202]) ).
thf(215,plain,
! [SV52: subst,SV40: term,SV21: term > $o] :
( ( ( ~ ( SV21 @ SV40 ) )
= $true )
| ( ( ! [SY246: term] :
( ~ ( var @ SY246 )
| ( SV21 @ ( sub @ SY246 @ ( push @ SV40 @ SV52 ) ) ) ) )
= $true )
| ( ( var @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(216,plain,
! [SV52: subst,SV40: term,SV21: term > $o] :
( ( ( SV21 @ SV40 )
= $false )
| ( ( ! [SY246: term] :
( ~ ( var @ SY246 )
| ( SV21 @ ( sub @ SY246 @ ( push @ SV40 @ SV52 ) ) ) ) )
= $true )
| ( ( SV21 @ ( sub @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) @ SV52 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(217,plain,
! [SV22: term > $o,SV58: term] :
( ( ( ~ ( var @ SV58 )
| ( SV22 @ SV58 ) )
= $true )
| ( ( var @ ( sK10_SY211 @ SV22 ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(218,plain,
! [SV22: term > $o] :
( ( ( SV22 @ ( sK10_SY211 @ SV22 ) )
= $true )
| ( ( ! [SY212: term] :
( ~ ( var @ SY212 )
| ( SV22 @ SY212 ) ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(219,plain,
! [SV22: term > $o,SV59: term] :
( ( ( ~ ( var @ SV59 )
| ( SV22 @ SV59 ) )
= $true )
| ( ( SV22 @ ( sub @ ( sK10_SY211 @ SV22 ) @ sh ) )
= $false )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(220,plain,
! [SV26: term > $o] :
( ( ( ! [SY256: term] :
( ~ ( SV26 @ ( sK15_SY219 @ SV26 ) )
| ~ ( SV26 @ SY256 )
| ( SV26 @ ( ap @ ( sK15_SY219 @ SV26 ) @ SY256 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[208]) ).
thf(221,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK12_SY219 @ SV26 ) )
| ~ ( SV26 @ ( sK16_SY254 @ SV26 ) )
| ( SV26 @ ( ap @ ( sK12_SY219 @ SV26 ) @ ( sK16_SY254 @ SV26 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[209]) ).
thf(222,plain,
! [SV19: term > $o] :
( ( ( ~ ! [SY257: term] :
( ~ ( SV19 @ SY257 )
| ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SY257 @ id ) ) ) )
| ( SV19 @ ( lam @ ( sK17_SY196 @ SV19 ) ) ) )
= $false )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[210]) ).
thf(223,plain,
! [SV19: term > $o] :
( ( ( ! [SY196: term] :
( ~ ! [SY197: term] :
( ~ ( SV19 @ SY197 )
| ( SV19 @ ( sub @ SY196 @ ( push @ SY197 @ id ) ) ) )
| ( SV19 @ ( lam @ SY196 ) ) ) )
= $false )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(224,plain,
! [SV19: term > $o] :
( ( ( ~ ! [SY258: term] :
( ~ ( SV19 @ SY258 )
| ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SY258 @ id ) ) ) )
| ( SV19 @ ( lam @ ( sK18_SY196 @ SV19 ) ) ) )
= $false )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[212]) ).
thf(225,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK13_SY202 @ SV20 ) )
| ~ ( SV20 @ ( sK19_SY255 @ SV20 ) )
| ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[213]) ).
thf(226,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK11_SY202 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(227,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK14_SY253 @ SV20 ) )
| ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(228,plain,
! [SV52: subst,SV40: term,SV21: term > $o] :
( ( ( SV21 @ SV40 )
= $false )
| ( ( ! [SY246: term] :
( ~ ( var @ SY246 )
| ( SV21 @ ( sub @ SY246 @ ( push @ SV40 @ SV52 ) ) ) ) )
= $true )
| ( ( var @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(229,plain,
! [SV52: subst,SV40: term,SV21: term > $o,SV60: term] :
( ( ( ~ ( var @ SV60 )
| ( SV21 @ ( sub @ SV60 @ ( push @ SV40 @ SV52 ) ) ) )
= $true )
| ( ( SV21 @ SV40 )
= $false )
| ( ( SV21 @ ( sub @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) @ SV52 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(230,plain,
! [SV22: term > $o,SV58: term] :
( ( ( ~ ( var @ SV58 ) )
= $true )
| ( ( SV22 @ SV58 )
= $true )
| ( ( var @ ( sK10_SY211 @ SV22 ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(231,plain,
! [SV22: term > $o,SV61: term] :
( ( ( ~ ( var @ SV61 )
| ( SV22 @ SV61 ) )
= $true )
| ( ( SV22 @ ( sK10_SY211 @ SV22 ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(232,plain,
! [SV22: term > $o,SV59: term] :
( ( ( ~ ( var @ SV59 ) )
= $true )
| ( ( SV22 @ SV59 )
= $true )
| ( ( SV22 @ ( sub @ ( sK10_SY211 @ SV22 ) @ sh ) )
= $false )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(233,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK15_SY219 @ SV26 ) )
| ~ ( SV26 @ ( sK20_SY256 @ SV26 ) )
| ( SV26 @ ( ap @ ( sK15_SY219 @ SV26 ) @ ( sK20_SY256 @ SV26 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[220]) ).
thf(234,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK12_SY219 @ SV26 ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(235,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK16_SY254 @ SV26 ) )
| ( SV26 @ ( ap @ ( sK12_SY219 @ SV26 ) @ ( sK16_SY254 @ SV26 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[221]) ).
thf(236,plain,
! [SV19: term > $o] :
( ( ( ~ ! [SY257: term] :
( ~ ( SV19 @ SY257 )
| ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SY257 @ id ) ) ) ) )
= $false )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(237,plain,
! [SV19: term > $o] :
( ( ( SV19 @ ( lam @ ( sK17_SY196 @ SV19 ) ) )
= $false )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[222]) ).
thf(238,plain,
! [SV19: term > $o] :
( ( ( ~ ! [SY259: term] :
( ~ ( SV19 @ SY259 )
| ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SY259 @ id ) ) ) )
| ( SV19 @ ( lam @ ( sK21_SY196 @ SV19 ) ) ) )
= $false )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[223]) ).
thf(239,plain,
! [SV19: term > $o] :
( ( ( ~ ! [SY258: term] :
( ~ ( SV19 @ SY258 )
| ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SY258 @ id ) ) ) ) )
= $false )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(240,plain,
! [SV19: term > $o] :
( ( ( SV19 @ ( lam @ ( sK18_SY196 @ SV19 ) ) )
= $false )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(241,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK13_SY202 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(242,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK19_SY255 @ SV20 ) )
| ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(243,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( sK11_SY202 @ SV20 ) )
= $true )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(244,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(245,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(246,plain,
! [SV52: subst,SV40: term,SV21: term > $o,SV62: term] :
( ( ( ~ ( var @ SV62 )
| ( SV21 @ ( sub @ SV62 @ ( push @ SV40 @ SV52 ) ) ) )
= $true )
| ( ( SV21 @ SV40 )
= $false )
| ( ( var @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(247,plain,
! [SV52: subst,SV40: term,SV21: term > $o,SV60: term] :
( ( ( ~ ( var @ SV60 ) )
= $true )
| ( ( SV21 @ ( sub @ SV60 @ ( push @ SV40 @ SV52 ) ) )
= $true )
| ( ( SV21 @ SV40 )
= $false )
| ( ( SV21 @ ( sub @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) @ SV52 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(248,plain,
! [SV22: term > $o,SV58: term] :
( ( ( var @ SV58 )
= $false )
| ( ( SV22 @ SV58 )
= $true )
| ( ( var @ ( sK10_SY211 @ SV22 ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(249,plain,
! [SV22: term > $o,SV61: term] :
( ( ( ~ ( var @ SV61 ) )
= $true )
| ( ( SV22 @ SV61 )
= $true )
| ( ( SV22 @ ( sK10_SY211 @ SV22 ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(250,plain,
! [SV22: term > $o,SV59: term] :
( ( ( var @ SV59 )
= $false )
| ( ( SV22 @ SV59 )
= $true )
| ( ( SV22 @ ( sub @ ( sK10_SY211 @ SV22 ) @ sh ) )
= $false )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(251,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK15_SY219 @ SV26 ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(252,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK20_SY256 @ SV26 ) )
| ( SV26 @ ( ap @ ( sK15_SY219 @ SV26 ) @ ( sK20_SY256 @ SV26 ) ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(253,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK12_SY219 @ SV26 ) )
= $true )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(254,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK16_SY254 @ SV26 ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(255,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( ap @ ( sK12_SY219 @ SV26 ) @ ( sK16_SY254 @ SV26 ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(256,plain,
! [SV19: term > $o] :
( ( ( ! [SY257: term] :
( ~ ( SV19 @ SY257 )
| ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SY257 @ id ) ) ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(257,plain,
! [SV63: term,SV19: term > $o] :
( ( ( ! [SY260: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY260 ) ) )
| ( SV19 @ ( sub @ SV63 @ SY260 ) ) ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK17_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(258,plain,
! [SV19: term > $o] :
( ( ( ~ ! [SY259: term] :
( ~ ( SV19 @ SY259 )
| ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SY259 @ id ) ) ) ) )
= $false )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(259,plain,
! [SV19: term > $o] :
( ( ( SV19 @ ( lam @ ( sK21_SY196 @ SV19 ) ) )
= $false )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(260,plain,
! [SV19: term > $o] :
( ( ( ! [SY258: term] :
( ~ ( SV19 @ SY258 )
| ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SY258 @ id ) ) ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[239]) ).
thf(261,plain,
! [SV64: term,SV19: term > $o] :
( ( ( ! [SY262: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY262 ) ) )
| ( SV19 @ ( sub @ SV64 @ SY262 ) ) ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK18_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(262,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( sK13_SY202 @ SV20 ) )
= $true )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[241]) ).
thf(263,plain,
! [SV20: term > $o] :
( ( ( ~ ( SV20 @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(264,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(265,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK11_SY202 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(266,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( sK14_SY253 @ SV20 ) )
= $true )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(267,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(268,plain,
! [SV52: subst,SV40: term,SV21: term > $o,SV62: term] :
( ( ( ~ ( var @ SV62 ) )
= $true )
| ( ( SV21 @ ( sub @ SV62 @ ( push @ SV40 @ SV52 ) ) )
= $true )
| ( ( SV21 @ SV40 )
= $false )
| ( ( var @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(269,plain,
! [SV52: subst,SV40: term,SV21: term > $o,SV60: term] :
( ( ( var @ SV60 )
= $false )
| ( ( SV21 @ ( sub @ SV60 @ ( push @ SV40 @ SV52 ) ) )
= $true )
| ( ( SV21 @ SV40 )
= $false )
| ( ( SV21 @ ( sub @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) @ SV52 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(270,plain,
! [SV22: term > $o,SV61: term] :
( ( ( var @ SV61 )
= $false )
| ( ( SV22 @ SV61 )
= $true )
| ( ( SV22 @ ( sK10_SY211 @ SV22 ) )
= $true )
| ( ( SV22 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(271,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK15_SY219 @ SV26 ) )
= $true )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(272,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK20_SY256 @ SV26 ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(273,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( ap @ ( sK15_SY219 @ SV26 ) @ ( sK20_SY256 @ SV26 ) ) )
= $false )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(274,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) ) )
= $true )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK12_SY219 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(275,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK16_SY254 @ SV26 ) )
= $true )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(276,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) ) )
= $true )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK12_SY219 @ SV26 ) @ ( sK16_SY254 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[255]) ).
thf(277,plain,
! [SV65: term,SV19: term > $o] :
( ( ( ~ ( SV19 @ SV65 )
| ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SV65 @ id ) ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(278,plain,
! [SV63: term,SV66: subst,SV19: term > $o] :
( ( ( ~ ! [SY264: term] :
( ~ ( var @ SY264 )
| ( SV19 @ ( sub @ SY264 @ SV66 ) ) )
| ( SV19 @ ( sub @ SV63 @ SV66 ) ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK17_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(279,plain,
! [SV19: term > $o] :
( ( ( ! [SY259: term] :
( ~ ( SV19 @ SY259 )
| ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SY259 @ id ) ) ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(280,plain,
! [SV67: term,SV19: term > $o] :
( ( ( ! [SY265: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY265 ) ) )
| ( SV19 @ ( sub @ SV67 @ SY265 ) ) ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK21_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(281,plain,
! [SV68: term,SV19: term > $o] :
( ( ( ~ ( SV19 @ SV68 )
| ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SV68 @ id ) ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(282,plain,
! [SV64: term,SV69: subst,SV19: term > $o] :
( ( ( ~ ! [SY267: term] :
( ~ ( var @ SY267 )
| ( SV19 @ ( sub @ SY267 @ SV69 ) ) )
| ( SV19 @ ( sub @ SV64 @ SV69 ) ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK18_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(283,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK13_SY202 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(284,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( sK19_SY255 @ SV20 ) )
= $true )
| ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) )
| ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[263]) ).
thf(285,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(286,plain,
! [SV20: term > $o] :
( ( ( ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK11_SY202 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(287,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK14_SY253 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(288,plain,
! [SV20: term > $o] :
( ( ( ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(289,plain,
! [SV52: subst,SV40: term,SV21: term > $o,SV62: term] :
( ( ( var @ SV62 )
= $false )
| ( ( SV21 @ ( sub @ SV62 @ ( push @ SV40 @ SV52 ) ) )
= $true )
| ( ( SV21 @ SV40 )
= $false )
| ( ( var @ ( sK9_SY245 @ SV40 @ SV52 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(290,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) ) )
= $true )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK15_SY219 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(291,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK20_SY256 @ SV26 ) )
= $true )
| ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) )
| ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(292,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) ) )
= $true )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK15_SY219 @ SV26 ) @ ( sK20_SY256 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(293,plain,
! [SV26: term > $o] :
( ( ( ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK12_SY219 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(294,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) ) )
= $true )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK16_SY254 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(295,plain,
! [SV26: term > $o] :
( ( ( ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK12_SY219 @ SV26 ) @ ( sK16_SY254 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(296,plain,
! [SV65: term,SV19: term > $o] :
( ( ( ~ ( SV19 @ SV65 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(297,plain,
! [SV63: term,SV66: subst,SV19: term > $o] :
( ( ( ~ ! [SY264: term] :
( ~ ( var @ SY264 )
| ( SV19 @ ( sub @ SY264 @ SV66 ) ) ) )
= $true )
| ( ( SV19 @ ( sub @ SV63 @ SV66 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK17_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[278]) ).
thf(298,plain,
! [SV70: term,SV19: term > $o] :
( ( ( ~ ( SV19 @ SV70 )
| ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SV70 @ id ) ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(299,plain,
! [SV67: term,SV71: subst,SV19: term > $o] :
( ( ( ~ ! [SY268: term] :
( ~ ( var @ SY268 )
| ( SV19 @ ( sub @ SY268 @ SV71 ) ) )
| ( SV19 @ ( sub @ SV67 @ SV71 ) ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK21_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(300,plain,
! [SV68: term,SV19: term > $o] :
( ( ( ~ ( SV19 @ SV68 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(301,plain,
! [SV64: term,SV69: subst,SV19: term > $o] :
( ( ( ~ ! [SY267: term] :
( ~ ( var @ SY267 )
| ( SV19 @ ( sub @ SY267 @ SV69 ) ) ) )
= $true )
| ( ( SV19 @ ( sub @ SV64 @ SV69 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK18_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(302,plain,
! [SV20: term > $o] :
( ( ( ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK13_SY202 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(303,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK19_SY255 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(304,plain,
! [SV20: term > $o] :
( ( ( ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(305,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY269: term] :
( ~ ( SV20 @ SY269 )
| ( SV20 @ ( sub @ ( sK22_SY204 @ SV20 ) @ ( push @ SY269 @ id ) ) ) )
| ( SV20 @ ( lam @ ( sK22_SY204 @ SV20 ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK11_SY202 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[286]) ).
thf(306,plain,
! [SV20: term > $o] :
( ( ( ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK14_SY253 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(307,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY270: term] :
( ~ ( SV20 @ SY270 )
| ( SV20 @ ( sub @ ( sK23_SY204 @ SV20 ) @ ( push @ SY270 @ id ) ) ) )
| ( SV20 @ ( lam @ ( sK23_SY204 @ SV20 ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[288]) ).
thf(308,plain,
! [SV26: term > $o] :
( ( ( ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK15_SY219 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(309,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) ) )
= $true )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK20_SY256 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(310,plain,
! [SV26: term > $o] :
( ( ( ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK15_SY219 @ SV26 ) @ ( sK20_SY256 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(311,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK24_SY221 @ SV26 ) )
| ( SV26 @ ( lam @ ( sK24_SY221 @ SV26 ) ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK12_SY219 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[293]) ).
thf(312,plain,
! [SV26: term > $o] :
( ( ( ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK16_SY254 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(313,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK25_SY221 @ SV26 ) )
| ( SV26 @ ( lam @ ( sK25_SY221 @ SV26 ) ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK12_SY219 @ SV26 ) @ ( sK16_SY254 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[295]) ).
thf(314,plain,
! [SV65: term,SV19: term > $o] :
( ( ( SV19 @ SV65 )
= $false )
| ( ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(315,plain,
! [SV63: term,SV66: subst,SV19: term > $o] :
( ( ( ! [SY264: term] :
( ~ ( var @ SY264 )
| ( SV19 @ ( sub @ SY264 @ SV66 ) ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV63 @ SV66 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK17_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(316,plain,
! [SV70: term,SV19: term > $o] :
( ( ( ~ ( SV19 @ SV70 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SV70 @ id ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(317,plain,
! [SV67: term,SV71: subst,SV19: term > $o] :
( ( ( ~ ! [SY268: term] :
( ~ ( var @ SY268 )
| ( SV19 @ ( sub @ SY268 @ SV71 ) ) ) )
= $true )
| ( ( SV19 @ ( sub @ SV67 @ SV71 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK21_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(318,plain,
! [SV68: term,SV19: term > $o] :
( ( ( SV19 @ SV68 )
= $false )
| ( ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(319,plain,
! [SV64: term,SV69: subst,SV19: term > $o] :
( ( ( ! [SY267: term] :
( ~ ( var @ SY267 )
| ( SV19 @ ( sub @ SY267 @ SV69 ) ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV64 @ SV69 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK18_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(320,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY271: term] :
( ~ ( SV20 @ SY271 )
| ( SV20 @ ( sub @ ( sK26_SY204 @ SV20 ) @ ( push @ SY271 @ id ) ) ) )
| ( SV20 @ ( lam @ ( sK26_SY204 @ SV20 ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK13_SY202 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[302]) ).
thf(321,plain,
! [SV20: term > $o] :
( ( ( ! [SY204: term] :
( ~ ! [SY205: term] :
( ~ ( SV20 @ SY205 )
| ( SV20 @ ( sub @ SY204 @ ( push @ SY205 @ id ) ) ) )
| ( SV20 @ ( lam @ SY204 ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK19_SY255 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(322,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY272: term] :
( ~ ( SV20 @ SY272 )
| ( SV20 @ ( sub @ ( sK27_SY204 @ SV20 ) @ ( push @ SY272 @ id ) ) ) )
| ( SV20 @ ( lam @ ( sK27_SY204 @ SV20 ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[304]) ).
thf(323,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY269: term] :
( ~ ( SV20 @ SY269 )
| ( SV20 @ ( sub @ ( sK22_SY204 @ SV20 ) @ ( push @ SY269 @ id ) ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK11_SY202 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(324,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( lam @ ( sK22_SY204 @ SV20 ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK11_SY202 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[305]) ).
thf(325,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY273: term] :
( ~ ( SV20 @ SY273 )
| ( SV20 @ ( sub @ ( sK28_SY204 @ SV20 ) @ ( push @ SY273 @ id ) ) ) )
| ( SV20 @ ( lam @ ( sK28_SY204 @ SV20 ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK14_SY253 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[306]) ).
thf(326,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY270: term] :
( ~ ( SV20 @ SY270 )
| ( SV20 @ ( sub @ ( sK23_SY204 @ SV20 ) @ ( push @ SY270 @ id ) ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(327,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( lam @ ( sK23_SY204 @ SV20 ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[307]) ).
thf(328,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK29_SY221 @ SV26 ) )
| ( SV26 @ ( lam @ ( sK29_SY221 @ SV26 ) ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK15_SY219 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[308]) ).
thf(329,plain,
! [SV26: term > $o] :
( ( ( ! [SY221: term] :
( ~ ( SV26 @ SY221 )
| ( SV26 @ ( lam @ SY221 ) ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK20_SY256 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(330,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK30_SY221 @ SV26 ) )
| ( SV26 @ ( lam @ ( sK30_SY221 @ SV26 ) ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK15_SY219 @ SV26 ) @ ( sK20_SY256 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[310]) ).
thf(331,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK24_SY221 @ SV26 ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK12_SY219 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(332,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( lam @ ( sK24_SY221 @ SV26 ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK12_SY219 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(333,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK31_SY221 @ SV26 ) )
| ( SV26 @ ( lam @ ( sK31_SY221 @ SV26 ) ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK16_SY254 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[312]) ).
thf(334,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK25_SY221 @ SV26 ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK12_SY219 @ SV26 ) @ ( sK16_SY254 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(335,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( lam @ ( sK25_SY221 @ SV26 ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK12_SY219 @ SV26 ) @ ( sK16_SY254 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(336,plain,
! [SV65: term,SV72: term,SV19: term > $o] :
( ( ( ! [SY274: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY274 ) ) )
| ( SV19 @ ( sub @ SV72 @ SY274 ) ) ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV19 @ SV65 )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(337,plain,
! [SV19: term > $o,SV66: subst,SV63: term] :
( ( ( ~ ( var @ ( sK32_SY264 @ SV63 @ SV66 @ SV19 ) )
| ( SV19 @ ( sub @ ( sK32_SY264 @ SV63 @ SV66 @ SV19 ) @ SV66 ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV63 @ SV66 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK17_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[315]) ).
thf(338,plain,
! [SV70: term,SV19: term > $o] :
( ( ( SV19 @ SV70 )
= $false )
| ( ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SV70 @ id ) ) )
= $true )
| ( ( ! [SY198: term,SY199: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY199 ) ) )
| ( SV19 @ ( sub @ SY198 @ SY199 ) ) ) )
= $true )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(339,plain,
! [SV67: term,SV71: subst,SV19: term > $o] :
( ( ( ! [SY268: term] :
( ~ ( var @ SY268 )
| ( SV19 @ ( sub @ SY268 @ SV71 ) ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV67 @ SV71 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK21_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(340,plain,
! [SV68: term,SV73: term,SV19: term > $o] :
( ( ( ! [SY276: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY276 ) ) )
| ( SV19 @ ( sub @ SV73 @ SY276 ) ) ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV19 @ SV68 )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(341,plain,
! [SV19: term > $o,SV69: subst,SV64: term] :
( ( ( ~ ( var @ ( sK33_SY267 @ SV64 @ SV69 @ SV19 ) )
| ( SV19 @ ( sub @ ( sK33_SY267 @ SV64 @ SV69 @ SV19 ) @ SV69 ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV64 @ SV69 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK18_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[319]) ).
thf(342,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY271: term] :
( ~ ( SV20 @ SY271 )
| ( SV20 @ ( sub @ ( sK26_SY204 @ SV20 ) @ ( push @ SY271 @ id ) ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK13_SY202 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(343,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( lam @ ( sK26_SY204 @ SV20 ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK13_SY202 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(344,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY278: term] :
( ~ ( SV20 @ SY278 )
| ( SV20 @ ( sub @ ( sK34_SY204 @ SV20 ) @ ( push @ SY278 @ id ) ) ) )
| ( SV20 @ ( lam @ ( sK34_SY204 @ SV20 ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK19_SY255 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[321]) ).
thf(345,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY272: term] :
( ~ ( SV20 @ SY272 )
| ( SV20 @ ( sub @ ( sK27_SY204 @ SV20 ) @ ( push @ SY272 @ id ) ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(346,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( lam @ ( sK27_SY204 @ SV20 ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(347,plain,
! [SV20: term > $o] :
( ( ( ! [SY269: term] :
( ~ ( SV20 @ SY269 )
| ( SV20 @ ( sub @ ( sK22_SY204 @ SV20 ) @ ( push @ SY269 @ id ) ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK11_SY202 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(348,plain,
! [SV74: term,SV20: term > $o] :
( ( ( SV20 @ SV74 )
= $true )
| ( ( SV20 @ ( lam @ ( sK22_SY204 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK11_SY202 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(349,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY273: term] :
( ~ ( SV20 @ SY273 )
| ( SV20 @ ( sub @ ( sK28_SY204 @ SV20 ) @ ( push @ SY273 @ id ) ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK14_SY253 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(350,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( lam @ ( sK28_SY204 @ SV20 ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK14_SY253 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[325]) ).
thf(351,plain,
! [SV20: term > $o] :
( ( ( ! [SY270: term] :
( ~ ( SV20 @ SY270 )
| ( SV20 @ ( sub @ ( sK23_SY204 @ SV20 ) @ ( push @ SY270 @ id ) ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[326]) ).
thf(352,plain,
! [SV75: term,SV20: term > $o] :
( ( ( SV20 @ SV75 )
= $true )
| ( ( SV20 @ ( lam @ ( sK23_SY204 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(353,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK29_SY221 @ SV26 ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK15_SY219 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(354,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( lam @ ( sK29_SY221 @ SV26 ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK15_SY219 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[328]) ).
thf(355,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK35_SY221 @ SV26 ) )
| ( SV26 @ ( lam @ ( sK35_SY221 @ SV26 ) ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK20_SY256 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[329]) ).
thf(356,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK30_SY221 @ SV26 ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK15_SY219 @ SV26 ) @ ( sK20_SY256 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(357,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( lam @ ( sK30_SY221 @ SV26 ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK15_SY219 @ SV26 ) @ ( sK20_SY256 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(358,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK24_SY221 @ SV26 ) )
= $true )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK12_SY219 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(359,plain,
! [SV76: term,SV26: term > $o] :
( ( ( SV26 @ SV76 )
= $true )
| ( ( SV26 @ ( lam @ ( sK24_SY221 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK12_SY219 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(360,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK31_SY221 @ SV26 ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK16_SY254 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(361,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( lam @ ( sK31_SY221 @ SV26 ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK16_SY254 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(362,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK25_SY221 @ SV26 ) )
= $true )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK12_SY219 @ SV26 ) @ ( sK16_SY254 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(363,plain,
! [SV77: term,SV26: term > $o] :
( ( ( SV26 @ SV77 )
= $true )
| ( ( SV26 @ ( lam @ ( sK25_SY221 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( ap @ ( sK12_SY219 @ SV26 ) @ ( sK16_SY254 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(364,plain,
! [SV65: term,SV72: term,SV78: subst,SV19: term > $o] :
( ( ( ~ ! [SY279: term] :
( ~ ( var @ SY279 )
| ( SV19 @ ( sub @ SY279 @ SV78 ) ) )
| ( SV19 @ ( sub @ SV72 @ SV78 ) ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV19 @ SV65 )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(365,plain,
! [SV19: term > $o,SV66: subst,SV63: term] :
( ( ( ~ ( var @ ( sK32_SY264 @ SV63 @ SV66 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV63 @ SV66 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK17_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(366,plain,
! [SV66: subst,SV63: term,SV19: term > $o] :
( ( ( SV19 @ ( sub @ ( sK32_SY264 @ SV63 @ SV66 @ SV19 ) @ SV66 ) )
= $false )
| ( ( SV19 @ ( sub @ SV63 @ SV66 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK17_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[337]) ).
thf(367,plain,
! [SV70: term,SV79: term,SV19: term > $o] :
( ( ( ! [SY280: subst] :
( ~ ! [SY200: term] :
( ~ ( var @ SY200 )
| ( SV19 @ ( sub @ SY200 @ SY280 ) ) )
| ( SV19 @ ( sub @ SV79 @ SY280 ) ) ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SV70 @ id ) ) )
= $true )
| ( ( SV19 @ SV70 )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(368,plain,
! [SV19: term > $o,SV71: subst,SV67: term] :
( ( ( ~ ( var @ ( sK36_SY268 @ SV67 @ SV71 @ SV19 ) )
| ( SV19 @ ( sub @ ( sK36_SY268 @ SV67 @ SV71 @ SV19 ) @ SV71 ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV67 @ SV71 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK21_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[339]) ).
thf(369,plain,
! [SV68: term,SV73: term,SV80: subst,SV19: term > $o] :
( ( ( ~ ! [SY282: term] :
( ~ ( var @ SY282 )
| ( SV19 @ ( sub @ SY282 @ SV80 ) ) )
| ( SV19 @ ( sub @ SV73 @ SV80 ) ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV19 @ SV68 )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(370,plain,
! [SV19: term > $o,SV69: subst,SV64: term] :
( ( ( ~ ( var @ ( sK33_SY267 @ SV64 @ SV69 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV64 @ SV69 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK18_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(371,plain,
! [SV69: subst,SV64: term,SV19: term > $o] :
( ( ( SV19 @ ( sub @ ( sK33_SY267 @ SV64 @ SV69 @ SV19 ) @ SV69 ) )
= $false )
| ( ( SV19 @ ( sub @ SV64 @ SV69 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK18_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[341]) ).
thf(372,plain,
! [SV20: term > $o] :
( ( ( ! [SY271: term] :
( ~ ( SV20 @ SY271 )
| ( SV20 @ ( sub @ ( sK26_SY204 @ SV20 ) @ ( push @ SY271 @ id ) ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK13_SY202 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(373,plain,
! [SV81: term,SV20: term > $o] :
( ( ( SV20 @ SV81 )
= $true )
| ( ( SV20 @ ( lam @ ( sK26_SY204 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK13_SY202 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(374,plain,
! [SV20: term > $o] :
( ( ( ~ ! [SY278: term] :
( ~ ( SV20 @ SY278 )
| ( SV20 @ ( sub @ ( sK34_SY204 @ SV20 ) @ ( push @ SY278 @ id ) ) ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK19_SY255 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(375,plain,
! [SV20: term > $o] :
( ( ( SV20 @ ( lam @ ( sK34_SY204 @ SV20 ) ) )
= $false )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK19_SY255 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(376,plain,
! [SV20: term > $o] :
( ( ( ! [SY272: term] :
( ~ ( SV20 @ SY272 )
| ( SV20 @ ( sub @ ( sK27_SY204 @ SV20 ) @ ( push @ SY272 @ id ) ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(377,plain,
! [SV82: term,SV20: term > $o] :
( ( ( SV20 @ SV82 )
= $true )
| ( ( SV20 @ ( lam @ ( sK27_SY204 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(378,plain,
! [SV83: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV83 )
| ( SV20 @ ( sub @ ( sK22_SY204 @ SV20 ) @ ( push @ SV83 @ id ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK11_SY202 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(379,plain,
! [SV20: term > $o] :
( ( ( ! [SY273: term] :
( ~ ( SV20 @ SY273 )
| ( SV20 @ ( sub @ ( sK28_SY204 @ SV20 ) @ ( push @ SY273 @ id ) ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK14_SY253 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[349]) ).
thf(380,plain,
! [SV84: term,SV20: term > $o] :
( ( ( SV20 @ SV84 )
= $true )
| ( ( SV20 @ ( lam @ ( sK28_SY204 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK14_SY253 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(381,plain,
! [SV85: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV85 )
| ( SV20 @ ( sub @ ( sK23_SY204 @ SV20 ) @ ( push @ SV85 @ id ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(382,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK29_SY221 @ SV26 ) )
= $true )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK15_SY219 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(383,plain,
! [SV86: term,SV26: term > $o] :
( ( ( SV26 @ SV86 )
= $true )
| ( ( SV26 @ ( lam @ ( sK29_SY221 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK15_SY219 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(384,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK35_SY221 @ SV26 ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK20_SY256 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(385,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( lam @ ( sK35_SY221 @ SV26 ) ) )
= $false )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK20_SY256 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(386,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK30_SY221 @ SV26 ) )
= $true )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK15_SY219 @ SV26 ) @ ( sK20_SY256 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(387,plain,
! [SV87: term,SV26: term > $o] :
( ( ( SV26 @ SV87 )
= $true )
| ( ( SV26 @ ( lam @ ( sK30_SY221 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( ap @ ( sK15_SY219 @ SV26 ) @ ( sK20_SY256 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(388,plain,
! [SV88: term,SV26: term > $o] :
( ( ( SV26 @ SV88 )
= $true )
| ( ( SV26 @ ( sK24_SY221 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK12_SY219 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(389,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK31_SY221 @ SV26 ) )
= $true )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK16_SY254 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[360]) ).
thf(390,plain,
! [SV89: term,SV26: term > $o] :
( ( ( SV26 @ SV89 )
= $true )
| ( ( SV26 @ ( lam @ ( sK31_SY221 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK16_SY254 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(391,plain,
! [SV90: term,SV26: term > $o] :
( ( ( SV26 @ SV90 )
= $true )
| ( ( SV26 @ ( sK25_SY221 @ SV26 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK12_SY219 @ SV26 ) @ ( sK16_SY254 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(392,plain,
! [SV65: term,SV72: term,SV78: subst,SV19: term > $o] :
( ( ( ~ ! [SY279: term] :
( ~ ( var @ SY279 )
| ( SV19 @ ( sub @ SY279 @ SV78 ) ) ) )
= $true )
| ( ( SV19 @ ( sub @ SV72 @ SV78 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV19 @ SV65 )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(393,plain,
! [SV19: term > $o,SV66: subst,SV63: term] :
( ( ( var @ ( sK32_SY264 @ SV63 @ SV66 @ SV19 ) )
= $true )
| ( ( SV19 @ ( sub @ SV63 @ SV66 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK17_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(394,plain,
! [SV70: term,SV79: term,SV91: subst,SV19: term > $o] :
( ( ( ~ ! [SY283: term] :
( ~ ( var @ SY283 )
| ( SV19 @ ( sub @ SY283 @ SV91 ) ) )
| ( SV19 @ ( sub @ SV79 @ SV91 ) ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SV70 @ id ) ) )
= $true )
| ( ( SV19 @ SV70 )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(395,plain,
! [SV19: term > $o,SV71: subst,SV67: term] :
( ( ( ~ ( var @ ( sK36_SY268 @ SV67 @ SV71 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV67 @ SV71 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK21_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(396,plain,
! [SV71: subst,SV67: term,SV19: term > $o] :
( ( ( SV19 @ ( sub @ ( sK36_SY268 @ SV67 @ SV71 @ SV19 ) @ SV71 ) )
= $false )
| ( ( SV19 @ ( sub @ SV67 @ SV71 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK21_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(397,plain,
! [SV68: term,SV73: term,SV80: subst,SV19: term > $o] :
( ( ( ~ ! [SY282: term] :
( ~ ( var @ SY282 )
| ( SV19 @ ( sub @ SY282 @ SV80 ) ) ) )
= $true )
| ( ( SV19 @ ( sub @ SV73 @ SV80 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV19 @ SV68 )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(398,plain,
! [SV19: term > $o,SV69: subst,SV64: term] :
( ( ( var @ ( sK33_SY267 @ SV64 @ SV69 @ SV19 ) )
= $true )
| ( ( SV19 @ ( sub @ SV64 @ SV69 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK18_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(399,plain,
! [SV92: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV92 )
| ( SV20 @ ( sub @ ( sK26_SY204 @ SV20 ) @ ( push @ SV92 @ id ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK13_SY202 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(400,plain,
! [SV20: term > $o] :
( ( ( ! [SY278: term] :
( ~ ( SV20 @ SY278 )
| ( SV20 @ ( sub @ ( sK34_SY204 @ SV20 ) @ ( push @ SY278 @ id ) ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK19_SY255 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(401,plain,
! [SV93: term,SV20: term > $o] :
( ( ( SV20 @ SV93 )
= $true )
| ( ( SV20 @ ( lam @ ( sK34_SY204 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK19_SY255 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(402,plain,
! [SV94: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV94 )
| ( SV20 @ ( sub @ ( sK27_SY204 @ SV20 ) @ ( push @ SV94 @ id ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(403,plain,
! [SV83: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV83 ) )
= $true )
| ( ( SV20 @ ( sub @ ( sK22_SY204 @ SV20 ) @ ( push @ SV83 @ id ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK11_SY202 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(404,plain,
! [SV95: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV95 )
| ( SV20 @ ( sub @ ( sK28_SY204 @ SV20 ) @ ( push @ SV95 @ id ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK14_SY253 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(405,plain,
! [SV85: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV85 ) )
= $true )
| ( ( SV20 @ ( sub @ ( sK23_SY204 @ SV20 ) @ ( push @ SV85 @ id ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(406,plain,
! [SV96: term,SV26: term > $o] :
( ( ( SV26 @ SV96 )
= $true )
| ( ( SV26 @ ( sK29_SY221 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK15_SY219 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(407,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK35_SY221 @ SV26 ) )
= $true )
| ( ( ! [SY222: term] : ( SV26 @ SY222 ) )
= $true )
| ( ( SV26 @ ( sK20_SY256 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(408,plain,
! [SV97: term,SV26: term > $o] :
( ( ( SV26 @ SV97 )
= $true )
| ( ( SV26 @ ( lam @ ( sK35_SY221 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK20_SY256 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(409,plain,
! [SV98: term,SV26: term > $o] :
( ( ( SV26 @ SV98 )
= $true )
| ( ( SV26 @ ( sK30_SY221 @ SV26 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK15_SY219 @ SV26 ) @ ( sK20_SY256 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(410,plain,
! [SV99: term,SV26: term > $o] :
( ( ( SV26 @ SV99 )
= $true )
| ( ( SV26 @ ( sK31_SY221 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK16_SY254 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK6_SY218 @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(411,plain,
! [SV65: term,SV72: term,SV78: subst,SV19: term > $o] :
( ( ( ! [SY279: term] :
( ~ ( var @ SY279 )
| ( SV19 @ ( sub @ SY279 @ SV78 ) ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV72 @ SV78 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV19 @ SV65 )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(412,plain,
! [SV70: term,SV79: term,SV91: subst,SV19: term > $o] :
( ( ( ~ ! [SY283: term] :
( ~ ( var @ SY283 )
| ( SV19 @ ( sub @ SY283 @ SV91 ) ) ) )
= $true )
| ( ( SV19 @ ( sub @ SV79 @ SV91 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SV70 @ id ) ) )
= $true )
| ( ( SV19 @ SV70 )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(413,plain,
! [SV19: term > $o,SV71: subst,SV67: term] :
( ( ( var @ ( sK36_SY268 @ SV67 @ SV71 @ SV19 ) )
= $true )
| ( ( SV19 @ ( sub @ SV67 @ SV71 ) )
= $true )
| ( ( SV19 @ ( lam @ ( sK21_SY196 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(414,plain,
! [SV68: term,SV73: term,SV80: subst,SV19: term > $o] :
( ( ( ! [SY282: term] :
( ~ ( var @ SY282 )
| ( SV19 @ ( sub @ SY282 @ SV80 ) ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV73 @ SV80 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV19 @ SV68 )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(415,plain,
! [SV92: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV92 ) )
= $true )
| ( ( SV20 @ ( sub @ ( sK26_SY204 @ SV20 ) @ ( push @ SV92 @ id ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK13_SY202 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(416,plain,
! [SV100: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV100 )
| ( SV20 @ ( sub @ ( sK34_SY204 @ SV20 ) @ ( push @ SV100 @ id ) ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK19_SY255 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(417,plain,
! [SV94: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV94 ) )
= $true )
| ( ( SV20 @ ( sub @ ( sK27_SY204 @ SV20 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(418,plain,
! [SV83: term,SV20: term > $o] :
( ( ( SV20 @ SV83 )
= $false )
| ( ( SV20 @ ( sub @ ( sK22_SY204 @ SV20 ) @ ( push @ SV83 @ id ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK11_SY202 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(419,plain,
! [SV95: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV95 ) )
= $true )
| ( ( SV20 @ ( sub @ ( sK28_SY204 @ SV20 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK14_SY253 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(420,plain,
! [SV85: term,SV20: term > $o] :
( ( ( SV20 @ SV85 )
= $false )
| ( ( SV20 @ ( sub @ ( sK23_SY204 @ SV20 ) @ ( push @ SV85 @ id ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(421,plain,
! [SV101: term,SV26: term > $o] :
( ( ( SV26 @ SV101 )
= $true )
| ( ( SV26 @ ( sK35_SY221 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK20_SY256 @ SV26 ) )
= $true )
| ( ( var @ ( sK6_SY218 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(422,plain,
! [SV19: term > $o,SV78: subst,SV72: term,SV65: term] :
( ( ( ~ ( var @ ( sK37_SY279 @ SV65 @ SV72 @ SV78 @ SV19 ) )
| ( SV19 @ ( sub @ ( sK37_SY279 @ SV65 @ SV72 @ SV78 @ SV19 ) @ SV78 ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV72 @ SV78 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV19 @ SV65 )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[411]) ).
thf(423,plain,
! [SV70: term,SV79: term,SV91: subst,SV19: term > $o] :
( ( ( ! [SY283: term] :
( ~ ( var @ SY283 )
| ( SV19 @ ( sub @ SY283 @ SV91 ) ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV79 @ SV91 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SV70 @ id ) ) )
= $true )
| ( ( SV19 @ SV70 )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(424,plain,
! [SV19: term > $o,SV80: subst,SV73: term,SV68: term] :
( ( ( ~ ( var @ ( sK38_SY282 @ SV68 @ SV73 @ SV80 @ SV19 ) )
| ( SV19 @ ( sub @ ( sK38_SY282 @ SV68 @ SV73 @ SV80 @ SV19 ) @ SV80 ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV73 @ SV80 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV19 @ SV68 )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[414]) ).
thf(425,plain,
! [SV92: term,SV20: term > $o] :
( ( ( SV20 @ SV92 )
= $false )
| ( ( SV20 @ ( sub @ ( sK26_SY204 @ SV20 ) @ ( push @ SV92 @ id ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK13_SY202 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(426,plain,
! [SV100: term,SV20: term > $o] :
( ( ( ~ ( SV20 @ SV100 ) )
= $true )
| ( ( SV20 @ ( sub @ ( sK34_SY204 @ SV20 ) @ ( push @ SV100 @ id ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK19_SY255 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(427,plain,
! [SV94: term,SV20: term > $o] :
( ( ( SV20 @ SV94 )
= $false )
| ( ( SV20 @ ( sub @ ( sK27_SY204 @ SV20 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(428,plain,
! [SV83: term,SV102: term,SV20: term > $o] :
( ( ( SV20 @ SV102 )
= $true )
| ( ( SV20 @ ( sub @ ( sK22_SY204 @ SV20 ) @ ( push @ SV83 @ id ) ) )
= $true )
| ( ( SV20 @ SV83 )
= $false )
| ( ( SV20 @ ( sK11_SY202 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(429,plain,
! [SV95: term,SV20: term > $o] :
( ( ( SV20 @ SV95 )
= $false )
| ( ( SV20 @ ( sub @ ( sK28_SY204 @ SV20 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK14_SY253 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(430,plain,
! [SV85: term,SV103: term,SV20: term > $o] :
( ( ( SV20 @ SV103 )
= $true )
| ( ( SV20 @ ( sub @ ( sK23_SY204 @ SV20 ) @ ( push @ SV85 @ id ) ) )
= $true )
| ( ( SV20 @ SV85 )
= $false )
| ( ( SV20 @ ( ap @ ( sK11_SY202 @ SV20 ) @ ( sK14_SY253 @ SV20 ) ) )
= $false )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(431,plain,
! [SV19: term > $o,SV78: subst,SV72: term,SV65: term] :
( ( ( ~ ( var @ ( sK37_SY279 @ SV65 @ SV72 @ SV78 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV72 @ SV78 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV19 @ SV65 )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(432,plain,
! [SV78: subst,SV72: term,SV65: term,SV19: term > $o] :
( ( ( SV19 @ ( sub @ ( sK37_SY279 @ SV65 @ SV72 @ SV78 @ SV19 ) @ SV78 ) )
= $false )
| ( ( SV19 @ ( sub @ SV72 @ SV78 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV19 @ SV65 )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(433,plain,
! [SV19: term > $o,SV91: subst,SV79: term,SV70: term] :
( ( ( ~ ( var @ ( sK39_SY283 @ SV70 @ SV79 @ SV91 @ SV19 ) )
| ( SV19 @ ( sub @ ( sK39_SY283 @ SV70 @ SV79 @ SV91 @ SV19 ) @ SV91 ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV79 @ SV91 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SV70 @ id ) ) )
= $true )
| ( ( SV19 @ SV70 )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[423]) ).
thf(434,plain,
! [SV19: term > $o,SV80: subst,SV73: term,SV68: term] :
( ( ( ~ ( var @ ( sK38_SY282 @ SV68 @ SV73 @ SV80 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV73 @ SV80 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV19 @ SV68 )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(435,plain,
! [SV80: subst,SV73: term,SV68: term,SV19: term > $o] :
( ( ( SV19 @ ( sub @ ( sK38_SY282 @ SV68 @ SV73 @ SV80 @ SV19 ) @ SV80 ) )
= $false )
| ( ( SV19 @ ( sub @ SV73 @ SV80 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV19 @ SV68 )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(436,plain,
! [SV92: term,SV104: term,SV20: term > $o] :
( ( ( SV20 @ SV104 )
= $true )
| ( ( SV20 @ ( sub @ ( sK26_SY204 @ SV20 ) @ ( push @ SV92 @ id ) ) )
= $true )
| ( ( SV20 @ SV92 )
= $false )
| ( ( SV20 @ ( sK13_SY202 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(437,plain,
! [SV100: term,SV20: term > $o] :
( ( ( SV20 @ SV100 )
= $false )
| ( ( SV20 @ ( sub @ ( sK34_SY204 @ SV20 ) @ ( push @ SV100 @ id ) ) )
= $true )
| ( ( ! [SY206: term] : ( SV20 @ SY206 ) )
= $true )
| ( ( SV20 @ ( sK19_SY255 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(438,plain,
! [SV94: term,SV105: term,SV20: term > $o] :
( ( ( SV20 @ SV105 )
= $true )
| ( ( SV20 @ ( sub @ ( sK27_SY204 @ SV20 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( SV20 @ SV94 )
= $false )
| ( ( SV20 @ ( ap @ ( sK13_SY202 @ SV20 ) @ ( sK19_SY255 @ SV20 ) ) )
= $false )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(439,plain,
! [SV95: term,SV106: term,SV20: term > $o] :
( ( ( SV20 @ SV106 )
= $true )
| ( ( SV20 @ ( sub @ ( sK28_SY204 @ SV20 ) @ ( push @ SV95 @ id ) ) )
= $true )
| ( ( SV20 @ SV95 )
= $false )
| ( ( SV20 @ ( sK14_SY253 @ SV20 ) )
= $true )
| ( ( SV20 @ ( sK4_SY201 @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(440,plain,
! [SV19: term > $o,SV78: subst,SV72: term,SV65: term] :
( ( ( var @ ( sK37_SY279 @ SV65 @ SV72 @ SV78 @ SV19 ) )
= $true )
| ( ( SV19 @ ( sub @ SV72 @ SV78 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK17_SY196 @ SV19 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV19 @ SV65 )
= $false )
| ( ( SV19 @ ( sK3_SY194 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[431]) ).
thf(441,plain,
! [SV19: term > $o,SV91: subst,SV79: term,SV70: term] :
( ( ( ~ ( var @ ( sK39_SY283 @ SV70 @ SV79 @ SV91 @ SV19 ) ) )
= $false )
| ( ( SV19 @ ( sub @ SV79 @ SV91 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SV70 @ id ) ) )
= $true )
| ( ( SV19 @ SV70 )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(442,plain,
! [SV91: subst,SV79: term,SV70: term,SV19: term > $o] :
( ( ( SV19 @ ( sub @ ( sK39_SY283 @ SV70 @ SV79 @ SV91 @ SV19 ) @ SV91 ) )
= $false )
| ( ( SV19 @ ( sub @ SV79 @ SV91 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SV70 @ id ) ) )
= $true )
| ( ( SV19 @ SV70 )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(443,plain,
! [SV19: term > $o,SV80: subst,SV73: term,SV68: term] :
( ( ( var @ ( sK38_SY282 @ SV68 @ SV73 @ SV80 @ SV19 ) )
= $true )
| ( ( SV19 @ ( sub @ SV73 @ SV80 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK18_SY196 @ SV19 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV19 @ SV68 )
= $false )
| ( ( SV19 @ ( ap @ ( sK3_SY194 @ SV19 ) @ ( sK7_SY251 @ SV19 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[434]) ).
thf(444,plain,
! [SV100: term,SV107: term,SV20: term > $o] :
( ( ( SV20 @ SV107 )
= $true )
| ( ( SV20 @ ( sub @ ( sK34_SY204 @ SV20 ) @ ( push @ SV100 @ id ) ) )
= $true )
| ( ( SV20 @ SV100 )
= $false )
| ( ( SV20 @ ( sK19_SY255 @ SV20 ) )
= $true )
| ( ( var @ ( sK4_SY201 @ SV20 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(445,plain,
! [SV19: term > $o,SV91: subst,SV79: term,SV70: term] :
( ( ( var @ ( sK39_SY283 @ SV70 @ SV79 @ SV91 @ SV19 ) )
= $true )
| ( ( SV19 @ ( sub @ SV79 @ SV91 ) )
= $true )
| ( ( SV19 @ ( sub @ ( sK21_SY196 @ SV19 ) @ ( push @ SV70 @ id ) ) )
= $true )
| ( ( SV19 @ SV70 )
= $false )
| ( ( SV19 @ ( sK7_SY251 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[441]) ).
thf(446,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[55,445,444,443,442,440,439,438,436,435,432,430,428,421,413,410,409,408,406,401,398,396,393,391,390,388,387,383,380,377,373,371,366,363,359,352,348,289,270,269,250,248,195,185,182,180,163,162,157,148,140,139,138,137,136,135,134,120,119,117,113,96,93,89,88,84,83,81,57]) ).
thf(447,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG256^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n026.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 18:12:32 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.59/0.55
% 1.59/0.55 No.of.Axioms: 0
% 1.59/0.55
% 1.59/0.55 Length.of.Defs: 38205
% 1.59/0.55
% 1.59/0.55 Contains.Choice.Funs: false
% 1.59/0.55 ...............
% 1.59/0.55
% 1.59/0.55 ********************************
% 1.59/0.55 * All subproblems solved! *
% 1.59/0.55 ********************************
% 1.59/0.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:31,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:446,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.59/0.55
% 1.59/0.55 %**** Beginning of derivation protocol ****
% 1.59/0.55 % SZS output start CNFRefutation
% See solution above
% 1.59/0.56
% 1.59/0.56 %**** End of derivation protocol ****
% 1.59/0.56 %**** no. of clauses in derivation: 447 ****
% 1.59/0.56 %**** clause counter: 446 ****
% 1.59/0.56
% 1.59/0.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:31,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:446,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------