%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG264^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 07:44:47 AM UTC 2026
% Result : Theorem 0.19s 0.35s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 39
% Syntax : Number of formulae : 59 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 346 ( 166 equ; 0 cnn)
% Maximal formula atoms : 79 ( 5 avg)
% Number of connectives : 2538 ( 124 ~; 155 |; 87 &;1866 @)
% ( 39 <=>; 267 =>; 0 <=; 0 <~>)
% Maximal formula depth : 172 ( 10 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 77 usr; 42 con; 0-4 aty)
% Number of variables : 538 ( 36 ^; 502 !; 0 ?; 538 :)
% 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_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_59,type,
hoasinduction_lem2: $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_109,type,
lamnotap: $o ).
thf(decl_111,type,
hoaslamnotvar: $o ).
thf(decl_112,type,
axidl: $o ).
thf(decl_117,type,
pushprop: $o ).
thf(decl_119,type,
hoasinduction_lem2_gthm: $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,
esk27_0: term ).
thf(decl_173,type,
esk28_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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',hoaslamnotvar) ).
thf(hoasvar,axiom,
( hoasvar
= ( ^ [X3: subst,X1: term,X4: subst] : ( var @ ( sub @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',hoasvar) ).
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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',hoaslamnotap) ).
thf(hoasapnotvar,axiom,
( hoasapnotvar
<=> ! [X1: term,X2: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',hoasapnotvar) ).
thf(thm,conjecture,
hoasinduction_lem2_gthm,
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',thm) ).
thf(hoasinduction_lem2_gthm,axiom,
( 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/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',hoasinduction_lem2_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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',axapp) ).
thf(axvarcons,axiom,
( axvarcons
<=> ! [X1: term,X3: subst] :
( ( sub @ one @ ( push @ X1 @ X3 ) )
= X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',axvarcons) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',axclos) ).
thf(axidl,axiom,
( axidl
<=> ! [X3: subst] :
( ( comp @ id @ X3 )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',axidl) ).
thf(axshiftcons,axiom,
( axshiftcons
<=> ! [X1: term,X3: subst] :
( ( comp @ sh @ ( push @ X1 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',axmap) ).
thf(axidr,axiom,
( axidr
<=> ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',axidr) ).
thf(axvarshift,axiom,
( axvarshift
<=> ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',axvarshift) ).
thf(axscons,axiom,
( axscons
<=> ! [X3: subst] :
( ( push @ ( sub @ one @ X3 ) @ ( comp @ sh @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',axscons) ).
thf(ulamvar1,axiom,
( ulamvar1
<=> ( var @ one ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',ulamvar1) ).
thf(ulamvarsh,axiom,
( ulamvarsh
<=> ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',apinj2) ).
thf(laminj,axiom,
( laminj
<=> ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',laminj) ).
thf(shinj,axiom,
( shinj
<=> ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',shinj) ).
thf(lamnotap,axiom,
( lamnotap
<=> ! [X1: term,X2: term,X7: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X7 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',lamnotap) ).
thf(apnotvar,axiom,
( apnotvar
<=> ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',apnotvar) ).
thf(lamnotvar,axiom,
( lamnotvar
<=> ! [X1: term] :
~ ( var @ ( lam @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',hoasapinj2) ).
thf(hoasinduction_lem2,axiom,
( hoasinduction_lem2
<=> ! [X21: subst > term > subst > $o] :
( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X21 @ X3 @ X1 @ ( comp @ X5 @ X4 ) )
=> ( X21 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 ) )
=> ( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X21 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 )
=> ( X21 @ X3 @ X1 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X1: term,X2: term] :
( ( X21 @ id @ X1 @ id )
=> ( ( X21 @ id @ X2 @ id )
=> ( X21 @ id @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ) )
=> ! [X1: term,X2: term] :
( ( X21 @ id @ X1 @ id )
=> ( ( X21 @ id @ X2 @ id )
=> ( X21 @ id @ ( ap @ X1 @ X2 ) @ id ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',hoasinduction_lem2) ).
thf(hoasap,axiom,
( hoasap
= ( ^ [X3: subst,X1: term,X4: subst,X2: term] : ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p',hoasap) ).
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,
( 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_42,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_43,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_44,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_45,negated_conjecture,
~ hoasinduction_lem2_gthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_46,axiom,
( hoasinduction_lem2_gthm
= ( ! [X2826: term,X2827: term,X2828: subst] :
( ( sub @ ( ap @ X2826 @ X2827 ) @ X2828 )
= ( ap @ ( sub @ X2826 @ X2828 ) @ ( sub @ X2827 @ X2828 ) ) )
=> ( ! [X2829: term,X2830: subst] :
( ( sub @ one @ ( push @ X2829 @ X2830 ) )
= X2829 )
=> ( ! [X2831: term] :
( ( sub @ X2831 @ id )
= X2831 )
=> ( ! [X2832: term,X2833: subst] :
( ( sub @ ( lam @ X2832 ) @ X2833 )
= ( lam @ ( sub @ X2832 @ ( push @ one @ ( comp @ X2833 @ sh ) ) ) ) )
=> ( ! [X2834: term,X2835: subst,X2836: subst] :
( ( sub @ ( sub @ X2834 @ X2835 ) @ X2836 )
= ( sub @ X2834 @ ( comp @ X2835 @ X2836 ) ) )
=> ( ! [X2837: subst] :
( ( comp @ id @ X2837 )
= X2837 )
=> ( ! [X2838: term,X2839: subst] :
( ( comp @ sh @ ( push @ X2838 @ X2839 ) )
= X2839 )
=> ( ! [X2840: subst,X2841: subst,X2842: subst] :
( ( comp @ ( comp @ X2840 @ X2841 ) @ X2842 )
= ( comp @ X2840 @ ( comp @ X2841 @ X2842 ) ) )
=> ( ! [X2843: term,X2844: subst,X2845: subst] :
( ( comp @ ( push @ X2843 @ X2844 ) @ X2845 )
= ( push @ ( sub @ X2843 @ X2845 ) @ ( comp @ X2844 @ X2845 ) ) )
=> ( ! [X2846: subst] :
( ( comp @ X2846 @ id )
= X2846 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X2847: subst] :
( ( push @ ( sub @ one @ X2847 ) @ ( comp @ sh @ X2847 ) )
= X2847 )
=> ( ( var @ one )
=> ( ! [X2848: term] :
( ( var @ X2848 )
=> ( var @ ( sub @ X2848 @ sh ) ) )
=> ( ! [X2849: term > $o] :
( ( X2849 @ one )
=> ( ! [X2850: term] :
( ( var @ X2850 )
=> ( ( X2849 @ X2850 )
=> ( X2849 @ ( sub @ X2850 @ sh ) ) ) )
=> ! [X2851: term] :
( ( var @ X2851 )
=> ( X2849 @ X2851 ) ) ) )
=> ( ! [X2852: term,X2853: term,X2854: term,X2855: term] :
( ( ( ap @ X2852 @ X2854 )
= ( ap @ X2853 @ X2855 ) )
=> ( X2852 = X2853 ) )
=> ( ! [X2856: term,X2857: term,X2858: term,X2859: term] :
( ( ( ap @ X2856 @ X2858 )
= ( ap @ X2857 @ X2859 ) )
=> ( X2858 = X2859 ) )
=> ( ! [X2860: term,X2861: term] :
( ( ( lam @ X2860 )
= ( lam @ X2861 ) )
=> ( X2860 = X2861 ) )
=> ( ! [X2862: term,X2863: term] :
( ( ( sub @ X2862 @ sh )
= ( sub @ X2863 @ sh ) )
=> ( X2862 = X2863 ) )
=> ( ! [X2864: term,X2865: term,X2866: term] :
( ( lam @ X2864 )
!= ( ap @ X2865 @ X2866 ) )
=> ( ! [X2867: term,X2868: term] :
~ ( var @ ( ap @ X2867 @ X2868 ) )
=> ( ! [X2869: term] :
~ ( var @ ( lam @ X2869 ) )
=> ( ! [X2870: term > $o] :
( ! [X2871: term] :
( ( var @ X2871 )
=> ( X2870 @ X2871 ) )
=> ( ! [X2872: term,X2873: term] :
( ( X2870 @ X2872 )
=> ( ( X2870 @ X2873 )
=> ( X2870 @ ( ap @ X2872 @ X2873 ) ) ) )
=> ( ! [X2874: term] :
( ( X2870 @ X2874 )
=> ( X2870 @ ( lam @ X2874 ) ) )
=> ! [X2875: term] : ( X2870 @ X2875 ) ) ) )
=> ( ! [X2876: term > $o,X2877: term,X2878: subst] :
( ! [X2879: term] :
( ( var @ X2879 )
=> ( X2876 @ ( sub @ X2879 @ X2878 ) ) )
=> ( ( X2876 @ X2877 )
=> ! [X2880: term] :
( ( var @ X2880 )
=> ( X2876 @ ( sub @ X2880 @ ( push @ X2877 @ X2878 ) ) ) ) ) )
=> ( ! [X2881: term > $o] :
( ! [X2882: term,X2883: term] :
( ( X2881 @ X2882 )
=> ( ( X2881 @ X2883 )
=> ( X2881 @ ( ap @ X2882 @ X2883 ) ) ) )
=> ( ! [X2884: term] :
( ! [X2885: term] :
( ( X2881 @ X2885 )
=> ( X2881 @ ( sub @ X2884 @ ( push @ X2885 @ id ) ) ) )
=> ( X2881 @ ( lam @ X2884 ) ) )
=> ! [X2886: term,X2887: subst] :
( ! [X2888: term] :
( ( var @ X2888 )
=> ( X2881 @ ( sub @ X2888 @ X2887 ) ) )
=> ( X2881 @ ( sub @ X2886 @ X2887 ) ) ) ) )
=> ( ! [X2889: term > $o] :
( ! [X2890: term] :
( ( var @ X2890 )
=> ( X2889 @ X2890 ) )
=> ( ! [X2891: term,X2892: term] :
( ( X2889 @ X2891 )
=> ( ( X2889 @ X2892 )
=> ( X2889 @ ( ap @ X2891 @ X2892 ) ) ) )
=> ( ! [X2893: term] :
( ! [X2894: term] :
( ( X2889 @ X2894 )
=> ( X2889 @ ( sub @ X2893 @ ( push @ X2894 @ id ) ) ) )
=> ( X2889 @ ( lam @ X2893 ) ) )
=> ! [X2895: term] : ( X2889 @ X2895 ) ) ) )
=> ( ( ! [X2896: subst,X2897: subst,X2898: subst] :
( ( comp @ ( comp @ X2896 @ X2897 ) @ X2898 )
= ( comp @ X2896 @ ( comp @ X2897 @ X2898 ) ) )
& ! [X2899: subst] :
( ( comp @ id @ X2899 )
= X2899 )
& ! [X2900: subst] :
( ( comp @ X2900 @ id )
= X2900 ) )
=> ( ( ! [X2901: term,X2902: subst,X2903: subst] :
( ( sub @ ( sub @ X2901 @ X2902 ) @ X2903 )
= ( sub @ X2901 @ ( comp @ X2902 @ X2903 ) ) )
& ! [X2904: term] :
( ( sub @ X2904 @ id )
= X2904 ) )
=> ( ! [X2905: term,X2906: term,X2907: term,X2908: term] :
( ( ( hoasap @ id @ X2905 @ id @ X2907 )
= ( hoasap @ id @ X2906 @ id @ X2908 ) )
=> ( X2905 = X2906 ) )
=> ( ! [X2909: term,X2910: term,X2911: term,X2912: term] :
( ( ( hoasap @ id @ X2909 @ id @ X2911 )
= ( hoasap @ id @ X2910 @ id @ X2912 ) )
=> ( X2911 = X2912 ) )
=> ( ! [X2913: subst > term > term] :
( ! [X2914: subst,X2915: term,X2916: subst] :
( ( sub @ ( X2913 @ X2914 @ X2915 ) @ X2916 )
= ( X2913 @ ( comp @ X2914 @ X2916 ) @ ( sub @ X2915 @ X2916 ) ) )
=> ! [X2917: subst > term > term] :
( ! [X2918: subst,X2919: term,X2920: subst] :
( ( sub @ ( X2917 @ X2918 @ X2919 ) @ X2920 )
= ( X2917 @ ( comp @ X2918 @ X2920 ) @ ( sub @ X2919 @ X2920 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X2913 @ Z0 @ Z1 ) )
= ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X2917 @ Z0 @ Z1 ) ) )
=> ! [X2921: subst,X2922: term] :
( ( X2913 @ X2921 @ X2922 )
= ( X2917 @ X2921 @ X2922 ) ) ) ) )
=> ( ! [X2923: subst > term > term] :
( ! [X2924: subst,X2925: term,X2926: subst] :
( ( sub @ ( X2923 @ X2924 @ X2925 ) @ X2926 )
= ( X2923 @ ( comp @ X2924 @ X2926 ) @ ( sub @ X2925 @ X2926 ) ) )
=> ! [X2927: term,X2928: term] :
( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X2923 @ Z0 @ Z1 ) )
!= ( hoasap @ id @ X2927 @ id @ X2928 ) ) )
=> ( ! [X2929: subst > term > term] :
( ! [X2930: subst,X2931: term,X2932: subst] :
( ( sub @ ( X2929 @ X2930 @ X2931 ) @ X2932 )
= ( X2929 @ ( comp @ X2930 @ X2932 ) @ ( sub @ X2931 @ X2932 ) ) )
=> ~ ( var
@ ( sub
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X2929 @ Z0 @ Z1 ) )
@ id ) ) )
=> ( ! [X2933: term,X2934: term] :
~ ( var @ ( sub @ ( hoasap @ id @ X2933 @ id @ X2934 ) @ id ) )
=> ! [X2935: subst > term > subst > $o] :
( ! [X2936: subst,X2937: term,X2938: subst,X2939: subst] :
( ( X2935 @ X2936 @ X2937 @ ( comp @ X2939 @ X2938 ) )
=> ( X2935 @ ( comp @ X2936 @ X2939 ) @ ( sub @ X2937 @ X2939 ) @ X2938 ) )
=> ( ! [X2940: subst,X2941: term,X2942: subst,X2943: subst] :
( ( X2935 @ ( comp @ X2940 @ X2943 ) @ ( sub @ X2941 @ X2943 ) @ X2942 )
=> ( X2935 @ X2940 @ X2941 @ ( comp @ X2943 @ X2942 ) ) )
=> ( ! [X2944: term,X2945: term] :
( ( X2935 @ id @ X2944 @ id )
=> ( ( X2935 @ id @ X2945 @ id )
=> ( X2935 @ id @ ( hoasap @ id @ X2944 @ id @ X2945 ) @ id ) ) )
=> ! [X2946: term,X2947: term] :
( ( X2935 @ id @ X2946 @ id )
=> ( ( X2935 @ id @ X2947 @ id )
=> ( X2935 @ id @ ( ap @ X2946 @ X2947 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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_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]),c_0_41]),c_0_42]),c_0_43]),c_0_44]),hoasinduction_lem2]) ).
thf(c_0_47,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: subst,X3484: term,X3485: subst,X3486: subst] :
( ( X3482 @ X3483 @ X3484 @ ( comp @ X3486 @ X3485 ) )
=> ( X3482 @ ( comp @ X3483 @ X3486 ) @ ( sub @ X3484 @ X3486 ) @ X3485 ) )
=> ( ! [X3487: subst,X3488: term,X3489: subst,X3490: subst] :
( ( X3482 @ ( comp @ X3487 @ X3490 ) @ ( sub @ X3488 @ X3490 ) @ X3489 )
=> ( X3482 @ X3487 @ X3488 @ ( comp @ X3490 @ X3489 ) ) )
=> ( ! [X3491: term,X3492: term] :
( ( X3482 @ id @ X3491 @ id )
=> ( ( X3482 @ id @ X3492 @ id )
=> ( X3482 @ id @ ( hoasap @ id @ X3491 @ id @ X3492 ) @ id ) ) )
=> ! [X3493: term,X3494: term] :
( ( X3482 @ id @ X3493 @ id )
=> ( ( X3482 @ id @ X3494 @ id )
=> ( X3482 @ id @ ( ap @ X3493 @ X3494 ) @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[c_0_45,c_0_46])])]) ).
thf(c_0_48,plain,
! [X3495: subst,X3496: term,X3497: subst,X3498: term] :
( ( hoasap @ X3495 @ X3496 @ X3497 @ X3498 )
= ( ap @ ( sub @ X3496 @ X3497 ) @ X3498 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoasap])]) ).
thf(c_0_49,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,X3617: subst,X3618: term,X3619: subst,X3620: subst,X3621: subst,X3622: term,X3623: subst,X3624: subst,X3625: term,X3626: 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 @ X3617 @ X3618 @ ( comp @ X3620 @ X3619 ) )
| ( epred1_0 @ ( comp @ X3617 @ X3620 ) @ ( sub @ X3618 @ X3620 ) @ X3619 ) )
& ( ~ ( epred1_0 @ ( comp @ X3621 @ X3624 ) @ ( sub @ X3622 @ X3624 ) @ X3623 )
| ( epred1_0 @ X3621 @ X3622 @ ( comp @ X3624 @ X3623 ) ) )
& ( ~ ( epred1_0 @ id @ X3625 @ id )
| ~ ( epred1_0 @ id @ X3626 @ id )
| ( epred1_0 @ id @ ( hoasap @ id @ X3625 @ id @ X3626 ) @ id ) )
& ( epred1_0 @ id @ esk27_0 @ id )
& ( epred1_0 @ id @ esk28_0 @ id )
& ~ ( epred1_0 @ id @ ( ap @ esk27_0 @ esk28_0 ) @ id ) ),
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_47])])])])])])]) ).
thf(c_0_50,plain,
! [X3501: subst,X3502: term,X3503: subst,X3504: term] :
( ( hoasap @ X3501 @ X3502 @ X3503 @ X3504 )
= ( ap @ ( sub @ X3502 @ X3503 ) @ X3504 ) ),
inference(variable_rename,[status(thm)],[c_0_48]) ).
thf(c_0_51,negated_conjecture,
! [X1: term,X2: term] :
( ( epred1_0 @ id @ ( hoasap @ id @ X1 @ id @ X2 ) @ id )
| ~ ( epred1_0 @ id @ X1 @ id )
| ~ ( epred1_0 @ id @ X2 @ id ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_52,plain,
! [X1: term,X3: subst,X4: subst,X2: term] :
( ( hoasap @ X3 @ X1 @ X4 @ X2 )
= ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
thf(c_0_53,negated_conjecture,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_54,negated_conjecture,
~ ( epred1_0 @ id @ ( ap @ esk27_0 @ esk28_0 ) @ id ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_55,negated_conjecture,
! [X2: term,X1: term] :
( ( epred1_0 @ id @ ( ap @ X1 @ X2 ) @ id )
| ~ ( epred1_0 @ id @ X2 @ id )
| ~ ( epred1_0 @ id @ X1 @ id ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
thf(c_0_56,negated_conjecture,
epred1_0 @ id @ esk28_0 @ id,
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_57,negated_conjecture,
epred1_0 @ id @ esk27_0 @ id,
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG264^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % 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 17:34:29 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.19/0.26 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.lAd8O1wflt/E---3.1_1062837.p
% 0.19/0.35 % Version: 3.5.1-ho
% 0.19/0.35 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.19/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.35 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.19/0.35 % Starting post_as_ho1 with 300s (1) cores
% 0.19/0.35 % Starting post_as_ho5 with 300s (1) cores
% 0.19/0.35 % Starting post_as_ho10 with 300s (1) cores
% 0.19/0.35 % new_ho_10_cnf2 with pid 1062850 completed with status 0
% 0.19/0.35 % Result found by new_ho_10_cnf2
% 0.19/0.35 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.19/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.35 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.19/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.35 % No SInE strategy applied
% 0.19/0.35 % Search class: HGHSM-FFMS31-MHFMMMBN
% 0.19/0.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.35 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.35 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.19/0.35 % Starting sh5l with 136s (1) cores
% 0.19/0.35 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.19/0.35 % Starting lpo1_def_fix with 136s (1) cores
% 0.19/0.35 % ehoh_best_sine_rwall with pid 1062874 completed with status 0
% 0.19/0.35 % Result found by ehoh_best_sine_rwall
% 0.19/0.35 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.19/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.35 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.19/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.19/0.35 % No SInE strategy applied
% 0.19/0.35 % Search class: HGHSM-FFMS31-MHFMMMBN
% 0.19/0.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.19/0.35 % Starting SubtermCWHack with 136s (1) cores
% 0.19/0.35 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.19/0.35 % Starting sh5l with 136s (1) cores
% 0.19/0.35 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.19/0.35 % Preprocessing time : 0.004 s
% 0.19/0.35 % Presaturation interreduction done
% 0.19/0.35
% 0.19/0.35 % Proof found!
% 0.19/0.35 % SZS status Theorem
% 0.19/0.35 % SZS output start CNFRefutation
% See solution above
% 0.19/0.35 % Parsed axioms : 238
% 0.19/0.35 % Removed by relevancy pruning/SinE : 0
% 0.19/0.35 % Initial clauses : 205
% 0.19/0.35 % Removed in clause preprocessing : 124
% 0.19/0.35 % Initial clauses in saturation : 81
% 0.19/0.35 % Processed clauses : 204
% 0.19/0.35 % ...of these trivial : 5
% 0.19/0.35 % ...subsumed : 67
% 0.19/0.35 % ...remaining for further processing : 132
% 0.19/0.35 % Other redundant clauses eliminated : 0
% 0.19/0.35 % Clauses deleted for lack of memory : 0
% 0.19/0.35 % Backward-subsumed : 0
% 0.19/0.35 % Backward-rewritten : 5
% 0.19/0.35 % Generated clauses : 237
% 0.19/0.35 % ...of the previous two non-redundant : 174
% 0.19/0.35 % ...aggressively subsumed : 0
% 0.19/0.35 % Contextual simplify-reflections : 0
% 0.19/0.35 % Paramodulations : 218
% 0.19/0.35 % Factorizations : 0
% 0.19/0.35 % NegExts : 0
% 0.19/0.35 % Equation resolutions : 4
% 0.19/0.35 % Disequality decompositions : 0
% 0.19/0.35 % Total rewrite steps : 83
% 0.19/0.35 % ...of those cached : 28
% 0.19/0.35 % Propositional unsat checks : 0
% 0.19/0.35 % Propositional check models : 0
% 0.19/0.35 % Propositional check unsatisfiable : 0
% 0.19/0.35 % Propositional clauses : 0
% 0.19/0.35 % Propositional clauses after purity: 0
% 0.19/0.35 % Propositional unsat core size : 0
% 0.19/0.35 % Propositional preprocessing time : 0.000
% 0.19/0.35 % Propositional encoding time : 0.000
% 0.19/0.35 % Propositional solver time : 0.000
% 0.19/0.35 % Success case prop preproc time : 0.000
% 0.19/0.35 % Success case prop encoding time : 0.000
% 0.19/0.35 % Success case prop solver time : 0.000
% 0.19/0.35 % Current number of processed clauses : 55
% 0.19/0.35 % Positive orientable unit clauses : 22
% 0.19/0.35 % Positive unorientable unit clauses: 3
% 0.19/0.35 % Negative unit clauses : 15
% 0.19/0.35 % Non-unit-clauses : 15
% 0.19/0.35 % Current number of unprocessed clauses: 123
% 0.19/0.35 % ...number of literals in the above : 284
% 0.19/0.35 % Current number of archived formulas : 0
% 0.19/0.35 % Current number of archived clauses : 77
% 0.19/0.35 % Clause-clause subsumption calls (NU) : 260
% 0.19/0.35 % Rec. Clause-clause subsumption calls : 139
% 0.19/0.35 % Non-unit clause-clause subsumptions : 8
% 0.19/0.35 % Unit Clause-clause subsumption calls : 27
% 0.19/0.35 % Rewrite failures with RHS unbound : 0
% 0.19/0.35 % BW rewrite match attempts : 27
% 0.19/0.35 % BW rewrite match successes : 8
% 0.19/0.35 % Condensation attempts : 0
% 0.19/0.35 % Condensation successes : 0
% 0.19/0.35 % Termbank termtop insertions : 43785
% 0.19/0.35 % Search garbage collected termcells : 4518
% 0.19/0.35
% 0.19/0.35 % -------------------------------------------------
% 0.19/0.35 % User time : 0.044 s
% 0.19/0.35 % System time : 0.012 s
% 0.19/0.35 % Total time : 0.056 s
% 0.19/0.35 % Maximum resident set size: 8032 pages
% 0.19/0.35
% 0.19/0.35 % -------------------------------------------------
% 0.19/0.35 % User time : 0.104 s
% 0.19/0.35 % System time : 0.044 s
% 0.19/0.35 % Total time : 0.149 s
% 0.19/0.35 % Maximum resident set size: 5120 pages
% 0.19/0.35 % E exiting
%------------------------------------------------------------------------------