%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ALG268^2 : TPTP v9.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n003.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 01:12:16 PM UTC 2025
% Result : Theorem 218.86s 216.91s
% Output : Proof 218.86s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_subst,type,
subst: $tType ).
thf(ty_term,type,
term: $tType ).
thf(ty_push,type,
push: term > subst > subst ).
thf(ty_hoaslam,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(ty_eigen__1,type,
eigen__1: term ).
thf(ty_eigen__0,type,
eigen__0: subst > term > subst > $o ).
thf(ty_id,type,
id: subst ).
thf(ty_one,type,
one: term ).
thf(ty_sub,type,
sub: term > subst > term ).
thf(ty_lam,type,
lam: term > term ).
thf(ty_sh,type,
sh: subst ).
thf(ty_comp,type,
comp: subst > subst > subst ).
thf(sP1,plain,
( sP1
<=> ! [X1: term] :
( ( eigen__0 @ id @ X1 @ id )
=> ( eigen__0 @ id @ ( sub @ eigen__1 @ ( push @ X1 @ id ) ) @ id ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( sub @ eigen__1 @ id )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( push @ one @ sh )
= id ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( eigen__1 = eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: subst,X2: subst] :
( ( X1 = X2 )
=> ( X2 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( id = id ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( sub @ eigen__1 @ ( push @ one @ sh ) )
= eigen__1 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [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 @ ( hoaslam @ id @ X2 ) @ 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,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( eigen__0 @ id @ ( lam @ ( sub @ eigen__1 @ ( push @ one @ sh ) ) ) @ id ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( id
= ( push @ one @ sh ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: subst] :
( ( ( push @ one @ sh )
= X1 )
=> ( X1
= ( push @ one @ sh ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP1
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [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,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [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 @ ( hoaslam @ id @ X1 ) @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( sP14
=> sP13 ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( eigen__0 @ id @ ( lam @ eigen__1 ) @ id ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( sP3
=> sP10 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( ( lam @ ( sub @ eigen__1 @ ( push @ one @ sh ) ) )
= ( lam @ eigen__1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( sub @ eigen__1 @ id )
= ( sub @ eigen__1 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(def_axvarid,definition,
axvarid = sP17 ).
thf(def_axvarshift,definition,
axvarshift = sP3 ).
thf(def_hoasinduction_lem3aa,definition,
hoasinduction_lem3aa = sP8 ).
thf(def_hoasinduction_lem3,definition,
( hoasinduction_lem3
= ( ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [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 @ ( hoaslam @ id @ X2 ) @ id ) ) )
=> ! [X2: term] :
( ! [X3: term] :
( ( X1 @ id @ X3 @ id )
=> ( X1 @ id @ ( sub @ X2 @ ( push @ X3 @ id ) ) @ id ) )
=> ( X1 @ id @ ( lam @ X2 ) @ id ) ) ) ) ) ) ) ).
thf(def_hoasinduction_lem3_lthm,definition,
( hoasinduction_lem3_lthm
= ( axvarid
=> ( axvarshift
=> ( hoasinduction_lem3aa
=> hoasinduction_lem3 ) ) ) ) ).
thf(thm,conjecture,
( sP17
=> ( sP3
=> ( sP8
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [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 @ ( hoaslam @ id @ X2 ) @ 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,
~ ( sP17
=> ( sP3
=> ( sP8
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [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 @ ( hoaslam @ id @ X2 ) @ 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,
sP17,
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( sP3
=> ( sP8
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [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 @ ( hoaslam @ id @ X2 ) @ 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,
sP3,
introduced(assumption,[]) ).
thf(h4,assumption,
~ ( sP8
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [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 @ ( hoaslam @ id @ X2 ) @ 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,
sP8,
introduced(assumption,[]) ).
thf(h6,assumption,
~ ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [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 @ ( hoaslam @ id @ X2 ) @ 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,
~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__0 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__0 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__0 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__0 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) )
=> ( sP14
=> ! [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,
! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__0 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( eigen__0 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) ),
introduced(assumption,[]) ).
thf(h9,assumption,
~ ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__0 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__0 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) )
=> ( sP14
=> ! [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,
! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( eigen__0 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( eigen__0 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( sP14
=> ! [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(h12,assumption,
sP14,
introduced(assumption,[]) ).
thf(h13,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(h14,assumption,
~ ( sP1
=> sP16 ),
introduced(assumption,[]) ).
thf(h15,assumption,
sP1,
introduced(assumption,[]) ).
thf(h16,assumption,
~ sP16,
introduced(assumption,[]) ).
thf(1,plain,
( sP20
| ~ sP4
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP2
| sP7
| ~ sP20
| ~ sP4 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
sP4,
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP19
| ~ sP7 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP9
| sP16
| ~ sP6
| ~ sP19
| ~ sP6 ),
inference(mating_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP12
| ~ sP1
| sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
sP6,
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP13
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP15
| ~ sP14
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP8
| sP15 ),
inference(all_rule,[status(thm)],[]) ).
thf(11,plain,
( ~ sP17
| sP2 ),
inference(all_rule,[status(thm)],[]) ).
thf(12,plain,
( ~ sP18
| ~ sP3
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( ~ sP11
| sP18 ),
inference(all_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP5
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(15,plain,
sP5,
inference(eq_sym,[status(thm)],[]) ).
thf(16,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h10,h11,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h1,h3,h5,h12,h15,h16]) ).
thf(17,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h10,h11,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h15,h16])],[h14,16,h15,h16]) ).
thf(18,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__1)],[h13,17,h14]) ).
thf(19,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h12,h13])],[h11,18,h12,h13]) ).
thf(20,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h8,h9,h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h10,h11])],[h9,19,h10,h11]) ).
thf(21,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h8,h9])],[h7,20,h8,h9]) ).
thf(22,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__0)],[h6,21,h7]) ).
thf(23,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,22,h5,h6]) ).
thf(24,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,23,h3,h4]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,24,h1,h2]) ).
thf(0,theorem,
( sP17
=> ( sP3
=> ( sP8
=> ! [X1: subst > term > subst > $o] :
( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X1 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [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 @ ( hoaslam @ id @ X2 ) @ 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])],[25,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : ALG268^2 : TPTP v9.2.0. Bugfixed v5.2.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n003.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 : Wed Oct 8 23:39:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 218.86/216.91 % SZS status Theorem
% 218.86/216.91 % Mode: mode406:USE_SINE=true:SINE_TOLERANCE=5.0:SINE_GENERALITY_THRESHOLD=256:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 218.86/216.91 % Inferences: 4888
% 218.86/216.91 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------