%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ALG258^1 : 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 : n026.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 07:44:55 AM UTC 2026
% Result : Theorem 0.61s 0.38s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 34
% Syntax : Number of formulae : 57 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 295 ( 161 equ; 0 cnn)
% Maximal formula atoms : 64 ( 5 avg)
% Number of connectives : 2031 ( 97 ~; 144 |; 81 &;1457 @)
% ( 33 <=>; 219 =>; 0 <=; 0 <~>)
% Maximal formula depth : 152 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 44 ( 44 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 61 usr; 38 con; 0-4 aty)
% Number of variables : 423 ( 14 ^; 409 !; 0 ?; 423 :)
% 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_68,type,
axapp: $o ).
thf(decl_72,type,
ulamvarind: $o ).
thf(decl_73,type,
induction: $o ).
thf(decl_83,type,
axclos: $o ).
thf(decl_84,type,
axassoc: $o ).
thf(decl_87,type,
apinj2: $o ).
thf(decl_88,type,
apinj1: $o ).
thf(decl_93,type,
axvarcons: $o ).
thf(decl_94,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(decl_95,type,
axscons: $o ).
thf(decl_97,type,
axidr: $o ).
thf(decl_99,type,
laminj: $o ).
thf(decl_103,type,
axabs: $o ).
thf(decl_109,type,
lamnotap: $o ).
thf(decl_112,type,
axidl: $o ).
thf(decl_113,type,
hoaslaminj_gthm: $o ).
thf(decl_117,type,
pushprop: $o ).
thf(decl_121,type,
substmonoid: $o ).
thf(decl_122,type,
lamnotvar: $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_0: subst > term > term ).
thf(decl_160,type,
esk16_0: subst > term > term ).
thf(decl_161,type,
esk17_0: subst ).
thf(decl_162,type,
esk18_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/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',hoaslaminj) ).
thf(thm,conjecture,
hoaslaminj_gthm,
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',thm) ).
thf(hoaslaminj_gthm,axiom,
( hoaslaminj_gthm
<=> ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> hoaslaminj ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',hoaslaminj_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.1O41S5OEI9/E---3.1_922373.p',axapp) ).
thf(axvarcons,axiom,
( axvarcons
<=> ! [X1: term,X3: subst] :
( ( sub @ one @ ( push @ X1 @ X3 ) )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',axvarcons) ).
thf(axvarid,axiom,
( axvarid
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.p',axclos) ).
thf(axidl,axiom,
( axidl
<=> ! [X3: subst] :
( ( comp @ id @ X3 )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',axidl) ).
thf(axshiftcons,axiom,
( axshiftcons
<=> ! [X1: term,X3: subst] :
( ( comp @ sh @ ( push @ X1 @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.p',axmap) ).
thf(axidr,axiom,
( axidr
<=> ! [X3: subst] :
( ( comp @ X3 @ id )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',axidr) ).
thf(axvarshift,axiom,
( axvarshift
<=> ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',axvarshift) ).
thf(axscons,axiom,
( axscons
<=> ! [X3: subst] :
( ( push @ ( sub @ one @ X3 ) @ ( comp @ sh @ X3 ) )
= X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',axscons) ).
thf(ulamvar1,axiom,
( ulamvar1
<=> ( var @ one ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',ulamvar1) ).
thf(ulamvarsh,axiom,
( ulamvarsh
<=> ! [X1: term] :
( ( var @ X1 )
=> ( var @ ( sub @ X1 @ sh ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.p',apinj2) ).
thf(laminj,axiom,
( laminj
<=> ! [X1: term,X2: term] :
( ( ( lam @ X1 )
= ( lam @ X2 ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',laminj) ).
thf(shinj,axiom,
( shinj
<=> ! [X1: term,X2: term] :
( ( ( sub @ X1 @ sh )
= ( sub @ X2 @ sh ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',shinj) ).
thf(lamnotap,axiom,
( lamnotap
<=> ! [X1: term,X2: term,X7: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X7 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',lamnotap) ).
thf(apnotvar,axiom,
( apnotvar
<=> ! [X1: term,X2: term] :
~ ( var @ ( ap @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',apnotvar) ).
thf(lamnotvar,axiom,
( lamnotvar
<=> ! [X1: term] :
~ ( var @ ( lam @ X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.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.1O41S5OEI9/E---3.1_922373.p',hoasapinj2) ).
thf(hoaslam,axiom,
( hoaslam
= ( ^ [X3: subst,X12: subst > term > term] : ( lam @ ( X12 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.1O41S5OEI9/E---3.1_922373.p',hoaslam) ).
thf(c_0_34,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_35,negated_conjecture,
~ hoaslaminj_gthm,
inference(assume_negation,[status(cth)],[thm]) ).
thf(c_0_36,axiom,
( hoaslaminj_gthm
= ( ! [X2551: term,X2552: term,X2553: subst] :
( ( sub @ ( ap @ X2551 @ X2552 ) @ X2553 )
= ( ap @ ( sub @ X2551 @ X2553 ) @ ( sub @ X2552 @ X2553 ) ) )
=> ( ! [X2554: term,X2555: subst] :
( ( sub @ one @ ( push @ X2554 @ X2555 ) )
= X2554 )
=> ( ! [X2556: term] :
( ( sub @ X2556 @ id )
= X2556 )
=> ( ! [X2557: term,X2558: subst] :
( ( sub @ ( lam @ X2557 ) @ X2558 )
= ( lam @ ( sub @ X2557 @ ( push @ one @ ( comp @ X2558 @ sh ) ) ) ) )
=> ( ! [X2559: term,X2560: subst,X2561: subst] :
( ( sub @ ( sub @ X2559 @ X2560 ) @ X2561 )
= ( sub @ X2559 @ ( comp @ X2560 @ X2561 ) ) )
=> ( ! [X2562: subst] :
( ( comp @ id @ X2562 )
= X2562 )
=> ( ! [X2563: term,X2564: subst] :
( ( comp @ sh @ ( push @ X2563 @ X2564 ) )
= X2564 )
=> ( ! [X2565: subst,X2566: subst,X2567: subst] :
( ( comp @ ( comp @ X2565 @ X2566 ) @ X2567 )
= ( comp @ X2565 @ ( comp @ X2566 @ X2567 ) ) )
=> ( ! [X2568: term,X2569: subst,X2570: subst] :
( ( comp @ ( push @ X2568 @ X2569 ) @ X2570 )
= ( push @ ( sub @ X2568 @ X2570 ) @ ( comp @ X2569 @ X2570 ) ) )
=> ( ! [X2571: subst] :
( ( comp @ X2571 @ id )
= X2571 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X2572: subst] :
( ( push @ ( sub @ one @ X2572 ) @ ( comp @ sh @ X2572 ) )
= X2572 )
=> ( ( var @ one )
=> ( ! [X2573: term] :
( ( var @ X2573 )
=> ( var @ ( sub @ X2573 @ sh ) ) )
=> ( ! [X2574: term > $o] :
( ( X2574 @ one )
=> ( ! [X2575: term] :
( ( var @ X2575 )
=> ( ( X2574 @ X2575 )
=> ( X2574 @ ( sub @ X2575 @ sh ) ) ) )
=> ! [X2576: term] :
( ( var @ X2576 )
=> ( X2574 @ X2576 ) ) ) )
=> ( ! [X2577: term,X2578: term,X2579: term,X2580: term] :
( ( ( ap @ X2577 @ X2579 )
= ( ap @ X2578 @ X2580 ) )
=> ( X2577 = X2578 ) )
=> ( ! [X2581: term,X2582: term,X2583: term,X2584: term] :
( ( ( ap @ X2581 @ X2583 )
= ( ap @ X2582 @ X2584 ) )
=> ( X2583 = X2584 ) )
=> ( ! [X2585: term,X2586: term] :
( ( ( lam @ X2585 )
= ( lam @ X2586 ) )
=> ( X2585 = X2586 ) )
=> ( ! [X2587: term,X2588: term] :
( ( ( sub @ X2587 @ sh )
= ( sub @ X2588 @ sh ) )
=> ( X2587 = X2588 ) )
=> ( ! [X2589: term,X2590: term,X2591: term] :
( ( lam @ X2589 )
!= ( ap @ X2590 @ X2591 ) )
=> ( ! [X2592: term,X2593: term] :
~ ( var @ ( ap @ X2592 @ X2593 ) )
=> ( ! [X2594: term] :
~ ( var @ ( lam @ X2594 ) )
=> ( ! [X2595: term > $o] :
( ! [X2596: term] :
( ( var @ X2596 )
=> ( X2595 @ X2596 ) )
=> ( ! [X2597: term,X2598: term] :
( ( X2595 @ X2597 )
=> ( ( X2595 @ X2598 )
=> ( X2595 @ ( ap @ X2597 @ X2598 ) ) ) )
=> ( ! [X2599: term] :
( ( X2595 @ X2599 )
=> ( X2595 @ ( lam @ X2599 ) ) )
=> ! [X2600: term] : ( X2595 @ X2600 ) ) ) )
=> ( ! [X2601: term > $o,X2602: term,X2603: subst] :
( ! [X2604: term] :
( ( var @ X2604 )
=> ( X2601 @ ( sub @ X2604 @ X2603 ) ) )
=> ( ( X2601 @ X2602 )
=> ! [X2605: term] :
( ( var @ X2605 )
=> ( X2601 @ ( sub @ X2605 @ ( push @ X2602 @ X2603 ) ) ) ) ) )
=> ( ! [X2606: term > $o] :
( ! [X2607: term,X2608: term] :
( ( X2606 @ X2607 )
=> ( ( X2606 @ X2608 )
=> ( X2606 @ ( ap @ X2607 @ X2608 ) ) ) )
=> ( ! [X2609: term] :
( ! [X2610: term] :
( ( X2606 @ X2610 )
=> ( X2606 @ ( sub @ X2609 @ ( push @ X2610 @ id ) ) ) )
=> ( X2606 @ ( lam @ X2609 ) ) )
=> ! [X2611: term,X2612: subst] :
( ! [X2613: term] :
( ( var @ X2613 )
=> ( X2606 @ ( sub @ X2613 @ X2612 ) ) )
=> ( X2606 @ ( sub @ X2611 @ X2612 ) ) ) ) )
=> ( ! [X2614: term > $o] :
( ! [X2615: term] :
( ( var @ X2615 )
=> ( X2614 @ X2615 ) )
=> ( ! [X2616: term,X2617: term] :
( ( X2614 @ X2616 )
=> ( ( X2614 @ X2617 )
=> ( X2614 @ ( ap @ X2616 @ X2617 ) ) ) )
=> ( ! [X2618: term] :
( ! [X2619: term] :
( ( X2614 @ X2619 )
=> ( X2614 @ ( sub @ X2618 @ ( push @ X2619 @ id ) ) ) )
=> ( X2614 @ ( lam @ X2618 ) ) )
=> ! [X2620: term] : ( X2614 @ X2620 ) ) ) )
=> ( ( ! [X2621: subst,X2622: subst,X2623: subst] :
( ( comp @ ( comp @ X2621 @ X2622 ) @ X2623 )
= ( comp @ X2621 @ ( comp @ X2622 @ X2623 ) ) )
& ! [X2624: subst] :
( ( comp @ id @ X2624 )
= X2624 )
& ! [X2625: subst] :
( ( comp @ X2625 @ id )
= X2625 ) )
=> ( ( ! [X2626: term,X2627: subst,X2628: subst] :
( ( sub @ ( sub @ X2626 @ X2627 ) @ X2628 )
= ( sub @ X2626 @ ( comp @ X2627 @ X2628 ) ) )
& ! [X2629: term] :
( ( sub @ X2629 @ id )
= X2629 ) )
=> ( ! [X2630: term,X2631: term,X2632: term,X2633: term] :
( ( ( hoasap @ id @ X2630 @ id @ X2632 )
= ( hoasap @ id @ X2631 @ id @ X2633 ) )
=> ( X2630 = X2631 ) )
=> ( ! [X2634: term,X2635: term,X2636: term,X2637: term] :
( ( ( hoasap @ id @ X2634 @ id @ X2636 )
= ( hoasap @ id @ X2635 @ id @ X2637 ) )
=> ( X2636 = X2637 ) )
=> ! [X2638: subst > term > term] :
( ! [X2639: subst,X2640: term,X2641: subst] :
( ( sub @ ( X2638 @ X2639 @ X2640 ) @ X2641 )
= ( X2638 @ ( comp @ X2639 @ X2641 ) @ ( sub @ X2640 @ X2641 ) ) )
=> ! [X2642: subst > term > term] :
( ! [X2643: subst,X2644: term,X2645: subst] :
( ( sub @ ( X2642 @ X2643 @ X2644 ) @ X2645 )
= ( X2642 @ ( comp @ X2643 @ X2645 ) @ ( sub @ X2644 @ X2645 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X2638 @ Z0 @ Z1 ) )
= ( hoaslam @ id
@ ^ [Z0: subst,Z1: term] : ( X2642 @ Z0 @ Z1 ) ) )
=> ! [X2646: subst,X2647: term] :
( ( X2638 @ X2646 @ X2647 )
= ( X2642 @ X2646 @ X2647 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
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)],[hoaslaminj_gthm,axapp]),axvarcons]),axvarid]),axabs]),axclos]),axidl]),axshiftcons]),axassoc]),axmap]),axidr]),axvarshift]),axscons]),ulamvar1]),ulamvarsh]),ulamvarind]),apinj1]),apinj2]),laminj]),shinj]),lamnotap]),apnotvar]),lamnotvar]),induction]),pushprop]),induction2lem]),induction2]),substmonoid]),termmset]),hoasapinj1]),hoasapinj2]),c_0_34]) ).
thf(c_0_37,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[c_0_35,c_0_36])])]) ).
thf(c_0_38,plain,
! [X3474: subst,X3475: subst > term > term] :
( ( hoaslam @ X3474 @ X3475 )
= ( lam @ ( X3475 @ sh @ one ) ) ),
inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[hoaslam])]) ).
thf(c_0_39,negated_conjecture,
! [X3482: term,X3483: term,X3484: subst,X3485: term,X3486: subst,X3487: term,X3488: term,X3489: subst,X3490: term,X3491: subst,X3492: subst,X3493: subst,X3494: term,X3495: subst,X3496: subst,X3497: subst,X3498: subst,X3499: term,X3500: subst,X3501: subst,X3502: subst,X3503: subst,X3504: term,X3505: term > $o,X3507: term,X3508: term,X3509: term,X3510: term,X3511: term,X3512: term,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 > $o,X3531: term,X3532: term > $o,X3533: term,X3534: subst,X3536: term,X3537: term > $o,X3541: term,X3542: term,X3543: subst,X3545: term > $o,X3550: term,X3551: term,X3552: subst,X3553: subst,X3554: subst,X3555: subst,X3556: subst,X3557: term,X3558: subst,X3559: subst,X3560: term,X3561: term,X3562: term,X3563: term,X3564: term,X3565: term,X3566: term,X3567: term,X3568: term,X3570: subst,X3571: term,X3572: subst,X3574: subst,X3575: term,X3576: subst] :
( ( ( sub @ ( ap @ X3482 @ X3483 ) @ X3484 )
= ( ap @ ( sub @ X3482 @ X3484 ) @ ( sub @ X3483 @ X3484 ) ) )
& ( ( sub @ one @ ( push @ X3485 @ X3486 ) )
= X3485 )
& ( ( sub @ X3487 @ id )
= X3487 )
& ( ( sub @ ( lam @ X3488 ) @ X3489 )
= ( lam @ ( sub @ X3488 @ ( push @ one @ ( comp @ X3489 @ sh ) ) ) ) )
& ( ( sub @ ( sub @ X3490 @ X3491 ) @ X3492 )
= ( sub @ X3490 @ ( comp @ X3491 @ X3492 ) ) )
& ( ( comp @ id @ X3493 )
= X3493 )
& ( ( comp @ sh @ ( push @ X3494 @ X3495 ) )
= X3495 )
& ( ( comp @ ( comp @ X3496 @ X3497 ) @ X3498 )
= ( comp @ X3496 @ ( comp @ X3497 @ X3498 ) ) )
& ( ( comp @ ( push @ X3499 @ X3500 ) @ X3501 )
= ( push @ ( sub @ X3499 @ X3501 ) @ ( comp @ X3500 @ X3501 ) ) )
& ( ( comp @ X3502 @ id )
= X3502 )
& ( ( push @ one @ sh )
= id )
& ( ( push @ ( sub @ one @ X3503 ) @ ( comp @ sh @ X3503 ) )
= X3503 )
& ( var @ one )
& ( ~ ( var @ X3504 )
| ( var @ ( sub @ X3504 @ sh ) ) )
& ( ( var @ ( esk1_1 @ X3505 ) )
| ~ ( var @ X3507 )
| ( X3505 @ X3507 )
| ~ ( X3505 @ one ) )
& ( ( X3505 @ ( esk1_1 @ X3505 ) )
| ~ ( var @ X3507 )
| ( X3505 @ X3507 )
| ~ ( X3505 @ one ) )
& ( ~ ( X3505 @ ( sub @ ( esk1_1 @ X3505 ) @ sh ) )
| ~ ( var @ X3507 )
| ( X3505 @ X3507 )
| ~ ( X3505 @ one ) )
& ( ( ( ap @ X3508 @ X3510 )
!= ( ap @ X3509 @ X3511 ) )
| ( X3508 = X3509 ) )
& ( ( ( ap @ X3512 @ X3514 )
!= ( ap @ X3513 @ X3515 ) )
| ( X3514 = X3515 ) )
& ( ( ( lam @ X3516 )
!= ( lam @ X3517 ) )
| ( X3516 = X3517 ) )
& ( ( ( sub @ X3518 @ sh )
!= ( sub @ X3519 @ sh ) )
| ( X3518 = X3519 ) )
& ( ( lam @ X3520 )
!= ( ap @ X3521 @ X3522 ) )
& ~ ( var @ ( ap @ X3523 @ X3524 ) )
& ~ ( var @ ( lam @ X3525 ) )
& ( ( X3526 @ ( esk5_1 @ X3526 ) )
| ( X3526 @ X3531 )
| ( X3526 @ ( esk3_1 @ X3526 ) )
| ( var @ ( esk2_1 @ X3526 ) ) )
& ( ~ ( X3526 @ ( lam @ ( esk5_1 @ X3526 ) ) )
| ( X3526 @ X3531 )
| ( X3526 @ ( esk3_1 @ X3526 ) )
| ( var @ ( esk2_1 @ X3526 ) ) )
& ( ( X3526 @ ( esk5_1 @ X3526 ) )
| ( X3526 @ X3531 )
| ( X3526 @ ( esk4_1 @ X3526 ) )
| ( var @ ( esk2_1 @ X3526 ) ) )
& ( ~ ( X3526 @ ( lam @ ( esk5_1 @ X3526 ) ) )
| ( X3526 @ X3531 )
| ( X3526 @ ( esk4_1 @ X3526 ) )
| ( var @ ( esk2_1 @ X3526 ) ) )
& ( ( X3526 @ ( esk5_1 @ X3526 ) )
| ( X3526 @ X3531 )
| ~ ( X3526 @ ( ap @ ( esk3_1 @ X3526 ) @ ( esk4_1 @ X3526 ) ) )
| ( var @ ( esk2_1 @ X3526 ) ) )
& ( ~ ( X3526 @ ( lam @ ( esk5_1 @ X3526 ) ) )
| ( X3526 @ X3531 )
| ~ ( X3526 @ ( ap @ ( esk3_1 @ X3526 ) @ ( esk4_1 @ X3526 ) ) )
| ( var @ ( esk2_1 @ X3526 ) ) )
& ( ( X3526 @ ( esk5_1 @ X3526 ) )
| ( X3526 @ X3531 )
| ( X3526 @ ( esk3_1 @ X3526 ) )
| ~ ( X3526 @ ( esk2_1 @ X3526 ) ) )
& ( ~ ( X3526 @ ( lam @ ( esk5_1 @ X3526 ) ) )
| ( X3526 @ X3531 )
| ( X3526 @ ( esk3_1 @ X3526 ) )
| ~ ( X3526 @ ( esk2_1 @ X3526 ) ) )
& ( ( X3526 @ ( esk5_1 @ X3526 ) )
| ( X3526 @ X3531 )
| ( X3526 @ ( esk4_1 @ X3526 ) )
| ~ ( X3526 @ ( esk2_1 @ X3526 ) ) )
& ( ~ ( X3526 @ ( lam @ ( esk5_1 @ X3526 ) ) )
| ( X3526 @ X3531 )
| ( X3526 @ ( esk4_1 @ X3526 ) )
| ~ ( X3526 @ ( esk2_1 @ X3526 ) ) )
& ( ( X3526 @ ( esk5_1 @ X3526 ) )
| ( X3526 @ X3531 )
| ~ ( X3526 @ ( ap @ ( esk3_1 @ X3526 ) @ ( esk4_1 @ X3526 ) ) )
| ~ ( X3526 @ ( esk2_1 @ X3526 ) ) )
& ( ~ ( X3526 @ ( lam @ ( esk5_1 @ X3526 ) ) )
| ( X3526 @ X3531 )
| ~ ( X3526 @ ( ap @ ( esk3_1 @ X3526 ) @ ( esk4_1 @ X3526 ) ) )
| ~ ( X3526 @ ( esk2_1 @ X3526 ) ) )
& ( ( var @ ( esk6_3 @ X3532 @ X3533 @ X3534 ) )
| ~ ( X3532 @ X3533 )
| ~ ( var @ X3536 )
| ( X3532 @ ( sub @ X3536 @ ( push @ X3533 @ X3534 ) ) ) )
& ( ~ ( X3532 @ ( sub @ ( esk6_3 @ X3532 @ X3533 @ X3534 ) @ X3534 ) )
| ~ ( X3532 @ X3533 )
| ~ ( var @ X3536 )
| ( X3532 @ ( sub @ X3536 @ ( push @ X3533 @ X3534 ) ) ) )
& ( ( var @ ( esk10_3 @ X3537 @ X3542 @ X3543 ) )
| ( X3537 @ ( sub @ X3542 @ X3543 ) )
| ~ ( X3537 @ X3541 )
| ( X3537 @ ( sub @ ( esk9_1 @ X3537 ) @ ( push @ X3541 @ id ) ) )
| ( X3537 @ ( esk7_1 @ X3537 ) ) )
& ( ~ ( X3537 @ ( sub @ ( esk10_3 @ X3537 @ X3542 @ X3543 ) @ X3543 ) )
| ( X3537 @ ( sub @ X3542 @ X3543 ) )
| ~ ( X3537 @ X3541 )
| ( X3537 @ ( sub @ ( esk9_1 @ X3537 ) @ ( push @ X3541 @ id ) ) )
| ( X3537 @ ( esk7_1 @ X3537 ) ) )
& ( ( var @ ( esk10_3 @ X3537 @ X3542 @ X3543 ) )
| ( X3537 @ ( sub @ X3542 @ X3543 ) )
| ~ ( X3537 @ ( lam @ ( esk9_1 @ X3537 ) ) )
| ( X3537 @ ( esk7_1 @ X3537 ) ) )
& ( ~ ( X3537 @ ( sub @ ( esk10_3 @ X3537 @ X3542 @ X3543 ) @ X3543 ) )
| ( X3537 @ ( sub @ X3542 @ X3543 ) )
| ~ ( X3537 @ ( lam @ ( esk9_1 @ X3537 ) ) )
| ( X3537 @ ( esk7_1 @ X3537 ) ) )
& ( ( var @ ( esk10_3 @ X3537 @ X3542 @ X3543 ) )
| ( X3537 @ ( sub @ X3542 @ X3543 ) )
| ~ ( X3537 @ X3541 )
| ( X3537 @ ( sub @ ( esk9_1 @ X3537 ) @ ( push @ X3541 @ id ) ) )
| ( X3537 @ ( esk8_1 @ X3537 ) ) )
& ( ~ ( X3537 @ ( sub @ ( esk10_3 @ X3537 @ X3542 @ X3543 ) @ X3543 ) )
| ( X3537 @ ( sub @ X3542 @ X3543 ) )
| ~ ( X3537 @ X3541 )
| ( X3537 @ ( sub @ ( esk9_1 @ X3537 ) @ ( push @ X3541 @ id ) ) )
| ( X3537 @ ( esk8_1 @ X3537 ) ) )
& ( ( var @ ( esk10_3 @ X3537 @ X3542 @ X3543 ) )
| ( X3537 @ ( sub @ X3542 @ X3543 ) )
| ~ ( X3537 @ ( lam @ ( esk9_1 @ X3537 ) ) )
| ( X3537 @ ( esk8_1 @ X3537 ) ) )
& ( ~ ( X3537 @ ( sub @ ( esk10_3 @ X3537 @ X3542 @ X3543 ) @ X3543 ) )
| ( X3537 @ ( sub @ X3542 @ X3543 ) )
| ~ ( X3537 @ ( lam @ ( esk9_1 @ X3537 ) ) )
| ( X3537 @ ( esk8_1 @ X3537 ) ) )
& ( ( var @ ( esk10_3 @ X3537 @ X3542 @ X3543 ) )
| ( X3537 @ ( sub @ X3542 @ X3543 ) )
| ~ ( X3537 @ X3541 )
| ( X3537 @ ( sub @ ( esk9_1 @ X3537 ) @ ( push @ X3541 @ id ) ) )
| ~ ( X3537 @ ( ap @ ( esk7_1 @ X3537 ) @ ( esk8_1 @ X3537 ) ) ) )
& ( ~ ( X3537 @ ( sub @ ( esk10_3 @ X3537 @ X3542 @ X3543 ) @ X3543 ) )
| ( X3537 @ ( sub @ X3542 @ X3543 ) )
| ~ ( X3537 @ X3541 )
| ( X3537 @ ( sub @ ( esk9_1 @ X3537 ) @ ( push @ X3541 @ id ) ) )
| ~ ( X3537 @ ( ap @ ( esk7_1 @ X3537 ) @ ( esk8_1 @ X3537 ) ) ) )
& ( ( var @ ( esk10_3 @ X3537 @ X3542 @ X3543 ) )
| ( X3537 @ ( sub @ X3542 @ X3543 ) )
| ~ ( X3537 @ ( lam @ ( esk9_1 @ X3537 ) ) )
| ~ ( X3537 @ ( ap @ ( esk7_1 @ X3537 ) @ ( esk8_1 @ X3537 ) ) ) )
& ( ~ ( X3537 @ ( sub @ ( esk10_3 @ X3537 @ X3542 @ X3543 ) @ X3543 ) )
| ( X3537 @ ( sub @ X3542 @ X3543 ) )
| ~ ( X3537 @ ( lam @ ( esk9_1 @ X3537 ) ) )
| ~ ( X3537 @ ( ap @ ( esk7_1 @ X3537 ) @ ( esk8_1 @ X3537 ) ) ) )
& ( ~ ( X3545 @ X3550 )
| ( X3545 @ ( sub @ ( esk14_1 @ X3545 ) @ ( push @ X3550 @ id ) ) )
| ( X3545 @ X3551 )
| ( X3545 @ ( esk12_1 @ X3545 ) )
| ( var @ ( esk11_1 @ X3545 ) ) )
& ( ~ ( X3545 @ ( lam @ ( esk14_1 @ X3545 ) ) )
| ( X3545 @ X3551 )
| ( X3545 @ ( esk12_1 @ X3545 ) )
| ( var @ ( esk11_1 @ X3545 ) ) )
& ( ~ ( X3545 @ X3550 )
| ( X3545 @ ( sub @ ( esk14_1 @ X3545 ) @ ( push @ X3550 @ id ) ) )
| ( X3545 @ X3551 )
| ( X3545 @ ( esk13_1 @ X3545 ) )
| ( var @ ( esk11_1 @ X3545 ) ) )
& ( ~ ( X3545 @ ( lam @ ( esk14_1 @ X3545 ) ) )
| ( X3545 @ X3551 )
| ( X3545 @ ( esk13_1 @ X3545 ) )
| ( var @ ( esk11_1 @ X3545 ) ) )
& ( ~ ( X3545 @ X3550 )
| ( X3545 @ ( sub @ ( esk14_1 @ X3545 ) @ ( push @ X3550 @ id ) ) )
| ( X3545 @ X3551 )
| ~ ( X3545 @ ( ap @ ( esk12_1 @ X3545 ) @ ( esk13_1 @ X3545 ) ) )
| ( var @ ( esk11_1 @ X3545 ) ) )
& ( ~ ( X3545 @ ( lam @ ( esk14_1 @ X3545 ) ) )
| ( X3545 @ X3551 )
| ~ ( X3545 @ ( ap @ ( esk12_1 @ X3545 ) @ ( esk13_1 @ X3545 ) ) )
| ( var @ ( esk11_1 @ X3545 ) ) )
& ( ~ ( X3545 @ X3550 )
| ( X3545 @ ( sub @ ( esk14_1 @ X3545 ) @ ( push @ X3550 @ id ) ) )
| ( X3545 @ X3551 )
| ( X3545 @ ( esk12_1 @ X3545 ) )
| ~ ( X3545 @ ( esk11_1 @ X3545 ) ) )
& ( ~ ( X3545 @ ( lam @ ( esk14_1 @ X3545 ) ) )
| ( X3545 @ X3551 )
| ( X3545 @ ( esk12_1 @ X3545 ) )
| ~ ( X3545 @ ( esk11_1 @ X3545 ) ) )
& ( ~ ( X3545 @ X3550 )
| ( X3545 @ ( sub @ ( esk14_1 @ X3545 ) @ ( push @ X3550 @ id ) ) )
| ( X3545 @ X3551 )
| ( X3545 @ ( esk13_1 @ X3545 ) )
| ~ ( X3545 @ ( esk11_1 @ X3545 ) ) )
& ( ~ ( X3545 @ ( lam @ ( esk14_1 @ X3545 ) ) )
| ( X3545 @ X3551 )
| ( X3545 @ ( esk13_1 @ X3545 ) )
| ~ ( X3545 @ ( esk11_1 @ X3545 ) ) )
& ( ~ ( X3545 @ X3550 )
| ( X3545 @ ( sub @ ( esk14_1 @ X3545 ) @ ( push @ X3550 @ id ) ) )
| ( X3545 @ X3551 )
| ~ ( X3545 @ ( ap @ ( esk12_1 @ X3545 ) @ ( esk13_1 @ X3545 ) ) )
| ~ ( X3545 @ ( esk11_1 @ X3545 ) ) )
& ( ~ ( X3545 @ ( lam @ ( esk14_1 @ X3545 ) ) )
| ( X3545 @ X3551 )
| ~ ( X3545 @ ( ap @ ( esk12_1 @ X3545 ) @ ( esk13_1 @ X3545 ) ) )
| ~ ( X3545 @ ( esk11_1 @ X3545 ) ) )
& ( ( comp @ ( comp @ X3552 @ X3553 ) @ X3554 )
= ( comp @ X3552 @ ( comp @ X3553 @ X3554 ) ) )
& ( ( comp @ id @ X3555 )
= X3555 )
& ( ( comp @ X3556 @ id )
= X3556 )
& ( ( sub @ ( sub @ X3557 @ X3558 ) @ X3559 )
= ( sub @ X3557 @ ( comp @ X3558 @ X3559 ) ) )
& ( ( sub @ X3560 @ id )
= X3560 )
& ( ( ( hoasap @ id @ X3561 @ id @ X3563 )
!= ( hoasap @ id @ X3562 @ id @ X3564 ) )
| ( X3561 = X3562 ) )
& ( ( ( hoasap @ id @ X3565 @ id @ X3567 )
!= ( hoasap @ id @ X3566 @ id @ X3568 ) )
| ( X3567 = X3568 ) )
& ( ( sub @ ( esk15_0 @ X3570 @ X3571 ) @ X3572 )
= ( esk15_0 @ ( comp @ X3570 @ X3572 ) @ ( sub @ X3571 @ X3572 ) ) )
& ( ( sub @ ( esk16_0 @ X3574 @ X3575 ) @ X3576 )
= ( esk16_0 @ ( comp @ X3574 @ X3576 ) @ ( sub @ X3575 @ X3576 ) ) )
& ( ( hoaslam @ id @ esk15_0 )
= ( hoaslam @ id @ esk16_0 ) )
& ( ( esk15_0 @ esk17_0 @ esk18_0 )
!= ( esk16_0 @ esk17_0 @ esk18_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_37])])])])])])]) ).
thf(c_0_40,plain,
! [X3480: subst,X3481: subst > term > term] :
( ( hoaslam @ X3480 @ X3481 )
= ( lam @ ( X3481 @ sh @ one ) ) ),
inference(variable_rename,[status(thm)],[c_0_38]) ).
thf(c_0_41,negated_conjecture,
( ( hoaslam @ id @ esk15_0 )
= ( hoaslam @ id @ esk16_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_42,plain,
! [X3: subst,X12: subst > term > term] :
( ( hoaslam @ X3 @ X12 )
= ( lam @ ( X12 @ sh @ one ) ) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
thf(c_0_43,negated_conjecture,
! [X1: term,X2: term] :
( ( X1 = X2 )
| ( ( lam @ X1 )
!= ( lam @ X2 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_44,negated_conjecture,
( ( lam @ ( esk15_0 @ sh @ one ) )
= ( lam @ ( esk16_0 @ sh @ one ) ) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_42]) ).
thf(c_0_45,negated_conjecture,
! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( esk15_0 @ X3 @ X1 ) @ X4 )
= ( esk15_0 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_46,negated_conjecture,
! [X3: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X3 ) )
= X1 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_47,negated_conjecture,
! [X1: term] :
( ( ( esk15_0 @ sh @ one )
= X1 )
| ( ( lam @ ( esk16_0 @ sh @ one ) )
!= ( lam @ X1 ) ) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
thf(c_0_48,negated_conjecture,
! [X1: term,X3: subst,X4: subst] :
( ( sub @ ( esk16_0 @ X3 @ X1 ) @ X4 )
= ( esk16_0 @ ( comp @ X3 @ X4 ) @ ( sub @ X1 @ X4 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_49,negated_conjecture,
! [X1: term,X3: subst,X4: subst] :
( ( esk15_0 @ ( comp @ X3 @ ( push @ X1 @ X4 ) ) @ X1 )
= ( sub @ ( esk15_0 @ X3 @ one ) @ ( push @ X1 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_50,negated_conjecture,
! [X1: term,X3: subst] :
( ( comp @ sh @ ( push @ X1 @ X3 ) )
= X3 ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_51,negated_conjecture,
( ( esk15_0 @ sh @ one )
= ( esk16_0 @ sh @ one ) ),
inference(er,[status(thm)],[c_0_47]) ).
thf(c_0_52,negated_conjecture,
! [X1: term,X3: subst,X4: subst] :
( ( esk16_0 @ ( comp @ X3 @ ( push @ X1 @ X4 ) ) @ X1 )
= ( sub @ ( esk16_0 @ X3 @ one ) @ ( push @ X1 @ X4 ) ) ),
inference(spm,[status(thm)],[c_0_48,c_0_46]) ).
thf(c_0_53,negated_conjecture,
! [X3: subst,X1: term] :
( ( sub @ ( esk16_0 @ sh @ one ) @ ( push @ X1 @ X3 ) )
= ( esk15_0 @ X3 @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
thf(c_0_54,negated_conjecture,
( ( esk15_0 @ esk17_0 @ esk18_0 )
!= ( esk16_0 @ esk17_0 @ esk18_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_55,negated_conjecture,
! [X3: subst,X1: term] :
( ( esk15_0 @ X3 @ X1 )
= ( esk16_0 @ X3 @ X1 ) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_50]),c_0_53]) ).
thf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG258^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n026.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 17:36:38 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.20/0.27 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.1O41S5OEI9/E---3.1_922373.p
% 0.61/0.38 % Version: 3.5.1-ho
% 0.61/0.38 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.61/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.38 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.61/0.38 % Starting post_as_ho1 with 300s (1) cores
% 0.61/0.38 % Starting post_as_ho5 with 300s (1) cores
% 0.61/0.38 % Starting post_as_ho10 with 300s (1) cores
% 0.61/0.38 % post_as_ho10 with pid 922412 completed with status 0
% 0.61/0.38 % Result found by post_as_ho10
% 0.61/0.38 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.61/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.38 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.61/0.38 % Starting post_as_ho1 with 300s (1) cores
% 0.61/0.38 % Starting post_as_ho5 with 300s (1) cores
% 0.61/0.38 % Starting post_as_ho10 with 300s (1) cores
% 0.61/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.61/0.38 % No SInE strategy applied
% 0.61/0.38 % Search class: HGUSM-FFMS31-MHFMMMBN
% 0.61/0.38 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.61/0.38 % Starting SubtermCWHack with 28s (1) cores
% 0.61/0.38 % SubtermCWHack with pid 922429 completed with status 0
% 0.61/0.38 % Result found by SubtermCWHack
% 0.61/0.38 % Preprocessing class: HSMMSLSSLLLNHFA.
% 0.61/0.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.38 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.61/0.38 % Starting post_as_ho1 with 300s (1) cores
% 0.61/0.38 % Starting post_as_ho5 with 300s (1) cores
% 0.61/0.38 % Starting post_as_ho10 with 300s (1) cores
% 0.61/0.38 % (lift_lambdas = 0, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.61/0.38 % No SInE strategy applied
% 0.61/0.38 % Search class: HGUSM-FFMS31-MHFMMMBN
% 0.61/0.38 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.61/0.38 % Starting SubtermCWHack with 28s (1) cores
% 0.61/0.38 % Preprocessing time : 0.002 s
% 0.61/0.38
% 0.61/0.38 % Proof found!
% 0.61/0.38 % SZS status Theorem
% 0.61/0.38 % SZS output start CNFRefutation
% See solution above
% 0.61/0.38 % Parsed axioms : 238
% 0.61/0.38 % Removed by relevancy pruning/SinE : 0
% 0.61/0.38 % Initial clauses : 199
% 0.61/0.38 % Removed in clause preprocessing : 124
% 0.61/0.38 % Initial clauses in saturation : 75
% 0.61/0.38 % Processed clauses : 778
% 0.61/0.38 % ...of these trivial : 13
% 0.61/0.38 % ...subsumed : 563
% 0.61/0.38 % ...remaining for further processing : 202
% 0.61/0.38 % Other redundant clauses eliminated : 0
% 0.61/0.38 % Clauses deleted for lack of memory : 0
% 0.61/0.38 % Backward-subsumed : 5
% 0.61/0.38 % Backward-rewritten : 21
% 0.61/0.38 % Generated clauses : 2365
% 0.61/0.38 % ...of the previous two non-redundant : 2074
% 0.61/0.38 % ...aggressively subsumed : 0
% 0.61/0.38 % Contextual simplify-reflections : 0
% 0.61/0.38 % Paramodulations : 2360
% 0.61/0.38 % Factorizations : 0
% 0.61/0.38 % NegExts : 0
% 0.61/0.38 % Equation resolutions : 5
% 0.61/0.38 % Disequality decompositions : 0
% 0.61/0.38 % Total rewrite steps : 1274
% 0.61/0.38 % ...of those cached : 531
% 0.61/0.38 % Propositional unsat checks : 0
% 0.61/0.38 % Propositional check models : 0
% 0.61/0.38 % Propositional check unsatisfiable : 0
% 0.61/0.38 % Propositional clauses : 0
% 0.61/0.38 % Propositional clauses after purity: 0
% 0.61/0.38 % Propositional unsat core size : 0
% 0.61/0.38 % Propositional preprocessing time : 0.000
% 0.61/0.38 % Propositional encoding time : 0.000
% 0.61/0.38 % Propositional solver time : 0.000
% 0.61/0.38 % Success case prop preproc time : 0.000
% 0.61/0.38 % Success case prop encoding time : 0.000
% 0.61/0.38 % Success case prop solver time : 0.000
% 0.61/0.38 % Current number of processed clauses : 176
% 0.61/0.38 % Positive orientable unit clauses : 51
% 0.61/0.38 % Positive unorientable unit clauses: 6
% 0.61/0.38 % Negative unit clauses : 27
% 0.61/0.38 % Non-unit-clauses : 92
% 0.61/0.38 % Current number of unprocessed clauses: 1358
% 0.61/0.38 % ...number of literals in the above : 2785
% 0.61/0.38 % Current number of archived formulas : 0
% 0.61/0.38 % Current number of archived clauses : 26
% 0.61/0.38 % Clause-clause subsumption calls (NU) : 965
% 0.61/0.38 % Rec. Clause-clause subsumption calls : 400
% 0.61/0.38 % Non-unit clause-clause subsumptions : 110
% 0.61/0.38 % Unit Clause-clause subsumption calls : 58
% 0.61/0.38 % Rewrite failures with RHS unbound : 7
% 0.61/0.38 % BW rewrite match attempts : 68
% 0.61/0.38 % BW rewrite match successes : 26
% 0.61/0.38 % Condensation attempts : 0
% 0.61/0.38 % Condensation successes : 0
% 0.61/0.38 % Termbank termtop insertions : 68059
% 0.61/0.38 % Search garbage collected termcells : 3950
% 0.61/0.38
% 0.61/0.38 % -------------------------------------------------
% 0.61/0.38 % User time : 0.061 s
% 0.61/0.38 % System time : 0.015 s
% 0.61/0.38 % Total time : 0.076 s
% 0.61/0.38 % Maximum resident set size: 7820 pages
% 0.61/0.38
% 0.61/0.38 % -------------------------------------------------
% 0.61/0.38 % User time : 0.071 s
% 0.61/0.38 % System time : 0.017 s
% 0.61/0.38 % Total time : 0.089 s
% 0.61/0.38 % Maximum resident set size: 4864 pages
% 0.61/0.38 % E exiting
%------------------------------------------------------------------------------