%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG264^3 : 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 : n019.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 0.25s 0.37s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 40
% Syntax : Number of formulae : 67 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 367 ( 169 equ; 0 cnn)
% Maximal formula atoms : 83 ( 5 avg)
% Number of connectives : 2642 ( 133 ~; 162 |; 89 &;1934 @)
% ( 44 <=>; 280 =>; 0 <=; 0 <~>)
% Maximal formula depth : 175 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 79 usr; 42 con; 0-4 aty)
% Number of variables : 569 ( 40 ^; 529 !; 0 ?; 569 :)
% 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_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_85,type,
hoasinduction_lem2v2: $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_96,type,
hoasinduction_lem2v2_gthm: $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(decl_174,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/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',hoaslamnotvar) ).
thf(hoasvar,axiom,
( hoasvar
= ( ^ [X3: subst,X1: term,X4: subst] : ( var @ ( sub @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.p',hoaslamnotap) ).
thf(hoasapnotvar,axiom,
( hoasapnotvar
<=> ! [X1: term,X2: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',hoasapnotvar) ).
thf(hoasinduction_lem2v2,axiom,
( hoasinduction_lem2v2
<=> ! [X17: subst > term > subst > $o,X9: term > $o] :
( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X17 @ X3 @ X1 @ ( comp @ X5 @ X4 ) )
=> ( X17 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 ) )
=> ( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X17 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 )
=> ( X17 @ X3 @ X1 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X1: term,X2: term] :
( ( X17 @ id @ X1 @ id )
=> ( ( X17 @ id @ X2 @ id )
=> ( X17 @ id @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X17 @ X9 )
=> ! [X1: term,X2: term] :
( ( X9 @ X1 )
=> ( ( X9 @ X2 )
=> ( X9 @ ( ap @ X1 @ X2 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',hoasinduction_lem2v2) ).
thf(thm,conjecture,
hoasinduction_lem2v2_gthm,
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',thm) ).
thf(hoasinduction_lem2v2_gthm,axiom,
( hoasinduction_lem2v2_gthm
<=> ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem2v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',hoasinduction_lem2v2_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.SvTdOhsVJb/E---3.1_1126747.p',axapp) ).
thf(axvarcons,axiom,
( axvarcons
<=> ! [X1: term,X3: subst] :
( ( sub @ one @ ( push @ X1 @ X3 ) )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',axvarcons) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.p',axclos) ).
thf(axidl,axiom,
( axidl
<=> ! [X3: subst] :
( ( comp @ id @ X3 )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',axidl) ).
thf(axshiftcons,axiom,
( axshiftcons
<=> ! [X1: term,X3: subst] :
( ( comp @ sh @ ( push @ X1 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.p',axmap) ).
thf(axidr,axiom,
( axidr
<=> ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',axidr) ).
thf(axvarshift,axiom,
( axvarshift
<=> ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',axvarshift) ).
thf(axscons,axiom,
( axscons
<=> ! [X3: subst] :
( ( push @ ( sub @ one @ X3 ) @ ( comp @ sh @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',axscons) ).
thf(ulamvar1,axiom,
( ulamvar1
<=> ( var @ one ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',ulamvar1) ).
thf(ulamvarsh,axiom,
( ulamvarsh
<=> ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.p',apinj2) ).
thf(laminj,axiom,
( laminj
<=> ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',laminj) ).
thf(shinj,axiom,
( shinj
<=> ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',shinj) ).
thf(lamnotap,axiom,
( lamnotap
<=> ! [X1: term,X2: term,X7: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',lamnotap) ).
thf(apnotvar,axiom,
( apnotvar
<=> ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',apnotvar) ).
thf(lamnotvar,axiom,
( lamnotvar
<=> ! [X1: term] :
~ ( var @ ( lam @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.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.SvTdOhsVJb/E---3.1_1126747.p',hoasapinj2) ).
thf(hoasap,axiom,
( hoasap
= ( ^ [X3: subst,X1: term,X4: subst,X2: term] : ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.SvTdOhsVJb/E---3.1_1126747.p',hoasap) ).
thf(c_0_40,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_41,plain,
( hoasvar
= ( ^ [Z0: subst,Z1: term,Z2: subst] : ( var @ ( sub @ Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[hoasvar]) ).
thf(c_0_42,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_43,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_44,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_45,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_40,c_0_41]) ).
thf(c_0_46,axiom,
( hoasapnotvar
= ( ! [X1: term,X2: term] :
~ ( var @ ( sub @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ) ) ),
inference(apply_def,[status(thm)],[hoasapnotvar,c_0_41]) ).
thf(c_0_47,axiom,
( hoasinduction_lem2v2
= ( ! [X17: subst > term > subst > $o,X9: term > $o] :
( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X17 @ X3 @ X1 @ ( comp @ X5 @ X4 ) )
=> ( X17 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 ) )
=> ( ! [X3: subst,X1: term,X4: subst,X5: subst] :
( ( X17 @ ( comp @ X3 @ X5 ) @ ( sub @ X1 @ X5 ) @ X4 )
=> ( X17 @ X3 @ X1 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X1: term,X2: term] :
( ( X17 @ id @ X1 @ id )
=> ( ( X17 @ id @ X2 @ id )
=> ( X17 @ id @ ( hoasap @ id @ X1 @ id @ X2 ) @ id ) ) )
=> ( ! [X1858: term] :
( ( X9 @ X1858 )
<=> ( X17 @ id @ X1858 @ id ) )
=> ! [X1: term,X2: term] :
( ( X9 @ X1 )
=> ( ( X9 @ X2 )
=> ( X9 @ ( ap @ X1 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[hoasinduction_lem2v2,c_0_42]) ).
thf(c_0_48,negated_conjecture,
~ hoasinduction_lem2v2_gthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_49,axiom,
( hoasinduction_lem2v2_gthm
= ( ! [X1913: term,X1914: term,X1915: subst] :
( ( sub @ ( ap @ X1913 @ X1914 ) @ X1915 )
= ( ap @ ( sub @ X1913 @ X1915 ) @ ( sub @ X1914 @ X1915 ) ) )
=> ( ! [X1916: term,X1917: subst] :
( ( sub @ one @ ( push @ X1916 @ X1917 ) )
= X1916 )
=> ( ! [X1918: term] :
( ( sub @ X1918 @ id )
= X1918 )
=> ( ! [X1919: term,X1920: subst] :
( ( sub @ ( lam @ X1919 ) @ X1920 )
= ( lam @ ( sub @ X1919 @ ( push @ one @ ( comp @ X1920 @ sh ) ) ) ) )
=> ( ! [X1921: term,X1922: subst,X1923: subst] :
( ( sub @ ( sub @ X1921 @ X1922 ) @ X1923 )
= ( sub @ X1921 @ ( comp @ X1922 @ X1923 ) ) )
=> ( ! [X1924: subst] :
( ( comp @ id @ X1924 )
= X1924 )
=> ( ! [X1925: term,X1926: subst] :
( ( comp @ sh @ ( push @ X1925 @ X1926 ) )
= X1926 )
=> ( ! [X1927: subst,X1928: subst,X1929: subst] :
( ( comp @ ( comp @ X1927 @ X1928 ) @ X1929 )
= ( comp @ X1927 @ ( comp @ X1928 @ X1929 ) ) )
=> ( ! [X1930: term,X1931: subst,X1932: subst] :
( ( comp @ ( push @ X1930 @ X1931 ) @ X1932 )
= ( push @ ( sub @ X1930 @ X1932 ) @ ( comp @ X1931 @ X1932 ) ) )
=> ( ! [X1933: subst] :
( ( comp @ X1933 @ id )
= X1933 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X1934: subst] :
( ( push @ ( sub @ one @ X1934 ) @ ( comp @ sh @ X1934 ) )
= X1934 )
=> ( ( var @ one )
=> ( ! [X1935: term] :
( ( var @ X1935 )
=> ( var @ ( sub @ X1935 @ sh ) ) )
=> ( ! [X1936: term > $o] :
( ( X1936 @ one )
=> ( ! [X1937: term] :
( ( var @ X1937 )
=> ( ( X1936 @ X1937 )
=> ( X1936 @ ( sub @ X1937 @ sh ) ) ) )
=> ! [X1938: term] :
( ( var @ X1938 )
=> ( X1936 @ X1938 ) ) ) )
=> ( ! [X1939: term,X1940: term,X1941: term,X1942: term] :
( ( ( ap @ X1939 @ X1941 )
= ( ap @ X1940 @ X1942 ) )
=> ( X1939 = X1940 ) )
=> ( ! [X1943: term,X1944: term,X1945: term,X1946: term] :
( ( ( ap @ X1943 @ X1945 )
= ( ap @ X1944 @ X1946 ) )
=> ( X1945 = X1946 ) )
=> ( ! [X1947: term,X1948: term] :
( ( ( lam @ X1947 )
= ( lam @ X1948 ) )
=> ( X1947 = X1948 ) )
=> ( ! [X1949: term,X1950: term] :
( ( ( sub @ X1949 @ sh )
= ( sub @ X1950 @ sh ) )
=> ( X1949 = X1950 ) )
=> ( ! [X1951: term,X1952: term,X1953: term] :
( ( lam @ X1951 )
!= ( ap @ X1952 @ X1953 ) )
=> ( ! [X1954: term,X1955: term] :
~ ( var @ ( ap @ X1954 @ X1955 ) )
=> ( ! [X1956: term] :
~ ( var @ ( lam @ X1956 ) )
=> ( ! [X1957: term > $o] :
( ! [X1958: term] :
( ( var @ X1958 )
=> ( X1957 @ X1958 ) )
=> ( ! [X1959: term,X1960: term] :
( ( X1957 @ X1959 )
=> ( ( X1957 @ X1960 )
=> ( X1957 @ ( ap @ X1959 @ X1960 ) ) ) )
=> ( ! [X1961: term] :
( ( X1957 @ X1961 )
=> ( X1957 @ ( lam @ X1961 ) ) )
=> ! [X1962: term] : ( X1957 @ X1962 ) ) ) )
=> ( ! [X1963: term > $o,X1964: term,X1965: subst] :
( ! [X1966: term] :
( ( var @ X1966 )
=> ( X1963 @ ( sub @ X1966 @ X1965 ) ) )
=> ( ( X1963 @ X1964 )
=> ! [X1967: term] :
( ( var @ X1967 )
=> ( X1963 @ ( sub @ X1967 @ ( push @ X1964 @ X1965 ) ) ) ) ) )
=> ( ! [X1968: term > $o] :
( ! [X1969: term,X1970: term] :
( ( X1968 @ X1969 )
=> ( ( X1968 @ X1970 )
=> ( X1968 @ ( ap @ X1969 @ X1970 ) ) ) )
=> ( ! [X1971: term] :
( ! [X1972: term] :
( ( X1968 @ X1972 )
=> ( X1968 @ ( sub @ X1971 @ ( push @ X1972 @ id ) ) ) )
=> ( X1968 @ ( lam @ X1971 ) ) )
=> ! [X1973: term,X1974: subst] :
( ! [X1975: term] :
( ( var @ X1975 )
=> ( X1968 @ ( sub @ X1975 @ X1974 ) ) )
=> ( X1968 @ ( sub @ X1973 @ X1974 ) ) ) ) )
=> ( ! [X1976: term > $o] :
( ! [X1977: term] :
( ( var @ X1977 )
=> ( X1976 @ X1977 ) )
=> ( ! [X1978: term,X1979: term] :
( ( X1976 @ X1978 )
=> ( ( X1976 @ X1979 )
=> ( X1976 @ ( ap @ X1978 @ X1979 ) ) ) )
=> ( ! [X1980: term] :
( ! [X1981: term] :
( ( X1976 @ X1981 )
=> ( X1976 @ ( sub @ X1980 @ ( push @ X1981 @ id ) ) ) )
=> ( X1976 @ ( lam @ X1980 ) ) )
=> ! [X1982: term] : ( X1976 @ X1982 ) ) ) )
=> ( ( ! [X1983: subst,X1984: subst,X1985: subst] :
( ( comp @ ( comp @ X1983 @ X1984 ) @ X1985 )
= ( comp @ X1983 @ ( comp @ X1984 @ X1985 ) ) )
& ! [X1986: subst] :
( ( comp @ id @ X1986 )
= X1986 )
& ! [X1987: subst] :
( ( comp @ X1987 @ id )
= X1987 ) )
=> ( ( ! [X1988: term,X1989: subst,X1990: subst] :
( ( sub @ ( sub @ X1988 @ X1989 ) @ X1990 )
= ( sub @ X1988 @ ( comp @ X1989 @ X1990 ) ) )
& ! [X1991: term] :
( ( sub @ X1991 @ id )
= X1991 ) )
=> ( ! [X1992: term,X1993: term,X1994: term,X1995: term] :
( ( ( hoasap @ id @ X1992 @ id @ X1994 )
= ( hoasap @ id @ X1993 @ id @ X1995 ) )
=> ( X1992 = X1993 ) )
=> ( ! [X1996: term,X1997: term,X1998: term,X1999: term] :
( ( ( hoasap @ id @ X1996 @ id @ X1998 )
= ( hoasap @ id @ X1997 @ id @ X1999 ) )
=> ( X1998 = X1999 ) )
=> ( ! [X2000: subst > term > term] :
( ! [X2001: subst,X2002: term,X2003: subst] :
( ( sub @ ( X2000 @ X2001 @ X2002 ) @ X2003 )
= ( X2000 @ ( comp @ X2001 @ X2003 ) @ ( sub @ X2002 @ X2003 ) ) )
=> ! [X2004: subst > term > term] :
( ! [X2005: subst,X2006: term,X2007: subst] :
( ( sub @ ( X2004 @ X2005 @ X2006 ) @ X2007 )
= ( X2004 @ ( comp @ X2005 @ X2007 ) @ ( sub @ X2006 @ X2007 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X2000 @ Z0 @ Z1 ) )
= ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X2004 @ Z0 @ Z1 ) ) )
=> ! [X2008: subst,X2009: term] :
( ( X2000 @ X2008 @ X2009 )
= ( X2004 @ X2008 @ X2009 ) ) ) ) )
=> ( ! [X2010: subst > term > term] :
( ! [X2011: subst,X2012: term,X2013: subst] :
( ( sub @ ( X2010 @ X2011 @ X2012 ) @ X2013 )
= ( X2010 @ ( comp @ X2011 @ X2013 ) @ ( sub @ X2012 @ X2013 ) ) )
=> ! [X2014: term,X2015: term] :
( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X2010 @ Z0 @ Z1 ) )
!= ( hoasap @ id @ X2014 @ id @ X2015 ) ) )
=> ( ! [X2016: subst > term > term] :
( ! [X2017: subst,X2018: term,X2019: subst] :
( ( sub @ ( X2016 @ X2017 @ X2018 ) @ X2019 )
= ( X2016 @ ( comp @ X2017 @ X2019 ) @ ( sub @ X2018 @ X2019 ) ) )
=> ~ ( var
@ ( sub
@ ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X2016 @ Z0 @ Z1 ) )
@ id ) ) )
=> ( ! [X2020: term,X2021: term] :
~ ( var @ ( sub @ ( hoasap @ id @ X2020 @ id @ X2021 ) @ id ) )
=> ! [X2022: subst > term > subst > $o,X2023: term > $o] :
( ! [X2024: subst,X2025: term,X2026: subst,X2027: subst] :
( ( X2022 @ X2024 @ X2025 @ ( comp @ X2027 @ X2026 ) )
=> ( X2022 @ ( comp @ X2024 @ X2027 ) @ ( sub @ X2025 @ X2027 ) @ X2026 ) )
=> ( ! [X2028: subst,X2029: term,X2030: subst,X2031: subst] :
( ( X2022 @ ( comp @ X2028 @ X2031 ) @ ( sub @ X2029 @ X2031 ) @ X2030 )
=> ( X2022 @ X2028 @ X2029 @ ( comp @ X2031 @ X2030 ) ) )
=> ( ! [X2032: term,X2033: term] :
( ( X2022 @ id @ X2032 @ id )
=> ( ( X2022 @ id @ X2033 @ id )
=> ( X2022 @ id @ ( hoasap @ id @ X2032 @ id @ X2033 ) @ id ) ) )
=> ( ! [X2034: term] :
( ( X2023 @ X2034 )
<=> ( X2022 @ id @ X2034 @ id ) )
=> ! [X2035: term,X2036: term] :
( ( X2023 @ X2035 )
=> ( ( X2023 @ X2036 )
=> ( X2023 @ ( ap @ X2035 @ X2036 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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_lem2v2_gthm,axapp]),axvarcons]),axvarid]),axabs]),axclos]),axidl]),axshiftcons]),axassoc]),axmap]),axidr]),axvarshift]),axscons]),ulamvar1]),ulamvarsh]),ulamvarind]),apinj1]),apinj2]),laminj]),shinj]),lamnotap]),apnotvar]),lamnotvar]),induction]),pushprop]),induction2lem]),induction2]),substmonoid]),termmset]),c_0_41]),hoasapinj1]),hoasapinj2]),c_0_43]),c_0_44]),c_0_45]),c_0_46]),c_0_47]) ).
thf(c_0_50,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,X3493: term] :
( ( X3482 @ id @ X3492 @ id )
=> ( ( X3482 @ id @ X3493 @ id )
=> ( X3482 @ id @ ( hoasap @ id @ X3492 @ id @ X3493 ) @ id ) ) )
=> ( ! [X3494: term] :
( ( X3483 @ X3494 )
<=> ( X3482 @ id @ X3494 @ id ) )
=> ! [X3495: term,X3496: term] :
( ( X3483 @ X3495 )
=> ( ( X3483 @ X3496 )
=> ( X3483 @ ( ap @ X3495 @ X3496 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[c_0_48,c_0_49])])]) ).
thf(c_0_51,plain,
! [X3497: subst,X3498: term,X3499: subst,X3500: term] :
( ( hoasap @ X3497 @ X3498 @ X3499 @ X3500 )
= ( ap @ ( sub @ X3498 @ X3499 ) @ X3500 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoasap])]) ).
thf(c_0_52,negated_conjecture,
! [X3509: term,X3510: term,X3511: subst,X3512: term,X3513: subst,X3514: term,X3515: term,X3516: subst,X3517: term,X3518: subst,X3519: subst,X3520: subst,X3521: term,X3522: subst,X3523: subst,X3524: subst,X3525: subst,X3526: term,X3527: subst,X3528: subst,X3529: subst,X3530: subst,X3531: term,X3532: term > $o,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,X3552: term,X3553: term > $o,X3558: term,X3559: term > $o,X3560: term,X3561: subst,X3563: term,X3564: term > $o,X3568: term,X3569: term,X3570: subst,X3572: term > $o,X3577: term,X3578: term,X3579: subst,X3580: subst,X3581: subst,X3582: subst,X3583: subst,X3584: term,X3585: subst,X3586: subst,X3587: term,X3588: term,X3589: term,X3590: term,X3591: term,X3592: term,X3593: term,X3594: term,X3595: term,X3596: subst > term > term,X3600: subst > term > term,X3604: subst,X3605: term,X3606: subst > term > term,X3610: term,X3611: term,X3612: subst > term > term,X3616: term,X3617: term,X3620: subst,X3621: term,X3622: subst,X3623: subst,X3624: subst,X3625: term,X3626: subst,X3627: subst,X3628: term,X3629: term,X3630: term] :
( ( ( sub @ ( ap @ X3509 @ X3510 ) @ X3511 )
= ( ap @ ( sub @ X3509 @ X3511 ) @ ( sub @ X3510 @ X3511 ) ) )
& ( ( sub @ one @ ( push @ X3512 @ X3513 ) )
= X3512 )
& ( ( sub @ X3514 @ id )
= X3514 )
& ( ( sub @ ( lam @ X3515 ) @ X3516 )
= ( lam @ ( sub @ X3515 @ ( push @ one @ ( comp @ X3516 @ sh ) ) ) ) )
& ( ( sub @ ( sub @ X3517 @ X3518 ) @ X3519 )
= ( sub @ X3517 @ ( comp @ X3518 @ X3519 ) ) )
& ( ( comp @ id @ X3520 )
= X3520 )
& ( ( comp @ sh @ ( push @ X3521 @ X3522 ) )
= X3522 )
& ( ( comp @ ( comp @ X3523 @ X3524 ) @ X3525 )
= ( comp @ X3523 @ ( comp @ X3524 @ X3525 ) ) )
& ( ( comp @ ( push @ X3526 @ X3527 ) @ X3528 )
= ( push @ ( sub @ X3526 @ X3528 ) @ ( comp @ X3527 @ X3528 ) ) )
& ( ( comp @ X3529 @ id )
= X3529 )
& ( ( push @ one @ sh )
= id )
& ( ( push @ ( sub @ one @ X3530 ) @ ( comp @ sh @ X3530 ) )
= X3530 )
& ( var @ one )
& ( ~ ( var @ X3531 )
| ( var @ ( sub @ X3531 @ sh ) ) )
& ( ( var @ ( esk1_1 @ X3532 ) )
| ~ ( var @ X3534 )
| ( X3532 @ X3534 )
| ~ ( X3532 @ one ) )
& ( ( X3532 @ ( esk1_1 @ X3532 ) )
| ~ ( var @ X3534 )
| ( X3532 @ X3534 )
| ~ ( X3532 @ one ) )
& ( ~ ( X3532 @ ( sub @ ( esk1_1 @ X3532 ) @ sh ) )
| ~ ( var @ X3534 )
| ( X3532 @ X3534 )
| ~ ( X3532 @ one ) )
& ( ( ( ap @ X3535 @ X3537 )
!= ( ap @ X3536 @ X3538 ) )
| ( X3535 = X3536 ) )
& ( ( ( ap @ X3539 @ X3541 )
!= ( ap @ X3540 @ X3542 ) )
| ( X3541 = X3542 ) )
& ( ( ( lam @ X3543 )
!= ( lam @ X3544 ) )
| ( X3543 = X3544 ) )
& ( ( ( sub @ X3545 @ sh )
!= ( sub @ X3546 @ sh ) )
| ( X3545 = X3546 ) )
& ( ( lam @ X3547 )
!= ( ap @ X3548 @ X3549 ) )
& ~ ( var @ ( ap @ X3550 @ X3551 ) )
& ~ ( var @ ( lam @ X3552 ) )
& ( ( X3553 @ ( esk5_1 @ X3553 ) )
| ( X3553 @ X3558 )
| ( X3553 @ ( esk3_1 @ X3553 ) )
| ( var @ ( esk2_1 @ X3553 ) ) )
& ( ~ ( X3553 @ ( lam @ ( esk5_1 @ X3553 ) ) )
| ( X3553 @ X3558 )
| ( X3553 @ ( esk3_1 @ X3553 ) )
| ( var @ ( esk2_1 @ X3553 ) ) )
& ( ( X3553 @ ( esk5_1 @ X3553 ) )
| ( X3553 @ X3558 )
| ( X3553 @ ( esk4_1 @ X3553 ) )
| ( var @ ( esk2_1 @ X3553 ) ) )
& ( ~ ( X3553 @ ( lam @ ( esk5_1 @ X3553 ) ) )
| ( X3553 @ X3558 )
| ( X3553 @ ( esk4_1 @ X3553 ) )
| ( var @ ( esk2_1 @ X3553 ) ) )
& ( ( X3553 @ ( esk5_1 @ X3553 ) )
| ( X3553 @ X3558 )
| ~ ( X3553 @ ( ap @ ( esk3_1 @ X3553 ) @ ( esk4_1 @ X3553 ) ) )
| ( var @ ( esk2_1 @ X3553 ) ) )
& ( ~ ( X3553 @ ( lam @ ( esk5_1 @ X3553 ) ) )
| ( X3553 @ X3558 )
| ~ ( X3553 @ ( ap @ ( esk3_1 @ X3553 ) @ ( esk4_1 @ X3553 ) ) )
| ( var @ ( esk2_1 @ X3553 ) ) )
& ( ( X3553 @ ( esk5_1 @ X3553 ) )
| ( X3553 @ X3558 )
| ( X3553 @ ( esk3_1 @ X3553 ) )
| ~ ( X3553 @ ( esk2_1 @ X3553 ) ) )
& ( ~ ( X3553 @ ( lam @ ( esk5_1 @ X3553 ) ) )
| ( X3553 @ X3558 )
| ( X3553 @ ( esk3_1 @ X3553 ) )
| ~ ( X3553 @ ( esk2_1 @ X3553 ) ) )
& ( ( X3553 @ ( esk5_1 @ X3553 ) )
| ( X3553 @ X3558 )
| ( X3553 @ ( esk4_1 @ X3553 ) )
| ~ ( X3553 @ ( esk2_1 @ X3553 ) ) )
& ( ~ ( X3553 @ ( lam @ ( esk5_1 @ X3553 ) ) )
| ( X3553 @ X3558 )
| ( X3553 @ ( esk4_1 @ X3553 ) )
| ~ ( X3553 @ ( esk2_1 @ X3553 ) ) )
& ( ( X3553 @ ( esk5_1 @ X3553 ) )
| ( X3553 @ X3558 )
| ~ ( X3553 @ ( ap @ ( esk3_1 @ X3553 ) @ ( esk4_1 @ X3553 ) ) )
| ~ ( X3553 @ ( esk2_1 @ X3553 ) ) )
& ( ~ ( X3553 @ ( lam @ ( esk5_1 @ X3553 ) ) )
| ( X3553 @ X3558 )
| ~ ( X3553 @ ( ap @ ( esk3_1 @ X3553 ) @ ( esk4_1 @ X3553 ) ) )
| ~ ( X3553 @ ( esk2_1 @ X3553 ) ) )
& ( ( var @ ( esk6_3 @ X3559 @ X3560 @ X3561 ) )
| ~ ( X3559 @ X3560 )
| ~ ( var @ X3563 )
| ( X3559 @ ( sub @ X3563 @ ( push @ X3560 @ X3561 ) ) ) )
& ( ~ ( X3559 @ ( sub @ ( esk6_3 @ X3559 @ X3560 @ X3561 ) @ X3561 ) )
| ~ ( X3559 @ X3560 )
| ~ ( var @ X3563 )
| ( X3559 @ ( sub @ X3563 @ ( push @ X3560 @ X3561 ) ) ) )
& ( ( var @ ( esk10_3 @ X3564 @ X3569 @ X3570 ) )
| ( X3564 @ ( sub @ X3569 @ X3570 ) )
| ~ ( X3564 @ X3568 )
| ( X3564 @ ( sub @ ( esk9_1 @ X3564 ) @ ( push @ X3568 @ id ) ) )
| ( X3564 @ ( esk7_1 @ X3564 ) ) )
& ( ~ ( X3564 @ ( sub @ ( esk10_3 @ X3564 @ X3569 @ X3570 ) @ X3570 ) )
| ( X3564 @ ( sub @ X3569 @ X3570 ) )
| ~ ( X3564 @ X3568 )
| ( X3564 @ ( sub @ ( esk9_1 @ X3564 ) @ ( push @ X3568 @ id ) ) )
| ( X3564 @ ( esk7_1 @ X3564 ) ) )
& ( ( var @ ( esk10_3 @ X3564 @ X3569 @ X3570 ) )
| ( X3564 @ ( sub @ X3569 @ X3570 ) )
| ~ ( X3564 @ ( lam @ ( esk9_1 @ X3564 ) ) )
| ( X3564 @ ( esk7_1 @ X3564 ) ) )
& ( ~ ( X3564 @ ( sub @ ( esk10_3 @ X3564 @ X3569 @ X3570 ) @ X3570 ) )
| ( X3564 @ ( sub @ X3569 @ X3570 ) )
| ~ ( X3564 @ ( lam @ ( esk9_1 @ X3564 ) ) )
| ( X3564 @ ( esk7_1 @ X3564 ) ) )
& ( ( var @ ( esk10_3 @ X3564 @ X3569 @ X3570 ) )
| ( X3564 @ ( sub @ X3569 @ X3570 ) )
| ~ ( X3564 @ X3568 )
| ( X3564 @ ( sub @ ( esk9_1 @ X3564 ) @ ( push @ X3568 @ id ) ) )
| ( X3564 @ ( esk8_1 @ X3564 ) ) )
& ( ~ ( X3564 @ ( sub @ ( esk10_3 @ X3564 @ X3569 @ X3570 ) @ X3570 ) )
| ( X3564 @ ( sub @ X3569 @ X3570 ) )
| ~ ( X3564 @ X3568 )
| ( X3564 @ ( sub @ ( esk9_1 @ X3564 ) @ ( push @ X3568 @ id ) ) )
| ( X3564 @ ( esk8_1 @ X3564 ) ) )
& ( ( var @ ( esk10_3 @ X3564 @ X3569 @ X3570 ) )
| ( X3564 @ ( sub @ X3569 @ X3570 ) )
| ~ ( X3564 @ ( lam @ ( esk9_1 @ X3564 ) ) )
| ( X3564 @ ( esk8_1 @ X3564 ) ) )
& ( ~ ( X3564 @ ( sub @ ( esk10_3 @ X3564 @ X3569 @ X3570 ) @ X3570 ) )
| ( X3564 @ ( sub @ X3569 @ X3570 ) )
| ~ ( X3564 @ ( lam @ ( esk9_1 @ X3564 ) ) )
| ( X3564 @ ( esk8_1 @ X3564 ) ) )
& ( ( var @ ( esk10_3 @ X3564 @ X3569 @ X3570 ) )
| ( X3564 @ ( sub @ X3569 @ X3570 ) )
| ~ ( X3564 @ X3568 )
| ( X3564 @ ( sub @ ( esk9_1 @ X3564 ) @ ( push @ X3568 @ id ) ) )
| ~ ( X3564 @ ( ap @ ( esk7_1 @ X3564 ) @ ( esk8_1 @ X3564 ) ) ) )
& ( ~ ( X3564 @ ( sub @ ( esk10_3 @ X3564 @ X3569 @ X3570 ) @ X3570 ) )
| ( X3564 @ ( sub @ X3569 @ X3570 ) )
| ~ ( X3564 @ X3568 )
| ( X3564 @ ( sub @ ( esk9_1 @ X3564 ) @ ( push @ X3568 @ id ) ) )
| ~ ( X3564 @ ( ap @ ( esk7_1 @ X3564 ) @ ( esk8_1 @ X3564 ) ) ) )
& ( ( var @ ( esk10_3 @ X3564 @ X3569 @ X3570 ) )
| ( X3564 @ ( sub @ X3569 @ X3570 ) )
| ~ ( X3564 @ ( lam @ ( esk9_1 @ X3564 ) ) )
| ~ ( X3564 @ ( ap @ ( esk7_1 @ X3564 ) @ ( esk8_1 @ X3564 ) ) ) )
& ( ~ ( X3564 @ ( sub @ ( esk10_3 @ X3564 @ X3569 @ X3570 ) @ X3570 ) )
| ( X3564 @ ( sub @ X3569 @ X3570 ) )
| ~ ( X3564 @ ( lam @ ( esk9_1 @ X3564 ) ) )
| ~ ( X3564 @ ( ap @ ( esk7_1 @ X3564 ) @ ( esk8_1 @ X3564 ) ) ) )
& ( ~ ( X3572 @ X3577 )
| ( X3572 @ ( sub @ ( esk14_1 @ X3572 ) @ ( push @ X3577 @ id ) ) )
| ( X3572 @ X3578 )
| ( X3572 @ ( esk12_1 @ X3572 ) )
| ( var @ ( esk11_1 @ X3572 ) ) )
& ( ~ ( X3572 @ ( lam @ ( esk14_1 @ X3572 ) ) )
| ( X3572 @ X3578 )
| ( X3572 @ ( esk12_1 @ X3572 ) )
| ( var @ ( esk11_1 @ X3572 ) ) )
& ( ~ ( X3572 @ X3577 )
| ( X3572 @ ( sub @ ( esk14_1 @ X3572 ) @ ( push @ X3577 @ id ) ) )
| ( X3572 @ X3578 )
| ( X3572 @ ( esk13_1 @ X3572 ) )
| ( var @ ( esk11_1 @ X3572 ) ) )
& ( ~ ( X3572 @ ( lam @ ( esk14_1 @ X3572 ) ) )
| ( X3572 @ X3578 )
| ( X3572 @ ( esk13_1 @ X3572 ) )
| ( var @ ( esk11_1 @ X3572 ) ) )
& ( ~ ( X3572 @ X3577 )
| ( X3572 @ ( sub @ ( esk14_1 @ X3572 ) @ ( push @ X3577 @ id ) ) )
| ( X3572 @ X3578 )
| ~ ( X3572 @ ( ap @ ( esk12_1 @ X3572 ) @ ( esk13_1 @ X3572 ) ) )
| ( var @ ( esk11_1 @ X3572 ) ) )
& ( ~ ( X3572 @ ( lam @ ( esk14_1 @ X3572 ) ) )
| ( X3572 @ X3578 )
| ~ ( X3572 @ ( ap @ ( esk12_1 @ X3572 ) @ ( esk13_1 @ X3572 ) ) )
| ( var @ ( esk11_1 @ X3572 ) ) )
& ( ~ ( X3572 @ X3577 )
| ( X3572 @ ( sub @ ( esk14_1 @ X3572 ) @ ( push @ X3577 @ id ) ) )
| ( X3572 @ X3578 )
| ( X3572 @ ( esk12_1 @ X3572 ) )
| ~ ( X3572 @ ( esk11_1 @ X3572 ) ) )
& ( ~ ( X3572 @ ( lam @ ( esk14_1 @ X3572 ) ) )
| ( X3572 @ X3578 )
| ( X3572 @ ( esk12_1 @ X3572 ) )
| ~ ( X3572 @ ( esk11_1 @ X3572 ) ) )
& ( ~ ( X3572 @ X3577 )
| ( X3572 @ ( sub @ ( esk14_1 @ X3572 ) @ ( push @ X3577 @ id ) ) )
| ( X3572 @ X3578 )
| ( X3572 @ ( esk13_1 @ X3572 ) )
| ~ ( X3572 @ ( esk11_1 @ X3572 ) ) )
& ( ~ ( X3572 @ ( lam @ ( esk14_1 @ X3572 ) ) )
| ( X3572 @ X3578 )
| ( X3572 @ ( esk13_1 @ X3572 ) )
| ~ ( X3572 @ ( esk11_1 @ X3572 ) ) )
& ( ~ ( X3572 @ X3577 )
| ( X3572 @ ( sub @ ( esk14_1 @ X3572 ) @ ( push @ X3577 @ id ) ) )
| ( X3572 @ X3578 )
| ~ ( X3572 @ ( ap @ ( esk12_1 @ X3572 ) @ ( esk13_1 @ X3572 ) ) )
| ~ ( X3572 @ ( esk11_1 @ X3572 ) ) )
& ( ~ ( X3572 @ ( lam @ ( esk14_1 @ X3572 ) ) )
| ( X3572 @ X3578 )
| ~ ( X3572 @ ( ap @ ( esk12_1 @ X3572 ) @ ( esk13_1 @ X3572 ) ) )
| ~ ( X3572 @ ( esk11_1 @ X3572 ) ) )
& ( ( comp @ ( comp @ X3579 @ X3580 ) @ X3581 )
= ( comp @ X3579 @ ( comp @ X3580 @ X3581 ) ) )
& ( ( comp @ id @ X3582 )
= X3582 )
& ( ( comp @ X3583 @ id )
= X3583 )
& ( ( sub @ ( sub @ X3584 @ X3585 ) @ X3586 )
= ( sub @ X3584 @ ( comp @ X3585 @ X3586 ) ) )
& ( ( sub @ X3587 @ id )
= X3587 )
& ( ( ( hoasap @ id @ X3588 @ id @ X3590 )
!= ( hoasap @ id @ X3589 @ id @ X3591 ) )
| ( X3588 = X3589 ) )
& ( ( ( hoasap @ id @ X3592 @ id @ X3594 )
!= ( hoasap @ id @ X3593 @ id @ X3595 ) )
| ( X3594 = X3595 ) )
& ( ( ( sub @ ( X3596 @ ( esk15_1 @ X3596 ) @ ( esk16_1 @ X3596 ) ) @ ( esk17_1 @ X3596 ) )
!= ( X3596 @ ( comp @ ( esk15_1 @ X3596 ) @ ( esk17_1 @ X3596 ) ) @ ( sub @ ( esk16_1 @ X3596 ) @ ( esk17_1 @ X3596 ) ) ) )
| ( ( sub @ ( X3600 @ ( esk18_2 @ X3596 @ X3600 ) @ ( esk19_2 @ X3596 @ X3600 ) ) @ ( esk20_2 @ X3596 @ X3600 ) )
!= ( X3600 @ ( comp @ ( esk18_2 @ X3596 @ X3600 ) @ ( esk20_2 @ X3596 @ X3600 ) ) @ ( sub @ ( esk19_2 @ X3596 @ X3600 ) @ ( esk20_2 @ X3596 @ X3600 ) ) ) )
| ( ( hoaslam @ id @ X3596 )
!= ( hoaslam @ id @ X3600 ) )
| ( ( X3596 @ X3604 @ X3605 )
= ( X3600 @ X3604 @ X3605 ) ) )
& ( ( ( sub @ ( X3606 @ ( esk21_1 @ X3606 ) @ ( esk22_1 @ X3606 ) ) @ ( esk23_1 @ X3606 ) )
!= ( X3606 @ ( comp @ ( esk21_1 @ X3606 ) @ ( esk23_1 @ X3606 ) ) @ ( sub @ ( esk22_1 @ X3606 ) @ ( esk23_1 @ X3606 ) ) ) )
| ( ( hoaslam @ id @ X3606 )
!= ( hoasap @ id @ X3610 @ id @ X3611 ) ) )
& ( ( ( sub @ ( X3612 @ ( esk24_1 @ X3612 ) @ ( esk25_1 @ X3612 ) ) @ ( esk26_1 @ X3612 ) )
!= ( X3612 @ ( comp @ ( esk24_1 @ X3612 ) @ ( esk26_1 @ X3612 ) ) @ ( sub @ ( esk25_1 @ X3612 ) @ ( esk26_1 @ X3612 ) ) ) )
| ~ ( var @ ( sub @ ( hoaslam @ id @ X3612 ) @ id ) ) )
& ~ ( var @ ( sub @ ( hoasap @ id @ X3616 @ id @ X3617 ) @ id ) )
& ( ~ ( epred1_0 @ X3620 @ X3621 @ ( comp @ X3623 @ X3622 ) )
| ( epred1_0 @ ( comp @ X3620 @ X3623 ) @ ( sub @ X3621 @ X3623 ) @ X3622 ) )
& ( ~ ( epred1_0 @ ( comp @ X3624 @ X3627 ) @ ( sub @ X3625 @ X3627 ) @ X3626 )
| ( epred1_0 @ X3624 @ X3625 @ ( comp @ X3627 @ X3626 ) ) )
& ( ~ ( epred1_0 @ id @ X3628 @ id )
| ~ ( epred1_0 @ id @ X3629 @ id )
| ( epred1_0 @ id @ ( hoasap @ id @ X3628 @ id @ X3629 ) @ id ) )
& ( ~ ( epred2_0 @ X3630 )
| ( epred1_0 @ id @ X3630 @ id ) )
& ( ~ ( epred1_0 @ id @ X3630 @ id )
| ( epred2_0 @ X3630 ) )
& ( epred2_0 @ esk27_0 )
& ( epred2_0 @ esk28_0 )
& ~ ( epred2_0 @ ( ap @ esk27_0 @ esk28_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_50])])])])])])]) ).
thf(c_0_53,plain,
! [X3503: subst,X3504: term,X3505: subst,X3506: term] :
( ( hoasap @ X3503 @ X3504 @ X3505 @ X3506 )
= ( ap @ ( sub @ X3504 @ X3505 ) @ X3506 ) ),
inference(variable_rename,[status(thm)],[c_0_51]) ).
thf(c_0_54,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_52]) ).
thf(c_0_55,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_53]) ).
thf(c_0_56,negated_conjecture,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_57,negated_conjecture,
! [X1: term] :
( ( epred2_0 @ X1 )
| ~ ( epred1_0 @ id @ X1 @ id ) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_58,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_54,c_0_55]),c_0_56]) ).
thf(c_0_59,negated_conjecture,
~ ( epred2_0 @ ( ap @ esk27_0 @ esk28_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_60,negated_conjecture,
! [X2: term,X1: term] :
( ( epred2_0 @ ( ap @ X1 @ X2 ) )
| ~ ( epred1_0 @ id @ X2 @ id )
| ~ ( epred1_0 @ id @ X1 @ id ) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_61,negated_conjecture,
( ~ ( epred1_0 @ id @ esk28_0 @ id )
| ~ ( epred1_0 @ id @ esk27_0 @ id ) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
thf(c_0_62,negated_conjecture,
! [X1: term] :
( ( epred1_0 @ id @ X1 @ id )
| ~ ( epred2_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_63,negated_conjecture,
epred2_0 @ esk28_0,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_64,negated_conjecture,
~ ( epred1_0 @ id @ esk27_0 @ id ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]) ).
thf(c_0_65,negated_conjecture,
epred2_0 @ esk27_0,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
thf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_62]),c_0_65])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG264^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n019.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 17:34:53 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 Running higher-order theorem proving
% 0.11/0.27 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.SvTdOhsVJb/E---3.1_1126747.p
% 0.25/0.37 % Version: 3.5.1-ho
% 0.25/0.37 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.25/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.37 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.25/0.37 % Starting post_as_ho1 with 300s (1) cores
% 0.25/0.37 % Starting post_as_ho5 with 300s (1) cores
% 0.25/0.37 % Starting post_as_ho10 with 300s (1) cores
% 0.25/0.37 % new_ho_10_cnf2 with pid 1126771 completed with status 0
% 0.25/0.37 % Result found by new_ho_10_cnf2
% 0.25/0.37 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.25/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.37 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.25/0.37 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.37 % No SInE strategy applied
% 0.25/0.37 % Search class: HGHSM-FFMS31-MHFMMMBN
% 0.25/0.37 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.37 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.37 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.25/0.37 % Starting sh5l with 136s (1) cores
% 0.25/0.37 % Starting ehoh_best_sine_rwall with 136s (1) cores
% 0.25/0.37 % Starting lpo1_def_fix with 136s (1) cores
% 0.25/0.37 % new_ho_10_cnf2 with pid 1126778 completed with status 0
% 0.25/0.37 % Result found by new_ho_10_cnf2
% 0.25/0.37 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.25/0.37 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.37 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.25/0.37 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.37 % No SInE strategy applied
% 0.25/0.37 % Search class: HGHSM-FFMS31-MHFMMMBN
% 0.25/0.37 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.37 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.37 % Starting new_ho_10_cnf2 with 151s (1) cores
% 0.25/0.37 % Preprocessing time : 0.003 s
% 0.25/0.37 % Presaturation interreduction done
% 0.25/0.37
% 0.25/0.37 % Proof found!
% 0.25/0.37 % SZS status Theorem
% 0.25/0.37 % SZS output start CNFRefutation
% See solution above
% 0.25/0.37 % Parsed axioms : 238
% 0.25/0.37 % Removed by relevancy pruning/SinE : 0
% 0.25/0.37 % Initial clauses : 207
% 0.25/0.37 % Removed in clause preprocessing : 124
% 0.25/0.37 % Initial clauses in saturation : 83
% 0.25/0.37 % Processed clauses : 205
% 0.25/0.37 % ...of these trivial : 5
% 0.25/0.37 % ...subsumed : 28
% 0.25/0.37 % ...remaining for further processing : 172
% 0.25/0.37 % Other redundant clauses eliminated : 0
% 0.25/0.37 % Clauses deleted for lack of memory : 0
% 0.25/0.37 % Backward-subsumed : 1
% 0.25/0.37 % Backward-rewritten : 8
% 0.25/0.37 % Generated clauses : 314
% 0.25/0.37 % ...of the previous two non-redundant : 275
% 0.25/0.37 % ...aggressively subsumed : 0
% 0.25/0.37 % Contextual simplify-reflections : 0
% 0.25/0.37 % Paramodulations : 302
% 0.25/0.37 % Factorizations : 0
% 0.25/0.37 % NegExts : 0
% 0.25/0.37 % Equation resolutions : 4
% 0.25/0.37 % Disequality decompositions : 0
% 0.25/0.37 % Total rewrite steps : 90
% 0.25/0.37 % ...of those cached : 33
% 0.25/0.37 % Propositional unsat checks : 0
% 0.25/0.37 % Propositional check models : 0
% 0.25/0.37 % Propositional check unsatisfiable : 0
% 0.25/0.37 % Propositional clauses : 0
% 0.25/0.37 % Propositional clauses after purity: 0
% 0.25/0.37 % Propositional unsat core size : 0
% 0.25/0.37 % Propositional preprocessing time : 0.000
% 0.25/0.37 % Propositional encoding time : 0.000
% 0.25/0.37 % Propositional solver time : 0.000
% 0.25/0.37 % Success case prop preproc time : 0.000
% 0.25/0.37 % Success case prop encoding time : 0.000
% 0.25/0.37 % Success case prop solver time : 0.000
% 0.25/0.37 % Current number of processed clauses : 91
% 0.25/0.37 % Positive orientable unit clauses : 21
% 0.25/0.37 % Positive unorientable unit clauses: 0
% 0.25/0.37 % Negative unit clauses : 9
% 0.25/0.37 % Non-unit-clauses : 61
% 0.25/0.37 % Current number of unprocessed clauses: 225
% 0.25/0.37 % ...number of literals in the above : 985
% 0.25/0.37 % Current number of archived formulas : 0
% 0.25/0.37 % Current number of archived clauses : 81
% 0.25/0.37 % Clause-clause subsumption calls (NU) : 537
% 0.25/0.37 % Rec. Clause-clause subsumption calls : 254
% 0.25/0.37 % Non-unit clause-clause subsumptions : 10
% 0.25/0.37 % Unit Clause-clause subsumption calls : 47
% 0.25/0.37 % Rewrite failures with RHS unbound : 0
% 0.25/0.37 % BW rewrite match attempts : 11
% 0.25/0.37 % BW rewrite match successes : 7
% 0.25/0.37 % Condensation attempts : 205
% 0.25/0.37 % Condensation successes : 0
% 0.25/0.37 % Termbank termtop insertions : 42800
% 0.25/0.37 % Search garbage collected termcells : 4603
% 0.25/0.37
% 0.25/0.37 % -------------------------------------------------
% 0.25/0.37 % User time : 0.052 s
% 0.25/0.37 % System time : 0.018 s
% 0.25/0.37 % Total time : 0.070 s
% 0.25/0.37 % Maximum resident set size: 8032 pages
% 0.25/0.37
% 0.25/0.37 % -------------------------------------------------
% 0.25/0.37 % User time : 0.160 s
% 0.25/0.37 % System time : 0.049 s
% 0.25/0.37 % Total time : 0.209 s
% 0.25/0.37 % Maximum resident set size: 5120 pages
% 0.25/0.37 % E exiting
%------------------------------------------------------------------------------