TSTP Solution File: ALG256^1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ALG256^1 : TPTP v8.1.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:25:28 EDT 2022
% Result : Theorem 1.46s 1.64s
% Output : CNFRefutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 277
% Syntax : Number of formulae : 747 ( 287 unt; 163 typ; 113 def)
% Number of atoms : 4821 (2012 equ; 0 cnn)
% Maximal formula atoms : 5 ( 8 avg)
% Number of connectives : 15335 (2464 ~;2825 |; 4 &;9026 @)
% ( 2 <=>;1014 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 637 ( 637 >; 0 *; 0 +; 0 <<)
% Number of symbols : 164 ( 161 usr; 117 con; 0-4 aty)
% Number of variables : 3371 ( 39 ^3327 !; 5 ?;3371 :)
% 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_SY36,type,
sK10_SY36: ( term > $o ) > term ).
thf(tp_sK11_SY68,type,
sK11_SY68: term ).
thf(tp_sK12_SY36,type,
sK12_SY36: ( term > $o ) > term ).
thf(tp_sK13_SY69,type,
sK13_SY69: ( term > $o ) > term ).
thf(tp_sK14_SY70,type,
sK14_SY70: ( term > $o ) > term ).
thf(tp_sK15_SY57,type,
sK15_SY57: ( term > $o ) > term ).
thf(tp_sK16_SY49,type,
sK16_SY49: ( term > $o ) > term ).
thf(tp_sK17_SY49,type,
sK17_SY49: ( term > $o ) > term ).
thf(tp_sK18_SY57,type,
sK18_SY57: ( term > $o ) > term ).
thf(tp_sK19_SY74,type,
sK19_SY74: ( term > $o ) > term ).
thf(tp_sK1_SY15,type,
sK1_SY15: ( term > $o ) > term ).
thf(tp_sK20_SY49,type,
sK20_SY49: ( term > $o ) > term ).
thf(tp_sK21_SY79,type,
sK21_SY79: ( term > $o ) > term ).
thf(tp_sK22_SY38,type,
sK22_SY38: ( term > $o ) > term ).
thf(tp_sK23_SY38,type,
sK23_SY38: ( term > $o ) > term ).
thf(tp_sK24_SY38,type,
sK24_SY38: ( term > $o ) > term ).
thf(tp_sK25_SY38,type,
sK25_SY38: ( term > $o ) > term ).
thf(tp_sK26_SY38,type,
sK26_SY38: ( term > $o ) > term ).
thf(tp_sK27_SY38,type,
sK27_SY38: ( term > $o ) > term ).
thf(tp_sK28_SY59,type,
sK28_SY59: ( term > $o ) > term ).
thf(tp_sK29_SY59,type,
sK29_SY59: ( term > $o ) > term ).
thf(tp_sK2_SY35,type,
sK2_SY35: ( term > $o ) > term ).
thf(tp_sK30_SY86,type,
sK30_SY86: term > subst > ( term > $o ) > term ).
thf(tp_sK31_SY89,type,
sK31_SY89: term > subst > ( term > $o ) > term ).
thf(tp_sK32_SY59,type,
sK32_SY59: ( term > $o ) > term ).
thf(tp_sK33_SY59,type,
sK33_SY59: ( term > $o ) > term ).
thf(tp_sK34_SY59,type,
sK34_SY59: ( term > $o ) > term ).
thf(tp_sK35_SY90,type,
sK35_SY90: term > subst > ( term > $o ) > term ).
thf(tp_sK36_SY59,type,
sK36_SY59: ( term > $o ) > term ).
thf(tp_sK37_SY100,type,
sK37_SY100: term > term > subst > ( term > $o ) > term ).
thf(tp_sK38_SY103,type,
sK38_SY103: term > term > subst > ( term > $o ) > term ).
thf(tp_sK39_SY105,type,
sK39_SY105: term > term > subst > ( term > $o ) > term ).
thf(tp_sK3_SX0,type,
sK3_SX0: term ).
thf(tp_sK4_SY47,type,
sK4_SY47: ( term > $o ) > term ).
thf(tp_sK5_SY62,type,
sK5_SY62: term ).
thf(tp_sK6_SY54,type,
sK6_SY54: term > subst > ( term > $o ) > term ).
thf(tp_sK7_SY65,type,
sK7_SY65: ( term > $o ) > term ).
thf(tp_sK8_SY56,type,
sK8_SY56: ( term > $o ) > term ).
thf(tp_sK9_SY66,type,
sK9_SY66: 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,
hoasapinj1_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
hoasapinj1_gthm = $false,
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ hoasapinj1_gthm )
= $true ),
inference(polarity_switch,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ hoasapinj1_gthm )
= $true ),
inference(copy,[status(thm)],[3]) ).
thf(5,plain,
( ( ~ ( ~ ! [SX0: term,SX1: term,SX2: subst] :
( ( sub @ ( ap @ SX0 @ SX1 ) @ SX2 )
= ( ap @ ( sub @ SX0 @ SX2 ) @ ( sub @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term,SX1: subst] :
( ( sub @ one @ ( push @ SX0 @ SX1 ) )
= SX0 )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 )
| ~ ! [SX0: term,SX1: subst] :
( ( sub @ ( lam @ SX0 ) @ SX1 )
= ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 )
| ~ ! [SX0: term,SX1: subst] :
( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
= SX1 )
| ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
= ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 )
| ( ( push @ one @ sh )
!= id )
| ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4,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(6,plain,
( ( ~ ! [SX0: term,SX1: term,SX2: subst] :
( ( sub @ ( ap @ SX0 @ SX1 ) @ SX2 )
= ( ap @ ( sub @ SX0 @ SX2 ) @ ( sub @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term,SX1: subst] :
( ( sub @ one @ ( push @ SX0 @ SX1 ) )
= SX0 )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 )
| ~ ! [SX0: term,SX1: subst] :
( ( sub @ ( lam @ SX0 ) @ SX1 )
= ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 )
| ~ ! [SX0: term,SX1: subst] :
( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
= SX1 )
| ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
= ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 )
| ( ( push @ one @ sh )
!= id )
| ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5]) ).
thf(7,plain,
( ( ~ ! [SX0: term,SX1: term,SX2: subst] :
( ( sub @ ( ap @ SX0 @ SX1 ) @ SX2 )
= ( ap @ ( sub @ SX0 @ SX2 ) @ ( sub @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6]) ).
thf(8,plain,
( ( ~ ! [SX0: term,SX1: subst] :
( ( sub @ one @ ( push @ SX0 @ SX1 ) )
= SX0 )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 )
| ~ ! [SX0: term,SX1: subst] :
( ( sub @ ( lam @ SX0 ) @ SX1 )
= ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 )
| ~ ! [SX0: term,SX1: subst] :
( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
= SX1 )
| ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
= ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 )
| ( ( push @ one @ sh )
!= id )
| ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [SX0: term,SX1: term,SX2: subst] :
( ( sub @ ( ap @ SX0 @ SX1 ) @ SX2 )
= ( ap @ ( sub @ SX0 @ SX2 ) @ ( sub @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[7]) ).
thf(10,plain,
( ( ~ ! [SX0: term,SX1: subst] :
( ( sub @ one @ ( push @ SX0 @ SX1 ) )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(11,plain,
( ( ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 )
| ~ ! [SX0: term,SX1: subst] :
( ( sub @ ( lam @ SX0 ) @ SX1 )
= ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 )
| ~ ! [SX0: term,SX1: subst] :
( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
= SX1 )
| ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
= ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 )
| ( ( push @ one @ sh )
!= id )
| ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[8]) ).
thf(12,plain,
! [SV1: term] :
( ( ! [SY0: term,SY1: subst] :
( ( sub @ ( ap @ SV1 @ SY0 ) @ SY1 )
= ( ap @ ( sub @ SV1 @ SY1 ) @ ( sub @ SY0 @ SY1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[9]) ).
thf(13,plain,
( ( ! [SX0: term,SX1: subst] :
( ( sub @ one @ ( push @ SX0 @ SX1 ) )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[10]) ).
thf(14,plain,
( ( ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(15,plain,
( ( ~ ! [SX0: term,SX1: subst] :
( ( sub @ ( lam @ SX0 ) @ SX1 )
= ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 )
| ~ ! [SX0: term,SX1: subst] :
( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
= SX1 )
| ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
= ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 )
| ( ( push @ one @ sh )
!= id )
| ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(16,plain,
! [SV2: term,SV1: term] :
( ( ! [SY2: subst] :
( ( sub @ ( ap @ SV1 @ SV2 ) @ SY2 )
= ( ap @ ( sub @ SV1 @ SY2 ) @ ( sub @ SV2 @ SY2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(17,plain,
! [SV3: term] :
( ( ! [SY3: subst] :
( ( sub @ one @ ( push @ SV3 @ SY3 ) )
= SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(18,plain,
( ( ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(19,plain,
( ( ~ ! [SX0: term,SX1: subst] :
( ( sub @ ( lam @ SX0 ) @ SX1 )
= ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(20,plain,
( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 )
| ~ ! [SX0: term,SX1: subst] :
( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
= SX1 )
| ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
= ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 )
| ( ( push @ one @ sh )
!= id )
| ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(21,plain,
! [SV4: subst,SV2: term,SV1: term] :
( ( ( sub @ ( ap @ SV1 @ SV2 ) @ SV4 )
= ( ap @ ( sub @ SV1 @ SV4 ) @ ( sub @ SV2 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(22,plain,
! [SV5: subst,SV3: term] :
( ( ( sub @ one @ ( push @ SV3 @ SV5 ) )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(23,plain,
! [SV6: term] :
( ( ( sub @ SV6 @ id )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(24,plain,
( ( ! [SX0: term,SX1: subst] :
( ( sub @ ( lam @ SX0 ) @ SX1 )
= ( lam @ ( sub @ SX0 @ ( push @ one @ ( comp @ SX1 @ sh ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(25,plain,
( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(26,plain,
( ( ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 )
| ~ ! [SX0: term,SX1: subst] :
( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
= SX1 )
| ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
= ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 )
| ( ( push @ one @ sh )
!= id )
| ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[20]) ).
thf(27,plain,
! [SV7: term] :
( ( ! [SY4: subst] :
( ( sub @ ( lam @ SV7 ) @ SY4 )
= ( lam @ ( sub @ SV7 @ ( push @ one @ ( comp @ SY4 @ sh ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(28,plain,
( ( ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(29,plain,
( ( ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
( ( ~ ! [SX0: term,SX1: subst] :
( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
= SX1 )
| ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
= ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 )
| ( ( push @ one @ sh )
!= id )
| ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(31,plain,
! [SV8: subst,SV7: term] :
( ( ( sub @ ( lam @ SV7 ) @ SV8 )
= ( lam @ ( sub @ SV7 @ ( push @ one @ ( comp @ SV8 @ sh ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV9: term] :
( ( ! [SY5: subst,SY6: subst] :
( ( sub @ ( sub @ SV9 @ SY5 ) @ SY6 )
= ( sub @ SV9 @ ( comp @ SY5 @ SY6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
( ( ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
( ( ~ ! [SX0: term,SX1: subst] :
( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
= SX1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(35,plain,
( ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
= ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 )
| ( ( push @ one @ sh )
!= id )
| ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(36,plain,
! [SV10: subst,SV9: term] :
( ( ! [SY7: subst] :
( ( sub @ ( sub @ SV9 @ SV10 ) @ SY7 )
= ( sub @ SV9 @ ( comp @ SV10 @ SY7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV11: subst] :
( ( ( comp @ id @ SV11 )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
( ( ! [SX0: term,SX1: subst] :
( ( comp @ sh @ ( push @ SX0 @ SX1 ) )
= SX1 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(39,plain,
( ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(40,plain,
( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
= ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 )
| ( ( push @ one @ sh )
!= id )
| ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(41,plain,
! [SV12: subst,SV10: subst,SV9: term] :
( ( ( sub @ ( sub @ SV9 @ SV10 ) @ SV12 )
= ( sub @ SV9 @ ( comp @ SV10 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV13: term] :
( ( ! [SY8: subst] :
( ( comp @ sh @ ( push @ SV13 @ SY8 ) )
= SY8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(43,plain,
( ( ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
= ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(45,plain,
( ( ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 )
| ( ( push @ one @ sh )
!= id )
| ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[40]) ).
thf(46,plain,
! [SV14: subst,SV13: term] :
( ( ( comp @ sh @ ( push @ SV13 @ SV14 ) )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV15: subst] :
( ( ! [SY9: subst,SY10: subst] :
( ( comp @ ( comp @ SV15 @ SY9 ) @ SY10 )
= ( comp @ SV15 @ ( comp @ SY9 @ SY10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(48,plain,
( ( ! [SX0: term,SX1: subst,SX2: subst] :
( ( comp @ ( push @ SX0 @ SX1 ) @ SX2 )
= ( push @ ( sub @ SX0 @ SX2 ) @ ( comp @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
( ( ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(50,plain,
( ( ( ( push @ one @ sh )
!= id )
| ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV16: subst,SV15: subst] :
( ( ! [SY11: subst] :
( ( comp @ ( comp @ SV15 @ SV16 ) @ SY11 )
= ( comp @ SV15 @ ( comp @ SV16 @ SY11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV17: term] :
( ( ! [SY12: subst,SY13: subst] :
( ( comp @ ( push @ SV17 @ SY12 ) @ SY13 )
= ( push @ ( sub @ SV17 @ SY13 ) @ ( comp @ SY12 @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(53,plain,
( ( ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[49]) ).
thf(54,plain,
( ( ( ( push @ one @ sh )
!= id ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(55,plain,
( ( ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 )
| ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(56,plain,
! [SV18: subst,SV16: subst,SV15: subst] :
( ( ( comp @ ( comp @ SV15 @ SV16 ) @ SV18 )
= ( comp @ SV15 @ ( comp @ SV16 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV19: subst,SV17: term] :
( ( ! [SY14: subst] :
( ( comp @ ( push @ SV17 @ SV19 ) @ SY14 )
= ( push @ ( sub @ SV17 @ SY14 ) @ ( comp @ SV19 @ SY14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV20: subst] :
( ( ( comp @ SV20 @ id )
= SV20 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(59,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(60,plain,
( ( ~ ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(61,plain,
( ( ~ ( var @ one )
| ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(62,plain,
! [SV21: subst,SV19: subst,SV17: term] :
( ( ( comp @ ( push @ SV17 @ SV19 ) @ SV21 )
= ( push @ ( sub @ SV17 @ SV21 ) @ ( comp @ SV19 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(63,plain,
( ( ! [SX0: subst] :
( ( push @ ( sub @ one @ SX0 ) @ ( comp @ sh @ SX0 ) )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(64,plain,
( ( ~ ( var @ one ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(65,plain,
( ( ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) )
| ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(66,plain,
! [SV22: subst] :
( ( ( push @ ( sub @ one @ SV22 ) @ ( comp @ sh @ SV22 ) )
= SV22 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(67,plain,
( ( var @ one )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(68,plain,
( ( ~ ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(69,plain,
( ( ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(70,plain,
( ( ! [SX0: term] :
( ~ ( var @ SX0 )
| ( var @ ( sub @ SX0 @ sh ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(71,plain,
( ( ~ ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(72,plain,
( ( ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(73,plain,
! [SV23: term] :
( ( ~ ( var @ SV23 )
| ( var @ ( sub @ SV23 @ sh ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(74,plain,
( ( ! [SX0: term > $o] :
( ~ ( SX0 @ one )
| ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ~ ( SX0 @ SX1 )
| ( SX0 @ ( sub @ SX1 @ sh ) ) )
| ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(75,plain,
( ( ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(76,plain,
( ( ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[72]) ).
thf(77,plain,
! [SV23: term] :
( ( ( ~ ( var @ SV23 ) )
= $true )
| ( ( var @ ( sub @ SV23 @ sh ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV24: term > $o] :
( ( ~ ( SV24 @ one )
| ~ ! [SY15: term] :
( ~ ( var @ SY15 )
| ~ ( SV24 @ SY15 )
| ( SV24 @ ( sub @ SY15 @ sh ) ) )
| ! [SY16: term] :
( ~ ( var @ SY16 )
| ( SV24 @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(79,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(80,plain,
( ( ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(81,plain,
( ( ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(82,plain,
! [SV23: term] :
( ( ( var @ SV23 )
= $false )
| ( ( var @ ( sub @ SV23 @ sh ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ one ) )
= $true )
| ( ( ~ ! [SY15: term] :
( ~ ( var @ SY15 )
| ~ ( SV24 @ SY15 )
| ( SV24 @ ( sub @ SY15 @ sh ) ) )
| ! [SY16: term] :
( ~ ( var @ SY16 )
| ( SV24 @ SY16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV25: term] :
( ( ! [SY17: term,SY18: term,SY19: term] :
( ( ( ap @ SV25 @ SY18 )
!= ( ap @ SY17 @ SY19 ) )
| ( SV25 = SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(85,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ SX0 @ SX2 )
!= ( ap @ SX1 @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(86,plain,
( ( ~ ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(87,plain,
( ( ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) )
| ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(88,plain,
! [SV24: term > $o] :
( ( ( SV24 @ one )
= $false )
| ( ( ~ ! [SY15: term] :
( ~ ( var @ SY15 )
| ~ ( SV24 @ SY15 )
| ( SV24 @ ( sub @ SY15 @ sh ) ) )
| ! [SY16: term] :
( ~ ( var @ SY16 )
| ( SV24 @ SY16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(89,plain,
! [SV26: term,SV25: term] :
( ( ! [SY20: term,SY21: term] :
( ( ( ap @ SV25 @ SY20 )
!= ( ap @ SV26 @ SY21 ) )
| ( SV25 = SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV27: term] :
( ( ! [SY22: term,SY23: term,SY24: term] :
( ( ( ap @ SV27 @ SY23 )
!= ( ap @ SY22 @ SY24 ) )
| ( SY23 = SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(91,plain,
( ( ! [SX0: term,SX1: term] :
( ( ( lam @ SX0 )
!= ( lam @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(92,plain,
( ( ~ ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(93,plain,
( ( ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[87]) ).
thf(94,plain,
! [SV24: term > $o] :
( ( ( ~ ! [SY15: term] :
( ~ ( var @ SY15 )
| ~ ( SV24 @ SY15 )
| ( SV24 @ ( sub @ SY15 @ sh ) ) ) )
= $true )
| ( ( ! [SY16: term] :
( ~ ( var @ SY16 )
| ( SV24 @ SY16 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV26: term,SV28: term,SV25: term] :
( ( ! [SY25: term] :
( ( ( ap @ SV25 @ SV28 )
!= ( ap @ SV26 @ SY25 ) )
| ( SV25 = SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV29: term,SV27: term] :
( ( ! [SY26: term,SY27: term] :
( ( ( ap @ SV27 @ SY26 )
!= ( ap @ SV29 @ SY27 ) )
| ( SY26 = SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(97,plain,
! [SV30: term] :
( ( ! [SY28: term] :
( ( ( lam @ SV30 )
!= ( lam @ SY28 ) )
| ( SV30 = SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(98,plain,
( ( ! [SX0: term,SX1: term] :
( ( ( sub @ SX0 @ sh )
!= ( sub @ SX1 @ sh ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[92]) ).
thf(99,plain,
( ( ~ ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(100,plain,
( ( ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) )
| ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[93]) ).
thf(101,plain,
! [SV24: term > $o] :
( ( ( ! [SY15: term] :
( ~ ( var @ SY15 )
| ~ ( SV24 @ SY15 )
| ( SV24 @ ( sub @ SY15 @ sh ) ) ) )
= $false )
| ( ( ! [SY16: term] :
( ~ ( var @ SY16 )
| ( SV24 @ SY16 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV31: term,SV26: term,SV28: term,SV25: term] :
( ( ( ( ap @ SV25 @ SV28 )
!= ( ap @ SV26 @ SV31 ) )
| ( SV25 = SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV29: term,SV32: term,SV27: term] :
( ( ! [SY29: term] :
( ( ( ap @ SV27 @ SV32 )
!= ( ap @ SV29 @ SY29 ) )
| ( SV32 = SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(104,plain,
! [SV33: term,SV30: term] :
( ( ( ( lam @ SV30 )
!= ( lam @ SV33 ) )
| ( SV30 = SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV34: term] :
( ( ! [SY30: term] :
( ( ( sub @ SV34 @ sh )
!= ( sub @ SY30 @ sh ) )
| ( SV34 = SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(106,plain,
( ( ! [SX0: term,SX1: term,SX2: term] :
( ( lam @ SX0 )
!= ( ap @ SX1 @ SX2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(107,plain,
( ( ~ ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(108,plain,
( ( ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(109,plain,
! [SV24: term > $o] :
( ( ( ~ ( var @ ( sK1_SY15 @ SV24 ) )
| ~ ( SV24 @ ( sK1_SY15 @ SV24 ) )
| ( SV24 @ ( sub @ ( sK1_SY15 @ SV24 ) @ sh ) ) )
= $false )
| ( ( ! [SY16: term] :
( ~ ( var @ SY16 )
| ( SV24 @ SY16 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[101]) ).
thf(110,plain,
! [SV31: term,SV26: term,SV28: term,SV25: term] :
( ( ( ( ( ap @ SV25 @ SV28 )
!= ( ap @ SV26 @ SV31 ) ) )
= $true )
| ( ( SV25 = SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV35: term,SV29: term,SV32: term,SV27: term] :
( ( ( ( ap @ SV27 @ SV32 )
!= ( ap @ SV29 @ SV35 ) )
| ( SV32 = SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(112,plain,
! [SV33: term,SV30: term] :
( ( ( ( ( lam @ SV30 )
!= ( lam @ SV33 ) ) )
= $true )
| ( ( SV30 = SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(113,plain,
! [SV36: term,SV34: term] :
( ( ( ( sub @ SV34 @ sh )
!= ( sub @ SV36 @ sh ) )
| ( SV34 = SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(114,plain,
! [SV37: term] :
( ( ! [SY31: term,SY32: term] :
( ( lam @ SV37 )
!= ( ap @ SY31 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(115,plain,
( ( ! [SX0: term,SX1: term] :
~ ( var @ ( ap @ SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(116,plain,
( ( ~ ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(117,plain,
( ( ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[108]) ).
thf(118,plain,
! [SV24: term > $o] :
( ( ( ~ ( var @ ( sK1_SY15 @ SV24 ) ) )
= $false )
| ( ( ! [SY16: term] :
( ~ ( var @ SY16 )
| ( SV24 @ SY16 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(119,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sK1_SY15 @ SV24 ) )
| ( SV24 @ ( sub @ ( sK1_SY15 @ SV24 ) @ sh ) ) )
= $false )
| ( ( ! [SY16: term] :
( ~ ( var @ SY16 )
| ( SV24 @ SY16 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[109]) ).
thf(120,plain,
! [SV31: term,SV26: term,SV28: term,SV25: term] :
( ( ( ( ap @ SV25 @ SV28 )
= ( ap @ SV26 @ SV31 ) )
= $false )
| ( ( SV25 = SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV35: term,SV29: term,SV32: term,SV27: term] :
( ( ( ( ( ap @ SV27 @ SV32 )
!= ( ap @ SV29 @ SV35 ) ) )
= $true )
| ( ( SV32 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV33: term,SV30: term] :
( ( ( ( lam @ SV30 )
= ( lam @ SV33 ) )
= $false )
| ( ( SV30 = SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV36: term,SV34: term] :
( ( ( ( ( sub @ SV34 @ sh )
!= ( sub @ SV36 @ sh ) ) )
= $true )
| ( ( SV34 = SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV38: term,SV37: term] :
( ( ! [SY33: term] :
( ( lam @ SV37 )
!= ( ap @ SV38 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV39: term] :
( ( ! [SY34: term] :
~ ( var @ ( ap @ SV39 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(126,plain,
( ( ! [SX0: term] :
~ ( var @ ( lam @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[116]) ).
thf(127,plain,
( ( ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(128,plain,
( ( ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(129,plain,
! [SV24: term > $o] :
( ( ( var @ ( sK1_SY15 @ SV24 ) )
= $true )
| ( ( ! [SY16: term] :
( ~ ( var @ SY16 )
| ( SV24 @ SY16 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(130,plain,
! [SV24: term > $o] :
( ( ( ~ ( SV24 @ ( sK1_SY15 @ SV24 ) ) )
= $false )
| ( ( ! [SY16: term] :
( ~ ( var @ SY16 )
| ( SV24 @ SY16 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(131,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( sub @ ( sK1_SY15 @ SV24 ) @ sh ) )
= $false )
| ( ( ! [SY16: term] :
( ~ ( var @ SY16 )
| ( SV24 @ SY16 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[119]) ).
thf(132,plain,
! [SV35: term,SV29: term,SV32: term,SV27: term] :
( ( ( ( ap @ SV27 @ SV32 )
= ( ap @ SV29 @ SV35 ) )
= $false )
| ( ( SV32 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(133,plain,
! [SV36: term,SV34: term] :
( ( ( ( sub @ SV34 @ sh )
= ( sub @ SV36 @ sh ) )
= $false )
| ( ( SV34 = SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV40: term,SV38: term,SV37: term] :
( ( ( ( lam @ SV37 )
!= ( ap @ SV38 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV41: term,SV39: term] :
( ( ~ ( var @ ( ap @ SV39 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV42: term] :
( ( ~ ( var @ ( lam @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(137,plain,
( ( ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ( SX0 @ SX1 )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(138,plain,
( ( ~ ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(139,plain,
( ( ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) )
| ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(140,plain,
! [SV24: term > $o,SV43: term] :
( ( ( ~ ( var @ SV43 )
| ( SV24 @ SV43 ) )
= $true )
| ( ( var @ ( sK1_SY15 @ SV24 ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(141,plain,
! [SV24: term > $o] :
( ( ( SV24 @ ( sK1_SY15 @ SV24 ) )
= $true )
| ( ( ! [SY16: term] :
( ~ ( var @ SY16 )
| ( SV24 @ SY16 ) ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(142,plain,
! [SV24: term > $o,SV44: term] :
( ( ( ~ ( var @ SV44 )
| ( SV24 @ SV44 ) )
= $true )
| ( ( SV24 @ ( sub @ ( sK1_SY15 @ SV24 ) @ sh ) )
= $false )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(143,plain,
! [SV40: term,SV38: term,SV37: term] :
( ( ( lam @ SV37 )
= ( ap @ SV38 @ SV40 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(144,plain,
! [SV41: term,SV39: term] :
( ( var @ ( ap @ SV39 @ SV41 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(145,plain,
! [SV42: term] :
( ( var @ ( lam @ SV42 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(146,plain,
! [SV45: term > $o] :
( ( ~ ! [SY35: term] :
( ~ ( var @ SY35 )
| ( SV45 @ SY35 ) )
| ~ ! [SY36: term,SY37: term] :
( ~ ( SV45 @ SY36 )
| ~ ( SV45 @ SY37 )
| ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
| ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(147,plain,
( ( ! [SX0: term > $o,SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ~ ( SX0 @ SX1 )
| ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ ( push @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(148,plain,
( ( ~ ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(149,plain,
( ( ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) )
| ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[139]) ).
thf(150,plain,
! [SV24: term > $o,SV43: term] :
( ( ( ~ ( var @ SV43 ) )
= $true )
| ( ( SV24 @ SV43 )
= $true )
| ( ( var @ ( sK1_SY15 @ SV24 ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(151,plain,
! [SV24: term > $o,SV46: term] :
( ( ( ~ ( var @ SV46 )
| ( SV24 @ SV46 ) )
= $true )
| ( ( SV24 @ ( sK1_SY15 @ SV24 ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(152,plain,
! [SV24: term > $o,SV44: term] :
( ( ( ~ ( var @ SV44 ) )
= $true )
| ( ( SV24 @ SV44 )
= $true )
| ( ( SV24 @ ( sub @ ( sK1_SY15 @ SV24 ) @ sh ) )
= $false )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(153,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY35: term] :
( ~ ( var @ SY35 )
| ( SV45 @ SY35 ) ) )
= $true )
| ( ( ~ ! [SY36: term,SY37: term] :
( ~ ( SV45 @ SY36 )
| ~ ( SV45 @ SY37 )
| ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
| ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(154,plain,
! [SV47: term > $o] :
( ( ! [SY40: term,SY41: subst] :
( ~ ! [SY42: term] :
( ~ ( var @ SY42 )
| ( SV47 @ ( sub @ SY42 @ SY41 ) ) )
| ~ ( SV47 @ SY40 )
| ! [SY43: term] :
( ~ ( var @ SY43 )
| ( SV47 @ ( sub @ SY43 @ ( push @ SY40 @ SY41 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(155,plain,
( ( ! [SX0: term > $o] :
( ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term,SX2: subst] :
( ~ ! [SX3: term] :
( ~ ( var @ SX3 )
| ( SX0 @ ( sub @ SX3 @ SX2 ) ) )
| ( SX0 @ ( sub @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(156,plain,
( ( ~ ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(157,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
| ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[149]) ).
thf(158,plain,
! [SV24: term > $o,SV43: term] :
( ( ( var @ SV43 )
= $false )
| ( ( SV24 @ SV43 )
= $true )
| ( ( var @ ( sK1_SY15 @ SV24 ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(159,plain,
! [SV24: term > $o,SV46: term] :
( ( ( ~ ( var @ SV46 ) )
= $true )
| ( ( SV24 @ SV46 )
= $true )
| ( ( SV24 @ ( sK1_SY15 @ SV24 ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[151]) ).
thf(160,plain,
! [SV24: term > $o,SV44: term] :
( ( ( var @ SV44 )
= $false )
| ( ( SV24 @ SV44 )
= $true )
| ( ( SV24 @ ( sub @ ( sK1_SY15 @ SV24 ) @ sh ) )
= $false )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(161,plain,
! [SV45: term > $o] :
( ( ( ! [SY35: term] :
( ~ ( var @ SY35 )
| ( SV45 @ SY35 ) ) )
= $false )
| ( ( ~ ! [SY36: term,SY37: term] :
( ~ ( SV45 @ SY36 )
| ~ ( SV45 @ SY37 )
| ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
| ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(162,plain,
! [SV48: term,SV47: term > $o] :
( ( ! [SY44: subst] :
( ~ ! [SY42: term] :
( ~ ( var @ SY42 )
| ( SV47 @ ( sub @ SY42 @ SY44 ) ) )
| ~ ( SV47 @ SV48 )
| ! [SY46: term] :
( ~ ( var @ SY46 )
| ( SV47 @ ( sub @ SY46 @ ( push @ SV48 @ SY44 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(163,plain,
! [SV49: term > $o] :
( ( ~ ! [SY47: term,SY48: term] :
( ~ ( SV49 @ SY47 )
| ~ ( SV49 @ SY48 )
| ( SV49 @ ( ap @ SY47 @ SY48 ) ) )
| ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) )
| ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(164,plain,
( ( ! [SX0: term > $o] :
( ~ ! [SX1: term] :
( ~ ( var @ SX1 )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: term,SX2: term] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX0 @ ( ap @ SX1 @ SX2 ) ) )
| ~ ! [SX1: term] :
( ~ ! [SX2: term] :
( ~ ( SX0 @ SX2 )
| ( SX0 @ ( sub @ SX1 @ ( push @ SX2 @ id ) ) ) )
| ( SX0 @ ( lam @ SX1 ) ) )
| ! [SX1: term] : ( SX0 @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(165,plain,
( ( ~ ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(166,plain,
( ( ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
| ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(167,plain,
! [SV24: term > $o,SV46: term] :
( ( ( var @ SV46 )
= $false )
| ( ( SV24 @ SV46 )
= $true )
| ( ( SV24 @ ( sK1_SY15 @ SV24 ) )
= $true )
| ( ( SV24 @ one )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(168,plain,
! [SV45: term > $o] :
( ( ( ~ ( var @ ( sK2_SY35 @ SV45 ) )
| ( SV45 @ ( sK2_SY35 @ SV45 ) ) )
= $false )
| ( ( ~ ! [SY36: term,SY37: term] :
( ~ ( SV45 @ SY36 )
| ~ ( SV45 @ SY37 )
| ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
| ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[161]) ).
thf(169,plain,
! [SV48: term,SV50: subst,SV47: term > $o] :
( ( ~ ! [SY54: term] :
( ~ ( var @ SY54 )
| ( SV47 @ ( sub @ SY54 @ SV50 ) ) )
| ~ ( SV47 @ SV48 )
| ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(170,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY47: term,SY48: term] :
( ~ ( SV49 @ SY47 )
| ~ ( SV49 @ SY48 )
| ( SV49 @ ( ap @ SY47 @ SY48 ) ) ) )
= $true )
| ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) )
| ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(171,plain,
! [SV51: term > $o] :
( ( ~ ! [SY56: term] :
( ~ ( var @ SY56 )
| ( SV51 @ SY56 ) )
| ~ ! [SY57: term,SY58: term] :
( ~ ( SV51 @ SY57 )
| ~ ( SV51 @ SY58 )
| ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
| ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(172,plain,
( ( ~ ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(173,plain,
( ( ~ ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(174,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(175,plain,
! [SV45: term > $o] :
( ( ( ~ ( var @ ( sK2_SY35 @ SV45 ) ) )
= $false )
| ( ( ~ ! [SY36: term,SY37: term] :
( ~ ( SV45 @ SY36 )
| ~ ( SV45 @ SY37 )
| ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
| ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(176,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false )
| ( ( ~ ! [SY36: term,SY37: term] :
( ~ ( SV45 @ SY36 )
| ~ ( SV45 @ SY37 )
| ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
| ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[168]) ).
thf(177,plain,
! [SV48: term,SV50: subst,SV47: term > $o] :
( ( ( ~ ! [SY54: term] :
( ~ ( var @ SY54 )
| ( SV47 @ ( sub @ SY54 @ SV50 ) ) ) )
= $true )
| ( ( ~ ( SV47 @ SV48 )
| ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(178,plain,
! [SV49: term > $o] :
( ( ( ! [SY47: term,SY48: term] :
( ~ ( SV49 @ SY47 )
| ~ ( SV49 @ SY48 )
| ( SV49 @ ( ap @ SY47 @ SY48 ) ) ) )
= $false )
| ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) )
| ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(179,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY56: term] :
( ~ ( var @ SY56 )
| ( SV51 @ SY56 ) ) )
= $true )
| ( ( ~ ! [SY57: term,SY58: term] :
( ~ ( SV51 @ SY57 )
| ~ ( SV51 @ SY58 )
| ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
| ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(180,plain,
( ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
| ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(181,plain,
( ( ~ ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(182,plain,
( ( ! [SY62: term,SY63: term,SY64: term] :
( ( ( ap @ ( sub @ sK3_SX0 @ id ) @ SY63 )
!= ( ap @ ( sub @ SY62 @ id ) @ SY64 ) )
| ( sK3_SX0 = SY62 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[174]) ).
thf(183,plain,
! [SV45: term > $o] :
( ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true )
| ( ( ~ ! [SY36: term,SY37: term] :
( ~ ( SV45 @ SY36 )
| ~ ( SV45 @ SY37 )
| ( SV45 @ ( ap @ SY36 @ SY37 ) ) )
| ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[175]) ).
thf(184,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY36: term,SY37: term] :
( ~ ( SV45 @ SY36 )
| ~ ( SV45 @ SY37 )
| ( SV45 @ ( ap @ SY36 @ SY37 ) ) ) )
= $true )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(185,plain,
! [SV48: term,SV50: subst,SV47: term > $o] :
( ( ( ! [SY54: term] :
( ~ ( var @ SY54 )
| ( SV47 @ ( sub @ SY54 @ SV50 ) ) ) )
= $false )
| ( ( ~ ( SV47 @ SV48 )
| ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(186,plain,
! [SV49: term > $o] :
( ( ( ! [SY65: term] :
( ~ ( SV49 @ ( sK4_SY47 @ SV49 ) )
| ~ ( SV49 @ SY65 )
| ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ SY65 ) ) ) )
= $false )
| ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) )
| ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[178]) ).
thf(187,plain,
! [SV51: term > $o] :
( ( ( ! [SY56: term] :
( ~ ( var @ SY56 )
| ( SV51 @ SY56 ) ) )
= $false )
| ( ( ~ ! [SY57: term,SY58: term] :
( ~ ( SV51 @ SY57 )
| ~ ( SV51 @ SY58 )
| ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
| ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(188,plain,
( ( ~ ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(189,plain,
( ( ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(190,plain,
( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(191,plain,
( ( ! [SY66: term,SY67: term] :
( ( ( ap @ ( sub @ sK3_SX0 @ id ) @ SY66 )
!= ( ap @ ( sub @ sK5_SY62 @ id ) @ SY67 ) )
| ( sK3_SX0 = sK5_SY62 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[182]) ).
thf(192,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY36: term,SY37: term] :
( ~ ( SV45 @ SY36 )
| ~ ( SV45 @ SY37 )
| ( SV45 @ ( ap @ SY36 @ SY37 ) ) ) )
= $true )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(193,plain,
! [SV45: term > $o] :
( ( ( ! [SY36: term,SY37: term] :
( ~ ( SV45 @ SY36 )
| ~ ( SV45 @ SY37 )
| ( SV45 @ ( ap @ SY36 @ SY37 ) ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(194,plain,
! [SV47: term > $o,SV50: subst,SV48: term] :
( ( ( ~ ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
| ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) ) )
= $false )
| ( ( ~ ( SV47 @ SV48 )
| ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[185]) ).
thf(195,plain,
! [SV49: term > $o] :
( ( ( ~ ( SV49 @ ( sK4_SY47 @ SV49 ) )
| ~ ( SV49 @ ( sK7_SY65 @ SV49 ) )
| ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) ) )
= $false )
| ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) )
| ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[186]) ).
thf(196,plain,
! [SV51: term > $o] :
( ( ( ~ ( var @ ( sK8_SY56 @ SV51 ) )
| ( SV51 @ ( sK8_SY56 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY57: term,SY58: term] :
( ~ ( SV51 @ SY57 )
| ~ ( SV51 @ SY58 )
| ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
| ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[187]) ).
thf(197,plain,
( ( ~ ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(198,plain,
( ( ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(199,plain,
( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(200,plain,
( ( ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[190]) ).
thf(201,plain,
( ( ! [SY68: term] :
( ( ( ap @ ( sub @ sK3_SX0 @ id ) @ sK9_SY66 )
!= ( ap @ ( sub @ sK5_SY62 @ id ) @ SY68 ) )
| ( sK3_SX0 = sK5_SY62 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[191]) ).
thf(202,plain,
! [SV45: term > $o] :
( ( ( ! [SY36: term,SY37: term] :
( ~ ( SV45 @ SY36 )
| ~ ( SV45 @ SY37 )
| ( SV45 @ ( ap @ SY36 @ SY37 ) ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(203,plain,
! [SV45: term > $o] :
( ( ( ! [SY69: term] :
( ~ ( SV45 @ ( sK10_SY36 @ SV45 ) )
| ~ ( SV45 @ SY69 )
| ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ SY69 ) ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[193]) ).
thf(204,plain,
! [SV47: term > $o,SV50: subst,SV48: term] :
( ( ( ~ ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) ) )
= $false )
| ( ( ~ ( SV47 @ SV48 )
| ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(205,plain,
! [SV50: subst,SV48: term,SV47: term > $o] :
( ( ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
= $false )
| ( ( ~ ( SV47 @ SV48 )
| ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(206,plain,
! [SV49: term > $o] :
( ( ( ~ ( SV49 @ ( sK4_SY47 @ SV49 ) ) )
= $false )
| ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) )
| ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(207,plain,
! [SV49: term > $o] :
( ( ( ~ ( SV49 @ ( sK7_SY65 @ SV49 ) )
| ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) ) )
= $false )
| ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) )
| ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[195]) ).
thf(208,plain,
! [SV51: term > $o] :
( ( ( ~ ( var @ ( sK8_SY56 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY57: term,SY58: term] :
( ~ ( SV51 @ SY57 )
| ~ ( SV51 @ SY58 )
| ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
| ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(209,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false )
| ( ( ~ ! [SY57: term,SY58: term] :
( ~ ( SV51 @ SY57 )
| ~ ( SV51 @ SY58 )
| ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
| ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[196]) ).
thf(210,plain,
( ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) )
| ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(211,plain,
! [SV52: subst] :
( ( ( comp @ SV52 @ id )
= SV52 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(212,plain,
( ( ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(213,plain,
( ( ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[200]) ).
thf(214,plain,
( ( ( ( ap @ ( sub @ sK3_SX0 @ id ) @ sK9_SY66 )
!= ( ap @ ( sub @ sK5_SY62 @ id ) @ sK11_SY68 ) )
| ( sK3_SX0 = sK5_SY62 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[201]) ).
thf(215,plain,
! [SV45: term > $o] :
( ( ( ! [SY70: term] :
( ~ ( SV45 @ ( sK12_SY36 @ SV45 ) )
| ~ ( SV45 @ SY70 )
| ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ SY70 ) ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[202]) ).
thf(216,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK10_SY36 @ SV45 ) )
| ~ ( SV45 @ ( sK13_SY69 @ SV45 ) )
| ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[203]) ).
thf(217,plain,
! [SV47: term > $o,SV50: subst,SV48: term] :
( ( ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
= $true )
| ( ( ~ ( SV47 @ SV48 )
| ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(218,plain,
! [SV50: subst,SV48: term,SV47: term > $o] :
( ( ( ~ ( SV47 @ SV48 ) )
= $true )
| ( ( ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true )
| ( ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(219,plain,
! [SV49: term > $o] :
( ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true )
| ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) )
| ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(220,plain,
! [SV49: term > $o] :
( ( ( ~ ( SV49 @ ( sK7_SY65 @ SV49 ) ) )
= $false )
| ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) )
| ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(221,plain,
! [SV49: term > $o] :
( ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false )
| ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) )
| ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(222,plain,
! [SV51: term > $o] :
( ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true )
| ( ( ~ ! [SY57: term,SY58: term] :
( ~ ( SV51 @ SY57 )
| ~ ( SV51 @ SY58 )
| ( SV51 @ ( ap @ SY57 @ SY58 ) ) )
| ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(223,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY57: term,SY58: term] :
( ~ ( SV51 @ SY57 )
| ~ ( SV51 @ SY58 )
| ( SV51 @ ( ap @ SY57 @ SY58 ) ) ) )
= $true )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(224,plain,
( ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(225,plain,
( ( ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[210]) ).
thf(226,plain,
! [SV53: term] :
( ( ! [SY71: subst,SY72: subst] :
( ( sub @ ( sub @ SV53 @ SY71 ) @ SY72 )
= ( sub @ SV53 @ ( comp @ SY71 @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(227,plain,
! [SV54: term] :
( ( ( sub @ SV54 @ id )
= SV54 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(228,plain,
( ( ( ( ap @ ( sub @ sK3_SX0 @ id ) @ sK9_SY66 )
!= ( ap @ ( sub @ sK5_SY62 @ id ) @ sK11_SY68 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(229,plain,
( ( sK3_SX0 = sK5_SY62 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(230,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK12_SY36 @ SV45 ) )
| ~ ( SV45 @ ( sK14_SY70 @ SV45 ) )
| ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[215]) ).
thf(231,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK10_SY36 @ SV45 ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(232,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK13_SY69 @ SV45 ) )
| ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(233,plain,
! [SV50: subst,SV48: term,SV47: term > $o] :
( ( ( ~ ( SV47 @ SV48 ) )
= $true )
| ( ( ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true )
| ( ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(234,plain,
! [SV50: subst,SV48: term,SV47: term > $o] :
( ( ( SV47 @ SV48 )
= $false )
| ( ( ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true )
| ( ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(235,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(236,plain,
! [SV49: term > $o] :
( ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true )
| ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) )
| ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[220]) ).
thf(237,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(238,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY57: term,SY58: term] :
( ~ ( SV51 @ SY57 )
| ~ ( SV51 @ SY58 )
| ( SV51 @ ( ap @ SY57 @ SY58 ) ) ) )
= $true )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(239,plain,
! [SV51: term > $o] :
( ( ( ! [SY57: term,SY58: term] :
( ~ ( SV51 @ SY57 )
| ~ ( SV51 @ SY58 )
| ( SV51 @ ( ap @ SY57 @ SY58 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(240,plain,
( ( ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[224]) ).
thf(241,plain,
( ( ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(242,plain,
! [SV55: subst,SV53: term] :
( ( ! [SY73: subst] :
( ( sub @ ( sub @ SV53 @ SV55 ) @ SY73 )
= ( sub @ SV53 @ ( comp @ SV55 @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(243,plain,
( ( ( ap @ ( sub @ sK3_SX0 @ id ) @ sK9_SY66 )
= ( ap @ ( sub @ sK5_SY62 @ id ) @ sK11_SY68 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(244,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK12_SY36 @ SV45 ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(245,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK14_SY70 @ SV45 ) )
| ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(246,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
= $true )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(247,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK13_SY69 @ SV45 ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(248,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(249,plain,
! [SV50: subst,SV48: term,SV47: term > $o] :
( ( ( SV47 @ SV48 )
= $false )
| ( ( ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true )
| ( ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(250,plain,
! [SV50: subst,SV48: term,SV47: term > $o,SV56: term] :
( ( ( ~ ( var @ SV56 )
| ( SV47 @ ( sub @ SV56 @ ( push @ SV48 @ SV50 ) ) ) )
= $true )
| ( ( SV47 @ SV48 )
= $false )
| ( ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(251,plain,
! [SV49: term > $o] :
( ( ( ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(252,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(253,plain,
! [SV49: term > $o] :
( ( ( ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(254,plain,
! [SV51: term > $o] :
( ( ( ! [SY57: term,SY58: term] :
( ~ ( SV51 @ SY57 )
| ~ ( SV51 @ SY58 )
| ( SV51 @ ( ap @ SY57 @ SY58 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(255,plain,
! [SV51: term > $o] :
( ( ( ! [SY74: term] :
( ~ ( SV51 @ ( sK15_SY57 @ SV51 ) )
| ~ ( SV51 @ SY74 )
| ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ SY74 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[239]) ).
thf(256,plain,
! [SV57: subst] :
( ( ! [SY75: subst,SY76: subst] :
( ( comp @ ( comp @ SV57 @ SY75 ) @ SY76 )
= ( comp @ SV57 @ ( comp @ SY75 @ SY76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(257,plain,
! [SV58: subst] :
( ( ( comp @ id @ SV58 )
= SV58 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(258,plain,
! [SV59: subst,SV55: subst,SV53: term] :
( ( ( sub @ ( sub @ SV53 @ SV55 ) @ SV59 )
= ( sub @ SV53 @ ( comp @ SV55 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(259,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
= $true )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(260,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK14_SY70 @ SV45 ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(261,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(262,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(263,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
= $true )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[247]) ).
thf(264,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(265,plain,
! [SV50: subst,SV48: term,SV47: term > $o,SV60: term] :
( ( ( ~ ( var @ SV60 )
| ( SV47 @ ( sub @ SV60 @ ( push @ SV48 @ SV50 ) ) ) )
= $true )
| ( ( SV47 @ SV48 )
= $false )
| ( ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(266,plain,
! [SV50: subst,SV48: term,SV47: term > $o,SV56: term] :
( ( ( ~ ( var @ SV56 ) )
= $true )
| ( ( SV47 @ ( sub @ SV56 @ ( push @ SV48 @ SV50 ) ) )
= $true )
| ( ( SV47 @ SV48 )
= $false )
| ( ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(267,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY77: term] :
( ~ ( SV49 @ SY77 )
| ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SY77 @ id ) ) ) )
| ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[251]) ).
thf(268,plain,
! [SV49: term > $o] :
( ( ( ! [SY49: term] :
( ~ ! [SY50: term] :
( ~ ( SV49 @ SY50 )
| ( SV49 @ ( sub @ SY49 @ ( push @ SY50 @ id ) ) ) )
| ( SV49 @ ( lam @ SY49 ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(269,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY78: term] :
( ~ ( SV49 @ SY78 )
| ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SY78 @ id ) ) ) )
| ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[253]) ).
thf(270,plain,
! [SV51: term > $o] :
( ( ( ! [SY79: term] :
( ~ ( SV51 @ ( sK18_SY57 @ SV51 ) )
| ~ ( SV51 @ SY79 )
| ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ SY79 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[254]) ).
thf(271,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK15_SY57 @ SV51 ) )
| ~ ( SV51 @ ( sK19_SY74 @ SV51 ) )
| ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[255]) ).
thf(272,plain,
! [SV61: subst,SV57: subst] :
( ( ! [SY80: subst] :
( ( comp @ ( comp @ SV57 @ SV61 ) @ SY80 )
= ( comp @ SV57 @ ( comp @ SV61 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(273,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(274,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
= $true )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(275,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(276,plain,
! [SV45: term > $o] :
( ( ( ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(277,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[263]) ).
thf(278,plain,
! [SV45: term > $o] :
( ( ( ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(279,plain,
! [SV50: subst,SV48: term,SV47: term > $o,SV60: term] :
( ( ( ~ ( var @ SV60 ) )
= $true )
| ( ( SV47 @ ( sub @ SV60 @ ( push @ SV48 @ SV50 ) ) )
= $true )
| ( ( SV47 @ SV48 )
= $false )
| ( ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(280,plain,
! [SV50: subst,SV48: term,SV47: term > $o,SV56: term] :
( ( ( var @ SV56 )
= $false )
| ( ( SV47 @ ( sub @ SV56 @ ( push @ SV48 @ SV50 ) ) )
= $true )
| ( ( SV47 @ SV48 )
= $false )
| ( ( SV47 @ ( sub @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(281,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY77: term] :
( ~ ( SV49 @ SY77 )
| ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SY77 @ id ) ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(282,plain,
! [SV49: term > $o] :
( ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[267]) ).
thf(283,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY81: term] :
( ~ ( SV49 @ SY81 )
| ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SY81 @ id ) ) ) )
| ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[268]) ).
thf(284,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY78: term] :
( ~ ( SV49 @ SY78 )
| ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SY78 @ id ) ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(285,plain,
! [SV49: term > $o] :
( ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(286,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK18_SY57 @ SV51 ) )
| ~ ( SV51 @ ( sK21_SY79 @ SV51 ) )
| ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[270]) ).
thf(287,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK15_SY57 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(288,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK19_SY74 @ SV51 ) )
| ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[271]) ).
thf(289,plain,
! [SV62: subst,SV61: subst,SV57: subst] :
( ( ( comp @ ( comp @ SV57 @ SV61 ) @ SV62 )
= ( comp @ SV57 @ ( comp @ SV61 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(290,plain,
! [SV45: term > $o] :
( ( ( ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[273]) ).
thf(291,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(292,plain,
! [SV45: term > $o] :
( ( ( ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(293,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK22_SY38 @ SV45 ) )
| ( SV45 @ ( lam @ ( sK22_SY38 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[276]) ).
thf(294,plain,
! [SV45: term > $o] :
( ( ( ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(295,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK23_SY38 @ SV45 ) )
| ( SV45 @ ( lam @ ( sK23_SY38 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[278]) ).
thf(296,plain,
! [SV50: subst,SV48: term,SV47: term > $o,SV60: term] :
( ( ( var @ SV60 )
= $false )
| ( ( SV47 @ ( sub @ SV60 @ ( push @ SV48 @ SV50 ) ) )
= $true )
| ( ( SV47 @ SV48 )
= $false )
| ( ( var @ ( sK6_SY54 @ SV48 @ SV50 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(297,plain,
! [SV49: term > $o] :
( ( ( ! [SY77: term] :
( ~ ( SV49 @ SY77 )
| ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SY77 @ id ) ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(298,plain,
! [SV63: term,SV49: term > $o] :
( ( ( ! [SY82: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY82 ) ) )
| ( SV49 @ ( sub @ SV63 @ SY82 ) ) ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(299,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY81: term] :
( ~ ( SV49 @ SY81 )
| ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SY81 @ id ) ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(300,plain,
! [SV49: term > $o] :
( ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[283]) ).
thf(301,plain,
! [SV49: term > $o] :
( ( ( ! [SY78: term] :
( ~ ( SV49 @ SY78 )
| ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SY78 @ id ) ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(302,plain,
! [SV64: term,SV49: term > $o] :
( ( ( ! [SY84: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY84 ) ) )
| ( SV49 @ ( sub @ SV64 @ SY84 ) ) ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(303,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK18_SY57 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(304,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK21_SY79 @ SV51 ) )
| ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[286]) ).
thf(305,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[287]) ).
thf(306,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(307,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[288]) ).
thf(308,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK24_SY38 @ SV45 ) )
| ( SV45 @ ( lam @ ( sK24_SY38 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[290]) ).
thf(309,plain,
! [SV45: term > $o] :
( ( ( ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(310,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK25_SY38 @ SV45 ) )
| ( SV45 @ ( lam @ ( sK25_SY38 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[292]) ).
thf(311,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK22_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(312,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( lam @ ( sK22_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[293]) ).
thf(313,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK26_SY38 @ SV45 ) )
| ( SV45 @ ( lam @ ( sK26_SY38 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[294]) ).
thf(314,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK23_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(315,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( lam @ ( sK23_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[295]) ).
thf(316,plain,
! [SV65: term,SV49: term > $o] :
( ( ( ~ ( SV49 @ SV65 )
| ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(317,plain,
! [SV63: term,SV66: subst,SV49: term > $o] :
( ( ( ~ ! [SY86: term] :
( ~ ( var @ SY86 )
| ( SV49 @ ( sub @ SY86 @ SV66 ) ) )
| ( SV49 @ ( sub @ SV63 @ SV66 ) ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(318,plain,
! [SV49: term > $o] :
( ( ( ! [SY81: term] :
( ~ ( SV49 @ SY81 )
| ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SY81 @ id ) ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(319,plain,
! [SV67: term,SV49: term > $o] :
( ( ( ! [SY87: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY87 ) ) )
| ( SV49 @ ( sub @ SV67 @ SY87 ) ) ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(320,plain,
! [SV68: term,SV49: term > $o] :
( ( ( ~ ( SV49 @ SV68 )
| ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(321,plain,
! [SV64: term,SV69: subst,SV49: term > $o] :
( ( ( ~ ! [SY89: term] :
( ~ ( var @ SY89 )
| ( SV49 @ ( sub @ SY89 @ SV69 ) ) )
| ( SV49 @ ( sub @ SV64 @ SV69 ) ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(322,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
= $true )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(323,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(324,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[304]) ).
thf(325,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(326,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
= $true )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(327,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(328,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK24_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(329,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( lam @ ( sK24_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[308]) ).
thf(330,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK27_SY38 @ SV45 ) )
| ( SV45 @ ( lam @ ( sK27_SY38 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[309]) ).
thf(331,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK25_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(332,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( lam @ ( sK25_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[310]) ).
thf(333,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK22_SY38 @ SV45 ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[311]) ).
thf(334,plain,
! [SV70: term,SV45: term > $o] :
( ( ( SV45 @ SV70 )
= $true )
| ( ( SV45 @ ( lam @ ( sK22_SY38 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(335,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK26_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(336,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( lam @ ( sK26_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[313]) ).
thf(337,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK23_SY38 @ SV45 ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[314]) ).
thf(338,plain,
! [SV71: term,SV45: term > $o] :
( ( ( SV45 @ SV71 )
= $true )
| ( ( SV45 @ ( lam @ ( sK23_SY38 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(339,plain,
! [SV65: term,SV49: term > $o] :
( ( ( ~ ( SV49 @ SV65 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(340,plain,
! [SV63: term,SV66: subst,SV49: term > $o] :
( ( ( ~ ! [SY86: term] :
( ~ ( var @ SY86 )
| ( SV49 @ ( sub @ SY86 @ SV66 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ SV63 @ SV66 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(341,plain,
! [SV72: term,SV49: term > $o] :
( ( ( ~ ( SV49 @ SV72 )
| ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(342,plain,
! [SV67: term,SV73: subst,SV49: term > $o] :
( ( ( ~ ! [SY90: term] :
( ~ ( var @ SY90 )
| ( SV49 @ ( sub @ SY90 @ SV73 ) ) )
| ( SV49 @ ( sub @ SV67 @ SV73 ) ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(343,plain,
! [SV68: term,SV49: term > $o] :
( ( ( ~ ( SV49 @ SV68 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(344,plain,
! [SV64: term,SV69: subst,SV49: term > $o] :
( ( ( ~ ! [SY89: term] :
( ~ ( var @ SY89 )
| ( SV49 @ ( sub @ SY89 @ SV69 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ SV64 @ SV69 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(345,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(346,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
= $true )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(347,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(348,plain,
! [SV51: term > $o] :
( ( ( ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(349,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(350,plain,
! [SV51: term > $o] :
( ( ( ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(351,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK24_SY38 @ SV45 ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[328]) ).
thf(352,plain,
! [SV74: term,SV45: term > $o] :
( ( ( SV45 @ SV74 )
= $true )
| ( ( SV45 @ ( lam @ ( sK24_SY38 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(353,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK27_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(354,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( lam @ ( sK27_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(355,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK25_SY38 @ SV45 ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[331]) ).
thf(356,plain,
! [SV75: term,SV45: term > $o] :
( ( ( SV45 @ SV75 )
= $true )
| ( ( SV45 @ ( lam @ ( sK25_SY38 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(357,plain,
! [SV76: term,SV45: term > $o] :
( ( ( SV45 @ SV76 )
= $true )
| ( ( SV45 @ ( sK22_SY38 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK10_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(358,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK26_SY38 @ SV45 ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[335]) ).
thf(359,plain,
! [SV77: term,SV45: term > $o] :
( ( ( SV45 @ SV77 )
= $true )
| ( ( SV45 @ ( lam @ ( sK26_SY38 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(360,plain,
! [SV78: term,SV45: term > $o] :
( ( ( SV45 @ SV78 )
= $true )
| ( ( SV45 @ ( sK23_SY38 @ SV45 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK10_SY36 @ SV45 ) @ ( sK13_SY69 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(361,plain,
! [SV65: term,SV49: term > $o] :
( ( ( SV49 @ SV65 )
= $false )
| ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(362,plain,
! [SV63: term,SV66: subst,SV49: term > $o] :
( ( ( ! [SY86: term] :
( ~ ( var @ SY86 )
| ( SV49 @ ( sub @ SY86 @ SV66 ) ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV63 @ SV66 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(363,plain,
! [SV72: term,SV49: term > $o] :
( ( ( ~ ( SV49 @ SV72 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(364,plain,
! [SV67: term,SV73: subst,SV49: term > $o] :
( ( ( ~ ! [SY90: term] :
( ~ ( var @ SY90 )
| ( SV49 @ ( sub @ SY90 @ SV73 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ SV67 @ SV73 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(365,plain,
! [SV68: term,SV49: term > $o] :
( ( ( SV49 @ SV68 )
= $false )
| ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(366,plain,
! [SV64: term,SV69: subst,SV49: term > $o] :
( ( ( ! [SY89: term] :
( ~ ( var @ SY89 )
| ( SV49 @ ( sub @ SY89 @ SV69 ) ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV64 @ SV69 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(367,plain,
! [SV51: term > $o] :
( ( ( ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(368,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(369,plain,
! [SV51: term > $o] :
( ( ( ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(370,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY91: term] :
( ~ ( SV51 @ SY91 )
| ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SY91 @ id ) ) ) )
| ( SV51 @ ( lam @ ( sK28_SY59 @ SV51 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[348]) ).
thf(371,plain,
! [SV51: term > $o] :
( ( ( ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(372,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY92: term] :
( ~ ( SV51 @ SY92 )
| ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SY92 @ id ) ) ) )
| ( SV51 @ ( lam @ ( sK29_SY59 @ SV51 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[350]) ).
thf(373,plain,
! [SV79: term,SV45: term > $o] :
( ( ( SV45 @ SV79 )
= $true )
| ( ( SV45 @ ( sK24_SY38 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK12_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(374,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK27_SY38 @ SV45 ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[353]) ).
thf(375,plain,
! [SV80: term,SV45: term > $o] :
( ( ( SV45 @ SV80 )
= $true )
| ( ( SV45 @ ( lam @ ( sK27_SY38 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(376,plain,
! [SV81: term,SV45: term > $o] :
( ( ( SV45 @ SV81 )
= $true )
| ( ( SV45 @ ( sK25_SY38 @ SV45 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK12_SY36 @ SV45 ) @ ( sK14_SY70 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(377,plain,
! [SV82: term,SV45: term > $o] :
( ( ( SV45 @ SV82 )
= $true )
| ( ( SV45 @ ( sK26_SY38 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK13_SY69 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(378,plain,
! [SV65: term,SV83: term,SV49: term > $o] :
( ( ( ! [SY93: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY93 ) ) )
| ( SV49 @ ( sub @ SV83 @ SY93 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV49 @ SV65 )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(379,plain,
! [SV49: term > $o,SV66: subst,SV63: term] :
( ( ( ~ ( var @ ( sK30_SY86 @ SV63 @ SV66 @ SV49 ) )
| ( SV49 @ ( sub @ ( sK30_SY86 @ SV63 @ SV66 @ SV49 ) @ SV66 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV63 @ SV66 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[362]) ).
thf(380,plain,
! [SV72: term,SV49: term > $o] :
( ( ( SV49 @ SV72 )
= $false )
| ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(381,plain,
! [SV67: term,SV73: subst,SV49: term > $o] :
( ( ( ! [SY90: term] :
( ~ ( var @ SY90 )
| ( SV49 @ ( sub @ SY90 @ SV73 ) ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV67 @ SV73 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(382,plain,
! [SV68: term,SV84: term,SV49: term > $o] :
( ( ( ! [SY95: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY95 ) ) )
| ( SV49 @ ( sub @ SV84 @ SY95 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV49 @ SV68 )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(383,plain,
! [SV49: term > $o,SV69: subst,SV64: term] :
( ( ( ~ ( var @ ( sK31_SY89 @ SV64 @ SV69 @ SV49 ) )
| ( SV49 @ ( sub @ ( sK31_SY89 @ SV64 @ SV69 @ SV49 ) @ SV69 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV64 @ SV69 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[366]) ).
thf(384,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY97: term] :
( ~ ( SV51 @ SY97 )
| ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SY97 @ id ) ) ) )
| ( SV51 @ ( lam @ ( sK32_SY59 @ SV51 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[367]) ).
thf(385,plain,
! [SV51: term > $o] :
( ( ( ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(386,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY98: term] :
( ~ ( SV51 @ SY98 )
| ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SY98 @ id ) ) ) )
| ( SV51 @ ( lam @ ( sK33_SY59 @ SV51 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[369]) ).
thf(387,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY91: term] :
( ~ ( SV51 @ SY91 )
| ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SY91 @ id ) ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(388,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( lam @ ( sK28_SY59 @ SV51 ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[370]) ).
thf(389,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY99: term] :
( ~ ( SV51 @ SY99 )
| ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SY99 @ id ) ) ) )
| ( SV51 @ ( lam @ ( sK34_SY59 @ SV51 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[371]) ).
thf(390,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY92: term] :
( ~ ( SV51 @ SY92 )
| ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SY92 @ id ) ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(391,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( lam @ ( sK29_SY59 @ SV51 ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[372]) ).
thf(392,plain,
! [SV85: term,SV45: term > $o] :
( ( ( SV45 @ SV85 )
= $true )
| ( ( SV45 @ ( sK27_SY38 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK14_SY70 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(393,plain,
! [SV65: term,SV83: term,SV86: subst,SV49: term > $o] :
( ( ( ~ ! [SY100: term] :
( ~ ( var @ SY100 )
| ( SV49 @ ( sub @ SY100 @ SV86 ) ) )
| ( SV49 @ ( sub @ SV83 @ SV86 ) ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV49 @ SV65 )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(394,plain,
! [SV49: term > $o,SV66: subst,SV63: term] :
( ( ( ~ ( var @ ( sK30_SY86 @ SV63 @ SV66 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV63 @ SV66 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(395,plain,
! [SV66: subst,SV63: term,SV49: term > $o] :
( ( ( SV49 @ ( sub @ ( sK30_SY86 @ SV63 @ SV66 @ SV49 ) @ SV66 ) )
= $false )
| ( ( SV49 @ ( sub @ SV63 @ SV66 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[379]) ).
thf(396,plain,
! [SV72: term,SV87: term,SV49: term > $o] :
( ( ( ! [SY101: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY101 ) ) )
| ( SV49 @ ( sub @ SV87 @ SY101 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV49 @ SV72 )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(397,plain,
! [SV49: term > $o,SV73: subst,SV67: term] :
( ( ( ~ ( var @ ( sK35_SY90 @ SV67 @ SV73 @ SV49 ) )
| ( SV49 @ ( sub @ ( sK35_SY90 @ SV67 @ SV73 @ SV49 ) @ SV73 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV67 @ SV73 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[381]) ).
thf(398,plain,
! [SV68: term,SV84: term,SV88: subst,SV49: term > $o] :
( ( ( ~ ! [SY103: term] :
( ~ ( var @ SY103 )
| ( SV49 @ ( sub @ SY103 @ SV88 ) ) )
| ( SV49 @ ( sub @ SV84 @ SV88 ) ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV49 @ SV68 )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(399,plain,
! [SV49: term > $o,SV69: subst,SV64: term] :
( ( ( ~ ( var @ ( sK31_SY89 @ SV64 @ SV69 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV64 @ SV69 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(400,plain,
! [SV69: subst,SV64: term,SV49: term > $o] :
( ( ( SV49 @ ( sub @ ( sK31_SY89 @ SV64 @ SV69 @ SV49 ) @ SV69 ) )
= $false )
| ( ( SV49 @ ( sub @ SV64 @ SV69 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[383]) ).
thf(401,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY97: term] :
( ~ ( SV51 @ SY97 )
| ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SY97 @ id ) ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(402,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( lam @ ( sK32_SY59 @ SV51 ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[384]) ).
thf(403,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY104: term] :
( ~ ( SV51 @ SY104 )
| ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SY104 @ id ) ) ) )
| ( SV51 @ ( lam @ ( sK36_SY59 @ SV51 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[385]) ).
thf(404,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY98: term] :
( ~ ( SV51 @ SY98 )
| ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SY98 @ id ) ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(405,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( lam @ ( sK33_SY59 @ SV51 ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[386]) ).
thf(406,plain,
! [SV51: term > $o] :
( ( ( ! [SY91: term] :
( ~ ( SV51 @ SY91 )
| ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SY91 @ id ) ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[387]) ).
thf(407,plain,
! [SV89: term,SV51: term > $o] :
( ( ( SV51 @ SV89 )
= $true )
| ( ( SV51 @ ( lam @ ( sK28_SY59 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(408,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY99: term] :
( ~ ( SV51 @ SY99 )
| ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SY99 @ id ) ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(409,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( lam @ ( sK34_SY59 @ SV51 ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(410,plain,
! [SV51: term > $o] :
( ( ( ! [SY92: term] :
( ~ ( SV51 @ SY92 )
| ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SY92 @ id ) ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(411,plain,
! [SV90: term,SV51: term > $o] :
( ( ( SV51 @ SV90 )
= $true )
| ( ( SV51 @ ( lam @ ( sK29_SY59 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(412,plain,
! [SV65: term,SV83: term,SV86: subst,SV49: term > $o] :
( ( ( ~ ! [SY100: term] :
( ~ ( var @ SY100 )
| ( SV49 @ ( sub @ SY100 @ SV86 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ SV83 @ SV86 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV49 @ SV65 )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(413,plain,
! [SV49: term > $o,SV66: subst,SV63: term] :
( ( ( var @ ( sK30_SY86 @ SV63 @ SV66 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sub @ SV63 @ SV66 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK16_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[394]) ).
thf(414,plain,
! [SV72: term,SV87: term,SV91: subst,SV49: term > $o] :
( ( ( ~ ! [SY105: term] :
( ~ ( var @ SY105 )
| ( SV49 @ ( sub @ SY105 @ SV91 ) ) )
| ( SV49 @ ( sub @ SV87 @ SV91 ) ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV49 @ SV72 )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(415,plain,
! [SV49: term > $o,SV73: subst,SV67: term] :
( ( ( ~ ( var @ ( sK35_SY90 @ SV67 @ SV73 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV67 @ SV73 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(416,plain,
! [SV73: subst,SV67: term,SV49: term > $o] :
( ( ( SV49 @ ( sub @ ( sK35_SY90 @ SV67 @ SV73 @ SV49 ) @ SV73 ) )
= $false )
| ( ( SV49 @ ( sub @ SV67 @ SV73 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(417,plain,
! [SV68: term,SV84: term,SV88: subst,SV49: term > $o] :
( ( ( ~ ! [SY103: term] :
( ~ ( var @ SY103 )
| ( SV49 @ ( sub @ SY103 @ SV88 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ SV84 @ SV88 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV49 @ SV68 )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(418,plain,
! [SV49: term > $o,SV69: subst,SV64: term] :
( ( ( var @ ( sK31_SY89 @ SV64 @ SV69 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sub @ SV64 @ SV69 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK17_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[399]) ).
thf(419,plain,
! [SV51: term > $o] :
( ( ( ! [SY97: term] :
( ~ ( SV51 @ SY97 )
| ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SY97 @ id ) ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[401]) ).
thf(420,plain,
! [SV92: term,SV51: term > $o] :
( ( ( SV51 @ SV92 )
= $true )
| ( ( SV51 @ ( lam @ ( sK32_SY59 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(421,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY104: term] :
( ~ ( SV51 @ SY104 )
| ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SY104 @ id ) ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(422,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( lam @ ( sK36_SY59 @ SV51 ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(423,plain,
! [SV51: term > $o] :
( ( ( ! [SY98: term] :
( ~ ( SV51 @ SY98 )
| ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SY98 @ id ) ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[404]) ).
thf(424,plain,
! [SV93: term,SV51: term > $o] :
( ( ( SV51 @ SV93 )
= $true )
| ( ( SV51 @ ( lam @ ( sK33_SY59 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(425,plain,
! [SV94: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV94 )
| ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SV94 @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(426,plain,
! [SV51: term > $o] :
( ( ( ! [SY99: term] :
( ~ ( SV51 @ SY99 )
| ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SY99 @ id ) ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[408]) ).
thf(427,plain,
! [SV95: term,SV51: term > $o] :
( ( ( SV51 @ SV95 )
= $true )
| ( ( SV51 @ ( lam @ ( sK34_SY59 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(428,plain,
! [SV96: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV96 )
| ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SV96 @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(429,plain,
! [SV65: term,SV83: term,SV86: subst,SV49: term > $o] :
( ( ( ! [SY100: term] :
( ~ ( var @ SY100 )
| ( SV49 @ ( sub @ SY100 @ SV86 ) ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV83 @ SV86 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV49 @ SV65 )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(430,plain,
! [SV72: term,SV87: term,SV91: subst,SV49: term > $o] :
( ( ( ~ ! [SY105: term] :
( ~ ( var @ SY105 )
| ( SV49 @ ( sub @ SY105 @ SV91 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ SV87 @ SV91 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV49 @ SV72 )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(431,plain,
! [SV49: term > $o,SV73: subst,SV67: term] :
( ( ( var @ ( sK35_SY90 @ SV67 @ SV73 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sub @ SV67 @ SV73 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK20_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[415]) ).
thf(432,plain,
! [SV68: term,SV84: term,SV88: subst,SV49: term > $o] :
( ( ( ! [SY103: term] :
( ~ ( var @ SY103 )
| ( SV49 @ ( sub @ SY103 @ SV88 ) ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV84 @ SV88 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV49 @ SV68 )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(433,plain,
! [SV97: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV97 )
| ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SV97 @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(434,plain,
! [SV51: term > $o] :
( ( ( ! [SY104: term] :
( ~ ( SV51 @ SY104 )
| ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SY104 @ id ) ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[421]) ).
thf(435,plain,
! [SV98: term,SV51: term > $o] :
( ( ( SV51 @ SV98 )
= $true )
| ( ( SV51 @ ( lam @ ( sK36_SY59 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(436,plain,
! [SV99: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV99 )
| ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SV99 @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(437,plain,
! [SV94: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV94 ) )
= $true )
| ( ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(438,plain,
! [SV100: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV100 )
| ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SV100 @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(439,plain,
! [SV96: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV96 ) )
= $true )
| ( ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SV96 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(440,plain,
! [SV49: term > $o,SV86: subst,SV83: term,SV65: term] :
( ( ( ~ ( var @ ( sK37_SY100 @ SV65 @ SV83 @ SV86 @ SV49 ) )
| ( SV49 @ ( sub @ ( sK37_SY100 @ SV65 @ SV83 @ SV86 @ SV49 ) @ SV86 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV83 @ SV86 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV49 @ SV65 )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[429]) ).
thf(441,plain,
! [SV72: term,SV87: term,SV91: subst,SV49: term > $o] :
( ( ( ! [SY105: term] :
( ~ ( var @ SY105 )
| ( SV49 @ ( sub @ SY105 @ SV91 ) ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV87 @ SV91 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV49 @ SV72 )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(442,plain,
! [SV49: term > $o,SV88: subst,SV84: term,SV68: term] :
( ( ( ~ ( var @ ( sK38_SY103 @ SV68 @ SV84 @ SV88 @ SV49 ) )
| ( SV49 @ ( sub @ ( sK38_SY103 @ SV68 @ SV84 @ SV88 @ SV49 ) @ SV88 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV84 @ SV88 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV49 @ SV68 )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[432]) ).
thf(443,plain,
! [SV97: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV97 ) )
= $true )
| ( ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SV97 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[433]) ).
thf(444,plain,
! [SV101: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV101 )
| ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SV101 @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(445,plain,
! [SV99: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV99 ) )
= $true )
| ( ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SV99 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[436]) ).
thf(446,plain,
! [SV94: term,SV51: term > $o] :
( ( ( SV51 @ SV94 )
= $false )
| ( ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(447,plain,
! [SV100: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV100 ) )
= $true )
| ( ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SV100 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[438]) ).
thf(448,plain,
! [SV96: term,SV51: term > $o] :
( ( ( SV51 @ SV96 )
= $false )
| ( ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SV96 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(449,plain,
! [SV49: term > $o,SV86: subst,SV83: term,SV65: term] :
( ( ( ~ ( var @ ( sK37_SY100 @ SV65 @ SV83 @ SV86 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV83 @ SV86 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV49 @ SV65 )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(450,plain,
! [SV86: subst,SV83: term,SV65: term,SV49: term > $o] :
( ( ( SV49 @ ( sub @ ( sK37_SY100 @ SV65 @ SV83 @ SV86 @ SV49 ) @ SV86 ) )
= $false )
| ( ( SV49 @ ( sub @ SV83 @ SV86 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV49 @ SV65 )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[440]) ).
thf(451,plain,
! [SV49: term > $o,SV91: subst,SV87: term,SV72: term] :
( ( ( ~ ( var @ ( sK39_SY105 @ SV72 @ SV87 @ SV91 @ SV49 ) )
| ( SV49 @ ( sub @ ( sK39_SY105 @ SV72 @ SV87 @ SV91 @ SV49 ) @ SV91 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV87 @ SV91 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV49 @ SV72 )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[441]) ).
thf(452,plain,
! [SV49: term > $o,SV88: subst,SV84: term,SV68: term] :
( ( ( ~ ( var @ ( sK38_SY103 @ SV68 @ SV84 @ SV88 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV84 @ SV88 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV49 @ SV68 )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(453,plain,
! [SV88: subst,SV84: term,SV68: term,SV49: term > $o] :
( ( ( SV49 @ ( sub @ ( sK38_SY103 @ SV68 @ SV84 @ SV88 @ SV49 ) @ SV88 ) )
= $false )
| ( ( SV49 @ ( sub @ SV84 @ SV88 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV49 @ SV68 )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[442]) ).
thf(454,plain,
! [SV97: term,SV51: term > $o] :
( ( ( SV51 @ SV97 )
= $false )
| ( ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SV97 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(455,plain,
! [SV101: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV101 ) )
= $true )
| ( ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SV101 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[444]) ).
thf(456,plain,
! [SV99: term,SV51: term > $o] :
( ( ( SV51 @ SV99 )
= $false )
| ( ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SV99 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(457,plain,
! [SV94: term,SV102: term,SV51: term > $o] :
( ( ( SV51 @ SV102 )
= $true )
| ( ( SV51 @ ( sub @ ( sK28_SY59 @ SV51 ) @ ( push @ SV94 @ id ) ) )
= $true )
| ( ( SV51 @ SV94 )
= $false )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(458,plain,
! [SV100: term,SV51: term > $o] :
( ( ( SV51 @ SV100 )
= $false )
| ( ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SV100 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(459,plain,
! [SV96: term,SV103: term,SV51: term > $o] :
( ( ( SV51 @ SV103 )
= $true )
| ( ( SV51 @ ( sub @ ( sK29_SY59 @ SV51 ) @ ( push @ SV96 @ id ) ) )
= $true )
| ( ( SV51 @ SV96 )
= $false )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK19_SY74 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(460,plain,
! [SV49: term > $o,SV86: subst,SV83: term,SV65: term] :
( ( ( var @ ( sK37_SY100 @ SV65 @ SV83 @ SV86 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sub @ SV83 @ SV86 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK16_SY49 @ SV49 ) @ ( push @ SV65 @ id ) ) )
= $true )
| ( ( SV49 @ SV65 )
= $false )
| ( ( SV49 @ ( sK4_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(461,plain,
! [SV49: term > $o,SV91: subst,SV87: term,SV72: term] :
( ( ( ~ ( var @ ( sK39_SY105 @ SV72 @ SV87 @ SV91 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV87 @ SV91 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV49 @ SV72 )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(462,plain,
! [SV91: subst,SV87: term,SV72: term,SV49: term > $o] :
( ( ( SV49 @ ( sub @ ( sK39_SY105 @ SV72 @ SV87 @ SV91 @ SV49 ) @ SV91 ) )
= $false )
| ( ( SV49 @ ( sub @ SV87 @ SV91 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV49 @ SV72 )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[451]) ).
thf(463,plain,
! [SV49: term > $o,SV88: subst,SV84: term,SV68: term] :
( ( ( var @ ( sK38_SY103 @ SV68 @ SV84 @ SV88 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sub @ SV84 @ SV88 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK17_SY49 @ SV49 ) @ ( push @ SV68 @ id ) ) )
= $true )
| ( ( SV49 @ SV68 )
= $false )
| ( ( SV49 @ ( ap @ ( sK4_SY47 @ SV49 ) @ ( sK7_SY65 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(464,plain,
! [SV97: term,SV104: term,SV51: term > $o] :
( ( ( SV51 @ SV104 )
= $true )
| ( ( SV51 @ ( sub @ ( sK32_SY59 @ SV51 ) @ ( push @ SV97 @ id ) ) )
= $true )
| ( ( SV51 @ SV97 )
= $false )
| ( ( SV51 @ ( sK18_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(465,plain,
! [SV101: term,SV51: term > $o] :
( ( ( SV51 @ SV101 )
= $false )
| ( ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SV101 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(466,plain,
! [SV99: term,SV105: term,SV51: term > $o] :
( ( ( SV51 @ SV105 )
= $true )
| ( ( SV51 @ ( sub @ ( sK33_SY59 @ SV51 ) @ ( push @ SV99 @ id ) ) )
= $true )
| ( ( SV51 @ SV99 )
= $false )
| ( ( SV51 @ ( ap @ ( sK18_SY57 @ SV51 ) @ ( sK21_SY79 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(467,plain,
! [SV100: term,SV106: term,SV51: term > $o] :
( ( ( SV51 @ SV106 )
= $true )
| ( ( SV51 @ ( sub @ ( sK34_SY59 @ SV51 ) @ ( push @ SV100 @ id ) ) )
= $true )
| ( ( SV51 @ SV100 )
= $false )
| ( ( SV51 @ ( sK19_SY74 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK8_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(468,plain,
! [SV49: term > $o,SV91: subst,SV87: term,SV72: term] :
( ( ( var @ ( sK39_SY105 @ SV72 @ SV87 @ SV91 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sub @ SV87 @ SV91 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK20_SY49 @ SV49 ) @ ( push @ SV72 @ id ) ) )
= $true )
| ( ( SV49 @ SV72 )
= $false )
| ( ( SV49 @ ( sK7_SY65 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(469,plain,
! [SV101: term,SV107: term,SV51: term > $o] :
( ( ( SV51 @ SV107 )
= $true )
| ( ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SV101 @ id ) ) )
= $true )
| ( ( SV51 @ SV101 )
= $false )
| ( ( SV51 @ ( sK21_SY79 @ SV51 ) )
= $true )
| ( ( var @ ( sK8_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(470,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,469,468,467,466,464,463,462,460,459,457,453,450,435,431,427,424,420,418,416,413,411,407,400,395,392,377,376,375,373,360,359,357,356,352,338,334,296,289,280,258,257,243,229,227,211,167,160,158,145,144,143,133,132,122,120,82,67,66,62,59,58,56,46,41,37,31,23,22]) ).
thf(471,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[470]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : ALG256^1 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.06/0.11 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Thu Jun 9 00:52:22 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.15/0.32 .
% 0.15/0.33
% 0.15/0.33 No.of.Axioms: 0
% 0.15/0.33
% 0.15/0.33 Length.of.Defs: 38092
% 0.15/0.33
% 0.15/0.33 Contains.Choice.Funs: false
% 0.15/0.34 .
% 0.15/0.34 (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)........................................................
% 1.46/1.64
% 1.46/1.64 ********************************
% 1.46/1.64 * All subproblems solved! *
% 1.46/1.64 ********************************
% 1.46/1.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:470,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.64/1.82
% 1.64/1.82 %**** Beginning of derivation protocol ****
% 1.64/1.82 % SZS output start CNFRefutation
% See solution above
% 1.64/1.82
% 1.64/1.82 %**** End of derivation protocol ****
% 1.64/1.82 %**** no. of clauses in derivation: 471 ****
% 1.64/1.82 %**** clause counter: 470 ****
% 1.64/1.82
% 1.64/1.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:0,ps:3,u:6,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:470,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------