%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG255^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:08:38 AM UTC 2026
% Result : Theorem 1.88s 0.53s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 114
% Syntax : Number of formulae : 1018 ( 346 unt; 0 typ; 113 def)
% Number of atoms : 7282 (3033 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 19479 (2831 ~;2978 |; 53 &;12500 @)
% ( 2 <=>;1115 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 792 ( 792 >; 0 *; 0 +; 0 <<)
% Number of symbols : 143 ( 140 usr; 117 con; 0-4 aty)
% Number of variables : 2856 ( 39 ^;2812 !; 5 ?;2856 :)
% 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_SY84,type,
sK14_SY84: ( 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_SY86,type,
sK17_SY86: ( term > $o ) > term ).
thf(tp_sK18_A,type,
sK18_A: ( term > $o ) > term ).
thf(tp_sK1_A,type,
sK1_A: term ).
thf(tp_sK2_SY79,type,
sK2_SY79: subst ).
thf(tp_sK3_SY81,type,
sK3_SY81: subst ).
thf(tp_sK4_A,type,
sK4_A: 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_SY82,type,
sK8_SY82: ( 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,
termmset_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
termmset_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $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 ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[33]) ).
thf(35,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[33]) ).
thf(36,plain,
( ( ~ ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[34]) ).
thf(37,plain,
( ( ~ ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(38,plain,
( ( ( sub @ ( sub @ sK1_A @ sK2_SY79 ) @ sK3_SY81 )
!= ( sub @ sK1_A @ ( comp @ sK2_SY79 @ sK3_SY81 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(39,plain,
( ( ( sub @ sK4_A @ id )
!= sK4_A )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(40,plain,
( ( ! [A: term] :
( ~ ( var @ A )
| ( var @ ( sub @ A @ sh ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(41,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(42,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(43,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(44,plain,
( ( ! [A: term,B: term] :
( ( ( lam @ A )
!= ( lam @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(45,plain,
( ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
!= ( sub @ B @ sh ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(46,plain,
( ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(47,plain,
( ( ! [P: term > $o] :
( ( ( var @ ( sK9_A @ P ) )
& ~ ( P @ ( sK9_A @ P ) ) )
| ( ( P @ ( sK7_A @ P ) )
& ( P @ ( sK8_SY82 @ P ) )
& ~ ( P @ ( ap @ ( sK7_A @ P ) @ ( sK8_SY82 @ P ) ) ) )
| ( ( P @ ( sK6_A @ P ) )
& ~ ( P @ ( lam @ ( sK6_A @ P ) ) ) )
| ! [A: term] : ( P @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(48,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(49,plain,
( ( ! [P: term > $o] :
( ( ( P @ ( sK13_A @ P ) )
& ( P @ ( sK14_SY84 @ P ) )
& ~ ( P @ ( ap @ ( sK13_A @ P ) @ ( sK14_SY84 @ P ) ) ) )
| ( ! [SY83: term] :
( ~ ( P @ SY83 )
| ( P @ ( sub @ ( sK12_A @ P ) @ ( push @ SY83 @ 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(50,plain,
( ( ! [P: term > $o] :
( ( ( var @ ( sK18_A @ P ) )
& ~ ( P @ ( sK18_A @ P ) ) )
| ( ( P @ ( sK16_A @ P ) )
& ( P @ ( sK17_SY86 @ P ) )
& ~ ( P @ ( ap @ ( sK16_A @ P ) @ ( sK17_SY86 @ P ) ) ) )
| ( ! [SY85: term] :
( ~ ( P @ SY85 )
| ( P @ ( sub @ ( sK15_A @ P ) @ ( push @ SY85 @ id ) ) ) )
& ~ ( P @ ( lam @ ( sK15_A @ P ) ) ) )
| ! [A: term] : ( P @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(51,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(52,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(53,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(54,plain,
( ( ! [P: term > $o] :
( ( ( var @ ( sK18_A @ P ) )
& ~ ( P @ ( sK18_A @ P ) ) )
| ( ( P @ ( sK16_A @ P ) )
& ( P @ ( sK17_SY86 @ P ) )
& ~ ( P @ ( ap @ ( sK16_A @ P ) @ ( sK17_SY86 @ P ) ) ) )
| ( ! [SY85: term] :
( ~ ( P @ SY85 )
| ( P @ ( sub @ ( sK15_A @ P ) @ ( push @ SY85 @ id ) ) ) )
& ~ ( P @ ( lam @ ( sK15_A @ P ) ) ) )
| ! [A: term] : ( P @ A ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(55,plain,
( ( ! [P: term > $o] :
( ( ( P @ ( sK13_A @ P ) )
& ( P @ ( sK14_SY84 @ P ) )
& ~ ( P @ ( ap @ ( sK13_A @ P ) @ ( sK14_SY84 @ P ) ) ) )
| ( ! [SY83: term] :
( ~ ( P @ SY83 )
| ( P @ ( sub @ ( sK12_A @ P ) @ ( push @ SY83 @ 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)],[49]) ).
thf(56,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)],[48]) ).
thf(57,plain,
( ( ! [P: term > $o] :
( ( ( var @ ( sK9_A @ P ) )
& ~ ( P @ ( sK9_A @ P ) ) )
| ( ( P @ ( sK7_A @ P ) )
& ( P @ ( sK8_SY82 @ P ) )
& ~ ( P @ ( ap @ ( sK7_A @ P ) @ ( sK8_SY82 @ P ) ) ) )
| ( ( P @ ( sK6_A @ P ) )
& ~ ( P @ ( lam @ ( sK6_A @ P ) ) ) )
| ! [A: term] : ( P @ A ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(58,plain,
( ( ! [A: term] :
~ ( var @ ( lam @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(59,plain,
( ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(60,plain,
( ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(61,plain,
( ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
!= ( sub @ B @ sh ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(62,plain,
( ( ! [A: term,B: term] :
( ( ( lam @ A )
!= ( lam @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(63,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
!= ( ap @ B @ D ) )
| ( C = D ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(64,plain,
( ( ! [A: term,B: term] :
( ! [C: term,D: term] :
( ( ap @ A @ C )
!= ( ap @ B @ D ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(65,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)],[41]) ).
thf(66,plain,
( ( ! [A: term] :
( ~ ( var @ A )
| ( var @ ( sub @ A @ sh ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(67,plain,
( ( var @ one )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(68,plain,
( ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(69,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(70,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(71,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(72,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(73,plain,
( ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(74,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(75,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(76,plain,
( ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(77,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(78,plain,
( ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(79,plain,
( ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(80,plain,
( ( ( sub @ ( sub @ sK1_A @ sK2_SY79 ) @ sK3_SY81 )
!= ( sub @ sK1_A @ ( comp @ sK2_SY79 @ sK3_SY81 ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(81,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)],[65,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(82,plain,
( ( ! [SX0: term > $o] :
( ~ ( ~ ( SX0 @ ( sK13_A @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK14_SY84 @ SX0 ) )
| ~ ~ ( SX0 @ ( ap @ ( sK13_A @ SX0 ) @ ( sK14_SY84 @ 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)],[55,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(83,plain,
( ( ! [SX0: term > $o] :
( ~ ( ~ ( var @ ( sK9_A @ SX0 ) )
| ~ ~ ( SX0 @ ( sK9_A @ SX0 ) ) )
| ~ ( ~ ( SX0 @ ( sK7_A @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK8_SY82 @ SX0 ) )
| ~ ~ ( SX0 @ ( ap @ ( sK7_A @ SX0 ) @ ( sK8_SY82 @ SX0 ) ) ) ) )
| ~ ( ~ ( SX0 @ ( sK6_A @ SX0 ) )
| ~ ~ ( SX0 @ ( lam @ ( sK6_A @ SX0 ) ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(84,plain,
( ( ! [SX0: term > $o] :
( ~ ( ~ ( var @ ( sK18_A @ SX0 ) )
| ~ ~ ( SX0 @ ( sK18_A @ SX0 ) ) )
| ~ ( ~ ( SX0 @ ( sK16_A @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK17_SY86 @ SX0 ) )
| ~ ~ ( SX0 @ ( ap @ ( sK16_A @ SX0 ) @ ( sK17_SY86 @ 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)],[54,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(85,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)],[56,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(86,plain,
! [SV1: subst] :
( ( ( comp @ SV1 @ id )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(87,plain,
! [SV2: subst] :
( ( ( comp @ id @ SV2 )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(88,plain,
! [SV3: subst] :
( ( ! [SY87: subst,SY88: subst] :
( ( comp @ ( comp @ SV3 @ SY87 ) @ SY88 )
= ( comp @ SV3 @ ( comp @ SY87 @ SY88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(89,plain,
! [SV4: term] :
( ( ~ ( var @ ( lam @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(90,plain,
! [SV5: term] :
( ( ! [SY89: term] :
~ ( var @ ( ap @ SV5 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(91,plain,
! [SV6: term] :
( ( ! [SY90: term,SY91: term] :
( ( lam @ SV6 )
!= ( ap @ SY90 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(92,plain,
! [SV7: term] :
( ( ! [SY92: term] :
( ( ( sub @ SV7 @ sh )
!= ( sub @ SY92 @ sh ) )
| ( SV7 = SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(93,plain,
! [SV8: term] :
( ( ! [SY93: term] :
( ( ( lam @ SV8 )
!= ( lam @ SY93 ) )
| ( SV8 = SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(94,plain,
! [SV9: term] :
( ( ! [SY94: term,SY95: term,SY96: term] :
( ( ( ap @ SV9 @ SY95 )
!= ( ap @ SY94 @ SY96 ) )
| ( SY95 = SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(95,plain,
! [SV10: term] :
( ( ! [SY97: term] :
( ! [SY98: term,SY99: term] :
( ( ap @ SV10 @ SY98 )
!= ( ap @ SY97 @ SY99 ) )
| ( SV10 = SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(96,plain,
! [SV11: term] :
( ( ~ ( var @ SV11 )
| ( var @ ( sub @ SV11 @ sh ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(97,plain,
! [SV12: subst] :
( ( ( push @ ( sub @ one @ SV12 ) @ ( comp @ sh @ SV12 ) )
= SV12 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(98,plain,
! [SV13: subst] :
( ( ( comp @ SV13 @ id )
= SV13 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(99,plain,
! [SV14: term] :
( ( ! [SY100: subst,SY101: subst] :
( ( comp @ ( push @ SV14 @ SY100 ) @ SY101 )
= ( push @ ( sub @ SV14 @ SY101 ) @ ( comp @ SY100 @ SY101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(100,plain,
! [SV15: subst] :
( ( ! [SY102: subst,SY103: subst] :
( ( comp @ ( comp @ SV15 @ SY102 ) @ SY103 )
= ( comp @ SV15 @ ( comp @ SY102 @ SY103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(101,plain,
! [SV16: term] :
( ( ! [SY104: subst] :
( ( comp @ sh @ ( push @ SV16 @ SY104 ) )
= SY104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(102,plain,
! [SV17: subst] :
( ( ( comp @ id @ SV17 )
= SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(103,plain,
! [SV18: term] :
( ( ! [SY105: subst,SY106: subst] :
( ( sub @ ( sub @ SV18 @ SY105 ) @ SY106 )
= ( sub @ SV18 @ ( comp @ SY105 @ SY106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(104,plain,
! [SV19: term] :
( ( ! [SY107: subst] :
( ( sub @ ( lam @ SV19 ) @ SY107 )
= ( lam @ ( sub @ SV19 @ ( push @ one @ ( comp @ SY107 @ sh ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(105,plain,
! [SV20: term] :
( ( ( sub @ SV20 @ id )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(106,plain,
! [SV21: term] :
( ( ! [SY108: subst] :
( ( sub @ one @ ( push @ SV21 @ SY108 ) )
= SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(107,plain,
! [SV22: term] :
( ( ! [SY109: term,SY110: subst] :
( ( sub @ ( ap @ SV22 @ SY109 ) @ SY110 )
= ( ap @ ( sub @ SV22 @ SY110 ) @ ( sub @ SY109 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(108,plain,
( ( ( sub @ ( sub @ sK1_A @ sK2_SY79 ) @ sK3_SY81 )
= ( sub @ sK1_A @ ( comp @ sK2_SY79 @ sK3_SY81 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(109,plain,
! [SV23: term > $o] :
( ( ~ ( SV23 @ one )
| ~ ( ~ ( var @ ( sK5_A @ SV23 ) )
| ~ ~ ( ~ ( SV23 @ ( sK5_A @ SV23 ) )
| ~ ~ ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) ) ) )
| ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(110,plain,
! [SV24: term > $o] :
( ( ~ ( ~ ( SV24 @ ( sK13_A @ SV24 ) )
| ~ ~ ( ~ ( SV24 @ ( sK14_SY84 @ SV24 ) )
| ~ ~ ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) ) ) )
| ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(111,plain,
! [SV25: term > $o] :
( ( ~ ( ~ ( var @ ( sK9_A @ SV25 ) )
| ~ ~ ( SV25 @ ( sK9_A @ SV25 ) ) )
| ~ ( ~ ( SV25 @ ( sK7_A @ SV25 ) )
| ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
| ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(112,plain,
! [SV26: term > $o] :
( ( ~ ( ~ ( var @ ( sK18_A @ SV26 ) )
| ~ ~ ( SV26 @ ( sK18_A @ SV26 ) ) )
| ~ ( ~ ( SV26 @ ( sK16_A @ SV26 ) )
| ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
| ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(113,plain,
! [SV27: term > $o] :
( ( ! [SY118: term,SY119: subst] :
( ~ ( ~ ( var @ ( sK10_B @ SY119 @ SY118 @ SV27 ) )
| ~ ~ ( SV27 @ ( sub @ ( sK10_B @ SY119 @ SY118 @ SV27 ) @ SY119 ) ) )
| ~ ( SV27 @ SY118 )
| ! [SY120: term] :
( ~ ( var @ SY120 )
| ( SV27 @ ( sub @ SY120 @ ( push @ SY118 @ SY119 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(114,plain,
! [SV28: subst,SV3: subst] :
( ( ! [SY121: subst] :
( ( comp @ ( comp @ SV3 @ SV28 ) @ SY121 )
= ( comp @ SV3 @ ( comp @ SV28 @ SY121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(115,plain,
! [SV4: term] :
( ( var @ ( lam @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(116,plain,
! [SV29: term,SV5: term] :
( ( ~ ( var @ ( ap @ SV5 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(117,plain,
! [SV30: term,SV6: term] :
( ( ! [SY122: term] :
( ( lam @ SV6 )
!= ( ap @ SV30 @ SY122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(118,plain,
! [SV31: term,SV7: term] :
( ( ( ( sub @ SV7 @ sh )
!= ( sub @ SV31 @ sh ) )
| ( SV7 = SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(119,plain,
! [SV32: term,SV8: term] :
( ( ( ( lam @ SV8 )
!= ( lam @ SV32 ) )
| ( SV8 = SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(120,plain,
! [SV33: term,SV9: term] :
( ( ! [SY123: term,SY124: term] :
( ( ( ap @ SV9 @ SY123 )
!= ( ap @ SV33 @ SY124 ) )
| ( SY123 = SY124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(121,plain,
! [SV34: term,SV10: term] :
( ( ! [SY125: term,SY126: term] :
( ( ap @ SV10 @ SY125 )
!= ( ap @ SV34 @ SY126 ) )
| ( SV10 = SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(122,plain,
! [SV11: term] :
( ( ( ~ ( var @ SV11 ) )
= $true )
| ( ( var @ ( sub @ SV11 @ sh ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(123,plain,
! [SV35: subst,SV14: term] :
( ( ! [SY127: subst] :
( ( comp @ ( push @ SV14 @ SV35 ) @ SY127 )
= ( push @ ( sub @ SV14 @ SY127 ) @ ( comp @ SV35 @ SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(124,plain,
! [SV36: subst,SV15: subst] :
( ( ! [SY128: subst] :
( ( comp @ ( comp @ SV15 @ SV36 ) @ SY128 )
= ( comp @ SV15 @ ( comp @ SV36 @ SY128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(125,plain,
! [SV37: subst,SV16: term] :
( ( ( comp @ sh @ ( push @ SV16 @ SV37 ) )
= SV37 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(126,plain,
! [SV38: subst,SV18: term] :
( ( ! [SY129: subst] :
( ( sub @ ( sub @ SV18 @ SV38 ) @ SY129 )
= ( sub @ SV18 @ ( comp @ SV38 @ SY129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(127,plain,
! [SV39: subst,SV19: term] :
( ( ( sub @ ( lam @ SV19 ) @ SV39 )
= ( lam @ ( sub @ SV19 @ ( push @ one @ ( comp @ SV39 @ sh ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(128,plain,
! [SV40: subst,SV21: term] :
( ( ( sub @ one @ ( push @ SV21 @ SV40 ) )
= SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(129,plain,
! [SV41: term,SV22: term] :
( ( ! [SY130: subst] :
( ( sub @ ( ap @ SV22 @ SV41 ) @ SY130 )
= ( ap @ ( sub @ SV22 @ SY130 ) @ ( sub @ SV41 @ SY130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(130,plain,
! [SV23: term > $o] :
( ( ( ~ ( SV23 @ one ) )
= $true )
| ( ( ~ ( ~ ( var @ ( sK5_A @ SV23 ) )
| ~ ~ ( ~ ( SV23 @ ( sK5_A @ SV23 ) )
| ~ ~ ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) ) ) )
| ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(131,plain,
! [SV24: term > $o] :
( ( ( ~ ( ~ ( SV24 @ ( sK13_A @ SV24 ) )
| ~ ~ ( ~ ( SV24 @ ( sK14_SY84 @ SV24 ) )
| ~ ~ ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(132,plain,
! [SV25: term > $o] :
( ( ( ~ ( ~ ( var @ ( sK9_A @ SV25 ) )
| ~ ~ ( SV25 @ ( sK9_A @ SV25 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK7_A @ SV25 ) )
| ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
| ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(133,plain,
! [SV26: term > $o] :
( ( ( ~ ( ~ ( var @ ( sK18_A @ SV26 ) )
| ~ ~ ( SV26 @ ( sK18_A @ SV26 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV26 @ ( sK16_A @ SV26 ) )
| ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
| ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(134,plain,
! [SV27: term > $o,SV42: term] :
( ( ! [SY131: subst] :
( ~ ( ~ ( var @ ( sK10_B @ SY131 @ SV42 @ SV27 ) )
| ~ ~ ( SV27 @ ( sub @ ( sK10_B @ SY131 @ SV42 @ SV27 ) @ SY131 ) ) )
| ~ ( SV27 @ SV42 )
| ! [SY132: term] :
( ~ ( var @ SY132 )
| ( SV27 @ ( sub @ SY132 @ ( push @ SV42 @ SY131 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(135,plain,
! [SV43: subst,SV28: subst,SV3: subst] :
( ( ( comp @ ( comp @ SV3 @ SV28 ) @ SV43 )
= ( comp @ SV3 @ ( comp @ SV28 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(136,plain,
! [SV29: term,SV5: term] :
( ( var @ ( ap @ SV5 @ SV29 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(137,plain,
! [SV44: term,SV30: term,SV6: term] :
( ( ( lam @ SV6 )
!= ( ap @ SV30 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(138,plain,
! [SV31: term,SV7: term] :
( ( ( ( sub @ SV7 @ sh )
!= ( sub @ SV31 @ sh ) )
= $true )
| ( ( SV7 = SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(139,plain,
! [SV32: term,SV8: term] :
( ( ( ( lam @ SV8 )
!= ( lam @ SV32 ) )
= $true )
| ( ( SV8 = SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(140,plain,
! [SV33: term,SV45: term,SV9: term] :
( ( ! [SY133: term] :
( ( ( ap @ SV9 @ SV45 )
!= ( ap @ SV33 @ SY133 ) )
| ( SV45 = SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(141,plain,
! [SV34: term,SV10: term] :
( ( ( ! [SY125: term,SY126: term] :
( ( ap @ SV10 @ SY125 )
!= ( ap @ SV34 @ SY126 ) ) )
= $true )
| ( ( SV10 = SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(142,plain,
! [SV11: term] :
( ( ( var @ SV11 )
= $false )
| ( ( var @ ( sub @ SV11 @ sh ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(143,plain,
! [SV46: subst,SV35: subst,SV14: term] :
( ( ( comp @ ( push @ SV14 @ SV35 ) @ SV46 )
= ( push @ ( sub @ SV14 @ SV46 ) @ ( comp @ SV35 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(144,plain,
! [SV47: subst,SV36: subst,SV15: subst] :
( ( ( comp @ ( comp @ SV15 @ SV36 ) @ SV47 )
= ( comp @ SV15 @ ( comp @ SV36 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(145,plain,
! [SV48: subst,SV38: subst,SV18: term] :
( ( ( sub @ ( sub @ SV18 @ SV38 ) @ SV48 )
= ( sub @ SV18 @ ( comp @ SV38 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(146,plain,
! [SV49: subst,SV41: term,SV22: term] :
( ( ( sub @ ( ap @ SV22 @ SV41 ) @ SV49 )
= ( ap @ ( sub @ SV22 @ SV49 ) @ ( sub @ SV41 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(147,plain,
! [SV23: term > $o] :
( ( ( SV23 @ one )
= $false )
| ( ( ~ ( ~ ( var @ ( sK5_A @ SV23 ) )
| ~ ~ ( ~ ( SV23 @ ( sK5_A @ SV23 ) )
| ~ ~ ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) ) ) )
| ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[130]) ).
thf(148,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sK13_A @ SV24 ) )
| ~ ~ ( ~ ( SV24 @ ( sK14_SY84 @ SV24 ) )
| ~ ~ ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(149,plain,
! [SV25: term > $o] :
( ( ( ~ ( var @ ( sK9_A @ SV25 ) )
| ~ ~ ( SV25 @ ( sK9_A @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK7_A @ SV25 ) )
| ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
| ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(150,plain,
! [SV26: term > $o] :
( ( ( ~ ( var @ ( sK18_A @ SV26 ) )
| ~ ~ ( SV26 @ ( sK18_A @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ( SV26 @ ( sK16_A @ SV26 ) )
| ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
| ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(151,plain,
! [SV27: term > $o,SV42: term,SV50: subst] :
( ( ~ ( ~ ( var @ ( sK10_B @ SV50 @ SV42 @ SV27 ) )
| ~ ~ ( SV27 @ ( sub @ ( sK10_B @ SV50 @ SV42 @ SV27 ) @ SV50 ) ) )
| ~ ( SV27 @ SV42 )
| ! [SY134: term] :
( ~ ( var @ SY134 )
| ( SV27 @ ( sub @ SY134 @ ( push @ SV42 @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(152,plain,
! [SV44: term,SV30: term,SV6: term] :
( ( ( lam @ SV6 )
= ( ap @ SV30 @ SV44 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(153,plain,
! [SV31: term,SV7: term] :
( ( ( ( sub @ SV7 @ sh )
= ( sub @ SV31 @ sh ) )
= $false )
| ( ( SV7 = SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(154,plain,
! [SV32: term,SV8: term] :
( ( ( ( lam @ SV8 )
= ( lam @ SV32 ) )
= $false )
| ( ( SV8 = SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(155,plain,
! [SV51: term,SV33: term,SV45: term,SV9: term] :
( ( ( ( ap @ SV9 @ SV45 )
!= ( ap @ SV33 @ SV51 ) )
| ( SV45 = SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(156,plain,
! [SV34: term,SV52: term,SV10: term] :
( ( ( ! [SY135: term] :
( ( ap @ SV10 @ SV52 )
!= ( ap @ SV34 @ SY135 ) ) )
= $true )
| ( ( SV10 = SV34 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(157,plain,
! [SV23: term > $o] :
( ( ( ~ ( ~ ( var @ ( sK5_A @ SV23 ) )
| ~ ~ ( ~ ( SV23 @ ( sK5_A @ SV23 ) )
| ~ ~ ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) ) ) ) )
= $true )
| ( ( ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(158,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sK13_A @ SV24 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(159,plain,
! [SV24: term > $o] :
( ( ( ~ ~ ( ~ ( SV24 @ ( sK14_SY84 @ SV24 ) )
| ~ ~ ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[148]) ).
thf(160,plain,
! [SV25: term > $o] :
( ( ( ~ ( var @ ( sK9_A @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK7_A @ SV25 ) )
| ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
| ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(161,plain,
! [SV25: term > $o] :
( ( ( ~ ~ ( SV25 @ ( sK9_A @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK7_A @ SV25 ) )
| ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
| ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(162,plain,
! [SV26: term > $o] :
( ( ( ~ ( var @ ( sK18_A @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ( SV26 @ ( sK16_A @ SV26 ) )
| ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
| ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(163,plain,
! [SV26: term > $o] :
( ( ( ~ ~ ( SV26 @ ( sK18_A @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ( SV26 @ ( sK16_A @ SV26 ) )
| ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
| ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(164,plain,
! [SV27: term > $o,SV42: term,SV50: subst] :
( ( ( ~ ( ~ ( var @ ( sK10_B @ SV50 @ SV42 @ SV27 ) )
| ~ ~ ( SV27 @ ( sub @ ( sK10_B @ SV50 @ SV42 @ SV27 ) @ SV50 ) ) ) )
= $true )
| ( ( ~ ( SV27 @ SV42 )
| ! [SY134: term] :
( ~ ( var @ SY134 )
| ( SV27 @ ( sub @ SY134 @ ( push @ SV42 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(165,plain,
! [SV51: term,SV33: term,SV45: term,SV9: term] :
( ( ( ( ap @ SV9 @ SV45 )
!= ( ap @ SV33 @ SV51 ) )
= $true )
| ( ( SV45 = SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV53: term,SV34: term,SV52: term,SV10: term] :
( ( ( ( ap @ SV10 @ SV52 )
!= ( ap @ SV34 @ SV53 ) )
= $true )
| ( ( SV10 = SV34 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV23: term > $o] :
( ( ( ~ ( var @ ( sK5_A @ SV23 ) )
| ~ ~ ( ~ ( SV23 @ ( sK5_A @ SV23 ) )
| ~ ~ ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) ) ) )
= $false )
| ( ( ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(168,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true )
| ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(169,plain,
! [SV24: term > $o] :
( ( ( ~ ( ~ ( SV24 @ ( sK14_SY84 @ SV24 ) )
| ~ ~ ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(170,plain,
! [SV25: term > $o] :
( ( ( var @ ( sK9_A @ SV25 ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK7_A @ SV25 ) )
| ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
| ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(171,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK9_A @ SV25 ) ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK7_A @ SV25 ) )
| ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
| ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(172,plain,
! [SV26: term > $o] :
( ( ( var @ ( sK18_A @ SV26 ) )
= $true )
| ( ( ~ ( ~ ( SV26 @ ( sK16_A @ SV26 ) )
| ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
| ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(173,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK18_A @ SV26 ) ) )
= $true )
| ( ( ~ ( ~ ( SV26 @ ( sK16_A @ SV26 ) )
| ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
| ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[163]) ).
thf(174,plain,
! [SV27: term > $o,SV42: term,SV50: subst] :
( ( ( ~ ( var @ ( sK10_B @ SV50 @ SV42 @ SV27 ) )
| ~ ~ ( SV27 @ ( sub @ ( sK10_B @ SV50 @ SV42 @ SV27 ) @ SV50 ) ) )
= $false )
| ( ( ~ ( SV27 @ SV42 )
| ! [SY134: term] :
( ~ ( var @ SY134 )
| ( SV27 @ ( sub @ SY134 @ ( push @ SV42 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(175,plain,
! [SV51: term,SV33: term,SV45: term,SV9: term] :
( ( ( ( ap @ SV9 @ SV45 )
= ( ap @ SV33 @ SV51 ) )
= $false )
| ( ( SV45 = SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(176,plain,
! [SV53: term,SV34: term,SV52: term,SV10: term] :
( ( ( ( ap @ SV10 @ SV52 )
= ( ap @ SV34 @ SV53 ) )
= $false )
| ( ( SV10 = SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV23: term > $o] :
( ( ( ~ ( var @ ( sK5_A @ SV23 ) ) )
= $false )
| ( ( ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(178,plain,
! [SV23: term > $o] :
( ( ( ~ ~ ( ~ ( SV23 @ ( sK5_A @ SV23 ) )
| ~ ~ ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) ) ) )
= $false )
| ( ( ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[167]) ).
thf(179,plain,
! [SV24: term > $o] :
( ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(180,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sK14_SY84 @ SV24 ) )
| ~ ~ ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(181,plain,
! [SV25: term > $o] :
( ( ( ~ ( ~ ( SV25 @ ( sK7_A @ SV25 ) )
| ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(182,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK7_A @ SV25 ) )
| ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
| ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(183,plain,
! [SV26: term > $o] :
( ( ( ~ ( ~ ( SV26 @ ( sK16_A @ SV26 ) )
| ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(184,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false )
| ( ( ~ ( ~ ( SV26 @ ( sK16_A @ SV26 ) )
| ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
| ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(185,plain,
! [SV27: term > $o,SV42: term,SV50: subst] :
( ( ( ~ ( var @ ( sK10_B @ SV50 @ SV42 @ SV27 ) ) )
= $false )
| ( ( ~ ( SV27 @ SV42 )
| ! [SY134: term] :
( ~ ( var @ SY134 )
| ( SV27 @ ( sub @ SY134 @ ( push @ SV42 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(186,plain,
! [SV42: term,SV50: subst,SV27: term > $o] :
( ( ( ~ ~ ( SV27 @ ( sub @ ( sK10_B @ SV50 @ SV42 @ SV27 ) @ SV50 ) ) )
= $false )
| ( ( ~ ( SV27 @ SV42 )
| ! [SY134: term] :
( ~ ( var @ SY134 )
| ( SV27 @ ( sub @ SY134 @ ( push @ SV42 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(187,plain,
! [SV23: term > $o] :
( ( ( var @ ( sK5_A @ SV23 ) )
= $true )
| ( ( ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[177]) ).
thf(188,plain,
! [SV23: term > $o] :
( ( ( ~ ( ~ ( SV23 @ ( sK5_A @ SV23 ) )
| ~ ~ ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) ) ) )
= $true )
| ( ( ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(189,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
= $false )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(190,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sK14_SY84 @ SV24 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(191,plain,
! [SV24: term > $o] :
( ( ( ~ ~ ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(192,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK7_A @ SV25 ) )
| ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(193,plain,
! [SV25: term > $o] :
( ( ( ~ ( ~ ( SV25 @ ( sK7_A @ SV25 ) )
| ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(194,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK16_A @ SV26 ) )
| ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(195,plain,
! [SV26: term > $o] :
( ( ( ~ ( ~ ( SV26 @ ( sK16_A @ SV26 ) )
| ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(196,plain,
! [SV27: term > $o,SV42: term,SV50: subst] :
( ( ( var @ ( sK10_B @ SV50 @ SV42 @ SV27 ) )
= $true )
| ( ( ~ ( SV27 @ SV42 )
| ! [SY134: term] :
( ~ ( var @ SY134 )
| ( SV27 @ ( sub @ SY134 @ ( push @ SV42 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(197,plain,
! [SV42: term,SV50: subst,SV27: term > $o] :
( ( ( ~ ( SV27 @ ( sub @ ( sK10_B @ SV50 @ SV42 @ SV27 ) @ SV50 ) ) )
= $true )
| ( ( ~ ( SV27 @ SV42 )
| ! [SY134: term] :
( ~ ( var @ SY134 )
| ( SV27 @ ( sub @ SY134 @ ( push @ SV42 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(198,plain,
! [SV23: term > $o,SV54: term] :
( ( ( ~ ( var @ SV54 )
| ( SV23 @ SV54 ) )
= $true )
| ( ( var @ ( sK5_A @ SV23 ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(199,plain,
! [SV23: term > $o] :
( ( ( ~ ( SV23 @ ( sK5_A @ SV23 ) )
| ~ ~ ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) ) )
= $false )
| ( ( ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(200,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) ) )
= $false )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(201,plain,
! [SV24: term > $o] :
( ( ( ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
= $false )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(202,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true )
| ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(203,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[191]) ).
thf(204,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK7_A @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(205,plain,
! [SV25: term > $o] :
( ( ( ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[192]) ).
thf(206,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK7_A @ SV25 ) )
| ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(207,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK16_A @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(208,plain,
! [SV26: term > $o] :
( ( ( ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(209,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK16_A @ SV26 ) )
| ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(210,plain,
! [SV50: subst,SV42: term,SV27: term > $o] :
( ( ( ~ ( SV27 @ SV42 ) )
= $true )
| ( ( ! [SY134: term] :
( ~ ( var @ SY134 )
| ( SV27 @ ( sub @ SY134 @ ( push @ SV42 @ SV50 ) ) ) ) )
= $true )
| ( ( var @ ( sK10_B @ SV50 @ SV42 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(211,plain,
! [SV42: term,SV50: subst,SV27: term > $o] :
( ( ( SV27 @ ( sub @ ( sK10_B @ SV50 @ SV42 @ SV27 ) @ SV50 ) )
= $false )
| ( ( ~ ( SV27 @ SV42 )
| ! [SY134: term] :
( ~ ( var @ SY134 )
| ( SV27 @ ( sub @ SY134 @ ( push @ SV42 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(212,plain,
! [SV23: term > $o,SV54: term] :
( ( ( ~ ( var @ SV54 ) )
= $true )
| ( ( SV23 @ SV54 )
= $true )
| ( ( var @ ( sK5_A @ SV23 ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(213,plain,
! [SV23: term > $o] :
( ( ( ~ ( SV23 @ ( sK5_A @ SV23 ) ) )
= $false )
| ( ( ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(214,plain,
! [SV23: term > $o] :
( ( ( ~ ~ ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) ) )
= $false )
| ( ( ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[199]) ).
thf(215,plain,
! [SV24: term > $o] :
( ( ( ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(216,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(217,plain,
! [SV24: term > $o] :
( ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(218,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
| ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(219,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(220,plain,
! [SV25: term > $o] :
( ( ( ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(221,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK7_A @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(222,plain,
! [SV25: term > $o] :
( ( ( ~ ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[206]) ).
thf(223,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[207]) ).
thf(224,plain,
! [SV26: term > $o] :
( ( ( ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(225,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK16_A @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(226,plain,
! [SV26: term > $o] :
( ( ( ~ ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[209]) ).
thf(227,plain,
! [SV50: subst,SV42: term,SV27: term > $o] :
( ( ( SV27 @ SV42 )
= $false )
| ( ( ! [SY134: term] :
( ~ ( var @ SY134 )
| ( SV27 @ ( sub @ SY134 @ ( push @ SV42 @ SV50 ) ) ) ) )
= $true )
| ( ( var @ ( sK10_B @ SV50 @ SV42 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(228,plain,
! [SV50: subst,SV42: term,SV27: term > $o] :
( ( ( ~ ( SV27 @ SV42 ) )
= $true )
| ( ( ! [SY134: term] :
( ~ ( var @ SY134 )
| ( SV27 @ ( sub @ SY134 @ ( push @ SV42 @ SV50 ) ) ) ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK10_B @ SV50 @ SV42 @ SV27 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(229,plain,
! [SV23: term > $o,SV54: term] :
( ( ( var @ SV54 )
= $false )
| ( ( SV23 @ SV54 )
= $true )
| ( ( var @ ( sK5_A @ SV23 ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(230,plain,
! [SV23: term > $o] :
( ( ( SV23 @ ( sK5_A @ SV23 ) )
= $true )
| ( ( ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[213]) ).
thf(231,plain,
! [SV23: term > $o] :
( ( ( ~ ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) ) )
= $true )
| ( ( ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(232,plain,
! [SV55: term,SV24: term > $o] :
( ( ( ~ ( SV24 @ SV55 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV55 @ id ) ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(233,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(234,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
= $false )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(235,plain,
! [SV24: term > $o] :
( ( ( ~ ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(236,plain,
! [SV25: term > $o] :
( ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(237,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(238,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[221]) ).
thf(239,plain,
! [SV25: term > $o] :
( ( ( ~ ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(240,plain,
! [SV26: term > $o] :
( ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[223]) ).
thf(241,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(242,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(243,plain,
! [SV26: term > $o] :
( ( ( ~ ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[226]) ).
thf(244,plain,
! [SV50: subst,SV42: term,SV27: term > $o,SV56: term] :
( ( ( ~ ( var @ SV56 )
| ( SV27 @ ( sub @ SV56 @ ( push @ SV42 @ SV50 ) ) ) )
= $true )
| ( ( SV27 @ SV42 )
= $false )
| ( ( var @ ( sK10_B @ SV50 @ SV42 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(245,plain,
! [SV50: subst,SV42: term,SV27: term > $o] :
( ( ( SV27 @ SV42 )
= $false )
| ( ( ! [SY134: term] :
( ~ ( var @ SY134 )
| ( SV27 @ ( sub @ SY134 @ ( push @ SV42 @ SV50 ) ) ) ) )
= $true )
| ( ( SV27 @ ( sub @ ( sK10_B @ SV50 @ SV42 @ SV27 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(246,plain,
! [SV23: term > $o,SV57: term] :
( ( ( ~ ( var @ SV57 )
| ( SV23 @ SV57 ) )
= $true )
| ( ( SV23 @ ( sK5_A @ SV23 ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(247,plain,
! [SV23: term > $o] :
( ( ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) )
= $false )
| ( ( ! [SY111: term] :
( ~ ( var @ SY111 )
| ( SV23 @ SY111 ) ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(248,plain,
! [SV55: term,SV24: term > $o] :
( ( ( ~ ( SV24 @ SV55 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV55 @ id ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(249,plain,
! [SV24: term > $o,SV58: term] :
( ( ( ! [SY136: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY136 @ SV58 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY136 @ SV58 @ SV24 ) @ SY136 ) ) )
| ( SV24 @ ( sub @ SV58 @ SY136 ) ) ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(250,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) ) )
= $false )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(251,plain,
! [SV24: term > $o] :
( ( ( ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
= $false )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(252,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) )
| ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
= $false )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(253,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(254,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(255,plain,
! [SV25: term > $o] :
( ( ( ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(256,plain,
! [SV25: term > $o] :
( ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(257,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) )
| ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(258,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(259,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(260,plain,
! [SV26: term > $o] :
( ( ( ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(261,plain,
! [SV26: term > $o] :
( ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(262,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) )
| ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(263,plain,
! [SV50: subst,SV42: term,SV27: term > $o,SV56: term] :
( ( ( ~ ( var @ SV56 ) )
= $true )
| ( ( SV27 @ ( sub @ SV56 @ ( push @ SV42 @ SV50 ) ) )
= $true )
| ( ( SV27 @ SV42 )
= $false )
| ( ( var @ ( sK10_B @ SV50 @ SV42 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(264,plain,
! [SV50: subst,SV42: term,SV27: term > $o,SV59: term] :
( ( ( ~ ( var @ SV59 )
| ( SV27 @ ( sub @ SV59 @ ( push @ SV42 @ SV50 ) ) ) )
= $true )
| ( ( SV27 @ SV42 )
= $false )
| ( ( SV27 @ ( sub @ ( sK10_B @ SV50 @ SV42 @ SV27 ) @ SV50 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(265,plain,
! [SV23: term > $o,SV57: term] :
( ( ( ~ ( var @ SV57 ) )
= $true )
| ( ( SV23 @ SV57 )
= $true )
| ( ( SV23 @ ( sK5_A @ SV23 ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(266,plain,
! [SV23: term > $o,SV60: term] :
( ( ( ~ ( var @ SV60 )
| ( SV23 @ SV60 ) )
= $true )
| ( ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) )
= $false )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(267,plain,
! [SV55: term,SV24: term > $o] :
( ( ( SV24 @ SV55 )
= $false )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV55 @ id ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(268,plain,
! [SV24: term > $o,SV58: term,SV61: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV61 @ SV58 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV61 @ SV58 @ SV24 ) @ SV61 ) ) )
| ( SV24 @ ( sub @ SV58 @ SV61 ) ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(269,plain,
! [SV24: term > $o] :
( ( ( ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[250]) ).
thf(270,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[251]) ).
thf(271,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) ) )
= $false )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(272,plain,
! [SV24: term > $o] :
( ( ( ~ ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
= $false )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[252]) ).
thf(273,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(274,plain,
! [SV25: term > $o] :
( ( ( ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(275,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[254]) ).
thf(276,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[255]) ).
thf(277,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(278,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(279,plain,
! [SV25: term > $o] :
( ( ( ~ ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(280,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(281,plain,
! [SV26: term > $o] :
( ( ( ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[258]) ).
thf(282,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(283,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(284,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(285,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(286,plain,
! [SV26: term > $o] :
( ( ( ~ ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[262]) ).
thf(287,plain,
! [SV50: subst,SV42: term,SV27: term > $o,SV56: term] :
( ( ( var @ SV56 )
= $false )
| ( ( SV27 @ ( sub @ SV56 @ ( push @ SV42 @ SV50 ) ) )
= $true )
| ( ( SV27 @ SV42 )
= $false )
| ( ( var @ ( sK10_B @ SV50 @ SV42 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(288,plain,
! [SV50: subst,SV42: term,SV27: term > $o,SV59: term] :
( ( ( ~ ( var @ SV59 ) )
= $true )
| ( ( SV27 @ ( sub @ SV59 @ ( push @ SV42 @ SV50 ) ) )
= $true )
| ( ( SV27 @ SV42 )
= $false )
| ( ( SV27 @ ( sub @ ( sK10_B @ SV50 @ SV42 @ SV27 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(289,plain,
! [SV23: term > $o,SV57: term] :
( ( ( var @ SV57 )
= $false )
| ( ( SV23 @ SV57 )
= $true )
| ( ( SV23 @ ( sK5_A @ SV23 ) )
= $true )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(290,plain,
! [SV23: term > $o,SV60: term] :
( ( ( ~ ( var @ SV60 ) )
= $true )
| ( ( SV23 @ SV60 )
= $true )
| ( ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) )
= $false )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(291,plain,
! [SV55: term,SV24: term > $o,SV62: term] :
( ( ( ! [SY137: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY137 @ SV62 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY137 @ SV62 @ SV24 ) @ SY137 ) ) )
| ( SV24 @ ( sub @ SV62 @ SY137 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV55 @ id ) ) )
= $true )
| ( ( SV24 @ SV55 )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(292,plain,
! [SV24: term > $o,SV58: term,SV61: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV61 @ SV58 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV61 @ SV58 @ SV24 ) @ SV61 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV58 @ SV61 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(293,plain,
! [SV63: term,SV24: term > $o] :
( ( ( ~ ( SV24 @ SV63 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV63 @ id ) ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(294,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(295,plain,
! [SV24: term > $o] :
( ( ( ! [SY112: term] :
( ~ ( SV24 @ SY112 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SY112 @ id ) ) ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(296,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(297,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sK6_A @ SV25 ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(298,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(299,plain,
! [SV25: term > $o] :
( ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(300,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(301,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(302,plain,
! [SV25: term > $o] :
( ( ( ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[277]) ).
thf(303,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(304,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(305,plain,
! [SV26: term > $o] :
( ( ( ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(306,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(307,plain,
! [SV26: term > $o] :
( ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(308,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(309,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(310,plain,
! [SV26: term > $o] :
( ( ( ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[284]) ).
thf(311,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[285]) ).
thf(312,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(313,plain,
! [SV50: subst,SV42: term,SV27: term > $o,SV59: term] :
( ( ( var @ SV59 )
= $false )
| ( ( SV27 @ ( sub @ SV59 @ ( push @ SV42 @ SV50 ) ) )
= $true )
| ( ( SV27 @ SV42 )
= $false )
| ( ( SV27 @ ( sub @ ( sK10_B @ SV50 @ SV42 @ SV27 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(314,plain,
! [SV23: term > $o,SV60: term] :
( ( ( var @ SV60 )
= $false )
| ( ( SV23 @ SV60 )
= $true )
| ( ( SV23 @ ( sub @ ( sK5_A @ SV23 ) @ sh ) )
= $false )
| ( ( SV23 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[290]) ).
thf(315,plain,
! [SV55: term,SV24: term > $o,SV62: term,SV64: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV64 @ SV62 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV64 @ SV62 @ SV24 ) @ SV64 ) ) )
| ( SV24 @ ( sub @ SV62 @ SV64 ) ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV55 @ id ) ) )
= $true )
| ( ( SV24 @ SV55 )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(316,plain,
! [SV24: term > $o,SV58: term,SV61: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV61 @ SV58 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV61 @ SV58 @ SV24 ) @ SV61 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV58 @ SV61 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(317,plain,
! [SV63: term,SV24: term > $o] :
( ( ( ~ ( SV24 @ SV63 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV63 @ id ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(318,plain,
! [SV24: term > $o,SV65: term] :
( ( ( ! [SY138: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY138 @ SV65 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY138 @ SV65 @ SV24 ) @ SY138 ) ) )
| ( SV24 @ ( sub @ SV65 @ SY138 ) ) ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(319,plain,
! [SV66: term,SV24: term > $o] :
( ( ( ~ ( SV24 @ SV66 )
| ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV66 @ id ) ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(320,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[296]) ).
thf(321,plain,
! [SV67: term,SV25: term > $o] :
( ( ( SV25 @ SV67 )
= $true )
| ( ( SV25 @ ( sK6_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(322,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(323,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[299]) ).
thf(324,plain,
! [SV25: term > $o] :
( ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(325,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sK6_A @ SV25 ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(326,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(327,plain,
! [SV25: term > $o] :
( ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(328,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
| ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(329,plain,
! [SV68: term,SV26: term > $o] :
( ( ( ~ ( SV26 @ SV68 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV68 @ id ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(330,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(331,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(332,plain,
! [SV26: term > $o] :
( ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(333,plain,
! [SV26: term > $o] :
( ( ( ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(334,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[310]) ).
thf(335,plain,
! [SV26: term > $o] :
( ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(336,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
| ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(337,plain,
! [SV55: term,SV24: term > $o,SV62: term,SV64: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV64 @ SV62 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV64 @ SV62 @ SV24 ) @ SV64 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV62 @ SV64 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV55 @ id ) ) )
= $true )
| ( ( SV24 @ SV55 )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(338,plain,
! [SV24: term > $o,SV58: term,SV61: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV61 @ SV58 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV58 @ SV61 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[316]) ).
thf(339,plain,
! [SV58: term,SV61: subst,SV24: term > $o] :
( ( ( ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV61 @ SV58 @ SV24 ) @ SV61 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV58 @ SV61 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[316]) ).
thf(340,plain,
! [SV63: term,SV24: term > $o] :
( ( ( SV24 @ SV63 )
= $false )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV63 @ id ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(341,plain,
! [SV24: term > $o,SV65: term,SV69: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV69 @ SV65 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV69 @ SV65 @ SV24 ) @ SV69 ) ) )
| ( SV24 @ ( sub @ SV65 @ SV69 ) ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(342,plain,
! [SV66: term,SV24: term > $o] :
( ( ( ~ ( SV24 @ SV66 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV66 @ id ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(343,plain,
! [SV24: term > $o,SV70: term] :
( ( ( ! [SY139: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY139 @ SV70 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY139 @ SV70 @ SV24 ) @ SY139 ) ) )
| ( SV24 @ ( sub @ SV70 @ SY139 ) ) ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(344,plain,
! [SV71: term,SV25: term > $o] :
( ( ( SV25 @ SV71 )
= $true )
| ( ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(345,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(346,plain,
! [SV25: term > $o] :
( ( ( ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[323]) ).
thf(347,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(348,plain,
! [SV72: term,SV25: term > $o] :
( ( ( SV25 @ SV72 )
= $true )
| ( ( SV25 @ ( sK6_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(349,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[326]) ).
thf(350,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(351,plain,
! [SV25: term > $o] :
( ( ( ~ ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(352,plain,
! [SV68: term,SV26: term > $o] :
( ( ( ~ ( SV26 @ SV68 ) )
= $true )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(353,plain,
! [SV73: term,SV26: term > $o] :
( ( ( SV26 @ SV73 )
= $true )
| ( ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(354,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(355,plain,
! [SV26: term > $o] :
( ( ( ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[331]) ).
thf(356,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(357,plain,
! [SV74: term,SV26: term > $o] :
( ( ( ~ ( SV26 @ SV74 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV74 @ id ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(358,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(359,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(360,plain,
! [SV26: term > $o] :
( ( ( ~ ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(361,plain,
! [SV55: term,SV24: term > $o,SV62: term,SV64: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV64 @ SV62 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV64 @ SV62 @ SV24 ) @ SV64 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV62 @ SV64 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV55 @ id ) ) )
= $true )
| ( ( SV24 @ SV55 )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(362,plain,
! [SV24: term > $o,SV58: term,SV61: subst] :
( ( ( var @ ( sK11_B @ SV61 @ SV58 @ SV24 ) )
= $true )
| ( ( SV24 @ ( sub @ SV58 @ SV61 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(363,plain,
! [SV58: term,SV61: subst,SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sub @ ( sK11_B @ SV61 @ SV58 @ SV24 ) @ SV61 ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV58 @ SV61 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[339]) ).
thf(364,plain,
! [SV63: term,SV24: term > $o,SV75: term] :
( ( ( ! [SY140: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY140 @ SV75 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY140 @ SV75 @ SV24 ) @ SY140 ) ) )
| ( SV24 @ ( sub @ SV75 @ SY140 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV63 @ id ) ) )
= $true )
| ( ( SV24 @ SV63 )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(365,plain,
! [SV24: term > $o,SV65: term,SV69: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV69 @ SV65 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV69 @ SV65 @ SV24 ) @ SV69 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV65 @ SV69 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(366,plain,
! [SV66: term,SV24: term > $o] :
( ( ( SV24 @ SV66 )
= $false )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV66 @ id ) ) )
= $true )
| ( ( ! [SY113: term,SY114: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY114 @ SY113 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY114 @ SY113 @ SV24 ) @ SY114 ) ) )
| ( SV24 @ ( sub @ SY113 @ SY114 ) ) ) )
= $true )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(367,plain,
! [SV24: term > $o,SV70: term,SV76: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV76 @ SV70 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV76 @ SV70 @ SV24 ) @ SV76 ) ) )
| ( SV24 @ ( sub @ SV70 @ SV76 ) ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(368,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sK6_A @ SV25 ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[345]) ).
thf(369,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[346]) ).
thf(370,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(371,plain,
! [SV25: term > $o] :
( ( ( ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[347]) ).
thf(372,plain,
! [SV77: term,SV25: term > $o] :
( ( ( SV25 @ SV77 )
= $true )
| ( ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK7_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(373,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(374,plain,
! [SV25: term > $o] :
( ( ( ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[350]) ).
thf(375,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK6_A @ SV25 ) )
| ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(376,plain,
! [SV68: term,SV26: term > $o] :
( ( ( SV26 @ SV68 )
= $false )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(377,plain,
! [SV26: term > $o] :
( ( ( ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(378,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[355]) ).
thf(379,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(380,plain,
! [SV26: term > $o] :
( ( ( ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(381,plain,
! [SV74: term,SV26: term > $o] :
( ( ( ~ ( SV26 @ SV74 ) )
= $true )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(382,plain,
! [SV78: term,SV26: term > $o] :
( ( ( SV26 @ SV78 )
= $true )
| ( ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(383,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(384,plain,
! [SV26: term > $o] :
( ( ( ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[359]) ).
thf(385,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) )
| ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(386,plain,
! [SV55: term,SV24: term > $o,SV62: term,SV64: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV64 @ SV62 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV62 @ SV64 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV55 @ id ) ) )
= $true )
| ( ( SV24 @ SV55 )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[361]) ).
thf(387,plain,
! [SV55: term,SV62: term,SV64: subst,SV24: term > $o] :
( ( ( ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV64 @ SV62 @ SV24 ) @ SV64 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV62 @ SV64 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV55 @ id ) ) )
= $true )
| ( ( SV24 @ SV55 )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[361]) ).
thf(388,plain,
! [SV58: term,SV61: subst,SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK11_B @ SV61 @ SV58 @ SV24 ) @ SV61 ) )
= $false )
| ( ( SV24 @ ( sub @ SV58 @ SV61 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(389,plain,
! [SV63: term,SV24: term > $o,SV75: term,SV79: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV79 @ SV75 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV79 @ SV75 @ SV24 ) @ SV79 ) ) )
| ( SV24 @ ( sub @ SV75 @ SV79 ) ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV63 @ id ) ) )
= $true )
| ( ( SV24 @ SV63 )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(390,plain,
! [SV24: term > $o,SV65: term,SV69: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV69 @ SV65 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV69 @ SV65 @ SV24 ) @ SV69 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV65 @ SV69 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(391,plain,
! [SV66: term,SV24: term > $o,SV80: term] :
( ( ( ! [SY141: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY141 @ SV80 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SY141 @ SV80 @ SV24 ) @ SY141 ) ) )
| ( SV24 @ ( sub @ SV80 @ SY141 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV66 @ id ) ) )
= $true )
| ( ( SV24 @ SV66 )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(392,plain,
! [SV24: term > $o,SV70: term,SV76: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV76 @ SV70 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV76 @ SV70 @ SV24 ) @ SV76 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV70 @ SV76 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(393,plain,
! [SV81: term,SV25: term > $o] :
( ( ( SV25 @ SV81 )
= $true )
| ( ( SV25 @ ( sK6_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(394,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(395,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sK6_A @ SV25 ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[370]) ).
thf(396,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(397,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sK6_A @ SV25 ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[373]) ).
thf(398,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[374]) ).
thf(399,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(400,plain,
! [SV25: term > $o] :
( ( ( ~ ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[375]) ).
thf(401,plain,
! [SV68: term,SV82: term,SV26: term > $o] :
( ( ( SV26 @ SV82 )
= $true )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV26 @ SV68 )
= $false )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(402,plain,
! [SV83: term,SV26: term > $o] :
( ( ( ~ ( SV26 @ SV83 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV83 @ id ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(403,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(404,plain,
! [SV26: term > $o] :
( ( ( ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[379]) ).
thf(405,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[380]) ).
thf(406,plain,
! [SV74: term,SV26: term > $o] :
( ( ( SV26 @ SV74 )
= $false )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(407,plain,
! [SV26: term > $o] :
( ( ( ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(408,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[384]) ).
thf(409,plain,
! [SV26: term > $o] :
( ( ( ~ ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(410,plain,
! [SV26: term > $o] :
( ( ( ~ ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(411,plain,
! [SV55: term,SV24: term > $o,SV62: term,SV64: subst] :
( ( ( var @ ( sK11_B @ SV64 @ SV62 @ SV24 ) )
= $true )
| ( ( SV24 @ ( sub @ SV62 @ SV64 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV55 @ id ) ) )
= $true )
| ( ( SV24 @ SV55 )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(412,plain,
! [SV55: term,SV62: term,SV64: subst,SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sub @ ( sK11_B @ SV64 @ SV62 @ SV24 ) @ SV64 ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV62 @ SV64 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV55 @ id ) ) )
= $true )
| ( ( SV24 @ SV55 )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(413,plain,
! [SV63: term,SV24: term > $o,SV75: term,SV79: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV79 @ SV75 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV79 @ SV75 @ SV24 ) @ SV79 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV75 @ SV79 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV63 @ id ) ) )
= $true )
| ( ( SV24 @ SV63 )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(414,plain,
! [SV24: term > $o,SV65: term,SV69: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV69 @ SV65 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV65 @ SV69 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(415,plain,
! [SV65: term,SV69: subst,SV24: term > $o] :
( ( ( ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV69 @ SV65 @ SV24 ) @ SV69 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV65 @ SV69 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(416,plain,
! [SV66: term,SV24: term > $o,SV80: term,SV84: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV84 @ SV80 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV84 @ SV80 @ SV24 ) @ SV84 ) ) )
| ( SV24 @ ( sub @ SV80 @ SV84 ) ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV66 @ id ) ) )
= $true )
| ( ( SV24 @ SV66 )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(417,plain,
! [SV24: term > $o,SV70: term,SV76: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV76 @ SV70 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV76 @ SV70 @ SV24 ) @ SV76 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV70 @ SV76 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(418,plain,
! [SV85: term,SV25: term > $o] :
( ( ( SV25 @ SV85 )
= $true )
| ( ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(419,plain,
! [SV86: term,SV25: term > $o] :
( ( ( SV25 @ SV86 )
= $true )
| ( ( SV25 @ ( sK6_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(420,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(421,plain,
! [SV87: term,SV25: term > $o] :
( ( ( SV25 @ SV87 )
= $true )
| ( ( SV25 @ ( sK6_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(422,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(423,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( sK6_A @ SV25 ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(424,plain,
! [SV25: term > $o] :
( ( ( ~ ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) ) )
= $true )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[400]) ).
thf(425,plain,
! [SV83: term,SV26: term > $o] :
( ( ( ~ ( SV26 @ SV83 ) )
= $true )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV83 @ id ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(426,plain,
! [SV88: term,SV26: term > $o] :
( ( ( SV26 @ SV88 )
= $true )
| ( ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(427,plain,
! [SV89: term,SV26: term > $o] :
( ( ( ~ ( SV26 @ SV89 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV89 @ id ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(428,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(429,plain,
! [SV74: term,SV90: term,SV26: term > $o] :
( ( ( SV26 @ SV90 )
= $true )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV74 @ id ) ) )
= $true )
| ( ( SV26 @ SV74 )
= $false )
| ( ( SV26 @ ( sK16_A @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(430,plain,
! [SV91: term,SV26: term > $o] :
( ( ( ~ ( SV26 @ SV91 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV91 @ id ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(431,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(432,plain,
! [SV26: term > $o] :
( ( ( ! [SY116: term] :
( ~ ( SV26 @ SY116 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SY116 @ id ) ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[409]) ).
thf(433,plain,
! [SV26: term > $o] :
( ( ( ~ ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[410]) ).
thf(434,plain,
! [SV55: term,SV62: term,SV64: subst,SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK11_B @ SV64 @ SV62 @ SV24 ) @ SV64 ) )
= $false )
| ( ( SV24 @ ( sub @ SV62 @ SV64 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV55 @ id ) ) )
= $true )
| ( ( SV24 @ SV55 )
= $false )
| ( ( SV24 @ ( sK13_A @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(435,plain,
! [SV63: term,SV24: term > $o,SV75: term,SV79: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV79 @ SV75 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV79 @ SV75 @ SV24 ) @ SV79 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV75 @ SV79 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV63 @ id ) ) )
= $true )
| ( ( SV24 @ SV63 )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(436,plain,
! [SV24: term > $o,SV65: term,SV69: subst] :
( ( ( var @ ( sK11_B @ SV69 @ SV65 @ SV24 ) )
= $true )
| ( ( SV24 @ ( sub @ SV65 @ SV69 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[414]) ).
thf(437,plain,
! [SV65: term,SV69: subst,SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sub @ ( sK11_B @ SV69 @ SV65 @ SV24 ) @ SV69 ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV65 @ SV69 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(438,plain,
! [SV66: term,SV24: term > $o,SV80: term,SV84: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV84 @ SV80 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV84 @ SV80 @ SV24 ) @ SV84 ) ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV80 @ SV84 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV66 @ id ) ) )
= $true )
| ( ( SV24 @ SV66 )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(439,plain,
! [SV24: term > $o,SV70: term,SV76: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV76 @ SV70 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV70 @ SV76 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(440,plain,
! [SV70: term,SV76: subst,SV24: term > $o] :
( ( ( ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV76 @ SV70 @ SV24 ) @ SV76 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV70 @ SV76 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(441,plain,
! [SV92: term,SV25: term > $o] :
( ( ( SV25 @ SV92 )
= $true )
| ( ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV25 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(442,plain,
! [SV93: term,SV25: term > $o] :
( ( ( SV25 @ SV93 )
= $true )
| ( ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK8_SY82 @ SV25 ) )
= $true )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(443,plain,
! [SV94: term,SV25: term > $o] :
( ( ( SV25 @ SV94 )
= $true )
| ( ( SV25 @ ( sK6_A @ SV25 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(444,plain,
! [SV25: term > $o] :
( ( ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( ! [SY115: term] : ( SV25 @ SY115 ) )
= $true )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(445,plain,
! [SV83: term,SV26: term > $o] :
( ( ( SV26 @ SV83 )
= $false )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV83 @ id ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[425]) ).
thf(446,plain,
! [SV89: term,SV26: term > $o] :
( ( ( ~ ( SV26 @ SV89 ) )
= $true )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV89 @ id ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(447,plain,
! [SV95: term,SV26: term > $o] :
( ( ( SV26 @ SV95 )
= $true )
| ( ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(448,plain,
! [SV91: term,SV26: term > $o] :
( ( ( ~ ( SV26 @ SV91 ) )
= $true )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV91 @ id ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(449,plain,
! [SV96: term,SV26: term > $o] :
( ( ( SV26 @ SV96 )
= $true )
| ( ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(450,plain,
! [SV97: term,SV26: term > $o] :
( ( ( ~ ( SV26 @ SV97 )
| ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV97 @ id ) ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(451,plain,
! [SV26: term > $o] :
( ( ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) )
= $false )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(452,plain,
! [SV63: term,SV24: term > $o,SV75: term,SV79: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV79 @ SV75 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV75 @ SV79 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV63 @ id ) ) )
= $true )
| ( ( SV24 @ SV63 )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(453,plain,
! [SV63: term,SV75: term,SV79: subst,SV24: term > $o] :
( ( ( ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV79 @ SV75 @ SV24 ) @ SV79 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV75 @ SV79 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV63 @ id ) ) )
= $true )
| ( ( SV24 @ SV63 )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(454,plain,
! [SV65: term,SV69: subst,SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK11_B @ SV69 @ SV65 @ SV24 ) @ SV69 ) )
= $false )
| ( ( SV24 @ ( sub @ SV65 @ SV69 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(455,plain,
! [SV66: term,SV24: term > $o,SV80: term,SV84: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV84 @ SV80 @ SV24 ) )
| ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV84 @ SV80 @ SV24 ) @ SV84 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV80 @ SV84 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV66 @ id ) ) )
= $true )
| ( ( SV24 @ SV66 )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(456,plain,
! [SV24: term > $o,SV70: term,SV76: subst] :
( ( ( var @ ( sK11_B @ SV76 @ SV70 @ SV24 ) )
= $true )
| ( ( SV24 @ ( sub @ SV70 @ SV76 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[439]) ).
thf(457,plain,
! [SV70: term,SV76: subst,SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sub @ ( sK11_B @ SV76 @ SV70 @ SV24 ) @ SV76 ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV70 @ SV76 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[440]) ).
thf(458,plain,
! [SV98: term,SV25: term > $o] :
( ( ( SV25 @ SV98 )
= $true )
| ( ( SV25 @ ( lam @ ( sK6_A @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( ap @ ( sK7_A @ SV25 ) @ ( sK8_SY82 @ SV25 ) ) )
= $false )
| ( ( SV25 @ ( sK9_A @ SV25 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(459,plain,
! [SV83: term,SV99: term,SV26: term > $o] :
( ( ( SV26 @ SV99 )
= $true )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV83 @ id ) ) )
= $true )
| ( ( SV26 @ SV83 )
= $false )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(460,plain,
! [SV89: term,SV26: term > $o] :
( ( ( SV26 @ SV89 )
= $false )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV89 @ id ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(461,plain,
! [SV91: term,SV26: term > $o] :
( ( ( SV26 @ SV91 )
= $false )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV91 @ id ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(462,plain,
! [SV97: term,SV26: term > $o] :
( ( ( ~ ( SV26 @ SV97 ) )
= $true )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV97 @ id ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(463,plain,
! [SV100: term,SV26: term > $o] :
( ( ( SV26 @ SV100 )
= $true )
| ( ( SV26 @ ( lam @ ( sK15_A @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(464,plain,
! [SV63: term,SV24: term > $o,SV75: term,SV79: subst] :
( ( ( var @ ( sK11_B @ SV79 @ SV75 @ SV24 ) )
= $true )
| ( ( SV24 @ ( sub @ SV75 @ SV79 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV63 @ id ) ) )
= $true )
| ( ( SV24 @ SV63 )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(465,plain,
! [SV63: term,SV75: term,SV79: subst,SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sub @ ( sK11_B @ SV79 @ SV75 @ SV24 ) @ SV79 ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV75 @ SV79 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV63 @ id ) ) )
= $true )
| ( ( SV24 @ SV63 )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(466,plain,
! [SV66: term,SV24: term > $o,SV80: term,SV84: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV84 @ SV80 @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV80 @ SV84 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV66 @ id ) ) )
= $true )
| ( ( SV24 @ SV66 )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(467,plain,
! [SV66: term,SV80: term,SV84: subst,SV24: term > $o] :
( ( ( ~ ~ ( SV24 @ ( sub @ ( sK11_B @ SV84 @ SV80 @ SV24 ) @ SV84 ) ) )
= $false )
| ( ( SV24 @ ( sub @ SV80 @ SV84 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV66 @ id ) ) )
= $true )
| ( ( SV24 @ SV66 )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(468,plain,
! [SV70: term,SV76: subst,SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK11_B @ SV76 @ SV70 @ SV24 ) @ SV76 ) )
= $false )
| ( ( SV24 @ ( sub @ SV70 @ SV76 ) )
= $true )
| ( ( SV24 @ ( lam @ ( sK12_A @ SV24 ) ) )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(469,plain,
! [SV89: term,SV101: term,SV26: term > $o] :
( ( ( SV26 @ SV101 )
= $true )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV89 @ id ) ) )
= $true )
| ( ( SV26 @ SV89 )
= $false )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(470,plain,
! [SV91: term,SV102: term,SV26: term > $o] :
( ( ( SV26 @ SV102 )
= $true )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV91 @ id ) ) )
= $true )
| ( ( SV26 @ SV91 )
= $false )
| ( ( SV26 @ ( sK17_SY86 @ SV26 ) )
= $true )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(471,plain,
! [SV97: term,SV26: term > $o] :
( ( ( SV26 @ SV97 )
= $false )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV97 @ id ) ) )
= $true )
| ( ( ! [SY117: term] : ( SV26 @ SY117 ) )
= $true )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(472,plain,
! [SV63: term,SV75: term,SV79: subst,SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK11_B @ SV79 @ SV75 @ SV24 ) @ SV79 ) )
= $false )
| ( ( SV24 @ ( sub @ SV75 @ SV79 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV63 @ id ) ) )
= $true )
| ( ( SV24 @ SV63 )
= $false )
| ( ( SV24 @ ( sK14_SY84 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(473,plain,
! [SV66: term,SV24: term > $o,SV80: term,SV84: subst] :
( ( ( var @ ( sK11_B @ SV84 @ SV80 @ SV24 ) )
= $true )
| ( ( SV24 @ ( sub @ SV80 @ SV84 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV66 @ id ) ) )
= $true )
| ( ( SV24 @ SV66 )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(474,plain,
! [SV66: term,SV80: term,SV84: subst,SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sub @ ( sK11_B @ SV84 @ SV80 @ SV24 ) @ SV84 ) ) )
= $true )
| ( ( SV24 @ ( sub @ SV80 @ SV84 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV66 @ id ) ) )
= $true )
| ( ( SV24 @ SV66 )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(475,plain,
! [SV97: term,SV103: term,SV26: term > $o] :
( ( ( SV26 @ SV103 )
= $true )
| ( ( SV26 @ ( sub @ ( sK15_A @ SV26 ) @ ( push @ SV97 @ id ) ) )
= $true )
| ( ( SV26 @ SV97 )
= $false )
| ( ( SV26 @ ( ap @ ( sK16_A @ SV26 ) @ ( sK17_SY86 @ SV26 ) ) )
= $false )
| ( ( SV26 @ ( sK18_A @ SV26 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(476,plain,
! [SV66: term,SV80: term,SV84: subst,SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK11_B @ SV84 @ SV80 @ SV24 ) @ SV84 ) )
= $false )
| ( ( SV24 @ ( sub @ SV80 @ SV84 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK12_A @ SV24 ) @ ( push @ SV66 @ id ) ) )
= $true )
| ( ( SV24 @ SV66 )
= $false )
| ( ( SV24 @ ( ap @ ( sK13_A @ SV24 ) @ ( sK14_SY84 @ SV24 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(477,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[67,476,475,473,472,470,469,468,464,463,459,458,456,454,449,447,443,442,441,436,434,429,426,421,419,418,411,401,393,388,382,372,362,353,348,344,321,314,313,289,287,229,176,175,154,153,152,146,145,144,143,142,136,135,128,127,125,115,108,105,102,98,97,87,86,69]) ).
thf(478,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(479,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(480,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(481,plain,
( ( ! [P: term > $o] :
( ( ( var @ ( sK18_A @ P ) )
& ~ ( P @ ( sK18_A @ P ) ) )
| ( ( P @ ( sK16_A @ P ) )
& ( P @ ( sK17_SY86 @ P ) )
& ~ ( P @ ( ap @ ( sK16_A @ P ) @ ( sK17_SY86 @ P ) ) ) )
| ( ! [SY85: term] :
( ~ ( P @ SY85 )
| ( P @ ( sub @ ( sK15_A @ P ) @ ( push @ SY85 @ id ) ) ) )
& ~ ( P @ ( lam @ ( sK15_A @ P ) ) ) )
| ! [A: term] : ( P @ A ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(482,plain,
( ( ! [P: term > $o] :
( ( ( P @ ( sK13_A @ P ) )
& ( P @ ( sK14_SY84 @ P ) )
& ~ ( P @ ( ap @ ( sK13_A @ P ) @ ( sK14_SY84 @ P ) ) ) )
| ( ! [SY83: term] :
( ~ ( P @ SY83 )
| ( P @ ( sub @ ( sK12_A @ P ) @ ( push @ SY83 @ 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)],[49]) ).
thf(483,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)],[48]) ).
thf(484,plain,
( ( ! [P: term > $o] :
( ( ( var @ ( sK9_A @ P ) )
& ~ ( P @ ( sK9_A @ P ) ) )
| ( ( P @ ( sK7_A @ P ) )
& ( P @ ( sK8_SY82 @ P ) )
& ~ ( P @ ( ap @ ( sK7_A @ P ) @ ( sK8_SY82 @ P ) ) ) )
| ( ( P @ ( sK6_A @ P ) )
& ~ ( P @ ( lam @ ( sK6_A @ P ) ) ) )
| ! [A: term] : ( P @ A ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(485,plain,
( ( ! [A: term] :
~ ( var @ ( lam @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(486,plain,
( ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(487,plain,
( ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(488,plain,
( ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
!= ( sub @ B @ sh ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(489,plain,
( ( ! [A: term,B: term] :
( ( ( lam @ A )
!= ( lam @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(490,plain,
( ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
!= ( ap @ B @ D ) )
| ( C = D ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(491,plain,
( ( ! [A: term,B: term] :
( ! [C: term,D: term] :
( ( ap @ A @ C )
!= ( ap @ B @ D ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(492,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)],[41]) ).
thf(493,plain,
( ( ! [A: term] :
( ~ ( var @ A )
| ( var @ ( sub @ A @ sh ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(494,plain,
( ( var @ one )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(495,plain,
( ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(496,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(497,plain,
( ( ! [M: subst] :
( ( comp @ M @ id )
= M ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(498,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(499,plain,
( ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(500,plain,
( ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(501,plain,
( ( ! [M: subst] :
( ( comp @ id @ M )
= M ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(502,plain,
( ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(503,plain,
( ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(504,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(505,plain,
( ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(506,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(507,plain,
( ( ( sub @ sK4_A @ id )
!= sK4_A )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(508,plain,
( ( ! [SX0: term > $o] :
( ~ ( ~ ( var @ ( sK18_A @ SX0 ) )
| ~ ~ ( SX0 @ ( sK18_A @ SX0 ) ) )
| ~ ( ~ ( SX0 @ ( sK16_A @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK17_SY86 @ SX0 ) )
| ~ ~ ( SX0 @ ( ap @ ( sK16_A @ SX0 ) @ ( sK17_SY86 @ 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)],[481,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(509,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)],[483,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(510,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)],[492,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(511,plain,
( ( ! [SX0: term > $o] :
( ~ ( ~ ( SX0 @ ( sK13_A @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK14_SY84 @ SX0 ) )
| ~ ~ ( SX0 @ ( ap @ ( sK13_A @ SX0 ) @ ( sK14_SY84 @ 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)],[482,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(512,plain,
( ( ! [SX0: term > $o] :
( ~ ( ~ ( var @ ( sK9_A @ SX0 ) )
| ~ ~ ( SX0 @ ( sK9_A @ SX0 ) ) )
| ~ ( ~ ( SX0 @ ( sK7_A @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK8_SY82 @ SX0 ) )
| ~ ~ ( SX0 @ ( ap @ ( sK7_A @ SX0 ) @ ( sK8_SY82 @ SX0 ) ) ) ) )
| ~ ( ~ ( SX0 @ ( sK6_A @ SX0 ) )
| ~ ~ ( SX0 @ ( lam @ ( sK6_A @ SX0 ) ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484,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(513,plain,
! [SV104: subst] :
( ( ( comp @ SV104 @ id )
= SV104 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(514,plain,
! [SV105: subst] :
( ( ( comp @ id @ SV105 )
= SV105 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(515,plain,
! [SV106: subst] :
( ( ! [SY142: subst,SY143: subst] :
( ( comp @ ( comp @ SV106 @ SY142 ) @ SY143 )
= ( comp @ SV106 @ ( comp @ SY142 @ SY143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(516,plain,
! [SV107: term] :
( ( ~ ( var @ ( lam @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(517,plain,
! [SV108: term] :
( ( ! [SY144: term] :
~ ( var @ ( ap @ SV108 @ SY144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(518,plain,
! [SV109: term] :
( ( ! [SY145: term,SY146: term] :
( ( lam @ SV109 )
!= ( ap @ SY145 @ SY146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(519,plain,
! [SV110: term] :
( ( ! [SY147: term] :
( ( ( sub @ SV110 @ sh )
!= ( sub @ SY147 @ sh ) )
| ( SV110 = SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(520,plain,
! [SV111: term] :
( ( ! [SY148: term] :
( ( ( lam @ SV111 )
!= ( lam @ SY148 ) )
| ( SV111 = SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(521,plain,
! [SV112: term] :
( ( ! [SY149: term,SY150: term,SY151: term] :
( ( ( ap @ SV112 @ SY150 )
!= ( ap @ SY149 @ SY151 ) )
| ( SY150 = SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(522,plain,
! [SV113: term] :
( ( ! [SY152: term] :
( ! [SY153: term,SY154: term] :
( ( ap @ SV113 @ SY153 )
!= ( ap @ SY152 @ SY154 ) )
| ( SV113 = SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(523,plain,
! [SV114: term] :
( ( ~ ( var @ SV114 )
| ( var @ ( sub @ SV114 @ sh ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(524,plain,
! [SV115: subst] :
( ( ( push @ ( sub @ one @ SV115 ) @ ( comp @ sh @ SV115 ) )
= SV115 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(525,plain,
! [SV116: subst] :
( ( ( comp @ SV116 @ id )
= SV116 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(526,plain,
! [SV117: term] :
( ( ! [SY155: subst,SY156: subst] :
( ( comp @ ( push @ SV117 @ SY155 ) @ SY156 )
= ( push @ ( sub @ SV117 @ SY156 ) @ ( comp @ SY155 @ SY156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(527,plain,
! [SV118: subst] :
( ( ! [SY157: subst,SY158: subst] :
( ( comp @ ( comp @ SV118 @ SY157 ) @ SY158 )
= ( comp @ SV118 @ ( comp @ SY157 @ SY158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(528,plain,
! [SV119: term] :
( ( ! [SY159: subst] :
( ( comp @ sh @ ( push @ SV119 @ SY159 ) )
= SY159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(529,plain,
! [SV120: subst] :
( ( ( comp @ id @ SV120 )
= SV120 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(530,plain,
! [SV121: term] :
( ( ! [SY160: subst,SY161: subst] :
( ( sub @ ( sub @ SV121 @ SY160 ) @ SY161 )
= ( sub @ SV121 @ ( comp @ SY160 @ SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(531,plain,
! [SV122: term] :
( ( ! [SY162: subst] :
( ( sub @ ( lam @ SV122 ) @ SY162 )
= ( lam @ ( sub @ SV122 @ ( push @ one @ ( comp @ SY162 @ sh ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(532,plain,
! [SV123: term] :
( ( ( sub @ SV123 @ id )
= SV123 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(533,plain,
! [SV124: term] :
( ( ! [SY163: subst] :
( ( sub @ one @ ( push @ SV124 @ SY163 ) )
= SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(534,plain,
! [SV125: term] :
( ( ! [SY164: term,SY165: subst] :
( ( sub @ ( ap @ SV125 @ SY164 ) @ SY165 )
= ( ap @ ( sub @ SV125 @ SY165 ) @ ( sub @ SY164 @ SY165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(535,plain,
( ( ( sub @ sK4_A @ id )
= sK4_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(536,plain,
! [SV126: term > $o] :
( ( ~ ( ~ ( var @ ( sK18_A @ SV126 ) )
| ~ ~ ( SV126 @ ( sK18_A @ SV126 ) ) )
| ~ ( ~ ( SV126 @ ( sK16_A @ SV126 ) )
| ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
| ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(537,plain,
! [SV127: term > $o] :
( ( ! [SY168: term,SY169: subst] :
( ~ ( ~ ( var @ ( sK10_B @ SY169 @ SY168 @ SV127 ) )
| ~ ~ ( SV127 @ ( sub @ ( sK10_B @ SY169 @ SY168 @ SV127 ) @ SY169 ) ) )
| ~ ( SV127 @ SY168 )
| ! [SY170: term] :
( ~ ( var @ SY170 )
| ( SV127 @ ( sub @ SY170 @ ( push @ SY168 @ SY169 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(538,plain,
! [SV128: term > $o] :
( ( ~ ( SV128 @ one )
| ~ ( ~ ( var @ ( sK5_A @ SV128 ) )
| ~ ~ ( ~ ( SV128 @ ( sK5_A @ SV128 ) )
| ~ ~ ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) ) ) )
| ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(539,plain,
! [SV129: term > $o] :
( ( ~ ( ~ ( SV129 @ ( sK13_A @ SV129 ) )
| ~ ~ ( ~ ( SV129 @ ( sK14_SY84 @ SV129 ) )
| ~ ~ ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) ) ) )
| ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(540,plain,
! [SV130: term > $o] :
( ( ~ ( ~ ( var @ ( sK9_A @ SV130 ) )
| ~ ~ ( SV130 @ ( sK9_A @ SV130 ) ) )
| ~ ( ~ ( SV130 @ ( sK7_A @ SV130 ) )
| ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
| ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(541,plain,
! [SV131: subst,SV106: subst] :
( ( ! [SY176: subst] :
( ( comp @ ( comp @ SV106 @ SV131 ) @ SY176 )
= ( comp @ SV106 @ ( comp @ SV131 @ SY176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(542,plain,
! [SV107: term] :
( ( var @ ( lam @ SV107 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(543,plain,
! [SV132: term,SV108: term] :
( ( ~ ( var @ ( ap @ SV108 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(544,plain,
! [SV133: term,SV109: term] :
( ( ! [SY177: term] :
( ( lam @ SV109 )
!= ( ap @ SV133 @ SY177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(545,plain,
! [SV134: term,SV110: term] :
( ( ( ( sub @ SV110 @ sh )
!= ( sub @ SV134 @ sh ) )
| ( SV110 = SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(546,plain,
! [SV135: term,SV111: term] :
( ( ( ( lam @ SV111 )
!= ( lam @ SV135 ) )
| ( SV111 = SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(547,plain,
! [SV136: term,SV112: term] :
( ( ! [SY178: term,SY179: term] :
( ( ( ap @ SV112 @ SY178 )
!= ( ap @ SV136 @ SY179 ) )
| ( SY178 = SY179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(548,plain,
! [SV137: term,SV113: term] :
( ( ! [SY180: term,SY181: term] :
( ( ap @ SV113 @ SY180 )
!= ( ap @ SV137 @ SY181 ) )
| ( SV113 = SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(549,plain,
! [SV114: term] :
( ( ( ~ ( var @ SV114 ) )
= $true )
| ( ( var @ ( sub @ SV114 @ sh ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(550,plain,
! [SV138: subst,SV117: term] :
( ( ! [SY182: subst] :
( ( comp @ ( push @ SV117 @ SV138 ) @ SY182 )
= ( push @ ( sub @ SV117 @ SY182 ) @ ( comp @ SV138 @ SY182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(551,plain,
! [SV139: subst,SV118: subst] :
( ( ! [SY183: subst] :
( ( comp @ ( comp @ SV118 @ SV139 ) @ SY183 )
= ( comp @ SV118 @ ( comp @ SV139 @ SY183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(552,plain,
! [SV140: subst,SV119: term] :
( ( ( comp @ sh @ ( push @ SV119 @ SV140 ) )
= SV140 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(553,plain,
! [SV141: subst,SV121: term] :
( ( ! [SY184: subst] :
( ( sub @ ( sub @ SV121 @ SV141 ) @ SY184 )
= ( sub @ SV121 @ ( comp @ SV141 @ SY184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(554,plain,
! [SV142: subst,SV122: term] :
( ( ( sub @ ( lam @ SV122 ) @ SV142 )
= ( lam @ ( sub @ SV122 @ ( push @ one @ ( comp @ SV142 @ sh ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(555,plain,
! [SV143: subst,SV124: term] :
( ( ( sub @ one @ ( push @ SV124 @ SV143 ) )
= SV124 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(556,plain,
! [SV144: term,SV125: term] :
( ( ! [SY185: subst] :
( ( sub @ ( ap @ SV125 @ SV144 ) @ SY185 )
= ( ap @ ( sub @ SV125 @ SY185 ) @ ( sub @ SV144 @ SY185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(557,plain,
! [SV126: term > $o] :
( ( ( ~ ( ~ ( var @ ( sK18_A @ SV126 ) )
| ~ ~ ( SV126 @ ( sK18_A @ SV126 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV126 @ ( sK16_A @ SV126 ) )
| ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
| ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(558,plain,
! [SV127: term > $o,SV145: term] :
( ( ! [SY186: subst] :
( ~ ( ~ ( var @ ( sK10_B @ SY186 @ SV145 @ SV127 ) )
| ~ ~ ( SV127 @ ( sub @ ( sK10_B @ SY186 @ SV145 @ SV127 ) @ SY186 ) ) )
| ~ ( SV127 @ SV145 )
| ! [SY187: term] :
( ~ ( var @ SY187 )
| ( SV127 @ ( sub @ SY187 @ ( push @ SV145 @ SY186 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(559,plain,
! [SV128: term > $o] :
( ( ( ~ ( SV128 @ one ) )
= $true )
| ( ( ~ ( ~ ( var @ ( sK5_A @ SV128 ) )
| ~ ~ ( ~ ( SV128 @ ( sK5_A @ SV128 ) )
| ~ ~ ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) ) ) )
| ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(560,plain,
! [SV129: term > $o] :
( ( ( ~ ( ~ ( SV129 @ ( sK13_A @ SV129 ) )
| ~ ~ ( ~ ( SV129 @ ( sK14_SY84 @ SV129 ) )
| ~ ~ ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(561,plain,
! [SV130: term > $o] :
( ( ( ~ ( ~ ( var @ ( sK9_A @ SV130 ) )
| ~ ~ ( SV130 @ ( sK9_A @ SV130 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK7_A @ SV130 ) )
| ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
| ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(562,plain,
! [SV146: subst,SV131: subst,SV106: subst] :
( ( ( comp @ ( comp @ SV106 @ SV131 ) @ SV146 )
= ( comp @ SV106 @ ( comp @ SV131 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(563,plain,
! [SV132: term,SV108: term] :
( ( var @ ( ap @ SV108 @ SV132 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(564,plain,
! [SV147: term,SV133: term,SV109: term] :
( ( ( lam @ SV109 )
!= ( ap @ SV133 @ SV147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(565,plain,
! [SV134: term,SV110: term] :
( ( ( ( sub @ SV110 @ sh )
!= ( sub @ SV134 @ sh ) )
= $true )
| ( ( SV110 = SV134 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(566,plain,
! [SV135: term,SV111: term] :
( ( ( ( lam @ SV111 )
!= ( lam @ SV135 ) )
= $true )
| ( ( SV111 = SV135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(567,plain,
! [SV136: term,SV148: term,SV112: term] :
( ( ! [SY188: term] :
( ( ( ap @ SV112 @ SV148 )
!= ( ap @ SV136 @ SY188 ) )
| ( SV148 = SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(568,plain,
! [SV137: term,SV113: term] :
( ( ( ! [SY180: term,SY181: term] :
( ( ap @ SV113 @ SY180 )
!= ( ap @ SV137 @ SY181 ) ) )
= $true )
| ( ( SV113 = SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(569,plain,
! [SV114: term] :
( ( ( var @ SV114 )
= $false )
| ( ( var @ ( sub @ SV114 @ sh ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(570,plain,
! [SV149: subst,SV138: subst,SV117: term] :
( ( ( comp @ ( push @ SV117 @ SV138 ) @ SV149 )
= ( push @ ( sub @ SV117 @ SV149 ) @ ( comp @ SV138 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(571,plain,
! [SV150: subst,SV139: subst,SV118: subst] :
( ( ( comp @ ( comp @ SV118 @ SV139 ) @ SV150 )
= ( comp @ SV118 @ ( comp @ SV139 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(572,plain,
! [SV151: subst,SV141: subst,SV121: term] :
( ( ( sub @ ( sub @ SV121 @ SV141 ) @ SV151 )
= ( sub @ SV121 @ ( comp @ SV141 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(573,plain,
! [SV152: subst,SV144: term,SV125: term] :
( ( ( sub @ ( ap @ SV125 @ SV144 ) @ SV152 )
= ( ap @ ( sub @ SV125 @ SV152 ) @ ( sub @ SV144 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(574,plain,
! [SV126: term > $o] :
( ( ( ~ ( var @ ( sK18_A @ SV126 ) )
| ~ ~ ( SV126 @ ( sK18_A @ SV126 ) ) )
= $false )
| ( ( ~ ( ~ ( SV126 @ ( sK16_A @ SV126 ) )
| ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
| ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(575,plain,
! [SV127: term > $o,SV145: term,SV153: subst] :
( ( ~ ( ~ ( var @ ( sK10_B @ SV153 @ SV145 @ SV127 ) )
| ~ ~ ( SV127 @ ( sub @ ( sK10_B @ SV153 @ SV145 @ SV127 ) @ SV153 ) ) )
| ~ ( SV127 @ SV145 )
| ! [SY189: term] :
( ~ ( var @ SY189 )
| ( SV127 @ ( sub @ SY189 @ ( push @ SV145 @ SV153 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(576,plain,
! [SV128: term > $o] :
( ( ( SV128 @ one )
= $false )
| ( ( ~ ( ~ ( var @ ( sK5_A @ SV128 ) )
| ~ ~ ( ~ ( SV128 @ ( sK5_A @ SV128 ) )
| ~ ~ ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) ) ) )
| ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(577,plain,
! [SV129: term > $o] :
( ( ( ~ ( SV129 @ ( sK13_A @ SV129 ) )
| ~ ~ ( ~ ( SV129 @ ( sK14_SY84 @ SV129 ) )
| ~ ~ ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(578,plain,
! [SV130: term > $o] :
( ( ( ~ ( var @ ( sK9_A @ SV130 ) )
| ~ ~ ( SV130 @ ( sK9_A @ SV130 ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK7_A @ SV130 ) )
| ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
| ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(579,plain,
! [SV147: term,SV133: term,SV109: term] :
( ( ( lam @ SV109 )
= ( ap @ SV133 @ SV147 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(580,plain,
! [SV134: term,SV110: term] :
( ( ( ( sub @ SV110 @ sh )
= ( sub @ SV134 @ sh ) )
= $false )
| ( ( SV110 = SV134 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(581,plain,
! [SV135: term,SV111: term] :
( ( ( ( lam @ SV111 )
= ( lam @ SV135 ) )
= $false )
| ( ( SV111 = SV135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(582,plain,
! [SV154: term,SV136: term,SV148: term,SV112: term] :
( ( ( ( ap @ SV112 @ SV148 )
!= ( ap @ SV136 @ SV154 ) )
| ( SV148 = SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(583,plain,
! [SV137: term,SV155: term,SV113: term] :
( ( ( ! [SY190: term] :
( ( ap @ SV113 @ SV155 )
!= ( ap @ SV137 @ SY190 ) ) )
= $true )
| ( ( SV113 = SV137 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(584,plain,
! [SV126: term > $o] :
( ( ( ~ ( var @ ( sK18_A @ SV126 ) ) )
= $false )
| ( ( ~ ( ~ ( SV126 @ ( sK16_A @ SV126 ) )
| ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
| ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(585,plain,
! [SV126: term > $o] :
( ( ( ~ ~ ( SV126 @ ( sK18_A @ SV126 ) ) )
= $false )
| ( ( ~ ( ~ ( SV126 @ ( sK16_A @ SV126 ) )
| ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
| ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[574]) ).
thf(586,plain,
! [SV127: term > $o,SV145: term,SV153: subst] :
( ( ( ~ ( ~ ( var @ ( sK10_B @ SV153 @ SV145 @ SV127 ) )
| ~ ~ ( SV127 @ ( sub @ ( sK10_B @ SV153 @ SV145 @ SV127 ) @ SV153 ) ) ) )
= $true )
| ( ( ~ ( SV127 @ SV145 )
| ! [SY189: term] :
( ~ ( var @ SY189 )
| ( SV127 @ ( sub @ SY189 @ ( push @ SV145 @ SV153 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(587,plain,
! [SV128: term > $o] :
( ( ( ~ ( ~ ( var @ ( sK5_A @ SV128 ) )
| ~ ~ ( ~ ( SV128 @ ( sK5_A @ SV128 ) )
| ~ ~ ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) ) ) ) )
= $true )
| ( ( ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(588,plain,
! [SV129: term > $o] :
( ( ( ~ ( SV129 @ ( sK13_A @ SV129 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(589,plain,
! [SV129: term > $o] :
( ( ( ~ ~ ( ~ ( SV129 @ ( sK14_SY84 @ SV129 ) )
| ~ ~ ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[577]) ).
thf(590,plain,
! [SV130: term > $o] :
( ( ( ~ ( var @ ( sK9_A @ SV130 ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK7_A @ SV130 ) )
| ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
| ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[578]) ).
thf(591,plain,
! [SV130: term > $o] :
( ( ( ~ ~ ( SV130 @ ( sK9_A @ SV130 ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK7_A @ SV130 ) )
| ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
| ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[578]) ).
thf(592,plain,
! [SV154: term,SV136: term,SV148: term,SV112: term] :
( ( ( ( ap @ SV112 @ SV148 )
!= ( ap @ SV136 @ SV154 ) )
= $true )
| ( ( SV148 = SV154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(593,plain,
! [SV156: term,SV137: term,SV155: term,SV113: term] :
( ( ( ( ap @ SV113 @ SV155 )
!= ( ap @ SV137 @ SV156 ) )
= $true )
| ( ( SV113 = SV137 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(594,plain,
! [SV126: term > $o] :
( ( ( var @ ( sK18_A @ SV126 ) )
= $true )
| ( ( ~ ( ~ ( SV126 @ ( sK16_A @ SV126 ) )
| ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
| ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[584]) ).
thf(595,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( sK18_A @ SV126 ) ) )
= $true )
| ( ( ~ ( ~ ( SV126 @ ( sK16_A @ SV126 ) )
| ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
| ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[585]) ).
thf(596,plain,
! [SV127: term > $o,SV145: term,SV153: subst] :
( ( ( ~ ( var @ ( sK10_B @ SV153 @ SV145 @ SV127 ) )
| ~ ~ ( SV127 @ ( sub @ ( sK10_B @ SV153 @ SV145 @ SV127 ) @ SV153 ) ) )
= $false )
| ( ( ~ ( SV127 @ SV145 )
| ! [SY189: term] :
( ~ ( var @ SY189 )
| ( SV127 @ ( sub @ SY189 @ ( push @ SV145 @ SV153 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(597,plain,
! [SV128: term > $o] :
( ( ( ~ ( var @ ( sK5_A @ SV128 ) )
| ~ ~ ( ~ ( SV128 @ ( sK5_A @ SV128 ) )
| ~ ~ ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) ) ) )
= $false )
| ( ( ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(598,plain,
! [SV129: term > $o] :
( ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true )
| ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[588]) ).
thf(599,plain,
! [SV129: term > $o] :
( ( ( ~ ( ~ ( SV129 @ ( sK14_SY84 @ SV129 ) )
| ~ ~ ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[589]) ).
thf(600,plain,
! [SV130: term > $o] :
( ( ( var @ ( sK9_A @ SV130 ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK7_A @ SV130 ) )
| ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
| ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[590]) ).
thf(601,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK9_A @ SV130 ) ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK7_A @ SV130 ) )
| ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
| ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[591]) ).
thf(602,plain,
! [SV154: term,SV136: term,SV148: term,SV112: term] :
( ( ( ( ap @ SV112 @ SV148 )
= ( ap @ SV136 @ SV154 ) )
= $false )
| ( ( SV148 = SV154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(603,plain,
! [SV156: term,SV137: term,SV155: term,SV113: term] :
( ( ( ( ap @ SV113 @ SV155 )
= ( ap @ SV137 @ SV156 ) )
= $false )
| ( ( SV113 = SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(604,plain,
! [SV126: term > $o] :
( ( ( ~ ( ~ ( SV126 @ ( sK16_A @ SV126 ) )
| ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(605,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false )
| ( ( ~ ( ~ ( SV126 @ ( sK16_A @ SV126 ) )
| ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
| ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(606,plain,
! [SV127: term > $o,SV145: term,SV153: subst] :
( ( ( ~ ( var @ ( sK10_B @ SV153 @ SV145 @ SV127 ) ) )
= $false )
| ( ( ~ ( SV127 @ SV145 )
| ! [SY189: term] :
( ~ ( var @ SY189 )
| ( SV127 @ ( sub @ SY189 @ ( push @ SV145 @ SV153 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(607,plain,
! [SV145: term,SV153: subst,SV127: term > $o] :
( ( ( ~ ~ ( SV127 @ ( sub @ ( sK10_B @ SV153 @ SV145 @ SV127 ) @ SV153 ) ) )
= $false )
| ( ( ~ ( SV127 @ SV145 )
| ! [SY189: term] :
( ~ ( var @ SY189 )
| ( SV127 @ ( sub @ SY189 @ ( push @ SV145 @ SV153 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[596]) ).
thf(608,plain,
! [SV128: term > $o] :
( ( ( ~ ( var @ ( sK5_A @ SV128 ) ) )
= $false )
| ( ( ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(609,plain,
! [SV128: term > $o] :
( ( ( ~ ~ ( ~ ( SV128 @ ( sK5_A @ SV128 ) )
| ~ ~ ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) ) ) )
= $false )
| ( ( ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[597]) ).
thf(610,plain,
! [SV129: term > $o] :
( ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(611,plain,
! [SV129: term > $o] :
( ( ( ~ ( SV129 @ ( sK14_SY84 @ SV129 ) )
| ~ ~ ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(612,plain,
! [SV130: term > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK7_A @ SV130 ) )
| ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(613,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK7_A @ SV130 ) )
| ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
| ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(614,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( sK16_A @ SV126 ) )
| ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(615,plain,
! [SV126: term > $o] :
( ( ( ~ ( ~ ( SV126 @ ( sK16_A @ SV126 ) )
| ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(616,plain,
! [SV127: term > $o,SV145: term,SV153: subst] :
( ( ( var @ ( sK10_B @ SV153 @ SV145 @ SV127 ) )
= $true )
| ( ( ~ ( SV127 @ SV145 )
| ! [SY189: term] :
( ~ ( var @ SY189 )
| ( SV127 @ ( sub @ SY189 @ ( push @ SV145 @ SV153 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[606]) ).
thf(617,plain,
! [SV145: term,SV153: subst,SV127: term > $o] :
( ( ( ~ ( SV127 @ ( sub @ ( sK10_B @ SV153 @ SV145 @ SV127 ) @ SV153 ) ) )
= $true )
| ( ( ~ ( SV127 @ SV145 )
| ! [SY189: term] :
( ~ ( var @ SY189 )
| ( SV127 @ ( sub @ SY189 @ ( push @ SV145 @ SV153 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[607]) ).
thf(618,plain,
! [SV128: term > $o] :
( ( ( var @ ( sK5_A @ SV128 ) )
= $true )
| ( ( ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[608]) ).
thf(619,plain,
! [SV128: term > $o] :
( ( ( ~ ( ~ ( SV128 @ ( sK5_A @ SV128 ) )
| ~ ~ ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) ) ) )
= $true )
| ( ( ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[609]) ).
thf(620,plain,
! [SV129: term > $o] :
( ( ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
= $false )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(621,plain,
! [SV129: term > $o] :
( ( ( ~ ( SV129 @ ( sK14_SY84 @ SV129 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[611]) ).
thf(622,plain,
! [SV129: term > $o] :
( ( ( ~ ~ ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[611]) ).
thf(623,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK7_A @ SV130 ) )
| ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(624,plain,
! [SV130: term > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK7_A @ SV130 ) )
| ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(625,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( sK16_A @ SV126 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(626,plain,
! [SV126: term > $o] :
( ( ( ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[614]) ).
thf(627,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( sK16_A @ SV126 ) )
| ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(628,plain,
! [SV153: subst,SV145: term,SV127: term > $o] :
( ( ( ~ ( SV127 @ SV145 ) )
= $true )
| ( ( ! [SY189: term] :
( ~ ( var @ SY189 )
| ( SV127 @ ( sub @ SY189 @ ( push @ SV145 @ SV153 ) ) ) ) )
= $true )
| ( ( var @ ( sK10_B @ SV153 @ SV145 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(629,plain,
! [SV145: term,SV153: subst,SV127: term > $o] :
( ( ( SV127 @ ( sub @ ( sK10_B @ SV153 @ SV145 @ SV127 ) @ SV153 ) )
= $false )
| ( ( ~ ( SV127 @ SV145 )
| ! [SY189: term] :
( ~ ( var @ SY189 )
| ( SV127 @ ( sub @ SY189 @ ( push @ SV145 @ SV153 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(630,plain,
! [SV128: term > $o,SV157: term] :
( ( ( ~ ( var @ SV157 )
| ( SV128 @ SV157 ) )
= $true )
| ( ( var @ ( sK5_A @ SV128 ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(631,plain,
! [SV128: term > $o] :
( ( ( ~ ( SV128 @ ( sK5_A @ SV128 ) )
| ~ ~ ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) ) )
= $false )
| ( ( ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(632,plain,
! [SV129: term > $o] :
( ( ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) ) )
= $false )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(633,plain,
! [SV129: term > $o] :
( ( ( ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
= $false )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[620]) ).
thf(634,plain,
! [SV129: term > $o] :
( ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true )
| ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[621]) ).
thf(635,plain,
! [SV129: term > $o] :
( ( ( ~ ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[622]) ).
thf(636,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK7_A @ SV130 ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(637,plain,
! [SV130: term > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[623]) ).
thf(638,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK7_A @ SV130 ) )
| ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[624]) ).
thf(639,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[625]) ).
thf(640,plain,
! [SV126: term > $o] :
( ( ( ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[626]) ).
thf(641,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( sK16_A @ SV126 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(642,plain,
! [SV126: term > $o] :
( ( ( ~ ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[627]) ).
thf(643,plain,
! [SV153: subst,SV145: term,SV127: term > $o] :
( ( ( SV127 @ SV145 )
= $false )
| ( ( ! [SY189: term] :
( ~ ( var @ SY189 )
| ( SV127 @ ( sub @ SY189 @ ( push @ SV145 @ SV153 ) ) ) ) )
= $true )
| ( ( var @ ( sK10_B @ SV153 @ SV145 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[628]) ).
thf(644,plain,
! [SV153: subst,SV145: term,SV127: term > $o] :
( ( ( ~ ( SV127 @ SV145 ) )
= $true )
| ( ( ! [SY189: term] :
( ~ ( var @ SY189 )
| ( SV127 @ ( sub @ SY189 @ ( push @ SV145 @ SV153 ) ) ) ) )
= $true )
| ( ( SV127 @ ( sub @ ( sK10_B @ SV153 @ SV145 @ SV127 ) @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(645,plain,
! [SV128: term > $o,SV157: term] :
( ( ( ~ ( var @ SV157 ) )
= $true )
| ( ( SV128 @ SV157 )
= $true )
| ( ( var @ ( sK5_A @ SV128 ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(646,plain,
! [SV128: term > $o] :
( ( ( ~ ( SV128 @ ( sK5_A @ SV128 ) ) )
= $false )
| ( ( ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[631]) ).
thf(647,plain,
! [SV128: term > $o] :
( ( ( ~ ~ ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) ) )
= $false )
| ( ( ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[631]) ).
thf(648,plain,
! [SV129: term > $o] :
( ( ( ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[632]) ).
thf(649,plain,
! [SV129: term > $o] :
( ( ( ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[633]) ).
thf(650,plain,
! [SV129: term > $o] :
( ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(651,plain,
! [SV129: term > $o] :
( ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
| ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[635]) ).
thf(652,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[636]) ).
thf(653,plain,
! [SV130: term > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[637]) ).
thf(654,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK7_A @ SV130 ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(655,plain,
! [SV130: term > $o] :
( ( ( ~ ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[638]) ).
thf(656,plain,
! [SV126: term > $o] :
( ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(657,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(658,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[641]) ).
thf(659,plain,
! [SV126: term > $o] :
( ( ( ~ ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[642]) ).
thf(660,plain,
! [SV153: subst,SV145: term,SV127: term > $o,SV158: term] :
( ( ( ~ ( var @ SV158 )
| ( SV127 @ ( sub @ SV158 @ ( push @ SV145 @ SV153 ) ) ) )
= $true )
| ( ( SV127 @ SV145 )
= $false )
| ( ( var @ ( sK10_B @ SV153 @ SV145 @ SV127 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(661,plain,
! [SV153: subst,SV145: term,SV127: term > $o] :
( ( ( SV127 @ SV145 )
= $false )
| ( ( ! [SY189: term] :
( ~ ( var @ SY189 )
| ( SV127 @ ( sub @ SY189 @ ( push @ SV145 @ SV153 ) ) ) ) )
= $true )
| ( ( SV127 @ ( sub @ ( sK10_B @ SV153 @ SV145 @ SV127 ) @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[644]) ).
thf(662,plain,
! [SV128: term > $o,SV157: term] :
( ( ( var @ SV157 )
= $false )
| ( ( SV128 @ SV157 )
= $true )
| ( ( var @ ( sK5_A @ SV128 ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[645]) ).
thf(663,plain,
! [SV128: term > $o] :
( ( ( SV128 @ ( sK5_A @ SV128 ) )
= $true )
| ( ( ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[646]) ).
thf(664,plain,
! [SV128: term > $o] :
( ( ( ~ ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) ) )
= $true )
| ( ( ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[647]) ).
thf(665,plain,
! [SV159: term,SV129: term > $o] :
( ( ( ~ ( SV129 @ SV159 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV159 @ id ) ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(666,plain,
! [SV129: term > $o] :
( ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(667,plain,
! [SV129: term > $o] :
( ( ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
= $false )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(668,plain,
! [SV129: term > $o] :
( ( ( ~ ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(669,plain,
! [SV130: term > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(670,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[653]) ).
thf(671,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[654]) ).
thf(672,plain,
! [SV130: term > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[655]) ).
thf(673,plain,
! [SV126: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(674,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(675,plain,
! [SV126: term > $o] :
( ( ( ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[657]) ).
thf(676,plain,
! [SV126: term > $o] :
( ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[658]) ).
thf(677,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) )
| ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(678,plain,
! [SV153: subst,SV145: term,SV127: term > $o,SV158: term] :
( ( ( ~ ( var @ SV158 ) )
= $true )
| ( ( SV127 @ ( sub @ SV158 @ ( push @ SV145 @ SV153 ) ) )
= $true )
| ( ( SV127 @ SV145 )
= $false )
| ( ( var @ ( sK10_B @ SV153 @ SV145 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(679,plain,
! [SV153: subst,SV145: term,SV127: term > $o,SV160: term] :
( ( ( ~ ( var @ SV160 )
| ( SV127 @ ( sub @ SV160 @ ( push @ SV145 @ SV153 ) ) ) )
= $true )
| ( ( SV127 @ SV145 )
= $false )
| ( ( SV127 @ ( sub @ ( sK10_B @ SV153 @ SV145 @ SV127 ) @ SV153 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(680,plain,
! [SV128: term > $o,SV161: term] :
( ( ( ~ ( var @ SV161 )
| ( SV128 @ SV161 ) )
= $true )
| ( ( SV128 @ ( sK5_A @ SV128 ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(681,plain,
! [SV128: term > $o] :
( ( ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) )
= $false )
| ( ( ! [SY171: term] :
( ~ ( var @ SY171 )
| ( SV128 @ SY171 ) ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(682,plain,
! [SV159: term,SV129: term > $o] :
( ( ( ~ ( SV129 @ SV159 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV159 @ id ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[665]) ).
thf(683,plain,
! [SV129: term > $o,SV162: term] :
( ( ( ! [SY191: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY191 @ SV162 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY191 @ SV162 @ SV129 ) @ SY191 ) ) )
| ( SV129 @ ( sub @ SV162 @ SY191 ) ) ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(684,plain,
! [SV129: term > $o] :
( ( ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) ) )
= $false )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(685,plain,
! [SV129: term > $o] :
( ( ( ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
= $false )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[667]) ).
thf(686,plain,
! [SV129: term > $o] :
( ( ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) )
| ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
= $false )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(687,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(688,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(689,plain,
! [SV130: term > $o] :
( ( ( ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[670]) ).
thf(690,plain,
! [SV130: term > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(691,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) )
| ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(692,plain,
! [SV126: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[673]) ).
thf(693,plain,
! [SV126: term > $o] :
( ( ( ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[673]) ).
thf(694,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[674]) ).
thf(695,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[675]) ).
thf(696,plain,
! [SV126: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(697,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[677]) ).
thf(698,plain,
! [SV126: term > $o] :
( ( ( ~ ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[677]) ).
thf(699,plain,
! [SV153: subst,SV145: term,SV127: term > $o,SV158: term] :
( ( ( var @ SV158 )
= $false )
| ( ( SV127 @ ( sub @ SV158 @ ( push @ SV145 @ SV153 ) ) )
= $true )
| ( ( SV127 @ SV145 )
= $false )
| ( ( var @ ( sK10_B @ SV153 @ SV145 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(700,plain,
! [SV153: subst,SV145: term,SV127: term > $o,SV160: term] :
( ( ( ~ ( var @ SV160 ) )
= $true )
| ( ( SV127 @ ( sub @ SV160 @ ( push @ SV145 @ SV153 ) ) )
= $true )
| ( ( SV127 @ SV145 )
= $false )
| ( ( SV127 @ ( sub @ ( sK10_B @ SV153 @ SV145 @ SV127 ) @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(701,plain,
! [SV128: term > $o,SV161: term] :
( ( ( ~ ( var @ SV161 ) )
= $true )
| ( ( SV128 @ SV161 )
= $true )
| ( ( SV128 @ ( sK5_A @ SV128 ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(702,plain,
! [SV128: term > $o,SV163: term] :
( ( ( ~ ( var @ SV163 )
| ( SV128 @ SV163 ) )
= $true )
| ( ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) )
= $false )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(703,plain,
! [SV159: term,SV129: term > $o] :
( ( ( SV129 @ SV159 )
= $false )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV159 @ id ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(704,plain,
! [SV129: term > $o,SV162: term,SV164: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV164 @ SV162 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV164 @ SV162 @ SV129 ) @ SV164 ) ) )
| ( SV129 @ ( sub @ SV162 @ SV164 ) ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(705,plain,
! [SV129: term > $o] :
( ( ( ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[684]) ).
thf(706,plain,
! [SV129: term > $o] :
( ( ( ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[685]) ).
thf(707,plain,
! [SV129: term > $o] :
( ( ( ~ ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) ) )
= $false )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(708,plain,
! [SV129: term > $o] :
( ( ( ~ ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
= $false )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[686]) ).
thf(709,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(710,plain,
! [SV130: term > $o] :
( ( ( ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[687]) ).
thf(711,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[688]) ).
thf(712,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[689]) ).
thf(713,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(714,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(715,plain,
! [SV130: term > $o] :
( ( ( ~ ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[691]) ).
thf(716,plain,
! [SV126: term > $o] :
( ( ( ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[692]) ).
thf(717,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[693]) ).
thf(718,plain,
! [SV126: term > $o] :
( ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(719,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(720,plain,
! [SV126: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(721,plain,
! [SV126: term > $o] :
( ( ( ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[696]) ).
thf(722,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[697]) ).
thf(723,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[698]) ).
thf(724,plain,
! [SV153: subst,SV145: term,SV127: term > $o,SV160: term] :
( ( ( var @ SV160 )
= $false )
| ( ( SV127 @ ( sub @ SV160 @ ( push @ SV145 @ SV153 ) ) )
= $true )
| ( ( SV127 @ SV145 )
= $false )
| ( ( SV127 @ ( sub @ ( sK10_B @ SV153 @ SV145 @ SV127 ) @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(725,plain,
! [SV128: term > $o,SV161: term] :
( ( ( var @ SV161 )
= $false )
| ( ( SV128 @ SV161 )
= $true )
| ( ( SV128 @ ( sK5_A @ SV128 ) )
= $true )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(726,plain,
! [SV128: term > $o,SV163: term] :
( ( ( ~ ( var @ SV163 ) )
= $true )
| ( ( SV128 @ SV163 )
= $true )
| ( ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) )
= $false )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(727,plain,
! [SV159: term,SV129: term > $o,SV165: term] :
( ( ( ! [SY192: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY192 @ SV165 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY192 @ SV165 @ SV129 ) @ SY192 ) ) )
| ( SV129 @ ( sub @ SV165 @ SY192 ) ) ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV159 @ id ) ) )
= $true )
| ( ( SV129 @ SV159 )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(728,plain,
! [SV129: term > $o,SV162: term,SV164: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV164 @ SV162 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV164 @ SV162 @ SV129 ) @ SV164 ) ) ) )
= $true )
| ( ( SV129 @ ( sub @ SV162 @ SV164 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(729,plain,
! [SV166: term,SV129: term > $o] :
( ( ( ~ ( SV129 @ SV166 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV166 @ id ) ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(730,plain,
! [SV129: term > $o] :
( ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(731,plain,
! [SV129: term > $o] :
( ( ( ! [SY172: term] :
( ~ ( SV129 @ SY172 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SY172 @ id ) ) ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[707]) ).
thf(732,plain,
! [SV129: term > $o] :
( ( ( ~ ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[708]) ).
thf(733,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( sK6_A @ SV130 ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[709]) ).
thf(734,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[710]) ).
thf(735,plain,
! [SV130: term > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(736,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(737,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[713]) ).
thf(738,plain,
! [SV130: term > $o] :
( ( ( ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[713]) ).
thf(739,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[714]) ).
thf(740,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[715]) ).
thf(741,plain,
! [SV167: term,SV126: term > $o] :
( ( ( ~ ( SV126 @ SV167 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV167 @ id ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(742,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(743,plain,
! [SV126: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(744,plain,
! [SV126: term > $o] :
( ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(745,plain,
! [SV126: term > $o] :
( ( ( ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[720]) ).
thf(746,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[721]) ).
thf(747,plain,
! [SV126: term > $o] :
( ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(748,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
| ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(749,plain,
! [SV128: term > $o,SV163: term] :
( ( ( var @ SV163 )
= $false )
| ( ( SV128 @ SV163 )
= $true )
| ( ( SV128 @ ( sub @ ( sK5_A @ SV128 ) @ sh ) )
= $false )
| ( ( SV128 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(750,plain,
! [SV159: term,SV129: term > $o,SV165: term,SV168: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV168 @ SV165 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV168 @ SV165 @ SV129 ) @ SV168 ) ) )
| ( SV129 @ ( sub @ SV165 @ SV168 ) ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV159 @ id ) ) )
= $true )
| ( ( SV129 @ SV159 )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(751,plain,
! [SV129: term > $o,SV162: term,SV164: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV164 @ SV162 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV164 @ SV162 @ SV129 ) @ SV164 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV162 @ SV164 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(752,plain,
! [SV166: term,SV129: term > $o] :
( ( ( ~ ( SV129 @ SV166 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV166 @ id ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[729]) ).
thf(753,plain,
! [SV129: term > $o,SV169: term] :
( ( ( ! [SY193: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY193 @ SV169 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY193 @ SV169 @ SV129 ) @ SY193 ) ) )
| ( SV129 @ ( sub @ SV169 @ SY193 ) ) ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(754,plain,
! [SV170: term,SV129: term > $o] :
( ( ( ~ ( SV129 @ SV170 )
| ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV170 @ id ) ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(755,plain,
! [SV129: term > $o] :
( ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(756,plain,
! [SV171: term,SV130: term > $o] :
( ( ( SV130 @ SV171 )
= $true )
| ( ( SV130 @ ( sK6_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(757,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(758,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(759,plain,
! [SV130: term > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(760,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( sK6_A @ SV130 ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[737]) ).
thf(761,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[738]) ).
thf(762,plain,
! [SV130: term > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[739]) ).
thf(763,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
| ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(764,plain,
! [SV167: term,SV126: term > $o] :
( ( ( ~ ( SV126 @ SV167 ) )
= $true )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV167 @ id ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[741]) ).
thf(765,plain,
! [SV172: term,SV126: term > $o] :
( ( ( SV126 @ SV172 )
= $true )
| ( ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(766,plain,
! [SV126: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[743]) ).
thf(767,plain,
! [SV126: term > $o] :
( ( ( ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[743]) ).
thf(768,plain,
! [SV126: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(769,plain,
! [SV173: term,SV126: term > $o] :
( ( ( ~ ( SV126 @ SV173 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV173 @ id ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(770,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(771,plain,
! [SV126: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(772,plain,
! [SV126: term > $o] :
( ( ( ~ ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(773,plain,
! [SV159: term,SV129: term > $o,SV165: term,SV168: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV168 @ SV165 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV168 @ SV165 @ SV129 ) @ SV168 ) ) ) )
= $true )
| ( ( SV129 @ ( sub @ SV165 @ SV168 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV159 @ id ) ) )
= $true )
| ( ( SV129 @ SV159 )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(774,plain,
! [SV129: term > $o,SV162: term,SV164: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV164 @ SV162 @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV162 @ SV164 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[751]) ).
thf(775,plain,
! [SV162: term,SV164: subst,SV129: term > $o] :
( ( ( ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV164 @ SV162 @ SV129 ) @ SV164 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV162 @ SV164 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[751]) ).
thf(776,plain,
! [SV166: term,SV129: term > $o] :
( ( ( SV129 @ SV166 )
= $false )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV166 @ id ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(777,plain,
! [SV129: term > $o,SV169: term,SV174: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV174 @ SV169 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV174 @ SV169 @ SV129 ) @ SV174 ) ) )
| ( SV129 @ ( sub @ SV169 @ SV174 ) ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(778,plain,
! [SV170: term,SV129: term > $o] :
( ( ( ~ ( SV129 @ SV170 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV170 @ id ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[754]) ).
thf(779,plain,
! [SV129: term > $o,SV175: term] :
( ( ( ! [SY194: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY194 @ SV175 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY194 @ SV175 @ SV129 ) @ SY194 ) ) )
| ( SV129 @ ( sub @ SV175 @ SY194 ) ) ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(780,plain,
! [SV176: term,SV130: term > $o] :
( ( ( SV130 @ SV176 )
= $true )
| ( ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(781,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(782,plain,
! [SV130: term > $o] :
( ( ( ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[758]) ).
thf(783,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(784,plain,
! [SV177: term,SV130: term > $o] :
( ( ( SV130 @ SV177 )
= $true )
| ( ( SV130 @ ( sK6_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(785,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(786,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[762]) ).
thf(787,plain,
! [SV130: term > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(788,plain,
! [SV167: term,SV126: term > $o] :
( ( ( SV126 @ SV167 )
= $false )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV167 @ id ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[764]) ).
thf(789,plain,
! [SV126: term > $o] :
( ( ( ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[766]) ).
thf(790,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[767]) ).
thf(791,plain,
! [SV126: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[768]) ).
thf(792,plain,
! [SV126: term > $o] :
( ( ( ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[768]) ).
thf(793,plain,
! [SV173: term,SV126: term > $o] :
( ( ( ~ ( SV126 @ SV173 ) )
= $true )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV173 @ id ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(794,plain,
! [SV178: term,SV126: term > $o] :
( ( ( SV126 @ SV178 )
= $true )
| ( ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(795,plain,
! [SV126: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[771]) ).
thf(796,plain,
! [SV126: term > $o] :
( ( ( ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[771]) ).
thf(797,plain,
! [SV126: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) )
| ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[772]) ).
thf(798,plain,
! [SV159: term,SV129: term > $o,SV165: term,SV168: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV168 @ SV165 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV168 @ SV165 @ SV129 ) @ SV168 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV165 @ SV168 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV159 @ id ) ) )
= $true )
| ( ( SV129 @ SV159 )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[773]) ).
thf(799,plain,
! [SV129: term > $o,SV162: term,SV164: subst] :
( ( ( var @ ( sK11_B @ SV164 @ SV162 @ SV129 ) )
= $true )
| ( ( SV129 @ ( sub @ SV162 @ SV164 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[774]) ).
thf(800,plain,
! [SV162: term,SV164: subst,SV129: term > $o] :
( ( ( ~ ( SV129 @ ( sub @ ( sK11_B @ SV164 @ SV162 @ SV129 ) @ SV164 ) ) )
= $true )
| ( ( SV129 @ ( sub @ SV162 @ SV164 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[775]) ).
thf(801,plain,
! [SV166: term,SV129: term > $o,SV179: term] :
( ( ( ! [SY195: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY195 @ SV179 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY195 @ SV179 @ SV129 ) @ SY195 ) ) )
| ( SV129 @ ( sub @ SV179 @ SY195 ) ) ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV166 @ id ) ) )
= $true )
| ( ( SV129 @ SV166 )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(802,plain,
! [SV129: term > $o,SV169: term,SV174: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV174 @ SV169 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV174 @ SV169 @ SV129 ) @ SV174 ) ) ) )
= $true )
| ( ( SV129 @ ( sub @ SV169 @ SV174 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[777]) ).
thf(803,plain,
! [SV170: term,SV129: term > $o] :
( ( ( SV129 @ SV170 )
= $false )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV170 @ id ) ) )
= $true )
| ( ( ! [SY173: term,SY174: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY174 @ SY173 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY174 @ SY173 @ SV129 ) @ SY174 ) ) )
| ( SV129 @ ( sub @ SY173 @ SY174 ) ) ) )
= $true )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[778]) ).
thf(804,plain,
! [SV129: term > $o,SV175: term,SV180: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV180 @ SV175 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV180 @ SV175 @ SV129 ) @ SV180 ) ) )
| ( SV129 @ ( sub @ SV175 @ SV180 ) ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(805,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( sK6_A @ SV130 ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[781]) ).
thf(806,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[782]) ).
thf(807,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[783]) ).
thf(808,plain,
! [SV130: term > $o] :
( ( ( ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[783]) ).
thf(809,plain,
! [SV181: term,SV130: term > $o] :
( ( ( SV130 @ SV181 )
= $true )
| ( ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK7_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(810,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(811,plain,
! [SV130: term > $o] :
( ( ( ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[786]) ).
thf(812,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK6_A @ SV130 ) )
| ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(813,plain,
! [SV167: term,SV182: term,SV126: term > $o] :
( ( ( SV126 @ SV182 )
= $true )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV167 @ id ) ) )
= $true )
| ( ( SV126 @ SV167 )
= $false )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(814,plain,
! [SV183: term,SV126: term > $o] :
( ( ( ~ ( SV126 @ SV183 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV183 @ id ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(815,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[790]) ).
thf(816,plain,
! [SV126: term > $o] :
( ( ( ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[791]) ).
thf(817,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(818,plain,
! [SV173: term,SV126: term > $o] :
( ( ( SV126 @ SV173 )
= $false )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV173 @ id ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(819,plain,
! [SV126: term > $o] :
( ( ( ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[795]) ).
thf(820,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[796]) ).
thf(821,plain,
! [SV126: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[797]) ).
thf(822,plain,
! [SV126: term > $o] :
( ( ( ~ ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[797]) ).
thf(823,plain,
! [SV159: term,SV129: term > $o,SV165: term,SV168: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV168 @ SV165 @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV165 @ SV168 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV159 @ id ) ) )
= $true )
| ( ( SV129 @ SV159 )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(824,plain,
! [SV159: term,SV165: term,SV168: subst,SV129: term > $o] :
( ( ( ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV168 @ SV165 @ SV129 ) @ SV168 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV165 @ SV168 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV159 @ id ) ) )
= $true )
| ( ( SV129 @ SV159 )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[798]) ).
thf(825,plain,
! [SV162: term,SV164: subst,SV129: term > $o] :
( ( ( SV129 @ ( sub @ ( sK11_B @ SV164 @ SV162 @ SV129 ) @ SV164 ) )
= $false )
| ( ( SV129 @ ( sub @ SV162 @ SV164 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[800]) ).
thf(826,plain,
! [SV166: term,SV129: term > $o,SV179: term,SV184: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV184 @ SV179 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV184 @ SV179 @ SV129 ) @ SV184 ) ) )
| ( SV129 @ ( sub @ SV179 @ SV184 ) ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV166 @ id ) ) )
= $true )
| ( ( SV129 @ SV166 )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(827,plain,
! [SV129: term > $o,SV169: term,SV174: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV174 @ SV169 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV174 @ SV169 @ SV129 ) @ SV174 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV169 @ SV174 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[802]) ).
thf(828,plain,
! [SV170: term,SV129: term > $o,SV185: term] :
( ( ( ! [SY196: subst] :
( ~ ( ~ ( var @ ( sK11_B @ SY196 @ SV185 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SY196 @ SV185 @ SV129 ) @ SY196 ) ) )
| ( SV129 @ ( sub @ SV185 @ SY196 ) ) ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV170 @ id ) ) )
= $true )
| ( ( SV129 @ SV170 )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(829,plain,
! [SV129: term > $o,SV175: term,SV180: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV180 @ SV175 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV180 @ SV175 @ SV129 ) @ SV180 ) ) ) )
= $true )
| ( ( SV129 @ ( sub @ SV175 @ SV180 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(830,plain,
! [SV186: term,SV130: term > $o] :
( ( ( SV130 @ SV186 )
= $true )
| ( ( SV130 @ ( sK6_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(831,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(832,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( sK6_A @ SV130 ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(833,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[808]) ).
thf(834,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( sK6_A @ SV130 ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[810]) ).
thf(835,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[811]) ).
thf(836,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(837,plain,
! [SV130: term > $o] :
( ( ( ~ ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[812]) ).
thf(838,plain,
! [SV183: term,SV126: term > $o] :
( ( ( ~ ( SV126 @ SV183 ) )
= $true )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV183 @ id ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(839,plain,
! [SV187: term,SV126: term > $o] :
( ( ( SV126 @ SV187 )
= $true )
| ( ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(840,plain,
! [SV188: term,SV126: term > $o] :
( ( ( ~ ( SV126 @ SV188 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV188 @ id ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(841,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[817]) ).
thf(842,plain,
! [SV173: term,SV189: term,SV126: term > $o] :
( ( ( SV126 @ SV189 )
= $true )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV173 @ id ) ) )
= $true )
| ( ( SV126 @ SV173 )
= $false )
| ( ( SV126 @ ( sK16_A @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(843,plain,
! [SV190: term,SV126: term > $o] :
( ( ( ~ ( SV126 @ SV190 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV190 @ id ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(844,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[820]) ).
thf(845,plain,
! [SV126: term > $o] :
( ( ( ! [SY166: term] :
( ~ ( SV126 @ SY166 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SY166 @ id ) ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(846,plain,
! [SV126: term > $o] :
( ( ( ~ ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(847,plain,
! [SV159: term,SV129: term > $o,SV165: term,SV168: subst] :
( ( ( var @ ( sK11_B @ SV168 @ SV165 @ SV129 ) )
= $true )
| ( ( SV129 @ ( sub @ SV165 @ SV168 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV159 @ id ) ) )
= $true )
| ( ( SV129 @ SV159 )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(848,plain,
! [SV159: term,SV165: term,SV168: subst,SV129: term > $o] :
( ( ( ~ ( SV129 @ ( sub @ ( sK11_B @ SV168 @ SV165 @ SV129 ) @ SV168 ) ) )
= $true )
| ( ( SV129 @ ( sub @ SV165 @ SV168 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV159 @ id ) ) )
= $true )
| ( ( SV129 @ SV159 )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(849,plain,
! [SV166: term,SV129: term > $o,SV179: term,SV184: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV184 @ SV179 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV184 @ SV179 @ SV129 ) @ SV184 ) ) ) )
= $true )
| ( ( SV129 @ ( sub @ SV179 @ SV184 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV166 @ id ) ) )
= $true )
| ( ( SV129 @ SV166 )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[826]) ).
thf(850,plain,
! [SV129: term > $o,SV169: term,SV174: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV174 @ SV169 @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV169 @ SV174 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[827]) ).
thf(851,plain,
! [SV169: term,SV174: subst,SV129: term > $o] :
( ( ( ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV174 @ SV169 @ SV129 ) @ SV174 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV169 @ SV174 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[827]) ).
thf(852,plain,
! [SV170: term,SV129: term > $o,SV185: term,SV191: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV191 @ SV185 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV191 @ SV185 @ SV129 ) @ SV191 ) ) )
| ( SV129 @ ( sub @ SV185 @ SV191 ) ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV170 @ id ) ) )
= $true )
| ( ( SV129 @ SV170 )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(853,plain,
! [SV129: term > $o,SV175: term,SV180: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV180 @ SV175 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV180 @ SV175 @ SV129 ) @ SV180 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV175 @ SV180 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[829]) ).
thf(854,plain,
! [SV192: term,SV130: term > $o] :
( ( ( SV130 @ SV192 )
= $true )
| ( ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(855,plain,
! [SV193: term,SV130: term > $o] :
( ( ( SV130 @ SV193 )
= $true )
| ( ( SV130 @ ( sK6_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(856,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(857,plain,
! [SV194: term,SV130: term > $o] :
( ( ( SV130 @ SV194 )
= $true )
| ( ( SV130 @ ( sK6_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(858,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(859,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( sK6_A @ SV130 ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[836]) ).
thf(860,plain,
! [SV130: term > $o] :
( ( ( ~ ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) ) )
= $true )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[837]) ).
thf(861,plain,
! [SV183: term,SV126: term > $o] :
( ( ( SV126 @ SV183 )
= $false )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV183 @ id ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[838]) ).
thf(862,plain,
! [SV188: term,SV126: term > $o] :
( ( ( ~ ( SV126 @ SV188 ) )
= $true )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV188 @ id ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(863,plain,
! [SV195: term,SV126: term > $o] :
( ( ( SV126 @ SV195 )
= $true )
| ( ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(864,plain,
! [SV190: term,SV126: term > $o] :
( ( ( ~ ( SV126 @ SV190 ) )
= $true )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV190 @ id ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(865,plain,
! [SV196: term,SV126: term > $o] :
( ( ( SV126 @ SV196 )
= $true )
| ( ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(866,plain,
! [SV197: term,SV126: term > $o] :
( ( ( ~ ( SV126 @ SV197 )
| ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV197 @ id ) ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(867,plain,
! [SV126: term > $o] :
( ( ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) )
= $false )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[846]) ).
thf(868,plain,
! [SV159: term,SV165: term,SV168: subst,SV129: term > $o] :
( ( ( SV129 @ ( sub @ ( sK11_B @ SV168 @ SV165 @ SV129 ) @ SV168 ) )
= $false )
| ( ( SV129 @ ( sub @ SV165 @ SV168 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV159 @ id ) ) )
= $true )
| ( ( SV129 @ SV159 )
= $false )
| ( ( SV129 @ ( sK13_A @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[848]) ).
thf(869,plain,
! [SV166: term,SV129: term > $o,SV179: term,SV184: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV184 @ SV179 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV184 @ SV179 @ SV129 ) @ SV184 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV179 @ SV184 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV166 @ id ) ) )
= $true )
| ( ( SV129 @ SV166 )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(870,plain,
! [SV129: term > $o,SV169: term,SV174: subst] :
( ( ( var @ ( sK11_B @ SV174 @ SV169 @ SV129 ) )
= $true )
| ( ( SV129 @ ( sub @ SV169 @ SV174 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[850]) ).
thf(871,plain,
! [SV169: term,SV174: subst,SV129: term > $o] :
( ( ( ~ ( SV129 @ ( sub @ ( sK11_B @ SV174 @ SV169 @ SV129 ) @ SV174 ) ) )
= $true )
| ( ( SV129 @ ( sub @ SV169 @ SV174 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[851]) ).
thf(872,plain,
! [SV170: term,SV129: term > $o,SV185: term,SV191: subst] :
( ( ( ~ ( ~ ( var @ ( sK11_B @ SV191 @ SV185 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV191 @ SV185 @ SV129 ) @ SV191 ) ) ) )
= $true )
| ( ( SV129 @ ( sub @ SV185 @ SV191 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV170 @ id ) ) )
= $true )
| ( ( SV129 @ SV170 )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(873,plain,
! [SV129: term > $o,SV175: term,SV180: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV180 @ SV175 @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV175 @ SV180 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(874,plain,
! [SV175: term,SV180: subst,SV129: term > $o] :
( ( ( ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV180 @ SV175 @ SV129 ) @ SV180 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV175 @ SV180 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[853]) ).
thf(875,plain,
! [SV198: term,SV130: term > $o] :
( ( ( SV130 @ SV198 )
= $true )
| ( ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( var @ ( sK9_A @ SV130 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(876,plain,
! [SV199: term,SV130: term > $o] :
( ( ( SV130 @ SV199 )
= $true )
| ( ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK8_SY82 @ SV130 ) )
= $true )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(877,plain,
! [SV200: term,SV130: term > $o] :
( ( ( SV130 @ SV200 )
= $true )
| ( ( SV130 @ ( sK6_A @ SV130 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(878,plain,
! [SV130: term > $o] :
( ( ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( ! [SY175: term] : ( SV130 @ SY175 ) )
= $true )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(879,plain,
! [SV183: term,SV201: term,SV126: term > $o] :
( ( ( SV126 @ SV201 )
= $true )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV183 @ id ) ) )
= $true )
| ( ( SV126 @ SV183 )
= $false )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(880,plain,
! [SV188: term,SV126: term > $o] :
( ( ( SV126 @ SV188 )
= $false )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV188 @ id ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[862]) ).
thf(881,plain,
! [SV190: term,SV126: term > $o] :
( ( ( SV126 @ SV190 )
= $false )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV190 @ id ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[864]) ).
thf(882,plain,
! [SV197: term,SV126: term > $o] :
( ( ( ~ ( SV126 @ SV197 ) )
= $true )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV197 @ id ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(883,plain,
! [SV202: term,SV126: term > $o] :
( ( ( SV126 @ SV202 )
= $true )
| ( ( SV126 @ ( lam @ ( sK15_A @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(884,plain,
! [SV166: term,SV129: term > $o,SV179: term,SV184: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV184 @ SV179 @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV179 @ SV184 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV166 @ id ) ) )
= $true )
| ( ( SV129 @ SV166 )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(885,plain,
! [SV166: term,SV179: term,SV184: subst,SV129: term > $o] :
( ( ( ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV184 @ SV179 @ SV129 ) @ SV184 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV179 @ SV184 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV166 @ id ) ) )
= $true )
| ( ( SV129 @ SV166 )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[869]) ).
thf(886,plain,
! [SV169: term,SV174: subst,SV129: term > $o] :
( ( ( SV129 @ ( sub @ ( sK11_B @ SV174 @ SV169 @ SV129 ) @ SV174 ) )
= $false )
| ( ( SV129 @ ( sub @ SV169 @ SV174 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(887,plain,
! [SV170: term,SV129: term > $o,SV185: term,SV191: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV191 @ SV185 @ SV129 ) )
| ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV191 @ SV185 @ SV129 ) @ SV191 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV185 @ SV191 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV170 @ id ) ) )
= $true )
| ( ( SV129 @ SV170 )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(888,plain,
! [SV129: term > $o,SV175: term,SV180: subst] :
( ( ( var @ ( sK11_B @ SV180 @ SV175 @ SV129 ) )
= $true )
| ( ( SV129 @ ( sub @ SV175 @ SV180 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[873]) ).
thf(889,plain,
! [SV175: term,SV180: subst,SV129: term > $o] :
( ( ( ~ ( SV129 @ ( sub @ ( sK11_B @ SV180 @ SV175 @ SV129 ) @ SV180 ) ) )
= $true )
| ( ( SV129 @ ( sub @ SV175 @ SV180 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[874]) ).
thf(890,plain,
! [SV203: term,SV130: term > $o] :
( ( ( SV130 @ SV203 )
= $true )
| ( ( SV130 @ ( lam @ ( sK6_A @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( ap @ ( sK7_A @ SV130 ) @ ( sK8_SY82 @ SV130 ) ) )
= $false )
| ( ( SV130 @ ( sK9_A @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(891,plain,
! [SV188: term,SV204: term,SV126: term > $o] :
( ( ( SV126 @ SV204 )
= $true )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV188 @ id ) ) )
= $true )
| ( ( SV126 @ SV188 )
= $false )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( var @ ( sK18_A @ SV126 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(892,plain,
! [SV190: term,SV205: term,SV126: term > $o] :
( ( ( SV126 @ SV205 )
= $true )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV190 @ id ) ) )
= $true )
| ( ( SV126 @ SV190 )
= $false )
| ( ( SV126 @ ( sK17_SY86 @ SV126 ) )
= $true )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(893,plain,
! [SV197: term,SV126: term > $o] :
( ( ( SV126 @ SV197 )
= $false )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV197 @ id ) ) )
= $true )
| ( ( ! [SY167: term] : ( SV126 @ SY167 ) )
= $true )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(894,plain,
! [SV166: term,SV129: term > $o,SV179: term,SV184: subst] :
( ( ( var @ ( sK11_B @ SV184 @ SV179 @ SV129 ) )
= $true )
| ( ( SV129 @ ( sub @ SV179 @ SV184 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV166 @ id ) ) )
= $true )
| ( ( SV129 @ SV166 )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[884]) ).
thf(895,plain,
! [SV166: term,SV179: term,SV184: subst,SV129: term > $o] :
( ( ( ~ ( SV129 @ ( sub @ ( sK11_B @ SV184 @ SV179 @ SV129 ) @ SV184 ) ) )
= $true )
| ( ( SV129 @ ( sub @ SV179 @ SV184 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV166 @ id ) ) )
= $true )
| ( ( SV129 @ SV166 )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[885]) ).
thf(896,plain,
! [SV170: term,SV129: term > $o,SV185: term,SV191: subst] :
( ( ( ~ ( var @ ( sK11_B @ SV191 @ SV185 @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV185 @ SV191 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV170 @ id ) ) )
= $true )
| ( ( SV129 @ SV170 )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[887]) ).
thf(897,plain,
! [SV170: term,SV185: term,SV191: subst,SV129: term > $o] :
( ( ( ~ ~ ( SV129 @ ( sub @ ( sK11_B @ SV191 @ SV185 @ SV129 ) @ SV191 ) ) )
= $false )
| ( ( SV129 @ ( sub @ SV185 @ SV191 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV170 @ id ) ) )
= $true )
| ( ( SV129 @ SV170 )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[887]) ).
thf(898,plain,
! [SV175: term,SV180: subst,SV129: term > $o] :
( ( ( SV129 @ ( sub @ ( sK11_B @ SV180 @ SV175 @ SV129 ) @ SV180 ) )
= $false )
| ( ( SV129 @ ( sub @ SV175 @ SV180 ) )
= $true )
| ( ( SV129 @ ( lam @ ( sK12_A @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(899,plain,
! [SV197: term,SV206: term,SV126: term > $o] :
( ( ( SV126 @ SV206 )
= $true )
| ( ( SV126 @ ( sub @ ( sK15_A @ SV126 ) @ ( push @ SV197 @ id ) ) )
= $true )
| ( ( SV126 @ SV197 )
= $false )
| ( ( SV126 @ ( ap @ ( sK16_A @ SV126 ) @ ( sK17_SY86 @ SV126 ) ) )
= $false )
| ( ( SV126 @ ( sK18_A @ SV126 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(900,plain,
! [SV166: term,SV179: term,SV184: subst,SV129: term > $o] :
( ( ( SV129 @ ( sub @ ( sK11_B @ SV184 @ SV179 @ SV129 ) @ SV184 ) )
= $false )
| ( ( SV129 @ ( sub @ SV179 @ SV184 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV166 @ id ) ) )
= $true )
| ( ( SV129 @ SV166 )
= $false )
| ( ( SV129 @ ( sK14_SY84 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(901,plain,
! [SV170: term,SV129: term > $o,SV185: term,SV191: subst] :
( ( ( var @ ( sK11_B @ SV191 @ SV185 @ SV129 ) )
= $true )
| ( ( SV129 @ ( sub @ SV185 @ SV191 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV170 @ id ) ) )
= $true )
| ( ( SV129 @ SV170 )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[896]) ).
thf(902,plain,
! [SV170: term,SV185: term,SV191: subst,SV129: term > $o] :
( ( ( ~ ( SV129 @ ( sub @ ( sK11_B @ SV191 @ SV185 @ SV129 ) @ SV191 ) ) )
= $true )
| ( ( SV129 @ ( sub @ SV185 @ SV191 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV170 @ id ) ) )
= $true )
| ( ( SV129 @ SV170 )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[897]) ).
thf(903,plain,
! [SV170: term,SV185: term,SV191: subst,SV129: term > $o] :
( ( ( SV129 @ ( sub @ ( sK11_B @ SV191 @ SV185 @ SV129 ) @ SV191 ) )
= $false )
| ( ( SV129 @ ( sub @ SV185 @ SV191 ) )
= $true )
| ( ( SV129 @ ( sub @ ( sK12_A @ SV129 ) @ ( push @ SV170 @ id ) ) )
= $true )
| ( ( SV129 @ SV170 )
= $false )
| ( ( SV129 @ ( ap @ ( sK13_A @ SV129 ) @ ( sK14_SY84 @ SV129 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(904,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[494,903,901,900,899,898,894,892,891,890,888,886,883,879,877,876,875,870,868,865,863,857,855,854,847,842,839,830,825,813,809,799,794,784,780,765,756,749,725,724,699,662,603,602,581,580,579,573,572,571,570,569,563,562,555,554,552,542,535,532,529,525,524,514,513,496]) ).
thf(905,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[904,477]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG255^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.02 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Oct 6 18:09:16 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.88/0.53
% 1.88/0.53 No.of.Axioms: 0
% 1.88/0.53
% 1.88/0.53 Length.of.Defs: 38092
% 1.88/0.53
% 1.88/0.53 Contains.Choice.Funs: false
% 1.88/0.53 .......................
% 1.88/0.53
% 1.88/0.53 ********************************
% 1.88/0.53 * All subproblems solved! *
% 1.88/0.53 ********************************
% 1.88/0.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:29,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:904,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 1.88/0.53
% 1.88/0.53 %**** Beginning of derivation protocol ****
% 1.88/0.53 % SZS output start CNFRefutation
% See solution above
% 0.49/0.53
% 0.49/0.53 %**** End of derivation protocol ****
% 0.49/0.53 %**** no. of clauses in derivation: 905 ****
% 0.49/0.53 %**** clause counter: 904 ****
% 0.49/0.53
% 0.49/0.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:29,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:904,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------