%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG264^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 10:08:43 AM UTC 2026
% Result : Theorem 1.79s 0.59s
% Output : CNFRefutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 114
% Syntax : Number of formulae : 707 ( 335 unt; 0 typ; 113 def)
% Number of atoms : 5067 (1941 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 13998 (1831 ~;1742 |; 51 &;9203 @)
% ( 5 <=>;1166 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 555 ( 555 >; 0 *; 0 +; 0 <<)
% Number of symbols : 155 ( 152 usr; 115 con; 0-4 aty)
% Number of variables : 2137 ( 39 ^;2093 !; 5 ?;2137 :)
% 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_B,type,
sK10_B: subst > term > ( term > $o ) > term ).
thf(tp_sK11_B,type,
sK11_B: subst > term > ( term > $o ) > term ).
thf(tp_sK12_A,type,
sK12_A: ( term > $o ) > term ).
thf(tp_sK13_A,type,
sK13_A: ( term > $o ) > term ).
thf(tp_sK14_SY336,type,
sK14_SY336: ( term > $o ) > term ).
thf(tp_sK15_A,type,
sK15_A: ( term > $o ) > term ).
thf(tp_sK16_A,type,
sK16_A: ( term > $o ) > term ).
thf(tp_sK17_SY338,type,
sK17_SY338: ( term > $o ) > term ).
thf(tp_sK18_A,type,
sK18_A: ( term > $o ) > term ).
thf(tp_sK19_M,type,
sK19_M: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(tp_sK1_SY167,type,
sK1_SY167: subst > term > subst > $o ).
thf(tp_sK20_SY339,type,
sK20_SY339: ( subst > term > term ) > ( subst > term > term ) > term ).
thf(tp_sK21_SY341,type,
sK21_SY341: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(tp_sK22_M,type,
sK22_M: ( subst > term > term ) > subst ).
thf(tp_sK23_SY342,type,
sK23_SY342: ( subst > term > term ) > term ).
thf(tp_sK24_SY344,type,
sK24_SY344: ( subst > term > term ) > subst ).
thf(tp_sK25_M,type,
sK25_M: ( subst > term > term ) > subst ).
thf(tp_sK26_SY345,type,
sK26_SY345: ( subst > term > term ) > term ).
thf(tp_sK27_SY347,type,
sK27_SY347: ( subst > term > term ) > subst ).
thf(tp_sK28_M,type,
sK28_M: ( subst > term > term ) > subst ).
thf(tp_sK29_SY348,type,
sK29_SY348: ( subst > term > term ) > term ).
thf(tp_sK2_SY324,type,
sK2_SY324: term > $o ).
thf(tp_sK30_SY350,type,
sK30_SY350: ( subst > term > term ) > subst ).
thf(tp_sK3_SY331,type,
sK3_SY331: term ).
thf(tp_sK4_SY333,type,
sK4_SY333: term ).
thf(tp_sK5_A,type,
sK5_A: ( term > $o ) > term ).
thf(tp_sK6_A,type,
sK6_A: ( term > $o ) > term ).
thf(tp_sK7_A,type,
sK7_A: ( term > $o ) > term ).
thf(tp_sK8_SY334,type,
sK8_SY334: ( term > $o ) > term ).
thf(tp_sK9_A,type,
sK9_A: ( term > $o ) > term ).
thf(tp_sh,type,
sh: subst ).
thf(tp_shinj,type,
shinj: $o ).
thf(tp_sub,type,
sub: term > subst > term ).
thf(tp_substmonoid,type,
substmonoid: $o ).
thf(tp_substmonoid_gthm,type,
substmonoid_gthm: $o ).
thf(tp_substmonoid_lthm,type,
substmonoid_lthm: $o ).
thf(tp_termmset,type,
termmset: $o ).
thf(tp_termmset_gthm,type,
termmset_gthm: $o ).
thf(tp_termmset_lthm,type,
termmset_lthm: $o ).
thf(tp_ulamvar1,type,
ulamvar1: $o ).
thf(tp_ulamvarind,type,
ulamvarind: $o ).
thf(tp_ulamvarsh,type,
ulamvarsh: $o ).
thf(tp_var,type,
var: term > $o ).
thf(apinj1,definition,
( apinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apinj1) ).
thf(apinj2,definition,
( apinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apinj2) ).
thf(apnotvar,definition,
( apnotvar
= ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apnotvar) ).
thf(axabs,definition,
( axabs
= ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axabs) ).
thf(axapp,definition,
( axapp
= ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axapp) ).
thf(axassoc,definition,
( axassoc
= ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axassoc) ).
thf(axclos,definition,
( axclos
= ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axclos) ).
thf(axidl,definition,
( axidl
= ( ! [M: subst] :
( ( comp @ id @ M )
= M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axidl) ).
thf(axidr,definition,
( axidr
= ( ! [M: subst] :
( ( comp @ M @ id )
= M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axidr) ).
thf(axmap,definition,
( axmap
= ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axmap) ).
thf(axscons,definition,
( axscons
= ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axscons) ).
thf(axshiftcons,definition,
( axshiftcons
= ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axshiftcons) ).
thf(axvarcons,definition,
( axvarcons
= ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarcons) ).
thf(axvarid,definition,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarid) ).
thf(axvarshift,definition,
( axvarshift
= ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarshift) ).
thf(hoasap,definition,
( hoasap
= ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasap) ).
thf(hoasapinj1,definition,
( hoasapinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj1) ).
thf(hoasapinj1_gthm,definition,
( hoasapinj1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> hoasapinj1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj1_gthm) ).
thf(hoasapinj1_lthm,definition,
( hoasapinj1_lthm
= ( axvarid
=> ( apinj1
=> hoasapinj1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj1_lthm) ).
thf(hoasapinj2,definition,
( hoasapinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj2) ).
thf(hoasapinj2_gthm,definition,
( hoasapinj2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> hoasapinj2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj2_gthm) ).
thf(hoasapinj2_lthm,definition,
( hoasapinj2_lthm
= ( apinj2
=> hoasapinj2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj2_lthm) ).
thf(hoasapnotvar,definition,
( hoasapnotvar
= ( ! [A: term,B: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapnotvar) ).
thf(hoasapnotvar_gthm,definition,
( hoasapnotvar_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapnotvar_gthm) ).
thf(hoasapnotvar_lthm,definition,
( hoasapnotvar_lthm
= ( axvarid
=> ( apnotvar
=> hoasapnotvar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapnotvar_lthm) ).
thf(hoasinduction,definition,
( hoasinduction
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] : ( P @ id @ A @ id ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction) ).
thf(hoasinduction_gthm,definition,
( hoasinduction_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_gthm) ).
thf(hoasinduction_lem0,definition,
( hoasinduction_lem0
= ( ! [P: subst > term > subst > $o] :
? [Q: term > $o] : ( hoasinduction_p_and_p_prime @ P @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem0) ).
thf(hoasinduction_lem0_lthm,definition,
hoasinduction_lem0_lthm = hoasinduction_lem0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem0_lthm) ).
thf(hoasinduction_lem1,definition,
( hoasinduction_lem1
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ id @ A @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1) ).
thf(hoasinduction_lem1_gthm,definition,
( hoasinduction_lem1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1_gthm) ).
thf(hoasinduction_lem1_lthm,definition,
( hoasinduction_lem1_lthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1_lthm) ).
thf(hoasinduction_lem1v2,definition,
( hoasinduction_lem1v2
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ( var @ A )
=> ( Q @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1v2) ).
thf(hoasinduction_lem1v2_gthm,definition,
( hoasinduction_lem1v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1v2_gthm) ).
thf(hoasinduction_lem2,definition,
( hoasinduction_lem2
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( ap @ A @ B ) @ id ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2) ).
thf(hoasinduction_lem2_gthm,definition,
( hoasinduction_lem2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2_gthm) ).
thf(hoasinduction_lem2_lthm,definition,
( hoasinduction_lem2_lthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2_lthm) ).
thf(hoasinduction_lem2v2,definition,
( hoasinduction_lem2v2
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term,B: term] :
( ( Q @ A )
=> ( ( Q @ B )
=> ( Q @ ( ap @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2v2) ).
thf(hoasinduction_lem2v2_gthm,definition,
( hoasinduction_lem2v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2v2_gthm) ).
thf(hoasinduction_lem3,definition,
( hoasinduction_lem3
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3) ).
thf(hoasinduction_lem3_gthm,definition,
( hoasinduction_lem3_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3_gthm) ).
thf(hoasinduction_lem3_lthm,definition,
( hoasinduction_lem3_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3_lthm) ).
thf(hoasinduction_lem3a,definition,
( hoasinduction_lem3a
= ( ! [P: subst > term > subst > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ A ) @ id ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3a) ).
thf(hoasinduction_lem3a_gthm,definition,
( hoasinduction_lem3a_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3a ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3a_gthm) ).
thf(hoasinduction_lem3a_lthm,definition,
( hoasinduction_lem3a_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3a_lthm) ).
thf(hoasinduction_lem3aa,definition,
( hoasinduction_lem3aa
= ( ! [P: subst > term > subst > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3aa) ).
thf(hoasinduction_lem3aa_lthm,definition,
( hoasinduction_lem3aa_lthm
= ( axclos
=> ( axmap
=> hoasinduction_lem3aa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3aa_lthm) ).
thf(hoasinduction_lem3aaa,definition,
( hoasinduction_lem3aaa
= ( ! [P: subst > term > subst > $o] :
( ! [F: subst > term > term] :
( ? [C: term] :
! [M: subst,A: term,N: subst] :
( ( ( sub @ ( F @ M @ A ) @ N )
= ( sub @ ( sub @ C @ ( push @ A @ M ) ) @ N ) )
& ( ( sub @ C @ ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3aaa) ).
thf(hoasinduction_lem3b,definition,
( hoasinduction_lem3b
= ( ! [B: term] :
? [F: subst > term > term] :
( ( sub @ B @ ( push @ one @ sh ) )
= ( F @ sh @ one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3b) ).
thf(hoasinduction_lem3b_gthm,definition,
( hoasinduction_lem3b_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3b_gthm) ).
thf(hoasinduction_lem3b_lthm,definition,
hoasinduction_lem3b_lthm = hoasinduction_lem3b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3b_lthm) ).
thf(hoasinduction_lem3v2,definition,
( hoasinduction_lem3v2
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ! [B: term] :
( ( Q @ B )
=> ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( Q @ ( lam @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2) ).
thf(hoasinduction_lem3v2_f,definition,
( hoasinduction_lem3v2_f
= ( ! [B: term] :
? [F: subst > term > term] :
! [A: term,M: subst] :
( ( F @ M @ A )
= ( sub @ B @ ( push @ A @ M ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2_f) ).
thf(hoasinduction_lem3v2_f_lthm,definition,
hoasinduction_lem3v2_f_lthm = hoasinduction_lem3v2_f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2_f_lthm) ).
thf(hoasinduction_lem3v2_gthm,definition,
( hoasinduction_lem3v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem3v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2_gthm) ).
thf(hoasinduction_lem3v2_lthm,definition,
( hoasinduction_lem3v2_lthm
= ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2_lthm) ).
thf(hoasinduction_lem3v2a,definition,
( hoasinduction_lem3v2a
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ! [B: term] :
( ( Q @ B )
=> ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( Q @ ( lam @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2a) ).
thf(hoasinduction_lem3v2a_lthm,definition,
( hoasinduction_lem3v2a_lthm
= ( hoasinduction_lem3v2_f
=> ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2a_lthm) ).
thf(hoasinduction_lthm,definition,
( hoasinduction_lthm
= ( induction2
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lthm) ).
thf(hoasinduction_lthm_3,definition,
( hoasinduction_lthm_3
= ( hoasinduction_lem0
=> ( induction2
=> ( axvarid
=> ( hoasinduction_lem3v2a
=> hoasinduction ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lthm_3) ).
thf(hoasinduction_no_psi_cond,definition,
( hoasinduction_no_psi_cond
= ( ! [P: subst > term > subst > $o] :
( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] : ( P @ id @ A @ id ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_no_psi_cond) ).
thf(hoasinduction_no_psi_cond_lthm,definition,
( hoasinduction_no_psi_cond_lthm
= ( hoasinduction_lem0
=> ( induction2
=> ( axvarid
=> ( hoasinduction_lem3v2a
=> hoasinduction_no_psi_cond ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_no_psi_cond_lthm) ).
thf(hoasinduction_p_and_p_prime,definition,
( hoasinduction_p_and_p_prime
= ( ^ [P: subst > term > subst > $o,Q: term > $o] :
! [X: term] :
( ( Q @ X )
<=> ( P @ id @ X @ id ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_p_and_p_prime) ).
thf(hoaslam,definition,
( hoaslam
= ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslam) ).
thf(hoaslaminj,definition,
( hoaslaminj
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [G: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( G @ M @ A ) @ N )
= ( G @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
= ( hoaslam @ id
@ ^ [M: subst,A: term] : ( G @ M @ A ) ) )
=> ! [M: subst,A: term] :
( ( F @ M @ A )
= ( G @ M @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj) ).
thf(hoaslaminj_gthm,definition,
( hoaslaminj_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> hoaslaminj ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj_gthm) ).
thf(hoaslaminj_lthm,definition,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj_lthm) ).
thf(hoaslamnotap,definition,
( hoaslamnotap
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [A: term,B: term] :
( ( hoaslam @ id
@ ^ [M: subst,C: term] : ( F @ M @ C ) )
!= ( hoasap @ id @ A @ id @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotap) ).
thf(hoaslamnotap_gthm,definition,
( hoaslamnotap_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotap_gthm) ).
thf(hoaslamnotap_lthm,definition,
( hoaslamnotap_lthm
= ( lamnotap
=> hoaslamnotap ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotap_lthm) ).
thf(hoaslamnotvar,definition,
( hoaslamnotvar
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotvar) ).
thf(hoaslamnotvar_gthm,definition,
( hoaslamnotvar_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotvar_gthm) ).
thf(hoaslamnotvar_lthm,definition,
( hoaslamnotvar_lthm
= ( axvarid
=> ( lamnotvar
=> hoaslamnotvar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotvar_lthm) ).
thf(hoasvar,definition,
( hoasvar
= ( ^ [M: subst,A: term,N: subst] : ( var @ ( sub @ A @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasvar) ).
thf(induction,definition,
( induction
= ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ( P @ A )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction) ).
thf(induction2,definition,
( induction2
= ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2) ).
thf(induction2_gthm,definition,
( induction2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2_gthm) ).
thf(induction2_lthm,definition,
( induction2_lthm
= ( axvarid
=> ( induction2lem
=> induction2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2_lthm) ).
thf(induction2lem,definition,
( induction2lem
= ( ! [P: term > $o] :
( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( P @ ( sub @ A @ M ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2lem) ).
thf(induction2lem_gthm,definition,
( induction2lem_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> induction2lem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2lem_gthm) ).
thf(induction2lem_lthm,definition,
( induction2lem_lthm
= ( axapp
=> ( axvarcons
=> ( axabs
=> ( axclos
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( induction
=> ( pushprop
=> induction2lem ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2lem_lthm) ).
thf(laminj,definition,
( laminj
= ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',laminj) ).
thf(lamnotap,definition,
( lamnotap
= ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamnotap) ).
thf(lamnotvar,definition,
( lamnotvar
= ( ! [A: term] :
~ ( var @ ( lam @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamnotvar) ).
thf(pushprop,definition,
( pushprop
= ( ! [P: term > $o,A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( ( P @ A )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop) ).
thf(pushprop_gthm,definition,
( pushprop_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_gthm) ).
thf(pushprop_lem0,definition,
( pushprop_lem0
= ( ! [P: term > $o,A: term,M: subst] :
? [Q: term > $o] : ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem0) ).
thf(pushprop_lem0_gthm,definition,
( pushprop_lem0_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem0_gthm) ).
thf(pushprop_lem0_lthm,definition,
pushprop_lem0_lthm = pushprop_lem0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem0_lthm) ).
thf(pushprop_lem1,definition,
( pushprop_lem1
= ( ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
( ( P @ A )
=> ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1) ).
thf(pushprop_lem1_gthm,definition,
( pushprop_lem1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1_gthm) ).
thf(pushprop_lem1_lthm,definition,
( pushprop_lem1_lthm
= ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop_lem1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1_lthm) ).
thf(pushprop_lem1v2,definition,
( pushprop_lem1v2
= ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
( ( P @ A )
=> ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
=> ( Q @ one ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1v2) ).
thf(pushprop_lem1v2_gthm,definition,
( pushprop_lem1v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1v2_gthm) ).
thf(pushprop_lem1v2_lthm,definition,
( pushprop_lem1v2_lthm
= ( axvarcons
=> pushprop_lem1v2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1v2_lthm) ).
thf(pushprop_lem2v2,definition,
( pushprop_lem2v2
= ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
=> ( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ! [C: term] :
( ( var @ C )
=> ( ( Q @ C )
=> ( Q @ ( sub @ C @ sh ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem2v2) ).
thf(pushprop_lem2v2_gthm,definition,
( pushprop_lem2v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem2v2_gthm) ).
thf(pushprop_lem2v2_lthm,definition,
( pushprop_lem2v2_lthm
= ( axclos
=> ( axshiftcons
=> pushprop_lem2v2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem2v2_lthm) ).
thf(pushprop_lem3v2,definition,
( pushprop_lem3v2
= ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
=> ( ! [B: term] :
( ( var @ B )
=> ( Q @ B ) )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem3v2) ).
thf(pushprop_lem3v2_lthm,definition,
pushprop_lem3v2_lthm = pushprop_lem3v2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem3v2_lthm) ).
thf(pushprop_lthm,definition,
( pushprop_lthm
= ( pushprop_lem0
=> ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lthm) ).
thf(pushprop_lthm_orig,definition,
( pushprop_lthm_orig
= ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lthm_orig) ).
thf(pushprop_p_and_p_prime,definition,
( pushprop_p_and_p_prime
= ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
! [X: term] :
( ( Q @ X )
<=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_p_and_p_prime) ).
thf(shinj,definition,
( shinj
= ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shinj) ).
thf(substmonoid,definition,
( substmonoid
= ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) )
& ! [M: subst] :
( ( comp @ id @ M )
= M )
& ! [M: subst] :
( ( comp @ M @ id )
= M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substmonoid) ).
thf(substmonoid_gthm,definition,
( substmonoid_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> substmonoid ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substmonoid_gthm) ).
thf(substmonoid_lthm,definition,
( substmonoid_lthm
= ( axidl
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substmonoid_lthm) ).
thf(termmset,definition,
( termmset
= ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',termmset) ).
thf(termmset_gthm,definition,
( termmset_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> termmset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',termmset_gthm) ).
thf(termmset_lthm,definition,
( termmset_lthm
= ( axvarid
=> ( axclos
=> termmset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',termmset_lthm) ).
thf(ulamvar1,definition,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvar1) ).
thf(ulamvarind,definition,
( ulamvarind
= ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvarind) ).
thf(ulamvarsh,definition,
( ulamvarsh
= ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvarsh) ).
thf(1,conjecture,
hoasinduction_lem2v2_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
hoasinduction_lem2v2_gthm = $false,
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) )
=> ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A )
=> ( ! [A: term] :
( ( sub @ A @ id )
= A )
=> ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) )
=> ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) )
=> ( ! [M: subst] :
( ( comp @ id @ M )
= M )
=> ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M )
=> ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) )
=> ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
=> ( ! [M: subst] :
( ( comp @ M @ id )
= M )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M )
=> ( ( var @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) )
=> ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) )
=> ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) )
=> ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) )
=> ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) )
=> ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) )
=> ( ! [A: term] :
~ ( var @ ( lam @ A ) )
=> ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ( P @ A )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) )
=> ( ! [P: term > $o,A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( ( P @ A )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) )
=> ( ! [P: term > $o] :
( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( P @ ( sub @ A @ M ) ) ) ) )
=> ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) )
=> ( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) )
& ! [M: subst] :
( ( comp @ id @ M )
= M )
& ! [M: subst] :
( ( comp @ M @ id )
= M ) )
=> ( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) )
=> ( ! [SY79: term,SY80: term,SY81: term,SY82: term] :
( ( ( ap @ ( sub @ SY79 @ id ) @ SY81 )
= ( ap @ ( sub @ SY80 @ id ) @ SY82 ) )
=> ( SY79 = SY80 ) )
=> ( ! [SY95: term,SY96: term,SY97: term,SY98: term] :
( ( ( ap @ ( sub @ SY95 @ id ) @ SY97 )
= ( ap @ ( sub @ SY96 @ id ) @ SY98 ) )
=> ( SY97 = SY98 ) )
=> ( ! [SY111: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY111 @ M @ A ) @ N )
= ( SY111 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY115: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY115 @ M @ A ) @ N )
= ( SY115 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( lam @ ( SY111 @ sh @ one ) )
= ( lam @ ( SY115 @ sh @ one ) ) )
=> ! [M: subst,A: term] :
( ( SY111 @ M @ A )
= ( SY115 @ M @ A ) ) ) ) )
=> ( ! [SY129: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY129 @ M @ A ) @ N )
= ( SY129 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY133: term,SY134: term] :
( ( lam @ ( SY129 @ sh @ one ) )
!= ( ap @ ( sub @ SY133 @ id ) @ SY134 ) ) )
=> ( ! [SY145: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY145 @ M @ A ) @ N )
= ( SY145 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( SY145 @ sh @ one ) ) @ id ) ) )
=> ( ! [SY156: term,SY157: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SY156 @ id ) @ SY157 ) @ id ) )
=> ! [SY167: subst > term > subst > $o,SY168: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ M @ A @ ( comp @ K @ N ) )
=> ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( SY167 @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [SY177: term,SY178: term] :
( ( SY167 @ id @ SY177 @ id )
=> ( ( SY167 @ id @ SY178 @ id )
=> ( SY167 @ id @ ( ap @ ( sub @ SY177 @ id ) @ SY178 ) @ id ) ) )
=> ( ! [SY187: term] :
( ( SY168 @ SY187 )
<=> ( SY167 @ id @ SY187 @ id ) )
=> ! [A: term,B: term] :
( ( SY168 @ A )
=> ( ( SY168 @ B )
=> ( SY168 @ ( ap @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(4,plain,
( ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( var @ one )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: term] :
~ ( var @ ( lam @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ( P @ A )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [P: term > $o,A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( ( P @ A )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [P: term > $o] :
( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( P @ ( sub @ A @ M ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(33,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [SY79: term,SY80: term,SY81: term,SY82: term] :
( ( ( ap @ ( sub @ SY79 @ id ) @ SY81 )
= ( ap @ ( sub @ SY80 @ id ) @ SY82 ) )
=> ( SY79 = SY80 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [SY95: term,SY96: term,SY97: term,SY98: term] :
( ( ( ap @ ( sub @ SY95 @ id ) @ SY97 )
= ( ap @ ( sub @ SY96 @ id ) @ SY98 ) )
=> ( SY97 = SY98 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [SY111: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY111 @ M @ A ) @ N )
= ( SY111 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY115: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY115 @ M @ A ) @ N )
= ( SY115 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( lam @ ( SY111 @ sh @ one ) )
= ( lam @ ( SY115 @ sh @ one ) ) )
=> ! [M: subst,A: term] :
( ( SY111 @ M @ A )
= ( SY115 @ M @ A ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [SY129: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY129 @ M @ A ) @ N )
= ( SY129 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [SY133: term,SY134: term] :
( ( lam @ ( SY129 @ sh @ one ) )
!= ( ap @ ( sub @ SY133 @ id ) @ SY134 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [SY145: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY145 @ M @ A ) @ N )
= ( SY145 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( SY145 @ sh @ one ) ) @ id ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [SY156: term,SY157: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SY156 @ id ) @ SY157 ) @ id ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [SY167: subst > term > subst > $o,SY168: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ M @ A @ ( comp @ K @ N ) )
=> ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( SY167 @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [SY177: term,SY178: term] :
( ( SY167 @ id @ SY177 @ id )
=> ( ( SY167 @ id @ SY178 @ id )
=> ( SY167 @ id @ ( ap @ ( sub @ SY177 @ id ) @ SY178 ) @ id ) ) )
=> ( ! [SY187: term] :
( ( SY168 @ SY187 )
<=> ( SY167 @ id @ SY187 @ id ) )
=> ! [A: term,B: term] :
( ( SY168 @ A )
=> ( ( SY168 @ B )
=> ( SY168 @ ( ap @ A @ B ) ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(42,plain,
( ( ~ ! [SY167: subst > term > subst > $o,SY168: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ M @ A @ ( comp @ K @ N ) )
=> ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( SY167 @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( SY167 @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [SY177: term,SY178: term] :
( ( SY167 @ id @ SY177 @ id )
=> ( ( SY167 @ id @ SY178 @ id )
=> ( SY167 @ id @ ( ap @ ( sub @ SY177 @ id ) @ SY178 ) @ id ) ) )
=> ( ! [SY187: term] :
( ( SY168 @ SY187 )
<=> ( SY167 @ id @ SY187 @ id ) )
=> ! [A: term,B: term] :
( ( SY168 @ A )
=> ( ( SY168 @ B )
=> ( SY168 @ ( ap @ A @ B ) ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[41]) ).
thf(43,plain,
( ( ! [SY314: subst,SY315: term,SY316: subst,SY317: subst] :
( ~ ( sK1_SY167 @ SY314 @ SY315 @ ( comp @ SY317 @ SY316 ) )
| ( sK1_SY167 @ ( comp @ SY314 @ SY317 ) @ ( sub @ SY315 @ SY317 ) @ SY316 ) )
& ! [SY318: subst,SY319: term,SY320: subst,SY321: subst] :
( ~ ( sK1_SY167 @ ( comp @ SY318 @ SY321 ) @ ( sub @ SY319 @ SY321 ) @ SY320 )
| ( sK1_SY167 @ SY318 @ SY319 @ ( comp @ SY321 @ SY320 ) ) )
& ! [SY322: term] :
( ~ ( sK1_SY167 @ id @ SY322 @ id )
| ! [SY323: term] :
( ~ ( sK1_SY167 @ id @ SY323 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SY322 @ id ) @ SY323 ) @ id ) ) )
& ! [SY329: term] :
( ~ ( sK1_SY167 @ id @ SY329 @ id )
| ( sK2_SY324 @ SY329 ) )
& ! [SY330: term] :
( ~ ( sK2_SY324 @ SY330 )
| ( sK1_SY167 @ id @ SY330 @ id ) )
& ( sK2_SY324 @ sK3_SY331 )
& ( sK2_SY324 @ sK4_SY333 )
& ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(44,plain,
( ( ! [A: term] :
( ~ ( var @ A )
| ( var @ ( sub @ A @ sh ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(45,plain,
( ( ! [P: term > $o] :
( ~ ( P @ one )
| ( ( var @ ( sK5_A @ P ) )
& ( P @ ( sK5_A @ P ) )
& ~ ( P @ ( sub @ ( sK5_A @ P ) @ sh ) ) )
| ! [A: term] :
( ~ ( var @ A )
| ( P @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(46,plain,
( ( ! [A: term,B: term] :
( ! [C: term,D: term] :
( ( ap @ A @ C )
!= ( ap @ B @ D ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(47,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
!= ( ap @ B @ D ) )
| ( C = D ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(48,plain,
( ( ! [A: term,B: term] :
( ( ( lam @ A )
!= ( lam @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(49,plain,
( ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
!= ( sub @ B @ sh ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(50,plain,
( ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(51,plain,
( ( ! [P: term > $o] :
( ( ( var @ ( sK9_A @ P ) )
& ~ ( P @ ( sK9_A @ P ) ) )
| ( ( P @ ( sK7_A @ P ) )
& ( P @ ( sK8_SY334 @ P ) )
& ~ ( P @ ( ap @ ( sK7_A @ P ) @ ( sK8_SY334 @ P ) ) ) )
| ( ( P @ ( sK6_A @ P ) )
& ~ ( P @ ( lam @ ( sK6_A @ P ) ) ) )
| ! [A: term] : ( P @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(52,plain,
( ( ! [P: term > $o,A: term,M: subst] :
( ( ( var @ ( sK10_B @ M @ A @ P ) )
& ~ ( P @ ( sub @ ( sK10_B @ M @ A @ P ) @ M ) ) )
| ~ ( P @ A )
| ! [B: term] :
( ~ ( var @ B )
| ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(53,plain,
( ( ! [P: term > $o] :
( ( ( P @ ( sK13_A @ P ) )
& ( P @ ( sK14_SY336 @ P ) )
& ~ ( P @ ( ap @ ( sK13_A @ P ) @ ( sK14_SY336 @ P ) ) ) )
| ( ! [SY335: term] :
( ~ ( P @ SY335 )
| ( P @ ( sub @ ( sK12_A @ P ) @ ( push @ SY335 @ id ) ) ) )
& ~ ( P @ ( lam @ ( sK12_A @ P ) ) ) )
| ! [A: term,M: subst] :
( ( ( var @ ( sK11_B @ M @ A @ P ) )
& ~ ( P @ ( sub @ ( sK11_B @ M @ A @ P ) @ M ) ) )
| ( P @ ( sub @ A @ M ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(54,plain,
( ( ! [P: term > $o] :
( ( ( var @ ( sK18_A @ P ) )
& ~ ( P @ ( sK18_A @ P ) ) )
| ( ( P @ ( sK16_A @ P ) )
& ( P @ ( sK17_SY338 @ P ) )
& ~ ( P @ ( ap @ ( sK16_A @ P ) @ ( sK17_SY338 @ P ) ) ) )
| ( ! [SY337: term] :
( ~ ( P @ SY337 )
| ( P @ ( sub @ ( sK15_A @ P ) @ ( push @ SY337 @ id ) ) ) )
& ~ ( P @ ( lam @ ( sK15_A @ P ) ) ) )
| ! [A: term] : ( P @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(55,plain,
( ( ! [SY79: term,SY80: term] :
( ! [SY81: term,SY82: term] :
( ( ap @ ( sub @ SY79 @ id ) @ SY81 )
!= ( ap @ ( sub @ SY80 @ id ) @ SY82 ) )
| ( SY79 = SY80 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(56,plain,
( ( ! [SY95: term,SY96: term,SY97: term,SY98: term] :
( ( ( ap @ ( sub @ SY95 @ id ) @ SY97 )
!= ( ap @ ( sub @ SY96 @ id ) @ SY98 ) )
| ( SY97 = SY98 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(57,plain,
( ( ! [SY111: subst > term > term] :
( ( ( sub @ ( SY111 @ ( sK22_M @ SY111 ) @ ( sK23_SY342 @ SY111 ) ) @ ( sK24_SY344 @ SY111 ) )
!= ( SY111 @ ( comp @ ( sK22_M @ SY111 ) @ ( sK24_SY344 @ SY111 ) ) @ ( sub @ ( sK23_SY342 @ SY111 ) @ ( sK24_SY344 @ SY111 ) ) ) )
| ! [SY115: subst > term > term] :
( ( ( sub @ ( SY115 @ ( sK19_M @ SY115 @ SY111 ) @ ( sK20_SY339 @ SY115 @ SY111 ) ) @ ( sK21_SY341 @ SY115 @ SY111 ) )
!= ( SY115 @ ( comp @ ( sK19_M @ SY115 @ SY111 ) @ ( sK21_SY341 @ SY115 @ SY111 ) ) @ ( sub @ ( sK20_SY339 @ SY115 @ SY111 ) @ ( sK21_SY341 @ SY115 @ SY111 ) ) ) )
| ( ( lam @ ( SY111 @ sh @ one ) )
!= ( lam @ ( SY115 @ sh @ one ) ) )
| ! [M: subst,A: term] :
( ( SY111 @ M @ A )
= ( SY115 @ M @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(58,plain,
( ( ! [SY129: subst > term > term] :
( ( ( sub @ ( SY129 @ ( sK25_M @ SY129 ) @ ( sK26_SY345 @ SY129 ) ) @ ( sK27_SY347 @ SY129 ) )
!= ( SY129 @ ( comp @ ( sK25_M @ SY129 ) @ ( sK27_SY347 @ SY129 ) ) @ ( sub @ ( sK26_SY345 @ SY129 ) @ ( sK27_SY347 @ SY129 ) ) ) )
| ! [SY133: term,SY134: term] :
( ( lam @ ( SY129 @ sh @ one ) )
!= ( ap @ ( sub @ SY133 @ id ) @ SY134 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(59,plain,
( ( ! [SY145: subst > term > term] :
( ( ( sub @ ( SY145 @ ( sK28_M @ SY145 ) @ ( sK29_SY348 @ SY145 ) ) @ ( sK30_SY350 @ SY145 ) )
!= ( SY145 @ ( comp @ ( sK28_M @ SY145 ) @ ( sK30_SY350 @ SY145 ) ) @ ( sub @ ( sK29_SY348 @ SY145 ) @ ( sK30_SY350 @ SY145 ) ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SY145 @ sh @ one ) ) @ id ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(60,plain,
( ( ! [SY156: term,SY157: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SY156 @ id ) @ SY157 ) @ id ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(61,plain,
( ( ! [SY145: subst > term > term] :
( ( ( sub @ ( SY145 @ ( sK28_M @ SY145 ) @ ( sK29_SY348 @ SY145 ) ) @ ( sK30_SY350 @ SY145 ) )
!= ( SY145 @ ( comp @ ( sK28_M @ SY145 ) @ ( sK30_SY350 @ SY145 ) ) @ ( sub @ ( sK29_SY348 @ SY145 ) @ ( sK30_SY350 @ SY145 ) ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SY145 @ sh @ one ) ) @ id ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(62,plain,
( ( ! [SY129: subst > term > term] :
( ( ( sub @ ( SY129 @ ( sK25_M @ SY129 ) @ ( sK26_SY345 @ SY129 ) ) @ ( sK27_SY347 @ SY129 ) )
!= ( SY129 @ ( comp @ ( sK25_M @ SY129 ) @ ( sK27_SY347 @ SY129 ) ) @ ( sub @ ( sK26_SY345 @ SY129 ) @ ( sK27_SY347 @ SY129 ) ) ) )
| ! [SY133: term,SY134: term] :
( ( lam @ ( SY129 @ sh @ one ) )
!= ( ap @ ( sub @ SY133 @ id ) @ SY134 ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(63,plain,
( ( ! [SY111: subst > term > term] :
( ( ( sub @ ( SY111 @ ( sK22_M @ SY111 ) @ ( sK23_SY342 @ SY111 ) ) @ ( sK24_SY344 @ SY111 ) )
!= ( SY111 @ ( comp @ ( sK22_M @ SY111 ) @ ( sK24_SY344 @ SY111 ) ) @ ( sub @ ( sK23_SY342 @ SY111 ) @ ( sK24_SY344 @ SY111 ) ) ) )
| ! [SY115: subst > term > term] :
( ( ( sub @ ( SY115 @ ( sK19_M @ SY115 @ SY111 ) @ ( sK20_SY339 @ SY115 @ SY111 ) ) @ ( sK21_SY341 @ SY115 @ SY111 ) )
!= ( SY115 @ ( comp @ ( sK19_M @ SY115 @ SY111 ) @ ( sK21_SY341 @ SY115 @ SY111 ) ) @ ( sub @ ( sK20_SY339 @ SY115 @ SY111 ) @ ( sK21_SY341 @ SY115 @ SY111 ) ) ) )
| ( ( lam @ ( SY111 @ sh @ one ) )
!= ( lam @ ( SY115 @ sh @ one ) ) )
| ! [M: subst,A: term] :
( ( SY111 @ M @ A )
= ( SY115 @ M @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(64,plain,
( ( ! [SY95: term,SY96: term,SY97: term,SY98: term] :
( ( ( ap @ ( sub @ SY95 @ id ) @ SY97 )
!= ( ap @ ( sub @ SY96 @ id ) @ SY98 ) )
| ( SY97 = SY98 ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(65,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)],[55]) ).
thf(66,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(67,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(68,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(69,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(70,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(71,plain,
( ( ! [P: term > $o] :
( ( ( var @ ( sK18_A @ P ) )
& ~ ( P @ ( sK18_A @ P ) ) )
| ( ( P @ ( sK16_A @ P ) )
& ( P @ ( sK17_SY338 @ P ) )
& ~ ( P @ ( ap @ ( sK16_A @ P ) @ ( sK17_SY338 @ P ) ) ) )
| ( ! [SY337: term] :
( ~ ( P @ SY337 )
| ( P @ ( sub @ ( sK15_A @ P ) @ ( push @ SY337 @ id ) ) ) )
& ~ ( P @ ( lam @ ( sK15_A @ P ) ) ) )
| ! [A: term] : ( P @ A ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(72,plain,
( ( ! [P: term > $o] :
( ( ( P @ ( sK13_A @ P ) )
& ( P @ ( sK14_SY336 @ P ) )
& ~ ( P @ ( ap @ ( sK13_A @ P ) @ ( sK14_SY336 @ P ) ) ) )
| ( ! [SY335: term] :
( ~ ( P @ SY335 )
| ( P @ ( sub @ ( sK12_A @ P ) @ ( push @ SY335 @ id ) ) ) )
& ~ ( P @ ( lam @ ( sK12_A @ P ) ) ) )
| ! [A: term,M: subst] :
( ( ( var @ ( sK11_B @ M @ A @ P ) )
& ~ ( P @ ( sub @ ( sK11_B @ M @ A @ P ) @ M ) ) )
| ( P @ ( sub @ A @ M ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(73,plain,
( ( ! [P: term > $o,A: term,M: subst] :
( ( ( var @ ( sK10_B @ M @ A @ P ) )
& ~ ( P @ ( sub @ ( sK10_B @ M @ A @ P ) @ M ) ) )
| ~ ( P @ A )
| ! [B: term] :
( ~ ( var @ B )
| ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(74,plain,
( ( ! [P: term > $o] :
( ( ( var @ ( sK9_A @ P ) )
& ~ ( P @ ( sK9_A @ P ) ) )
| ( ( P @ ( sK7_A @ P ) )
& ( P @ ( sK8_SY334 @ P ) )
& ~ ( P @ ( ap @ ( sK7_A @ P ) @ ( sK8_SY334 @ P ) ) ) )
| ( ( P @ ( sK6_A @ P ) )
& ~ ( P @ ( lam @ ( sK6_A @ P ) ) ) )
| ! [A: term] : ( P @ A ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(75,plain,
( ( ! [A: term] :
~ ( var @ ( lam @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(76,plain,
( ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(77,plain,
( ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(78,plain,
( ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
!= ( sub @ B @ sh ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(79,plain,
( ( ! [A: term,B: term] :
( ( ( lam @ A )
!= ( lam @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(80,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
!= ( ap @ B @ D ) )
| ( C = D ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(81,plain,
( ( ! [A: term,B: term] :
( ! [C: term,D: term] :
( ( ap @ A @ C )
!= ( ap @ B @ D ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(82,plain,
( ( ! [P: term > $o] :
( ~ ( P @ one )
| ( ( var @ ( sK5_A @ P ) )
& ( P @ ( sK5_A @ P ) )
& ~ ( P @ ( sub @ ( sK5_A @ P ) @ sh ) ) )
| ! [A: term] :
( ~ ( var @ A )
| ( P @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(83,plain,
( ( ! [A: term] :
( ~ ( var @ A )
| ( var @ ( sub @ A @ sh ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(84,plain,
( ( var @ one )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(85,plain,
( ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(86,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(87,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(88,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(89,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(90,plain,
( ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(91,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(92,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(93,plain,
( ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(94,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(95,plain,
( ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(96,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(97,plain,
( ( ! [SY314: subst,SY315: term,SY316: subst,SY317: subst] :
( ~ ( sK1_SY167 @ SY314 @ SY315 @ ( comp @ SY317 @ SY316 ) )
| ( sK1_SY167 @ ( comp @ SY314 @ SY317 ) @ ( sub @ SY315 @ SY317 ) @ SY316 ) )
& ! [SY318: subst,SY319: term,SY320: subst,SY321: subst] :
( ~ ( sK1_SY167 @ ( comp @ SY318 @ SY321 ) @ ( sub @ SY319 @ SY321 ) @ SY320 )
| ( sK1_SY167 @ SY318 @ SY319 @ ( comp @ SY321 @ SY320 ) ) )
& ! [SY322: term] :
( ~ ( sK1_SY167 @ id @ SY322 @ id )
| ! [SY323: term] :
( ~ ( sK1_SY167 @ id @ SY323 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SY322 @ id ) @ SY323 ) @ id ) ) )
& ! [SY329: term] :
( ~ ( sK1_SY167 @ id @ SY329 @ id )
| ( sK2_SY324 @ SY329 ) )
& ! [SY330: term] :
( ~ ( sK2_SY324 @ SY330 )
| ( sK1_SY167 @ id @ SY330 @ id ) )
& ( sK2_SY324 @ sK3_SY331 )
& ( sK2_SY324 @ sK4_SY333 )
& ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(98,plain,
( ( ! [SX0: term > $o] :
( ~ ( ~ ( SX0 @ ( sK13_A @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK14_SY336 @ SX0 ) )
| ~ ~ ( SX0 @ ( ap @ ( sK13_A @ SX0 ) @ ( sK14_SY336 @ SX0 ) ) ) ) )
| ~ ( ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ ( sK12_A @ SX0 ) @ ( push @ SX1 @ id ) ) ) )
| ~ ~ ( SX0 @ ( lam @ ( sK12_A @ SX0 ) ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( SX0 @ ( sub @ ( sK11_B @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72,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(99,plain,
( ( ~ ( ~ ! [SX0: subst,SX1: term,SX2: subst,SX3: subst] :
( ~ ( sK1_SY167 @ SX0 @ SX1 @ ( comp @ SX3 @ SX2 ) )
| ( sK1_SY167 @ ( comp @ SX0 @ SX3 ) @ ( sub @ SX1 @ SX3 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX0: subst,SX1: term,SX2: subst,SX3: subst] :
( ~ ( sK1_SY167 @ ( comp @ SX0 @ SX3 ) @ ( sub @ SX1 @ SX3 ) @ SX2 )
| ( sK1_SY167 @ SX0 @ SX1 @ ( comp @ SX3 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ! [SX1: term] :
( ~ ( sK1_SY167 @ id @ SX1 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
| ~ ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97,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(100,plain,
( ( ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ( ~ ( var @ ( sK10_B @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( SX0 @ ( sub @ ( sK10_B @ SX2 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73,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(101,plain,
( ( ! [SX0: term > $o] :
( ~ ( ~ ( var @ ( sK18_A @ SX0 ) )
| ~ ~ ( SX0 @ ( sK18_A @ SX0 ) ) )
| ~ ( ~ ( SX0 @ ( sK16_A @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK17_SY338 @ SX0 ) )
| ~ ~ ( SX0 @ ( ap @ ( sK16_A @ SX0 ) @ ( sK17_SY338 @ SX0 ) ) ) ) )
| ~ ( ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ ( sK15_A @ SX0 ) @ ( push @ SX1 @ id ) ) ) )
| ~ ~ ( SX0 @ ( lam @ ( sK15_A @ SX0 ) ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71,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(102,plain,
( ( ! [SX0: term > $o] :
( ~ ( ~ ( var @ ( sK9_A @ SX0 ) )
| ~ ~ ( SX0 @ ( sK9_A @ SX0 ) ) )
| ~ ( ~ ( SX0 @ ( sK7_A @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK8_SY334 @ SX0 ) )
| ~ ~ ( SX0 @ ( ap @ ( sK7_A @ SX0 ) @ ( sK8_SY334 @ SX0 ) ) ) ) )
| ~ ( ~ ( SX0 @ ( sK6_A @ SX0 ) )
| ~ ~ ( SX0 @ ( lam @ ( sK6_A @ SX0 ) ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74,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(103,plain,
( ( ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ( ~ ( var @ ( sK5_A @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK5_A @ SX0 ) )
| ~ ~ ( SX0 @ ( sub @ ( sK5_A @ SX0 ) @ sh ) ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82,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(104,plain,
! [SV1: term] :
( ( ! [SY351: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SV1 @ id ) @ SY351 ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(105,plain,
! [SV2: subst > term > term] :
( ( ( ( sub @ ( SV2 @ ( sK28_M @ SV2 ) @ ( sK29_SY348 @ SV2 ) ) @ ( sK30_SY350 @ SV2 ) )
!= ( SV2 @ ( comp @ ( sK28_M @ SV2 ) @ ( sK30_SY350 @ SV2 ) ) @ ( sub @ ( sK29_SY348 @ SV2 ) @ ( sK30_SY350 @ SV2 ) ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SV2 @ sh @ one ) ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(106,plain,
! [SV3: subst > term > term] :
( ( ( ( sub @ ( SV3 @ ( sK25_M @ SV3 ) @ ( sK26_SY345 @ SV3 ) ) @ ( sK27_SY347 @ SV3 ) )
!= ( SV3 @ ( comp @ ( sK25_M @ SV3 ) @ ( sK27_SY347 @ SV3 ) ) @ ( sub @ ( sK26_SY345 @ SV3 ) @ ( sK27_SY347 @ SV3 ) ) ) )
| ! [SY352: term,SY353: term] :
( ( lam @ ( SV3 @ sh @ one ) )
!= ( ap @ ( sub @ SY352 @ id ) @ SY353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(107,plain,
! [SV4: subst > term > term] :
( ( ( ( sub @ ( SV4 @ ( sK22_M @ SV4 ) @ ( sK23_SY342 @ SV4 ) ) @ ( sK24_SY344 @ SV4 ) )
!= ( SV4 @ ( comp @ ( sK22_M @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) @ ( sub @ ( sK23_SY342 @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) ) )
| ! [SY354: subst > term > term] :
( ( ( sub @ ( SY354 @ ( sK19_M @ SY354 @ SV4 ) @ ( sK20_SY339 @ SY354 @ SV4 ) ) @ ( sK21_SY341 @ SY354 @ SV4 ) )
!= ( SY354 @ ( comp @ ( sK19_M @ SY354 @ SV4 ) @ ( sK21_SY341 @ SY354 @ SV4 ) ) @ ( sub @ ( sK20_SY339 @ SY354 @ SV4 ) @ ( sK21_SY341 @ SY354 @ SV4 ) ) ) )
| ( ( lam @ ( SV4 @ sh @ one ) )
!= ( lam @ ( SY354 @ sh @ one ) ) )
| ! [SY355: subst,SY356: term] :
( ( SV4 @ SY355 @ SY356 )
= ( SY354 @ SY355 @ SY356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(108,plain,
! [SV5: term] :
( ( ! [SY357: term,SY358: term,SY359: term] :
( ( ( ap @ ( sub @ SV5 @ id ) @ SY358 )
!= ( ap @ ( sub @ SY357 @ id ) @ SY359 ) )
| ( SY358 = SY359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(109,plain,
! [SV6: term] :
( ( ! [SY360: term] :
( ! [SY361: term,SY362: term] :
( ( ap @ ( sub @ SV6 @ id ) @ SY361 )
!= ( ap @ ( sub @ SY360 @ id ) @ SY362 ) )
| ( SV6 = SY360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(110,plain,
! [SV7: term] :
( ( ( sub @ SV7 @ id )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(111,plain,
! [SV8: term] :
( ( ! [SY363: subst,SY364: subst] :
( ( sub @ ( sub @ SV8 @ SY363 ) @ SY364 )
= ( sub @ SV8 @ ( comp @ SY363 @ SY364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(112,plain,
! [SV9: subst] :
( ( ( comp @ SV9 @ id )
= SV9 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(113,plain,
! [SV10: subst] :
( ( ( comp @ id @ SV10 )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(114,plain,
! [SV11: subst] :
( ( ! [SY365: subst,SY366: subst] :
( ( comp @ ( comp @ SV11 @ SY365 ) @ SY366 )
= ( comp @ SV11 @ ( comp @ SY365 @ SY366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(115,plain,
! [SV12: term] :
( ( ~ ( var @ ( lam @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(116,plain,
! [SV13: term] :
( ( ! [SY367: term] :
~ ( var @ ( ap @ SV13 @ SY367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(117,plain,
! [SV14: term] :
( ( ! [SY368: term,SY369: term] :
( ( lam @ SV14 )
!= ( ap @ SY368 @ SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(118,plain,
! [SV15: term] :
( ( ! [SY370: term] :
( ( ( sub @ SV15 @ sh )
!= ( sub @ SY370 @ sh ) )
| ( SV15 = SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(119,plain,
! [SV16: term] :
( ( ! [SY371: term] :
( ( ( lam @ SV16 )
!= ( lam @ SY371 ) )
| ( SV16 = SY371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(120,plain,
! [SV17: term] :
( ( ! [SY372: term,SY373: term,SY374: term] :
( ( ( ap @ SV17 @ SY373 )
!= ( ap @ SY372 @ SY374 ) )
| ( SY373 = SY374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(121,plain,
! [SV18: term] :
( ( ! [SY375: term] :
( ! [SY376: term,SY377: term] :
( ( ap @ SV18 @ SY376 )
!= ( ap @ SY375 @ SY377 ) )
| ( SV18 = SY375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(122,plain,
! [SV19: term] :
( ( ~ ( var @ SV19 )
| ( var @ ( sub @ SV19 @ sh ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(123,plain,
! [SV20: subst] :
( ( ( push @ ( sub @ one @ SV20 ) @ ( comp @ sh @ SV20 ) )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(124,plain,
! [SV21: subst] :
( ( ( comp @ SV21 @ id )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(125,plain,
! [SV22: term] :
( ( ! [SY378: subst,SY379: subst] :
( ( comp @ ( push @ SV22 @ SY378 ) @ SY379 )
= ( push @ ( sub @ SV22 @ SY379 ) @ ( comp @ SY378 @ SY379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(126,plain,
! [SV23: subst] :
( ( ! [SY380: subst,SY381: subst] :
( ( comp @ ( comp @ SV23 @ SY380 ) @ SY381 )
= ( comp @ SV23 @ ( comp @ SY380 @ SY381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(127,plain,
! [SV24: term] :
( ( ! [SY382: subst] :
( ( comp @ sh @ ( push @ SV24 @ SY382 ) )
= SY382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(128,plain,
! [SV25: subst] :
( ( ( comp @ id @ SV25 )
= SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(129,plain,
! [SV26: term] :
( ( ! [SY383: subst,SY384: subst] :
( ( sub @ ( sub @ SV26 @ SY383 ) @ SY384 )
= ( sub @ SV26 @ ( comp @ SY383 @ SY384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(130,plain,
! [SV27: term] :
( ( ! [SY385: subst] :
( ( sub @ ( lam @ SV27 ) @ SY385 )
= ( lam @ ( sub @ SV27 @ ( push @ one @ ( comp @ SY385 @ sh ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(131,plain,
! [SV28: term] :
( ( ( sub @ SV28 @ id )
= SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(132,plain,
! [SV29: term] :
( ( ! [SY386: subst] :
( ( sub @ one @ ( push @ SV29 @ SY386 ) )
= SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(133,plain,
! [SV30: term] :
( ( ! [SY387: term,SY388: subst] :
( ( sub @ ( ap @ SV30 @ SY387 ) @ SY388 )
= ( ap @ ( sub @ SV30 @ SY388 ) @ ( sub @ SY387 @ SY388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(134,plain,
! [SV31: term > $o] :
( ( ~ ( ~ ( SV31 @ ( sK13_A @ SV31 ) )
| ~ ~ ( ~ ( SV31 @ ( sK14_SY336 @ SV31 ) )
| ~ ~ ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) ) ) )
| ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(135,plain,
( ( ~ ! [SX0: subst,SX1: term,SX2: subst,SX3: subst] :
( ~ ( sK1_SY167 @ SX0 @ SX1 @ ( comp @ SX3 @ SX2 ) )
| ( sK1_SY167 @ ( comp @ SX0 @ SX3 ) @ ( sub @ SX1 @ SX3 ) @ SX2 ) )
| ~ ~ ( ~ ! [SX0: subst,SX1: term,SX2: subst,SX3: subst] :
( ~ ( sK1_SY167 @ ( comp @ SX0 @ SX3 ) @ ( sub @ SX1 @ SX3 ) @ SX2 )
| ( sK1_SY167 @ SX0 @ SX1 @ ( comp @ SX3 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ! [SX1: term] :
( ~ ( sK1_SY167 @ id @ SX1 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
| ~ ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(136,plain,
! [SV32: term > $o] :
( ( ! [SY392: term,SY393: subst] :
( ~ ( ~ ( var @ ( sK10_B @ SY393 @ SY392 @ SV32 ) )
| ~ ~ ( SV32 @ ( sub @ ( sK10_B @ SY393 @ SY392 @ SV32 ) @ SY393 ) ) )
| ~ ( SV32 @ SY392 )
| ! [SY394: term] :
( ~ ( var @ SY394 )
| ( SV32 @ ( sub @ SY394 @ ( push @ SY392 @ SY393 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(137,plain,
! [SV33: term > $o] :
( ( ~ ( ~ ( var @ ( sK18_A @ SV33 ) )
| ~ ~ ( SV33 @ ( sK18_A @ SV33 ) ) )
| ~ ( ~ ( SV33 @ ( sK16_A @ SV33 ) )
| ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
| ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(138,plain,
! [SV34: term > $o] :
( ( ~ ( ~ ( var @ ( sK9_A @ SV34 ) )
| ~ ~ ( SV34 @ ( sK9_A @ SV34 ) ) )
| ~ ( ~ ( SV34 @ ( sK7_A @ SV34 ) )
| ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
| ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(139,plain,
! [SV35: term > $o] :
( ( ~ ( SV35 @ one )
| ~ ( ~ ( var @ ( sK5_A @ SV35 ) )
| ~ ~ ( ~ ( SV35 @ ( sK5_A @ SV35 ) )
| ~ ~ ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) ) ) )
| ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(140,plain,
! [SV36: term,SV1: term] :
( ( ~ ( var @ ( sub @ ( ap @ ( sub @ SV1 @ id ) @ SV36 ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(141,plain,
! [SV2: subst > term > term] :
( ( ( ( sub @ ( SV2 @ ( sK28_M @ SV2 ) @ ( sK29_SY348 @ SV2 ) ) @ ( sK30_SY350 @ SV2 ) )
!= ( SV2 @ ( comp @ ( sK28_M @ SV2 ) @ ( sK30_SY350 @ SV2 ) ) @ ( sub @ ( sK29_SY348 @ SV2 ) @ ( sK30_SY350 @ SV2 ) ) ) )
= $true )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV2 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(142,plain,
! [SV3: subst > term > term] :
( ( ( ( sub @ ( SV3 @ ( sK25_M @ SV3 ) @ ( sK26_SY345 @ SV3 ) ) @ ( sK27_SY347 @ SV3 ) )
!= ( SV3 @ ( comp @ ( sK25_M @ SV3 ) @ ( sK27_SY347 @ SV3 ) ) @ ( sub @ ( sK26_SY345 @ SV3 ) @ ( sK27_SY347 @ SV3 ) ) ) )
= $true )
| ( ( ! [SY352: term,SY353: term] :
( ( lam @ ( SV3 @ sh @ one ) )
!= ( ap @ ( sub @ SY352 @ id ) @ SY353 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(143,plain,
! [SV4: subst > term > term] :
( ( ( ( sub @ ( SV4 @ ( sK22_M @ SV4 ) @ ( sK23_SY342 @ SV4 ) ) @ ( sK24_SY344 @ SV4 ) )
!= ( SV4 @ ( comp @ ( sK22_M @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) @ ( sub @ ( sK23_SY342 @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) ) )
= $true )
| ( ( ! [SY354: subst > term > term] :
( ( ( sub @ ( SY354 @ ( sK19_M @ SY354 @ SV4 ) @ ( sK20_SY339 @ SY354 @ SV4 ) ) @ ( sK21_SY341 @ SY354 @ SV4 ) )
!= ( SY354 @ ( comp @ ( sK19_M @ SY354 @ SV4 ) @ ( sK21_SY341 @ SY354 @ SV4 ) ) @ ( sub @ ( sK20_SY339 @ SY354 @ SV4 ) @ ( sK21_SY341 @ SY354 @ SV4 ) ) ) )
| ( ( lam @ ( SV4 @ sh @ one ) )
!= ( lam @ ( SY354 @ sh @ one ) ) )
| ! [SY355: subst,SY356: term] :
( ( SV4 @ SY355 @ SY356 )
= ( SY354 @ SY355 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(144,plain,
! [SV37: term,SV5: term] :
( ( ! [SY399: term,SY400: term] :
( ( ( ap @ ( sub @ SV5 @ id ) @ SY399 )
!= ( ap @ ( sub @ SV37 @ id ) @ SY400 ) )
| ( SY399 = SY400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(145,plain,
! [SV38: term,SV6: term] :
( ( ! [SY401: term,SY402: term] :
( ( ap @ ( sub @ SV6 @ id ) @ SY401 )
!= ( ap @ ( sub @ SV38 @ id ) @ SY402 ) )
| ( SV6 = SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(146,plain,
! [SV39: subst,SV8: term] :
( ( ! [SY403: subst] :
( ( sub @ ( sub @ SV8 @ SV39 ) @ SY403 )
= ( sub @ SV8 @ ( comp @ SV39 @ SY403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(147,plain,
! [SV40: subst,SV11: subst] :
( ( ! [SY404: subst] :
( ( comp @ ( comp @ SV11 @ SV40 ) @ SY404 )
= ( comp @ SV11 @ ( comp @ SV40 @ SY404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(148,plain,
! [SV12: term] :
( ( var @ ( lam @ SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(149,plain,
! [SV41: term,SV13: term] :
( ( ~ ( var @ ( ap @ SV13 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(150,plain,
! [SV42: term,SV14: term] :
( ( ! [SY405: term] :
( ( lam @ SV14 )
!= ( ap @ SV42 @ SY405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(151,plain,
! [SV43: term,SV15: term] :
( ( ( ( sub @ SV15 @ sh )
!= ( sub @ SV43 @ sh ) )
| ( SV15 = SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(152,plain,
! [SV44: term,SV16: term] :
( ( ( ( lam @ SV16 )
!= ( lam @ SV44 ) )
| ( SV16 = SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(153,plain,
! [SV45: term,SV17: term] :
( ( ! [SY406: term,SY407: term] :
( ( ( ap @ SV17 @ SY406 )
!= ( ap @ SV45 @ SY407 ) )
| ( SY406 = SY407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(154,plain,
! [SV46: term,SV18: term] :
( ( ! [SY408: term,SY409: term] :
( ( ap @ SV18 @ SY408 )
!= ( ap @ SV46 @ SY409 ) )
| ( SV18 = SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(155,plain,
! [SV19: term] :
( ( ( ~ ( var @ SV19 ) )
= $true )
| ( ( var @ ( sub @ SV19 @ sh ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(156,plain,
! [SV47: subst,SV22: term] :
( ( ! [SY410: subst] :
( ( comp @ ( push @ SV22 @ SV47 ) @ SY410 )
= ( push @ ( sub @ SV22 @ SY410 ) @ ( comp @ SV47 @ SY410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(157,plain,
! [SV48: subst,SV23: subst] :
( ( ! [SY411: subst] :
( ( comp @ ( comp @ SV23 @ SV48 ) @ SY411 )
= ( comp @ SV23 @ ( comp @ SV48 @ SY411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(158,plain,
! [SV49: subst,SV24: term] :
( ( ( comp @ sh @ ( push @ SV24 @ SV49 ) )
= SV49 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(159,plain,
! [SV50: subst,SV26: term] :
( ( ! [SY412: subst] :
( ( sub @ ( sub @ SV26 @ SV50 ) @ SY412 )
= ( sub @ SV26 @ ( comp @ SV50 @ SY412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(160,plain,
! [SV51: subst,SV27: term] :
( ( ( sub @ ( lam @ SV27 ) @ SV51 )
= ( lam @ ( sub @ SV27 @ ( push @ one @ ( comp @ SV51 @ sh ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(161,plain,
! [SV52: subst,SV29: term] :
( ( ( sub @ one @ ( push @ SV29 @ SV52 ) )
= SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(162,plain,
! [SV53: term,SV30: term] :
( ( ! [SY413: subst] :
( ( sub @ ( ap @ SV30 @ SV53 ) @ SY413 )
= ( ap @ ( sub @ SV30 @ SY413 ) @ ( sub @ SV53 @ SY413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(163,plain,
! [SV31: term > $o] :
( ( ( ~ ( ~ ( SV31 @ ( sK13_A @ SV31 ) )
| ~ ~ ( ~ ( SV31 @ ( sK14_SY336 @ SV31 ) )
| ~ ~ ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[134]) ).
thf(164,plain,
( ( ~ ! [SX0: subst,SX1: term,SX2: subst,SX3: subst] :
( ~ ( sK1_SY167 @ SX0 @ SX1 @ ( comp @ SX3 @ SX2 ) )
| ( sK1_SY167 @ ( comp @ SX0 @ SX3 ) @ ( sub @ SX1 @ SX3 ) @ SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(165,plain,
( ( ~ ~ ( ~ ! [SX0: subst,SX1: term,SX2: subst,SX3: subst] :
( ~ ( sK1_SY167 @ ( comp @ SX0 @ SX3 ) @ ( sub @ SX1 @ SX3 ) @ SX2 )
| ( sK1_SY167 @ SX0 @ SX1 @ ( comp @ SX3 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ! [SX1: term] :
( ~ ( sK1_SY167 @ id @ SX1 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
| ~ ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[135]) ).
thf(166,plain,
! [SV32: term > $o,SV54: term] :
( ( ! [SY414: subst] :
( ~ ( ~ ( var @ ( sK10_B @ SY414 @ SV54 @ SV32 ) )
| ~ ~ ( SV32 @ ( sub @ ( sK10_B @ SY414 @ SV54 @ SV32 ) @ SY414 ) ) )
| ~ ( SV32 @ SV54 )
| ! [SY415: term] :
( ~ ( var @ SY415 )
| ( SV32 @ ( sub @ SY415 @ ( push @ SV54 @ SY414 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(167,plain,
! [SV33: term > $o] :
( ( ( ~ ( ~ ( var @ ( sK18_A @ SV33 ) )
| ~ ~ ( SV33 @ ( sK18_A @ SV33 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV33 @ ( sK16_A @ SV33 ) )
| ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
| ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(168,plain,
! [SV34: term > $o] :
( ( ( ~ ( ~ ( var @ ( sK9_A @ SV34 ) )
| ~ ~ ( SV34 @ ( sK9_A @ SV34 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK7_A @ SV34 ) )
| ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
| ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(169,plain,
! [SV35: term > $o] :
( ( ( ~ ( SV35 @ one ) )
= $true )
| ( ( ~ ( ~ ( var @ ( sK5_A @ SV35 ) )
| ~ ~ ( ~ ( SV35 @ ( sK5_A @ SV35 ) )
| ~ ~ ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) ) ) )
| ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(170,plain,
! [SV36: term,SV1: term] :
( ( var @ ( sub @ ( ap @ ( sub @ SV1 @ id ) @ SV36 ) @ id ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(171,plain,
! [SV2: subst > term > term] :
( ( ( ( sub @ ( SV2 @ ( sK28_M @ SV2 ) @ ( sK29_SY348 @ SV2 ) ) @ ( sK30_SY350 @ SV2 ) )
= ( SV2 @ ( comp @ ( sK28_M @ SV2 ) @ ( sK30_SY350 @ SV2 ) ) @ ( sub @ ( sK29_SY348 @ SV2 ) @ ( sK30_SY350 @ SV2 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV2 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(172,plain,
! [SV3: subst > term > term] :
( ( ( ( sub @ ( SV3 @ ( sK25_M @ SV3 ) @ ( sK26_SY345 @ SV3 ) ) @ ( sK27_SY347 @ SV3 ) )
= ( SV3 @ ( comp @ ( sK25_M @ SV3 ) @ ( sK27_SY347 @ SV3 ) ) @ ( sub @ ( sK26_SY345 @ SV3 ) @ ( sK27_SY347 @ SV3 ) ) ) )
= $false )
| ( ( ! [SY352: term,SY353: term] :
( ( lam @ ( SV3 @ sh @ one ) )
!= ( ap @ ( sub @ SY352 @ id ) @ SY353 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(173,plain,
! [SV4: subst > term > term] :
( ( ( ( sub @ ( SV4 @ ( sK22_M @ SV4 ) @ ( sK23_SY342 @ SV4 ) ) @ ( sK24_SY344 @ SV4 ) )
= ( SV4 @ ( comp @ ( sK22_M @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) @ ( sub @ ( sK23_SY342 @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) ) )
= $false )
| ( ( ! [SY354: subst > term > term] :
( ( ( sub @ ( SY354 @ ( sK19_M @ SY354 @ SV4 ) @ ( sK20_SY339 @ SY354 @ SV4 ) ) @ ( sK21_SY341 @ SY354 @ SV4 ) )
!= ( SY354 @ ( comp @ ( sK19_M @ SY354 @ SV4 ) @ ( sK21_SY341 @ SY354 @ SV4 ) ) @ ( sub @ ( sK20_SY339 @ SY354 @ SV4 ) @ ( sK21_SY341 @ SY354 @ SV4 ) ) ) )
| ( ( lam @ ( SV4 @ sh @ one ) )
!= ( lam @ ( SY354 @ sh @ one ) ) )
| ! [SY355: subst,SY356: term] :
( ( SV4 @ SY355 @ SY356 )
= ( SY354 @ SY355 @ SY356 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(174,plain,
! [SV37: term,SV55: term,SV5: term] :
( ( ! [SY416: term] :
( ( ( ap @ ( sub @ SV5 @ id ) @ SV55 )
!= ( ap @ ( sub @ SV37 @ id ) @ SY416 ) )
| ( SV55 = SY416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(175,plain,
! [SV38: term,SV6: term] :
( ( ( ! [SY401: term,SY402: term] :
( ( ap @ ( sub @ SV6 @ id ) @ SY401 )
!= ( ap @ ( sub @ SV38 @ id ) @ SY402 ) ) )
= $true )
| ( ( SV6 = SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(176,plain,
! [SV56: subst,SV39: subst,SV8: term] :
( ( ( sub @ ( sub @ SV8 @ SV39 ) @ SV56 )
= ( sub @ SV8 @ ( comp @ SV39 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(177,plain,
! [SV57: subst,SV40: subst,SV11: subst] :
( ( ( comp @ ( comp @ SV11 @ SV40 ) @ SV57 )
= ( comp @ SV11 @ ( comp @ SV40 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(178,plain,
! [SV41: term,SV13: term] :
( ( var @ ( ap @ SV13 @ SV41 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(179,plain,
! [SV58: term,SV42: term,SV14: term] :
( ( ( lam @ SV14 )
!= ( ap @ SV42 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(180,plain,
! [SV43: term,SV15: term] :
( ( ( ( sub @ SV15 @ sh )
!= ( sub @ SV43 @ sh ) )
= $true )
| ( ( SV15 = SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(181,plain,
! [SV44: term,SV16: term] :
( ( ( ( lam @ SV16 )
!= ( lam @ SV44 ) )
= $true )
| ( ( SV16 = SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[152]) ).
thf(182,plain,
! [SV45: term,SV59: term,SV17: term] :
( ( ! [SY417: term] :
( ( ( ap @ SV17 @ SV59 )
!= ( ap @ SV45 @ SY417 ) )
| ( SV59 = SY417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(183,plain,
! [SV46: term,SV18: term] :
( ( ( ! [SY408: term,SY409: term] :
( ( ap @ SV18 @ SY408 )
!= ( ap @ SV46 @ SY409 ) ) )
= $true )
| ( ( SV18 = SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(184,plain,
! [SV19: term] :
( ( ( var @ SV19 )
= $false )
| ( ( var @ ( sub @ SV19 @ sh ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(185,plain,
! [SV60: subst,SV47: subst,SV22: term] :
( ( ( comp @ ( push @ SV22 @ SV47 ) @ SV60 )
= ( push @ ( sub @ SV22 @ SV60 ) @ ( comp @ SV47 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(186,plain,
! [SV61: subst,SV48: subst,SV23: subst] :
( ( ( comp @ ( comp @ SV23 @ SV48 ) @ SV61 )
= ( comp @ SV23 @ ( comp @ SV48 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(187,plain,
! [SV62: subst,SV50: subst,SV26: term] :
( ( ( sub @ ( sub @ SV26 @ SV50 ) @ SV62 )
= ( sub @ SV26 @ ( comp @ SV50 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(188,plain,
! [SV63: subst,SV53: term,SV30: term] :
( ( ( sub @ ( ap @ SV30 @ SV53 ) @ SV63 )
= ( ap @ ( sub @ SV30 @ SV63 ) @ ( sub @ SV53 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(189,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK13_A @ SV31 ) )
| ~ ~ ( ~ ( SV31 @ ( sK14_SY336 @ SV31 ) )
| ~ ~ ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(190,plain,
( ( ! [SX0: subst,SX1: term,SX2: subst,SX3: subst] :
( ~ ( sK1_SY167 @ SX0 @ SX1 @ ( comp @ SX3 @ SX2 ) )
| ( sK1_SY167 @ ( comp @ SX0 @ SX3 ) @ ( sub @ SX1 @ SX3 ) @ SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[164]) ).
thf(191,plain,
( ( ~ ( ~ ! [SX0: subst,SX1: term,SX2: subst,SX3: subst] :
( ~ ( sK1_SY167 @ ( comp @ SX0 @ SX3 ) @ ( sub @ SX1 @ SX3 ) @ SX2 )
| ( sK1_SY167 @ SX0 @ SX1 @ ( comp @ SX3 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ! [SX1: term] :
( ~ ( sK1_SY167 @ id @ SX1 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
| ~ ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(192,plain,
! [SV32: term > $o,SV54: term,SV64: subst] :
( ( ~ ( ~ ( var @ ( sK10_B @ SV64 @ SV54 @ SV32 ) )
| ~ ~ ( SV32 @ ( sub @ ( sK10_B @ SV64 @ SV54 @ SV32 ) @ SV64 ) ) )
| ~ ( SV32 @ SV54 )
| ! [SY418: term] :
( ~ ( var @ SY418 )
| ( SV32 @ ( sub @ SY418 @ ( push @ SV54 @ SV64 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(193,plain,
! [SV33: term > $o] :
( ( ( ~ ( var @ ( sK18_A @ SV33 ) )
| ~ ~ ( SV33 @ ( sK18_A @ SV33 ) ) )
= $false )
| ( ( ~ ( ~ ( SV33 @ ( sK16_A @ SV33 ) )
| ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
| ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(194,plain,
! [SV34: term > $o] :
( ( ( ~ ( var @ ( sK9_A @ SV34 ) )
| ~ ~ ( SV34 @ ( sK9_A @ SV34 ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK7_A @ SV34 ) )
| ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
| ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(195,plain,
! [SV35: term > $o] :
( ( ( SV35 @ one )
= $false )
| ( ( ~ ( ~ ( var @ ( sK5_A @ SV35 ) )
| ~ ~ ( ~ ( SV35 @ ( sK5_A @ SV35 ) )
| ~ ~ ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) ) ) )
| ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(196,plain,
! [SV2: subst > term > term] :
( ( ( var @ ( sub @ ( lam @ ( SV2 @ sh @ one ) ) @ id ) )
= $false )
| ( ( ( sub @ ( SV2 @ ( sK28_M @ SV2 ) @ ( sK29_SY348 @ SV2 ) ) @ ( sK30_SY350 @ SV2 ) )
= ( SV2 @ ( comp @ ( sK28_M @ SV2 ) @ ( sK30_SY350 @ SV2 ) ) @ ( sub @ ( sK29_SY348 @ SV2 ) @ ( sK30_SY350 @ SV2 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(197,plain,
! [SV65: term,SV3: subst > term > term] :
( ( ( ! [SY419: term] :
( ( lam @ ( SV3 @ sh @ one ) )
!= ( ap @ ( sub @ SV65 @ id ) @ SY419 ) ) )
= $true )
| ( ( ( sub @ ( SV3 @ ( sK25_M @ SV3 ) @ ( sK26_SY345 @ SV3 ) ) @ ( sK27_SY347 @ SV3 ) )
= ( SV3 @ ( comp @ ( sK25_M @ SV3 ) @ ( sK27_SY347 @ SV3 ) ) @ ( sub @ ( sK26_SY345 @ SV3 ) @ ( sK27_SY347 @ SV3 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(198,plain,
! [SV4: subst > term > term,SV66: subst > term > term] :
( ( ( ( ( sub @ ( SV66 @ ( sK19_M @ SV66 @ SV4 ) @ ( sK20_SY339 @ SV66 @ SV4 ) ) @ ( sK21_SY341 @ SV66 @ SV4 ) )
!= ( SV66 @ ( comp @ ( sK19_M @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) @ ( sub @ ( sK20_SY339 @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) ) )
| ( ( lam @ ( SV4 @ sh @ one ) )
!= ( lam @ ( SV66 @ sh @ one ) ) )
| ! [SY420: subst,SY421: term] :
( ( SV4 @ SY420 @ SY421 )
= ( SV66 @ SY420 @ SY421 ) ) )
= $true )
| ( ( ( sub @ ( SV4 @ ( sK22_M @ SV4 ) @ ( sK23_SY342 @ SV4 ) ) @ ( sK24_SY344 @ SV4 ) )
= ( SV4 @ ( comp @ ( sK22_M @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) @ ( sub @ ( sK23_SY342 @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(199,plain,
! [SV67: term,SV37: term,SV55: term,SV5: term] :
( ( ( ( ap @ ( sub @ SV5 @ id ) @ SV55 )
!= ( ap @ ( sub @ SV37 @ id ) @ SV67 ) )
| ( SV55 = SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(200,plain,
! [SV38: term,SV68: term,SV6: term] :
( ( ( ! [SY422: term] :
( ( ap @ ( sub @ SV6 @ id ) @ SV68 )
!= ( ap @ ( sub @ SV38 @ id ) @ SY422 ) ) )
= $true )
| ( ( SV6 = SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(201,plain,
! [SV58: term,SV42: term,SV14: term] :
( ( ( lam @ SV14 )
= ( ap @ SV42 @ SV58 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(202,plain,
! [SV43: term,SV15: term] :
( ( ( ( sub @ SV15 @ sh )
= ( sub @ SV43 @ sh ) )
= $false )
| ( ( SV15 = SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(203,plain,
! [SV44: term,SV16: term] :
( ( ( ( lam @ SV16 )
= ( lam @ SV44 ) )
= $false )
| ( ( SV16 = SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(204,plain,
! [SV69: term,SV45: term,SV59: term,SV17: term] :
( ( ( ( ap @ SV17 @ SV59 )
!= ( ap @ SV45 @ SV69 ) )
| ( SV59 = SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(205,plain,
! [SV46: term,SV70: term,SV18: term] :
( ( ( ! [SY423: term] :
( ( ap @ SV18 @ SV70 )
!= ( ap @ SV46 @ SY423 ) ) )
= $true )
| ( ( SV18 = SV46 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(206,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK13_A @ SV31 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(207,plain,
! [SV31: term > $o] :
( ( ( ~ ~ ( ~ ( SV31 @ ( sK14_SY336 @ SV31 ) )
| ~ ~ ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(208,plain,
! [SV71: subst] :
( ( ! [SY424: term,SY425: subst,SY426: subst] :
( ~ ( sK1_SY167 @ SV71 @ SY424 @ ( comp @ SY426 @ SY425 ) )
| ( sK1_SY167 @ ( comp @ SV71 @ SY426 ) @ ( sub @ SY424 @ SY426 ) @ SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(209,plain,
( ( ~ ! [SX0: subst,SX1: term,SX2: subst,SX3: subst] :
( ~ ( sK1_SY167 @ ( comp @ SX0 @ SX3 ) @ ( sub @ SX1 @ SX3 ) @ SX2 )
| ( sK1_SY167 @ SX0 @ SX1 @ ( comp @ SX3 @ SX2 ) ) )
| ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ! [SX1: term] :
( ~ ( sK1_SY167 @ id @ SX1 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
| ~ ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(210,plain,
! [SV32: term > $o,SV54: term,SV64: subst] :
( ( ( ~ ( ~ ( var @ ( sK10_B @ SV64 @ SV54 @ SV32 ) )
| ~ ~ ( SV32 @ ( sub @ ( sK10_B @ SV64 @ SV54 @ SV32 ) @ SV64 ) ) ) )
= $true )
| ( ( ~ ( SV32 @ SV54 )
| ! [SY418: term] :
( ~ ( var @ SY418 )
| ( SV32 @ ( sub @ SY418 @ ( push @ SV54 @ SV64 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(211,plain,
! [SV33: term > $o] :
( ( ( ~ ( var @ ( sK18_A @ SV33 ) ) )
= $false )
| ( ( ~ ( ~ ( SV33 @ ( sK16_A @ SV33 ) )
| ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
| ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(212,plain,
! [SV33: term > $o] :
( ( ( ~ ~ ( SV33 @ ( sK18_A @ SV33 ) ) )
= $false )
| ( ( ~ ( ~ ( SV33 @ ( sK16_A @ SV33 ) )
| ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
| ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[193]) ).
thf(213,plain,
! [SV34: term > $o] :
( ( ( ~ ( var @ ( sK9_A @ SV34 ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK7_A @ SV34 ) )
| ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
| ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(214,plain,
! [SV34: term > $o] :
( ( ( ~ ~ ( SV34 @ ( sK9_A @ SV34 ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK7_A @ SV34 ) )
| ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
| ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(215,plain,
! [SV35: term > $o] :
( ( ( ~ ( ~ ( var @ ( sK5_A @ SV35 ) )
| ~ ~ ( ~ ( SV35 @ ( sK5_A @ SV35 ) )
| ~ ~ ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) ) ) ) )
= $true )
| ( ( ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(216,plain,
! [SV72: term,SV65: term,SV3: subst > term > term] :
( ( ( ( lam @ ( SV3 @ sh @ one ) )
!= ( ap @ ( sub @ SV65 @ id ) @ SV72 ) )
= $true )
| ( ( ( sub @ ( SV3 @ ( sK25_M @ SV3 ) @ ( sK26_SY345 @ SV3 ) ) @ ( sK27_SY347 @ SV3 ) )
= ( SV3 @ ( comp @ ( sK25_M @ SV3 ) @ ( sK27_SY347 @ SV3 ) ) @ ( sub @ ( sK26_SY345 @ SV3 ) @ ( sK27_SY347 @ SV3 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(217,plain,
! [SV4: subst > term > term,SV66: subst > term > term] :
( ( ( ( sub @ ( SV66 @ ( sK19_M @ SV66 @ SV4 ) @ ( sK20_SY339 @ SV66 @ SV4 ) ) @ ( sK21_SY341 @ SV66 @ SV4 ) )
!= ( SV66 @ ( comp @ ( sK19_M @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) @ ( sub @ ( sK20_SY339 @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) ) )
= $true )
| ( ( ( ( lam @ ( SV4 @ sh @ one ) )
!= ( lam @ ( SV66 @ sh @ one ) ) )
| ! [SY420: subst,SY421: term] :
( ( SV4 @ SY420 @ SY421 )
= ( SV66 @ SY420 @ SY421 ) ) )
= $true )
| ( ( ( sub @ ( SV4 @ ( sK22_M @ SV4 ) @ ( sK23_SY342 @ SV4 ) ) @ ( sK24_SY344 @ SV4 ) )
= ( SV4 @ ( comp @ ( sK22_M @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) @ ( sub @ ( sK23_SY342 @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(218,plain,
! [SV67: term,SV37: term,SV55: term,SV5: term] :
( ( ( ( ap @ ( sub @ SV5 @ id ) @ SV55 )
!= ( ap @ ( sub @ SV37 @ id ) @ SV67 ) )
= $true )
| ( ( SV55 = SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(219,plain,
! [SV73: term,SV38: term,SV68: term,SV6: term] :
( ( ( ( ap @ ( sub @ SV6 @ id ) @ SV68 )
!= ( ap @ ( sub @ SV38 @ id ) @ SV73 ) )
= $true )
| ( ( SV6 = SV38 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(220,plain,
! [SV69: term,SV45: term,SV59: term,SV17: term] :
( ( ( ( ap @ SV17 @ SV59 )
!= ( ap @ SV45 @ SV69 ) )
= $true )
| ( ( SV59 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(221,plain,
! [SV74: term,SV46: term,SV70: term,SV18: term] :
( ( ( ( ap @ SV18 @ SV70 )
!= ( ap @ SV46 @ SV74 ) )
= $true )
| ( ( SV18 = SV46 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(222,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true )
| ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(223,plain,
! [SV31: term > $o] :
( ( ( ~ ( ~ ( SV31 @ ( sK14_SY336 @ SV31 ) )
| ~ ~ ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(224,plain,
! [SV75: term,SV71: subst] :
( ( ! [SY427: subst,SY428: subst] :
( ~ ( sK1_SY167 @ SV71 @ SV75 @ ( comp @ SY428 @ SY427 ) )
| ( sK1_SY167 @ ( comp @ SV71 @ SY428 ) @ ( sub @ SV75 @ SY428 ) @ SY427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(225,plain,
( ( ~ ! [SX0: subst,SX1: term,SX2: subst,SX3: subst] :
( ~ ( sK1_SY167 @ ( comp @ SX0 @ SX3 ) @ ( sub @ SX1 @ SX3 ) @ SX2 )
| ( sK1_SY167 @ SX0 @ SX1 @ ( comp @ SX3 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(226,plain,
( ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ! [SX1: term] :
( ~ ( sK1_SY167 @ id @ SX1 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
| ~ ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(227,plain,
! [SV32: term > $o,SV54: term,SV64: subst] :
( ( ( ~ ( var @ ( sK10_B @ SV64 @ SV54 @ SV32 ) )
| ~ ~ ( SV32 @ ( sub @ ( sK10_B @ SV64 @ SV54 @ SV32 ) @ SV64 ) ) )
= $false )
| ( ( ~ ( SV32 @ SV54 )
| ! [SY418: term] :
( ~ ( var @ SY418 )
| ( SV32 @ ( sub @ SY418 @ ( push @ SV54 @ SV64 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(228,plain,
! [SV33: term > $o] :
( ( ( var @ ( sK18_A @ SV33 ) )
= $true )
| ( ( ~ ( ~ ( SV33 @ ( sK16_A @ SV33 ) )
| ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
| ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[211]) ).
thf(229,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( sK18_A @ SV33 ) ) )
= $true )
| ( ( ~ ( ~ ( SV33 @ ( sK16_A @ SV33 ) )
| ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
| ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[212]) ).
thf(230,plain,
! [SV34: term > $o] :
( ( ( var @ ( sK9_A @ SV34 ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK7_A @ SV34 ) )
| ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
| ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(231,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK9_A @ SV34 ) ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK7_A @ SV34 ) )
| ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
| ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(232,plain,
! [SV35: term > $o] :
( ( ( ~ ( var @ ( sK5_A @ SV35 ) )
| ~ ~ ( ~ ( SV35 @ ( sK5_A @ SV35 ) )
| ~ ~ ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) ) ) )
= $false )
| ( ( ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(233,plain,
! [SV72: term,SV65: term,SV3: subst > term > term] :
( ( ( ( lam @ ( SV3 @ sh @ one ) )
= ( ap @ ( sub @ SV65 @ id ) @ SV72 ) )
= $false )
| ( ( ( sub @ ( SV3 @ ( sK25_M @ SV3 ) @ ( sK26_SY345 @ SV3 ) ) @ ( sK27_SY347 @ SV3 ) )
= ( SV3 @ ( comp @ ( sK25_M @ SV3 ) @ ( sK27_SY347 @ SV3 ) ) @ ( sub @ ( sK26_SY345 @ SV3 ) @ ( sK27_SY347 @ SV3 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(234,plain,
! [SV4: subst > term > term,SV66: subst > term > term] :
( ( ( ( sub @ ( SV66 @ ( sK19_M @ SV66 @ SV4 ) @ ( sK20_SY339 @ SV66 @ SV4 ) ) @ ( sK21_SY341 @ SV66 @ SV4 ) )
= ( SV66 @ ( comp @ ( sK19_M @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) @ ( sub @ ( sK20_SY339 @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV4 @ sh @ one ) )
!= ( lam @ ( SV66 @ sh @ one ) ) )
| ! [SY420: subst,SY421: term] :
( ( SV4 @ SY420 @ SY421 )
= ( SV66 @ SY420 @ SY421 ) ) )
= $true )
| ( ( ( sub @ ( SV4 @ ( sK22_M @ SV4 ) @ ( sK23_SY342 @ SV4 ) ) @ ( sK24_SY344 @ SV4 ) )
= ( SV4 @ ( comp @ ( sK22_M @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) @ ( sub @ ( sK23_SY342 @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(235,plain,
! [SV67: term,SV37: term,SV55: term,SV5: term] :
( ( ( ( ap @ ( sub @ SV5 @ id ) @ SV55 )
= ( ap @ ( sub @ SV37 @ id ) @ SV67 ) )
= $false )
| ( ( SV55 = SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(236,plain,
! [SV73: term,SV38: term,SV68: term,SV6: term] :
( ( ( ( ap @ ( sub @ SV6 @ id ) @ SV68 )
= ( ap @ ( sub @ SV38 @ id ) @ SV73 ) )
= $false )
| ( ( SV6 = SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(237,plain,
! [SV69: term,SV45: term,SV59: term,SV17: term] :
( ( ( ( ap @ SV17 @ SV59 )
= ( ap @ SV45 @ SV69 ) )
= $false )
| ( ( SV59 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(238,plain,
! [SV74: term,SV46: term,SV70: term,SV18: term] :
( ( ( ( ap @ SV18 @ SV70 )
= ( ap @ SV46 @ SV74 ) )
= $false )
| ( ( SV18 = SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(239,plain,
! [SV31: term > $o] :
( ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(240,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK14_SY336 @ SV31 ) )
| ~ ~ ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(241,plain,
! [SV76: subst,SV75: term,SV71: subst] :
( ( ! [SY429: subst] :
( ~ ( sK1_SY167 @ SV71 @ SV75 @ ( comp @ SY429 @ SV76 ) )
| ( sK1_SY167 @ ( comp @ SV71 @ SY429 ) @ ( sub @ SV75 @ SY429 ) @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(242,plain,
( ( ! [SX0: subst,SX1: term,SX2: subst,SX3: subst] :
( ~ ( sK1_SY167 @ ( comp @ SX0 @ SX3 ) @ ( sub @ SX1 @ SX3 ) @ SX2 )
| ( sK1_SY167 @ SX0 @ SX1 @ ( comp @ SX3 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(243,plain,
( ( ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ! [SX1: term] :
( ~ ( sK1_SY167 @ id @ SX1 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
| ~ ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(244,plain,
! [SV32: term > $o,SV54: term,SV64: subst] :
( ( ( ~ ( var @ ( sK10_B @ SV64 @ SV54 @ SV32 ) ) )
= $false )
| ( ( ~ ( SV32 @ SV54 )
| ! [SY418: term] :
( ~ ( var @ SY418 )
| ( SV32 @ ( sub @ SY418 @ ( push @ SV54 @ SV64 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(245,plain,
! [SV54: term,SV64: subst,SV32: term > $o] :
( ( ( ~ ~ ( SV32 @ ( sub @ ( sK10_B @ SV64 @ SV54 @ SV32 ) @ SV64 ) ) )
= $false )
| ( ( ~ ( SV32 @ SV54 )
| ! [SY418: term] :
( ~ ( var @ SY418 )
| ( SV32 @ ( sub @ SY418 @ ( push @ SV54 @ SV64 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(246,plain,
! [SV33: term > $o] :
( ( ( ~ ( ~ ( SV33 @ ( sK16_A @ SV33 ) )
| ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(247,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false )
| ( ( ~ ( ~ ( SV33 @ ( sK16_A @ SV33 ) )
| ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
| ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(248,plain,
! [SV34: term > $o] :
( ( ( ~ ( ~ ( SV34 @ ( sK7_A @ SV34 ) )
| ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(249,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK7_A @ SV34 ) )
| ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
| ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(250,plain,
! [SV35: term > $o] :
( ( ( ~ ( var @ ( sK5_A @ SV35 ) ) )
= $false )
| ( ( ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(251,plain,
! [SV35: term > $o] :
( ( ( ~ ~ ( ~ ( SV35 @ ( sK5_A @ SV35 ) )
| ~ ~ ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) ) ) )
= $false )
| ( ( ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(252,plain,
! [SV66: subst > term > term,SV4: subst > term > term] :
( ( ( ( lam @ ( SV4 @ sh @ one ) )
!= ( lam @ ( SV66 @ sh @ one ) ) )
= $true )
| ( ( ! [SY420: subst,SY421: term] :
( ( SV4 @ SY420 @ SY421 )
= ( SV66 @ SY420 @ SY421 ) ) )
= $true )
| ( ( ( sub @ ( SV66 @ ( sK19_M @ SV66 @ SV4 ) @ ( sK20_SY339 @ SV66 @ SV4 ) ) @ ( sK21_SY341 @ SV66 @ SV4 ) )
= ( SV66 @ ( comp @ ( sK19_M @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) @ ( sub @ ( sK20_SY339 @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) ) )
= $false )
| ( ( ( sub @ ( SV4 @ ( sK22_M @ SV4 ) @ ( sK23_SY342 @ SV4 ) ) @ ( sK24_SY344 @ SV4 ) )
= ( SV4 @ ( comp @ ( sK22_M @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) @ ( sub @ ( sK23_SY342 @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(253,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
= $false )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(254,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sK14_SY336 @ SV31 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(255,plain,
! [SV31: term > $o] :
( ( ( ~ ~ ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(256,plain,
! [SV76: subst,SV77: subst,SV75: term,SV71: subst] :
( ( ~ ( sK1_SY167 @ SV71 @ SV75 @ ( comp @ SV77 @ SV76 ) )
| ( sK1_SY167 @ ( comp @ SV71 @ SV77 ) @ ( sub @ SV75 @ SV77 ) @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(257,plain,
! [SV78: subst] :
( ( ! [SY430: term,SY431: subst,SY432: subst] :
( ~ ( sK1_SY167 @ ( comp @ SV78 @ SY432 ) @ ( sub @ SY430 @ SY432 ) @ SY431 )
| ( sK1_SY167 @ SV78 @ SY430 @ ( comp @ SY432 @ SY431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(258,plain,
( ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ! [SX1: term] :
( ~ ( sK1_SY167 @ id @ SX1 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
| ~ ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(259,plain,
! [SV32: term > $o,SV54: term,SV64: subst] :
( ( ( var @ ( sK10_B @ SV64 @ SV54 @ SV32 ) )
= $true )
| ( ( ~ ( SV32 @ SV54 )
| ! [SY418: term] :
( ~ ( var @ SY418 )
| ( SV32 @ ( sub @ SY418 @ ( push @ SV54 @ SV64 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(260,plain,
! [SV54: term,SV64: subst,SV32: term > $o] :
( ( ( ~ ( SV32 @ ( sub @ ( sK10_B @ SV64 @ SV54 @ SV32 ) @ SV64 ) ) )
= $true )
| ( ( ~ ( SV32 @ SV54 )
| ! [SY418: term] :
( ~ ( var @ SY418 )
| ( SV32 @ ( sub @ SY418 @ ( push @ SV54 @ SV64 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(261,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( sK16_A @ SV33 ) )
| ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(262,plain,
! [SV33: term > $o] :
( ( ( ~ ( ~ ( SV33 @ ( sK16_A @ SV33 ) )
| ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(263,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK7_A @ SV34 ) )
| ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(264,plain,
! [SV34: term > $o] :
( ( ( ~ ( ~ ( SV34 @ ( sK7_A @ SV34 ) )
| ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[249]) ).
thf(265,plain,
! [SV35: term > $o] :
( ( ( var @ ( sK5_A @ SV35 ) )
= $true )
| ( ( ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(266,plain,
! [SV35: term > $o] :
( ( ( ~ ( ~ ( SV35 @ ( sK5_A @ SV35 ) )
| ~ ~ ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) ) ) )
= $true )
| ( ( ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(267,plain,
! [SV66: subst > term > term,SV4: subst > term > term] :
( ( ( ( lam @ ( SV4 @ sh @ one ) )
= ( lam @ ( SV66 @ sh @ one ) ) )
= $false )
| ( ( ! [SY420: subst,SY421: term] :
( ( SV4 @ SY420 @ SY421 )
= ( SV66 @ SY420 @ SY421 ) ) )
= $true )
| ( ( ( sub @ ( SV66 @ ( sK19_M @ SV66 @ SV4 ) @ ( sK20_SY339 @ SV66 @ SV4 ) ) @ ( sK21_SY341 @ SV66 @ SV4 ) )
= ( SV66 @ ( comp @ ( sK19_M @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) @ ( sub @ ( sK20_SY339 @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) ) )
= $false )
| ( ( ( sub @ ( SV4 @ ( sK22_M @ SV4 ) @ ( sK23_SY342 @ SV4 ) ) @ ( sK24_SY344 @ SV4 ) )
= ( SV4 @ ( comp @ ( sK22_M @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) @ ( sub @ ( sK23_SY342 @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(268,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) ) )
= $false )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(269,plain,
! [SV31: term > $o] :
( ( ( ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
= $false )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(270,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true )
| ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(271,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(272,plain,
! [SV76: subst,SV77: subst,SV75: term,SV71: subst] :
( ( ( ~ ( sK1_SY167 @ SV71 @ SV75 @ ( comp @ SV77 @ SV76 ) ) )
= $true )
| ( ( sK1_SY167 @ ( comp @ SV71 @ SV77 ) @ ( sub @ SV75 @ SV77 ) @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(273,plain,
! [SV79: term,SV78: subst] :
( ( ! [SY433: subst,SY434: subst] :
( ~ ( sK1_SY167 @ ( comp @ SV78 @ SY434 ) @ ( sub @ SV79 @ SY434 ) @ SY433 )
| ( sK1_SY167 @ SV78 @ SV79 @ ( comp @ SY434 @ SY433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(274,plain,
( ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ! [SX1: term] :
( ~ ( sK1_SY167 @ id @ SX1 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(275,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
| ~ ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(276,plain,
! [SV64: subst,SV54: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV54 ) )
= $true )
| ( ( ! [SY418: term] :
( ~ ( var @ SY418 )
| ( SV32 @ ( sub @ SY418 @ ( push @ SV54 @ SV64 ) ) ) ) )
= $true )
| ( ( var @ ( sK10_B @ SV64 @ SV54 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(277,plain,
! [SV54: term,SV64: subst,SV32: term > $o] :
( ( ( SV32 @ ( sub @ ( sK10_B @ SV64 @ SV54 @ SV32 ) @ SV64 ) )
= $false )
| ( ( ~ ( SV32 @ SV54 )
| ! [SY418: term] :
( ~ ( var @ SY418 )
| ( SV32 @ ( sub @ SY418 @ ( push @ SV54 @ SV64 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(278,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( sK16_A @ SV33 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(279,plain,
! [SV33: term > $o] :
( ( ( ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[261]) ).
thf(280,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( sK16_A @ SV33 ) )
| ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(281,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK7_A @ SV34 ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(282,plain,
! [SV34: term > $o] :
( ( ( ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[263]) ).
thf(283,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK7_A @ SV34 ) )
| ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(284,plain,
! [SV35: term > $o,SV80: term] :
( ( ( ~ ( var @ SV80 )
| ( SV35 @ SV80 ) )
= $true )
| ( ( var @ ( sK5_A @ SV35 ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(285,plain,
! [SV35: term > $o] :
( ( ( ~ ( SV35 @ ( sK5_A @ SV35 ) )
| ~ ~ ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) ) )
= $false )
| ( ( ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(286,plain,
! [SV66: subst > term > term,SV81: subst,SV4: subst > term > term] :
( ( ( ! [SY435: term] :
( ( SV4 @ SV81 @ SY435 )
= ( SV66 @ SV81 @ SY435 ) ) )
= $true )
| ( ( ( lam @ ( SV4 @ sh @ one ) )
= ( lam @ ( SV66 @ sh @ one ) ) )
= $false )
| ( ( ( sub @ ( SV66 @ ( sK19_M @ SV66 @ SV4 ) @ ( sK20_SY339 @ SV66 @ SV4 ) ) @ ( sK21_SY341 @ SV66 @ SV4 ) )
= ( SV66 @ ( comp @ ( sK19_M @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) @ ( sub @ ( sK20_SY339 @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) ) )
= $false )
| ( ( ( sub @ ( SV4 @ ( sK22_M @ SV4 ) @ ( sK23_SY342 @ SV4 ) ) @ ( sK24_SY344 @ SV4 ) )
= ( SV4 @ ( comp @ ( sK22_M @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) @ ( sub @ ( sK23_SY342 @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(287,plain,
! [SV31: term > $o] :
( ( ( ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(288,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(289,plain,
! [SV31: term > $o] :
( ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(290,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
| ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[271]) ).
thf(291,plain,
! [SV76: subst,SV77: subst,SV75: term,SV71: subst] :
( ( ( sK1_SY167 @ SV71 @ SV75 @ ( comp @ SV77 @ SV76 ) )
= $false )
| ( ( sK1_SY167 @ ( comp @ SV71 @ SV77 ) @ ( sub @ SV75 @ SV77 ) @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(292,plain,
! [SV82: subst,SV79: term,SV78: subst] :
( ( ! [SY436: subst] :
( ~ ( sK1_SY167 @ ( comp @ SV78 @ SY436 ) @ ( sub @ SV79 @ SY436 ) @ SV82 )
| ( sK1_SY167 @ SV78 @ SV79 @ ( comp @ SY436 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(293,plain,
( ( ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ! [SX1: term] :
( ~ ( sK1_SY167 @ id @ SX1 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(294,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
| ~ ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(295,plain,
! [SV64: subst,SV54: term,SV32: term > $o] :
( ( ( SV32 @ SV54 )
= $false )
| ( ( ! [SY418: term] :
( ~ ( var @ SY418 )
| ( SV32 @ ( sub @ SY418 @ ( push @ SV54 @ SV64 ) ) ) ) )
= $true )
| ( ( var @ ( sK10_B @ SV64 @ SV54 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(296,plain,
! [SV64: subst,SV54: term,SV32: term > $o] :
( ( ( ~ ( SV32 @ SV54 ) )
= $true )
| ( ( ! [SY418: term] :
( ~ ( var @ SY418 )
| ( SV32 @ ( sub @ SY418 @ ( push @ SV54 @ SV64 ) ) ) ) )
= $true )
| ( ( SV32 @ ( sub @ ( sK10_B @ SV64 @ SV54 @ SV32 ) @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[277]) ).
thf(297,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(298,plain,
! [SV33: term > $o] :
( ( ( ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(299,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( sK16_A @ SV33 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(300,plain,
! [SV33: term > $o] :
( ( ( ~ ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[280]) ).
thf(301,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(302,plain,
! [SV34: term > $o] :
( ( ( ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(303,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK7_A @ SV34 ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(304,plain,
! [SV34: term > $o] :
( ( ( ~ ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(305,plain,
! [SV35: term > $o,SV80: term] :
( ( ( ~ ( var @ SV80 ) )
= $true )
| ( ( SV35 @ SV80 )
= $true )
| ( ( var @ ( sK5_A @ SV35 ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(306,plain,
! [SV35: term > $o] :
( ( ( ~ ( SV35 @ ( sK5_A @ SV35 ) ) )
= $false )
| ( ( ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(307,plain,
! [SV35: term > $o] :
( ( ( ~ ~ ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) ) )
= $false )
| ( ( ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[285]) ).
thf(308,plain,
! [SV66: subst > term > term,SV83: term,SV81: subst,SV4: subst > term > term] :
( ( ( ( SV4 @ SV81 @ SV83 )
= ( SV66 @ SV81 @ SV83 ) )
= $true )
| ( ( ( lam @ ( SV4 @ sh @ one ) )
= ( lam @ ( SV66 @ sh @ one ) ) )
= $false )
| ( ( ( sub @ ( SV66 @ ( sK19_M @ SV66 @ SV4 ) @ ( sK20_SY339 @ SV66 @ SV4 ) ) @ ( sK21_SY341 @ SV66 @ SV4 ) )
= ( SV66 @ ( comp @ ( sK19_M @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) @ ( sub @ ( sK20_SY339 @ SV66 @ SV4 ) @ ( sK21_SY341 @ SV66 @ SV4 ) ) ) )
= $false )
| ( ( ( sub @ ( SV4 @ ( sK22_M @ SV4 ) @ ( sK23_SY342 @ SV4 ) ) @ ( sK24_SY344 @ SV4 ) )
= ( SV4 @ ( comp @ ( sK22_M @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) @ ( sub @ ( sK23_SY342 @ SV4 ) @ ( sK24_SY344 @ SV4 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(309,plain,
! [SV84: term,SV31: term > $o] :
( ( ( ~ ( SV31 @ SV84 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV84 @ id ) ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(310,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(311,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
= $false )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(312,plain,
! [SV31: term > $o] :
( ( ( ~ ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(313,plain,
! [SV82: subst,SV79: term,SV85: subst,SV78: subst] :
( ( ~ ( sK1_SY167 @ ( comp @ SV78 @ SV85 ) @ ( sub @ SV79 @ SV85 ) @ SV82 )
| ( sK1_SY167 @ SV78 @ SV79 @ ( comp @ SV85 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(314,plain,
! [SV86: term] :
( ( ~ ( sK1_SY167 @ id @ SV86 @ id )
| ! [SY437: term] :
( ~ ( sK1_SY167 @ id @ SY437 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SV86 @ id ) @ SY437 ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(315,plain,
( ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
| ~ ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(316,plain,
! [SV64: subst,SV54: term,SV32: term > $o,SV87: term] :
( ( ( ~ ( var @ SV87 )
| ( SV32 @ ( sub @ SV87 @ ( push @ SV54 @ SV64 ) ) ) )
= $true )
| ( ( SV32 @ SV54 )
= $false )
| ( ( var @ ( sK10_B @ SV64 @ SV54 @ SV32 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(317,plain,
! [SV64: subst,SV54: term,SV32: term > $o] :
( ( ( SV32 @ SV54 )
= $false )
| ( ( ! [SY418: term] :
( ~ ( var @ SY418 )
| ( SV32 @ ( sub @ SY418 @ ( push @ SV54 @ SV64 ) ) ) ) )
= $true )
| ( ( SV32 @ ( sub @ ( sK10_B @ SV64 @ SV54 @ SV32 ) @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(318,plain,
! [SV33: term > $o] :
( ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(319,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(320,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(321,plain,
! [SV33: term > $o] :
( ( ( ~ ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(322,plain,
! [SV34: term > $o] :
( ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(323,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(324,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(325,plain,
! [SV34: term > $o] :
( ( ( ~ ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(326,plain,
! [SV35: term > $o,SV80: term] :
( ( ( var @ SV80 )
= $false )
| ( ( SV35 @ SV80 )
= $true )
| ( ( var @ ( sK5_A @ SV35 ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(327,plain,
! [SV35: term > $o] :
( ( ( SV35 @ ( sK5_A @ SV35 ) )
= $true )
| ( ( ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(328,plain,
! [SV35: term > $o] :
( ( ( ~ ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) ) )
= $true )
| ( ( ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[307]) ).
thf(329,plain,
! [SV84: term,SV31: term > $o] :
( ( ( ~ ( SV31 @ SV84 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[309]) ).
thf(330,plain,
! [SV31: term > $o,SV88: term] :
( ( ( ! [SY438: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY438 @ SV88 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY438 @ SV88 @ SV31 ) @ SY438 ) ) )
| ( SV31 @ ( sub @ SV88 @ SY438 ) ) ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(331,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) ) )
= $false )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(332,plain,
! [SV31: term > $o] :
( ( ( ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
= $false )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[311]) ).
thf(333,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) )
| ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
= $false )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(334,plain,
! [SV82: subst,SV79: term,SV85: subst,SV78: subst] :
( ( ( ~ ( sK1_SY167 @ ( comp @ SV78 @ SV85 ) @ ( sub @ SV79 @ SV85 ) @ SV82 ) )
= $true )
| ( ( sK1_SY167 @ SV78 @ SV79 @ ( comp @ SV85 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(335,plain,
! [SV86: term] :
( ( ( ~ ( sK1_SY167 @ id @ SV86 @ id ) )
= $true )
| ( ( ! [SY437: term] :
( ~ ( sK1_SY167 @ id @ SY437 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SV86 @ id ) @ SY437 ) @ id ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(336,plain,
( ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(337,plain,
( ( ~ ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[315]) ).
thf(338,plain,
! [SV64: subst,SV54: term,SV32: term > $o,SV87: term] :
( ( ( ~ ( var @ SV87 ) )
= $true )
| ( ( SV32 @ ( sub @ SV87 @ ( push @ SV54 @ SV64 ) ) )
= $true )
| ( ( SV32 @ SV54 )
= $false )
| ( ( var @ ( sK10_B @ SV64 @ SV54 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(339,plain,
! [SV64: subst,SV54: term,SV32: term > $o,SV89: term] :
( ( ( ~ ( var @ SV89 )
| ( SV32 @ ( sub @ SV89 @ ( push @ SV54 @ SV64 ) ) ) )
= $true )
| ( ( SV32 @ SV54 )
= $false )
| ( ( SV32 @ ( sub @ ( sK10_B @ SV64 @ SV54 @ SV32 ) @ SV64 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(340,plain,
! [SV33: term > $o] :
( ( ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(341,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(342,plain,
! [SV33: term > $o] :
( ( ( ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(343,plain,
! [SV33: term > $o] :
( ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(344,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) )
| ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[321]) ).
thf(345,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(346,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(347,plain,
! [SV34: term > $o] :
( ( ( ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(348,plain,
! [SV34: term > $o] :
( ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(349,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) )
| ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(350,plain,
! [SV35: term > $o,SV90: term] :
( ( ( ~ ( var @ SV90 )
| ( SV35 @ SV90 ) )
= $true )
| ( ( SV35 @ ( sK5_A @ SV35 ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(351,plain,
! [SV35: term > $o] :
( ( ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) )
= $false )
| ( ( ! [SY398: term] :
( ~ ( var @ SY398 )
| ( SV35 @ SY398 ) ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(352,plain,
! [SV84: term,SV31: term > $o] :
( ( ( SV31 @ SV84 )
= $false )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(353,plain,
! [SV31: term > $o,SV88: term,SV91: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV91 @ SV88 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV91 @ SV88 @ SV31 ) @ SV91 ) ) )
| ( SV31 @ ( sub @ SV88 @ SV91 ) ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(354,plain,
! [SV31: term > $o] :
( ( ( ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(355,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[332]) ).
thf(356,plain,
! [SV31: term > $o] :
( ( ( ~ ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) ) )
= $false )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(357,plain,
! [SV31: term > $o] :
( ( ( ~ ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
= $false )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[333]) ).
thf(358,plain,
! [SV82: subst,SV79: term,SV85: subst,SV78: subst] :
( ( ( sK1_SY167 @ ( comp @ SV78 @ SV85 ) @ ( sub @ SV79 @ SV85 ) @ SV82 )
= $false )
| ( ( sK1_SY167 @ SV78 @ SV79 @ ( comp @ SV85 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(359,plain,
! [SV86: term] :
( ( ( sK1_SY167 @ id @ SV86 @ id )
= $false )
| ( ( ! [SY437: term] :
( ~ ( sK1_SY167 @ id @ SY437 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SV86 @ id ) @ SY437 ) @ id ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(360,plain,
( ( ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[336]) ).
thf(361,plain,
( ( ~ ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(362,plain,
! [SV64: subst,SV54: term,SV32: term > $o,SV87: term] :
( ( ( var @ SV87 )
= $false )
| ( ( SV32 @ ( sub @ SV87 @ ( push @ SV54 @ SV64 ) ) )
= $true )
| ( ( SV32 @ SV54 )
= $false )
| ( ( var @ ( sK10_B @ SV64 @ SV54 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(363,plain,
! [SV64: subst,SV54: term,SV32: term > $o,SV89: term] :
( ( ( ~ ( var @ SV89 ) )
= $true )
| ( ( SV32 @ ( sub @ SV89 @ ( push @ SV54 @ SV64 ) ) )
= $true )
| ( ( SV32 @ SV54 )
= $false )
| ( ( SV32 @ ( sub @ ( sK10_B @ SV64 @ SV54 @ SV32 ) @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(364,plain,
! [SV33: term > $o] :
( ( ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(365,plain,
! [SV33: term > $o] :
( ( ( ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[340]) ).
thf(366,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[341]) ).
thf(367,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[342]) ).
thf(368,plain,
! [SV33: term > $o] :
( ( ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(369,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(370,plain,
! [SV33: term > $o] :
( ( ( ~ ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[344]) ).
thf(371,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(372,plain,
! [SV34: term > $o] :
( ( ( ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(373,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(374,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(375,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(376,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(377,plain,
! [SV34: term > $o] :
( ( ( ~ ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[349]) ).
thf(378,plain,
! [SV35: term > $o,SV90: term] :
( ( ( ~ ( var @ SV90 ) )
= $true )
| ( ( SV35 @ SV90 )
= $true )
| ( ( SV35 @ ( sK5_A @ SV35 ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(379,plain,
! [SV35: term > $o,SV92: term] :
( ( ( ~ ( var @ SV92 )
| ( SV35 @ SV92 ) )
= $true )
| ( ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) )
= $false )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(380,plain,
! [SV84: term,SV31: term > $o,SV93: term] :
( ( ( ! [SY439: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY439 @ SV93 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY439 @ SV93 @ SV31 ) @ SY439 ) ) )
| ( SV31 @ ( sub @ SV93 @ SY439 ) ) ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV31 @ SV84 )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(381,plain,
! [SV31: term > $o,SV88: term,SV91: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV91 @ SV88 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV91 @ SV88 @ SV31 ) @ SV91 ) ) ) )
= $true )
| ( ( SV31 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(382,plain,
! [SV94: term,SV31: term > $o] :
( ( ( ~ ( SV31 @ SV94 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV94 @ id ) ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(383,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(384,plain,
! [SV31: term > $o] :
( ( ( ! [SY389: term] :
( ~ ( SV31 @ SY389 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SY389 @ id ) ) ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[356]) ).
thf(385,plain,
! [SV31: term > $o] :
( ( ( ~ ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[357]) ).
thf(386,plain,
! [SV86: term,SV95: term] :
( ( ( ~ ( sK1_SY167 @ id @ SV95 @ id )
| ( sK1_SY167 @ id @ ( ap @ ( sub @ SV86 @ id ) @ SV95 ) @ id ) )
= $true )
| ( ( sK1_SY167 @ id @ SV86 @ id )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(387,plain,
( ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) )
| ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(388,plain,
( ( ~ ( sK2_SY324 @ sK3_SY331 )
| ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(389,plain,
! [SV64: subst,SV54: term,SV32: term > $o,SV89: term] :
( ( ( var @ SV89 )
= $false )
| ( ( SV32 @ ( sub @ SV89 @ ( push @ SV54 @ SV64 ) ) )
= $true )
| ( ( SV32 @ SV54 )
= $false )
| ( ( SV32 @ ( sub @ ( sK10_B @ SV64 @ SV54 @ SV32 ) @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(390,plain,
! [SV33: term > $o] :
( ( ( ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[364]) ).
thf(391,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[365]) ).
thf(392,plain,
! [SV33: term > $o] :
( ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(393,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(394,plain,
! [SV33: term > $o] :
( ( ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(395,plain,
! [SV33: term > $o] :
( ( ( ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[368]) ).
thf(396,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[369]) ).
thf(397,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(398,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK6_A @ SV34 ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(399,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[372]) ).
thf(400,plain,
! [SV34: term > $o] :
( ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(401,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(402,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(403,plain,
! [SV34: term > $o] :
( ( ( ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(404,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[376]) ).
thf(405,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[377]) ).
thf(406,plain,
! [SV35: term > $o,SV90: term] :
( ( ( var @ SV90 )
= $false )
| ( ( SV35 @ SV90 )
= $true )
| ( ( SV35 @ ( sK5_A @ SV35 ) )
= $true )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(407,plain,
! [SV35: term > $o,SV92: term] :
( ( ( ~ ( var @ SV92 ) )
= $true )
| ( ( SV35 @ SV92 )
= $true )
| ( ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) )
= $false )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(408,plain,
! [SV84: term,SV31: term > $o,SV93: term,SV96: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV96 @ SV93 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV96 @ SV93 @ SV31 ) @ SV96 ) ) )
| ( SV31 @ ( sub @ SV93 @ SV96 ) ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV31 @ SV84 )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(409,plain,
! [SV31: term > $o,SV88: term,SV91: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV91 @ SV88 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV91 @ SV88 @ SV31 ) @ SV91 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(410,plain,
! [SV94: term,SV31: term > $o] :
( ( ( ~ ( SV31 @ SV94 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(411,plain,
! [SV31: term > $o,SV97: term] :
( ( ( ! [SY440: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY440 @ SV97 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY440 @ SV97 @ SV31 ) @ SY440 ) ) )
| ( SV31 @ ( sub @ SV97 @ SY440 ) ) ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(412,plain,
! [SV98: term,SV31: term > $o] :
( ( ( ~ ( SV31 @ SV98 )
| ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV98 @ id ) ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(413,plain,
! [SV31: term > $o] :
( ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(414,plain,
! [SV86: term,SV95: term] :
( ( ( ~ ( sK1_SY167 @ id @ SV95 @ id ) )
= $true )
| ( ( sK1_SY167 @ id @ ( ap @ ( sub @ SV86 @ id ) @ SV95 ) @ id )
= $true )
| ( ( sK1_SY167 @ id @ SV86 @ id )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(415,plain,
( ( ~ ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(416,plain,
( ( ~ ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(417,plain,
( ( ~ ( sK2_SY324 @ sK3_SY331 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(418,plain,
( ( ~ ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(419,plain,
! [SV99: term,SV33: term > $o] :
( ( ( ~ ( SV33 @ SV99 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV99 @ id ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(420,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[391]) ).
thf(421,plain,
! [SV33: term > $o] :
( ( ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(422,plain,
! [SV33: term > $o] :
( ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(423,plain,
! [SV33: term > $o] :
( ( ( ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(424,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[395]) ).
thf(425,plain,
! [SV33: term > $o] :
( ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(426,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
| ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(427,plain,
! [SV100: term,SV34: term > $o] :
( ( ( SV34 @ SV100 )
= $true )
| ( ( SV34 @ ( sK6_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(428,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(429,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(430,plain,
! [SV34: term > $o] :
( ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(431,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK6_A @ SV34 ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[402]) ).
thf(432,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[403]) ).
thf(433,plain,
! [SV34: term > $o] :
( ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(434,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
| ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(435,plain,
! [SV35: term > $o,SV92: term] :
( ( ( var @ SV92 )
= $false )
| ( ( SV35 @ SV92 )
= $true )
| ( ( SV35 @ ( sub @ ( sK5_A @ SV35 ) @ sh ) )
= $false )
| ( ( SV35 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(436,plain,
! [SV84: term,SV31: term > $o,SV93: term,SV96: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV96 @ SV93 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV96 @ SV93 @ SV31 ) @ SV96 ) ) ) )
= $true )
| ( ( SV31 @ ( sub @ SV93 @ SV96 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV31 @ SV84 )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(437,plain,
! [SV31: term > $o,SV88: term,SV91: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV91 @ SV88 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(438,plain,
! [SV88: term,SV91: subst,SV31: term > $o] :
( ( ( ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV91 @ SV88 @ SV31 ) @ SV91 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(439,plain,
! [SV94: term,SV31: term > $o] :
( ( ( SV31 @ SV94 )
= $false )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(440,plain,
! [SV31: term > $o,SV97: term,SV101: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV101 @ SV97 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV101 @ SV97 @ SV31 ) @ SV101 ) ) )
| ( SV31 @ ( sub @ SV97 @ SV101 ) ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(441,plain,
! [SV98: term,SV31: term > $o] :
( ( ( ~ ( SV31 @ SV98 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(442,plain,
! [SV31: term > $o,SV102: term] :
( ( ( ! [SY441: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY441 @ SV102 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY441 @ SV102 @ SV31 ) @ SY441 ) ) )
| ( SV31 @ ( sub @ SV102 @ SY441 ) ) ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(443,plain,
! [SV86: term,SV95: term] :
( ( ( sK1_SY167 @ id @ SV95 @ id )
= $false )
| ( ( sK1_SY167 @ id @ ( ap @ ( sub @ SV86 @ id ) @ SV95 ) @ id )
= $true )
| ( ( sK1_SY167 @ id @ SV86 @ id )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(444,plain,
( ( ! [SX0: term] :
( ~ ( sK1_SY167 @ id @ SX0 @ id )
| ( sK2_SY324 @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(445,plain,
( ( ! [SX0: term] :
( ~ ( sK2_SY324 @ SX0 )
| ( sK1_SY167 @ id @ SX0 @ id ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(446,plain,
( ( sK2_SY324 @ sK3_SY331 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[417]) ).
thf(447,plain,
( ( ~ ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[418]) ).
thf(448,plain,
! [SV99: term,SV33: term > $o] :
( ( ( ~ ( SV33 @ SV99 ) )
= $true )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV99 @ id ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(449,plain,
! [SV103: term,SV33: term > $o] :
( ( ( SV33 @ SV103 )
= $true )
| ( ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(450,plain,
! [SV33: term > $o] :
( ( ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(451,plain,
! [SV33: term > $o] :
( ( ( ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(452,plain,
! [SV33: term > $o] :
( ( ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[422]) ).
thf(453,plain,
! [SV104: term,SV33: term > $o] :
( ( ( ~ ( SV33 @ SV104 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV104 @ id ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(454,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(455,plain,
! [SV33: term > $o] :
( ( ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(456,plain,
! [SV33: term > $o] :
( ( ( ~ ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(457,plain,
! [SV105: term,SV34: term > $o] :
( ( ( SV34 @ SV105 )
= $true )
| ( ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(458,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(459,plain,
! [SV34: term > $o] :
( ( ( ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(460,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(461,plain,
! [SV106: term,SV34: term > $o] :
( ( ( SV34 @ SV106 )
= $true )
| ( ( SV34 @ ( sK6_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(462,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(463,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(464,plain,
! [SV34: term > $o] :
( ( ( ~ ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(465,plain,
! [SV84: term,SV31: term > $o,SV93: term,SV96: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV96 @ SV93 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV96 @ SV93 @ SV31 ) @ SV96 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV93 @ SV96 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV31 @ SV84 )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(466,plain,
! [SV31: term > $o,SV88: term,SV91: subst] :
( ( ( var @ ( sK11_B @ SV91 @ SV88 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[437]) ).
thf(467,plain,
! [SV88: term,SV91: subst,SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sub @ ( sK11_B @ SV91 @ SV88 @ SV31 ) @ SV91 ) ) )
= $true )
| ( ( SV31 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[438]) ).
thf(468,plain,
! [SV94: term,SV31: term > $o,SV107: term] :
( ( ( ! [SY442: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY442 @ SV107 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY442 @ SV107 @ SV31 ) @ SY442 ) ) )
| ( SV31 @ ( sub @ SV107 @ SY442 ) ) ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( SV31 @ SV94 )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(469,plain,
! [SV31: term > $o,SV97: term,SV101: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV101 @ SV97 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV101 @ SV97 @ SV31 ) @ SV101 ) ) ) )
= $true )
| ( ( SV31 @ ( sub @ SV97 @ SV101 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(470,plain,
! [SV98: term,SV31: term > $o] :
( ( ( SV31 @ SV98 )
= $false )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( ! [SY390: term,SY391: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY391 @ SY390 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY391 @ SY390 @ SV31 ) @ SY391 ) ) )
| ( SV31 @ ( sub @ SY390 @ SY391 ) ) ) )
= $true )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(471,plain,
! [SV31: term > $o,SV102: term,SV108: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV108 @ SV102 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV108 @ SV102 @ SV31 ) @ SV108 ) ) )
| ( SV31 @ ( sub @ SV102 @ SV108 ) ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(472,plain,
! [SV109: term] :
( ( ~ ( sK1_SY167 @ id @ SV109 @ id )
| ( sK2_SY324 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(473,plain,
! [SV110: term] :
( ( ~ ( sK2_SY324 @ SV110 )
| ( sK1_SY167 @ id @ SV110 @ id ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(474,plain,
( ( ~ ( sK2_SY324 @ sK4_SY333 )
| ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(475,plain,
! [SV99: term,SV33: term > $o] :
( ( ( SV33 @ SV99 )
= $false )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV99 @ id ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(476,plain,
! [SV33: term > $o] :
( ( ( ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(477,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(478,plain,
! [SV33: term > $o] :
( ( ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(479,plain,
! [SV33: term > $o] :
( ( ( ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[452]) ).
thf(480,plain,
! [SV104: term,SV33: term > $o] :
( ( ( ~ ( SV33 @ SV104 ) )
= $true )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV104 @ id ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(481,plain,
! [SV111: term,SV33: term > $o] :
( ( ( SV33 @ SV111 )
= $true )
| ( ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(482,plain,
! [SV33: term > $o] :
( ( ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(483,plain,
! [SV33: term > $o] :
( ( ( ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(484,plain,
! [SV33: term > $o] :
( ( ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) )
| ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(485,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK6_A @ SV34 ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(486,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(487,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(488,plain,
! [SV34: term > $o] :
( ( ( ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(489,plain,
! [SV112: term,SV34: term > $o] :
( ( ( SV34 @ SV112 )
= $true )
| ( ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK7_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(490,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(491,plain,
! [SV34: term > $o] :
( ( ( ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[463]) ).
thf(492,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK6_A @ SV34 ) )
| ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(493,plain,
! [SV84: term,SV31: term > $o,SV93: term,SV96: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV96 @ SV93 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV93 @ SV96 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV31 @ SV84 )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(494,plain,
! [SV84: term,SV93: term,SV96: subst,SV31: term > $o] :
( ( ( ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV96 @ SV93 @ SV31 ) @ SV96 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV93 @ SV96 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV31 @ SV84 )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[465]) ).
thf(495,plain,
! [SV88: term,SV91: subst,SV31: term > $o] :
( ( ( SV31 @ ( sub @ ( sK11_B @ SV91 @ SV88 @ SV31 ) @ SV91 ) )
= $false )
| ( ( SV31 @ ( sub @ SV88 @ SV91 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(496,plain,
! [SV94: term,SV31: term > $o,SV107: term,SV113: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV113 @ SV107 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV113 @ SV107 @ SV31 ) @ SV113 ) ) )
| ( SV31 @ ( sub @ SV107 @ SV113 ) ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( SV31 @ SV94 )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(497,plain,
! [SV31: term > $o,SV97: term,SV101: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV101 @ SV97 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV101 @ SV97 @ SV31 ) @ SV101 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV97 @ SV101 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(498,plain,
! [SV98: term,SV31: term > $o,SV114: term] :
( ( ( ! [SY443: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY443 @ SV114 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SY443 @ SV114 @ SV31 ) @ SY443 ) ) )
| ( SV31 @ ( sub @ SV114 @ SY443 ) ) ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( SV31 @ SV98 )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(499,plain,
! [SV31: term > $o,SV102: term,SV108: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV108 @ SV102 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV108 @ SV102 @ SV31 ) @ SV108 ) ) ) )
= $true )
| ( ( SV31 @ ( sub @ SV102 @ SV108 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(500,plain,
! [SV109: term] :
( ( ( ~ ( sK1_SY167 @ id @ SV109 @ id ) )
= $true )
| ( ( sK2_SY324 @ SV109 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(501,plain,
! [SV110: term] :
( ( ( ~ ( sK2_SY324 @ SV110 ) )
= $true )
| ( ( sK1_SY167 @ id @ SV110 @ id )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(502,plain,
( ( ~ ( sK2_SY324 @ sK4_SY333 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(503,plain,
( ( ~ ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[474]) ).
thf(504,plain,
! [SV99: term,SV115: term,SV33: term > $o] :
( ( ( SV33 @ SV115 )
= $true )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV99 @ id ) ) )
= $true )
| ( ( SV33 @ SV99 )
= $false )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(505,plain,
! [SV116: term,SV33: term > $o] :
( ( ( ~ ( SV33 @ SV116 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV116 @ id ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(506,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(507,plain,
! [SV33: term > $o] :
( ( ( ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(508,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(509,plain,
! [SV104: term,SV33: term > $o] :
( ( ( SV33 @ SV104 )
= $false )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV104 @ id ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(510,plain,
! [SV33: term > $o] :
( ( ( ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(511,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(512,plain,
! [SV33: term > $o] :
( ( ( ~ ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(513,plain,
! [SV33: term > $o] :
( ( ( ~ ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[484]) ).
thf(514,plain,
! [SV117: term,SV34: term > $o] :
( ( ( SV34 @ SV117 )
= $true )
| ( ( SV34 @ ( sK6_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(515,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(516,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK6_A @ SV34 ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(517,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[488]) ).
thf(518,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK6_A @ SV34 ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(519,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(520,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(521,plain,
! [SV34: term > $o] :
( ( ( ~ ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[492]) ).
thf(522,plain,
! [SV84: term,SV31: term > $o,SV93: term,SV96: subst] :
( ( ( var @ ( sK11_B @ SV96 @ SV93 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sub @ SV93 @ SV96 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV31 @ SV84 )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(523,plain,
! [SV84: term,SV93: term,SV96: subst,SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sub @ ( sK11_B @ SV96 @ SV93 @ SV31 ) @ SV96 ) ) )
= $true )
| ( ( SV31 @ ( sub @ SV93 @ SV96 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV31 @ SV84 )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(524,plain,
! [SV94: term,SV31: term > $o,SV107: term,SV113: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV113 @ SV107 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV113 @ SV107 @ SV31 ) @ SV113 ) ) ) )
= $true )
| ( ( SV31 @ ( sub @ SV107 @ SV113 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( SV31 @ SV94 )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(525,plain,
! [SV31: term > $o,SV97: term,SV101: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV101 @ SV97 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV97 @ SV101 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[497]) ).
thf(526,plain,
! [SV97: term,SV101: subst,SV31: term > $o] :
( ( ( ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV101 @ SV97 @ SV31 ) @ SV101 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV97 @ SV101 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[497]) ).
thf(527,plain,
! [SV98: term,SV31: term > $o,SV114: term,SV118: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV118 @ SV114 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV118 @ SV114 @ SV31 ) @ SV118 ) ) )
| ( SV31 @ ( sub @ SV114 @ SV118 ) ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( SV31 @ SV98 )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(528,plain,
! [SV31: term > $o,SV102: term,SV108: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV108 @ SV102 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV108 @ SV102 @ SV31 ) @ SV108 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV102 @ SV108 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(529,plain,
! [SV109: term] :
( ( ( sK1_SY167 @ id @ SV109 @ id )
= $false )
| ( ( sK2_SY324 @ SV109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(530,plain,
! [SV110: term] :
( ( ( sK2_SY324 @ SV110 )
= $false )
| ( ( sK1_SY167 @ id @ SV110 @ id )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(531,plain,
( ( sK2_SY324 @ sK4_SY333 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(532,plain,
( ( ~ ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(533,plain,
! [SV116: term,SV33: term > $o] :
( ( ( ~ ( SV33 @ SV116 ) )
= $true )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV116 @ id ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(534,plain,
! [SV119: term,SV33: term > $o] :
( ( ( SV33 @ SV119 )
= $true )
| ( ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(535,plain,
! [SV120: term,SV33: term > $o] :
( ( ( ~ ( SV33 @ SV120 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV120 @ id ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(536,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(537,plain,
! [SV104: term,SV121: term,SV33: term > $o] :
( ( ( SV33 @ SV121 )
= $true )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV104 @ id ) ) )
= $true )
| ( ( SV33 @ SV104 )
= $false )
| ( ( SV33 @ ( sK16_A @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(538,plain,
! [SV122: term,SV33: term > $o] :
( ( ( ~ ( SV33 @ SV122 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV122 @ id ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(539,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(540,plain,
! [SV33: term > $o] :
( ( ( ! [SY395: term] :
( ~ ( SV33 @ SY395 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SY395 @ id ) ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(541,plain,
! [SV33: term > $o] :
( ( ( ~ ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(542,plain,
! [SV123: term,SV34: term > $o] :
( ( ( SV34 @ SV123 )
= $true )
| ( ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(543,plain,
! [SV124: term,SV34: term > $o] :
( ( ( SV34 @ SV124 )
= $true )
| ( ( SV34 @ ( sK6_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(544,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(545,plain,
! [SV125: term,SV34: term > $o] :
( ( ( SV34 @ SV125 )
= $true )
| ( ( SV34 @ ( sK6_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(546,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(547,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( sK6_A @ SV34 ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(548,plain,
! [SV34: term > $o] :
( ( ( ~ ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) ) )
= $true )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(549,plain,
! [SV84: term,SV93: term,SV96: subst,SV31: term > $o] :
( ( ( SV31 @ ( sub @ ( sK11_B @ SV96 @ SV93 @ SV31 ) @ SV96 ) )
= $false )
| ( ( SV31 @ ( sub @ SV93 @ SV96 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV84 @ id ) ) )
= $true )
| ( ( SV31 @ SV84 )
= $false )
| ( ( SV31 @ ( sK13_A @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(550,plain,
! [SV94: term,SV31: term > $o,SV107: term,SV113: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV113 @ SV107 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV113 @ SV107 @ SV31 ) @ SV113 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV107 @ SV113 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( SV31 @ SV94 )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(551,plain,
! [SV31: term > $o,SV97: term,SV101: subst] :
( ( ( var @ ( sK11_B @ SV101 @ SV97 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sub @ SV97 @ SV101 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(552,plain,
! [SV97: term,SV101: subst,SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sub @ ( sK11_B @ SV101 @ SV97 @ SV31 ) @ SV101 ) ) )
= $true )
| ( ( SV31 @ ( sub @ SV97 @ SV101 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(553,plain,
! [SV98: term,SV31: term > $o,SV114: term,SV118: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV118 @ SV114 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV118 @ SV114 @ SV31 ) @ SV118 ) ) ) )
= $true )
| ( ( SV31 @ ( sub @ SV114 @ SV118 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( SV31 @ SV98 )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(554,plain,
! [SV31: term > $o,SV102: term,SV108: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV108 @ SV102 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV102 @ SV108 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(555,plain,
! [SV102: term,SV108: subst,SV31: term > $o] :
( ( ( ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV108 @ SV102 @ SV31 ) @ SV108 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV102 @ SV108 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[528]) ).
thf(556,plain,
( ( sK2_SY324 @ ( ap @ sK3_SY331 @ sK4_SY333 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(557,plain,
! [SV116: term,SV33: term > $o] :
( ( ( SV33 @ SV116 )
= $false )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV116 @ id ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(558,plain,
! [SV120: term,SV33: term > $o] :
( ( ( ~ ( SV33 @ SV120 ) )
= $true )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV120 @ id ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[535]) ).
thf(559,plain,
! [SV126: term,SV33: term > $o] :
( ( ( SV33 @ SV126 )
= $true )
| ( ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(560,plain,
! [SV122: term,SV33: term > $o] :
( ( ( ~ ( SV33 @ SV122 ) )
= $true )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV122 @ id ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(561,plain,
! [SV127: term,SV33: term > $o] :
( ( ( SV33 @ SV127 )
= $true )
| ( ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(562,plain,
! [SV128: term,SV33: term > $o] :
( ( ( ~ ( SV33 @ SV128 )
| ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV128 @ id ) ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(563,plain,
! [SV33: term > $o] :
( ( ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) )
= $false )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(564,plain,
! [SV129: term,SV34: term > $o] :
( ( ( SV34 @ SV129 )
= $true )
| ( ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV34 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(565,plain,
! [SV130: term,SV34: term > $o] :
( ( ( SV34 @ SV130 )
= $true )
| ( ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK8_SY334 @ SV34 ) )
= $true )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(566,plain,
! [SV131: term,SV34: term > $o] :
( ( ( SV34 @ SV131 )
= $true )
| ( ( SV34 @ ( sK6_A @ SV34 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(567,plain,
! [SV34: term > $o] :
( ( ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( ! [SY397: term] : ( SV34 @ SY397 ) )
= $true )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(568,plain,
! [SV94: term,SV31: term > $o,SV107: term,SV113: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV113 @ SV107 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV107 @ SV113 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( SV31 @ SV94 )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(569,plain,
! [SV94: term,SV107: term,SV113: subst,SV31: term > $o] :
( ( ( ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV113 @ SV107 @ SV31 ) @ SV113 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV107 @ SV113 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( SV31 @ SV94 )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[550]) ).
thf(570,plain,
! [SV97: term,SV101: subst,SV31: term > $o] :
( ( ( SV31 @ ( sub @ ( sK11_B @ SV101 @ SV97 @ SV31 ) @ SV101 ) )
= $false )
| ( ( SV31 @ ( sub @ SV97 @ SV101 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(571,plain,
! [SV98: term,SV31: term > $o,SV114: term,SV118: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV118 @ SV114 @ SV31 ) )
| ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV118 @ SV114 @ SV31 ) @ SV118 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV114 @ SV118 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( SV31 @ SV98 )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(572,plain,
! [SV31: term > $o,SV102: term,SV108: subst] :
( ( ( var @ ( sK11_B @ SV108 @ SV102 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sub @ SV102 @ SV108 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[554]) ).
thf(573,plain,
! [SV102: term,SV108: subst,SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sub @ ( sK11_B @ SV108 @ SV102 @ SV31 ) @ SV108 ) ) )
= $true )
| ( ( SV31 @ ( sub @ SV102 @ SV108 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[555]) ).
thf(574,plain,
! [SV116: term,SV132: term,SV33: term > $o] :
( ( ( SV33 @ SV132 )
= $true )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV116 @ id ) ) )
= $true )
| ( ( SV33 @ SV116 )
= $false )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(575,plain,
! [SV120: term,SV33: term > $o] :
( ( ( SV33 @ SV120 )
= $false )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV120 @ id ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(576,plain,
! [SV122: term,SV33: term > $o] :
( ( ( SV33 @ SV122 )
= $false )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV122 @ id ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(577,plain,
! [SV128: term,SV33: term > $o] :
( ( ( ~ ( SV33 @ SV128 ) )
= $true )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV128 @ id ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(578,plain,
! [SV133: term,SV33: term > $o] :
( ( ( SV33 @ SV133 )
= $true )
| ( ( SV33 @ ( lam @ ( sK15_A @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(579,plain,
! [SV134: term,SV34: term > $o] :
( ( ( SV34 @ SV134 )
= $true )
| ( ( SV34 @ ( lam @ ( sK6_A @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( ap @ ( sK7_A @ SV34 ) @ ( sK8_SY334 @ SV34 ) ) )
= $false )
| ( ( SV34 @ ( sK9_A @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(580,plain,
! [SV94: term,SV31: term > $o,SV107: term,SV113: subst] :
( ( ( var @ ( sK11_B @ SV113 @ SV107 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sub @ SV107 @ SV113 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( SV31 @ SV94 )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(581,plain,
! [SV94: term,SV107: term,SV113: subst,SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sub @ ( sK11_B @ SV113 @ SV107 @ SV31 ) @ SV113 ) ) )
= $true )
| ( ( SV31 @ ( sub @ SV107 @ SV113 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( SV31 @ SV94 )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[569]) ).
thf(582,plain,
! [SV98: term,SV31: term > $o,SV114: term,SV118: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV118 @ SV114 @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV114 @ SV118 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( SV31 @ SV98 )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(583,plain,
! [SV98: term,SV114: term,SV118: subst,SV31: term > $o] :
( ( ( ~ ~ ( SV31 @ ( sub @ ( sK11_B @ SV118 @ SV114 @ SV31 ) @ SV118 ) ) )
= $false )
| ( ( SV31 @ ( sub @ SV114 @ SV118 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( SV31 @ SV98 )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[571]) ).
thf(584,plain,
! [SV102: term,SV108: subst,SV31: term > $o] :
( ( ( SV31 @ ( sub @ ( sK11_B @ SV108 @ SV102 @ SV31 ) @ SV108 ) )
= $false )
| ( ( SV31 @ ( sub @ SV102 @ SV108 ) )
= $true )
| ( ( SV31 @ ( lam @ ( sK12_A @ SV31 ) ) )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(585,plain,
! [SV120: term,SV135: term,SV33: term > $o] :
( ( ( SV33 @ SV135 )
= $true )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV120 @ id ) ) )
= $true )
| ( ( SV33 @ SV120 )
= $false )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(586,plain,
! [SV122: term,SV136: term,SV33: term > $o] :
( ( ( SV33 @ SV136 )
= $true )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV122 @ id ) ) )
= $true )
| ( ( SV33 @ SV122 )
= $false )
| ( ( SV33 @ ( sK17_SY338 @ SV33 ) )
= $true )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(587,plain,
! [SV128: term,SV33: term > $o] :
( ( ( SV33 @ SV128 )
= $false )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV128 @ id ) ) )
= $true )
| ( ( ! [SY396: term] : ( SV33 @ SY396 ) )
= $true )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(588,plain,
! [SV94: term,SV107: term,SV113: subst,SV31: term > $o] :
( ( ( SV31 @ ( sub @ ( sK11_B @ SV113 @ SV107 @ SV31 ) @ SV113 ) )
= $false )
| ( ( SV31 @ ( sub @ SV107 @ SV113 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( SV31 @ SV94 )
= $false )
| ( ( SV31 @ ( sK14_SY336 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(589,plain,
! [SV98: term,SV31: term > $o,SV114: term,SV118: subst] :
( ( ( var @ ( sK11_B @ SV118 @ SV114 @ SV31 ) )
= $true )
| ( ( SV31 @ ( sub @ SV114 @ SV118 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( SV31 @ SV98 )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[582]) ).
thf(590,plain,
! [SV98: term,SV114: term,SV118: subst,SV31: term > $o] :
( ( ( ~ ( SV31 @ ( sub @ ( sK11_B @ SV118 @ SV114 @ SV31 ) @ SV118 ) ) )
= $true )
| ( ( SV31 @ ( sub @ SV114 @ SV118 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( SV31 @ SV98 )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[583]) ).
thf(591,plain,
! [SV128: term,SV137: term,SV33: term > $o] :
( ( ( SV33 @ SV137 )
= $true )
| ( ( SV33 @ ( sub @ ( sK15_A @ SV33 ) @ ( push @ SV128 @ id ) ) )
= $true )
| ( ( SV33 @ SV128 )
= $false )
| ( ( SV33 @ ( ap @ ( sK16_A @ SV33 ) @ ( sK17_SY338 @ SV33 ) ) )
= $false )
| ( ( SV33 @ ( sK18_A @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(592,plain,
! [SV98: term,SV114: term,SV118: subst,SV31: term > $o] :
( ( ( SV31 @ ( sub @ ( sK11_B @ SV118 @ SV114 @ SV31 ) @ SV118 ) )
= $false )
| ( ( SV31 @ ( sub @ SV114 @ SV118 ) )
= $true )
| ( ( SV31 @ ( sub @ ( sK12_A @ SV31 ) @ ( push @ SV98 @ id ) ) )
= $true )
| ( ( SV31 @ SV98 )
= $false )
| ( ( SV31 @ ( ap @ ( sK13_A @ SV31 ) @ ( sK14_SY336 @ SV31 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(593,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[84,592,591,589,588,586,585,584,580,579,578,574,572,570,566,565,564,561,559,556,551,549,545,543,542,537,534,531,530,529,522,514,504,495,489,481,466,461,457,449,446,443,435,427,406,389,362,358,326,308,291,238,237,236,235,233,203,202,201,196,188,187,186,185,184,178,177,176,170,161,160,158,148,131,128,124,123,113,112,110,86]) ).
thf(594,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[593]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG264^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 18:10:25 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.79/0.59
% 1.79/0.59 No.of.Axioms: 0
% 1.79/0.59
% 1.79/0.59 Length.of.Defs: 38092
% 1.79/0.59
% 1.79/0.59 Contains.Choice.Funs: false
% 1.79/0.59 .......................
% 1.79/0.59
% 1.79/0.59 ********************************
% 1.79/0.59 * All subproblems solved! *
% 1.79/0.59 ********************************
% 1.79/0.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:37,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:593,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.79/0.59
% 1.79/0.59 %**** Beginning of derivation protocol ****
% 1.79/0.59 % SZS output start CNFRefutation
% See solution above
% 1.79/0.59
% 1.79/0.59 %**** End of derivation protocol ****
% 1.79/0.59 %**** no. of clauses in derivation: 594 ****
% 1.79/0.59 %**** clause counter: 593 ****
% 1.79/0.59
% 1.79/0.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:37,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:593,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------