%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ALG266^2 : TPTP v9.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n015.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 : Thu Oct 9 01:11:38 PM UTC 2025
% Result : Theorem 21.54s 21.77s
% Output : Proof 21.54s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subst,type,
subst: $tType ).
thf(ty_term,type,
term: $tType ).
thf(ty_eigen__1,type,
eigen__1: term ).
thf(ty_id,type,
id: subst ).
thf(ty_comp,type,
comp: subst > subst > subst ).
thf(ty_lam,type,
lam: term > term ).
thf(ty_sub,type,
sub: term > subst > term ).
thf(ty_eigen__0,type,
eigen__0: subst > term > subst > $o ).
thf(ty_push,type,
push: term > subst > subst ).
thf(ty_one,type,
one: term ).
thf(ty_sh,type,
sh: subst ).
thf(sP1,plain,
( sP1
<=> ! [X1: term] :
( ! [X2: term] :
( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
=> ( eigen__0 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: term] :
( ( eigen__0 @ id @ X1 @ id )
=> ( eigen__0 @ id @ ( sub @ eigen__1 @ ( push @ X1 @ id ) ) @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> $false ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ! [X1: subst > term > term] :
( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ( ! [X2: term] :
( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( X1 @ id @ X2 ) @ id ) )
=> ( eigen__0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( push @ one @ sh )
= id ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( sub @ eigen__1 @ ( push @ one @ sh ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP2
=> ( eigen__0 @ id @ ( lam @ ( sub @ eigen__1 @ ( push @ one @ sh ) ) ) @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( sub @ eigen__1 @ id )
= ( sub @ eigen__1 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( sub @ ( sub @ eigen__1 @ id ) @ id )
= ( sub @ eigen__1 @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( sub @ eigen__1 @ id )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( id
= ( push @ one @ sh ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: subst > term > term] :
( ! [X2: subst,X3: term,X4: subst] :
( ( sub @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ ( comp @ X2 @ X4 ) @ ( sub @ X3 @ X4 ) ) )
=> ( ! [X2: term] :
( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( X1 @ id @ X2 ) @ id ) )
=> ( eigen__0 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( eigen__0 @ id @ ( lam @ eigen__1 ) @ id ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( eigen__0 @ id @ ( lam @ ( sub @ eigen__1 @ ( push @ one @ sh ) ) ) @ id ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( lam @ ( sub @ eigen__1 @ ( push @ one @ sh ) ) )
= ( lam @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(def_axvarid,definition,
axvarid = sP9 ).
thf(def_axvarshift,definition,
axvarshift = sP5 ).
thf(def_hoaslam,definition,
( hoaslam
= ( ^ [X1: subst,X2: subst > term > term] : ( lam @ ( X2 @ sh @ one ) ) ) ) ).
thf(def_hoasinduction_lem3aa,definition,
( hoasinduction_lem3aa
= ( ! [X1: subst > term > subst > $o] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ! [X2: subst > term > term] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
@ ( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: term] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ id @ X3 @ id )
@ ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
@ ( X1 @ id
@ ( hoaslam @ id
@ ^ [X3: subst,X4: term] : ( X2 @ X3 @ X4 ) )
@ id ) ) )
@ ! [X2: term] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: term] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ id @ X3 @ id )
@ ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
@ ( X1 @ id @ ( lam @ ( sub @ X2 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ).
thf(def_hoasinduction_lem3a,definition,
( hoasinduction_lem3a
= ( ! [X1: subst > term > subst > $o] :
( ^ [X2: $o,X3: $o] :
( X2
=> X3 )
@ ! [X2: subst > term > term] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
@ ( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: term] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ id @ X3 @ id )
@ ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
@ ( X1 @ id
@ ( hoaslam @ id
@ ^ [X3: subst,X4: term] : ( X2 @ X3 @ X4 ) )
@ id ) ) )
@ ! [X2: term] :
( ^ [X3: $o,X4: $o] :
( X3
=> X4 )
@ ! [X3: term] :
( ^ [X4: $o,X5: $o] :
( X4
=> X5 )
@ ( X1 @ id @ X3 @ id )
@ ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
@ ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) ).
thf(def_hoasinduction_lem3a_lthm,definition,
( hoasinduction_lem3a_lthm
= ( ^ [X1: $o,X2: $o] :
( X1
=> X2 )
@ axvarid
@ ( ^ [X1: $o,X2: $o] :
( X1
=> X2 )
@ axvarshift
@ ( ^ [X1: $o,X2: $o] :
( X1
=> X2 )
@ hoasinduction_lem3aa
@ hoasinduction_lem3a ) ) ) ) ).
thf(thm,conjecture,
( sP9
=> ( sP5
=> ( sP17
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
~ ( sP9
=> ( sP5
=> ( sP17
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[thm]) ).
thf(h1,assumption,
sP9,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP5
=> ( sP17
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ),
introduced(assumption,[]) ).
thf(h3,assumption,
sP5,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP17
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ),
introduced(assumption,[]) ).
thf(h5,assumption,
sP17,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: subst > term > subst > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( sP13
=> ! [X1: term] :
( ! [X2: term] :
( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
=> ( eigen__0 @ id @ ( lam @ X1 ) @ id ) ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP13,
introduced(assumption,[]) ).
thf(h9,assumption,
~ ! [X1: term] :
( ! [X2: term] :
( ( eigen__0 @ id @ X2 @ id )
=> ( eigen__0 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id ) )
=> ( eigen__0 @ id @ ( lam @ X1 ) @ id ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP2
=> sP14 ),
introduced(assumption,[]) ).
thf(h11,assumption,
sP2,
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP14,
introduced(assumption,[]) ).
thf(1,plain,
( sP8
| ~ sP12
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP10
| sP6
| ~ sP8
| ~ sP11 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP9
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( sP16
| ~ sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP15
| sP14
| sP3
| ~ sP16
| sP3 ),
inference(mating_rule,[status(thm)],[]) ).
thf(6,plain,
~ sP3,
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP7
| ~ sP2
| sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP4
| ~ sP13
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP5
| sP12 ),
inference(symeq,[status(thm)],[]) ).
thf(12,plain,
( ~ sP17
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(13,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h11,h12,h10,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,h1,h3,h5,h8,h11,h12]) ).
thf(14,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[h10,13,h11,h12]) ).
thf(15,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h10]),tab_negall(eigenvar,eigen__1)],[h9,14,h10]) ).
thf(16,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,15,h8,h9]) ).
thf(17,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,16,h7]) ).
thf(18,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,17,h5,h6]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,18,h3,h4]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,19,h1,h2]) ).
thf(0,theorem,
( sP9
=> ( sP5
=> ( sP17
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( X2 @ id @ X3 ) @ id ) )
=> ( X1 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[20,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG266^2 : TPTP v9.2.0. Bugfixed v5.2.0.
% 0.00/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Oct 8 23:24:38 EDT 2025
% 0.11/0.33 % CPUTime :
% 21.54/21.77 % SZS status Theorem
% 21.54/21.77 % Mode: cade22sinegrackle2xfaf3
% 21.54/21.77 % Steps: 29458
% 21.54/21.77 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------