%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ALG266^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:08:43 AM UTC 2026
% Result : Theorem 0.60s 0.29s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 114
% Syntax : Number of formulae : 199 ( 146 unt; 0 typ; 113 def)
% Number of atoms : 1695 ( 383 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 4835 ( 285 ~; 214 |; 16 &;3271 @)
% ( 2 <=>;1047 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 290 ( 290 >; 0 *; 0 +; 0 <<)
% Number of symbols : 133 ( 130 usr; 114 con; 0-4 aty)
% Number of variables : 570 ( 39 ^; 526 !; 5 ?; 570 :)
% 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_sK1_SY13,type,
sK1_SY13: subst > term > subst > $o ).
thf(tp_sK2_SY47,type,
sK2_SY47: term ).
thf(tp_sK3_SY46,type,
sK3_SY46: ( subst > term > term ) > term ).
thf(tp_sK4_M,type,
sK4_M: ( subst > term > term ) > subst ).
thf(tp_sK5_SY50,type,
sK5_SY50: ( subst > term > term ) > term ).
thf(tp_sK6_SY52,type,
sK6_SY52: ( subst > term > term ) > subst ).
thf(tp_sK7_B,type,
sK7_B: term > ( subst > term > subst > $o ) > term ).
thf(tp_sK8_SY2,type,
sK8_SY2: ( subst > term > subst > $o ) > subst > term > term ).
thf(tp_sh,type,
sh: subst ).
thf(tp_shinj,type,
shinj: $o ).
thf(tp_sub,type,
sub: term > subst > term ).
thf(tp_substmonoid,type,
substmonoid: $o ).
thf(tp_substmonoid_gthm,type,
substmonoid_gthm: $o ).
thf(tp_substmonoid_lthm,type,
substmonoid_lthm: $o ).
thf(tp_termmset,type,
termmset: $o ).
thf(tp_termmset_gthm,type,
termmset_gthm: $o ).
thf(tp_termmset_lthm,type,
termmset_lthm: $o ).
thf(tp_ulamvar1,type,
ulamvar1: $o ).
thf(tp_ulamvarind,type,
ulamvarind: $o ).
thf(tp_ulamvarsh,type,
ulamvarsh: $o ).
thf(tp_var,type,
var: term > $o ).
thf(apinj1,definition,
( apinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apinj1) ).
thf(apinj2,definition,
( apinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apinj2) ).
thf(apnotvar,definition,
( apnotvar
= ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apnotvar) ).
thf(axabs,definition,
( axabs
= ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axabs) ).
thf(axapp,definition,
( axapp
= ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axapp) ).
thf(axassoc,definition,
( axassoc
= ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axassoc) ).
thf(axclos,definition,
( axclos
= ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axclos) ).
thf(axidl,definition,
( axidl
= ( ! [M: subst] :
( ( comp @ id @ M )
= M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axidl) ).
thf(axidr,definition,
( axidr
= ( ! [M: subst] :
( ( comp @ M @ id )
= M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axidr) ).
thf(axmap,definition,
( axmap
= ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axmap) ).
thf(axscons,definition,
( axscons
= ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axscons) ).
thf(axshiftcons,definition,
( axshiftcons
= ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axshiftcons) ).
thf(axvarcons,definition,
( axvarcons
= ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarcons) ).
thf(axvarid,definition,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarid) ).
thf(axvarshift,definition,
( axvarshift
= ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axvarshift) ).
thf(hoasap,definition,
( hoasap
= ( ^ [M: subst,A: term,N: subst,B: term] : ( ap @ ( sub @ A @ N ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasap) ).
thf(hoasapinj1,definition,
( hoasapinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj1) ).
thf(hoasapinj1_gthm,definition,
( hoasapinj1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> hoasapinj1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj1_gthm) ).
thf(hoasapinj1_lthm,definition,
( hoasapinj1_lthm
= ( axvarid
=> ( apinj1
=> hoasapinj1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj1_lthm) ).
thf(hoasapinj2,definition,
( hoasapinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( hoasap @ id @ A @ id @ C )
= ( hoasap @ id @ B @ id @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj2) ).
thf(hoasapinj2_gthm,definition,
( hoasapinj2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> hoasapinj2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj2_gthm) ).
thf(hoasapinj2_lthm,definition,
( hoasapinj2_lthm
= ( apinj2
=> hoasapinj2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapinj2_lthm) ).
thf(hoasapnotvar,definition,
( hoasapnotvar
= ( ! [A: term,B: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapnotvar) ).
thf(hoasapnotvar_gthm,definition,
( hoasapnotvar_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapnotvar_gthm) ).
thf(hoasapnotvar_lthm,definition,
( hoasapnotvar_lthm
= ( axvarid
=> ( apnotvar
=> hoasapnotvar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasapnotvar_lthm) ).
thf(hoasinduction,definition,
( hoasinduction
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] : ( P @ id @ A @ id ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction) ).
thf(hoasinduction_gthm,definition,
( hoasinduction_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_gthm) ).
thf(hoasinduction_lem0,definition,
( hoasinduction_lem0
= ( ! [P: subst > term > subst > $o] :
? [Q: term > $o] : ( hoasinduction_p_and_p_prime @ P @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem0) ).
thf(hoasinduction_lem0_lthm,definition,
hoasinduction_lem0_lthm = hoasinduction_lem0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem0_lthm) ).
thf(hoasinduction_lem1,definition,
( hoasinduction_lem1
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ id @ A @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1) ).
thf(hoasinduction_lem1_gthm,definition,
( hoasinduction_lem1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1_gthm) ).
thf(hoasinduction_lem1_lthm,definition,
( hoasinduction_lem1_lthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1_lthm) ).
thf(hoasinduction_lem1v2,definition,
( hoasinduction_lem1v2
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term] :
( ( hoasvar @ id @ A @ id )
=> ( P @ id @ A @ id ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ( var @ A )
=> ( Q @ A ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1v2) ).
thf(hoasinduction_lem1v2_gthm,definition,
( hoasinduction_lem1v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem1v2_gthm) ).
thf(hoasinduction_lem2,definition,
( hoasinduction_lem2
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( ap @ A @ B ) @ id ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2) ).
thf(hoasinduction_lem2_gthm,definition,
( hoasinduction_lem2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2_gthm) ).
thf(hoasinduction_lem2_lthm,definition,
( hoasinduction_lem2_lthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2_lthm) ).
thf(hoasinduction_lem2v2,definition,
( hoasinduction_lem2v2
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term,B: term] :
( ( Q @ A )
=> ( ( Q @ B )
=> ( Q @ ( ap @ A @ B ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2v2) ).
thf(hoasinduction_lem2v2_gthm,definition,
( hoasinduction_lem2v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem2v2_gthm) ).
thf(hoasinduction_lem3,definition,
( hoasinduction_lem3
= ( ! [P: subst > term > subst > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3) ).
thf(hoasinduction_lem3_gthm,definition,
( hoasinduction_lem3_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3_gthm) ).
thf(hoasinduction_lem3_lthm,definition,
( hoasinduction_lem3_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3_lthm) ).
thf(hoasinduction_lem3a,definition,
( hoasinduction_lem3a
= ( ! [P: subst > term > subst > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ A ) @ id ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3a) ).
thf(hoasinduction_lem3a_gthm,definition,
( hoasinduction_lem3a_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3a ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3a_gthm) ).
thf(hoasinduction_lem3a_lthm,definition,
( hoasinduction_lem3a_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3a_lthm) ).
thf(hoasinduction_lem3aa,definition,
( hoasinduction_lem3aa
= ( ! [P: subst > term > subst > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3aa) ).
thf(hoasinduction_lem3aa_lthm,definition,
( hoasinduction_lem3aa_lthm
= ( axclos
=> ( axmap
=> hoasinduction_lem3aa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3aa_lthm) ).
thf(hoasinduction_lem3aaa,definition,
( hoasinduction_lem3aaa
= ( ! [P: subst > term > subst > $o] :
( ! [F: subst > term > term] :
( ? [C: term] :
! [M: subst,A: term,N: subst] :
( ( ( sub @ ( F @ M @ A ) @ N )
= ( sub @ ( sub @ C @ ( push @ A @ M ) ) @ N ) )
& ( ( sub @ C @ ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( P @ id @ B @ id )
=> ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3aaa) ).
thf(hoasinduction_lem3b,definition,
( hoasinduction_lem3b
= ( ! [B: term] :
? [F: subst > term > term] :
( ( sub @ B @ ( push @ one @ sh ) )
= ( F @ sh @ one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3b) ).
thf(hoasinduction_lem3b_gthm,definition,
( hoasinduction_lem3b_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3b_gthm) ).
thf(hoasinduction_lem3b_lthm,definition,
hoasinduction_lem3b_lthm = hoasinduction_lem3b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3b_lthm) ).
thf(hoasinduction_lem3v2,definition,
( hoasinduction_lem3v2
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ M @ A @ ( comp @ K @ N ) )
=> ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
=> ( ! [M: subst,A: term,N: subst,K: subst] :
( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
=> ( P @ M @ A @ ( comp @ K @ N ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ! [B: term] :
( ( Q @ B )
=> ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( Q @ ( lam @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2) ).
thf(hoasinduction_lem3v2_f,definition,
( hoasinduction_lem3v2_f
= ( ! [B: term] :
? [F: subst > term > term] :
! [A: term,M: subst] :
( ( F @ M @ A )
= ( sub @ B @ ( push @ A @ M ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2_f) ).
thf(hoasinduction_lem3v2_f_lthm,definition,
hoasinduction_lem3v2_f_lthm = hoasinduction_lem3v2_f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2_f_lthm) ).
thf(hoasinduction_lem3v2_gthm,definition,
( hoasinduction_lem3v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem3v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2_gthm) ).
thf(hoasinduction_lem3v2_lthm,definition,
( hoasinduction_lem3v2_lthm
= ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2_lthm) ).
thf(hoasinduction_lem3v2a,definition,
( hoasinduction_lem3v2a
= ( ! [P: subst > term > subst > $o,Q: term > $o] :
( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ P @ Q )
=> ! [A: term] :
( ! [B: term] :
( ( Q @ B )
=> ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( Q @ ( lam @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2a) ).
thf(hoasinduction_lem3v2a_lthm,definition,
( hoasinduction_lem3v2a_lthm
= ( hoasinduction_lem3v2_f
=> ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lem3v2a_lthm) ).
thf(hoasinduction_lthm,definition,
( hoasinduction_lthm
= ( induction2
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> ( hoasinduction_lem3
=> hoasinduction ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lthm) ).
thf(hoasinduction_lthm_3,definition,
( hoasinduction_lthm_3
= ( hoasinduction_lem0
=> ( induction2
=> ( axvarid
=> ( hoasinduction_lem3v2a
=> hoasinduction ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_lthm_3) ).
thf(hoasinduction_no_psi_cond,definition,
( hoasinduction_no_psi_cond
= ( ! [P: subst > term > subst > $o] :
( ! [A: term,B: term] :
( ( P @ id @ A @ id )
=> ( ( P @ id @ B @ id )
=> ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) )
=> ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( P @ id @ A @ id )
=> ( P @ id @ ( F @ id @ A ) @ id ) )
=> ( P @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) )
=> ! [A: term] : ( P @ id @ A @ id ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_no_psi_cond) ).
thf(hoasinduction_no_psi_cond_lthm,definition,
( hoasinduction_no_psi_cond_lthm
= ( hoasinduction_lem0
=> ( induction2
=> ( axvarid
=> ( hoasinduction_lem3v2a
=> hoasinduction_no_psi_cond ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_no_psi_cond_lthm) ).
thf(hoasinduction_p_and_p_prime,definition,
( hoasinduction_p_and_p_prime
= ( ^ [P: subst > term > subst > $o,Q: term > $o] :
! [X: term] :
( ( Q @ X )
<=> ( P @ id @ X @ id ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasinduction_p_and_p_prime) ).
thf(hoaslam,definition,
( hoaslam
= ( ^ [M: subst,F: subst > term > term] : ( lam @ ( F @ sh @ one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslam) ).
thf(hoaslaminj,definition,
( hoaslaminj
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [G: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( G @ M @ A ) @ N )
= ( G @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ( ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
= ( hoaslam @ id
@ ^ [M: subst,A: term] : ( G @ M @ A ) ) )
=> ! [M: subst,A: term] :
( ( F @ M @ A )
= ( G @ M @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj) ).
thf(hoaslaminj_gthm,definition,
( hoaslaminj_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> hoaslaminj ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj_gthm) ).
thf(hoaslaminj_lthm,definition,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslaminj_lthm) ).
thf(hoaslamnotap,definition,
( hoaslamnotap
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ! [A: term,B: term] :
( ( hoaslam @ id
@ ^ [M: subst,C: term] : ( F @ M @ C ) )
!= ( hoasap @ id @ A @ id @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotap) ).
thf(hoaslamnotap_gthm,definition,
( hoaslamnotap_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotap_gthm) ).
thf(hoaslamnotap_lthm,definition,
( hoaslamnotap_lthm
= ( lamnotap
=> hoaslamnotap ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotap_lthm) ).
thf(hoaslamnotvar,definition,
( hoaslamnotvar
= ( ! [F: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( F @ M @ A ) @ N )
= ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [M: subst,A: term] : ( F @ M @ A ) )
@ id ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotvar) ).
thf(hoaslamnotvar_gthm,definition,
( hoaslamnotvar_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotvar_gthm) ).
thf(hoaslamnotvar_lthm,definition,
( hoaslamnotvar_lthm
= ( axvarid
=> ( lamnotvar
=> hoaslamnotvar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoaslamnotvar_lthm) ).
thf(hoasvar,definition,
( hoasvar
= ( ^ [M: subst,A: term,N: subst] : ( var @ ( sub @ A @ N ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hoasvar) ).
thf(induction,definition,
( induction
= ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ( P @ A )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction) ).
thf(induction2,definition,
( induction2
= ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2) ).
thf(induction2_gthm,definition,
( induction2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> induction2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2_gthm) ).
thf(induction2_lthm,definition,
( induction2_lthm
= ( axvarid
=> ( induction2lem
=> induction2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2_lthm) ).
thf(induction2lem,definition,
( induction2lem
= ( ! [P: term > $o] :
( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ! [B: term] :
( ( P @ B )
=> ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( P @ ( sub @ A @ M ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2lem) ).
thf(induction2lem_gthm,definition,
( induction2lem_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> induction2lem ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2lem_gthm) ).
thf(induction2lem_lthm,definition,
( induction2lem_lthm
= ( axapp
=> ( axvarcons
=> ( axabs
=> ( axclos
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( induction
=> ( pushprop
=> induction2lem ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction2lem_lthm) ).
thf(laminj,definition,
( laminj
= ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',laminj) ).
thf(lamnotap,definition,
( lamnotap
= ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamnotap) ).
thf(lamnotvar,definition,
( lamnotvar
= ( ! [A: term] :
~ ( var @ ( lam @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamnotvar) ).
thf(pushprop,definition,
( pushprop
= ( ! [P: term > $o,A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( ( P @ A )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop) ).
thf(pushprop_gthm,definition,
( pushprop_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_gthm) ).
thf(pushprop_lem0,definition,
( pushprop_lem0
= ( ! [P: term > $o,A: term,M: subst] :
? [Q: term > $o] : ( pushprop_p_and_p_prime @ A @ M @ P @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem0) ).
thf(pushprop_lem0_gthm,definition,
( pushprop_lem0_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem0_gthm) ).
thf(pushprop_lem0_lthm,definition,
pushprop_lem0_lthm = pushprop_lem0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem0_lthm) ).
thf(pushprop_lem1,definition,
( pushprop_lem1
= ( ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
( ( P @ A )
=> ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1) ).
thf(pushprop_lem1_gthm,definition,
( pushprop_lem1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1_gthm) ).
thf(pushprop_lem1_lthm,definition,
( pushprop_lem1_lthm
= ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop_lem1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1_lthm) ).
thf(pushprop_lem1v2,definition,
( pushprop_lem1v2
= ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
( ( P @ A )
=> ( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
=> ( Q @ one ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1v2) ).
thf(pushprop_lem1v2_gthm,definition,
( pushprop_lem1v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1v2_gthm) ).
thf(pushprop_lem1v2_lthm,definition,
( pushprop_lem1v2_lthm
= ( axvarcons
=> pushprop_lem1v2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem1v2_lthm) ).
thf(pushprop_lem2v2,definition,
( pushprop_lem2v2
= ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
=> ( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ! [C: term] :
( ( var @ C )
=> ( ( Q @ C )
=> ( Q @ ( sub @ C @ sh ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem2v2) ).
thf(pushprop_lem2v2_gthm,definition,
( pushprop_lem2v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem2v2_gthm) ).
thf(pushprop_lem2v2_lthm,definition,
( pushprop_lem2v2_lthm
= ( axclos
=> ( axshiftcons
=> pushprop_lem2v2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem2v2_lthm) ).
thf(pushprop_lem3v2,definition,
( pushprop_lem3v2
= ( ! [P: term > $o,Q: term > $o,A: term,M: subst] :
( ( pushprop_p_and_p_prime @ A @ M @ P @ Q )
=> ( ! [B: term] :
( ( var @ B )
=> ( Q @ B ) )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem3v2) ).
thf(pushprop_lem3v2_lthm,definition,
pushprop_lem3v2_lthm = pushprop_lem3v2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lem3v2_lthm) ).
thf(pushprop_lthm,definition,
( pushprop_lthm
= ( pushprop_lem0
=> ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lthm) ).
thf(pushprop_lthm_orig,definition,
( pushprop_lthm_orig
= ( ulamvar1
=> ( axvarcons
=> ( axclos
=> ( axshiftcons
=> ( ulamvarind
=> pushprop ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_lthm_orig) ).
thf(pushprop_p_and_p_prime,definition,
( pushprop_p_and_p_prime
= ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
! [X: term] :
( ( Q @ X )
<=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pushprop_p_and_p_prime) ).
thf(shinj,definition,
( shinj
= ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shinj) ).
thf(substmonoid,definition,
( substmonoid
= ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) )
& ! [M: subst] :
( ( comp @ id @ M )
= M )
& ! [M: subst] :
( ( comp @ M @ id )
= M ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substmonoid) ).
thf(substmonoid_gthm,definition,
( substmonoid_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> substmonoid ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substmonoid_gthm) ).
thf(substmonoid_lthm,definition,
( substmonoid_lthm
= ( axidl
=> ( axassoc
=> ( axidr
=> substmonoid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substmonoid_lthm) ).
thf(termmset,definition,
( termmset
= ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) )
& ! [A: term] :
( ( sub @ A @ id )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',termmset) ).
thf(termmset_gthm,definition,
( termmset_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> termmset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',termmset_gthm) ).
thf(termmset_lthm,definition,
( termmset_lthm
= ( axvarid
=> ( axclos
=> termmset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',termmset_lthm) ).
thf(ulamvar1,definition,
( ulamvar1
= ( var @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvar1) ).
thf(ulamvarind,definition,
( ulamvarind
= ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvarind) ).
thf(ulamvarsh,definition,
( ulamvarsh
= ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ulamvarsh) ).
thf(1,conjecture,
hoasinduction_lem3a_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
hoasinduction_lem3a_lthm = $false,
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [SY1: subst > term > subst > $o] :
( ! [SY2: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY2 @ M @ A ) @ N )
= ( SY2 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( SY1 @ id @ A @ id )
=> ( SY1 @ id @ ( SY2 @ id @ A ) @ id ) )
=> ( SY1 @ id @ ( lam @ ( SY2 @ sh @ one ) ) @ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( SY1 @ id @ B @ id )
=> ( SY1 @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( SY1 @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [SY13: subst > term > subst > $o] :
( ! [SY14: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY14 @ M @ A ) @ N )
= ( SY14 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( SY13 @ id @ A @ id )
=> ( SY13 @ id @ ( SY14 @ id @ A ) @ id ) )
=> ( SY13 @ id @ ( lam @ ( SY14 @ sh @ one ) ) @ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( SY13 @ id @ B @ id )
=> ( SY13 @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( SY13 @ id @ ( lam @ A ) @ id ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,apinj1,apinj2,apnotvar,axabs,axapp,axassoc,axclos,axidl,axidr,axmap,axscons,axshiftcons,axvarcons,axvarid,axvarshift,hoasap,hoasapinj1,hoasapinj1_gthm,hoasapinj1_lthm,hoasapinj2,hoasapinj2_gthm,hoasapinj2_lthm,hoasapnotvar,hoasapnotvar_gthm,hoasapnotvar_lthm,hoasinduction,hoasinduction_gthm,hoasinduction_lem0,hoasinduction_lem0_lthm,hoasinduction_lem1,hoasinduction_lem1_gthm,hoasinduction_lem1_lthm,hoasinduction_lem1v2,hoasinduction_lem1v2_gthm,hoasinduction_lem2,hoasinduction_lem2_gthm,hoasinduction_lem2_lthm,hoasinduction_lem2v2,hoasinduction_lem2v2_gthm,hoasinduction_lem3,hoasinduction_lem3_gthm,hoasinduction_lem3_lthm,hoasinduction_lem3a,hoasinduction_lem3a_gthm,hoasinduction_lem3a_lthm,hoasinduction_lem3aa,hoasinduction_lem3aa_lthm,hoasinduction_lem3aaa,hoasinduction_lem3b,hoasinduction_lem3b_gthm,hoasinduction_lem3b_lthm,hoasinduction_lem3v2,hoasinduction_lem3v2_f,hoasinduction_lem3v2_f_lthm,hoasinduction_lem3v2_gthm,hoasinduction_lem3v2_lthm,hoasinduction_lem3v2a,hoasinduction_lem3v2a_lthm,hoasinduction_lthm,hoasinduction_lthm_3,hoasinduction_no_psi_cond,hoasinduction_no_psi_cond_lthm,hoasinduction_p_and_p_prime,hoaslam,hoaslaminj,hoaslaminj_gthm,hoaslaminj_lthm,hoaslamnotap,hoaslamnotap_gthm,hoaslamnotap_lthm,hoaslamnotvar,hoaslamnotvar_gthm,hoaslamnotvar_lthm,hoasvar,induction,induction2,induction2_gthm,induction2_lthm,induction2lem,induction2lem_gthm,induction2lem_lthm,laminj,lamnotap,lamnotvar,pushprop,pushprop_gthm,pushprop_lem0,pushprop_lem0_gthm,pushprop_lem0_lthm,pushprop_lem1,pushprop_lem1_gthm,pushprop_lem1_lthm,pushprop_lem1v2,pushprop_lem1v2_gthm,pushprop_lem1v2_lthm,pushprop_lem2v2,pushprop_lem2v2_gthm,pushprop_lem2v2_lthm,pushprop_lem3v2,pushprop_lem3v2_lthm,pushprop_lthm,pushprop_lthm_orig,pushprop_p_and_p_prime,shinj,substmonoid,substmonoid_gthm,substmonoid_lthm,termmset,termmset_gthm,termmset_lthm,ulamvar1,ulamvarind,ulamvarsh]) ).
thf(4,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [SY1: subst > term > subst > $o] :
( ! [SY2: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY2 @ M @ A ) @ N )
= ( SY2 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( SY1 @ id @ A @ id )
=> ( SY1 @ id @ ( SY2 @ id @ A ) @ id ) )
=> ( SY1 @ id @ ( lam @ ( SY2 @ sh @ one ) ) @ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( SY1 @ id @ B @ id )
=> ( SY1 @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( SY1 @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [SY13: subst > term > subst > $o] :
( ! [SY14: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY14 @ M @ A ) @ N )
= ( SY14 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( SY13 @ id @ A @ id )
=> ( SY13 @ id @ ( SY14 @ id @ A ) @ id ) )
=> ( SY13 @ id @ ( lam @ ( SY14 @ sh @ one ) ) @ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( SY13 @ id @ B @ id )
=> ( SY13 @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( SY13 @ id @ ( lam @ A ) @ id ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [SY13: subst > term > subst > $o] :
( ! [SY14: subst > term > term] :
( ! [M: subst,A: term,N: subst] :
( ( sub @ ( SY14 @ M @ A ) @ N )
= ( SY14 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
=> ( ! [A: term] :
( ( SY13 @ id @ A @ id )
=> ( SY13 @ id @ ( SY14 @ id @ A ) @ id ) )
=> ( SY13 @ id @ ( lam @ ( SY14 @ sh @ one ) ) @ id ) ) )
=> ! [A: term] :
( ! [B: term] :
( ( SY13 @ id @ B @ id )
=> ( SY13 @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
=> ( SY13 @ id @ ( lam @ A ) @ id ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ! [SY42: subst > term > term] :
( ( ( sub @ ( SY42 @ ( sK4_M @ SY42 ) @ ( sK5_SY50 @ SY42 ) ) @ ( sK6_SY52 @ SY42 ) )
!= ( SY42 @ ( comp @ ( sK4_M @ SY42 ) @ ( sK6_SY52 @ SY42 ) ) @ ( sub @ ( sK5_SY50 @ SY42 ) @ ( sK6_SY52 @ SY42 ) ) ) )
| ( ( sK1_SY13 @ id @ ( sK3_SY46 @ SY42 ) @ id )
& ~ ( sK1_SY13 @ id @ ( SY42 @ id @ ( sK3_SY46 @ SY42 ) ) @ id ) )
| ( sK1_SY13 @ id @ ( lam @ ( SY42 @ sh @ one ) ) @ id ) )
& ! [SY49: term] :
( ~ ( sK1_SY13 @ id @ SY49 @ id )
| ( sK1_SY13 @ id @ ( sub @ sK2_SY47 @ ( push @ SY49 @ id ) ) @ id ) )
& ~ ( sK1_SY13 @ id @ ( lam @ sK2_SY47 ) @ id ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [SY1: subst > term > subst > $o] :
( ( ! [SY53: subst,SY54: term,SY55: subst] :
( ( sub @ ( sK8_SY2 @ SY1 @ SY53 @ SY54 ) @ SY55 )
= ( sK8_SY2 @ SY1 @ ( comp @ SY53 @ SY55 ) @ ( sub @ SY54 @ SY55 ) ) )
& ! [SY56: term] :
( ~ ( SY1 @ id @ SY56 @ id )
| ( SY1 @ id @ ( sK8_SY2 @ SY1 @ id @ SY56 ) @ id ) )
& ~ ( SY1 @ id @ ( lam @ ( sK8_SY2 @ SY1 @ sh @ one ) ) @ id ) )
| ! [A: term] :
( ( ( SY1 @ id @ ( sK7_B @ A @ SY1 ) @ id )
& ~ ( SY1 @ id @ ( sub @ A @ ( push @ ( sK7_B @ A @ SY1 ) @ id ) ) @ id ) )
| ( SY1 @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(11,plain,
( ( ! [SY1: subst > term > subst > $o] :
( ( ! [SY53: subst,SY54: term,SY55: subst] :
( ( sub @ ( sK8_SY2 @ SY1 @ SY53 @ SY54 ) @ SY55 )
= ( sK8_SY2 @ SY1 @ ( comp @ SY53 @ SY55 ) @ ( sub @ SY54 @ SY55 ) ) )
& ! [SY56: term] :
( ~ ( SY1 @ id @ SY56 @ id )
| ( SY1 @ id @ ( sK8_SY2 @ SY1 @ id @ SY56 ) @ id ) )
& ~ ( SY1 @ id @ ( lam @ ( sK8_SY2 @ SY1 @ sh @ one ) ) @ id ) )
| ! [A: term] :
( ( ( SY1 @ id @ ( sK7_B @ A @ SY1 ) @ id )
& ~ ( SY1 @ id @ ( sub @ A @ ( push @ ( sK7_B @ A @ SY1 ) @ id ) ) @ id ) )
| ( SY1 @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(12,plain,
( ( ( push @ one @ sh )
= id )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(13,plain,
( ( ! [A: term] :
( ( sub @ A @ id )
= A ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [SY42: subst > term > term] :
( ( ( sub @ ( SY42 @ ( sK4_M @ SY42 ) @ ( sK5_SY50 @ SY42 ) ) @ ( sK6_SY52 @ SY42 ) )
!= ( SY42 @ ( comp @ ( sK4_M @ SY42 ) @ ( sK6_SY52 @ SY42 ) ) @ ( sub @ ( sK5_SY50 @ SY42 ) @ ( sK6_SY52 @ SY42 ) ) ) )
| ( ( sK1_SY13 @ id @ ( sK3_SY46 @ SY42 ) @ id )
& ~ ( sK1_SY13 @ id @ ( SY42 @ id @ ( sK3_SY46 @ SY42 ) ) @ id ) )
| ( sK1_SY13 @ id @ ( lam @ ( SY42 @ sh @ one ) ) @ id ) )
& ! [SY49: term] :
( ~ ( sK1_SY13 @ id @ SY49 @ id )
| ( sK1_SY13 @ id @ ( sub @ sK2_SY47 @ ( push @ SY49 @ id ) ) @ id ) )
& ~ ( sK1_SY13 @ id @ ( lam @ sK2_SY47 ) @ id ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(15,plain,
( ( ~ ( ~ ! [SX0: subst > term > term] :
( ( ( sub @ ( SX0 @ ( sK4_M @ SX0 ) @ ( sK5_SY50 @ SX0 ) ) @ ( sK6_SY52 @ SX0 ) )
!= ( SX0 @ ( comp @ ( sK4_M @ SX0 ) @ ( sK6_SY52 @ SX0 ) ) @ ( sub @ ( sK5_SY50 @ SX0 ) @ ( sK6_SY52 @ SX0 ) ) ) )
| ~ ( ~ ( sK1_SY13 @ id @ ( sK3_SY46 @ SX0 ) @ id )
| ~ ~ ( sK1_SY13 @ id @ ( SX0 @ id @ ( sK3_SY46 @ SX0 ) ) @ id ) )
| ( sK1_SY13 @ id @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) )
| ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY13 @ id @ SX0 @ id )
| ( sK1_SY13 @ id @ ( sub @ sK2_SY47 @ ( push @ SX0 @ id ) ) @ id ) )
| ~ ~ ( sK1_SY13 @ id @ ( lam @ sK2_SY47 ) @ id ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,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(16,plain,
( ( ! [SX0: subst > term > subst > $o] :
( ~ ( ~ ! [SX1: subst,SX2: term,SX3: subst] :
( ( sub @ ( sK8_SY2 @ SX0 @ SX1 @ SX2 ) @ SX3 )
= ( sK8_SY2 @ SX0 @ ( comp @ SX1 @ SX3 ) @ ( sub @ SX2 @ SX3 ) ) )
| ~ ~ ( ~ ! [SX1: term] :
( ~ ( SX0 @ id @ SX1 @ id )
| ( SX0 @ id @ ( sK8_SY2 @ SX0 @ id @ SX1 ) @ id ) )
| ~ ~ ( SX0 @ id @ ( lam @ ( sK8_SY2 @ SX0 @ sh @ one ) ) @ id ) ) )
| ! [SX1: term] :
( ~ ( ~ ( SX0 @ id @ ( sK7_B @ SX1 @ SX0 ) @ id )
| ~ ~ ( SX0 @ id @ ( sub @ SX1 @ ( push @ ( sK7_B @ SX1 @ SX0 ) @ id ) ) @ id ) )
| ( SX0 @ id @ ( lam @ ( sub @ SX1 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,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(17,plain,
! [SV1: term] :
( ( ( sub @ SV1 @ id )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(18,plain,
( ( ~ ! [SX0: subst > term > term] :
( ( ( sub @ ( SX0 @ ( sK4_M @ SX0 ) @ ( sK5_SY50 @ SX0 ) ) @ ( sK6_SY52 @ SX0 ) )
!= ( SX0 @ ( comp @ ( sK4_M @ SX0 ) @ ( sK6_SY52 @ SX0 ) ) @ ( sub @ ( sK5_SY50 @ SX0 ) @ ( sK6_SY52 @ SX0 ) ) ) )
| ~ ( ~ ( sK1_SY13 @ id @ ( sK3_SY46 @ SX0 ) @ id )
| ~ ~ ( sK1_SY13 @ id @ ( SX0 @ id @ ( sK3_SY46 @ SX0 ) ) @ id ) )
| ( sK1_SY13 @ id @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) )
| ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY13 @ id @ SX0 @ id )
| ( sK1_SY13 @ id @ ( sub @ sK2_SY47 @ ( push @ SX0 @ id ) ) @ id ) )
| ~ ~ ( sK1_SY13 @ id @ ( lam @ sK2_SY47 ) @ id ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(19,plain,
! [SV2: subst > term > subst > $o] :
( ( ~ ( ~ ! [SY57: subst,SY58: term,SY59: subst] :
( ( sub @ ( sK8_SY2 @ SV2 @ SY57 @ SY58 ) @ SY59 )
= ( sK8_SY2 @ SV2 @ ( comp @ SY57 @ SY59 ) @ ( sub @ SY58 @ SY59 ) ) )
| ~ ~ ( ~ ! [SY60: term] :
( ~ ( SV2 @ id @ SY60 @ id )
| ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SY60 ) @ id ) )
| ~ ~ ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id ) ) )
| ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ! [SX0: subst > term > term] :
( ( ( sub @ ( SX0 @ ( sK4_M @ SX0 ) @ ( sK5_SY50 @ SX0 ) ) @ ( sK6_SY52 @ SX0 ) )
!= ( SX0 @ ( comp @ ( sK4_M @ SX0 ) @ ( sK6_SY52 @ SX0 ) ) @ ( sub @ ( sK5_SY50 @ SX0 ) @ ( sK6_SY52 @ SX0 ) ) ) )
| ~ ( ~ ( sK1_SY13 @ id @ ( sK3_SY46 @ SX0 ) @ id )
| ~ ~ ( sK1_SY13 @ id @ ( SX0 @ id @ ( sK3_SY46 @ SX0 ) ) @ id ) )
| ( sK1_SY13 @ id @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY13 @ id @ SX0 @ id )
| ( sK1_SY13 @ id @ ( sub @ sK2_SY47 @ ( push @ SX0 @ id ) ) @ id ) )
| ~ ~ ( sK1_SY13 @ id @ ( lam @ sK2_SY47 ) @ id ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[18]) ).
thf(22,plain,
! [SV2: subst > term > subst > $o] :
( ( ( ~ ( ~ ! [SY57: subst,SY58: term,SY59: subst] :
( ( sub @ ( sK8_SY2 @ SV2 @ SY57 @ SY58 ) @ SY59 )
= ( sK8_SY2 @ SV2 @ ( comp @ SY57 @ SY59 ) @ ( sub @ SY58 @ SY59 ) ) )
| ~ ~ ( ~ ! [SY60: term] :
( ~ ( SV2 @ id @ SY60 @ id )
| ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SY60 ) @ id ) )
| ~ ~ ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id ) ) ) )
= $true )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[19]) ).
thf(23,plain,
( ( ! [SX0: subst > term > term] :
( ( ( sub @ ( SX0 @ ( sK4_M @ SX0 ) @ ( sK5_SY50 @ SX0 ) ) @ ( sK6_SY52 @ SX0 ) )
!= ( SX0 @ ( comp @ ( sK4_M @ SX0 ) @ ( sK6_SY52 @ SX0 ) ) @ ( sub @ ( sK5_SY50 @ SX0 ) @ ( sK6_SY52 @ SX0 ) ) ) )
| ~ ( ~ ( sK1_SY13 @ id @ ( sK3_SY46 @ SX0 ) @ id )
| ~ ~ ( sK1_SY13 @ id @ ( SX0 @ id @ ( sK3_SY46 @ SX0 ) ) @ id ) )
| ( sK1_SY13 @ id @ ( lam @ ( SX0 @ sh @ one ) ) @ id ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
( ( ~ ( ~ ! [SX0: term] :
( ~ ( sK1_SY13 @ id @ SX0 @ id )
| ( sK1_SY13 @ id @ ( sub @ sK2_SY47 @ ( push @ SX0 @ id ) ) @ id ) )
| ~ ~ ( sK1_SY13 @ id @ ( lam @ sK2_SY47 ) @ id ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV2: subst > term > subst > $o] :
( ( ( ~ ! [SY57: subst,SY58: term,SY59: subst] :
( ( sub @ ( sK8_SY2 @ SV2 @ SY57 @ SY58 ) @ SY59 )
= ( sK8_SY2 @ SV2 @ ( comp @ SY57 @ SY59 ) @ ( sub @ SY58 @ SY59 ) ) )
| ~ ~ ( ~ ! [SY60: term] :
( ~ ( SV2 @ id @ SY60 @ id )
| ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SY60 ) @ id ) )
| ~ ~ ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id ) ) )
= $false )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV3: subst > term > term] :
( ( ( ( sub @ ( SV3 @ ( sK4_M @ SV3 ) @ ( sK5_SY50 @ SV3 ) ) @ ( sK6_SY52 @ SV3 ) )
!= ( SV3 @ ( comp @ ( sK4_M @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) @ ( sub @ ( sK5_SY50 @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) ) )
| ~ ( ~ ( sK1_SY13 @ id @ ( sK3_SY46 @ SV3 ) @ id )
| ~ ~ ( sK1_SY13 @ id @ ( SV3 @ id @ ( sK3_SY46 @ SV3 ) ) @ id ) )
| ( sK1_SY13 @ id @ ( lam @ ( SV3 @ sh @ one ) ) @ id ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ! [SX0: term] :
( ~ ( sK1_SY13 @ id @ SX0 @ id )
| ( sK1_SY13 @ id @ ( sub @ sK2_SY47 @ ( push @ SX0 @ id ) ) @ id ) )
| ~ ~ ( sK1_SY13 @ id @ ( lam @ sK2_SY47 ) @ id ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(28,plain,
! [SV2: subst > term > subst > $o] :
( ( ( ~ ! [SY57: subst,SY58: term,SY59: subst] :
( ( sub @ ( sK8_SY2 @ SV2 @ SY57 @ SY58 ) @ SY59 )
= ( sK8_SY2 @ SV2 @ ( comp @ SY57 @ SY59 ) @ ( sub @ SY58 @ SY59 ) ) ) )
= $false )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV2: subst > term > subst > $o] :
( ( ( ~ ~ ( ~ ! [SY60: term] :
( ~ ( SV2 @ id @ SY60 @ id )
| ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SY60 ) @ id ) )
| ~ ~ ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id ) ) )
= $false )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(30,plain,
! [SV3: subst > term > term] :
( ( ( ( sub @ ( SV3 @ ( sK4_M @ SV3 ) @ ( sK5_SY50 @ SV3 ) ) @ ( sK6_SY52 @ SV3 ) )
!= ( SV3 @ ( comp @ ( sK4_M @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) @ ( sub @ ( sK5_SY50 @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) ) )
= $true )
| ( ( ~ ( ~ ( sK1_SY13 @ id @ ( sK3_SY46 @ SV3 ) @ id )
| ~ ~ ( sK1_SY13 @ id @ ( SV3 @ id @ ( sK3_SY46 @ SV3 ) ) @ id ) )
| ( sK1_SY13 @ id @ ( lam @ ( SV3 @ sh @ one ) ) @ id ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(31,plain,
( ( ~ ! [SX0: term] :
( ~ ( sK1_SY13 @ id @ SX0 @ id )
| ( sK1_SY13 @ id @ ( sub @ sK2_SY47 @ ( push @ SX0 @ id ) ) @ id ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( ~ ~ ( sK1_SY13 @ id @ ( lam @ sK2_SY47 ) @ id ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(33,plain,
! [SV2: subst > term > subst > $o] :
( ( ( ! [SY57: subst,SY58: term,SY59: subst] :
( ( sub @ ( sK8_SY2 @ SV2 @ SY57 @ SY58 ) @ SY59 )
= ( sK8_SY2 @ SV2 @ ( comp @ SY57 @ SY59 ) @ ( sub @ SY58 @ SY59 ) ) ) )
= $true )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(34,plain,
! [SV2: subst > term > subst > $o] :
( ( ( ~ ( ~ ! [SY60: term] :
( ~ ( SV2 @ id @ SY60 @ id )
| ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SY60 ) @ id ) )
| ~ ~ ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id ) ) )
= $true )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(35,plain,
! [SV3: subst > term > term] :
( ( ( ( sub @ ( SV3 @ ( sK4_M @ SV3 ) @ ( sK5_SY50 @ SV3 ) ) @ ( sK6_SY52 @ SV3 ) )
= ( SV3 @ ( comp @ ( sK4_M @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) @ ( sub @ ( sK5_SY50 @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) ) )
= $false )
| ( ( ~ ( ~ ( sK1_SY13 @ id @ ( sK3_SY46 @ SV3 ) @ id )
| ~ ~ ( sK1_SY13 @ id @ ( SV3 @ id @ ( sK3_SY46 @ SV3 ) ) @ id ) )
| ( sK1_SY13 @ id @ ( lam @ ( SV3 @ sh @ one ) ) @ id ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(36,plain,
( ( ! [SX0: term] :
( ~ ( sK1_SY13 @ id @ SX0 @ id )
| ( sK1_SY13 @ id @ ( sub @ sK2_SY47 @ ( push @ SX0 @ id ) ) @ id ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[31]) ).
thf(37,plain,
( ( ~ ( sK1_SY13 @ id @ ( lam @ sK2_SY47 ) @ id ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(38,plain,
! [SV4: subst,SV2: subst > term > subst > $o] :
( ( ( ! [SY62: term,SY63: subst] :
( ( sub @ ( sK8_SY2 @ SV2 @ SV4 @ SY62 ) @ SY63 )
= ( sK8_SY2 @ SV2 @ ( comp @ SV4 @ SY63 ) @ ( sub @ SY62 @ SY63 ) ) ) )
= $true )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV2: subst > term > subst > $o] :
( ( ( ~ ! [SY60: term] :
( ~ ( SV2 @ id @ SY60 @ id )
| ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SY60 ) @ id ) )
| ~ ~ ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id ) )
= $false )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(40,plain,
! [SV3: subst > term > term] :
( ( ( ~ ( ~ ( sK1_SY13 @ id @ ( sK3_SY46 @ SV3 ) @ id )
| ~ ~ ( sK1_SY13 @ id @ ( SV3 @ id @ ( sK3_SY46 @ SV3 ) ) @ id ) ) )
= $true )
| ( ( sK1_SY13 @ id @ ( lam @ ( SV3 @ sh @ one ) ) @ id )
= $true )
| ( ( ( sub @ ( SV3 @ ( sK4_M @ SV3 ) @ ( sK5_SY50 @ SV3 ) ) @ ( sK6_SY52 @ SV3 ) )
= ( SV3 @ ( comp @ ( sK4_M @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) @ ( sub @ ( sK5_SY50 @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(41,plain,
! [SV5: term] :
( ( ~ ( sK1_SY13 @ id @ SV5 @ id )
| ( sK1_SY13 @ id @ ( sub @ sK2_SY47 @ ( push @ SV5 @ id ) ) @ id ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(42,plain,
( ( sK1_SY13 @ id @ ( lam @ sK2_SY47 ) @ id )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV6: term,SV4: subst,SV2: subst > term > subst > $o] :
( ( ( ! [SY64: subst] :
( ( sub @ ( sK8_SY2 @ SV2 @ SV4 @ SV6 ) @ SY64 )
= ( sK8_SY2 @ SV2 @ ( comp @ SV4 @ SY64 ) @ ( sub @ SV6 @ SY64 ) ) ) )
= $true )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV2: subst > term > subst > $o] :
( ( ( ~ ! [SY60: term] :
( ~ ( SV2 @ id @ SY60 @ id )
| ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SY60 ) @ id ) ) )
= $false )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(45,plain,
! [SV2: subst > term > subst > $o] :
( ( ( ~ ~ ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id ) )
= $false )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(46,plain,
! [SV3: subst > term > term] :
( ( ( ~ ( sK1_SY13 @ id @ ( sK3_SY46 @ SV3 ) @ id )
| ~ ~ ( sK1_SY13 @ id @ ( SV3 @ id @ ( sK3_SY46 @ SV3 ) ) @ id ) )
= $false )
| ( ( sK1_SY13 @ id @ ( lam @ ( SV3 @ sh @ one ) ) @ id )
= $true )
| ( ( ( sub @ ( SV3 @ ( sK4_M @ SV3 ) @ ( sK5_SY50 @ SV3 ) ) @ ( sK6_SY52 @ SV3 ) )
= ( SV3 @ ( comp @ ( sK4_M @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) @ ( sub @ ( sK5_SY50 @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV5: term] :
( ( ( ~ ( sK1_SY13 @ id @ SV5 @ id ) )
= $true )
| ( ( sK1_SY13 @ id @ ( sub @ sK2_SY47 @ ( push @ SV5 @ id ) ) @ id )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(48,plain,
! [SV7: subst,SV6: term,SV4: subst,SV2: subst > term > subst > $o] :
( ( ( ( sub @ ( sK8_SY2 @ SV2 @ SV4 @ SV6 ) @ SV7 )
= ( sK8_SY2 @ SV2 @ ( comp @ SV4 @ SV7 ) @ ( sub @ SV6 @ SV7 ) ) )
= $true )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV2: subst > term > subst > $o] :
( ( ( ! [SY60: term] :
( ~ ( SV2 @ id @ SY60 @ id )
| ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SY60 ) @ id ) ) )
= $true )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(50,plain,
! [SV2: subst > term > subst > $o] :
( ( ( ~ ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id ) )
= $true )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(51,plain,
! [SV3: subst > term > term] :
( ( ( ~ ( sK1_SY13 @ id @ ( sK3_SY46 @ SV3 ) @ id ) )
= $false )
| ( ( sK1_SY13 @ id @ ( lam @ ( SV3 @ sh @ one ) ) @ id )
= $true )
| ( ( ( sub @ ( SV3 @ ( sK4_M @ SV3 ) @ ( sK5_SY50 @ SV3 ) ) @ ( sK6_SY52 @ SV3 ) )
= ( SV3 @ ( comp @ ( sK4_M @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) @ ( sub @ ( sK5_SY50 @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(52,plain,
! [SV3: subst > term > term] :
( ( ( ~ ~ ( sK1_SY13 @ id @ ( SV3 @ id @ ( sK3_SY46 @ SV3 ) ) @ id ) )
= $false )
| ( ( sK1_SY13 @ id @ ( lam @ ( SV3 @ sh @ one ) ) @ id )
= $true )
| ( ( ( sub @ ( SV3 @ ( sK4_M @ SV3 ) @ ( sK5_SY50 @ SV3 ) ) @ ( sK6_SY52 @ SV3 ) )
= ( SV3 @ ( comp @ ( sK4_M @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) @ ( sub @ ( sK5_SY50 @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[46]) ).
thf(53,plain,
! [SV5: term] :
( ( ( sK1_SY13 @ id @ SV5 @ id )
= $false )
| ( ( sK1_SY13 @ id @ ( sub @ sK2_SY47 @ ( push @ SV5 @ id ) ) @ id )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV7: subst,SV6: term,SV4: subst,SV8: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SV8 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SV8 @ ( push @ ( sK7_B @ SV8 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SV8 @ ( push @ one @ sh ) ) ) @ id ) )
= $true )
| ( ( ( sub @ ( sK8_SY2 @ SV2 @ SV4 @ SV6 ) @ SV7 )
= ( sK8_SY2 @ SV2 @ ( comp @ SV4 @ SV7 ) @ ( sub @ SV6 @ SV7 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV9: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( SV2 @ id @ SV9 @ id )
| ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SV9 ) @ id ) )
= $true )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV2: subst > term > subst > $o] :
( ( ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id )
= $false )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV3: subst > term > term] :
( ( ( sK1_SY13 @ id @ ( sK3_SY46 @ SV3 ) @ id )
= $true )
| ( ( sK1_SY13 @ id @ ( lam @ ( SV3 @ sh @ one ) ) @ id )
= $true )
| ( ( ( sub @ ( SV3 @ ( sK4_M @ SV3 ) @ ( sK5_SY50 @ SV3 ) ) @ ( sK6_SY52 @ SV3 ) )
= ( SV3 @ ( comp @ ( sK4_M @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) @ ( sub @ ( sK5_SY50 @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(58,plain,
! [SV3: subst > term > term] :
( ( ( ~ ( sK1_SY13 @ id @ ( SV3 @ id @ ( sK3_SY46 @ SV3 ) ) @ id ) )
= $true )
| ( ( sK1_SY13 @ id @ ( lam @ ( SV3 @ sh @ one ) ) @ id )
= $true )
| ( ( ( sub @ ( SV3 @ ( sK4_M @ SV3 ) @ ( sK5_SY50 @ SV3 ) ) @ ( sK6_SY52 @ SV3 ) )
= ( SV3 @ ( comp @ ( sK4_M @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) @ ( sub @ ( sK5_SY50 @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(59,plain,
! [SV7: subst,SV6: term,SV4: subst,SV8: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SV8 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SV8 @ ( push @ ( sK7_B @ SV8 @ SV2 ) @ id ) ) @ id ) ) )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV8 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( ( sub @ ( sK8_SY2 @ SV2 @ SV4 @ SV6 ) @ SV7 )
= ( sK8_SY2 @ SV2 @ ( comp @ SV4 @ SV7 ) @ ( sub @ SV6 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV9: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( SV2 @ id @ SV9 @ id ) )
= $true )
| ( ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SV9 ) @ id )
= $true )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV10: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SV10 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SV10 @ ( push @ ( sK7_B @ SV10 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SV10 @ ( push @ one @ sh ) ) ) @ id ) )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV3: subst > term > term] :
( ( ( sK1_SY13 @ id @ ( SV3 @ id @ ( sK3_SY46 @ SV3 ) ) @ id )
= $false )
| ( ( sK1_SY13 @ id @ ( lam @ ( SV3 @ sh @ one ) ) @ id )
= $true )
| ( ( ( sub @ ( SV3 @ ( sK4_M @ SV3 ) @ ( sK5_SY50 @ SV3 ) ) @ ( sK6_SY52 @ SV3 ) )
= ( SV3 @ ( comp @ ( sK4_M @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) @ ( sub @ ( sK5_SY50 @ SV3 ) @ ( sK6_SY52 @ SV3 ) ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV7: subst,SV6: term,SV4: subst,SV8: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( SV2 @ id @ ( sK7_B @ SV8 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SV8 @ ( push @ ( sK7_B @ SV8 @ SV2 ) @ id ) ) @ id ) )
= $false )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV8 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( ( sub @ ( sK8_SY2 @ SV2 @ SV4 @ SV6 ) @ SV7 )
= ( sK8_SY2 @ SV2 @ ( comp @ SV4 @ SV7 ) @ ( sub @ SV6 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV9: term,SV2: subst > term > subst > $o] :
( ( ( SV2 @ id @ SV9 @ id )
= $false )
| ( ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SV9 ) @ id )
= $true )
| ( ( ! [SY61: term] :
( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SY61 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SY61 @ ( push @ ( sK7_B @ SY61 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SY61 @ ( push @ one @ sh ) ) ) @ id ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV10: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SV10 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SV10 @ ( push @ ( sK7_B @ SV10 @ SV2 ) @ id ) ) @ id ) ) )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV10 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV7: subst,SV6: term,SV4: subst,SV8: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( SV2 @ id @ ( sK7_B @ SV8 @ SV2 ) @ id ) )
= $false )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV8 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( ( sub @ ( sK8_SY2 @ SV2 @ SV4 @ SV6 ) @ SV7 )
= ( sK8_SY2 @ SV2 @ ( comp @ SV4 @ SV7 ) @ ( sub @ SV6 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(67,plain,
! [SV7: subst,SV6: term,SV4: subst,SV8: term,SV2: subst > term > subst > $o] :
( ( ( ~ ~ ( SV2 @ id @ ( sub @ SV8 @ ( push @ ( sK7_B @ SV8 @ SV2 ) @ id ) ) @ id ) )
= $false )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV8 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( ( sub @ ( sK8_SY2 @ SV2 @ SV4 @ SV6 ) @ SV7 )
= ( sK8_SY2 @ SV2 @ ( comp @ SV4 @ SV7 ) @ ( sub @ SV6 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV9: term,SV11: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SV11 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SV11 @ ( push @ ( sK7_B @ SV11 @ SV2 ) @ id ) ) @ id ) )
| ( SV2 @ id @ ( lam @ ( sub @ SV11 @ ( push @ one @ sh ) ) ) @ id ) )
= $true )
| ( ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SV9 ) @ id )
= $true )
| ( ( SV2 @ id @ SV9 @ id )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV10: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( SV2 @ id @ ( sK7_B @ SV10 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SV10 @ ( push @ ( sK7_B @ SV10 @ SV2 ) @ id ) ) @ id ) )
= $false )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV10 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV7: subst,SV6: term,SV4: subst,SV8: term,SV2: subst > term > subst > $o] :
( ( ( SV2 @ id @ ( sK7_B @ SV8 @ SV2 ) @ id )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV8 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( ( sub @ ( sK8_SY2 @ SV2 @ SV4 @ SV6 ) @ SV7 )
= ( sK8_SY2 @ SV2 @ ( comp @ SV4 @ SV7 ) @ ( sub @ SV6 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(71,plain,
! [SV7: subst,SV6: term,SV4: subst,SV8: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( SV2 @ id @ ( sub @ SV8 @ ( push @ ( sK7_B @ SV8 @ SV2 ) @ id ) ) @ id ) )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV8 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( ( sub @ ( sK8_SY2 @ SV2 @ SV4 @ SV6 ) @ SV7 )
= ( sK8_SY2 @ SV2 @ ( comp @ SV4 @ SV7 ) @ ( sub @ SV6 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
! [SV9: term,SV11: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( ~ ( SV2 @ id @ ( sK7_B @ SV11 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SV11 @ ( push @ ( sK7_B @ SV11 @ SV2 ) @ id ) ) @ id ) ) )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV11 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SV9 ) @ id )
= $true )
| ( ( SV2 @ id @ SV9 @ id )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(73,plain,
! [SV10: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( SV2 @ id @ ( sK7_B @ SV10 @ SV2 ) @ id ) )
= $false )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV10 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(74,plain,
! [SV10: term,SV2: subst > term > subst > $o] :
( ( ( ~ ~ ( SV2 @ id @ ( sub @ SV10 @ ( push @ ( sK7_B @ SV10 @ SV2 ) @ id ) ) @ id ) )
= $false )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV10 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(75,plain,
! [SV7: subst,SV6: term,SV4: subst,SV8: term,SV2: subst > term > subst > $o] :
( ( ( SV2 @ id @ ( sub @ SV8 @ ( push @ ( sK7_B @ SV8 @ SV2 ) @ id ) ) @ id )
= $false )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV8 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( ( sub @ ( sK8_SY2 @ SV2 @ SV4 @ SV6 ) @ SV7 )
= ( sK8_SY2 @ SV2 @ ( comp @ SV4 @ SV7 ) @ ( sub @ SV6 @ SV7 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV9: term,SV11: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( SV2 @ id @ ( sK7_B @ SV11 @ SV2 ) @ id )
| ~ ~ ( SV2 @ id @ ( sub @ SV11 @ ( push @ ( sK7_B @ SV11 @ SV2 ) @ id ) ) @ id ) )
= $false )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV11 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SV9 ) @ id )
= $true )
| ( ( SV2 @ id @ SV9 @ id )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV10: term,SV2: subst > term > subst > $o] :
( ( ( SV2 @ id @ ( sK7_B @ SV10 @ SV2 ) @ id )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV10 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV10: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( SV2 @ id @ ( sub @ SV10 @ ( push @ ( sK7_B @ SV10 @ SV2 ) @ id ) ) @ id ) )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV10 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(79,plain,
! [SV9: term,SV11: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( SV2 @ id @ ( sK7_B @ SV11 @ SV2 ) @ id ) )
= $false )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV11 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SV9 ) @ id )
= $true )
| ( ( SV2 @ id @ SV9 @ id )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(80,plain,
! [SV9: term,SV11: term,SV2: subst > term > subst > $o] :
( ( ( ~ ~ ( SV2 @ id @ ( sub @ SV11 @ ( push @ ( sK7_B @ SV11 @ SV2 ) @ id ) ) @ id ) )
= $false )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV11 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SV9 ) @ id )
= $true )
| ( ( SV2 @ id @ SV9 @ id )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(81,plain,
! [SV10: term,SV2: subst > term > subst > $o] :
( ( ( SV2 @ id @ ( sub @ SV10 @ ( push @ ( sK7_B @ SV10 @ SV2 ) @ id ) ) @ id )
= $false )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV10 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sK8_SY2 @ SV2 @ sh @ one ) ) @ id )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(82,plain,
! [SV9: term,SV11: term,SV2: subst > term > subst > $o] :
( ( ( SV2 @ id @ ( sK7_B @ SV11 @ SV2 ) @ id )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV11 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SV9 ) @ id )
= $true )
| ( ( SV2 @ id @ SV9 @ id )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(83,plain,
! [SV9: term,SV11: term,SV2: subst > term > subst > $o] :
( ( ( ~ ( SV2 @ id @ ( sub @ SV11 @ ( push @ ( sK7_B @ SV11 @ SV2 ) @ id ) ) @ id ) )
= $true )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV11 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SV9 ) @ id )
= $true )
| ( ( SV2 @ id @ SV9 @ id )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(84,plain,
! [SV9: term,SV11: term,SV2: subst > term > subst > $o] :
( ( ( SV2 @ id @ ( sub @ SV11 @ ( push @ ( sK7_B @ SV11 @ SV2 ) @ id ) ) @ id )
= $false )
| ( ( SV2 @ id @ ( lam @ ( sub @ SV11 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ( ( SV2 @ id @ ( sK8_SY2 @ SV2 @ id @ SV9 ) @ id )
= $true )
| ( ( SV2 @ id @ SV9 @ id )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(85,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[12,84,82,81,77,75,70,62,57,53,42,17]) ).
thf(86,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG266^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n001.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 18:16:09 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.29
% 0.60/0.29 No.of.Axioms: 0
% 0.60/0.29
% 0.60/0.29 Length.of.Defs: 38092
% 0.60/0.29
% 0.60/0.29 Contains.Choice.Funs: false
% 0.60/0.29 .....
% 0.60/0.29
% 0.60/0.29 ********************************
% 0.60/0.29 * All subproblems solved! *
% 0.60/0.29 ********************************
% 0.60/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:85,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.60/0.29
% 0.60/0.29 %**** Beginning of derivation protocol ****
% 0.60/0.29 % SZS output start CNFRefutation
% See solution above
% 0.60/0.29
% 0.60/0.29 %**** End of derivation protocol ****
% 0.60/0.29 %**** no. of clauses in derivation: 86 ****
% 0.60/0.29 %**** clause counter: 85 ****
% 0.60/0.29
% 0.60/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:3,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:85,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------