TSTP Solution File: ALG259^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : ALG259^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:05:54 EDT 2024
% Result : Theorem 0.18s 0.53s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 105
% Syntax : Number of formulae : 121 ( 15 unt; 69 typ; 0 def)
% Number of atoms : 299 ( 163 equ; 0 cnn)
% Maximal formula atoms : 66 ( 5 avg)
% Number of connectives : 2106 ( 100 ~; 145 |; 80 &;1520 @)
% ( 35 <=>; 226 =>; 0 <=; 0 <~>)
% Maximal formula depth : 155 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 135 ( 135 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 67 usr; 39 con; 0-4 aty)
% Number of variables : 451 ( 24 ^ 427 !; 0 ?; 451 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
term: $tType ).
thf(decl_sort2,type,
subst: $tType ).
thf(decl_22,type,
one: term ).
thf(decl_23,type,
ap: term > term > term ).
thf(decl_24,type,
lam: term > term ).
thf(decl_25,type,
sub: term > subst > term ).
thf(decl_26,type,
id: subst ).
thf(decl_27,type,
sh: subst ).
thf(decl_28,type,
push: term > subst > subst ).
thf(decl_29,type,
comp: subst > subst > subst ).
thf(decl_30,type,
var: term > $o ).
thf(decl_33,type,
axmap: $o ).
thf(decl_35,type,
shinj: $o ).
thf(decl_38,type,
hoasap: subst > term > subst > term > term ).
thf(decl_39,type,
induction2lem: $o ).
thf(decl_41,type,
axvarshift: $o ).
thf(decl_42,type,
hoasapinj2: $o ).
thf(decl_44,type,
hoasapinj1: $o ).
thf(decl_45,type,
ulamvar1: $o ).
thf(decl_48,type,
apnotvar: $o ).
thf(decl_53,type,
hoaslaminj: $o ).
thf(decl_67,type,
axapp: $o ).
thf(decl_71,type,
ulamvarind: $o ).
thf(decl_72,type,
induction: $o ).
thf(decl_77,type,
hoaslamnotap_gthm: $o ).
thf(decl_82,type,
axclos: $o ).
thf(decl_83,type,
axassoc: $o ).
thf(decl_86,type,
apinj2: $o ).
thf(decl_87,type,
apinj1: $o ).
thf(decl_92,type,
axvarcons: $o ).
thf(decl_93,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(decl_94,type,
axscons: $o ).
thf(decl_96,type,
axidr: $o ).
thf(decl_98,type,
laminj: $o ).
thf(decl_102,type,
axabs: $o ).
thf(decl_108,type,
lamnotap: $o ).
thf(decl_111,type,
axidl: $o ).
thf(decl_116,type,
pushprop: $o ).
thf(decl_120,type,
substmonoid: $o ).
thf(decl_121,type,
lamnotvar: $o ).
thf(decl_128,type,
hoaslamnotap: $o ).
thf(decl_130,type,
ulamvarsh: $o ).
thf(decl_131,type,
induction2: $o ).
thf(decl_136,type,
axshiftcons: $o ).
thf(decl_137,type,
termmset: $o ).
thf(decl_142,type,
axvarid: $o ).
thf(decl_144,type,
esk1_1: ( term > $o ) > term ).
thf(decl_145,type,
esk2_1: ( term > $o ) > term ).
thf(decl_146,type,
esk3_1: ( term > $o ) > term ).
thf(decl_147,type,
esk4_1: ( term > $o ) > term ).
thf(decl_148,type,
esk5_1: ( term > $o ) > term ).
thf(decl_149,type,
esk6_3: ( term > $o ) > term > subst > term ).
thf(decl_150,type,
esk7_1: ( term > $o ) > term ).
thf(decl_151,type,
esk8_1: ( term > $o ) > term ).
thf(decl_152,type,
esk9_1: ( term > $o ) > term ).
thf(decl_153,type,
esk10_3: ( term > $o ) > term > subst > term ).
thf(decl_154,type,
esk11_1: ( term > $o ) > term ).
thf(decl_155,type,
esk12_1: ( term > $o ) > term ).
thf(decl_156,type,
esk13_1: ( term > $o ) > term ).
thf(decl_157,type,
esk14_1: ( term > $o ) > term ).
thf(decl_158,type,
esk15_1: ( subst > term > term ) > subst ).
thf(decl_159,type,
esk16_1: ( subst > term > term ) > term ).
thf(decl_160,type,
esk17_1: ( subst > term > term ) > subst ).
thf(decl_161,type,
esk18_2: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(decl_162,type,
esk19_2: ( subst > term > term ) > ( subst > term > term ) > term ).
thf(decl_163,type,
esk20_2: ( subst > term > term ) > ( subst > term > term ) > subst ).
thf(decl_164,type,
esk21_0: subst > term > term ).
thf(decl_165,type,
esk22_0: term ).
thf(decl_166,type,
esk23_0: term ).
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/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',hoaslamnotap) ).
thf(hoaslamnotap_gthm,axiom,
( hoaslamnotap_gthm
<=> ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslamnotap_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/benchmark/Axioms/ALG003^0.ax',axapp) ).
thf(axvarcons,axiom,
( axvarcons
<=> ! [X1: term,X3: subst] :
( ( sub @ one @ ( push @ X1 @ X3 ) )
= X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axvarcons) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',axclos) ).
thf(axidl,axiom,
( axidl
<=> ! [X3: subst] :
( ( comp @ id @ X3 )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axidl) ).
thf(axshiftcons,axiom,
( axshiftcons
<=> ! [X1: term,X3: subst] :
( ( comp @ sh @ ( push @ X1 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',axmap) ).
thf(axidr,axiom,
( axidr
<=> ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axidr) ).
thf(axvarshift,axiom,
( axvarshift
<=> ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axvarshift) ).
thf(axscons,axiom,
( axscons
<=> ! [X3: subst] :
( ( push @ ( sub @ one @ X3 ) @ ( comp @ sh @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axscons) ).
thf(ulamvar1,axiom,
( ulamvar1
<=> ( var @ one ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',ulamvar1) ).
thf(ulamvarsh,axiom,
( ulamvarsh
<=> ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',apinj2) ).
thf(laminj,axiom,
( laminj
<=> ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',laminj) ).
thf(shinj,axiom,
( shinj
<=> ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',shinj) ).
thf(lamnotap,axiom,
( lamnotap
<=> ! [X1: term,X2: term,X7: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X7 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',lamnotap) ).
thf(apnotvar,axiom,
( apnotvar
<=> ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',apnotvar) ).
thf(lamnotvar,axiom,
( lamnotvar
<=> ! [X1: term] :
~ ( var @ ( lam @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',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/benchmark/Axioms/ALG003^0.ax',hoasapinj2) ).
thf(thm,conjecture,
hoaslamnotap_gthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(hoaslam,axiom,
( hoaslam
= ( ^ [X3: subst,X12: subst > term > term] : ( lam @ ( X12 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslam) ).
thf(hoasap,axiom,
( hoasap
= ( ^ [X3: subst,X1: term,X4: subst,X2: term] : ( ap @ ( sub @ X1 @ X4 ) @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasap) ).
thf(c_0_36,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_37,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_38,axiom,
( hoaslamnotap_gthm
= ( ! [X1371: term,X1372: term,X1373: subst] :
( ( sub @ ( ap @ X1371 @ X1372 ) @ X1373 )
= ( ap @ ( sub @ X1371 @ X1373 ) @ ( sub @ X1372 @ X1373 ) ) )
=> ( ! [X1374: term,X1375: subst] :
( ( sub @ one @ ( push @ X1374 @ X1375 ) )
= X1374 )
=> ( ! [X1376: term] :
( ( sub @ X1376 @ id )
= X1376 )
=> ( ! [X1377: term,X1378: subst] :
( ( sub @ ( lam @ X1377 ) @ X1378 )
= ( lam @ ( sub @ X1377 @ ( push @ one @ ( comp @ X1378 @ sh ) ) ) ) )
=> ( ! [X1379: term,X1380: subst,X1381: subst] :
( ( sub @ ( sub @ X1379 @ X1380 ) @ X1381 )
= ( sub @ X1379 @ ( comp @ X1380 @ X1381 ) ) )
=> ( ! [X1382: subst] :
( ( comp @ id @ X1382 )
= X1382 )
=> ( ! [X1383: term,X1384: subst] :
( ( comp @ sh @ ( push @ X1383 @ X1384 ) )
= X1384 )
=> ( ! [X1385: subst,X1386: subst,X1387: subst] :
( ( comp @ ( comp @ X1385 @ X1386 ) @ X1387 )
= ( comp @ X1385 @ ( comp @ X1386 @ X1387 ) ) )
=> ( ! [X1388: term,X1389: subst,X1390: subst] :
( ( comp @ ( push @ X1388 @ X1389 ) @ X1390 )
= ( push @ ( sub @ X1388 @ X1390 ) @ ( comp @ X1389 @ X1390 ) ) )
=> ( ! [X1391: subst] :
( ( comp @ X1391 @ id )
= X1391 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X1392: subst] :
( ( push @ ( sub @ one @ X1392 ) @ ( comp @ sh @ X1392 ) )
= X1392 )
=> ( ( var @ one )
=> ( ! [X1393: term] :
( ( var @ X1393 )
=> ( var @ ( sub @ X1393 @ sh ) ) )
=> ( ! [X1394: term > $o] :
( ( X1394 @ one )
=> ( ! [X1395: term] :
( ( var @ X1395 )
=> ( ( X1394 @ X1395 )
=> ( X1394 @ ( sub @ X1395 @ sh ) ) ) )
=> ! [X1396: term] :
( ( var @ X1396 )
=> ( X1394 @ X1396 ) ) ) )
=> ( ! [X1397: term,X1398: term,X1399: term,X1400: term] :
( ( ( ap @ X1397 @ X1399 )
= ( ap @ X1398 @ X1400 ) )
=> ( X1397 = X1398 ) )
=> ( ! [X1401: term,X1402: term,X1403: term,X1404: term] :
( ( ( ap @ X1401 @ X1403 )
= ( ap @ X1402 @ X1404 ) )
=> ( X1403 = X1404 ) )
=> ( ! [X1405: term,X1406: term] :
( ( ( lam @ X1405 )
= ( lam @ X1406 ) )
=> ( X1405 = X1406 ) )
=> ( ! [X1407: term,X1408: term] :
( ( ( sub @ X1407 @ sh )
= ( sub @ X1408 @ sh ) )
=> ( X1407 = X1408 ) )
=> ( ! [X1409: term,X1410: term,X1411: term] :
( ( lam @ X1409 )
!= ( ap @ X1410 @ X1411 ) )
=> ( ! [X1412: term,X1413: term] :
~ ( var @ ( ap @ X1412 @ X1413 ) )
=> ( ! [X1414: term] :
~ ( var @ ( lam @ X1414 ) )
=> ( ! [X1415: term > $o] :
( ! [X1416: term] :
( ( var @ X1416 )
=> ( X1415 @ X1416 ) )
=> ( ! [X1417: term,X1418: term] :
( ( X1415 @ X1417 )
=> ( ( X1415 @ X1418 )
=> ( X1415 @ ( ap @ X1417 @ X1418 ) ) ) )
=> ( ! [X1419: term] :
( ( X1415 @ X1419 )
=> ( X1415 @ ( lam @ X1419 ) ) )
=> ! [X1420: term] : ( X1415 @ X1420 ) ) ) )
=> ( ! [X1421: term > $o,X1422: term,X1423: subst] :
( ! [X1424: term] :
( ( var @ X1424 )
=> ( X1421 @ ( sub @ X1424 @ X1423 ) ) )
=> ( ( X1421 @ X1422 )
=> ! [X1425: term] :
( ( var @ X1425 )
=> ( X1421 @ ( sub @ X1425 @ ( push @ X1422 @ X1423 ) ) ) ) ) )
=> ( ! [X1426: term > $o] :
( ! [X1427: term,X1428: term] :
( ( X1426 @ X1427 )
=> ( ( X1426 @ X1428 )
=> ( X1426 @ ( ap @ X1427 @ X1428 ) ) ) )
=> ( ! [X1429: term] :
( ! [X1430: term] :
( ( X1426 @ X1430 )
=> ( X1426 @ ( sub @ X1429 @ ( push @ X1430 @ id ) ) ) )
=> ( X1426 @ ( lam @ X1429 ) ) )
=> ! [X1431: term,X1432: subst] :
( ! [X1433: term] :
( ( var @ X1433 )
=> ( X1426 @ ( sub @ X1433 @ X1432 ) ) )
=> ( X1426 @ ( sub @ X1431 @ X1432 ) ) ) ) )
=> ( ! [X1434: term > $o] :
( ! [X1435: term] :
( ( var @ X1435 )
=> ( X1434 @ X1435 ) )
=> ( ! [X1436: term,X1437: term] :
( ( X1434 @ X1436 )
=> ( ( X1434 @ X1437 )
=> ( X1434 @ ( ap @ X1436 @ X1437 ) ) ) )
=> ( ! [X1438: term] :
( ! [X1439: term] :
( ( X1434 @ X1439 )
=> ( X1434 @ ( sub @ X1438 @ ( push @ X1439 @ id ) ) ) )
=> ( X1434 @ ( lam @ X1438 ) ) )
=> ! [X1440: term] : ( X1434 @ X1440 ) ) ) )
=> ( ( ! [X1441: subst,X1442: subst,X1443: subst] :
( ( comp @ ( comp @ X1441 @ X1442 ) @ X1443 )
= ( comp @ X1441 @ ( comp @ X1442 @ X1443 ) ) )
& ! [X1444: subst] :
( ( comp @ id @ X1444 )
= X1444 )
& ! [X1445: subst] :
( ( comp @ X1445 @ id )
= X1445 ) )
=> ( ( ! [X1446: term,X1447: subst,X1448: subst] :
( ( sub @ ( sub @ X1446 @ X1447 ) @ X1448 )
= ( sub @ X1446 @ ( comp @ X1447 @ X1448 ) ) )
& ! [X1449: term] :
( ( sub @ X1449 @ id )
= X1449 ) )
=> ( ! [X1450: term,X1451: term,X1452: term,X1453: term] :
( ( ( hoasap @ id @ X1450 @ id @ X1452 )
= ( hoasap @ id @ X1451 @ id @ X1453 ) )
=> ( X1450 = X1451 ) )
=> ( ! [X1454: term,X1455: term,X1456: term,X1457: term] :
( ( ( hoasap @ id @ X1454 @ id @ X1456 )
= ( hoasap @ id @ X1455 @ id @ X1457 ) )
=> ( X1456 = X1457 ) )
=> ( ! [X1458: subst > term > term] :
( ! [X1459: subst,X1460: term,X1461: subst] :
( ( sub @ ( X1458 @ X1459 @ X1460 ) @ X1461 )
= ( X1458 @ ( comp @ X1459 @ X1461 ) @ ( sub @ X1460 @ X1461 ) ) )
=> ! [X1462: subst > term > term] :
( ! [X1463: subst,X1464: term,X1465: subst] :
( ( sub @ ( X1462 @ X1463 @ X1464 ) @ X1465 )
= ( X1462 @ ( comp @ X1463 @ X1465 ) @ ( sub @ X1464 @ X1465 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X1458 @ Z0 @ Z1 ) )
= ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X1462 @ Z0 @ Z1 ) ) )
=> ! [X1466: subst,X1467: term] :
( ( X1458 @ X1466 @ X1467 )
= ( X1462 @ X1466 @ X1467 ) ) ) ) )
=> ! [X1468: subst > term > term] :
( ! [X1469: subst,X1470: term,X1471: subst] :
( ( sub @ ( X1468 @ X1469 @ X1470 ) @ X1471 )
= ( X1468 @ ( comp @ X1469 @ X1471 ) @ ( sub @ X1470 @ X1471 ) ) )
=> ! [X1472: term,X1473: term] :
( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X1468 @ Z0 @ Z1 ) )
!= ( hoasap @ id @ X1472 @ id @ X1473 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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)],[hoaslamnotap_gthm,axapp]),axvarcons]),axvarid]),axabs]),axclos]),axidl]),axshiftcons]),axassoc]),axmap]),axidr]),axvarshift]),axscons]),ulamvar1]),ulamvarsh]),ulamvarind]),apinj1]),apinj2]),laminj]),shinj]),lamnotap]),apnotvar]),lamnotvar]),induction]),pushprop]),induction2lem]),induction2]),substmonoid]),termmset]),hoasapinj1]),hoasapinj2]),c_0_36]),c_0_37]) ).
thf(c_0_39,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[thm]),c_0_38])])]) ).
thf(c_0_40,plain,
! [X3480: subst,X3481: subst > term > term] :
( ( hoaslam @ X3480 @ X3481 )
= ( lam @ ( X3481 @ sh @ one ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoaslam])]) ).
thf(c_0_41,negated_conjecture,
! [X3488: term,X3489: term,X3490: subst,X3491: term,X3492: subst,X3493: term,X3494: term,X3495: subst,X3496: term,X3497: subst,X3498: subst,X3499: subst,X3500: term,X3501: subst,X3502: subst,X3503: subst,X3504: subst,X3505: term,X3506: subst,X3507: subst,X3508: subst,X3509: subst,X3510: term,X3511: term > $o,X3513: term,X3514: term,X3515: term,X3516: term,X3517: term,X3518: term,X3519: term,X3520: term,X3521: term,X3522: term,X3523: term,X3524: term,X3525: term,X3526: term,X3527: term,X3528: term,X3529: term,X3530: term,X3531: term,X3532: term > $o,X3537: term,X3538: term > $o,X3539: term,X3540: subst,X3542: term,X3543: term > $o,X3547: term,X3548: term,X3549: subst,X3551: term > $o,X3556: term,X3557: term,X3558: subst,X3559: subst,X3560: subst,X3561: subst,X3562: subst,X3563: term,X3564: subst,X3565: subst,X3566: term,X3567: term,X3568: term,X3569: term,X3570: term,X3571: term,X3572: term,X3573: term,X3574: term,X3575: subst > term > term,X3579: subst > term > term,X3583: subst,X3584: term,X3586: subst,X3587: term,X3588: subst] :
( ( ( sub @ ( ap @ X3488 @ X3489 ) @ X3490 )
= ( ap @ ( sub @ X3488 @ X3490 ) @ ( sub @ X3489 @ X3490 ) ) )
& ( ( sub @ one @ ( push @ X3491 @ X3492 ) )
= X3491 )
& ( ( sub @ X3493 @ id )
= X3493 )
& ( ( sub @ ( lam @ X3494 ) @ X3495 )
= ( lam @ ( sub @ X3494 @ ( push @ one @ ( comp @ X3495 @ sh ) ) ) ) )
& ( ( sub @ ( sub @ X3496 @ X3497 ) @ X3498 )
= ( sub @ X3496 @ ( comp @ X3497 @ X3498 ) ) )
& ( ( comp @ id @ X3499 )
= X3499 )
& ( ( comp @ sh @ ( push @ X3500 @ X3501 ) )
= X3501 )
& ( ( comp @ ( comp @ X3502 @ X3503 ) @ X3504 )
= ( comp @ X3502 @ ( comp @ X3503 @ X3504 ) ) )
& ( ( comp @ ( push @ X3505 @ X3506 ) @ X3507 )
= ( push @ ( sub @ X3505 @ X3507 ) @ ( comp @ X3506 @ X3507 ) ) )
& ( ( comp @ X3508 @ id )
= X3508 )
& ( ( push @ one @ sh )
= id )
& ( ( push @ ( sub @ one @ X3509 ) @ ( comp @ sh @ X3509 ) )
= X3509 )
& ( var @ one )
& ( ~ ( var @ X3510 )
| ( var @ ( sub @ X3510 @ sh ) ) )
& ( ( var @ ( esk1_1 @ X3511 ) )
| ~ ( var @ X3513 )
| ( X3511 @ X3513 )
| ~ ( X3511 @ one ) )
& ( ( X3511 @ ( esk1_1 @ X3511 ) )
| ~ ( var @ X3513 )
| ( X3511 @ X3513 )
| ~ ( X3511 @ one ) )
& ( ~ ( X3511 @ ( sub @ ( esk1_1 @ X3511 ) @ sh ) )
| ~ ( var @ X3513 )
| ( X3511 @ X3513 )
| ~ ( X3511 @ one ) )
& ( ( ( ap @ X3514 @ X3516 )
!= ( ap @ X3515 @ X3517 ) )
| ( X3514 = X3515 ) )
& ( ( ( ap @ X3518 @ X3520 )
!= ( ap @ X3519 @ X3521 ) )
| ( X3520 = X3521 ) )
& ( ( ( lam @ X3522 )
!= ( lam @ X3523 ) )
| ( X3522 = X3523 ) )
& ( ( ( sub @ X3524 @ sh )
!= ( sub @ X3525 @ sh ) )
| ( X3524 = X3525 ) )
& ( ( lam @ X3526 )
!= ( ap @ X3527 @ X3528 ) )
& ~ ( var @ ( ap @ X3529 @ X3530 ) )
& ~ ( var @ ( lam @ X3531 ) )
& ( ( X3532 @ ( esk5_1 @ X3532 ) )
| ( X3532 @ X3537 )
| ( X3532 @ ( esk3_1 @ X3532 ) )
| ( var @ ( esk2_1 @ X3532 ) ) )
& ( ~ ( X3532 @ ( lam @ ( esk5_1 @ X3532 ) ) )
| ( X3532 @ X3537 )
| ( X3532 @ ( esk3_1 @ X3532 ) )
| ( var @ ( esk2_1 @ X3532 ) ) )
& ( ( X3532 @ ( esk5_1 @ X3532 ) )
| ( X3532 @ X3537 )
| ( X3532 @ ( esk4_1 @ X3532 ) )
| ( var @ ( esk2_1 @ X3532 ) ) )
& ( ~ ( X3532 @ ( lam @ ( esk5_1 @ X3532 ) ) )
| ( X3532 @ X3537 )
| ( X3532 @ ( esk4_1 @ X3532 ) )
| ( var @ ( esk2_1 @ X3532 ) ) )
& ( ( X3532 @ ( esk5_1 @ X3532 ) )
| ( X3532 @ X3537 )
| ~ ( X3532 @ ( ap @ ( esk3_1 @ X3532 ) @ ( esk4_1 @ X3532 ) ) )
| ( var @ ( esk2_1 @ X3532 ) ) )
& ( ~ ( X3532 @ ( lam @ ( esk5_1 @ X3532 ) ) )
| ( X3532 @ X3537 )
| ~ ( X3532 @ ( ap @ ( esk3_1 @ X3532 ) @ ( esk4_1 @ X3532 ) ) )
| ( var @ ( esk2_1 @ X3532 ) ) )
& ( ( X3532 @ ( esk5_1 @ X3532 ) )
| ( X3532 @ X3537 )
| ( X3532 @ ( esk3_1 @ X3532 ) )
| ~ ( X3532 @ ( esk2_1 @ X3532 ) ) )
& ( ~ ( X3532 @ ( lam @ ( esk5_1 @ X3532 ) ) )
| ( X3532 @ X3537 )
| ( X3532 @ ( esk3_1 @ X3532 ) )
| ~ ( X3532 @ ( esk2_1 @ X3532 ) ) )
& ( ( X3532 @ ( esk5_1 @ X3532 ) )
| ( X3532 @ X3537 )
| ( X3532 @ ( esk4_1 @ X3532 ) )
| ~ ( X3532 @ ( esk2_1 @ X3532 ) ) )
& ( ~ ( X3532 @ ( lam @ ( esk5_1 @ X3532 ) ) )
| ( X3532 @ X3537 )
| ( X3532 @ ( esk4_1 @ X3532 ) )
| ~ ( X3532 @ ( esk2_1 @ X3532 ) ) )
& ( ( X3532 @ ( esk5_1 @ X3532 ) )
| ( X3532 @ X3537 )
| ~ ( X3532 @ ( ap @ ( esk3_1 @ X3532 ) @ ( esk4_1 @ X3532 ) ) )
| ~ ( X3532 @ ( esk2_1 @ X3532 ) ) )
& ( ~ ( X3532 @ ( lam @ ( esk5_1 @ X3532 ) ) )
| ( X3532 @ X3537 )
| ~ ( X3532 @ ( ap @ ( esk3_1 @ X3532 ) @ ( esk4_1 @ X3532 ) ) )
| ~ ( X3532 @ ( esk2_1 @ X3532 ) ) )
& ( ( var @ ( esk6_3 @ X3538 @ X3539 @ X3540 ) )
| ~ ( X3538 @ X3539 )
| ~ ( var @ X3542 )
| ( X3538 @ ( sub @ X3542 @ ( push @ X3539 @ X3540 ) ) ) )
& ( ~ ( X3538 @ ( sub @ ( esk6_3 @ X3538 @ X3539 @ X3540 ) @ X3540 ) )
| ~ ( X3538 @ X3539 )
| ~ ( var @ X3542 )
| ( X3538 @ ( sub @ X3542 @ ( push @ X3539 @ X3540 ) ) ) )
& ( ( var @ ( esk10_3 @ X3543 @ X3548 @ X3549 ) )
| ( X3543 @ ( sub @ X3548 @ X3549 ) )
| ~ ( X3543 @ X3547 )
| ( X3543 @ ( sub @ ( esk9_1 @ X3543 ) @ ( push @ X3547 @ id ) ) )
| ( X3543 @ ( esk7_1 @ X3543 ) ) )
& ( ~ ( X3543 @ ( sub @ ( esk10_3 @ X3543 @ X3548 @ X3549 ) @ X3549 ) )
| ( X3543 @ ( sub @ X3548 @ X3549 ) )
| ~ ( X3543 @ X3547 )
| ( X3543 @ ( sub @ ( esk9_1 @ X3543 ) @ ( push @ X3547 @ id ) ) )
| ( X3543 @ ( esk7_1 @ X3543 ) ) )
& ( ( var @ ( esk10_3 @ X3543 @ X3548 @ X3549 ) )
| ( X3543 @ ( sub @ X3548 @ X3549 ) )
| ~ ( X3543 @ ( lam @ ( esk9_1 @ X3543 ) ) )
| ( X3543 @ ( esk7_1 @ X3543 ) ) )
& ( ~ ( X3543 @ ( sub @ ( esk10_3 @ X3543 @ X3548 @ X3549 ) @ X3549 ) )
| ( X3543 @ ( sub @ X3548 @ X3549 ) )
| ~ ( X3543 @ ( lam @ ( esk9_1 @ X3543 ) ) )
| ( X3543 @ ( esk7_1 @ X3543 ) ) )
& ( ( var @ ( esk10_3 @ X3543 @ X3548 @ X3549 ) )
| ( X3543 @ ( sub @ X3548 @ X3549 ) )
| ~ ( X3543 @ X3547 )
| ( X3543 @ ( sub @ ( esk9_1 @ X3543 ) @ ( push @ X3547 @ id ) ) )
| ( X3543 @ ( esk8_1 @ X3543 ) ) )
& ( ~ ( X3543 @ ( sub @ ( esk10_3 @ X3543 @ X3548 @ X3549 ) @ X3549 ) )
| ( X3543 @ ( sub @ X3548 @ X3549 ) )
| ~ ( X3543 @ X3547 )
| ( X3543 @ ( sub @ ( esk9_1 @ X3543 ) @ ( push @ X3547 @ id ) ) )
| ( X3543 @ ( esk8_1 @ X3543 ) ) )
& ( ( var @ ( esk10_3 @ X3543 @ X3548 @ X3549 ) )
| ( X3543 @ ( sub @ X3548 @ X3549 ) )
| ~ ( X3543 @ ( lam @ ( esk9_1 @ X3543 ) ) )
| ( X3543 @ ( esk8_1 @ X3543 ) ) )
& ( ~ ( X3543 @ ( sub @ ( esk10_3 @ X3543 @ X3548 @ X3549 ) @ X3549 ) )
| ( X3543 @ ( sub @ X3548 @ X3549 ) )
| ~ ( X3543 @ ( lam @ ( esk9_1 @ X3543 ) ) )
| ( X3543 @ ( esk8_1 @ X3543 ) ) )
& ( ( var @ ( esk10_3 @ X3543 @ X3548 @ X3549 ) )
| ( X3543 @ ( sub @ X3548 @ X3549 ) )
| ~ ( X3543 @ X3547 )
| ( X3543 @ ( sub @ ( esk9_1 @ X3543 ) @ ( push @ X3547 @ id ) ) )
| ~ ( X3543 @ ( ap @ ( esk7_1 @ X3543 ) @ ( esk8_1 @ X3543 ) ) ) )
& ( ~ ( X3543 @ ( sub @ ( esk10_3 @ X3543 @ X3548 @ X3549 ) @ X3549 ) )
| ( X3543 @ ( sub @ X3548 @ X3549 ) )
| ~ ( X3543 @ X3547 )
| ( X3543 @ ( sub @ ( esk9_1 @ X3543 ) @ ( push @ X3547 @ id ) ) )
| ~ ( X3543 @ ( ap @ ( esk7_1 @ X3543 ) @ ( esk8_1 @ X3543 ) ) ) )
& ( ( var @ ( esk10_3 @ X3543 @ X3548 @ X3549 ) )
| ( X3543 @ ( sub @ X3548 @ X3549 ) )
| ~ ( X3543 @ ( lam @ ( esk9_1 @ X3543 ) ) )
| ~ ( X3543 @ ( ap @ ( esk7_1 @ X3543 ) @ ( esk8_1 @ X3543 ) ) ) )
& ( ~ ( X3543 @ ( sub @ ( esk10_3 @ X3543 @ X3548 @ X3549 ) @ X3549 ) )
| ( X3543 @ ( sub @ X3548 @ X3549 ) )
| ~ ( X3543 @ ( lam @ ( esk9_1 @ X3543 ) ) )
| ~ ( X3543 @ ( ap @ ( esk7_1 @ X3543 ) @ ( esk8_1 @ X3543 ) ) ) )
& ( ~ ( X3551 @ X3556 )
| ( X3551 @ ( sub @ ( esk14_1 @ X3551 ) @ ( push @ X3556 @ id ) ) )
| ( X3551 @ X3557 )
| ( X3551 @ ( esk12_1 @ X3551 ) )
| ( var @ ( esk11_1 @ X3551 ) ) )
& ( ~ ( X3551 @ ( lam @ ( esk14_1 @ X3551 ) ) )
| ( X3551 @ X3557 )
| ( X3551 @ ( esk12_1 @ X3551 ) )
| ( var @ ( esk11_1 @ X3551 ) ) )
& ( ~ ( X3551 @ X3556 )
| ( X3551 @ ( sub @ ( esk14_1 @ X3551 ) @ ( push @ X3556 @ id ) ) )
| ( X3551 @ X3557 )
| ( X3551 @ ( esk13_1 @ X3551 ) )
| ( var @ ( esk11_1 @ X3551 ) ) )
& ( ~ ( X3551 @ ( lam @ ( esk14_1 @ X3551 ) ) )
| ( X3551 @ X3557 )
| ( X3551 @ ( esk13_1 @ X3551 ) )
| ( var @ ( esk11_1 @ X3551 ) ) )
& ( ~ ( X3551 @ X3556 )
| ( X3551 @ ( sub @ ( esk14_1 @ X3551 ) @ ( push @ X3556 @ id ) ) )
| ( X3551 @ X3557 )
| ~ ( X3551 @ ( ap @ ( esk12_1 @ X3551 ) @ ( esk13_1 @ X3551 ) ) )
| ( var @ ( esk11_1 @ X3551 ) ) )
& ( ~ ( X3551 @ ( lam @ ( esk14_1 @ X3551 ) ) )
| ( X3551 @ X3557 )
| ~ ( X3551 @ ( ap @ ( esk12_1 @ X3551 ) @ ( esk13_1 @ X3551 ) ) )
| ( var @ ( esk11_1 @ X3551 ) ) )
& ( ~ ( X3551 @ X3556 )
| ( X3551 @ ( sub @ ( esk14_1 @ X3551 ) @ ( push @ X3556 @ id ) ) )
| ( X3551 @ X3557 )
| ( X3551 @ ( esk12_1 @ X3551 ) )
| ~ ( X3551 @ ( esk11_1 @ X3551 ) ) )
& ( ~ ( X3551 @ ( lam @ ( esk14_1 @ X3551 ) ) )
| ( X3551 @ X3557 )
| ( X3551 @ ( esk12_1 @ X3551 ) )
| ~ ( X3551 @ ( esk11_1 @ X3551 ) ) )
& ( ~ ( X3551 @ X3556 )
| ( X3551 @ ( sub @ ( esk14_1 @ X3551 ) @ ( push @ X3556 @ id ) ) )
| ( X3551 @ X3557 )
| ( X3551 @ ( esk13_1 @ X3551 ) )
| ~ ( X3551 @ ( esk11_1 @ X3551 ) ) )
& ( ~ ( X3551 @ ( lam @ ( esk14_1 @ X3551 ) ) )
| ( X3551 @ X3557 )
| ( X3551 @ ( esk13_1 @ X3551 ) )
| ~ ( X3551 @ ( esk11_1 @ X3551 ) ) )
& ( ~ ( X3551 @ X3556 )
| ( X3551 @ ( sub @ ( esk14_1 @ X3551 ) @ ( push @ X3556 @ id ) ) )
| ( X3551 @ X3557 )
| ~ ( X3551 @ ( ap @ ( esk12_1 @ X3551 ) @ ( esk13_1 @ X3551 ) ) )
| ~ ( X3551 @ ( esk11_1 @ X3551 ) ) )
& ( ~ ( X3551 @ ( lam @ ( esk14_1 @ X3551 ) ) )
| ( X3551 @ X3557 )
| ~ ( X3551 @ ( ap @ ( esk12_1 @ X3551 ) @ ( esk13_1 @ X3551 ) ) )
| ~ ( X3551 @ ( esk11_1 @ X3551 ) ) )
& ( ( comp @ ( comp @ X3558 @ X3559 ) @ X3560 )
= ( comp @ X3558 @ ( comp @ X3559 @ X3560 ) ) )
& ( ( comp @ id @ X3561 )
= X3561 )
& ( ( comp @ X3562 @ id )
= X3562 )
& ( ( sub @ ( sub @ X3563 @ X3564 ) @ X3565 )
= ( sub @ X3563 @ ( comp @ X3564 @ X3565 ) ) )
& ( ( sub @ X3566 @ id )
= X3566 )
& ( ( ( hoasap @ id @ X3567 @ id @ X3569 )
!= ( hoasap @ id @ X3568 @ id @ X3570 ) )
| ( X3567 = X3568 ) )
& ( ( ( hoasap @ id @ X3571 @ id @ X3573 )
!= ( hoasap @ id @ X3572 @ id @ X3574 ) )
| ( X3573 = X3574 ) )
& ( ( ( sub @ ( X3575 @ ( esk15_1 @ X3575 ) @ ( esk16_1 @ X3575 ) ) @ ( esk17_1 @ X3575 ) )
!= ( X3575 @ ( comp @ ( esk15_1 @ X3575 ) @ ( esk17_1 @ X3575 ) ) @ ( sub @ ( esk16_1 @ X3575 ) @ ( esk17_1 @ X3575 ) ) ) )
| ( ( sub @ ( X3579 @ ( esk18_2 @ X3575 @ X3579 ) @ ( esk19_2 @ X3575 @ X3579 ) ) @ ( esk20_2 @ X3575 @ X3579 ) )
!= ( X3579 @ ( comp @ ( esk18_2 @ X3575 @ X3579 ) @ ( esk20_2 @ X3575 @ X3579 ) ) @ ( sub @ ( esk19_2 @ X3575 @ X3579 ) @ ( esk20_2 @ X3575 @ X3579 ) ) ) )
| ( ( hoaslam @ id @ X3575 )
!= ( hoaslam @ id @ X3579 ) )
| ( ( X3575 @ X3583 @ X3584 )
= ( X3579 @ X3583 @ X3584 ) ) )
& ( ( sub @ ( esk21_0 @ X3586 @ X3587 ) @ X3588 )
= ( esk21_0 @ ( comp @ X3586 @ X3588 ) @ ( sub @ X3587 @ X3588 ) ) )
& ( ( hoaslam @ id @ esk21_0 )
= ( hoasap @ id @ esk22_0 @ id @ esk23_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_39])])])])])])]) ).
thf(c_0_42,plain,
! [X3486: subst,X3487: subst > term > term] :
( ( hoaslam @ X3486 @ X3487 )
= ( lam @ ( X3487 @ sh @ one ) ) ),
inference(variable_rename,[status(thm)],[c_0_40]) ).
thf(c_0_43,plain,
! [X3476: subst,X3477: term,X3478: subst,X3479: term] :
( ( hoasap @ X3476 @ X3477 @ X3478 @ X3479 )
= ( ap @ ( sub @ X3477 @ X3478 ) @ X3479 ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoasap])]) ).
thf(c_0_44,negated_conjecture,
( ( hoaslam @ id @ esk21_0 )
= ( hoasap @ id @ esk22_0 @ id @ esk23_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_45,plain,
! [X3: subst,X12: subst > term > term] :
( ( hoaslam @ X3 @ X12 )
= ( lam @ ( X12 @ sh @ one ) ) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_46,plain,
! [X3482: subst,X3483: term,X3484: subst,X3485: term] :
( ( hoasap @ X3482 @ X3483 @ X3484 @ X3485 )
= ( ap @ ( sub @ X3483 @ X3484 ) @ X3485 ) ),
inference(variable_rename,[status(thm)],[c_0_43]) ).
thf(c_0_47,negated_conjecture,
( ( hoasap @ id @ esk22_0 @ id @ esk23_0 )
= ( lam @ ( esk21_0 @ sh @ one ) ) ),
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
thf(c_0_48,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_46]) ).
thf(c_0_49,negated_conjecture,
! [X1: term] :
( ( sub @ X1 @ id )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_50,negated_conjecture,
! [X1: term,X2: term,X7: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X7 ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_51,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG259^1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat May 18 23:17:22 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.18/0.47 Running higher-order theorem proving
% 0.18/0.47 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/benchmark/theBenchmark.p
% 0.18/0.53 # Version: 3.1.0-ho
% 0.18/0.53 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.53 # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.53 # Starting post_as_ho5 with 300s (1) cores
% 0.18/0.53 # Starting post_as_ho10 with 300s (1) cores
% 0.18/0.53 # post_as_ho10 with pid 26186 completed with status 0
% 0.18/0.53 # Result found by post_as_ho10
% 0.18/0.53 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.53 # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.53 # Starting post_as_ho5 with 300s (1) cores
% 0.18/0.53 # Starting post_as_ho10 with 300s (1) cores
% 0.18/0.53 # No SInE strategy applied
% 0.18/0.53 # Search class: HGUSM-FFMS31-MHFMMMBN
% 0.18/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.53 # Starting new_ho_10 with 163s (1) cores
% 0.18/0.53 # new_ho_10 with pid 26188 completed with status 0
% 0.18/0.53 # Result found by new_ho_10
% 0.18/0.53 # Preprocessing class: HSMMSLSSLLLNHFA.
% 0.18/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.53 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.18/0.53 # Starting post_as_ho1 with 300s (1) cores
% 0.18/0.53 # Starting post_as_ho5 with 300s (1) cores
% 0.18/0.53 # Starting post_as_ho10 with 300s (1) cores
% 0.18/0.53 # No SInE strategy applied
% 0.18/0.53 # Search class: HGUSM-FFMS31-MHFMMMBN
% 0.18/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.18/0.53 # Starting new_ho_10 with 163s (1) cores
% 0.18/0.53 # Preprocessing time : 0.004 s
% 0.18/0.53 # Presaturation interreduction done
% 0.18/0.53
% 0.18/0.53 # Proof found!
% 0.18/0.53 # SZS status Theorem
% 0.18/0.53 # SZS output start CNFRefutation
% See solution above
% 0.18/0.53 # Parsed axioms : 238
% 0.18/0.53 # Removed by relevancy pruning/SinE : 0
% 0.18/0.53 # Initial clauses : 198
% 0.18/0.53 # Removed in clause preprocessing : 124
% 0.18/0.53 # Initial clauses in saturation : 74
% 0.18/0.53 # Processed clauses : 34
% 0.18/0.53 # ...of these trivial : 5
% 0.18/0.53 # ...subsumed : 0
% 0.18/0.53 # ...remaining for further processing : 29
% 0.18/0.53 # Other redundant clauses eliminated : 0
% 0.18/0.53 # Clauses deleted for lack of memory : 0
% 0.18/0.53 # Backward-subsumed : 0
% 0.18/0.53 # Backward-rewritten : 4
% 0.18/0.53 # Generated clauses : 0
% 0.18/0.53 # ...of the previous two non-redundant : 3
% 0.18/0.53 # ...aggressively subsumed : 0
% 0.18/0.53 # Contextual simplify-reflections : 0
% 0.18/0.53 # Paramodulations : 0
% 0.18/0.53 # Factorizations : 0
% 0.18/0.53 # NegExts : 0
% 0.18/0.53 # Equation resolutions : 0
% 0.18/0.53 # Disequality decompositions : 0
% 0.18/0.53 # Total rewrite steps : 16
% 0.18/0.53 # ...of those cached : 1
% 0.18/0.53 # Propositional unsat checks : 0
% 0.18/0.53 # Propositional check models : 0
% 0.18/0.53 # Propositional check unsatisfiable : 0
% 0.18/0.53 # Propositional clauses : 0
% 0.18/0.53 # Propositional clauses after purity: 0
% 0.18/0.53 # Propositional unsat core size : 0
% 0.18/0.53 # Propositional preprocessing time : 0.000
% 0.18/0.53 # Propositional encoding time : 0.000
% 0.18/0.53 # Propositional solver time : 0.000
% 0.18/0.53 # Success case prop preproc time : 0.000
% 0.18/0.53 # Success case prop encoding time : 0.000
% 0.18/0.53 # Success case prop solver time : 0.000
% 0.18/0.53 # Current number of processed clauses : 25
% 0.18/0.53 # Positive orientable unit clauses : 13
% 0.18/0.53 # Positive unorientable unit clauses: 0
% 0.18/0.53 # Negative unit clauses : 3
% 0.18/0.53 # Non-unit-clauses : 9
% 0.18/0.53 # Current number of unprocessed clauses: 41
% 0.18/0.53 # ...number of literals in the above : 167
% 0.18/0.53 # Current number of archived formulas : 0
% 0.18/0.53 # Current number of archived clauses : 4
% 0.18/0.53 # Clause-clause subsumption calls (NU) : 14
% 0.18/0.53 # Rec. Clause-clause subsumption calls : 8
% 0.18/0.53 # Non-unit clause-clause subsumptions : 0
% 0.18/0.53 # Unit Clause-clause subsumption calls : 4
% 0.18/0.53 # Rewrite failures with RHS unbound : 0
% 0.18/0.53 # BW rewrite match attempts : 6
% 0.18/0.53 # BW rewrite match successes : 6
% 0.18/0.53 # Condensation attempts : 34
% 0.18/0.53 # Condensation successes : 0
% 0.18/0.53 # Termbank termtop insertions : 32341
% 0.18/0.53 # Search garbage collected termcells : 4064
% 0.18/0.53
% 0.18/0.53 # -------------------------------------------------
% 0.18/0.53 # User time : 0.023 s
% 0.18/0.53 # System time : 0.011 s
% 0.18/0.53 # Total time : 0.034 s
% 0.18/0.53 # Maximum resident set size: 6056 pages
% 0.18/0.53
% 0.18/0.53 # -------------------------------------------------
% 0.18/0.53 # User time : 0.031 s
% 0.18/0.53 # System time : 0.013 s
% 0.18/0.53 # Total time : 0.045 s
% 0.18/0.53 # Maximum resident set size: 2072 pages
% 0.18/0.53 % E---3.1 exiting
% 0.18/0.53 % E exiting
%------------------------------------------------------------------------------