TSTP Solution File: ALG264^3 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ALG264^3 : 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 17:25:36 EDT 2022
% Result : Theorem 1.51s 1.69s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 289
% Syntax : Number of formulae : 867 ( 350 unt; 175 typ; 113 def)
% Number of atoms : 5810 (2594 equ; 0 cnn)
% Maximal formula atoms : 5 ( 8 avg)
% Number of connectives : 23748 (3697 ~;3879 |; 4 &;15152 @)
% ( 2 <=>;1014 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 1205 (1205 >; 0 *; 0 +; 0 <<)
% Number of symbols : 176 ( 173 usr; 115 con; 0-4 aty)
% Number of variables : 5170 ( 39 ^5126 !; 5 ?;5170 :)
% 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_SY72,type,
sK10_SY72: ( term > $o ) > term ).
thf(tp_sK11_SY57,type,
sK11_SY57: ( term > $o ) > term ).
thf(tp_sK12_SX0,type,
sK12_SX0: subst > term > subst > $o ).
thf(tp_sK13_SY49,type,
sK13_SY49: ( term > $o ) > term ).
thf(tp_sK14_SY49,type,
sK14_SY49: ( term > $o ) > term ).
thf(tp_sK15_SY57,type,
sK15_SY57: ( term > $o ) > term ).
thf(tp_sK16_SY94,type,
sK16_SY94: ( term > $o ) > term ).
thf(tp_sK17_SY78,type,
sK17_SY78: ( subst > term > term ) > subst ).
thf(tp_sK18_SY100,type,
sK18_SY100: term > $o ).
thf(tp_sK19_SY49,type,
sK19_SY49: ( term > $o ) > term ).
thf(tp_sK1_SY15,type,
sK1_SY15: ( term > $o ) > term ).
thf(tp_sK20_SY116,type,
sK20_SY116: ( term > $o ) > term ).
thf(tp_sK21_SY118,type,
sK21_SY118: ( subst > term > term ) > term ).
thf(tp_sK22_SY89,type,
sK22_SY89: ( subst > term > term ) > subst ).
thf(tp_sK23_SY38,type,
sK23_SY38: ( term > $o ) > term ).
thf(tp_sK24_SY38,type,
sK24_SY38: ( term > $o ) > term ).
thf(tp_sK25_SY135,type,
sK25_SY135: ( subst > term > term ) > subst ).
thf(tp_sK26_SY136,type,
sK26_SY136: ( subst > term > term ) > term ).
thf(tp_sK27_SY97,type,
sK27_SY97: ( subst > term > term ) > subst ).
thf(tp_sK28_SY38,type,
sK28_SY38: ( term > $o ) > term ).
thf(tp_sK29_SY38,type,
sK29_SY38: ( term > $o ) > term ).
thf(tp_sK2_SY35,type,
sK2_SY35: ( term > $o ) > term ).
thf(tp_sK30_SY38,type,
sK30_SY38: ( term > $o ) > term ).
thf(tp_sK31_SY142,type,
sK31_SY142: ( subst > term > term ) > subst ).
thf(tp_sK32_SY143,type,
sK32_SY143: ( subst > term > term ) > term ).
thf(tp_sK33_SY38,type,
sK33_SY38: ( term > $o ) > term ).
thf(tp_sK34_SY154,type,
sK34_SY154: ( subst > term > term ) > subst ).
thf(tp_sK35_SY59,type,
sK35_SY59: ( term > $o ) > term ).
thf(tp_sK36_SY59,type,
sK36_SY59: ( term > $o ) > term ).
thf(tp_sK37_SY132,type,
sK37_SY132: term ).
thf(tp_sK38_SY145,type,
sK38_SY145: term > subst > ( term > $o ) > term ).
thf(tp_sK39_SY148,type,
sK39_SY148: term > subst > ( term > $o ) > term ).
thf(tp_sK3_SY47,type,
sK3_SY47: ( term > $o ) > term ).
thf(tp_sK40_SY59,type,
sK40_SY59: ( term > $o ) > term ).
thf(tp_sK41_SY59,type,
sK41_SY59: ( term > $o ) > term ).
thf(tp_sK42_SY59,type,
sK42_SY59: ( term > $o ) > term ).
thf(tp_sK43_SY149,type,
sK43_SY149: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(tp_sK44_SY171,type,
sK44_SY171: term ).
thf(tp_sK45_SY158,type,
sK45_SY158: term > subst > ( term > $o ) > term ).
thf(tp_sK46_SY59,type,
sK46_SY59: ( term > $o ) > term ).
thf(tp_sK47_SY179,type,
sK47_SY179: ( subst > term > term ) > ( subst > term > term ) > term ).
thf(tp_sK48_SY187,type,
sK48_SY187: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(tp_sK49_SY182,type,
sK49_SY182: term > term > subst > ( term > $o ) > term ).
thf(tp_sK4_SY54,type,
sK4_SY54: term > subst > ( term > $o ) > term ).
thf(tp_sK50_SY185,type,
sK50_SY185: term > term > subst > ( term > $o ) > term ).
thf(tp_sK51_SY188,type,
sK51_SY188: term > term > subst > ( term > $o ) > term ).
thf(tp_sK5_SY62,type,
sK5_SY62: ( term > $o ) > term ).
thf(tp_sK6_SY56,type,
sK6_SY56: ( term > $o ) > term ).
thf(tp_sK7_SY36,type,
sK7_SY36: ( term > $o ) > term ).
thf(tp_sK8_SY36,type,
sK8_SY36: ( term > $o ) > term ).
thf(tp_sK9_SY66,type,
sK9_SY66: ( term > $o ) > term ).
thf(tp_sh,type,
sh: subst ).
thf(tp_shinj,type,
shinj: $o ).
thf(tp_sub,type,
sub: term > subst > term ).
thf(tp_substmonoid,type,
substmonoid: $o ).
thf(tp_substmonoid_gthm,type,
substmonoid_gthm: $o ).
thf(tp_substmonoid_lthm,type,
substmonoid_lthm: $o ).
thf(tp_termmset,type,
termmset: $o ).
thf(tp_termmset_gthm,type,
termmset_gthm: $o ).
thf(tp_termmset_lthm,type,
termmset_lthm: $o ).
thf(tp_ulamvar1,type,
ulamvar1: $o ).
thf(tp_ulamvarind,type,
ulamvarind: $o ).
thf(tp_ulamvarsh,type,
ulamvarsh: $o ).
thf(tp_var,type,
var: term > $o ).
thf(apinj1,definition,
( apinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apinj1) ).
thf(apinj2,definition,
( apinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apinj2) ).
thf(apnotvar,definition,
( apnotvar
= ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apnotvar) ).
thf(axabs,definition,
( axabs
= ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axabs) ).
thf(axapp,definition,
( axapp
= ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axapp) ).
thf(axassoc,definition,
( axassoc
= ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axassoc) ).
thf(axclos,definition,
( axclos
= ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axclos) ).
thf(axidl,definition,
( axidl
= ( ! [M: subst] :
( ( comp @ id @ M )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axidl) ).
thf(axidr,definition,
( axidr
= ( ! [M: subst] :
( ( comp @ M @ id )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axidr) ).
thf(axmap,definition,
( axmap
= ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axmap) ).
thf(axscons,definition,
( axscons
= ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axscons) ).
thf(axshiftcons,definition,
( axshiftcons
= ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axshiftcons) ).
thf(axvarcons,definition,
( axvarcons
= ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarcons) ).
thf(axvarid,definition,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarid) ).
thf(axvarshift,definition,
( axvarshift
= ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axvarshift) ).
thf(hoasap,definition,
( hoasap
= ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasap) ).
thf(hoasapinj1,definition,
( hoasapinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj1) ).
thf(hoasapinj1_gthm,definition,
( hoasapinj1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> hoasapinj1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj1_gthm) ).
thf(hoasapinj1_lthm,definition,
( hoasapinj1_lthm
= ( axvarid
=> ( apinj1
=> hoasapinj1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj1_lthm) ).
thf(hoasapinj2,definition,
( hoasapinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj2) ).
thf(hoasapinj2_gthm,definition,
( hoasapinj2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> hoasapinj2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj2_gthm) ).
thf(hoasapinj2_lthm,definition,
( hoasapinj2_lthm
= ( apinj2
=> hoasapinj2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapinj2_lthm) ).
thf(hoasapnotvar,definition,
( hoasapnotvar
= ( ! [A: term,B: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapnotvar) ).
thf(hoasapnotvar_gthm,definition,
( hoasapnotvar_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapnotvar_gthm) ).
thf(hoasapnotvar_lthm,definition,
( hoasapnotvar_lthm
= ( axvarid
=> ( apnotvar
=> hoasapnotvar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasapnotvar_lthm) ).
thf(hoasinduction,definition,
( hoasinduction
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] : ( P @ id @ A @ id ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction) ).
thf(hoasinduction_gthm,definition,
( hoasinduction_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_gthm) ).
thf(hoasinduction_lem0,definition,
( hoasinduction_lem0
= ( ! [P: subst > term > subst > $o] :
? [Q: term > $o] : ( hoasinduction_p_and_p_prime @ P @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem0) ).
thf(hoasinduction_lem0_lthm,definition,
hoasinduction_lem0_lthm = hoasinduction_lem0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem0_lthm) ).
thf(hoasinduction_lem1,definition,
( hoasinduction_lem1
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ id @ A @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1) ).
thf(hoasinduction_lem1_gthm,definition,
( hoasinduction_lem1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1_gthm) ).
thf(hoasinduction_lem1_lthm,definition,
( hoasinduction_lem1_lthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1_lthm) ).
thf(hoasinduction_lem1v2,definition,
( hoasinduction_lem1v2
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ( var @ A )
=> ( Q @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1v2) ).
thf(hoasinduction_lem1v2_gthm,definition,
( hoasinduction_lem1v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem1v2_gthm) ).
thf(hoasinduction_lem2,definition,
( hoasinduction_lem2
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( ap @ A @ B ) @ id ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2) ).
thf(hoasinduction_lem2_gthm,definition,
( hoasinduction_lem2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2_gthm) ).
thf(hoasinduction_lem2_lthm,definition,
( hoasinduction_lem2_lthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2_lthm) ).
thf(hoasinduction_lem2v2,definition,
( hoasinduction_lem2v2
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term,B: term] :
( ( Q @ A )
=> ( ( Q @ B )
=> ( Q @ ( ap @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2v2) ).
thf(hoasinduction_lem2v2_gthm,definition,
( hoasinduction_lem2v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem2v2_gthm) ).
thf(hoasinduction_lem3,definition,
( hoasinduction_lem3
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3) ).
thf(hoasinduction_lem3_gthm,definition,
( hoasinduction_lem3_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3_gthm) ).
thf(hoasinduction_lem3_lthm,definition,
( hoasinduction_lem3_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3_lthm) ).
thf(hoasinduction_lem3a,definition,
( hoasinduction_lem3a
= ( ! [P: subst > term > subst > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ A ) @ id ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3a) ).
thf(hoasinduction_lem3a_gthm,definition,
( hoasinduction_lem3a_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3a ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3a_gthm) ).
thf(hoasinduction_lem3a_lthm,definition,
( hoasinduction_lem3a_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3a_lthm) ).
thf(hoasinduction_lem3aa,definition,
( hoasinduction_lem3aa
= ( ! [P: subst > term > subst > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3aa) ).
thf(hoasinduction_lem3aa_lthm,definition,
( hoasinduction_lem3aa_lthm
= ( axclos
=> ( axmap
=> hoasinduction_lem3aa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3aa_lthm) ).
thf(hoasinduction_lem3aaa,definition,
( hoasinduction_lem3aaa
= ( ! [P: subst > term > subst > $o] :
( ! [F: subst > term > term] :
( ? [C: term] :
! [M: subst,A: term,N: subst] :
( ( ( sub @ ( F @ M @ A ) @ N )
= ( sub @ ( sub @ C @ ( push @ A @ M ) ) @ N ) )
& ( ( sub @ C @ ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3aaa) ).
thf(hoasinduction_lem3b,definition,
( hoasinduction_lem3b
= ( ! [B: term] :
? [F: subst > term > term] :
( ( sub @ B @ ( push @ one @ sh ) )
= ( F @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3b) ).
thf(hoasinduction_lem3b_gthm,definition,
( hoasinduction_lem3b_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3b_gthm) ).
thf(hoasinduction_lem3b_lthm,definition,
hoasinduction_lem3b_lthm = hoasinduction_lem3b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3b_lthm) ).
thf(hoasinduction_lem3v2,definition,
( hoasinduction_lem3v2
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ! [B: term] :
( ( Q @ B )
=> ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( Q @ ( lam @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2) ).
thf(hoasinduction_lem3v2_f,definition,
( hoasinduction_lem3v2_f
= ( ! [B: term] :
? [F: subst > term > term] :
! [A: term,M: subst] :
( ( F @ M @ A )
= ( sub @ B @ ( push @ A @ M ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2_f) ).
thf(hoasinduction_lem3v2_f_lthm,definition,
hoasinduction_lem3v2_f_lthm = hoasinduction_lem3v2_f,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2_f_lthm) ).
thf(hoasinduction_lem3v2_gthm,definition,
( hoasinduction_lem3v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem3v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2_gthm) ).
thf(hoasinduction_lem3v2_lthm,definition,
( hoasinduction_lem3v2_lthm
= ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2_lthm) ).
thf(hoasinduction_lem3v2a,definition,
( hoasinduction_lem3v2a
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ! [B: term] :
( ( Q @ B )
=> ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( Q @ ( lam @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2a) ).
thf(hoasinduction_lem3v2a_lthm,definition,
( hoasinduction_lem3v2a_lthm
= ( hoasinduction_lem3v2_f
=> ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lem3v2a_lthm) ).
thf(hoasinduction_lthm,definition,
( hoasinduction_lthm
= ( induction2
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lthm) ).
thf(hoasinduction_lthm_3,definition,
( hoasinduction_lthm_3
= ( hoasinduction_lem0
=> ( induction2
=> ( axvarid
=> ( hoasinduction_lem3v2a
=> hoasinduction ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_lthm_3) ).
thf(hoasinduction_no_psi_cond,definition,
( hoasinduction_no_psi_cond
= ( ! [P: subst > term > subst > $o] :
( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] : ( P @ id @ A @ id ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_no_psi_cond) ).
thf(hoasinduction_no_psi_cond_lthm,definition,
( hoasinduction_no_psi_cond_lthm
= ( hoasinduction_lem0
=> ( induction2
=> ( axvarid
=> ( hoasinduction_lem3v2a
=> hoasinduction_no_psi_cond ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_no_psi_cond_lthm) ).
thf(hoasinduction_p_and_p_prime,definition,
( hoasinduction_p_and_p_prime
= ( ^ [P: subst > term > subst > $o,Q: term > $o] :
! [X: term] :
( ( Q @ X )
<=> ( P @ id @ X @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasinduction_p_and_p_prime) ).
thf(hoaslam,definition,
( hoaslam
= ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslam) ).
thf(hoaslaminj,definition,
( hoaslaminj
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [G: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( G @ M @ A ) @ N )
= ( G @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
= ( hoaslam @ id
@ ^ [M: subst,A: term] : ( G @ M @ A ) ) )
=> ! [M: subst,A: term] :
( ( F @ M @ A )
= ( G @ M @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslaminj) ).
thf(hoaslaminj_gthm,definition,
( hoaslaminj_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> hoaslaminj ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslaminj_gthm) ).
thf(hoaslaminj_lthm,definition,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslaminj_lthm) ).
thf(hoaslamnotap,definition,
( hoaslamnotap
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [A: term,B: term] :
( ( hoaslam @ id
@ ^ [M: subst,C: term] : ( F @ M @ C ) )
!= ( hoasap @ id @ A @ id @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotap) ).
thf(hoaslamnotap_gthm,definition,
( hoaslamnotap_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotap_gthm) ).
thf(hoaslamnotap_lthm,definition,
( hoaslamnotap_lthm
= ( lamnotap
=> hoaslamnotap ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotap_lthm) ).
thf(hoaslamnotvar,definition,
( hoaslamnotvar
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotvar) ).
thf(hoaslamnotvar_gthm,definition,
( hoaslamnotvar_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotvar_gthm) ).
thf(hoaslamnotvar_lthm,definition,
( hoaslamnotvar_lthm
= ( axvarid
=> ( lamnotvar
=> hoaslamnotvar ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoaslamnotvar_lthm) ).
thf(hoasvar,definition,
( hoasvar
= ( ^ [M: subst,A: term,N: subst] : ( var @ ( sub @ A @ N ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hoasvar) ).
thf(induction,definition,
( induction
= ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ( P @ A )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction) ).
thf(induction2,definition,
( induction2
= ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2) ).
thf(induction2_gthm,definition,
( induction2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2_gthm) ).
thf(induction2_lthm,definition,
( induction2_lthm
= ( axvarid
=> ( induction2lem
=> induction2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2_lthm) ).
thf(induction2lem,definition,
( induction2lem
= ( ! [P: term > $o] :
( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( P @ ( sub @ A @ M ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2lem) ).
thf(induction2lem_gthm,definition,
( induction2lem_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> induction2lem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2lem_gthm) ).
thf(induction2lem_lthm,definition,
( induction2lem_lthm
= ( axapp
=> ( axvarcons
=> ( axabs
=> ( axclos
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( induction
=> ( pushprop
=> induction2lem ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction2lem_lthm) ).
thf(laminj,definition,
( laminj
= ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',laminj) ).
thf(lamnotap,definition,
( lamnotap
= ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotap) ).
thf(lamnotvar,definition,
( lamnotvar
= ( ! [A: term] :
~ ( var @ ( lam @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamnotvar) ).
thf(pushprop,definition,
( pushprop
= ( ! [P: term > $o,A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( ( P @ A )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop) ).
thf(pushprop_gthm,definition,
( pushprop_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_gthm) ).
thf(pushprop_lem0,definition,
( pushprop_lem0
= ( ! [P: term > $o,A: term,M: subst] :
? [Q: term > $o] : ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem0) ).
thf(pushprop_lem0_gthm,definition,
( pushprop_lem0_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem0_gthm) ).
thf(pushprop_lem0_lthm,definition,
pushprop_lem0_lthm = pushprop_lem0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem0_lthm) ).
thf(pushprop_lem1,definition,
( pushprop_lem1
= ( ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
( ( P @ A )
=> ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1) ).
thf(pushprop_lem1_gthm,definition,
( pushprop_lem1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1_gthm) ).
thf(pushprop_lem1_lthm,definition,
( pushprop_lem1_lthm
= ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop_lem1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1_lthm) ).
thf(pushprop_lem1v2,definition,
( pushprop_lem1v2
= ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
( ( P @ A )
=> ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
=> ( Q @ one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1v2) ).
thf(pushprop_lem1v2_gthm,definition,
( pushprop_lem1v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1v2_gthm) ).
thf(pushprop_lem1v2_lthm,definition,
( pushprop_lem1v2_lthm
= ( axvarcons
=> pushprop_lem1v2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem1v2_lthm) ).
thf(pushprop_lem2v2,definition,
( pushprop_lem2v2
= ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
=> ( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ! [C: term] :
( ( var @ C )
=> ( ( Q @ C )
=> ( Q @ ( sub @ C @ sh ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem2v2) ).
thf(pushprop_lem2v2_gthm,definition,
( pushprop_lem2v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem2v2_gthm) ).
thf(pushprop_lem2v2_lthm,definition,
( pushprop_lem2v2_lthm
= ( axclos
=> ( axshiftcons
=> pushprop_lem2v2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem2v2_lthm) ).
thf(pushprop_lem3v2,definition,
( pushprop_lem3v2
= ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
=> ( ! [B: term] :
( ( var @ B )
=> ( Q @ B ) )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem3v2) ).
thf(pushprop_lem3v2_lthm,definition,
pushprop_lem3v2_lthm = pushprop_lem3v2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lem3v2_lthm) ).
thf(pushprop_lthm,definition,
( pushprop_lthm
= ( pushprop_lem0
=> ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lthm) ).
thf(pushprop_lthm_orig,definition,
( pushprop_lthm_orig
= ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_lthm_orig) ).
thf(pushprop_p_and_p_prime,definition,
( pushprop_p_and_p_prime
= ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
! [X: term] :
( ( Q @ X )
<=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pushprop_p_and_p_prime) ).
thf(shinj,definition,
( shinj
= ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shinj) ).
thf(substmonoid,definition,
( substmonoid
= ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) )
& ! [M: subst] :
( ( comp @ id @ M )
= M )
& ! [M: subst] :
( ( comp @ M @ id )
= M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substmonoid) ).
thf(substmonoid_gthm,definition,
( substmonoid_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> substmonoid ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substmonoid_gthm) ).
thf(substmonoid_lthm,definition,
( substmonoid_lthm
= ( axidl
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substmonoid_lthm) ).
thf(termmset,definition,
( termmset
= ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',termmset) ).
thf(termmset_gthm,definition,
( termmset_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> termmset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',termmset_gthm) ).
thf(termmset_lthm,definition,
( termmset_lthm
= ( axvarid
=> ( axclos
=> termmset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',termmset_lthm) ).
thf(ulamvar1,definition,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvar1) ).
thf(ulamvarind,definition,
( ulamvarind
= ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvarind) ).
thf(ulamvarsh,definition,
( ulamvarsh
= ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ulamvarsh) ).
thf(1,conjecture,
hoasinduction_lem2v2_gthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
hoasinduction_lem2v2_gthm = $false,
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ~ hoasinduction_lem2v2_gthm )
= $true ),
inference(polarity_switch,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ hoasinduction_lem2v2_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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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 ) )
| ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $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,
( ( ~ ! [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)],[174]) ).
thf(183,plain,
( ( ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(184,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(185,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(186,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(187,plain,
! [SV49: term > $o] :
( ( ( ! [SY62: term] :
( ~ ( SV49 @ ( sK3_SY47 @ SV49 ) )
| ~ ( SV49 @ SY62 )
| ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ SY62 ) ) ) )
= $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(188,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(189,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(190,plain,
( ( ~ ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[180]) ).
thf(191,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(192,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(193,plain,
( ( ~ ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(194,plain,
( ( ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[183]) ).
thf(195,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)],[184]) ).
thf(196,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)],[185]) ).
thf(197,plain,
! [SV47: term > $o,SV50: subst,SV48: term] :
( ( ( ~ ( var @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) )
| ( SV47 @ ( sub @ ( sK4_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)],[186]) ).
thf(198,plain,
! [SV49: term > $o] :
( ( ( ~ ( SV49 @ ( sK3_SY47 @ SV49 ) )
| ~ ( SV49 @ ( sK5_SY62 @ SV49 ) )
| ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ 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)],[187]) ).
thf(199,plain,
! [SV51: term > $o] :
( ( ( ~ ( var @ ( sK6_SY56 @ SV51 ) )
| ( SV51 @ ( sK6_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)],[188]) ).
thf(200,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)],[189]) ).
thf(201,plain,
( ( ! [SX0: subst] :
( ( comp @ SX0 @ id )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[190]) ).
thf(202,plain,
( ( ~ ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(203,plain,
( ( ~ ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[191]) ).
thf(204,plain,
! [SV52: term] :
( ( ! [SY63: term,SY64: term,SY65: term] :
( ( ( ap @ ( sub @ SV52 @ id ) @ SY64 )
!= ( ap @ ( sub @ SY63 @ id ) @ SY65 ) )
| ( SV52 = SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(205,plain,
( ( ! [SX0: term,SX1: term,SX2: term,SX3: term] :
( ( ( ap @ ( sub @ SX0 @ id ) @ SX2 )
!= ( ap @ ( sub @ SX1 @ id ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(206,plain,
( ( ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(207,plain,
( ( ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) )
| ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[194]) ).
thf(208,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)],[195]) ).
thf(209,plain,
! [SV45: term > $o] :
( ( ( ! [SY66: term] :
( ~ ( SV45 @ ( sK7_SY36 @ SV45 ) )
| ~ ( SV45 @ SY66 )
| ( SV45 @ ( ap @ ( sK7_SY36 @ SV45 ) @ SY66 ) ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[196]) ).
thf(210,plain,
! [SV47: term > $o,SV50: subst,SV48: term] :
( ( ( ~ ( var @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) ) )
= $false )
| ( ( ~ ( SV47 @ SV48 )
| ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[197]) ).
thf(211,plain,
! [SV50: subst,SV48: term,SV47: term > $o] :
( ( ( SV47 @ ( sub @ ( sK4_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)],[197]) ).
thf(212,plain,
! [SV49: term > $o] :
( ( ( ~ ( SV49 @ ( sK3_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)],[198]) ).
thf(213,plain,
! [SV49: term > $o] :
( ( ( ~ ( SV49 @ ( sK5_SY62 @ SV49 ) )
| ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ 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)],[198]) ).
thf(214,plain,
! [SV51: term > $o] :
( ( ( ~ ( var @ ( sK6_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)],[199]) ).
thf(215,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( sK6_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)],[199]) ).
thf(216,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)],[200]) ).
thf(217,plain,
! [SV53: subst] :
( ( ( comp @ SV53 @ id )
= SV53 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(218,plain,
( ( ! [SX0: term,SX1: subst,SX2: subst] :
( ( sub @ ( sub @ SX0 @ SX1 ) @ SX2 )
= ( sub @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(219,plain,
( ( ! [SX0: term] :
( ( sub @ SX0 @ id )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[203]) ).
thf(220,plain,
! [SV54: term,SV52: term] :
( ( ! [SY67: term,SY68: term] :
( ( ( ap @ ( sub @ SV52 @ id ) @ SY67 )
!= ( ap @ ( sub @ SV54 @ id ) @ SY68 ) )
| ( SV52 = SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(221,plain,
! [SV55: term] :
( ( ! [SY69: term,SY70: term,SY71: term] :
( ( ( ap @ ( sub @ SV55 @ id ) @ SY70 )
!= ( ap @ ( sub @ SY69 @ id ) @ SY71 ) )
| ( SY70 = SY71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(222,plain,
( ( ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SX1 @ SX2 @ SX3 ) @ SX4 )
= ( SX1 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SX0 @ sh @ one ) )
!= ( lam @ ( SX1 @ sh @ one ) ) )
| ! [SX2: subst,SX3: term] :
( ( SX0 @ SX2 @ SX3 )
= ( SX1 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[206]) ).
thf(223,plain,
( ( ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(224,plain,
( ( ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
| ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[207]) ).
thf(225,plain,
! [SV45: term > $o] :
( ( ( ! [SY72: term] :
( ~ ( SV45 @ ( sK8_SY36 @ SV45 ) )
| ~ ( SV45 @ SY72 )
| ( SV45 @ ( ap @ ( sK8_SY36 @ SV45 ) @ SY72 ) ) ) )
= $false )
| ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) )
| ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[208]) ).
thf(226,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK7_SY36 @ SV45 ) )
| ~ ( SV45 @ ( sK9_SY66 @ SV45 ) )
| ( SV45 @ ( ap @ ( sK7_SY36 @ SV45 ) @ ( sK9_SY66 @ 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)],[209]) ).
thf(227,plain,
! [SV47: term > $o,SV50: subst,SV48: term] :
( ( ( var @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) )
= $true )
| ( ( ~ ( SV47 @ SV48 )
| ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[210]) ).
thf(228,plain,
! [SV50: subst,SV48: term,SV47: term > $o] :
( ( ( ~ ( SV47 @ SV48 ) )
= $true )
| ( ( ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true )
| ( ( SV47 @ ( sub @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(229,plain,
! [SV49: term > $o] :
( ( ( SV49 @ ( sK3_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)],[212]) ).
thf(230,plain,
! [SV49: term > $o] :
( ( ( ~ ( SV49 @ ( sK5_SY62 @ 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)],[213]) ).
thf(231,plain,
! [SV49: term > $o] :
( ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ 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)],[213]) ).
thf(232,plain,
! [SV51: term > $o] :
( ( ( var @ ( sK6_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)],[214]) ).
thf(233,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 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(234,plain,
( ( ~ ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(235,plain,
( ( ~ ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[216]) ).
thf(236,plain,
! [SV56: term] :
( ( ! [SY73: subst,SY74: subst] :
( ( sub @ ( sub @ SV56 @ SY73 ) @ SY74 )
= ( sub @ SV56 @ ( comp @ SY73 @ SY74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(237,plain,
! [SV57: term] :
( ( ( sub @ SV57 @ id )
= SV57 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(238,plain,
! [SV54: term,SV58: term,SV52: term] :
( ( ! [SY75: term] :
( ( ( ap @ ( sub @ SV52 @ id ) @ SV58 )
!= ( ap @ ( sub @ SV54 @ id ) @ SY75 ) )
| ( SV52 = SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(239,plain,
! [SV59: term,SV55: term] :
( ( ! [SY76: term,SY77: term] :
( ( ( ap @ ( sub @ SV55 @ id ) @ SY76 )
!= ( ap @ ( sub @ SV59 @ id ) @ SY77 ) )
| ( SY76 = SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(240,plain,
! [SV60: subst > term > term] :
( ( ~ ! [SY78: subst,SY79: term,SY80: subst] :
( ( sub @ ( SV60 @ SY78 @ SY79 ) @ SY80 )
= ( SV60 @ ( comp @ SY78 @ SY80 ) @ ( sub @ SY79 @ SY80 ) ) )
| ! [SY81: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY81 @ SX2 @ SX3 ) @ SX4 )
= ( SY81 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SY81 @ sh @ one ) ) )
| ! [SY85: subst,SY86: term] :
( ( SV60 @ SY85 @ SY86 )
= ( SY81 @ SY85 @ SY86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(241,plain,
( ( ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ! [SX1: term,SX2: term] :
( ( lam @ ( SX0 @ sh @ one ) )
!= ( ap @ ( sub @ SX1 @ id ) @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[223]) ).
thf(242,plain,
( ( ~ ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(243,plain,
( ( ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) )
| ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[224]) ).
thf(244,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK8_SY36 @ SV45 ) )
| ~ ( SV45 @ ( sK10_SY72 @ SV45 ) )
| ( SV45 @ ( ap @ ( sK8_SY36 @ SV45 ) @ ( sK10_SY72 @ 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)],[225]) ).
thf(245,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK7_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)],[226]) ).
thf(246,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK9_SY66 @ SV45 ) )
| ( SV45 @ ( ap @ ( sK7_SY36 @ SV45 ) @ ( sK9_SY66 @ 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)],[226]) ).
thf(247,plain,
! [SV50: subst,SV48: term,SV47: term > $o] :
( ( ( ~ ( SV47 @ SV48 ) )
= $true )
| ( ( ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true )
| ( ( var @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(248,plain,
! [SV50: subst,SV48: term,SV47: term > $o] :
( ( ( SV47 @ SV48 )
= $false )
| ( ( ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true )
| ( ( SV47 @ ( sub @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(249,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 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(250,plain,
! [SV49: term > $o] :
( ( ( SV49 @ ( sK5_SY62 @ 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)],[230]) ).
thf(251,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 @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(252,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 @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(253,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 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(254,plain,
( ( ! [SX0: subst,SX1: subst,SX2: subst] :
( ( comp @ ( comp @ SX0 @ SX1 ) @ SX2 )
= ( comp @ SX0 @ ( comp @ SX1 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[234]) ).
thf(255,plain,
( ( ! [SX0: subst] :
( ( comp @ id @ SX0 )
= SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[235]) ).
thf(256,plain,
! [SV61: subst,SV56: term] :
( ( ! [SY87: subst] :
( ( sub @ ( sub @ SV56 @ SV61 ) @ SY87 )
= ( sub @ SV56 @ ( comp @ SV61 @ SY87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(257,plain,
! [SV62: term,SV54: term,SV58: term,SV52: term] :
( ( ( ( ap @ ( sub @ SV52 @ id ) @ SV58 )
!= ( ap @ ( sub @ SV54 @ id ) @ SV62 ) )
| ( SV52 = SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(258,plain,
! [SV59: term,SV63: term,SV55: term] :
( ( ! [SY88: term] :
( ( ( ap @ ( sub @ SV55 @ id ) @ SV63 )
!= ( ap @ ( sub @ SV59 @ id ) @ SY88 ) )
| ( SV63 = SY88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(259,plain,
! [SV60: subst > term > term] :
( ( ( ~ ! [SY78: subst,SY79: term,SY80: subst] :
( ( sub @ ( SV60 @ SY78 @ SY79 ) @ SY80 )
= ( SV60 @ ( comp @ SY78 @ SY80 ) @ ( sub @ SY79 @ SY80 ) ) ) )
= $true )
| ( ( ! [SY81: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY81 @ SX2 @ SX3 ) @ SX4 )
= ( SY81 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SY81 @ sh @ one ) ) )
| ! [SY85: subst,SY86: term] :
( ( SV60 @ SY85 @ SY86 )
= ( SY81 @ SY85 @ SY86 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(260,plain,
! [SV64: subst > term > term] :
( ( ~ ! [SY89: subst,SY90: term,SY91: subst] :
( ( sub @ ( SV64 @ SY89 @ SY90 ) @ SY91 )
= ( SV64 @ ( comp @ SY89 @ SY91 ) @ ( sub @ SY90 @ SY91 ) ) )
| ! [SY92: term,SY93: term] :
( ( lam @ ( SV64 @ sh @ one ) )
!= ( ap @ ( sub @ SY92 @ id ) @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(261,plain,
( ( ! [SX0: subst > term > term] :
( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( SX0 @ SX1 @ SX2 ) @ SX3 )
= ( SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[242]) ).
thf(262,plain,
( ( ~ ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(263,plain,
( ( ! [SX0: subst > term > subst > $o,SX1: term > $o] :
( ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) )
| ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 ) )
| ~ ! [SX2: subst,SX3: term,SX4: subst,SX5: subst] :
( ~ ( SX0 @ ( comp @ SX2 @ SX5 ) @ ( sub @ SX3 @ SX5 ) @ SX4 )
| ( SX0 @ SX2 @ SX3 @ ( comp @ SX5 @ SX4 ) ) )
| ~ ! [SX2: term,SX3: term] :
( ~ ( SX0 @ id @ SX2 @ id )
| ~ ( SX0 @ id @ SX3 @ id )
| ( SX0 @ id @ ( ap @ ( sub @ SX2 @ id ) @ SX3 ) @ id ) )
| ~ ! [SX2: term] :
~ ( ~ ( ~ ( SX1 @ SX2 )
| ( SX0 @ id @ SX2 @ id ) )
| ~ ( ~ ( SX0 @ id @ SX2 @ id )
| ( SX1 @ SX2 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX1 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(264,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK8_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)],[244]) ).
thf(265,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK10_SY72 @ SV45 ) )
| ( SV45 @ ( ap @ ( sK8_SY36 @ SV45 ) @ ( sK10_SY72 @ 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)],[244]) ).
thf(266,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK7_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)],[245]) ).
thf(267,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK9_SY66 @ 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)],[246]) ).
thf(268,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( ap @ ( sK7_SY36 @ SV45 ) @ ( sK9_SY66 @ 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)],[246]) ).
thf(269,plain,
! [SV50: subst,SV48: term,SV47: term > $o] :
( ( ( SV47 @ SV48 )
= $false )
| ( ( ! [SY55: term] :
( ~ ( var @ SY55 )
| ( SV47 @ ( sub @ SY55 @ ( push @ SV48 @ SV50 ) ) ) ) )
= $true )
| ( ( var @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(270,plain,
! [SV50: subst,SV48: term,SV47: term > $o,SV65: term] :
( ( ( ~ ( var @ SV65 )
| ( SV47 @ ( sub @ SV65 @ ( push @ SV48 @ SV50 ) ) ) )
= $true )
| ( ( SV47 @ SV48 )
= $false )
| ( ( SV47 @ ( sub @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(271,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 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(272,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 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(273,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 @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(274,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 @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(275,plain,
! [SV51: term > $o] :
( ( ( ! [SY94: term] :
( ~ ( SV51 @ ( sK11_SY57 @ SV51 ) )
| ~ ( SV51 @ SY94 )
| ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ SY94 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[253]) ).
thf(276,plain,
! [SV66: subst] :
( ( ! [SY95: subst,SY96: subst] :
( ( comp @ ( comp @ SV66 @ SY95 ) @ SY96 )
= ( comp @ SV66 @ ( comp @ SY95 @ SY96 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(277,plain,
! [SV67: subst] :
( ( ( comp @ id @ SV67 )
= SV67 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(278,plain,
! [SV68: subst,SV61: subst,SV56: term] :
( ( ( sub @ ( sub @ SV56 @ SV61 ) @ SV68 )
= ( sub @ SV56 @ ( comp @ SV61 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(279,plain,
! [SV62: term,SV54: term,SV58: term,SV52: term] :
( ( ( ( ( ap @ ( sub @ SV52 @ id ) @ SV58 )
!= ( ap @ ( sub @ SV54 @ id ) @ SV62 ) ) )
= $true )
| ( ( SV52 = SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(280,plain,
! [SV69: term,SV59: term,SV63: term,SV55: term] :
( ( ( ( ap @ ( sub @ SV55 @ id ) @ SV63 )
!= ( ap @ ( sub @ SV59 @ id ) @ SV69 ) )
| ( SV63 = SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(281,plain,
! [SV60: subst > term > term] :
( ( ( ! [SY78: subst,SY79: term,SY80: subst] :
( ( sub @ ( SV60 @ SY78 @ SY79 ) @ SY80 )
= ( SV60 @ ( comp @ SY78 @ SY80 ) @ ( sub @ SY79 @ SY80 ) ) ) )
= $false )
| ( ( ! [SY81: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY81 @ SX2 @ SX3 ) @ SX4 )
= ( SY81 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SY81 @ sh @ one ) ) )
| ! [SY85: subst,SY86: term] :
( ( SV60 @ SY85 @ SY86 )
= ( SY81 @ SY85 @ SY86 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(282,plain,
! [SV64: subst > term > term] :
( ( ( ~ ! [SY89: subst,SY90: term,SY91: subst] :
( ( sub @ ( SV64 @ SY89 @ SY90 ) @ SY91 )
= ( SV64 @ ( comp @ SY89 @ SY91 ) @ ( sub @ SY90 @ SY91 ) ) ) )
= $true )
| ( ( ! [SY92: term,SY93: term] :
( ( lam @ ( SV64 @ sh @ one ) )
!= ( ap @ ( sub @ SY92 @ id ) @ SY93 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(283,plain,
! [SV70: subst > term > term] :
( ( ~ ! [SY97: subst,SY98: term,SY99: subst] :
( ( sub @ ( SV70 @ SY97 @ SY98 ) @ SY99 )
= ( SV70 @ ( comp @ SY97 @ SY99 ) @ ( sub @ SY98 @ SY99 ) ) )
| ~ ( var @ ( sub @ ( lam @ ( SV70 @ sh @ one ) ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(284,plain,
( ( ! [SX0: term,SX1: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SX0 @ id ) @ SX1 ) @ id ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(285,plain,
( ( ! [SY100: term > $o] :
( ~ ! [SY101: subst,SY102: term,SY103: subst,SY104: subst] :
( ~ ( sK12_SX0 @ SY101 @ SY102 @ ( comp @ SY104 @ SY103 ) )
| ( sK12_SX0 @ ( comp @ SY101 @ SY104 ) @ ( sub @ SY102 @ SY104 ) @ SY103 ) )
| ~ ! [SY105: subst,SY106: term,SY107: subst,SY108: subst] :
( ~ ( sK12_SX0 @ ( comp @ SY105 @ SY108 ) @ ( sub @ SY106 @ SY108 ) @ SY107 )
| ( sK12_SX0 @ SY105 @ SY106 @ ( comp @ SY108 @ SY107 ) ) )
| ~ ! [SY109: term,SY110: term] :
( ~ ( sK12_SX0 @ id @ SY109 @ id )
| ~ ( sK12_SX0 @ id @ SY110 @ id )
| ( sK12_SX0 @ id @ ( ap @ ( sub @ SY109 @ id ) @ SY110 ) @ id ) )
| ~ ! [SY111: term] :
~ ( ~ ( ~ ( SY100 @ SY111 )
| ( sK12_SX0 @ id @ SY111 @ id ) )
| ~ ( ~ ( sK12_SX0 @ id @ SY111 @ id )
| ( SY100 @ SY111 ) ) )
| ! [SX2: term,SX3: term] :
( ~ ( SY100 @ SX2 )
| ~ ( SY100 @ SX3 )
| ( SY100 @ ( ap @ SX2 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[263]) ).
thf(286,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK8_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)],[264]) ).
thf(287,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK10_SY72 @ 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)],[265]) ).
thf(288,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( ap @ ( sK8_SY36 @ SV45 ) @ ( sK10_SY72 @ 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)],[265]) ).
thf(289,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK7_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(290,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK9_SY66 @ 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)],[267]) ).
thf(291,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK7_SY36 @ SV45 ) @ ( sK9_SY66 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(292,plain,
! [SV50: subst,SV48: term,SV47: term > $o,SV71: term] :
( ( ( ~ ( var @ SV71 )
| ( SV47 @ ( sub @ SV71 @ ( push @ SV48 @ SV50 ) ) ) )
= $true )
| ( ( SV47 @ SV48 )
= $false )
| ( ( var @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(293,plain,
! [SV50: subst,SV48: term,SV47: term > $o,SV65: term] :
( ( ( ~ ( var @ SV65 ) )
= $true )
| ( ( SV47 @ ( sub @ SV65 @ ( push @ SV48 @ SV50 ) ) )
= $true )
| ( ( SV47 @ SV48 )
= $false )
| ( ( SV47 @ ( sub @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[270]) ).
thf(294,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY114: term] :
( ~ ( SV49 @ SY114 )
| ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SY114 @ id ) ) ) )
| ( SV49 @ ( lam @ ( sK13_SY49 @ SV49 ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[271]) ).
thf(295,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 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[272]) ).
thf(296,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY115: term] :
( ~ ( SV49 @ SY115 )
| ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SY115 @ id ) ) ) )
| ( SV49 @ ( lam @ ( sK14_SY49 @ SV49 ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[273]) ).
thf(297,plain,
! [SV51: term > $o] :
( ( ( ! [SY116: term] :
( ~ ( SV51 @ ( sK15_SY57 @ SV51 ) )
| ~ ( SV51 @ SY116 )
| ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ SY116 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[274]) ).
thf(298,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK11_SY57 @ SV51 ) )
| ~ ( SV51 @ ( sK16_SY94 @ SV51 ) )
| ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[275]) ).
thf(299,plain,
! [SV72: subst,SV66: subst] :
( ( ! [SY117: subst] :
( ( comp @ ( comp @ SV66 @ SV72 ) @ SY117 )
= ( comp @ SV66 @ ( comp @ SV72 @ SY117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(300,plain,
! [SV62: term,SV54: term,SV58: term,SV52: term] :
( ( ( ( ap @ ( sub @ SV52 @ id ) @ SV58 )
= ( ap @ ( sub @ SV54 @ id ) @ SV62 ) )
= $false )
| ( ( SV52 = SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(301,plain,
! [SV69: term,SV59: term,SV63: term,SV55: term] :
( ( ( ( ( ap @ ( sub @ SV55 @ id ) @ SV63 )
!= ( ap @ ( sub @ SV59 @ id ) @ SV69 ) ) )
= $true )
| ( ( SV63 = SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(302,plain,
! [SV60: subst > term > term] :
( ( ( ! [SY118: term,SY119: subst] :
( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ SY118 ) @ SY119 )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ SY119 ) @ ( sub @ SY118 @ SY119 ) ) ) )
= $false )
| ( ( ! [SY81: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY81 @ SX2 @ SX3 ) @ SX4 )
= ( SY81 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SY81 @ sh @ one ) ) )
| ! [SY85: subst,SY86: term] :
( ( SV60 @ SY85 @ SY86 )
= ( SY81 @ SY85 @ SY86 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[281]) ).
thf(303,plain,
! [SV64: subst > term > term] :
( ( ( ! [SY89: subst,SY90: term,SY91: subst] :
( ( sub @ ( SV64 @ SY89 @ SY90 ) @ SY91 )
= ( SV64 @ ( comp @ SY89 @ SY91 ) @ ( sub @ SY90 @ SY91 ) ) ) )
= $false )
| ( ( ! [SY92: term,SY93: term] :
( ( lam @ ( SV64 @ sh @ one ) )
!= ( ap @ ( sub @ SY92 @ id ) @ SY93 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(304,plain,
! [SV70: subst > term > term] :
( ( ( ~ ! [SY97: subst,SY98: term,SY99: subst] :
( ( sub @ ( SV70 @ SY97 @ SY98 ) @ SY99 )
= ( SV70 @ ( comp @ SY97 @ SY99 ) @ ( sub @ SY98 @ SY99 ) ) ) )
= $true )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV70 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(305,plain,
! [SV73: term] :
( ( ! [SY120: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ SV73 @ id ) @ SY120 ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(306,plain,
( ( ~ ! [SY101: subst,SY102: term,SY103: subst,SY104: subst] :
( ~ ( sK12_SX0 @ SY101 @ SY102 @ ( comp @ SY104 @ SY103 ) )
| ( sK12_SX0 @ ( comp @ SY101 @ SY104 ) @ ( sub @ SY102 @ SY104 ) @ SY103 ) )
| ~ ! [SY105: subst,SY106: term,SY107: subst,SY108: subst] :
( ~ ( sK12_SX0 @ ( comp @ SY105 @ SY108 ) @ ( sub @ SY106 @ SY108 ) @ SY107 )
| ( sK12_SX0 @ SY105 @ SY106 @ ( comp @ SY108 @ SY107 ) ) )
| ~ ! [SY109: term,SY110: term] :
( ~ ( sK12_SX0 @ id @ SY109 @ id )
| ~ ( sK12_SX0 @ id @ SY110 @ id )
| ( sK12_SX0 @ id @ ( ap @ ( sub @ SY109 @ id ) @ SY110 ) @ id ) )
| ~ ! [SY131: term] :
~ ( ~ ( ~ ( sK18_SY100 @ SY131 )
| ( sK12_SX0 @ id @ SY131 @ id ) )
| ~ ( ~ ( sK12_SX0 @ id @ SY131 @ id )
| ( sK18_SY100 @ SY131 ) ) )
| ! [SY132: term,SY133: term] :
( ~ ( sK18_SY100 @ SY132 )
| ~ ( sK18_SY100 @ SY133 )
| ( sK18_SY100 @ ( ap @ SY132 @ SY133 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[285]) ).
thf(307,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK8_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(308,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK10_SY72 @ 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)],[287]) ).
thf(309,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK8_SY36 @ SV45 ) @ ( sK10_SY72 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(310,plain,
! [SV45: term > $o] :
( ( ( ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK7_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[289]) ).
thf(311,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK9_SY66 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(312,plain,
! [SV45: term > $o] :
( ( ( ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK7_SY36 @ SV45 ) @ ( sK9_SY66 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(313,plain,
! [SV50: subst,SV48: term,SV47: term > $o,SV71: term] :
( ( ( ~ ( var @ SV71 ) )
= $true )
| ( ( SV47 @ ( sub @ SV71 @ ( push @ SV48 @ SV50 ) ) )
= $true )
| ( ( SV47 @ SV48 )
= $false )
| ( ( var @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(314,plain,
! [SV50: subst,SV48: term,SV47: term > $o,SV65: term] :
( ( ( var @ SV65 )
= $false )
| ( ( SV47 @ ( sub @ SV65 @ ( push @ SV48 @ SV50 ) ) )
= $true )
| ( ( SV47 @ SV48 )
= $false )
| ( ( SV47 @ ( sub @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[293]) ).
thf(315,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY114: term] :
( ~ ( SV49 @ SY114 )
| ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SY114 @ id ) ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(316,plain,
! [SV49: term > $o] :
( ( ( SV49 @ ( lam @ ( sK13_SY49 @ SV49 ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[294]) ).
thf(317,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY134: term] :
( ~ ( SV49 @ SY134 )
| ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SY134 @ id ) ) ) )
| ( SV49 @ ( lam @ ( sK19_SY49 @ SV49 ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[295]) ).
thf(318,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY115: term] :
( ~ ( SV49 @ SY115 )
| ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SY115 @ id ) ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(319,plain,
! [SV49: term > $o] :
( ( ( SV49 @ ( lam @ ( sK14_SY49 @ SV49 ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(320,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK15_SY57 @ SV51 ) )
| ~ ( SV51 @ ( sK20_SY116 @ SV51 ) )
| ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK20_SY116 @ SV51 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[297]) ).
thf(321,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK11_SY57 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(322,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK16_SY94 @ SV51 ) )
| ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[298]) ).
thf(323,plain,
! [SV74: subst,SV72: subst,SV66: subst] :
( ( ( comp @ ( comp @ SV66 @ SV72 ) @ SV74 )
= ( comp @ SV66 @ ( comp @ SV72 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(324,plain,
! [SV69: term,SV59: term,SV63: term,SV55: term] :
( ( ( ( ap @ ( sub @ SV55 @ id ) @ SV63 )
= ( ap @ ( sub @ SV59 @ id ) @ SV69 ) )
= $false )
| ( ( SV63 = SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(325,plain,
! [SV60: subst > term > term] :
( ( ( ! [SY135: subst] :
( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ ( sK21_SY118 @ SV60 ) ) @ SY135 )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ SY135 ) @ ( sub @ ( sK21_SY118 @ SV60 ) @ SY135 ) ) ) )
= $false )
| ( ( ! [SY81: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY81 @ SX2 @ SX3 ) @ SX4 )
= ( SY81 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SY81 @ sh @ one ) ) )
| ! [SY85: subst,SY86: term] :
( ( SV60 @ SY85 @ SY86 )
= ( SY81 @ SY85 @ SY86 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[302]) ).
thf(326,plain,
! [SV64: subst > term > term] :
( ( ( ! [SY136: term,SY137: subst] :
( ( sub @ ( SV64 @ ( sK22_SY89 @ SV64 ) @ SY136 ) @ SY137 )
= ( SV64 @ ( comp @ ( sK22_SY89 @ SV64 ) @ SY137 ) @ ( sub @ SY136 @ SY137 ) ) ) )
= $false )
| ( ( ! [SY92: term,SY93: term] :
( ( lam @ ( SV64 @ sh @ one ) )
!= ( ap @ ( sub @ SY92 @ id ) @ SY93 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[303]) ).
thf(327,plain,
! [SV70: subst > term > term] :
( ( ( ! [SY97: subst,SY98: term,SY99: subst] :
( ( sub @ ( SV70 @ SY97 @ SY98 ) @ SY99 )
= ( SV70 @ ( comp @ SY97 @ SY99 ) @ ( sub @ SY98 @ SY99 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV70 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(328,plain,
! [SV75: term,SV73: term] :
( ( ~ ( var @ ( sub @ ( ap @ ( sub @ SV73 @ id ) @ SV75 ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(329,plain,
( ( ~ ! [SY101: subst,SY102: term,SY103: subst,SY104: subst] :
( ~ ( sK12_SX0 @ SY101 @ SY102 @ ( comp @ SY104 @ SY103 ) )
| ( sK12_SX0 @ ( comp @ SY101 @ SY104 ) @ ( sub @ SY102 @ SY104 ) @ SY103 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(330,plain,
( ( ~ ! [SY105: subst,SY106: term,SY107: subst,SY108: subst] :
( ~ ( sK12_SX0 @ ( comp @ SY105 @ SY108 ) @ ( sub @ SY106 @ SY108 ) @ SY107 )
| ( sK12_SX0 @ SY105 @ SY106 @ ( comp @ SY108 @ SY107 ) ) )
| ~ ! [SY109: term,SY110: term] :
( ~ ( sK12_SX0 @ id @ SY109 @ id )
| ~ ( sK12_SX0 @ id @ SY110 @ id )
| ( sK12_SX0 @ id @ ( ap @ ( sub @ SY109 @ id ) @ SY110 ) @ id ) )
| ~ ! [SY131: term] :
~ ( ~ ( ~ ( sK18_SY100 @ SY131 )
| ( sK12_SX0 @ id @ SY131 @ id ) )
| ~ ( ~ ( sK12_SX0 @ id @ SY131 @ id )
| ( sK18_SY100 @ SY131 ) ) )
| ! [SY132: term,SY133: term] :
( ~ ( sK18_SY100 @ SY132 )
| ~ ( sK18_SY100 @ SY133 )
| ( sK18_SY100 @ ( ap @ SY132 @ SY133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[306]) ).
thf(331,plain,
! [SV45: term > $o] :
( ( ( ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK8_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(332,plain,
! [SV45: term > $o] :
( ( ( ~ ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK10_SY72 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(333,plain,
! [SV45: term > $o] :
( ( ( ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK8_SY36 @ SV45 ) @ ( sK10_SY72 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(334,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK23_SY38 @ SV45 ) )
| ( SV45 @ ( lam @ ( sK23_SY38 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK7_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[310]) ).
thf(335,plain,
! [SV45: term > $o] :
( ( ( ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK9_SY66 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(336,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK24_SY38 @ SV45 ) )
| ( SV45 @ ( lam @ ( sK24_SY38 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK7_SY36 @ SV45 ) @ ( sK9_SY66 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[312]) ).
thf(337,plain,
! [SV50: subst,SV48: term,SV47: term > $o,SV71: term] :
( ( ( var @ SV71 )
= $false )
| ( ( SV47 @ ( sub @ SV71 @ ( push @ SV48 @ SV50 ) ) )
= $true )
| ( ( SV47 @ SV48 )
= $false )
| ( ( var @ ( sK4_SY54 @ SV48 @ SV50 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(338,plain,
! [SV49: term > $o] :
( ( ( ! [SY114: term] :
( ~ ( SV49 @ SY114 )
| ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SY114 @ id ) ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[315]) ).
thf(339,plain,
! [SV76: term,SV49: term > $o] :
( ( ( ! [SY138: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY138 ) ) )
| ( SV49 @ ( sub @ SV76 @ SY138 ) ) ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK13_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(340,plain,
! [SV49: term > $o] :
( ( ( ~ ! [SY134: term] :
( ~ ( SV49 @ SY134 )
| ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SY134 @ id ) ) ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(341,plain,
! [SV49: term > $o] :
( ( ( SV49 @ ( lam @ ( sK19_SY49 @ SV49 ) ) )
= $false )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[317]) ).
thf(342,plain,
! [SV49: term > $o] :
( ( ( ! [SY115: term] :
( ~ ( SV49 @ SY115 )
| ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SY115 @ id ) ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[318]) ).
thf(343,plain,
! [SV77: term,SV49: term > $o] :
( ( ( ! [SY140: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY140 ) ) )
| ( SV49 @ ( sub @ SV77 @ SY140 ) ) ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK14_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(344,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 )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(345,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK20_SY116 @ SV51 ) )
| ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK20_SY116 @ SV51 ) ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(346,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( sK11_SY57 @ SV51 ) )
= $true )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[321]) ).
thf(347,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(348,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[322]) ).
thf(349,plain,
! [SV60: subst > term > term] :
( ( ( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ ( sK21_SY118 @ SV60 ) ) @ ( sK25_SY135 @ SV60 ) )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) @ ( sub @ ( sK21_SY118 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) ) )
= $false )
| ( ( ! [SY81: subst > term > term] :
( ~ ! [SX2: subst,SX3: term,SX4: subst] :
( ( sub @ ( SY81 @ SX2 @ SX3 ) @ SX4 )
= ( SY81 @ ( comp @ SX2 @ SX4 ) @ ( sub @ SX3 @ SX4 ) ) )
| ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SY81 @ sh @ one ) ) )
| ! [SY85: subst,SY86: term] :
( ( SV60 @ SY85 @ SY86 )
= ( SY81 @ SY85 @ SY86 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[325]) ).
thf(350,plain,
! [SV64: subst > term > term] :
( ( ( ! [SY142: subst] :
( ( sub @ ( SV64 @ ( sK22_SY89 @ SV64 ) @ ( sK26_SY136 @ SV64 ) ) @ SY142 )
= ( SV64 @ ( comp @ ( sK22_SY89 @ SV64 ) @ SY142 ) @ ( sub @ ( sK26_SY136 @ SV64 ) @ SY142 ) ) ) )
= $false )
| ( ( ! [SY92: term,SY93: term] :
( ( lam @ ( SV64 @ sh @ one ) )
!= ( ap @ ( sub @ SY92 @ id ) @ SY93 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[326]) ).
thf(351,plain,
! [SV70: subst > term > term] :
( ( ( ! [SY143: term,SY144: subst] :
( ( sub @ ( SV70 @ ( sK27_SY97 @ SV70 ) @ SY143 ) @ SY144 )
= ( SV70 @ ( comp @ ( sK27_SY97 @ SV70 ) @ SY144 ) @ ( sub @ SY143 @ SY144 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV70 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[327]) ).
thf(352,plain,
! [SV75: term,SV73: term] :
( ( var @ ( sub @ ( ap @ ( sub @ SV73 @ id ) @ SV75 ) @ id ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(353,plain,
( ( ! [SY101: subst,SY102: term,SY103: subst,SY104: subst] :
( ~ ( sK12_SX0 @ SY101 @ SY102 @ ( comp @ SY104 @ SY103 ) )
| ( sK12_SX0 @ ( comp @ SY101 @ SY104 ) @ ( sub @ SY102 @ SY104 ) @ SY103 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[329]) ).
thf(354,plain,
( ( ~ ! [SY105: subst,SY106: term,SY107: subst,SY108: subst] :
( ~ ( sK12_SX0 @ ( comp @ SY105 @ SY108 ) @ ( sub @ SY106 @ SY108 ) @ SY107 )
| ( sK12_SX0 @ SY105 @ SY106 @ ( comp @ SY108 @ SY107 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(355,plain,
( ( ~ ! [SY109: term,SY110: term] :
( ~ ( sK12_SX0 @ id @ SY109 @ id )
| ~ ( sK12_SX0 @ id @ SY110 @ id )
| ( sK12_SX0 @ id @ ( ap @ ( sub @ SY109 @ id ) @ SY110 ) @ id ) )
| ~ ! [SY131: term] :
~ ( ~ ( ~ ( sK18_SY100 @ SY131 )
| ( sK12_SX0 @ id @ SY131 @ id ) )
| ~ ( ~ ( sK12_SX0 @ id @ SY131 @ id )
| ( sK18_SY100 @ SY131 ) ) )
| ! [SY132: term,SY133: term] :
( ~ ( sK18_SY100 @ SY132 )
| ~ ( sK18_SY100 @ SY133 )
| ( sK18_SY100 @ ( ap @ SY132 @ SY133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[330]) ).
thf(356,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK28_SY38 @ SV45 ) )
| ( SV45 @ ( lam @ ( sK28_SY38 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK8_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[331]) ).
thf(357,plain,
! [SV45: term > $o] :
( ( ( ! [SY38: term] :
( ~ ( SV45 @ SY38 )
| ( SV45 @ ( lam @ SY38 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK10_SY72 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(358,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK29_SY38 @ SV45 ) )
| ( SV45 @ ( lam @ ( sK29_SY38 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK8_SY36 @ SV45 ) @ ( sK10_SY72 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[333]) ).
thf(359,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK23_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK7_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(360,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( lam @ ( sK23_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK7_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[334]) ).
thf(361,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK30_SY38 @ SV45 ) )
| ( SV45 @ ( lam @ ( sK30_SY38 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK9_SY66 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[335]) ).
thf(362,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK24_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK7_SY36 @ SV45 ) @ ( sK9_SY66 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(363,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( lam @ ( sK24_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK7_SY36 @ SV45 ) @ ( sK9_SY66 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(364,plain,
! [SV78: term,SV49: term > $o] :
( ( ( ~ ( SV49 @ SV78 )
| ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SV78 @ id ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(365,plain,
! [SV76: term,SV79: subst,SV49: term > $o] :
( ( ( ~ ! [SY145: term] :
( ~ ( var @ SY145 )
| ( SV49 @ ( sub @ SY145 @ SV79 ) ) )
| ( SV49 @ ( sub @ SV76 @ SV79 ) ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK13_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(366,plain,
! [SV49: term > $o] :
( ( ( ! [SY134: term] :
( ~ ( SV49 @ SY134 )
| ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SY134 @ id ) ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[340]) ).
thf(367,plain,
! [SV80: term,SV49: term > $o] :
( ( ( ! [SY146: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY146 ) ) )
| ( SV49 @ ( sub @ SV80 @ SY146 ) ) ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK19_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(368,plain,
! [SV81: term,SV49: term > $o] :
( ( ( ~ ( SV49 @ SV81 )
| ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SV81 @ id ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(369,plain,
! [SV77: term,SV82: subst,SV49: term > $o] :
( ( ( ~ ! [SY148: term] :
( ~ ( var @ SY148 )
| ( SV49 @ ( sub @ SY148 @ SV82 ) ) )
| ( SV49 @ ( sub @ SV77 @ SV82 ) ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK14_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(370,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 )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[344]) ).
thf(371,plain,
! [SV51: term > $o] :
( ( ( ~ ( SV51 @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(372,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[345]) ).
thf(373,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 @ ( sK11_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(374,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( sK16_SY94 @ SV51 ) )
= $true )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[347]) ).
thf(375,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 @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(376,plain,
! [SV60: subst > term > term,SV83: subst > term > term] :
( ( ( ~ ! [SY149: subst,SY150: term,SY151: subst] :
( ( sub @ ( SV83 @ SY149 @ SY150 ) @ SY151 )
= ( SV83 @ ( comp @ SY149 @ SY151 ) @ ( sub @ SY150 @ SY151 ) ) )
| ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SV83 @ sh @ one ) ) )
| ! [SY152: subst,SY153: term] :
( ( SV60 @ SY152 @ SY153 )
= ( SV83 @ SY152 @ SY153 ) ) )
= $true )
| ( ( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ ( sK21_SY118 @ SV60 ) ) @ ( sK25_SY135 @ SV60 ) )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) @ ( sub @ ( sK21_SY118 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(377,plain,
! [SV64: subst > term > term] :
( ( ( ( sub @ ( SV64 @ ( sK22_SY89 @ SV64 ) @ ( sK26_SY136 @ SV64 ) ) @ ( sK31_SY142 @ SV64 ) )
= ( SV64 @ ( comp @ ( sK22_SY89 @ SV64 ) @ ( sK31_SY142 @ SV64 ) ) @ ( sub @ ( sK26_SY136 @ SV64 ) @ ( sK31_SY142 @ SV64 ) ) ) )
= $false )
| ( ( ! [SY92: term,SY93: term] :
( ( lam @ ( SV64 @ sh @ one ) )
!= ( ap @ ( sub @ SY92 @ id ) @ SY93 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[350]) ).
thf(378,plain,
! [SV70: subst > term > term] :
( ( ( ! [SY154: subst] :
( ( sub @ ( SV70 @ ( sK27_SY97 @ SV70 ) @ ( sK32_SY143 @ SV70 ) ) @ SY154 )
= ( SV70 @ ( comp @ ( sK27_SY97 @ SV70 ) @ SY154 ) @ ( sub @ ( sK32_SY143 @ SV70 ) @ SY154 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV70 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[351]) ).
thf(379,plain,
! [SV84: subst] :
( ( ! [SY155: term,SY156: subst,SY157: subst] :
( ~ ( sK12_SX0 @ SV84 @ SY155 @ ( comp @ SY157 @ SY156 ) )
| ( sK12_SX0 @ ( comp @ SV84 @ SY157 ) @ ( sub @ SY155 @ SY157 ) @ SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(380,plain,
( ( ! [SY105: subst,SY106: term,SY107: subst,SY108: subst] :
( ~ ( sK12_SX0 @ ( comp @ SY105 @ SY108 ) @ ( sub @ SY106 @ SY108 ) @ SY107 )
| ( sK12_SX0 @ SY105 @ SY106 @ ( comp @ SY108 @ SY107 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[354]) ).
thf(381,plain,
( ( ~ ! [SY109: term,SY110: term] :
( ~ ( sK12_SX0 @ id @ SY109 @ id )
| ~ ( sK12_SX0 @ id @ SY110 @ id )
| ( sK12_SX0 @ id @ ( ap @ ( sub @ SY109 @ id ) @ SY110 ) @ id ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(382,plain,
( ( ~ ! [SY131: term] :
~ ( ~ ( ~ ( sK18_SY100 @ SY131 )
| ( sK12_SX0 @ id @ SY131 @ id ) )
| ~ ( ~ ( sK12_SX0 @ id @ SY131 @ id )
| ( sK18_SY100 @ SY131 ) ) )
| ! [SY132: term,SY133: term] :
( ~ ( sK18_SY100 @ SY132 )
| ~ ( sK18_SY100 @ SY133 )
| ( sK18_SY100 @ ( ap @ SY132 @ SY133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[355]) ).
thf(383,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK28_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK8_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(384,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( lam @ ( sK28_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK8_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[356]) ).
thf(385,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK33_SY38 @ SV45 ) )
| ( SV45 @ ( lam @ ( sK33_SY38 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK10_SY72 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[357]) ).
thf(386,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK29_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK8_SY36 @ SV45 ) @ ( sK10_SY72 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(387,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( lam @ ( sK29_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK8_SY36 @ SV45 ) @ ( sK10_SY72 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[358]) ).
thf(388,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK23_SY38 @ SV45 ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK7_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[359]) ).
thf(389,plain,
! [SV85: term,SV45: term > $o] :
( ( ( SV45 @ SV85 )
= $true )
| ( ( SV45 @ ( lam @ ( sK23_SY38 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK7_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(390,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK30_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK9_SY66 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[361]) ).
thf(391,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( lam @ ( sK30_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK9_SY66 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[361]) ).
thf(392,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK24_SY38 @ SV45 ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK7_SY36 @ SV45 ) @ ( sK9_SY66 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[362]) ).
thf(393,plain,
! [SV86: term,SV45: term > $o] :
( ( ( SV45 @ SV86 )
= $true )
| ( ( SV45 @ ( lam @ ( sK24_SY38 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( ap @ ( sK7_SY36 @ SV45 ) @ ( sK9_SY66 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(394,plain,
! [SV78: term,SV49: term > $o] :
( ( ( ~ ( SV49 @ SV78 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SV78 @ id ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(395,plain,
! [SV76: term,SV79: subst,SV49: term > $o] :
( ( ( ~ ! [SY145: term] :
( ~ ( var @ SY145 )
| ( SV49 @ ( sub @ SY145 @ SV79 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ SV76 @ SV79 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK13_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(396,plain,
! [SV87: term,SV49: term > $o] :
( ( ( ~ ( SV49 @ SV87 )
| ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SV87 @ id ) ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(397,plain,
! [SV80: term,SV88: subst,SV49: term > $o] :
( ( ( ~ ! [SY158: term] :
( ~ ( var @ SY158 )
| ( SV49 @ ( sub @ SY158 @ SV88 ) ) )
| ( SV49 @ ( sub @ SV80 @ SV88 ) ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK19_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(398,plain,
! [SV81: term,SV49: term > $o] :
( ( ( ~ ( SV49 @ SV81 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SV81 @ id ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(399,plain,
! [SV77: term,SV82: subst,SV49: term > $o] :
( ( ( ~ ! [SY148: term] :
( ~ ( var @ SY148 )
| ( SV49 @ ( sub @ SY148 @ SV82 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ SV77 @ SV82 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK14_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(400,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 )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(401,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( sK20_SY116 @ SV51 ) )
= $true )
| ( ( ~ ! [SY59: term] :
( ~ ! [SY60: term] :
( ~ ( SV51 @ SY60 )
| ( SV51 @ ( sub @ SY59 @ ( push @ SY60 @ id ) ) ) )
| ( SV51 @ ( lam @ SY59 ) ) )
| ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[371]) ).
thf(402,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 ) @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(403,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 @ ( sK11_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(404,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 @ ( sK16_SY94 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(405,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 @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(406,plain,
! [SV60: subst > term > term,SV83: subst > term > term] :
( ( ( ~ ! [SY149: subst,SY150: term,SY151: subst] :
( ( sub @ ( SV83 @ SY149 @ SY150 ) @ SY151 )
= ( SV83 @ ( comp @ SY149 @ SY151 ) @ ( sub @ SY150 @ SY151 ) ) ) )
= $true )
| ( ( ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SV83 @ sh @ one ) ) )
| ! [SY152: subst,SY153: term] :
( ( SV60 @ SY152 @ SY153 )
= ( SV83 @ SY152 @ SY153 ) ) )
= $true )
| ( ( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ ( sK21_SY118 @ SV60 ) ) @ ( sK25_SY135 @ SV60 ) )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) @ ( sub @ ( sK21_SY118 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(407,plain,
! [SV89: term,SV64: subst > term > term] :
( ( ( ! [SY159: term] :
( ( lam @ ( SV64 @ sh @ one ) )
!= ( ap @ ( sub @ SV89 @ id ) @ SY159 ) ) )
= $true )
| ( ( ( sub @ ( SV64 @ ( sK22_SY89 @ SV64 ) @ ( sK26_SY136 @ SV64 ) ) @ ( sK31_SY142 @ SV64 ) )
= ( SV64 @ ( comp @ ( sK22_SY89 @ SV64 ) @ ( sK31_SY142 @ SV64 ) ) @ ( sub @ ( sK26_SY136 @ SV64 ) @ ( sK31_SY142 @ SV64 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(408,plain,
! [SV70: subst > term > term] :
( ( ( ( sub @ ( SV70 @ ( sK27_SY97 @ SV70 ) @ ( sK32_SY143 @ SV70 ) ) @ ( sK34_SY154 @ SV70 ) )
= ( SV70 @ ( comp @ ( sK27_SY97 @ SV70 ) @ ( sK34_SY154 @ SV70 ) ) @ ( sub @ ( sK32_SY143 @ SV70 ) @ ( sK34_SY154 @ SV70 ) ) ) )
= $false )
| ( ( ~ ( var @ ( sub @ ( lam @ ( SV70 @ sh @ one ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[378]) ).
thf(409,plain,
! [SV90: term,SV84: subst] :
( ( ! [SY160: subst,SY161: subst] :
( ~ ( sK12_SX0 @ SV84 @ SV90 @ ( comp @ SY161 @ SY160 ) )
| ( sK12_SX0 @ ( comp @ SV84 @ SY161 ) @ ( sub @ SV90 @ SY161 ) @ SY160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(410,plain,
! [SV91: subst] :
( ( ! [SY162: term,SY163: subst,SY164: subst] :
( ~ ( sK12_SX0 @ ( comp @ SV91 @ SY164 ) @ ( sub @ SY162 @ SY164 ) @ SY163 )
| ( sK12_SX0 @ SV91 @ SY162 @ ( comp @ SY164 @ SY163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(411,plain,
( ( ! [SY109: term,SY110: term] :
( ~ ( sK12_SX0 @ id @ SY109 @ id )
| ~ ( sK12_SX0 @ id @ SY110 @ id )
| ( sK12_SX0 @ id @ ( ap @ ( sub @ SY109 @ id ) @ SY110 ) @ id ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[381]) ).
thf(412,plain,
( ( ~ ! [SY131: term] :
~ ( ~ ( ~ ( sK18_SY100 @ SY131 )
| ( sK12_SX0 @ id @ SY131 @ id ) )
| ~ ( ~ ( sK12_SX0 @ id @ SY131 @ id )
| ( sK18_SY100 @ SY131 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(413,plain,
( ( ! [SY132: term,SY133: term] :
( ~ ( sK18_SY100 @ SY132 )
| ~ ( sK18_SY100 @ SY133 )
| ( sK18_SY100 @ ( ap @ SY132 @ SY133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[382]) ).
thf(414,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK28_SY38 @ SV45 ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK8_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[383]) ).
thf(415,plain,
! [SV92: term,SV45: term > $o] :
( ( ( SV45 @ SV92 )
= $true )
| ( ( SV45 @ ( lam @ ( sK28_SY38 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK8_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(416,plain,
! [SV45: term > $o] :
( ( ( ~ ( SV45 @ ( sK33_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK10_SY72 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(417,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( lam @ ( sK33_SY38 @ SV45 ) ) )
= $false )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK10_SY72 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[385]) ).
thf(418,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK29_SY38 @ SV45 ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK8_SY36 @ SV45 ) @ ( sK10_SY72 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[386]) ).
thf(419,plain,
! [SV93: term,SV45: term > $o] :
( ( ( SV45 @ SV93 )
= $true )
| ( ( SV45 @ ( lam @ ( sK29_SY38 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( ap @ ( sK8_SY36 @ SV45 ) @ ( sK10_SY72 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(420,plain,
! [SV94: term,SV45: term > $o] :
( ( ( SV45 @ SV94 )
= $true )
| ( ( SV45 @ ( sK23_SY38 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK7_SY36 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(421,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK30_SY38 @ SV45 ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK9_SY66 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[390]) ).
thf(422,plain,
! [SV95: term,SV45: term > $o] :
( ( ( SV45 @ SV95 )
= $true )
| ( ( SV45 @ ( lam @ ( sK30_SY38 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK9_SY66 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(423,plain,
! [SV96: term,SV45: term > $o] :
( ( ( SV45 @ SV96 )
= $true )
| ( ( SV45 @ ( sK24_SY38 @ SV45 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK7_SY36 @ SV45 ) @ ( sK9_SY66 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(424,plain,
! [SV78: term,SV49: term > $o] :
( ( ( SV49 @ SV78 )
= $false )
| ( ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SV78 @ id ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(425,plain,
! [SV76: term,SV79: subst,SV49: term > $o] :
( ( ( ! [SY145: term] :
( ~ ( var @ SY145 )
| ( SV49 @ ( sub @ SY145 @ SV79 ) ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV76 @ SV79 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK13_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(426,plain,
! [SV87: term,SV49: term > $o] :
( ( ( ~ ( SV49 @ SV87 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SV87 @ id ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(427,plain,
! [SV80: term,SV88: subst,SV49: term > $o] :
( ( ( ~ ! [SY158: term] :
( ~ ( var @ SY158 )
| ( SV49 @ ( sub @ SY158 @ SV88 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ SV80 @ SV88 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK19_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(428,plain,
! [SV81: term,SV49: term > $o] :
( ( ( SV49 @ SV81 )
= $false )
| ( ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SV81 @ id ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(429,plain,
! [SV77: term,SV82: subst,SV49: term > $o] :
( ( ( ! [SY148: term] :
( ~ ( var @ SY148 )
| ( SV49 @ ( sub @ SY148 @ SV82 ) ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV77 @ SV82 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK14_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(430,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 )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(431,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 @ ( sK20_SY116 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(432,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 ) @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(433,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY165: term] :
( ~ ( SV51 @ SY165 )
| ( SV51 @ ( sub @ ( sK35_SY59 @ SV51 ) @ ( push @ SY165 @ id ) ) ) )
| ( SV51 @ ( lam @ ( sK35_SY59 @ SV51 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK11_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[403]) ).
thf(434,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 @ ( sK16_SY94 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(435,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV51 @ SY166 )
| ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SY166 @ id ) ) ) )
| ( SV51 @ ( lam @ ( sK36_SY59 @ SV51 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[405]) ).
thf(436,plain,
! [SV60: subst > term > term,SV83: subst > term > term] :
( ( ( ! [SY149: subst,SY150: term,SY151: subst] :
( ( sub @ ( SV83 @ SY149 @ SY150 ) @ SY151 )
= ( SV83 @ ( comp @ SY149 @ SY151 ) @ ( sub @ SY150 @ SY151 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SV83 @ sh @ one ) ) )
| ! [SY152: subst,SY153: term] :
( ( SV60 @ SY152 @ SY153 )
= ( SV83 @ SY152 @ SY153 ) ) )
= $true )
| ( ( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ ( sK21_SY118 @ SV60 ) ) @ ( sK25_SY135 @ SV60 ) )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) @ ( sub @ ( sK21_SY118 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(437,plain,
! [SV97: term,SV89: term,SV64: subst > term > term] :
( ( ( ( ( lam @ ( SV64 @ sh @ one ) )
!= ( ap @ ( sub @ SV89 @ id ) @ SV97 ) ) )
= $true )
| ( ( ( sub @ ( SV64 @ ( sK22_SY89 @ SV64 ) @ ( sK26_SY136 @ SV64 ) ) @ ( sK31_SY142 @ SV64 ) )
= ( SV64 @ ( comp @ ( sK22_SY89 @ SV64 ) @ ( sK31_SY142 @ SV64 ) ) @ ( sub @ ( sK26_SY136 @ SV64 ) @ ( sK31_SY142 @ SV64 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(438,plain,
! [SV70: subst > term > term] :
( ( ( var @ ( sub @ ( lam @ ( SV70 @ sh @ one ) ) @ id ) )
= $false )
| ( ( ( sub @ ( SV70 @ ( sK27_SY97 @ SV70 ) @ ( sK32_SY143 @ SV70 ) ) @ ( sK34_SY154 @ SV70 ) )
= ( SV70 @ ( comp @ ( sK27_SY97 @ SV70 ) @ ( sK34_SY154 @ SV70 ) ) @ ( sub @ ( sK32_SY143 @ SV70 ) @ ( sK34_SY154 @ SV70 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(439,plain,
! [SV98: subst,SV90: term,SV84: subst] :
( ( ! [SY167: subst] :
( ~ ( sK12_SX0 @ SV84 @ SV90 @ ( comp @ SY167 @ SV98 ) )
| ( sK12_SX0 @ ( comp @ SV84 @ SY167 ) @ ( sub @ SV90 @ SY167 ) @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(440,plain,
! [SV99: term,SV91: subst] :
( ( ! [SY168: subst,SY169: subst] :
( ~ ( sK12_SX0 @ ( comp @ SV91 @ SY169 ) @ ( sub @ SV99 @ SY169 ) @ SY168 )
| ( sK12_SX0 @ SV91 @ SV99 @ ( comp @ SY169 @ SY168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(441,plain,
! [SV100: term] :
( ( ! [SY170: term] :
( ~ ( sK12_SX0 @ id @ SV100 @ id )
| ~ ( sK12_SX0 @ id @ SY170 @ id )
| ( sK12_SX0 @ id @ ( ap @ ( sub @ SV100 @ id ) @ SY170 ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(442,plain,
( ( ! [SY131: term] :
~ ( ~ ( ~ ( sK18_SY100 @ SY131 )
| ( sK12_SX0 @ id @ SY131 @ id ) )
| ~ ( ~ ( sK12_SX0 @ id @ SY131 @ id )
| ( sK18_SY100 @ SY131 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[412]) ).
thf(443,plain,
( ( ! [SY171: term] :
( ~ ( sK18_SY100 @ sK37_SY132 )
| ~ ( sK18_SY100 @ SY171 )
| ( sK18_SY100 @ ( ap @ sK37_SY132 @ SY171 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[413]) ).
thf(444,plain,
! [SV101: term,SV45: term > $o] :
( ( ( SV45 @ SV101 )
= $true )
| ( ( SV45 @ ( sK28_SY38 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK8_SY36 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(445,plain,
! [SV45: term > $o] :
( ( ( SV45 @ ( sK33_SY38 @ SV45 ) )
= $true )
| ( ( ! [SY39: term] : ( SV45 @ SY39 ) )
= $true )
| ( ( SV45 @ ( sK10_SY72 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[416]) ).
thf(446,plain,
! [SV102: term,SV45: term > $o] :
( ( ( SV45 @ SV102 )
= $true )
| ( ( SV45 @ ( lam @ ( sK33_SY38 @ SV45 ) ) )
= $false )
| ( ( SV45 @ ( sK10_SY72 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(447,plain,
! [SV103: term,SV45: term > $o] :
( ( ( SV45 @ SV103 )
= $true )
| ( ( SV45 @ ( sK29_SY38 @ SV45 ) )
= $true )
| ( ( SV45 @ ( ap @ ( sK8_SY36 @ SV45 ) @ ( sK10_SY72 @ SV45 ) ) )
= $false )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(448,plain,
! [SV104: term,SV45: term > $o] :
( ( ( SV45 @ SV104 )
= $true )
| ( ( SV45 @ ( sK30_SY38 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK9_SY66 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK2_SY35 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(449,plain,
! [SV78: term,SV105: term,SV49: term > $o] :
( ( ( ! [SY172: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY172 ) ) )
| ( SV49 @ ( sub @ SV105 @ SY172 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SV78 @ id ) ) )
= $true )
| ( ( SV49 @ SV78 )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(450,plain,
! [SV49: term > $o,SV79: subst,SV76: term] :
( ( ( ~ ( var @ ( sK38_SY145 @ SV76 @ SV79 @ SV49 ) )
| ( SV49 @ ( sub @ ( sK38_SY145 @ SV76 @ SV79 @ SV49 ) @ SV79 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV76 @ SV79 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK13_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[425]) ).
thf(451,plain,
! [SV87: term,SV49: term > $o] :
( ( ( SV49 @ SV87 )
= $false )
| ( ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SV87 @ id ) ) )
= $true )
| ( ( ! [SY51: term,SY52: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY52 ) ) )
| ( SV49 @ ( sub @ SY51 @ SY52 ) ) ) )
= $true )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(452,plain,
! [SV80: term,SV88: subst,SV49: term > $o] :
( ( ( ! [SY158: term] :
( ~ ( var @ SY158 )
| ( SV49 @ ( sub @ SY158 @ SV88 ) ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV80 @ SV88 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK19_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(453,plain,
! [SV81: term,SV106: term,SV49: term > $o] :
( ( ( ! [SY174: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY174 ) ) )
| ( SV49 @ ( sub @ SV106 @ SY174 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SV81 @ id ) ) )
= $true )
| ( ( SV49 @ SV81 )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(454,plain,
! [SV49: term > $o,SV82: subst,SV77: term] :
( ( ( ~ ( var @ ( sK39_SY148 @ SV77 @ SV82 @ SV49 ) )
| ( SV49 @ ( sub @ ( sK39_SY148 @ SV77 @ SV82 @ SV49 ) @ SV82 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV77 @ SV82 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK14_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[429]) ).
thf(455,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY176: term] :
( ~ ( SV51 @ SY176 )
| ( SV51 @ ( sub @ ( sK40_SY59 @ SV51 ) @ ( push @ SY176 @ id ) ) ) )
| ( SV51 @ ( lam @ ( sK40_SY59 @ SV51 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[430]) ).
thf(456,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 @ ( sK20_SY116 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(457,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY177: term] :
( ~ ( SV51 @ SY177 )
| ( SV51 @ ( sub @ ( sK41_SY59 @ SV51 ) @ ( push @ SY177 @ id ) ) ) )
| ( SV51 @ ( lam @ ( sK41_SY59 @ SV51 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[432]) ).
thf(458,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY165: term] :
( ~ ( SV51 @ SY165 )
| ( SV51 @ ( sub @ ( sK35_SY59 @ SV51 ) @ ( push @ SY165 @ id ) ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK11_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(459,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( lam @ ( sK35_SY59 @ SV51 ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK11_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(460,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY178: term] :
( ~ ( SV51 @ SY178 )
| ( SV51 @ ( sub @ ( sK42_SY59 @ SV51 ) @ ( push @ SY178 @ id ) ) ) )
| ( SV51 @ ( lam @ ( sK42_SY59 @ SV51 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK16_SY94 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[434]) ).
thf(461,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY166: term] :
( ~ ( SV51 @ SY166 )
| ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SY166 @ id ) ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(462,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( lam @ ( sK36_SY59 @ SV51 ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(463,plain,
! [SV60: subst > term > term,SV83: subst > term > term] :
( ( ( ! [SY179: term,SY180: subst] :
( ( sub @ ( SV83 @ ( sK43_SY149 @ SV60 @ SV83 ) @ SY179 ) @ SY180 )
= ( SV83 @ ( comp @ ( sK43_SY149 @ SV60 @ SV83 ) @ SY180 ) @ ( sub @ SY179 @ SY180 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SV83 @ sh @ one ) ) )
| ! [SY152: subst,SY153: term] :
( ( SV60 @ SY152 @ SY153 )
= ( SV83 @ SY152 @ SY153 ) ) )
= $true )
| ( ( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ ( sK21_SY118 @ SV60 ) ) @ ( sK25_SY135 @ SV60 ) )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) @ ( sub @ ( sK21_SY118 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[436]) ).
thf(464,plain,
! [SV97: term,SV89: term,SV64: subst > term > term] :
( ( ( ( lam @ ( SV64 @ sh @ one ) )
= ( ap @ ( sub @ SV89 @ id ) @ SV97 ) )
= $false )
| ( ( ( sub @ ( SV64 @ ( sK22_SY89 @ SV64 ) @ ( sK26_SY136 @ SV64 ) ) @ ( sK31_SY142 @ SV64 ) )
= ( SV64 @ ( comp @ ( sK22_SY89 @ SV64 ) @ ( sK31_SY142 @ SV64 ) ) @ ( sub @ ( sK26_SY136 @ SV64 ) @ ( sK31_SY142 @ SV64 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(465,plain,
! [SV98: subst,SV107: subst,SV90: term,SV84: subst] :
( ( ~ ( sK12_SX0 @ SV84 @ SV90 @ ( comp @ SV107 @ SV98 ) )
| ( sK12_SX0 @ ( comp @ SV84 @ SV107 ) @ ( sub @ SV90 @ SV107 ) @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(466,plain,
! [SV108: subst,SV99: term,SV91: subst] :
( ( ! [SY181: subst] :
( ~ ( sK12_SX0 @ ( comp @ SV91 @ SY181 ) @ ( sub @ SV99 @ SY181 ) @ SV108 )
| ( sK12_SX0 @ SV91 @ SV99 @ ( comp @ SY181 @ SV108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(467,plain,
! [SV109: term,SV100: term] :
( ( ~ ( sK12_SX0 @ id @ SV100 @ id )
| ~ ( sK12_SX0 @ id @ SV109 @ id )
| ( sK12_SX0 @ id @ ( ap @ ( sub @ SV100 @ id ) @ SV109 ) @ id ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(468,plain,
! [SV110: term] :
( ( ~ ( ~ ( ~ ( sK18_SY100 @ SV110 )
| ( sK12_SX0 @ id @ SV110 @ id ) )
| ~ ( ~ ( sK12_SX0 @ id @ SV110 @ id )
| ( sK18_SY100 @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(469,plain,
( ( ~ ( sK18_SY100 @ sK37_SY132 )
| ~ ( sK18_SY100 @ sK44_SY171 )
| ( sK18_SY100 @ ( ap @ sK37_SY132 @ sK44_SY171 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[443]) ).
thf(470,plain,
! [SV111: term,SV45: term > $o] :
( ( ( SV45 @ SV111 )
= $true )
| ( ( SV45 @ ( sK33_SY38 @ SV45 ) )
= $true )
| ( ( SV45 @ ( sK10_SY72 @ SV45 ) )
= $true )
| ( ( var @ ( sK2_SY35 @ SV45 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(471,plain,
! [SV78: term,SV105: term,SV112: subst,SV49: term > $o] :
( ( ( ~ ! [SY182: term] :
( ~ ( var @ SY182 )
| ( SV49 @ ( sub @ SY182 @ SV112 ) ) )
| ( SV49 @ ( sub @ SV105 @ SV112 ) ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SV78 @ id ) ) )
= $true )
| ( ( SV49 @ SV78 )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(472,plain,
! [SV49: term > $o,SV79: subst,SV76: term] :
( ( ( ~ ( var @ ( sK38_SY145 @ SV76 @ SV79 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV76 @ SV79 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK13_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(473,plain,
! [SV79: subst,SV76: term,SV49: term > $o] :
( ( ( SV49 @ ( sub @ ( sK38_SY145 @ SV76 @ SV79 @ SV49 ) @ SV79 ) )
= $false )
| ( ( SV49 @ ( sub @ SV76 @ SV79 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK13_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[450]) ).
thf(474,plain,
! [SV87: term,SV113: term,SV49: term > $o] :
( ( ( ! [SY183: subst] :
( ~ ! [SY53: term] :
( ~ ( var @ SY53 )
| ( SV49 @ ( sub @ SY53 @ SY183 ) ) )
| ( SV49 @ ( sub @ SV113 @ SY183 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SV87 @ id ) ) )
= $true )
| ( ( SV49 @ SV87 )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(475,plain,
! [SV49: term > $o,SV88: subst,SV80: term] :
( ( ( ~ ( var @ ( sK45_SY158 @ SV80 @ SV88 @ SV49 ) )
| ( SV49 @ ( sub @ ( sK45_SY158 @ SV80 @ SV88 @ SV49 ) @ SV88 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV80 @ SV88 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK19_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[452]) ).
thf(476,plain,
! [SV81: term,SV106: term,SV114: subst,SV49: term > $o] :
( ( ( ~ ! [SY185: term] :
( ~ ( var @ SY185 )
| ( SV49 @ ( sub @ SY185 @ SV114 ) ) )
| ( SV49 @ ( sub @ SV106 @ SV114 ) ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SV81 @ id ) ) )
= $true )
| ( ( SV49 @ SV81 )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(477,plain,
! [SV49: term > $o,SV82: subst,SV77: term] :
( ( ( ~ ( var @ ( sK39_SY148 @ SV77 @ SV82 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV77 @ SV82 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK14_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(478,plain,
! [SV82: subst,SV77: term,SV49: term > $o] :
( ( ( SV49 @ ( sub @ ( sK39_SY148 @ SV77 @ SV82 @ SV49 ) @ SV82 ) )
= $false )
| ( ( SV49 @ ( sub @ SV77 @ SV82 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK14_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[454]) ).
thf(479,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY176: term] :
( ~ ( SV51 @ SY176 )
| ( SV51 @ ( sub @ ( sK40_SY59 @ SV51 ) @ ( push @ SY176 @ id ) ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(480,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( lam @ ( sK40_SY59 @ SV51 ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[455]) ).
thf(481,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY186: term] :
( ~ ( SV51 @ SY186 )
| ( SV51 @ ( sub @ ( sK46_SY59 @ SV51 ) @ ( push @ SY186 @ id ) ) ) )
| ( SV51 @ ( lam @ ( sK46_SY59 @ SV51 ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK20_SY116 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[456]) ).
thf(482,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY177: term] :
( ~ ( SV51 @ SY177 )
| ( SV51 @ ( sub @ ( sK41_SY59 @ SV51 ) @ ( push @ SY177 @ id ) ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(483,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( lam @ ( sK41_SY59 @ SV51 ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[457]) ).
thf(484,plain,
! [SV51: term > $o] :
( ( ( ! [SY165: term] :
( ~ ( SV51 @ SY165 )
| ( SV51 @ ( sub @ ( sK35_SY59 @ SV51 ) @ ( push @ SY165 @ id ) ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK11_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(485,plain,
! [SV115: term,SV51: term > $o] :
( ( ( SV51 @ SV115 )
= $true )
| ( ( SV51 @ ( lam @ ( sK35_SY59 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK11_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(486,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY178: term] :
( ~ ( SV51 @ SY178 )
| ( SV51 @ ( sub @ ( sK42_SY59 @ SV51 ) @ ( push @ SY178 @ id ) ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK16_SY94 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(487,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( lam @ ( sK42_SY59 @ SV51 ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK16_SY94 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[460]) ).
thf(488,plain,
! [SV51: term > $o] :
( ( ( ! [SY166: term] :
( ~ ( SV51 @ SY166 )
| ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SY166 @ id ) ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(489,plain,
! [SV116: term,SV51: term > $o] :
( ( ( SV51 @ SV116 )
= $true )
| ( ( SV51 @ ( lam @ ( sK36_SY59 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(490,plain,
! [SV60: subst > term > term,SV83: subst > term > term] :
( ( ( ! [SY187: subst] :
( ( sub @ ( SV83 @ ( sK43_SY149 @ SV60 @ SV83 ) @ ( sK47_SY179 @ SV60 @ SV83 ) ) @ SY187 )
= ( SV83 @ ( comp @ ( sK43_SY149 @ SV60 @ SV83 ) @ SY187 ) @ ( sub @ ( sK47_SY179 @ SV60 @ SV83 ) @ SY187 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SV83 @ sh @ one ) ) )
| ! [SY152: subst,SY153: term] :
( ( SV60 @ SY152 @ SY153 )
= ( SV83 @ SY152 @ SY153 ) ) )
= $true )
| ( ( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ ( sK21_SY118 @ SV60 ) ) @ ( sK25_SY135 @ SV60 ) )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) @ ( sub @ ( sK21_SY118 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[463]) ).
thf(491,plain,
! [SV98: subst,SV107: subst,SV90: term,SV84: subst] :
( ( ( ~ ( sK12_SX0 @ SV84 @ SV90 @ ( comp @ SV107 @ SV98 ) ) )
= $true )
| ( ( sK12_SX0 @ ( comp @ SV84 @ SV107 ) @ ( sub @ SV90 @ SV107 ) @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(492,plain,
! [SV108: subst,SV99: term,SV117: subst,SV91: subst] :
( ( ~ ( sK12_SX0 @ ( comp @ SV91 @ SV117 ) @ ( sub @ SV99 @ SV117 ) @ SV108 )
| ( sK12_SX0 @ SV91 @ SV99 @ ( comp @ SV117 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(493,plain,
! [SV109: term,SV100: term] :
( ( ( ~ ( sK12_SX0 @ id @ SV100 @ id ) )
= $true )
| ( ( ~ ( sK12_SX0 @ id @ SV109 @ id )
| ( sK12_SX0 @ id @ ( ap @ ( sub @ SV100 @ id ) @ SV109 ) @ id ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(494,plain,
! [SV110: term] :
( ( ~ ( ~ ( sK18_SY100 @ SV110 )
| ( sK12_SX0 @ id @ SV110 @ id ) )
| ~ ( ~ ( sK12_SX0 @ id @ SV110 @ id )
| ( sK18_SY100 @ SV110 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(495,plain,
( ( ~ ( sK18_SY100 @ sK37_SY132 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(496,plain,
( ( ~ ( sK18_SY100 @ sK44_SY171 )
| ( sK18_SY100 @ ( ap @ sK37_SY132 @ sK44_SY171 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[469]) ).
thf(497,plain,
! [SV78: term,SV105: term,SV112: subst,SV49: term > $o] :
( ( ( ~ ! [SY182: term] :
( ~ ( var @ SY182 )
| ( SV49 @ ( sub @ SY182 @ SV112 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ SV105 @ SV112 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SV78 @ id ) ) )
= $true )
| ( ( SV49 @ SV78 )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(498,plain,
! [SV49: term > $o,SV79: subst,SV76: term] :
( ( ( var @ ( sK38_SY145 @ SV76 @ SV79 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sub @ SV76 @ SV79 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK13_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(499,plain,
! [SV87: term,SV113: term,SV118: subst,SV49: term > $o] :
( ( ( ~ ! [SY188: term] :
( ~ ( var @ SY188 )
| ( SV49 @ ( sub @ SY188 @ SV118 ) ) )
| ( SV49 @ ( sub @ SV113 @ SV118 ) ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SV87 @ id ) ) )
= $true )
| ( ( SV49 @ SV87 )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(500,plain,
! [SV49: term > $o,SV88: subst,SV80: term] :
( ( ( ~ ( var @ ( sK45_SY158 @ SV80 @ SV88 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV80 @ SV88 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK19_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(501,plain,
! [SV88: subst,SV80: term,SV49: term > $o] :
( ( ( SV49 @ ( sub @ ( sK45_SY158 @ SV80 @ SV88 @ SV49 ) @ SV88 ) )
= $false )
| ( ( SV49 @ ( sub @ SV80 @ SV88 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK19_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[475]) ).
thf(502,plain,
! [SV81: term,SV106: term,SV114: subst,SV49: term > $o] :
( ( ( ~ ! [SY185: term] :
( ~ ( var @ SY185 )
| ( SV49 @ ( sub @ SY185 @ SV114 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ SV106 @ SV114 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SV81 @ id ) ) )
= $true )
| ( ( SV49 @ SV81 )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(503,plain,
! [SV49: term > $o,SV82: subst,SV77: term] :
( ( ( var @ ( sK39_SY148 @ SV77 @ SV82 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sub @ SV77 @ SV82 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK14_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(504,plain,
! [SV51: term > $o] :
( ( ( ! [SY176: term] :
( ~ ( SV51 @ SY176 )
| ( SV51 @ ( sub @ ( sK40_SY59 @ SV51 ) @ ( push @ SY176 @ id ) ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(505,plain,
! [SV119: term,SV51: term > $o] :
( ( ( SV51 @ SV119 )
= $true )
| ( ( SV51 @ ( lam @ ( sK40_SY59 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(506,plain,
! [SV51: term > $o] :
( ( ( ~ ! [SY186: term] :
( ~ ( SV51 @ SY186 )
| ( SV51 @ ( sub @ ( sK46_SY59 @ SV51 ) @ ( push @ SY186 @ id ) ) ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK20_SY116 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(507,plain,
! [SV51: term > $o] :
( ( ( SV51 @ ( lam @ ( sK46_SY59 @ SV51 ) ) )
= $false )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK20_SY116 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[481]) ).
thf(508,plain,
! [SV51: term > $o] :
( ( ( ! [SY177: term] :
( ~ ( SV51 @ SY177 )
| ( SV51 @ ( sub @ ( sK41_SY59 @ SV51 ) @ ( push @ SY177 @ id ) ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(509,plain,
! [SV120: term,SV51: term > $o] :
( ( ( SV51 @ SV120 )
= $true )
| ( ( SV51 @ ( lam @ ( sK41_SY59 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(510,plain,
! [SV121: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV121 )
| ( SV51 @ ( sub @ ( sK35_SY59 @ SV51 ) @ ( push @ SV121 @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK11_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(511,plain,
! [SV51: term > $o] :
( ( ( ! [SY178: term] :
( ~ ( SV51 @ SY178 )
| ( SV51 @ ( sub @ ( sK42_SY59 @ SV51 ) @ ( push @ SY178 @ id ) ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK16_SY94 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(512,plain,
! [SV122: term,SV51: term > $o] :
( ( ( SV51 @ SV122 )
= $true )
| ( ( SV51 @ ( lam @ ( sK42_SY59 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK16_SY94 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(513,plain,
! [SV123: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV123 )
| ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SV123 @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(514,plain,
! [SV60: subst > term > term,SV83: subst > term > term] :
( ( ( ( sub @ ( SV83 @ ( sK43_SY149 @ SV60 @ SV83 ) @ ( sK47_SY179 @ SV60 @ SV83 ) ) @ ( sK48_SY187 @ SV60 @ SV83 ) )
= ( SV83 @ ( comp @ ( sK43_SY149 @ SV60 @ SV83 ) @ ( sK48_SY187 @ SV60 @ SV83 ) ) @ ( sub @ ( sK47_SY179 @ SV60 @ SV83 ) @ ( sK48_SY187 @ SV60 @ SV83 ) ) ) )
= $false )
| ( ( ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SV83 @ sh @ one ) ) )
| ! [SY152: subst,SY153: term] :
( ( SV60 @ SY152 @ SY153 )
= ( SV83 @ SY152 @ SY153 ) ) )
= $true )
| ( ( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ ( sK21_SY118 @ SV60 ) ) @ ( sK25_SY135 @ SV60 ) )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) @ ( sub @ ( sK21_SY118 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[490]) ).
thf(515,plain,
! [SV98: subst,SV107: subst,SV90: term,SV84: subst] :
( ( ( sK12_SX0 @ SV84 @ SV90 @ ( comp @ SV107 @ SV98 ) )
= $false )
| ( ( sK12_SX0 @ ( comp @ SV84 @ SV107 ) @ ( sub @ SV90 @ SV107 ) @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(516,plain,
! [SV108: subst,SV99: term,SV117: subst,SV91: subst] :
( ( ( ~ ( sK12_SX0 @ ( comp @ SV91 @ SV117 ) @ ( sub @ SV99 @ SV117 ) @ SV108 ) )
= $true )
| ( ( sK12_SX0 @ SV91 @ SV99 @ ( comp @ SV117 @ SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(517,plain,
! [SV109: term,SV100: term] :
( ( ( sK12_SX0 @ id @ SV100 @ id )
= $false )
| ( ( ~ ( sK12_SX0 @ id @ SV109 @ id )
| ( sK12_SX0 @ id @ ( ap @ ( sub @ SV100 @ id ) @ SV109 ) @ id ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(518,plain,
! [SV110: term] :
( ( ~ ( ~ ( sK18_SY100 @ SV110 )
| ( sK12_SX0 @ id @ SV110 @ id ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(519,plain,
! [SV110: term] :
( ( ~ ( ~ ( sK12_SX0 @ id @ SV110 @ id )
| ( sK18_SY100 @ SV110 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[494]) ).
thf(520,plain,
( ( sK18_SY100 @ sK37_SY132 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(521,plain,
( ( ~ ( sK18_SY100 @ sK44_SY171 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(522,plain,
( ( sK18_SY100 @ ( ap @ sK37_SY132 @ sK44_SY171 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[496]) ).
thf(523,plain,
! [SV78: term,SV105: term,SV112: subst,SV49: term > $o] :
( ( ( ! [SY182: term] :
( ~ ( var @ SY182 )
| ( SV49 @ ( sub @ SY182 @ SV112 ) ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV105 @ SV112 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SV78 @ id ) ) )
= $true )
| ( ( SV49 @ SV78 )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(524,plain,
! [SV87: term,SV113: term,SV118: subst,SV49: term > $o] :
( ( ( ~ ! [SY188: term] :
( ~ ( var @ SY188 )
| ( SV49 @ ( sub @ SY188 @ SV118 ) ) ) )
= $true )
| ( ( SV49 @ ( sub @ SV113 @ SV118 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SV87 @ id ) ) )
= $true )
| ( ( SV49 @ SV87 )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(525,plain,
! [SV49: term > $o,SV88: subst,SV80: term] :
( ( ( var @ ( sK45_SY158 @ SV80 @ SV88 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sub @ SV80 @ SV88 ) )
= $true )
| ( ( SV49 @ ( lam @ ( sK19_SY49 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(526,plain,
! [SV81: term,SV106: term,SV114: subst,SV49: term > $o] :
( ( ( ! [SY185: term] :
( ~ ( var @ SY185 )
| ( SV49 @ ( sub @ SY185 @ SV114 ) ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV106 @ SV114 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SV81 @ id ) ) )
= $true )
| ( ( SV49 @ SV81 )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(527,plain,
! [SV124: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV124 )
| ( SV51 @ ( sub @ ( sK40_SY59 @ SV51 ) @ ( push @ SV124 @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(528,plain,
! [SV51: term > $o] :
( ( ( ! [SY186: term] :
( ~ ( SV51 @ SY186 )
| ( SV51 @ ( sub @ ( sK46_SY59 @ SV51 ) @ ( push @ SY186 @ id ) ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK20_SY116 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(529,plain,
! [SV125: term,SV51: term > $o] :
( ( ( SV51 @ SV125 )
= $true )
| ( ( SV51 @ ( lam @ ( sK46_SY59 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK20_SY116 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(530,plain,
! [SV126: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV126 )
| ( SV51 @ ( sub @ ( sK41_SY59 @ SV51 ) @ ( push @ SV126 @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(531,plain,
! [SV121: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV121 ) )
= $true )
| ( ( SV51 @ ( sub @ ( sK35_SY59 @ SV51 ) @ ( push @ SV121 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK11_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[510]) ).
thf(532,plain,
! [SV127: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV127 )
| ( SV51 @ ( sub @ ( sK42_SY59 @ SV51 ) @ ( push @ SV127 @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK16_SY94 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(533,plain,
! [SV123: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV123 ) )
= $true )
| ( ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SV123 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(534,plain,
! [SV83: subst > term > term,SV60: subst > term > term] :
( ( ( ( ( lam @ ( SV60 @ sh @ one ) )
!= ( lam @ ( SV83 @ sh @ one ) ) ) )
= $true )
| ( ( ! [SY152: subst,SY153: term] :
( ( SV60 @ SY152 @ SY153 )
= ( SV83 @ SY152 @ SY153 ) ) )
= $true )
| ( ( ( sub @ ( SV83 @ ( sK43_SY149 @ SV60 @ SV83 ) @ ( sK47_SY179 @ SV60 @ SV83 ) ) @ ( sK48_SY187 @ SV60 @ SV83 ) )
= ( SV83 @ ( comp @ ( sK43_SY149 @ SV60 @ SV83 ) @ ( sK48_SY187 @ SV60 @ SV83 ) ) @ ( sub @ ( sK47_SY179 @ SV60 @ SV83 ) @ ( sK48_SY187 @ SV60 @ SV83 ) ) ) )
= $false )
| ( ( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ ( sK21_SY118 @ SV60 ) ) @ ( sK25_SY135 @ SV60 ) )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) @ ( sub @ ( sK21_SY118 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(535,plain,
! [SV108: subst,SV99: term,SV117: subst,SV91: subst] :
( ( ( sK12_SX0 @ ( comp @ SV91 @ SV117 ) @ ( sub @ SV99 @ SV117 ) @ SV108 )
= $false )
| ( ( sK12_SX0 @ SV91 @ SV99 @ ( comp @ SV117 @ SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(536,plain,
! [SV100: term,SV109: term] :
( ( ( ~ ( sK12_SX0 @ id @ SV109 @ id ) )
= $true )
| ( ( sK12_SX0 @ id @ ( ap @ ( sub @ SV100 @ id ) @ SV109 ) @ id )
= $true )
| ( ( sK12_SX0 @ id @ SV100 @ id )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(537,plain,
! [SV110: term] :
( ( ~ ( sK18_SY100 @ SV110 )
| ( sK12_SX0 @ id @ SV110 @ id ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(538,plain,
! [SV110: term] :
( ( ~ ( sK12_SX0 @ id @ SV110 @ id )
| ( sK18_SY100 @ SV110 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(539,plain,
( ( sK18_SY100 @ sK44_SY171 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(540,plain,
! [SV49: term > $o,SV112: subst,SV105: term,SV78: term] :
( ( ( ~ ( var @ ( sK49_SY182 @ SV78 @ SV105 @ SV112 @ SV49 ) )
| ( SV49 @ ( sub @ ( sK49_SY182 @ SV78 @ SV105 @ SV112 @ SV49 ) @ SV112 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV105 @ SV112 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SV78 @ id ) ) )
= $true )
| ( ( SV49 @ SV78 )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[523]) ).
thf(541,plain,
! [SV87: term,SV113: term,SV118: subst,SV49: term > $o] :
( ( ( ! [SY188: term] :
( ~ ( var @ SY188 )
| ( SV49 @ ( sub @ SY188 @ SV118 ) ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV113 @ SV118 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SV87 @ id ) ) )
= $true )
| ( ( SV49 @ SV87 )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[524]) ).
thf(542,plain,
! [SV49: term > $o,SV114: subst,SV106: term,SV81: term] :
( ( ( ~ ( var @ ( sK50_SY185 @ SV81 @ SV106 @ SV114 @ SV49 ) )
| ( SV49 @ ( sub @ ( sK50_SY185 @ SV81 @ SV106 @ SV114 @ SV49 ) @ SV114 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV106 @ SV114 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SV81 @ id ) ) )
= $true )
| ( ( SV49 @ SV81 )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[526]) ).
thf(543,plain,
! [SV124: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV124 ) )
= $true )
| ( ( SV51 @ ( sub @ ( sK40_SY59 @ SV51 ) @ ( push @ SV124 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(544,plain,
! [SV128: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV128 )
| ( SV51 @ ( sub @ ( sK46_SY59 @ SV51 ) @ ( push @ SV128 @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK20_SY116 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(545,plain,
! [SV126: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV126 ) )
= $true )
| ( ( SV51 @ ( sub @ ( sK41_SY59 @ SV51 ) @ ( push @ SV126 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(546,plain,
! [SV121: term,SV51: term > $o] :
( ( ( SV51 @ SV121 )
= $false )
| ( ( SV51 @ ( sub @ ( sK35_SY59 @ SV51 ) @ ( push @ SV121 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK11_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(547,plain,
! [SV127: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV127 ) )
= $true )
| ( ( SV51 @ ( sub @ ( sK42_SY59 @ SV51 ) @ ( push @ SV127 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK16_SY94 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(548,plain,
! [SV123: term,SV51: term > $o] :
( ( ( SV51 @ SV123 )
= $false )
| ( ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SV123 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[533]) ).
thf(549,plain,
! [SV83: subst > term > term,SV60: subst > term > term] :
( ( ( ( lam @ ( SV60 @ sh @ one ) )
= ( lam @ ( SV83 @ sh @ one ) ) )
= $false )
| ( ( ! [SY152: subst,SY153: term] :
( ( SV60 @ SY152 @ SY153 )
= ( SV83 @ SY152 @ SY153 ) ) )
= $true )
| ( ( ( sub @ ( SV83 @ ( sK43_SY149 @ SV60 @ SV83 ) @ ( sK47_SY179 @ SV60 @ SV83 ) ) @ ( sK48_SY187 @ SV60 @ SV83 ) )
= ( SV83 @ ( comp @ ( sK43_SY149 @ SV60 @ SV83 ) @ ( sK48_SY187 @ SV60 @ SV83 ) ) @ ( sub @ ( sK47_SY179 @ SV60 @ SV83 ) @ ( sK48_SY187 @ SV60 @ SV83 ) ) ) )
= $false )
| ( ( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ ( sK21_SY118 @ SV60 ) ) @ ( sK25_SY135 @ SV60 ) )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) @ ( sub @ ( sK21_SY118 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(550,plain,
! [SV100: term,SV109: term] :
( ( ( sK12_SX0 @ id @ SV109 @ id )
= $false )
| ( ( sK12_SX0 @ id @ ( ap @ ( sub @ SV100 @ id ) @ SV109 ) @ id )
= $true )
| ( ( sK12_SX0 @ id @ SV100 @ id )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(551,plain,
! [SV110: term] :
( ( ( ~ ( sK18_SY100 @ SV110 ) )
= $true )
| ( ( sK12_SX0 @ id @ SV110 @ id )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(552,plain,
! [SV110: term] :
( ( ( ~ ( sK12_SX0 @ id @ SV110 @ id ) )
= $true )
| ( ( sK18_SY100 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[538]) ).
thf(553,plain,
! [SV49: term > $o,SV112: subst,SV105: term,SV78: term] :
( ( ( ~ ( var @ ( sK49_SY182 @ SV78 @ SV105 @ SV112 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV105 @ SV112 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SV78 @ id ) ) )
= $true )
| ( ( SV49 @ SV78 )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[540]) ).
thf(554,plain,
! [SV112: subst,SV105: term,SV78: term,SV49: term > $o] :
( ( ( SV49 @ ( sub @ ( sK49_SY182 @ SV78 @ SV105 @ SV112 @ SV49 ) @ SV112 ) )
= $false )
| ( ( SV49 @ ( sub @ SV105 @ SV112 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SV78 @ id ) ) )
= $true )
| ( ( SV49 @ SV78 )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[540]) ).
thf(555,plain,
! [SV49: term > $o,SV118: subst,SV113: term,SV87: term] :
( ( ( ~ ( var @ ( sK51_SY188 @ SV87 @ SV113 @ SV118 @ SV49 ) )
| ( SV49 @ ( sub @ ( sK51_SY188 @ SV87 @ SV113 @ SV118 @ SV49 ) @ SV118 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV113 @ SV118 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SV87 @ id ) ) )
= $true )
| ( ( SV49 @ SV87 )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[541]) ).
thf(556,plain,
! [SV49: term > $o,SV114: subst,SV106: term,SV81: term] :
( ( ( ~ ( var @ ( sK50_SY185 @ SV81 @ SV106 @ SV114 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV106 @ SV114 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SV81 @ id ) ) )
= $true )
| ( ( SV49 @ SV81 )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(557,plain,
! [SV114: subst,SV106: term,SV81: term,SV49: term > $o] :
( ( ( SV49 @ ( sub @ ( sK50_SY185 @ SV81 @ SV106 @ SV114 @ SV49 ) @ SV114 ) )
= $false )
| ( ( SV49 @ ( sub @ SV106 @ SV114 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SV81 @ id ) ) )
= $true )
| ( ( SV49 @ SV81 )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[542]) ).
thf(558,plain,
! [SV124: term,SV51: term > $o] :
( ( ( SV51 @ SV124 )
= $false )
| ( ( SV51 @ ( sub @ ( sK40_SY59 @ SV51 ) @ ( push @ SV124 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(559,plain,
! [SV128: term,SV51: term > $o] :
( ( ( ~ ( SV51 @ SV128 ) )
= $true )
| ( ( SV51 @ ( sub @ ( sK46_SY59 @ SV51 ) @ ( push @ SV128 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK20_SY116 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(560,plain,
! [SV126: term,SV51: term > $o] :
( ( ( SV51 @ SV126 )
= $false )
| ( ( SV51 @ ( sub @ ( sK41_SY59 @ SV51 ) @ ( push @ SV126 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[545]) ).
thf(561,plain,
! [SV121: term,SV129: term,SV51: term > $o] :
( ( ( SV51 @ SV129 )
= $true )
| ( ( SV51 @ ( sub @ ( sK35_SY59 @ SV51 ) @ ( push @ SV121 @ id ) ) )
= $true )
| ( ( SV51 @ SV121 )
= $false )
| ( ( SV51 @ ( sK11_SY57 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(562,plain,
! [SV127: term,SV51: term > $o] :
( ( ( SV51 @ SV127 )
= $false )
| ( ( SV51 @ ( sub @ ( sK42_SY59 @ SV51 ) @ ( push @ SV127 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK16_SY94 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(563,plain,
! [SV123: term,SV130: term,SV51: term > $o] :
( ( ( SV51 @ SV130 )
= $true )
| ( ( SV51 @ ( sub @ ( sK36_SY59 @ SV51 ) @ ( push @ SV123 @ id ) ) )
= $true )
| ( ( SV51 @ SV123 )
= $false )
| ( ( SV51 @ ( ap @ ( sK11_SY57 @ SV51 ) @ ( sK16_SY94 @ SV51 ) ) )
= $false )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(564,plain,
! [SV83: subst > term > term,SV131: subst,SV60: subst > term > term] :
( ( ( ! [SY189: term] :
( ( SV60 @ SV131 @ SY189 )
= ( SV83 @ SV131 @ SY189 ) ) )
= $true )
| ( ( ( lam @ ( SV60 @ sh @ one ) )
= ( lam @ ( SV83 @ sh @ one ) ) )
= $false )
| ( ( ( sub @ ( SV83 @ ( sK43_SY149 @ SV60 @ SV83 ) @ ( sK47_SY179 @ SV60 @ SV83 ) ) @ ( sK48_SY187 @ SV60 @ SV83 ) )
= ( SV83 @ ( comp @ ( sK43_SY149 @ SV60 @ SV83 ) @ ( sK48_SY187 @ SV60 @ SV83 ) ) @ ( sub @ ( sK47_SY179 @ SV60 @ SV83 ) @ ( sK48_SY187 @ SV60 @ SV83 ) ) ) )
= $false )
| ( ( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ ( sK21_SY118 @ SV60 ) ) @ ( sK25_SY135 @ SV60 ) )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) @ ( sub @ ( sK21_SY118 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(565,plain,
! [SV110: term] :
( ( ( sK18_SY100 @ SV110 )
= $false )
| ( ( sK12_SX0 @ id @ SV110 @ id )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(566,plain,
! [SV110: term] :
( ( ( sK12_SX0 @ id @ SV110 @ id )
= $false )
| ( ( sK18_SY100 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(567,plain,
! [SV49: term > $o,SV112: subst,SV105: term,SV78: term] :
( ( ( var @ ( sK49_SY182 @ SV78 @ SV105 @ SV112 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sub @ SV105 @ SV112 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK13_SY49 @ SV49 ) @ ( push @ SV78 @ id ) ) )
= $true )
| ( ( SV49 @ SV78 )
= $false )
| ( ( SV49 @ ( sK3_SY47 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[553]) ).
thf(568,plain,
! [SV49: term > $o,SV118: subst,SV113: term,SV87: term] :
( ( ( ~ ( var @ ( sK51_SY188 @ SV87 @ SV113 @ SV118 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sub @ SV113 @ SV118 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SV87 @ id ) ) )
= $true )
| ( ( SV49 @ SV87 )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(569,plain,
! [SV118: subst,SV113: term,SV87: term,SV49: term > $o] :
( ( ( SV49 @ ( sub @ ( sK51_SY188 @ SV87 @ SV113 @ SV118 @ SV49 ) @ SV118 ) )
= $false )
| ( ( SV49 @ ( sub @ SV113 @ SV118 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SV87 @ id ) ) )
= $true )
| ( ( SV49 @ SV87 )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[555]) ).
thf(570,plain,
! [SV49: term > $o,SV114: subst,SV106: term,SV81: term] :
( ( ( var @ ( sK50_SY185 @ SV81 @ SV106 @ SV114 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sub @ SV106 @ SV114 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK14_SY49 @ SV49 ) @ ( push @ SV81 @ id ) ) )
= $true )
| ( ( SV49 @ SV81 )
= $false )
| ( ( SV49 @ ( ap @ ( sK3_SY47 @ SV49 ) @ ( sK5_SY62 @ SV49 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[556]) ).
thf(571,plain,
! [SV124: term,SV132: term,SV51: term > $o] :
( ( ( SV51 @ SV132 )
= $true )
| ( ( SV51 @ ( sub @ ( sK40_SY59 @ SV51 ) @ ( push @ SV124 @ id ) ) )
= $true )
| ( ( SV51 @ SV124 )
= $false )
| ( ( SV51 @ ( sK15_SY57 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(572,plain,
! [SV128: term,SV51: term > $o] :
( ( ( SV51 @ SV128 )
= $false )
| ( ( SV51 @ ( sub @ ( sK46_SY59 @ SV51 ) @ ( push @ SV128 @ id ) ) )
= $true )
| ( ( ! [SY61: term] : ( SV51 @ SY61 ) )
= $true )
| ( ( SV51 @ ( sK20_SY116 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(573,plain,
! [SV126: term,SV133: term,SV51: term > $o] :
( ( ( SV51 @ SV133 )
= $true )
| ( ( SV51 @ ( sub @ ( sK41_SY59 @ SV51 ) @ ( push @ SV126 @ id ) ) )
= $true )
| ( ( SV51 @ SV126 )
= $false )
| ( ( SV51 @ ( ap @ ( sK15_SY57 @ SV51 ) @ ( sK20_SY116 @ SV51 ) ) )
= $false )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(574,plain,
! [SV127: term,SV134: term,SV51: term > $o] :
( ( ( SV51 @ SV134 )
= $true )
| ( ( SV51 @ ( sub @ ( sK42_SY59 @ SV51 ) @ ( push @ SV127 @ id ) ) )
= $true )
| ( ( SV51 @ SV127 )
= $false )
| ( ( SV51 @ ( sK16_SY94 @ SV51 ) )
= $true )
| ( ( SV51 @ ( sK6_SY56 @ SV51 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(575,plain,
! [SV83: subst > term > term,SV135: term,SV131: subst,SV60: subst > term > term] :
( ( ( ( SV60 @ SV131 @ SV135 )
= ( SV83 @ SV131 @ SV135 ) )
= $true )
| ( ( ( lam @ ( SV60 @ sh @ one ) )
= ( lam @ ( SV83 @ sh @ one ) ) )
= $false )
| ( ( ( sub @ ( SV83 @ ( sK43_SY149 @ SV60 @ SV83 ) @ ( sK47_SY179 @ SV60 @ SV83 ) ) @ ( sK48_SY187 @ SV60 @ SV83 ) )
= ( SV83 @ ( comp @ ( sK43_SY149 @ SV60 @ SV83 ) @ ( sK48_SY187 @ SV60 @ SV83 ) ) @ ( sub @ ( sK47_SY179 @ SV60 @ SV83 ) @ ( sK48_SY187 @ SV60 @ SV83 ) ) ) )
= $false )
| ( ( ( sub @ ( SV60 @ ( sK17_SY78 @ SV60 ) @ ( sK21_SY118 @ SV60 ) ) @ ( sK25_SY135 @ SV60 ) )
= ( SV60 @ ( comp @ ( sK17_SY78 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) @ ( sub @ ( sK21_SY118 @ SV60 ) @ ( sK25_SY135 @ SV60 ) ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(576,plain,
! [SV49: term > $o,SV118: subst,SV113: term,SV87: term] :
( ( ( var @ ( sK51_SY188 @ SV87 @ SV113 @ SV118 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sub @ SV113 @ SV118 ) )
= $true )
| ( ( SV49 @ ( sub @ ( sK19_SY49 @ SV49 ) @ ( push @ SV87 @ id ) ) )
= $true )
| ( ( SV49 @ SV87 )
= $false )
| ( ( SV49 @ ( sK5_SY62 @ SV49 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[568]) ).
thf(577,plain,
! [SV128: term,SV136: term,SV51: term > $o] :
( ( ( SV51 @ SV136 )
= $true )
| ( ( SV51 @ ( sub @ ( sK46_SY59 @ SV51 ) @ ( push @ SV128 @ id ) ) )
= $true )
| ( ( SV51 @ SV128 )
= $false )
| ( ( SV51 @ ( sK20_SY116 @ SV51 ) )
= $true )
| ( ( var @ ( sK6_SY56 @ SV51 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(578,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,577,576,575,574,573,571,570,569,567,566,565,563,561,557,554,550,539,535,529,525,522,520,515,512,509,505,503,501,498,489,485,478,473,470,464,448,447,446,444,438,423,422,420,419,415,393,389,352,337,324,323,314,300,278,277,237,217,167,160,158,145,144,143,133,132,122,120,82,67,66,62,59,58,56,46,41,37,31,23,22]) ).
thf(579,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[578]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : ALG264^3 : TPTP v8.1.0. Bugfixed v5.2.0.
% 0.00/0.08 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 600
% 0.07/0.27 % DateTime : Thu Jun 9 00:36:22 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.07/0.29 .
% 0.07/0.29
% 0.07/0.29 No.of.Axioms: 0
% 0.07/0.29
% 0.07/0.29 Length.of.Defs: 38205
% 0.07/0.29
% 0.07/0.29 Contains.Choice.Funs: false
% 0.11/0.31 .
% 0.11/0.31 (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)..................................................................................
% 1.51/1.69
% 1.51/1.69 ********************************
% 1.51/1.69 * All subproblems solved! *
% 1.51/1.69 ********************************
% 1.51/1.69 % SZS status Theorem for /export/starexec/sandbox2/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:578,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.68/1.92
% 1.68/1.92 %**** Beginning of derivation protocol ****
% 1.68/1.92 % SZS output start CNFRefutation
% See solution above
% 1.68/1.92
% 1.68/1.92 %**** End of derivation protocol ****
% 1.68/1.92 %**** no. of clauses in derivation: 579 ****
% 1.68/1.92 %**** clause counter: 578 ****
% 1.68/1.92
% 1.68/1.92 % SZS status Theorem for /export/starexec/sandbox2/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:578,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------