%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ALG263^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 Sep 30 07:44:56 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 39
% Syntax : Number of formulae : 59 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 359 ( 165 equ; 0 cnn)
% Maximal formula atoms : 81 ( 6 avg)
% Number of connectives : 2503 ( 124 ~; 155 |; 88 &;1820 @)
% ( 44 <=>; 272 =>; 0 <=; 0 <~>)
% Maximal formula depth : 173 ( 10 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 78 usr; 41 con; 0-4 aty)
% Number of variables : 539 ( 36 ^; 503 !; 0 ?; 539 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_23,type,
one: term ).
thf(decl_24,type,
ap: term > term > term ).
thf(decl_25,type,
lam: term > term ).
thf(decl_26,type,
sub: term > subst > term ).
thf(decl_27,type,
id: subst ).
thf(decl_28,type,
sh: subst ).
thf(decl_29,type,
push: term > subst > subst ).
thf(decl_30,type,
comp: subst > subst > subst ).
thf(decl_31,type,
var: term > $o ).
thf(decl_34,type,
axmap: $o ).
thf(decl_36,type,
shinj: $o ).
thf(decl_37,type,
hoasinduction_lem1v2: $o ).
thf(decl_38,type,
hoasinduction_lem1v2_gthm: $o ).
thf(decl_39,type,
hoasap: subst > term > subst > term > term ).
thf(decl_40,type,
induction2lem: $o ).
thf(decl_42,type,
axvarshift: $o ).
thf(decl_43,type,
hoasapinj2: $o ).
thf(decl_45,type,
hoasapinj1: $o ).
thf(decl_46,type,
ulamvar1: $o ).
thf(decl_49,type,
apnotvar: $o ).
thf(decl_54,type,
hoaslaminj: $o ).
thf(decl_64,type,
hoasapnotvar: $o ).
thf(decl_68,type,
axapp: $o ).
thf(decl_72,type,
ulamvarind: $o ).
thf(decl_73,type,
induction: $o ).
thf(decl_83,type,
axclos: $o ).
thf(decl_84,type,
axassoc: $o ).
thf(decl_87,type,
apinj2: $o ).
thf(decl_88,type,
apinj1: $o ).
thf(decl_93,type,
axvarcons: $o ).
thf(decl_94,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(decl_95,type,
axscons: $o ).
thf(decl_97,type,
axidr: $o ).
thf(decl_99,type,
laminj: $o ).
thf(decl_103,type,
axabs: $o ).
thf(decl_107,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(decl_109,type,
lamnotap: $o ).
thf(decl_111,type,
hoaslamnotvar: $o ).
thf(decl_112,type,
axidl: $o ).
thf(decl_117,type,
pushprop: $o ).
thf(decl_121,type,
substmonoid: $o ).
thf(decl_122,type,
lamnotvar: $o ).
thf(decl_128,type,
hoasvar: subst > term > subst > $o ).
thf(decl_129,type,
hoaslamnotap: $o ).
thf(decl_131,type,
ulamvarsh: $o ).
thf(decl_132,type,
induction2: $o ).
thf(decl_137,type,
axshiftcons: $o ).
thf(decl_138,type,
termmset: $o ).
thf(decl_143,type,
axvarid: $o ).
thf(decl_145,type,
esk1_1: ( term > $o ) > term ).
thf(decl_146,type,
esk2_1: ( term > $o ) > term ).
thf(decl_147,type,
esk3_1: ( term > $o ) > term ).
thf(decl_148,type,
esk4_1: ( term > $o ) > term ).
thf(decl_149,type,
esk5_1: ( term > $o ) > term ).
thf(decl_150,type,
esk6_3: ( term > $o ) > term > subst > term ).
thf(decl_151,type,
esk7_1: ( term > $o ) > term ).
thf(decl_152,type,
esk8_1: ( term > $o ) > term ).
thf(decl_153,type,
esk9_1: ( term > $o ) > term ).
thf(decl_154,type,
esk10_3: ( term > $o ) > term > subst > term ).
thf(decl_155,type,
esk11_1: ( term > $o ) > term ).
thf(decl_156,type,
esk12_1: ( term > $o ) > term ).
thf(decl_157,type,
esk13_1: ( term > $o ) > term ).
thf(decl_158,type,
esk14_1: ( term > $o ) > term ).
thf(decl_159,type,
esk15_1: ( subst > term > term ) > subst ).
thf(decl_160,type,
esk16_1: ( subst > term > term ) > term ).
thf(decl_161,type,
esk17_1: ( subst > term > term ) > subst ).
thf(decl_162,type,
esk18_2: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(decl_163,type,
esk19_2: ( subst > term > term ) > ( subst > term > term ) > term ).
thf(decl_164,type,
esk20_2: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(decl_165,type,
esk21_1: ( subst > term > term ) > subst ).
thf(decl_166,type,
esk22_1: ( subst > term > term ) > term ).
thf(decl_167,type,
esk23_1: ( subst > term > term ) > subst ).
thf(decl_168,type,
esk24_1: ( subst > term > term ) > subst ).
thf(decl_169,type,
esk25_1: ( subst > term > term ) > term ).
thf(decl_170,type,
esk26_1: ( subst > term > term ) > subst ).
thf(decl_171,type,
epred1_0: subst > term > subst > $o ).
thf(decl_172,type,
epred2_0: term > $o ).
thf(decl_173,type,
esk27_0: term ).
thf(hoaslamnotvar,axiom,
( hoaslamnotvar
<=> ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [X3: subst,X1: term] : ( X12 @ X3 @ X1 ) )
@ id ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',hoaslamnotvar) ).
thf(hoasvar,axiom,
( hoasvar
= ( ^ [X3: subst,X1: term,X4: subst] : ( var @ ( sub @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',hoasvar) ).
thf(hoasinduction_p_and_p_prime,axiom,
( hoasinduction_p_and_p_prime
= ( ^ [X14: subst > term > subst > $o,X9: term > $o] :
! [X10: term] :
( ( X9 @ X10 )
<=> ( X14 @ id @ X10 @ id ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',hoasinduction_p_and_p_prime) ).
thf(hoaslaminj,axiom,
( hoaslaminj
<=> ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ! [X13: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X13 @ X3 @ X1 ) @ X4 )
= ( X13 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X3: subst,X1: term] : ( X12 @ X3 @ X1 ) )
= ( hoaslam @ id
@ ^ [X3: subst,X1: term] : ( X13 @ X3 @ X1 ) ) )
=> ! [X3: subst,X1: term] :
( ( X12 @ X3 @ X1 )
= ( X13 @ X3 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',hoaslaminj) ).
thf(hoaslamnotap,axiom,
( hoaslamnotap
<=> ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ! [X1: term,X2: term] :
( ( hoaslam @ id
@ ^ [X3: subst,X7: term] : ( X12 @ X3 @ X7 ) )
!= ( hoasap @ id @ X1 @ id @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',hoaslamnotap) ).
thf(hoasapnotvar,axiom,
( hoasapnotvar
<=> ! [X1: term,X2: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',hoasapnotvar) ).
thf(hoasinduction_lem1v2,axiom,
( hoasinduction_lem1v2
<=> ! [X16: subst > term > subst > $o,X9: term > $o] :
( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X16 @ X3 @ X1 @ ( comp @ X5 @ X4 ) )
=> ( X16 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 ) )
=> ( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X16 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 )
=> ( X16 @ X3 @ X1 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X1: term] :
( ( hoasvar @ id @ X1 @ id )
=> ( X16 @ id @ X1 @ id ) )
=> ( ( hoasinduction_p_and_p_prime @ X16 @ X9 )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X9 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',hoasinduction_lem1v2) ).
thf(thm,conjecture,
hoasinduction_lem1v2_gthm,
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',thm) ).
thf(hoasinduction_lem1v2_gthm,axiom,
( hoasinduction_lem1v2_gthm
<=> ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',hoasinduction_lem1v2_gthm) ).
thf(axapp,axiom,
( axapp
<=> ! [X1: term,X2: term,X3: subst] :
( ( sub @ ( ap @ X1 @ X2 ) @ X3 )
= ( ap @ ( sub @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',axapp) ).
thf(axvarcons,axiom,
( axvarcons
<=> ! [X1: term,X3: subst] :
( ( sub @ one @ ( push @ X1 @ X3 ) )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',axvarcons) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',axvarid) ).
thf(axabs,axiom,
( axabs
<=> ! [X1: term,X3: subst] :
( ( sub @ ( lam @ X1 ) @ X3 )
= ( lam @ ( sub @ X1 @ ( push @ one @ ( comp @ X3 @ sh ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',axabs) ).
thf(axclos,axiom,
( axclos
<=> ! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
= ( sub @ X1 @ ( comp @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',axclos) ).
thf(axidl,axiom,
( axidl
<=> ! [X3: subst] :
( ( comp @ id @ X3 )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',axidl) ).
thf(axshiftcons,axiom,
( axshiftcons
<=> ! [X1: term,X3: subst] :
( ( comp @ sh @ ( push @ X1 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',axshiftcons) ).
thf(axassoc,axiom,
( axassoc
<=> ! [X3: subst,X4: subst,X5: subst] :
( ( comp @ ( comp @ X3 @ X4 ) @ X5 )
= ( comp @ X3 @ ( comp @ X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',axassoc) ).
thf(axmap,axiom,
( axmap
<=> ! [X1: term,X3: subst,X4: subst] :
( ( comp @ ( push @ X1 @ X3 ) @ X4 )
= ( push @ ( sub @ X1 @ X4 ) @ ( comp @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',axmap) ).
thf(axidr,axiom,
( axidr
<=> ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',axidr) ).
thf(axvarshift,axiom,
( axvarshift
<=> ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',axvarshift) ).
thf(axscons,axiom,
( axscons
<=> ! [X3: subst] :
( ( push @ ( sub @ one @ X3 ) @ ( comp @ sh @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',axscons) ).
thf(ulamvar1,axiom,
( ulamvar1
<=> ( var @ one ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',ulamvar1) ).
thf(ulamvarsh,axiom,
( ulamvarsh
<=> ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',ulamvarsh) ).
thf(ulamvarind,axiom,
( ulamvarind
<=> ! [X6: term > $o] :
( ( X6 @ one )
=> ( ! [X1: term] :
( ( var @ X1 )
=> ( ( X6 @ X1 )
=> ( X6 @ ( sub @ X1 @ sh ) ) ) )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X6 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',ulamvarind) ).
thf(apinj1,axiom,
( apinj1
<=> ! [X1: term,X2: term,X7: term,X8: term] :
( ( ( ap @ X1 @ X7 )
= ( ap @ X2 @ X8 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',apinj1) ).
thf(apinj2,axiom,
( apinj2
<=> ! [X1: term,X2: term,X7: term,X8: term] :
( ( ( ap @ X1 @ X7 )
= ( ap @ X2 @ X8 ) )
=> ( X7 = X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',apinj2) ).
thf(laminj,axiom,
( laminj
<=> ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',laminj) ).
thf(shinj,axiom,
( shinj
<=> ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',shinj) ).
thf(lamnotap,axiom,
( lamnotap
<=> ! [X1: term,X2: term,X7: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',lamnotap) ).
thf(apnotvar,axiom,
( apnotvar
<=> ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',apnotvar) ).
thf(lamnotvar,axiom,
( lamnotvar
<=> ! [X1: term] :
~ ( var @ ( lam @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',lamnotvar) ).
thf(induction,axiom,
( induction
<=> ! [X6: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X6 @ X1 ) )
=> ( ! [X1: term,X2: term] :
( ( X6 @ X1 )
=> ( ( X6 @ X2 )
=> ( X6 @ ( ap @ X1 @ X2 ) ) ) )
=> ( ! [X1: term] :
( ( X6 @ X1 )
=> ( X6 @ ( lam @ X1 ) ) )
=> ! [X1: term] : ( X6 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',induction) ).
thf(pushprop,axiom,
( pushprop
<=> ! [X6: term > $o,X1: term,X3: subst] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ X3 ) ) )
=> ( ( X6 @ X1 )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ ( push @ X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',pushprop) ).
thf(induction2lem,axiom,
( induction2lem
<=> ! [X6: term > $o] :
( ! [X1: term,X2: term] :
( ( X6 @ X1 )
=> ( ( X6 @ X2 )
=> ( X6 @ ( ap @ X1 @ X2 ) ) ) )
=> ( ! [X1: term] :
( ! [X2: term] :
( ( X6 @ X2 )
=> ( X6 @ ( sub @ X1 @ ( push @ X2 @ id ) ) ) )
=> ( X6 @ ( lam @ X1 ) ) )
=> ! [X1: term,X3: subst] :
( ! [X2: term] :
( ( var @ X2 )
=> ( X6 @ ( sub @ X2 @ X3 ) ) )
=> ( X6 @ ( sub @ X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',induction2lem) ).
thf(induction2,axiom,
( induction2
<=> ! [X6: term > $o] :
( ! [X1: term] :
( ( var @ X1 )
=> ( X6 @ X1 ) )
=> ( ! [X1: term,X2: term] :
( ( X6 @ X1 )
=> ( ( X6 @ X2 )
=> ( X6 @ ( ap @ X1 @ X2 ) ) ) )
=> ( ! [X1: term] :
( ! [X2: term] :
( ( X6 @ X2 )
=> ( X6 @ ( sub @ X1 @ ( push @ X2 @ id ) ) ) )
=> ( X6 @ ( lam @ X1 ) ) )
=> ! [X1: term] : ( X6 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',induction2) ).
thf(substmonoid,axiom,
( substmonoid
<=> ( ! [X3: subst,X4: subst,X5: subst] :
( ( comp @ ( comp @ X3 @ X4 ) @ X5 )
= ( comp @ X3 @ ( comp @ X4 @ X5 ) ) )
& ! [X3: subst] :
( ( comp @ id @ X3 )
= X3 )
& ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',substmonoid) ).
thf(termmset,axiom,
( termmset
<=> ( ! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( sub @ X1 @ X3 ) @ X4 )
= ( sub @ X1 @ ( comp @ X3 @ X4 ) ) )
& ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',termmset) ).
thf(hoasapinj1,axiom,
( hoasapinj1
<=> ! [X1: term,X2: term,X7: term,X8: term] :
( ( ( hoasap @ id @ X1 @ id @ X7 )
= ( hoasap @ id @ X2 @ id @ X8 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',hoasapinj1) ).
thf(hoasapinj2,axiom,
( hoasapinj2
<=> ! [X1: term,X2: term,X7: term,X8: term] :
( ( ( hoasap @ id @ X1 @ id @ X7 )
= ( hoasap @ id @ X2 @ id @ X8 ) )
=> ( X7 = X8 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p',hoasapinj2) ).
thf(c_0_39,plain,
( hoaslamnotvar
<=> ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
@ id ) ) ),
inference(fof_simplification,[status(thm)],[hoaslamnotvar]) ).
thf(c_0_40,plain,
( hoasvar
= ( ^ [Z0: subst,Z1: term,Z2: subst] : ( var @ ( sub @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[hoasvar]) ).
thf(c_0_41,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Z0: subst > term > subst > $o,Z1: term > $o] :
! [X10: term] :
( ( Z1 @ X10 )
<=> ( Z0 @ id @ X10 @ id ) ) ) ),
inference(fof_simplification,[status(thm)],[hoasinduction_p_and_p_prime]) ).
thf(c_0_42,plain,
( hoaslaminj
<=> ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ! [X13: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X13 @ X3 @ X1 ) @ X4 )
= ( X13 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
= ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X13 @ Z0 @ Z1 ) ) )
=> ! [X3: subst,X1: term] :
( ( X12 @ X3 @ X1 )
= ( X13 @ X3 @ X1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[hoaslaminj]) ).
thf(c_0_43,plain,
( hoaslamnotap
<=> ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ! [X1: term,X2: term] :
( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
!= ( hoasap @ id @ X1 @ id @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[hoaslamnotap]) ).
thf(c_0_44,plain,
( hoaslamnotvar
= ( ! [X12: subst > term > term] :
( ! [X3: subst,X1: term,X4: subst] :
( ( sub @ ( X12 @ X3 @ X1 ) @ X4 )
= ( X12 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) )
=> ~ ( var
@ ( sub
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X12 @ Z0 @ Z1 ) )
@ id ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_39,c_0_40]) ).
thf(c_0_45,axiom,
( hoasapnotvar
= ( ! [X1: term,X2: term] :
~ ( var @ ( sub @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ) ) ),
inference(apply_def,[status(thm)],[hoasapnotvar,c_0_40]) ).
thf(c_0_46,axiom,
( hoasinduction_lem1v2
= ( ! [X16: subst > term > subst > $o,X9: term > $o] :
( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X16 @ X3 @ X1 @ ( comp @ X5 @ X4 ) )
=> ( X16 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 ) )
=> ( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X16 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 )
=> ( X16 @ X3 @ X1 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X1: term] :
( ( var @ ( sub @ X1 @ id ) )
=> ( X16 @ id @ X1 @ id ) )
=> ( ! [X425: term] :
( ( X9 @ X425 )
<=> ( X16 @ id @ X425 @ id ) )
=> ! [X1: term] :
( ( var @ X1 )
=> ( X9 @ X1 ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[hoasinduction_lem1v2,c_0_40]),c_0_41]) ).
thf(c_0_47,negated_conjecture,
~ hoasinduction_lem1v2_gthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_48,axiom,
( hoasinduction_lem1v2_gthm
= ( ! [X426: term,X427: term,X428: subst] :
( ( sub @ ( ap @ X426 @ X427 ) @ X428 )
= ( ap @ ( sub @ X426 @ X428 ) @ ( sub @ X427 @ X428 ) ) )
=> ( ! [X429: term,X430: subst] :
( ( sub @ one @ ( push @ X429 @ X430 ) )
= X429 )
=> ( ! [X431: term] :
( ( sub @ X431 @ id )
= X431 )
=> ( ! [X432: term,X433: subst] :
( ( sub @ ( lam @ X432 ) @ X433 )
= ( lam @ ( sub @ X432 @ ( push @ one @ ( comp @ X433 @ sh ) ) ) ) )
=> ( ! [X434: term,X435: subst,X436: subst] :
( ( sub @ ( sub @ X434 @ X435 ) @ X436 )
= ( sub @ X434 @ ( comp @ X435 @ X436 ) ) )
=> ( ! [X437: subst] :
( ( comp @ id @ X437 )
= X437 )
=> ( ! [X438: term,X439: subst] :
( ( comp @ sh @ ( push @ X438 @ X439 ) )
= X439 )
=> ( ! [X440: subst,X441: subst,X442: subst] :
( ( comp @ ( comp @ X440 @ X441 ) @ X442 )
= ( comp @ X440 @ ( comp @ X441 @ X442 ) ) )
=> ( ! [X443: term,X444: subst,X445: subst] :
( ( comp @ ( push @ X443 @ X444 ) @ X445 )
= ( push @ ( sub @ X443 @ X445 ) @ ( comp @ X444 @ X445 ) ) )
=> ( ! [X446: subst] :
( ( comp @ X446 @ id )
= X446 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X447: subst] :
( ( push @ ( sub @ one @ X447 ) @ ( comp @ sh @ X447 ) )
= X447 )
=> ( ( var @ one )
=> ( ! [X448: term] :
( ( var @ X448 )
=> ( var @ ( sub @ X448 @ sh ) ) )
=> ( ! [X449: term > $o] :
( ( X449 @ one )
=> ( ! [X450: term] :
( ( var @ X450 )
=> ( ( X449 @ X450 )
=> ( X449 @ ( sub @ X450 @ sh ) ) ) )
=> ! [X451: term] :
( ( var @ X451 )
=> ( X449 @ X451 ) ) ) )
=> ( ! [X452: term,X453: term,X454: term,X455: term] :
( ( ( ap @ X452 @ X454 )
= ( ap @ X453 @ X455 ) )
=> ( X452 = X453 ) )
=> ( ! [X456: term,X457: term,X458: term,X459: term] :
( ( ( ap @ X456 @ X458 )
= ( ap @ X457 @ X459 ) )
=> ( X458 = X459 ) )
=> ( ! [X460: term,X461: term] :
( ( ( lam @ X460 )
= ( lam @ X461 ) )
=> ( X460 = X461 ) )
=> ( ! [X462: term,X463: term] :
( ( ( sub @ X462 @ sh )
= ( sub @ X463 @ sh ) )
=> ( X462 = X463 ) )
=> ( ! [X464: term,X465: term,X466: term] :
( ( lam @ X464 )
!= ( ap @ X465 @ X466 ) )
=> ( ! [X467: term,X468: term] :
~ ( var @ ( ap @ X467 @ X468 ) )
=> ( ! [X469: term] :
~ ( var @ ( lam @ X469 ) )
=> ( ! [X470: term > $o] :
( ! [X471: term] :
( ( var @ X471 )
=> ( X470 @ X471 ) )
=> ( ! [X472: term,X473: term] :
( ( X470 @ X472 )
=> ( ( X470 @ X473 )
=> ( X470 @ ( ap @ X472 @ X473 ) ) ) )
=> ( ! [X474: term] :
( ( X470 @ X474 )
=> ( X470 @ ( lam @ X474 ) ) )
=> ! [X475: term] : ( X470 @ X475 ) ) ) )
=> ( ! [X476: term > $o,X477: term,X478: subst] :
( ! [X479: term] :
( ( var @ X479 )
=> ( X476 @ ( sub @ X479 @ X478 ) ) )
=> ( ( X476 @ X477 )
=> ! [X480: term] :
( ( var @ X480 )
=> ( X476 @ ( sub @ X480 @ ( push @ X477 @ X478 ) ) ) ) ) )
=> ( ! [X481: term > $o] :
( ! [X482: term,X483: term] :
( ( X481 @ X482 )
=> ( ( X481 @ X483 )
=> ( X481 @ ( ap @ X482 @ X483 ) ) ) )
=> ( ! [X484: term] :
( ! [X485: term] :
( ( X481 @ X485 )
=> ( X481 @ ( sub @ X484 @ ( push @ X485 @ id ) ) ) )
=> ( X481 @ ( lam @ X484 ) ) )
=> ! [X486: term,X487: subst] :
( ! [X488: term] :
( ( var @ X488 )
=> ( X481 @ ( sub @ X488 @ X487 ) ) )
=> ( X481 @ ( sub @ X486 @ X487 ) ) ) ) )
=> ( ! [X489: term > $o] :
( ! [X490: term] :
( ( var @ X490 )
=> ( X489 @ X490 ) )
=> ( ! [X491: term,X492: term] :
( ( X489 @ X491 )
=> ( ( X489 @ X492 )
=> ( X489 @ ( ap @ X491 @ X492 ) ) ) )
=> ( ! [X493: term] :
( ! [X494: term] :
( ( X489 @ X494 )
=> ( X489 @ ( sub @ X493 @ ( push @ X494 @ id ) ) ) )
=> ( X489 @ ( lam @ X493 ) ) )
=> ! [X495: term] : ( X489 @ X495 ) ) ) )
=> ( ( ! [X496: subst,X497: subst,X498: subst] :
( ( comp @ ( comp @ X496 @ X497 ) @ X498 )
= ( comp @ X496 @ ( comp @ X497 @ X498 ) ) )
& ! [X499: subst] :
( ( comp @ id @ X499 )
= X499 )
& ! [X500: subst] :
( ( comp @ X500 @ id )
= X500 ) )
=> ( ( ! [X501: term,X502: subst,X503: subst] :
( ( sub @ ( sub @ X501 @ X502 ) @ X503 )
= ( sub @ X501 @ ( comp @ X502 @ X503 ) ) )
& ! [X504: term] :
( ( sub @ X504 @ id )
= X504 ) )
=> ( ! [X505: term,X506: term,X507: term,X508: term] :
( ( ( hoasap @ id @ X505 @ id @ X507 )
= ( hoasap @ id @ X506 @ id @ X508 ) )
=> ( X505 = X506 ) )
=> ( ! [X509: term,X510: term,X511: term,X512: term] :
( ( ( hoasap @ id @ X509 @ id @ X511 )
= ( hoasap @ id @ X510 @ id @ X512 ) )
=> ( X511 = X512 ) )
=> ( ! [X513: subst > term > term] :
( ! [X514: subst,X515: term,X516: subst] :
( ( sub @ ( X513 @ X514 @ X515 ) @ X516 )
= ( X513 @ ( comp @ X514 @ X516 ) @ ( sub @ X515 @ X516 ) ) )
=> ! [X517: subst > term > term] :
( ! [X518: subst,X519: term,X520: subst] :
( ( sub @ ( X517 @ X518 @ X519 ) @ X520 )
= ( X517 @ ( comp @ X518 @ X520 ) @ ( sub @ X519 @ X520 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X513 @ Z0 @ Z1 ) )
= ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X517 @ Z0 @ Z1 ) ) )
=> ! [X521: subst,X522: term] :
( ( X513 @ X521 @ X522 )
= ( X517 @ X521 @ X522 ) ) ) ) )
=> ( ! [X523: subst > term > term] :
( ! [X524: subst,X525: term,X526: subst] :
( ( sub @ ( X523 @ X524 @ X525 ) @ X526 )
= ( X523 @ ( comp @ X524 @ X526 ) @ ( sub @ X525 @ X526 ) ) )
=> ! [X527: term,X528: term] :
( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X523 @ Z0 @ Z1 ) )
!= ( hoasap @ id @ X527 @ id @ X528 ) ) )
=> ( ! [X529: subst > term > term] :
( ! [X530: subst,X531: term,X532: subst] :
( ( sub @ ( X529 @ X530 @ X531 ) @ X532 )
= ( X529 @ ( comp @ X530 @ X532 ) @ ( sub @ X531 @ X532 ) ) )
=> ~ ( var
@ ( sub
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X529 @ Z0 @ Z1 ) )
@ id ) ) )
=> ( ! [X533: term,X534: term] :
~ ( var @ ( sub @ ( hoasap @ id @ X533 @ id @ X534 ) @ id ) )
=> ! [X535: subst > term > subst > $o,X536: term > $o] :
( ! [X537: subst,X538: term,X539: subst,X540: subst] :
( ( X535 @ X537 @ X538 @ ( comp @ X540 @ X539 ) )
=> ( X535 @ ( comp @ X537 @ X540 ) @ ( sub @ X538 @ X540 ) @ X539 ) )
=> ( ! [X541: subst,X542: term,X543: subst,X544: subst] :
( ( X535 @ ( comp @ X541 @ X544 ) @ ( sub @ X542 @ X544 ) @ X543 )
=> ( X535 @ X541 @ X542 @ ( comp @ X544 @ X543 ) ) )
=> ( ! [X545: term] :
( ( var @ ( sub @ X545 @ id ) )
=> ( X535 @ id @ X545 @ id ) )
=> ( ! [X546: term] :
( ( X536 @ X546 )
<=> ( X535 @ id @ X546 @ id ) )
=> ! [X547: term] :
( ( var @ X547 )
=> ( X536 @ X547 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[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]),c_0_40]),hoasapinj1]),hoasapinj2]),c_0_42]),c_0_43]),c_0_44]),c_0_45]),c_0_46]) ).
thf(c_0_49,negated_conjecture,
~ ( ! [X3373: term,X3374: term,X3375: subst] :
( ( sub @ ( ap @ X3373 @ X3374 ) @ X3375 )
= ( ap @ ( sub @ X3373 @ X3375 ) @ ( sub @ X3374 @ X3375 ) ) )
=> ( ! [X3376: term,X3377: subst] :
( ( sub @ one @ ( push @ X3376 @ X3377 ) )
= X3376 )
=> ( ! [X3378: term] :
( ( sub @ X3378 @ id )
= X3378 )
=> ( ! [X3379: term,X3380: subst] :
( ( sub @ ( lam @ X3379 ) @ X3380 )
= ( lam @ ( sub @ X3379 @ ( push @ one @ ( comp @ X3380 @ sh ) ) ) ) )
=> ( ! [X3381: term,X3382: subst,X3383: subst] :
( ( sub @ ( sub @ X3381 @ X3382 ) @ X3383 )
= ( sub @ X3381 @ ( comp @ X3382 @ X3383 ) ) )
=> ( ! [X3384: subst] :
( ( comp @ id @ X3384 )
= X3384 )
=> ( ! [X3385: term,X3386: subst] :
( ( comp @ sh @ ( push @ X3385 @ X3386 ) )
= X3386 )
=> ( ! [X3387: subst,X3388: subst,X3389: subst] :
( ( comp @ ( comp @ X3387 @ X3388 ) @ X3389 )
= ( comp @ X3387 @ ( comp @ X3388 @ X3389 ) ) )
=> ( ! [X3390: term,X3391: subst,X3392: subst] :
( ( comp @ ( push @ X3390 @ X3391 ) @ X3392 )
= ( push @ ( sub @ X3390 @ X3392 ) @ ( comp @ X3391 @ X3392 ) ) )
=> ( ! [X3393: subst] :
( ( comp @ X3393 @ id )
= X3393 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X3394: subst] :
( ( push @ ( sub @ one @ X3394 ) @ ( comp @ sh @ X3394 ) )
= X3394 )
=> ( ( var @ one )
=> ( ! [X3395: term] :
( ( var @ X3395 )
=> ( var @ ( sub @ X3395 @ sh ) ) )
=> ( ! [X3396: term > $o] :
( ( X3396 @ one )
=> ( ! [X3397: term] :
( ( var @ X3397 )
=> ( ( X3396 @ X3397 )
=> ( X3396 @ ( sub @ X3397 @ sh ) ) ) )
=> ! [X3398: term] :
( ( var @ X3398 )
=> ( X3396 @ X3398 ) ) ) )
=> ( ! [X3399: term,X3400: term,X3401: term,X3402: term] :
( ( ( ap @ X3399 @ X3401 )
= ( ap @ X3400 @ X3402 ) )
=> ( X3399 = X3400 ) )
=> ( ! [X3403: term,X3404: term,X3405: term,X3406: term] :
( ( ( ap @ X3403 @ X3405 )
= ( ap @ X3404 @ X3406 ) )
=> ( X3405 = X3406 ) )
=> ( ! [X3407: term,X3408: term] :
( ( ( lam @ X3407 )
= ( lam @ X3408 ) )
=> ( X3407 = X3408 ) )
=> ( ! [X3409: term,X3410: term] :
( ( ( sub @ X3409 @ sh )
= ( sub @ X3410 @ sh ) )
=> ( X3409 = X3410 ) )
=> ( ! [X3411: term,X3412: term,X3413: term] :
( ( lam @ X3411 )
!= ( ap @ X3412 @ X3413 ) )
=> ( ! [X3414: term,X3415: term] :
~ ( var @ ( ap @ X3414 @ X3415 ) )
=> ( ! [X3416: term] :
~ ( var @ ( lam @ X3416 ) )
=> ( ! [X3417: term > $o] :
( ! [X3418: term] :
( ( var @ X3418 )
=> ( X3417 @ X3418 ) )
=> ( ! [X3419: term,X3420: term] :
( ( X3417 @ X3419 )
=> ( ( X3417 @ X3420 )
=> ( X3417 @ ( ap @ X3419 @ X3420 ) ) ) )
=> ( ! [X3421: term] :
( ( X3417 @ X3421 )
=> ( X3417 @ ( lam @ X3421 ) ) )
=> ! [X3422: term] : ( X3417 @ X3422 ) ) ) )
=> ( ! [X3423: term > $o,X3424: term,X3425: subst] :
( ! [X3426: term] :
( ( var @ X3426 )
=> ( X3423 @ ( sub @ X3426 @ X3425 ) ) )
=> ( ( X3423 @ X3424 )
=> ! [X3427: term] :
( ( var @ X3427 )
=> ( X3423 @ ( sub @ X3427 @ ( push @ X3424 @ X3425 ) ) ) ) ) )
=> ( ! [X3428: term > $o] :
( ! [X3429: term,X3430: term] :
( ( X3428 @ X3429 )
=> ( ( X3428 @ X3430 )
=> ( X3428 @ ( ap @ X3429 @ X3430 ) ) ) )
=> ( ! [X3431: term] :
( ! [X3432: term] :
( ( X3428 @ X3432 )
=> ( X3428 @ ( sub @ X3431 @ ( push @ X3432 @ id ) ) ) )
=> ( X3428 @ ( lam @ X3431 ) ) )
=> ! [X3433: term,X3434: subst] :
( ! [X3435: term] :
( ( var @ X3435 )
=> ( X3428 @ ( sub @ X3435 @ X3434 ) ) )
=> ( X3428 @ ( sub @ X3433 @ X3434 ) ) ) ) )
=> ( ! [X3436: term > $o] :
( ! [X3437: term] :
( ( var @ X3437 )
=> ( X3436 @ X3437 ) )
=> ( ! [X3438: term,X3439: term] :
( ( X3436 @ X3438 )
=> ( ( X3436 @ X3439 )
=> ( X3436 @ ( ap @ X3438 @ X3439 ) ) ) )
=> ( ! [X3440: term] :
( ! [X3441: term] :
( ( X3436 @ X3441 )
=> ( X3436 @ ( sub @ X3440 @ ( push @ X3441 @ id ) ) ) )
=> ( X3436 @ ( lam @ X3440 ) ) )
=> ! [X3442: term] : ( X3436 @ X3442 ) ) ) )
=> ( ( ! [X3443: subst,X3444: subst,X3445: subst] :
( ( comp @ ( comp @ X3443 @ X3444 ) @ X3445 )
= ( comp @ X3443 @ ( comp @ X3444 @ X3445 ) ) )
& ! [X3446: subst] :
( ( comp @ id @ X3446 )
= X3446 )
& ! [X3447: subst] :
( ( comp @ X3447 @ id )
= X3447 ) )
=> ( ( ! [X3448: term,X3449: subst,X3450: subst] :
( ( sub @ ( sub @ X3448 @ X3449 ) @ X3450 )
= ( sub @ X3448 @ ( comp @ X3449 @ X3450 ) ) )
& ! [X3451: term] :
( ( sub @ X3451 @ id )
= X3451 ) )
=> ( ! [X3452: term,X3453: term,X3454: term,X3455: term] :
( ( ( hoasap @ id @ X3452 @ id @ X3454 )
= ( hoasap @ id @ X3453 @ id @ X3455 ) )
=> ( X3452 = X3453 ) )
=> ( ! [X3456: term,X3457: term,X3458: term,X3459: term] :
( ( ( hoasap @ id @ X3456 @ id @ X3458 )
= ( hoasap @ id @ X3457 @ id @ X3459 ) )
=> ( X3458 = X3459 ) )
=> ( ! [X3460: subst > term > term] :
( ! [X3461: subst,X3462: term,X3463: subst] :
( ( sub @ ( X3460 @ X3461 @ X3462 ) @ X3463 )
= ( X3460 @ ( comp @ X3461 @ X3463 ) @ ( sub @ X3462 @ X3463 ) ) )
=> ! [X3464: subst > term > term] :
( ! [X3465: subst,X3466: term,X3467: subst] :
( ( sub @ ( X3464 @ X3465 @ X3466 ) @ X3467 )
= ( X3464 @ ( comp @ X3465 @ X3467 ) @ ( sub @ X3466 @ X3467 ) ) )
=> ( ( ( hoaslam @ id @ X3460 )
= ( hoaslam @ id @ X3464 ) )
=> ! [X3468: subst,X3469: term] :
( ( X3460 @ X3468 @ X3469 )
= ( X3464 @ X3468 @ X3469 ) ) ) ) )
=> ( ! [X3470: subst > term > term] :
( ! [X3471: subst,X3472: term,X3473: subst] :
( ( sub @ ( X3470 @ X3471 @ X3472 ) @ X3473 )
= ( X3470 @ ( comp @ X3471 @ X3473 ) @ ( sub @ X3472 @ X3473 ) ) )
=> ! [X3474: term,X3475: term] :
( ( hoaslam @ id @ X3470 )
!= ( hoasap @ id @ X3474 @ id @ X3475 ) ) )
=> ( ! [X3476: subst > term > term] :
( ! [X3477: subst,X3478: term,X3479: subst] :
( ( sub @ ( X3476 @ X3477 @ X3478 ) @ X3479 )
= ( X3476 @ ( comp @ X3477 @ X3479 ) @ ( sub @ X3478 @ X3479 ) ) )
=> ~ ( var @ ( sub @ ( hoaslam @ id @ X3476 ) @ id ) ) )
=> ( ! [X3480: term,X3481: term] :
~ ( var @ ( sub @ ( hoasap @ id @ X3480 @ id @ X3481 ) @ id ) )
=> ! [X3482: subst > term > subst > $o,X3483: term > $o] :
( ! [X3484: subst,X3485: term,X3486: subst,X3487: subst] :
( ( X3482 @ X3484 @ X3485 @ ( comp @ X3487 @ X3486 ) )
=> ( X3482 @ ( comp @ X3484 @ X3487 ) @ ( sub @ X3485 @ X3487 ) @ X3486 ) )
=> ( ! [X3488: subst,X3489: term,X3490: subst,X3491: subst] :
( ( X3482 @ ( comp @ X3488 @ X3491 ) @ ( sub @ X3489 @ X3491 ) @ X3490 )
=> ( X3482 @ X3488 @ X3489 @ ( comp @ X3491 @ X3490 ) ) )
=> ( ! [X3492: term] :
( ( var @ ( sub @ X3492 @ id ) )
=> ( X3482 @ id @ X3492 @ id ) )
=> ( ! [X3493: term] :
( ( X3483 @ X3493 )
<=> ( X3482 @ id @ X3493 @ id ) )
=> ! [X3494: term] :
( ( var @ X3494 )
=> ( X3483 @ X3494 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[c_0_47,c_0_48])])]) ).
thf(c_0_50,negated_conjecture,
! [X3507: term,X3508: term,X3509: subst,X3510: term,X3511: subst,X3512: term,X3513: term,X3514: subst,X3515: term,X3516: subst,X3517: subst,X3518: subst,X3519: term,X3520: subst,X3521: subst,X3522: subst,X3523: subst,X3524: term,X3525: subst,X3526: subst,X3527: subst,X3528: subst,X3529: term,X3530: term > $o,X3532: term,X3533: term,X3534: term,X3535: term,X3536: term,X3537: term,X3538: term,X3539: term,X3540: term,X3541: term,X3542: term,X3543: term,X3544: term,X3545: term,X3546: term,X3547: term,X3548: term,X3549: term,X3550: term,X3551: term > $o,X3556: term,X3557: term > $o,X3558: term,X3559: subst,X3561: term,X3562: term > $o,X3566: term,X3567: term,X3568: subst,X3570: term > $o,X3575: term,X3576: term,X3577: subst,X3578: subst,X3579: subst,X3580: subst,X3581: subst,X3582: term,X3583: subst,X3584: subst,X3585: term,X3586: term,X3587: term,X3588: term,X3589: term,X3590: term,X3591: term,X3592: term,X3593: term,X3594: subst > term > term,X3598: subst > term > term,X3602: subst,X3603: term,X3604: subst > term > term,X3608: term,X3609: term,X3610: subst > term > term,X3614: term,X3615: term,X3618: subst,X3619: term,X3620: subst,X3621: subst,X3622: subst,X3623: term,X3624: subst,X3625: subst,X3626: term,X3627: term] :
( ( ( sub @ ( ap @ X3507 @ X3508 ) @ X3509 )
= ( ap @ ( sub @ X3507 @ X3509 ) @ ( sub @ X3508 @ X3509 ) ) )
& ( ( sub @ one @ ( push @ X3510 @ X3511 ) )
= X3510 )
& ( ( sub @ X3512 @ id )
= X3512 )
& ( ( sub @ ( lam @ X3513 ) @ X3514 )
= ( lam @ ( sub @ X3513 @ ( push @ one @ ( comp @ X3514 @ sh ) ) ) ) )
& ( ( sub @ ( sub @ X3515 @ X3516 ) @ X3517 )
= ( sub @ X3515 @ ( comp @ X3516 @ X3517 ) ) )
& ( ( comp @ id @ X3518 )
= X3518 )
& ( ( comp @ sh @ ( push @ X3519 @ X3520 ) )
= X3520 )
& ( ( comp @ ( comp @ X3521 @ X3522 ) @ X3523 )
= ( comp @ X3521 @ ( comp @ X3522 @ X3523 ) ) )
& ( ( comp @ ( push @ X3524 @ X3525 ) @ X3526 )
= ( push @ ( sub @ X3524 @ X3526 ) @ ( comp @ X3525 @ X3526 ) ) )
& ( ( comp @ X3527 @ id )
= X3527 )
& ( ( push @ one @ sh )
= id )
& ( ( push @ ( sub @ one @ X3528 ) @ ( comp @ sh @ X3528 ) )
= X3528 )
& ( var @ one )
& ( ~ ( var @ X3529 )
| ( var @ ( sub @ X3529 @ sh ) ) )
& ( ( var @ ( esk1_1 @ X3530 ) )
| ~ ( var @ X3532 )
| ( X3530 @ X3532 )
| ~ ( X3530 @ one ) )
& ( ( X3530 @ ( esk1_1 @ X3530 ) )
| ~ ( var @ X3532 )
| ( X3530 @ X3532 )
| ~ ( X3530 @ one ) )
& ( ~ ( X3530 @ ( sub @ ( esk1_1 @ X3530 ) @ sh ) )
| ~ ( var @ X3532 )
| ( X3530 @ X3532 )
| ~ ( X3530 @ one ) )
& ( ( ( ap @ X3533 @ X3535 )
!= ( ap @ X3534 @ X3536 ) )
| ( X3533 = X3534 ) )
& ( ( ( ap @ X3537 @ X3539 )
!= ( ap @ X3538 @ X3540 ) )
| ( X3539 = X3540 ) )
& ( ( ( lam @ X3541 )
!= ( lam @ X3542 ) )
| ( X3541 = X3542 ) )
& ( ( ( sub @ X3543 @ sh )
!= ( sub @ X3544 @ sh ) )
| ( X3543 = X3544 ) )
& ( ( lam @ X3545 )
!= ( ap @ X3546 @ X3547 ) )
& ~ ( var @ ( ap @ X3548 @ X3549 ) )
& ~ ( var @ ( lam @ X3550 ) )
& ( ( X3551 @ ( esk5_1 @ X3551 ) )
| ( X3551 @ X3556 )
| ( X3551 @ ( esk3_1 @ X3551 ) )
| ( var @ ( esk2_1 @ X3551 ) ) )
& ( ~ ( X3551 @ ( lam @ ( esk5_1 @ X3551 ) ) )
| ( X3551 @ X3556 )
| ( X3551 @ ( esk3_1 @ X3551 ) )
| ( var @ ( esk2_1 @ X3551 ) ) )
& ( ( X3551 @ ( esk5_1 @ X3551 ) )
| ( X3551 @ X3556 )
| ( X3551 @ ( esk4_1 @ X3551 ) )
| ( var @ ( esk2_1 @ X3551 ) ) )
& ( ~ ( X3551 @ ( lam @ ( esk5_1 @ X3551 ) ) )
| ( X3551 @ X3556 )
| ( X3551 @ ( esk4_1 @ X3551 ) )
| ( var @ ( esk2_1 @ X3551 ) ) )
& ( ( X3551 @ ( esk5_1 @ X3551 ) )
| ( X3551 @ X3556 )
| ~ ( X3551 @ ( ap @ ( esk3_1 @ X3551 ) @ ( esk4_1 @ X3551 ) ) )
| ( var @ ( esk2_1 @ X3551 ) ) )
& ( ~ ( X3551 @ ( lam @ ( esk5_1 @ X3551 ) ) )
| ( X3551 @ X3556 )
| ~ ( X3551 @ ( ap @ ( esk3_1 @ X3551 ) @ ( esk4_1 @ X3551 ) ) )
| ( var @ ( esk2_1 @ X3551 ) ) )
& ( ( X3551 @ ( esk5_1 @ X3551 ) )
| ( X3551 @ X3556 )
| ( X3551 @ ( esk3_1 @ X3551 ) )
| ~ ( X3551 @ ( esk2_1 @ X3551 ) ) )
& ( ~ ( X3551 @ ( lam @ ( esk5_1 @ X3551 ) ) )
| ( X3551 @ X3556 )
| ( X3551 @ ( esk3_1 @ X3551 ) )
| ~ ( X3551 @ ( esk2_1 @ X3551 ) ) )
& ( ( X3551 @ ( esk5_1 @ X3551 ) )
| ( X3551 @ X3556 )
| ( X3551 @ ( esk4_1 @ X3551 ) )
| ~ ( X3551 @ ( esk2_1 @ X3551 ) ) )
& ( ~ ( X3551 @ ( lam @ ( esk5_1 @ X3551 ) ) )
| ( X3551 @ X3556 )
| ( X3551 @ ( esk4_1 @ X3551 ) )
| ~ ( X3551 @ ( esk2_1 @ X3551 ) ) )
& ( ( X3551 @ ( esk5_1 @ X3551 ) )
| ( X3551 @ X3556 )
| ~ ( X3551 @ ( ap @ ( esk3_1 @ X3551 ) @ ( esk4_1 @ X3551 ) ) )
| ~ ( X3551 @ ( esk2_1 @ X3551 ) ) )
& ( ~ ( X3551 @ ( lam @ ( esk5_1 @ X3551 ) ) )
| ( X3551 @ X3556 )
| ~ ( X3551 @ ( ap @ ( esk3_1 @ X3551 ) @ ( esk4_1 @ X3551 ) ) )
| ~ ( X3551 @ ( esk2_1 @ X3551 ) ) )
& ( ( var @ ( esk6_3 @ X3557 @ X3558 @ X3559 ) )
| ~ ( X3557 @ X3558 )
| ~ ( var @ X3561 )
| ( X3557 @ ( sub @ X3561 @ ( push @ X3558 @ X3559 ) ) ) )
& ( ~ ( X3557 @ ( sub @ ( esk6_3 @ X3557 @ X3558 @ X3559 ) @ X3559 ) )
| ~ ( X3557 @ X3558 )
| ~ ( var @ X3561 )
| ( X3557 @ ( sub @ X3561 @ ( push @ X3558 @ X3559 ) ) ) )
& ( ( var @ ( esk10_3 @ X3562 @ X3567 @ X3568 ) )
| ( X3562 @ ( sub @ X3567 @ X3568 ) )
| ~ ( X3562 @ X3566 )
| ( X3562 @ ( sub @ ( esk9_1 @ X3562 ) @ ( push @ X3566 @ id ) ) )
| ( X3562 @ ( esk7_1 @ X3562 ) ) )
& ( ~ ( X3562 @ ( sub @ ( esk10_3 @ X3562 @ X3567 @ X3568 ) @ X3568 ) )
| ( X3562 @ ( sub @ X3567 @ X3568 ) )
| ~ ( X3562 @ X3566 )
| ( X3562 @ ( sub @ ( esk9_1 @ X3562 ) @ ( push @ X3566 @ id ) ) )
| ( X3562 @ ( esk7_1 @ X3562 ) ) )
& ( ( var @ ( esk10_3 @ X3562 @ X3567 @ X3568 ) )
| ( X3562 @ ( sub @ X3567 @ X3568 ) )
| ~ ( X3562 @ ( lam @ ( esk9_1 @ X3562 ) ) )
| ( X3562 @ ( esk7_1 @ X3562 ) ) )
& ( ~ ( X3562 @ ( sub @ ( esk10_3 @ X3562 @ X3567 @ X3568 ) @ X3568 ) )
| ( X3562 @ ( sub @ X3567 @ X3568 ) )
| ~ ( X3562 @ ( lam @ ( esk9_1 @ X3562 ) ) )
| ( X3562 @ ( esk7_1 @ X3562 ) ) )
& ( ( var @ ( esk10_3 @ X3562 @ X3567 @ X3568 ) )
| ( X3562 @ ( sub @ X3567 @ X3568 ) )
| ~ ( X3562 @ X3566 )
| ( X3562 @ ( sub @ ( esk9_1 @ X3562 ) @ ( push @ X3566 @ id ) ) )
| ( X3562 @ ( esk8_1 @ X3562 ) ) )
& ( ~ ( X3562 @ ( sub @ ( esk10_3 @ X3562 @ X3567 @ X3568 ) @ X3568 ) )
| ( X3562 @ ( sub @ X3567 @ X3568 ) )
| ~ ( X3562 @ X3566 )
| ( X3562 @ ( sub @ ( esk9_1 @ X3562 ) @ ( push @ X3566 @ id ) ) )
| ( X3562 @ ( esk8_1 @ X3562 ) ) )
& ( ( var @ ( esk10_3 @ X3562 @ X3567 @ X3568 ) )
| ( X3562 @ ( sub @ X3567 @ X3568 ) )
| ~ ( X3562 @ ( lam @ ( esk9_1 @ X3562 ) ) )
| ( X3562 @ ( esk8_1 @ X3562 ) ) )
& ( ~ ( X3562 @ ( sub @ ( esk10_3 @ X3562 @ X3567 @ X3568 ) @ X3568 ) )
| ( X3562 @ ( sub @ X3567 @ X3568 ) )
| ~ ( X3562 @ ( lam @ ( esk9_1 @ X3562 ) ) )
| ( X3562 @ ( esk8_1 @ X3562 ) ) )
& ( ( var @ ( esk10_3 @ X3562 @ X3567 @ X3568 ) )
| ( X3562 @ ( sub @ X3567 @ X3568 ) )
| ~ ( X3562 @ X3566 )
| ( X3562 @ ( sub @ ( esk9_1 @ X3562 ) @ ( push @ X3566 @ id ) ) )
| ~ ( X3562 @ ( ap @ ( esk7_1 @ X3562 ) @ ( esk8_1 @ X3562 ) ) ) )
& ( ~ ( X3562 @ ( sub @ ( esk10_3 @ X3562 @ X3567 @ X3568 ) @ X3568 ) )
| ( X3562 @ ( sub @ X3567 @ X3568 ) )
| ~ ( X3562 @ X3566 )
| ( X3562 @ ( sub @ ( esk9_1 @ X3562 ) @ ( push @ X3566 @ id ) ) )
| ~ ( X3562 @ ( ap @ ( esk7_1 @ X3562 ) @ ( esk8_1 @ X3562 ) ) ) )
& ( ( var @ ( esk10_3 @ X3562 @ X3567 @ X3568 ) )
| ( X3562 @ ( sub @ X3567 @ X3568 ) )
| ~ ( X3562 @ ( lam @ ( esk9_1 @ X3562 ) ) )
| ~ ( X3562 @ ( ap @ ( esk7_1 @ X3562 ) @ ( esk8_1 @ X3562 ) ) ) )
& ( ~ ( X3562 @ ( sub @ ( esk10_3 @ X3562 @ X3567 @ X3568 ) @ X3568 ) )
| ( X3562 @ ( sub @ X3567 @ X3568 ) )
| ~ ( X3562 @ ( lam @ ( esk9_1 @ X3562 ) ) )
| ~ ( X3562 @ ( ap @ ( esk7_1 @ X3562 ) @ ( esk8_1 @ X3562 ) ) ) )
& ( ~ ( X3570 @ X3575 )
| ( X3570 @ ( sub @ ( esk14_1 @ X3570 ) @ ( push @ X3575 @ id ) ) )
| ( X3570 @ X3576 )
| ( X3570 @ ( esk12_1 @ X3570 ) )
| ( var @ ( esk11_1 @ X3570 ) ) )
& ( ~ ( X3570 @ ( lam @ ( esk14_1 @ X3570 ) ) )
| ( X3570 @ X3576 )
| ( X3570 @ ( esk12_1 @ X3570 ) )
| ( var @ ( esk11_1 @ X3570 ) ) )
& ( ~ ( X3570 @ X3575 )
| ( X3570 @ ( sub @ ( esk14_1 @ X3570 ) @ ( push @ X3575 @ id ) ) )
| ( X3570 @ X3576 )
| ( X3570 @ ( esk13_1 @ X3570 ) )
| ( var @ ( esk11_1 @ X3570 ) ) )
& ( ~ ( X3570 @ ( lam @ ( esk14_1 @ X3570 ) ) )
| ( X3570 @ X3576 )
| ( X3570 @ ( esk13_1 @ X3570 ) )
| ( var @ ( esk11_1 @ X3570 ) ) )
& ( ~ ( X3570 @ X3575 )
| ( X3570 @ ( sub @ ( esk14_1 @ X3570 ) @ ( push @ X3575 @ id ) ) )
| ( X3570 @ X3576 )
| ~ ( X3570 @ ( ap @ ( esk12_1 @ X3570 ) @ ( esk13_1 @ X3570 ) ) )
| ( var @ ( esk11_1 @ X3570 ) ) )
& ( ~ ( X3570 @ ( lam @ ( esk14_1 @ X3570 ) ) )
| ( X3570 @ X3576 )
| ~ ( X3570 @ ( ap @ ( esk12_1 @ X3570 ) @ ( esk13_1 @ X3570 ) ) )
| ( var @ ( esk11_1 @ X3570 ) ) )
& ( ~ ( X3570 @ X3575 )
| ( X3570 @ ( sub @ ( esk14_1 @ X3570 ) @ ( push @ X3575 @ id ) ) )
| ( X3570 @ X3576 )
| ( X3570 @ ( esk12_1 @ X3570 ) )
| ~ ( X3570 @ ( esk11_1 @ X3570 ) ) )
& ( ~ ( X3570 @ ( lam @ ( esk14_1 @ X3570 ) ) )
| ( X3570 @ X3576 )
| ( X3570 @ ( esk12_1 @ X3570 ) )
| ~ ( X3570 @ ( esk11_1 @ X3570 ) ) )
& ( ~ ( X3570 @ X3575 )
| ( X3570 @ ( sub @ ( esk14_1 @ X3570 ) @ ( push @ X3575 @ id ) ) )
| ( X3570 @ X3576 )
| ( X3570 @ ( esk13_1 @ X3570 ) )
| ~ ( X3570 @ ( esk11_1 @ X3570 ) ) )
& ( ~ ( X3570 @ ( lam @ ( esk14_1 @ X3570 ) ) )
| ( X3570 @ X3576 )
| ( X3570 @ ( esk13_1 @ X3570 ) )
| ~ ( X3570 @ ( esk11_1 @ X3570 ) ) )
& ( ~ ( X3570 @ X3575 )
| ( X3570 @ ( sub @ ( esk14_1 @ X3570 ) @ ( push @ X3575 @ id ) ) )
| ( X3570 @ X3576 )
| ~ ( X3570 @ ( ap @ ( esk12_1 @ X3570 ) @ ( esk13_1 @ X3570 ) ) )
| ~ ( X3570 @ ( esk11_1 @ X3570 ) ) )
& ( ~ ( X3570 @ ( lam @ ( esk14_1 @ X3570 ) ) )
| ( X3570 @ X3576 )
| ~ ( X3570 @ ( ap @ ( esk12_1 @ X3570 ) @ ( esk13_1 @ X3570 ) ) )
| ~ ( X3570 @ ( esk11_1 @ X3570 ) ) )
& ( ( comp @ ( comp @ X3577 @ X3578 ) @ X3579 )
= ( comp @ X3577 @ ( comp @ X3578 @ X3579 ) ) )
& ( ( comp @ id @ X3580 )
= X3580 )
& ( ( comp @ X3581 @ id )
= X3581 )
& ( ( sub @ ( sub @ X3582 @ X3583 ) @ X3584 )
= ( sub @ X3582 @ ( comp @ X3583 @ X3584 ) ) )
& ( ( sub @ X3585 @ id )
= X3585 )
& ( ( ( hoasap @ id @ X3586 @ id @ X3588 )
!= ( hoasap @ id @ X3587 @ id @ X3589 ) )
| ( X3586 = X3587 ) )
& ( ( ( hoasap @ id @ X3590 @ id @ X3592 )
!= ( hoasap @ id @ X3591 @ id @ X3593 ) )
| ( X3592 = X3593 ) )
& ( ( ( sub @ ( X3594 @ ( esk15_1 @ X3594 ) @ ( esk16_1 @ X3594 ) ) @ ( esk17_1 @ X3594 ) )
!= ( X3594 @ ( comp @ ( esk15_1 @ X3594 ) @ ( esk17_1 @ X3594 ) ) @ ( sub @ ( esk16_1 @ X3594 ) @ ( esk17_1 @ X3594 ) ) ) )
| ( ( sub @ ( X3598 @ ( esk18_2 @ X3594 @ X3598 ) @ ( esk19_2 @ X3594 @ X3598 ) ) @ ( esk20_2 @ X3594 @ X3598 ) )
!= ( X3598 @ ( comp @ ( esk18_2 @ X3594 @ X3598 ) @ ( esk20_2 @ X3594 @ X3598 ) ) @ ( sub @ ( esk19_2 @ X3594 @ X3598 ) @ ( esk20_2 @ X3594 @ X3598 ) ) ) )
| ( ( hoaslam @ id @ X3594 )
!= ( hoaslam @ id @ X3598 ) )
| ( ( X3594 @ X3602 @ X3603 )
= ( X3598 @ X3602 @ X3603 ) ) )
& ( ( ( sub @ ( X3604 @ ( esk21_1 @ X3604 ) @ ( esk22_1 @ X3604 ) ) @ ( esk23_1 @ X3604 ) )
!= ( X3604 @ ( comp @ ( esk21_1 @ X3604 ) @ ( esk23_1 @ X3604 ) ) @ ( sub @ ( esk22_1 @ X3604 ) @ ( esk23_1 @ X3604 ) ) ) )
| ( ( hoaslam @ id @ X3604 )
!= ( hoasap @ id @ X3608 @ id @ X3609 ) ) )
& ( ( ( sub @ ( X3610 @ ( esk24_1 @ X3610 ) @ ( esk25_1 @ X3610 ) ) @ ( esk26_1 @ X3610 ) )
!= ( X3610 @ ( comp @ ( esk24_1 @ X3610 ) @ ( esk26_1 @ X3610 ) ) @ ( sub @ ( esk25_1 @ X3610 ) @ ( esk26_1 @ X3610 ) ) ) )
| ~ ( var @ ( sub @ ( hoaslam @ id @ X3610 ) @ id ) ) )
& ~ ( var @ ( sub @ ( hoasap @ id @ X3614 @ id @ X3615 ) @ id ) )
& ( ~ ( epred1_0 @ X3618 @ X3619 @ ( comp @ X3621 @ X3620 ) )
| ( epred1_0 @ ( comp @ X3618 @ X3621 ) @ ( sub @ X3619 @ X3621 ) @ X3620 ) )
& ( ~ ( epred1_0 @ ( comp @ X3622 @ X3625 ) @ ( sub @ X3623 @ X3625 ) @ X3624 )
| ( epred1_0 @ X3622 @ X3623 @ ( comp @ X3625 @ X3624 ) ) )
& ( ~ ( var @ ( sub @ X3626 @ id ) )
| ( epred1_0 @ id @ X3626 @ id ) )
& ( ~ ( epred2_0 @ X3627 )
| ( epred1_0 @ id @ X3627 @ id ) )
& ( ~ ( epred1_0 @ id @ X3627 @ id )
| ( epred2_0 @ X3627 ) )
& ( var @ esk27_0 )
& ~ ( epred2_0 @ esk27_0 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])])])])]) ).
thf(c_0_51,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ X1 @ id )
| ~ ( var @ ( sub @ X1 @ id ) ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_52,negated_conjecture,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_53,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ X1 @ id )
| ~ ( var @ X1 ) ),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_54,negated_conjecture,
var @ esk27_0,
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_55,negated_conjecture,
! [X1: term] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ id @ X1 @ id ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_56,negated_conjecture,
epred1_0 @ id @ esk27_0 @ id,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
thf(c_0_57,negated_conjecture,
~ ( epred2_0 @ esk27_0 ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_58,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG263^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n018.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:37:01 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.26 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.2LgqS7UJ8W/E---3.1_396028.p
% 0.22/0.32 % Version: 3.5.1-ho
% 0.22/0.32 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.32 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.32 % Starting post_as_ho5 with 300s (1) cores
% 0.22/0.32 % Starting post_as_ho10 with 300s (1) cores
% 0.22/0.32 % post_as_ho10 with pid 396044 completed with status 0
% 0.22/0.32 % Result found by post_as_ho10
% 0.22/0.32 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.32 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.32 % Starting post_as_ho5 with 300s (1) cores
% 0.22/0.32 % Starting post_as_ho10 with 300s (1) cores
% 0.22/0.32 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.32 % No SInE strategy applied
% 0.22/0.32 % Search class: HGHSM-FFMS31-MHFMMMBN
% 0.22/0.32 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.32 % SubtermCWHack with pid 396049 completed with status 0
% 0.22/0.32 % Result found by SubtermCWHack
% 0.22/0.32 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.22/0.32 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.32 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.22/0.32 % Starting post_as_ho1 with 300s (1) cores
% 0.22/0.32 % Starting post_as_ho5 with 300s (1) cores
% 0.22/0.32 % Starting post_as_ho10 with 300s (1) cores
% 0.22/0.32 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/0.32 % No SInE strategy applied
% 0.22/0.32 % Search class: HGHSM-FFMS31-MHFMMMBN
% 0.22/0.32 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.32 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.32 % Preprocessing time : 0.003 s
% 0.22/0.32
% 0.22/0.32 % Proof found!
% 0.22/0.32 % SZS status Theorem
% 0.22/0.32 % SZS output start CNFRefutation
% See solution above
% 0.22/0.32 % Parsed axioms : 238
% 0.22/0.32 % Removed by relevancy pruning/SinE : 0
% 0.22/0.32 % Initial clauses : 206
% 0.22/0.32 % Removed in clause preprocessing : 124
% 0.22/0.32 % Initial clauses in saturation : 82
% 0.22/0.32 % Processed clauses : 21
% 0.22/0.32 % ...of these trivial : 3
% 0.22/0.32 % ...subsumed : 0
% 0.22/0.32 % ...remaining for further processing : 18
% 0.22/0.32 % Other redundant clauses eliminated : 0
% 0.22/0.32 % Clauses deleted for lack of memory : 0
% 0.22/0.32 % Backward-subsumed : 0
% 0.22/0.32 % Backward-rewritten : 0
% 0.22/0.32 % Generated clauses : 8
% 0.22/0.32 % ...of the previous two non-redundant : 3
% 0.22/0.32 % ...aggressively subsumed : 0
% 0.22/0.32 % Contextual simplify-reflections : 0
% 0.22/0.32 % Paramodulations : 7
% 0.22/0.32 % Factorizations : 0
% 0.22/0.32 % NegExts : 0
% 0.22/0.32 % Equation resolutions : 1
% 0.22/0.32 % Disequality decompositions : 0
% 0.22/0.32 % Total rewrite steps : 6
% 0.22/0.32 % ...of those cached : 1
% 0.22/0.32 % Propositional unsat checks : 0
% 0.22/0.32 % Propositional check models : 0
% 0.22/0.32 % Propositional check unsatisfiable : 0
% 0.22/0.32 % Propositional clauses : 0
% 0.22/0.32 % Propositional clauses after purity: 0
% 0.22/0.32 % Propositional unsat core size : 0
% 0.22/0.32 % Propositional preprocessing time : 0.000
% 0.22/0.32 % Propositional encoding time : 0.000
% 0.22/0.32 % Propositional solver time : 0.000
% 0.22/0.32 % Success case prop preproc time : 0.000
% 0.22/0.32 % Success case prop encoding time : 0.000
% 0.22/0.32 % Success case prop solver time : 0.000
% 0.22/0.32 % Current number of processed clauses : 18
% 0.22/0.32 % Positive orientable unit clauses : 9
% 0.22/0.32 % Positive unorientable unit clauses: 0
% 0.22/0.32 % Negative unit clauses : 4
% 0.22/0.32 % Non-unit-clauses : 5
% 0.22/0.32 % Current number of unprocessed clauses: 64
% 0.22/0.32 % ...number of literals in the above : 212
% 0.22/0.32 % Current number of archived formulas : 0
% 0.22/0.32 % Current number of archived clauses : 0
% 0.22/0.32 % Clause-clause subsumption calls (NU) : 1
% 0.22/0.32 % Rec. Clause-clause subsumption calls : 1
% 0.22/0.32 % Non-unit clause-clause subsumptions : 0
% 0.22/0.32 % Unit Clause-clause subsumption calls : 2
% 0.22/0.32 % Rewrite failures with RHS unbound : 0
% 0.22/0.32 % BW rewrite match attempts : 0
% 0.22/0.32 % BW rewrite match successes : 0
% 0.22/0.32 % Condensation attempts : 0
% 0.22/0.32 % Condensation successes : 0
% 0.22/0.32 % Termbank termtop insertions : 33593
% 0.22/0.32 % Search garbage collected termcells : 4542
% 0.22/0.32
% 0.22/0.32 % -------------------------------------------------
% 0.22/0.32 % User time : 0.039 s
% 0.22/0.32 % System time : 0.011 s
% 0.22/0.32 % Total time : 0.050 s
% 0.22/0.32 % Maximum resident set size: 8076 pages
% 0.22/0.32
% 0.22/0.32 % -------------------------------------------------
% 0.22/0.32 % User time : 0.044 s
% 0.22/0.32 % System time : 0.014 s
% 0.22/0.32 % Total time : 0.058 s
% 0.22/0.32 % Maximum resident set size: 5120 pages
% 0.22/0.32 % E exiting
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