%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX061+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 : Tue Sep 29 01:45:47 PM UTC 2026
% Result : Theorem 6.22s 1.92s
% Output : Refutation 9.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 21
% Syntax : Number of formulae : 127 ( 27 unt; 10 def)
% Number of atoms : 338 ( 118 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 324 ( 113 ~; 155 |; 34 &)
% ( 9 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 11 con; 0-2 aty)
% Number of variables : 152 ( 0 sgn 127 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f88,axiom,
! [X0] :
( list_succeeds(X0)
<=> ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2) )
| X0 = nil ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id88) ).
fof(f199,axiom,
! [X0] : list_succeeds(cons(X0,nil)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(list:1)') ).
fof(f218,axiom,
! [X0] : '**'(nil,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(app:nil)') ).
fof(f219,axiom,
! [X0,X1,X2] :
( list_succeeds(X1)
=> '**'(cons(X0,X1),X2) = cons(X0,'**'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(app:cons)') ).
fof(f224,axiom,
! [X0,X1,X2] :
( ( list_succeeds(X0)
& list_succeeds(X1) )
=> '**'('**'(X0,X1),X2) = '**'(X0,'**'(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(app:associative)') ).
fof(f334,axiom,
! [X0,X1,X2] :
( a_reverse_succeeds(X0,X1,X2)
=> list_succeeds(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(a_reverse:types:1)') ).
fof(f342,axiom,
rev(nil) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(rev:nil)') ).
fof(f343,axiom,
! [X0] :
( list_succeeds(X0)
=> list_succeeds(rev(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(rev:types)') ).
fof(f344,axiom,
! [X0,X1] :
( list_succeeds(X1)
=> rev(cons(X0,X1)) = '**'(rev(X1),cons(X0,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary-(rev:cons)') ).
fof(f345,axiom,
( ! [X0,X1,X2] :
( ( ? [X3,X4] :
( X0 = cons(X3,X4)
& a_reverse_succeeds(X4,cons(X3,X1),X2)
& '**'(rev(X4),cons(X3,X1)) = X2 )
| ( X0 = nil
& X2 = X1 ) )
=> '**'(rev(X0),X1) = X2 )
=> ! [X0,X1,X2] :
( a_reverse_succeeds(X0,X1,X2)
=> '**'(rev(X0),X1) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction) ).
fof(f346,conjecture,
! [X0,X1,X2] :
( a_reverse_succeeds(X0,X1,X2)
=> '**'(rev(X0),X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(a_reverse:n_reverse)') ).
fof(f347,negated_conjecture,
~ ! [X0,X1,X2] :
( a_reverse_succeeds(X0,X1,X2)
=> '**'(rev(X0),X1) = X2 ),
inference(negated_conjecture,[status(cth)],[f346]) ).
fof(f374,plain,
( ! [X0,X1,X2] :
( ( ? [X3,X4] :
( X0 = cons(X3,X4)
& a_reverse_succeeds(X4,cons(X3,X1),X2)
& '**'(rev(X4),cons(X3,X1)) = X2 )
| ( X0 = nil
& X2 = X1 ) )
=> '**'(rev(X0),X1) = X2 )
=> ! [X5,X6,X7] :
( a_reverse_succeeds(X5,X6,X7)
=> '**'(rev(X5),X6) = X7 ) ),
inference(rectify,[],[f345]) ).
fof(f604,plain,
! [X0,X1,X2] :
( '**'(cons(X0,X1),X2) = cons(X0,'**'(X1,X2))
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f219]) ).
fof(f613,plain,
! [X0,X1,X2] :
( '**'('**'(X0,X1),X2) = '**'(X0,'**'(X1,X2))
| ~ list_succeeds(X0)
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f224]) ).
fof(f614,plain,
! [X0,X1,X2] :
( '**'('**'(X0,X1),X2) = '**'(X0,'**'(X1,X2))
| ~ list_succeeds(X0)
| ~ list_succeeds(X1) ),
inference(flattening,[],[f613]) ).
fof(f780,plain,
! [X0,X1,X2] :
( list_succeeds(X0)
| ~ a_reverse_succeeds(X0,X1,X2) ),
inference(ennf_transformation,[],[f334]) ).
fof(f792,plain,
! [X0] :
( list_succeeds(rev(X0))
| ~ list_succeeds(X0) ),
inference(ennf_transformation,[],[f343]) ).
fof(f793,plain,
! [X0,X1] :
( rev(cons(X0,X1)) = '**'(rev(X1),cons(X0,nil))
| ~ list_succeeds(X1) ),
inference(ennf_transformation,[],[f344]) ).
fof(f794,plain,
( ! [X5,X6,X7] :
( '**'(rev(X5),X6) = X7
| ~ a_reverse_succeeds(X5,X6,X7) )
| ? [X0,X1,X2] :
( '**'(rev(X0),X1) != X2
& ( ? [X3,X4] :
( X0 = cons(X3,X4)
& a_reverse_succeeds(X4,cons(X3,X1),X2)
& '**'(rev(X4),cons(X3,X1)) = X2 )
| ( X0 = nil
& X2 = X1 ) ) ) ),
inference(ennf_transformation,[],[f374]) ).
fof(f795,plain,
? [X0,X1,X2] :
( '**'(rev(X0),X1) != X2
& a_reverse_succeeds(X0,X1,X2) ),
inference(ennf_transformation,[],[f347]) ).
fof(f931,plain,
! [X0] :
( ( list_succeeds(X0)
| ( ! [X1,X2] :
( cons(X1,X2) != X0
| ~ list_succeeds(X2) )
& nil != X0 ) )
& ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2) )
| X0 = nil
| ~ list_succeeds(X0) ) ),
inference(nnf_transformation,[],[f88]) ).
fof(f932,plain,
! [X0] :
( ( list_succeeds(X0)
| ( ! [X1,X2] :
( cons(X1,X2) != X0
| ~ list_succeeds(X2) )
& nil != X0 ) )
& ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2) )
| X0 = nil
| ~ list_succeeds(X0) ) ),
inference(flattening,[],[f931]) ).
fof(f933,plain,
! [X0] :
( ( list_succeeds(X0)
| ( ! [X1,X2] :
( cons(X1,X2) != X0
| ~ list_succeeds(X2) )
& nil != X0 ) )
& ( ? [X3,X4] :
( cons(X3,X4) = X0
& list_succeeds(X4) )
| X0 = nil
| ~ list_succeeds(X0) ) ),
inference(rectify,[],[f932]) ).
fof(f934,plain,
! [X0] :
( ( list_succeeds(X0)
| ( ! [X1,X2] :
( cons(X1,X2) != X0
| ~ list_succeeds(X2) )
& nil != X0 ) )
& ( ( cons(sK86(X0),sK87(X0)) = X0
& list_succeeds(sK87(X0)) )
| X0 = nil
| ~ list_succeeds(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86,sK87]),skolemize(X3,sK86(X0)),skolemize(X4,sK87(X0))],[f933]) ).
fof(f1039,plain,
( ! [X0,X1,X2] :
( '**'(rev(X0),X1) = X2
| ~ a_reverse_succeeds(X0,X1,X2) )
| ? [X3,X4,X5] :
( '**'(rev(X3),X4) != X5
& ( ? [X6,X7] :
( cons(X6,X7) = X3
& a_reverse_succeeds(X7,cons(X6,X4),X5)
& '**'(rev(X7),cons(X6,X4)) = X5 )
| ( nil = X3
& X4 = X5 ) ) ) ),
inference(rectify,[],[f794]) ).
fof(f1040,plain,
( ! [X0,X1,X2] :
( '**'(rev(X0),X1) = X2
| ~ a_reverse_succeeds(X0,X1,X2) )
| ( sK154 != '**'(rev(sK152),sK153)
& ( ( sK152 = cons(sK155,sK156)
& a_reverse_succeeds(sK156,cons(sK155,sK153),sK154)
& sK154 = '**'(rev(sK156),cons(sK155,sK153)) )
| ( nil = sK152
& sK153 = sK154 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152,sK153,sK154,sK155,sK156]),skolemize(X3,sK152),skolemize(X4,sK153),skolemize(X5,sK154),skolemize(X6,sK155),skolemize(X7,sK156)],[f1039]) ).
fof(f1041,plain,
( sK159 != '**'(rev(sK157),sK158)
& a_reverse_succeeds(sK157,sK158,sK159) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157,sK158,sK159]),skolemize(X0,sK157),skolemize(X1,sK158),skolemize(X2,sK159)],[f795]) ).
fof(f1304,plain,
! [X0] :
( list_succeeds(X0)
| nil != X0 ),
inference(cnf_transformation,[],[f934]) ).
fof(f1504,plain,
! [X0] : list_succeeds(cons(X0,nil)),
inference(cnf_transformation,[],[f199]) ).
fof(f1525,plain,
! [X0] : '**'(nil,X0) = X0,
inference(cnf_transformation,[],[f218]) ).
fof(f1526,plain,
! [X2,X0,X1] :
( ~ list_succeeds(X1)
| '**'(cons(X0,X1),X2) = cons(X0,'**'(X1,X2)) ),
inference(cnf_transformation,[],[f604]) ).
fof(f1532,plain,
! [X2,X0,X1] :
( ~ list_succeeds(X1)
| ~ list_succeeds(X0)
| '**'('**'(X0,X1),X2) = '**'(X0,'**'(X1,X2)) ),
inference(cnf_transformation,[],[f614]) ).
fof(f1658,plain,
! [X2,X0,X1] :
( ~ a_reverse_succeeds(X0,X1,X2)
| list_succeeds(X0) ),
inference(cnf_transformation,[],[f780]) ).
fof(f1667,plain,
nil = rev(nil),
inference(cnf_transformation,[],[f342]) ).
fof(f1668,plain,
! [X0] :
( list_succeeds(rev(X0))
| ~ list_succeeds(X0) ),
inference(cnf_transformation,[],[f792]) ).
fof(f1669,plain,
! [X0,X1] :
( ~ list_succeeds(X1)
| rev(cons(X0,X1)) = '**'(rev(X1),cons(X0,nil)) ),
inference(cnf_transformation,[],[f793]) ).
fof(f1670,plain,
! [X2,X0,X1] :
( '**'(rev(X0),X1) = X2
| ~ a_reverse_succeeds(X0,X1,X2)
| sK154 = '**'(rev(sK156),cons(sK155,sK153))
| sK153 = sK154 ),
inference(cnf_transformation,[],[f1040]) ).
fof(f1671,plain,
! [X2,X0,X1] :
( '**'(rev(X0),X1) = X2
| ~ a_reverse_succeeds(X0,X1,X2)
| sK154 = '**'(rev(sK156),cons(sK155,sK153))
| nil = sK152 ),
inference(cnf_transformation,[],[f1040]) ).
fof(f1672,plain,
! [X2,X0,X1] :
( '**'(rev(X0),X1) = X2
| ~ a_reverse_succeeds(X0,X1,X2)
| a_reverse_succeeds(sK156,cons(sK155,sK153),sK154)
| sK153 = sK154 ),
inference(cnf_transformation,[],[f1040]) ).
fof(f1673,plain,
! [X2,X0,X1] :
( '**'(rev(X0),X1) = X2
| ~ a_reverse_succeeds(X0,X1,X2)
| a_reverse_succeeds(sK156,cons(sK155,sK153),sK154)
| nil = sK152 ),
inference(cnf_transformation,[],[f1040]) ).
fof(f1674,plain,
! [X2,X0,X1] :
( '**'(rev(X0),X1) = X2
| ~ a_reverse_succeeds(X0,X1,X2)
| sK152 = cons(sK155,sK156)
| sK153 = sK154 ),
inference(cnf_transformation,[],[f1040]) ).
fof(f1675,plain,
! [X2,X0,X1] :
( '**'(rev(X0),X1) = X2
| ~ a_reverse_succeeds(X0,X1,X2)
| sK152 = cons(sK155,sK156)
| nil = sK152 ),
inference(cnf_transformation,[],[f1040]) ).
fof(f1676,plain,
! [X2,X0,X1] :
( '**'(rev(X0),X1) = X2
| ~ a_reverse_succeeds(X0,X1,X2)
| sK154 != '**'(rev(sK152),sK153) ),
inference(cnf_transformation,[],[f1040]) ).
fof(f1677,plain,
a_reverse_succeeds(sK157,sK158,sK159),
inference(cnf_transformation,[],[f1041]) ).
fof(f1678,plain,
sK159 != '**'(rev(sK157),sK158),
inference(cnf_transformation,[],[f1041]) ).
fof(f1751,plain,
list_succeeds(nil),
inference(equality_resolution,[],[f1304]) ).
fof(f1810,definition,
sF160 = rev(sK157),
introduced(definition,[new_symbols(definition,[sF160])],[function_definition]) ).
fof(f1811,plain,
rev(sK157) = sF160,
inference(reorient_equations,[],[f1810]) ).
fof(f1812,definition,
sF161 = '**'(sF160,sK158),
introduced(definition,[new_symbols(definition,[sF161])],[function_definition]) ).
fof(f1813,plain,
'**'(sF160,sK158) = sF161,
inference(reorient_equations,[],[f1812]) ).
fof(f1814,plain,
sK159 != sF161,
inference(definition_folding,[],[f1678,f1813,f1811]) ).
fof(f1816,definition,
( spl162_1
<=> sK153 = sK154 ),
introduced(definition,[new_symbols(definition,[spl162_1])],[avatar_definition]) ).
fof(f1818,plain,
( sK153 = sK154
| ~ spl162_1 ),
inference(avatar_component_clause,[],[f1816]) ).
fof(f1820,definition,
( spl162_2
<=> sK154 = '**'(rev(sK156),cons(sK155,sK153)) ),
introduced(definition,[new_symbols(definition,[spl162_2])],[avatar_definition]) ).
fof(f1822,plain,
( sK154 = '**'(rev(sK156),cons(sK155,sK153))
| ~ spl162_2 ),
inference(avatar_component_clause,[],[f1820]) ).
fof(f1824,definition,
( spl162_3
<=> ! [X2,X0,X1] :
( '**'(rev(X0),X1) = X2
| ~ a_reverse_succeeds(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[spl162_3])],[avatar_definition]) ).
fof(f1825,plain,
( ! [X2,X0,X1] :
( ~ a_reverse_succeeds(X0,X1,X2)
| '**'(rev(X0),X1) = X2 )
| ~ spl162_3 ),
inference(avatar_component_clause,[],[f1824]) ).
fof(f1826,plain,
( spl162_1
| spl162_2
| spl162_3 ),
inference(avatar_split_clause,[],[f1670,f1824,f1820,f1816]) ).
fof(f1828,definition,
( spl162_4
<=> nil = sK152 ),
introduced(definition,[new_symbols(definition,[spl162_4])],[avatar_definition]) ).
fof(f1830,plain,
( nil = sK152
| ~ spl162_4 ),
inference(avatar_component_clause,[],[f1828]) ).
fof(f1831,plain,
( spl162_4
| spl162_2
| spl162_3 ),
inference(avatar_split_clause,[],[f1671,f1824,f1820,f1828]) ).
fof(f1833,definition,
( spl162_5
<=> a_reverse_succeeds(sK156,cons(sK155,sK153),sK154) ),
introduced(definition,[new_symbols(definition,[spl162_5])],[avatar_definition]) ).
fof(f1835,plain,
( a_reverse_succeeds(sK156,cons(sK155,sK153),sK154)
| ~ spl162_5 ),
inference(avatar_component_clause,[],[f1833]) ).
fof(f1836,plain,
( spl162_1
| spl162_5
| spl162_3 ),
inference(avatar_split_clause,[],[f1672,f1824,f1833,f1816]) ).
fof(f1837,plain,
( spl162_4
| spl162_5
| spl162_3 ),
inference(avatar_split_clause,[],[f1673,f1824,f1833,f1828]) ).
fof(f1839,definition,
( spl162_6
<=> sK152 = cons(sK155,sK156) ),
introduced(definition,[new_symbols(definition,[spl162_6])],[avatar_definition]) ).
fof(f1841,plain,
( sK152 = cons(sK155,sK156)
| ~ spl162_6 ),
inference(avatar_component_clause,[],[f1839]) ).
fof(f1842,plain,
( spl162_1
| spl162_6
| spl162_3 ),
inference(avatar_split_clause,[],[f1674,f1824,f1839,f1816]) ).
fof(f1843,plain,
( spl162_4
| spl162_6
| spl162_3 ),
inference(avatar_split_clause,[],[f1675,f1824,f1839,f1828]) ).
fof(f1845,definition,
( spl162_7
<=> sK154 = '**'(rev(sK152),sK153) ),
introduced(definition,[new_symbols(definition,[spl162_7])],[avatar_definition]) ).
fof(f1847,plain,
( sK154 != '**'(rev(sK152),sK153)
| spl162_7 ),
inference(avatar_component_clause,[],[f1845]) ).
fof(f1848,plain,
( ~ spl162_7
| spl162_3 ),
inference(avatar_split_clause,[],[f1676,f1824,f1845]) ).
fof(f1851,plain,
( sK159 = '**'(rev(sK157),sK158)
| ~ spl162_3 ),
inference(resolution,[],[f1677,f1825]) ).
fof(f1852,plain,
( sK159 = '**'(sF160,sK158)
| ~ spl162_3 ),
inference(forward_demodulation,[],[f1851,f1811]) ).
fof(f1853,plain,
( sK159 = sF161
| ~ spl162_3 ),
inference(forward_demodulation,[],[f1852,f1813]) ).
fof(f1854,plain,
( $false
| ~ spl162_3 ),
inference(forward_subsumption_resolution,[],[f1853,f1814]) ).
fof(f1855,plain,
~ spl162_3,
inference(avatar_contradiction_clause,[],[f1854]) ).
fof(f1856,plain,
( sK154 != '**'(rev(nil),sK153)
| ~ spl162_4
| spl162_7 ),
inference(forward_demodulation,[],[f1847,f1830]) ).
fof(f1857,plain,
( sK154 != '**'(nil,sK153)
| ~ spl162_4
| spl162_7 ),
inference(forward_demodulation,[],[f1856,f1667]) ).
fof(f1858,plain,
( sK153 != sK154
| ~ spl162_4
| spl162_7 ),
inference(forward_demodulation,[],[f1857,f1525]) ).
fof(f1859,plain,
( $false
| ~ spl162_1
| ~ spl162_4
| spl162_7 ),
inference(forward_subsumption_resolution,[],[f1858,f1818]) ).
fof(f1860,plain,
( ~ spl162_1
| ~ spl162_4
| spl162_7 ),
inference(avatar_contradiction_clause,[],[f1859]) ).
fof(f1865,plain,
( list_succeeds(sK156)
| ~ spl162_5 ),
inference(resolution,[],[f1658,f1835]) ).
fof(f1919,plain,
( ! [X0] : rev(cons(X0,sK156)) = '**'(rev(sK156),cons(X0,nil))
| ~ spl162_5 ),
inference(resolution,[],[f1865,f1669]) ).
fof(f2029,definition,
( spl162_20
<=> list_succeeds(rev(sK156)) ),
introduced(definition,[new_symbols(definition,[spl162_20])],[avatar_definition]) ).
fof(f2030,plain,
( list_succeeds(rev(sK156))
| ~ spl162_20 ),
inference(avatar_component_clause,[],[f2029]) ).
fof(f2031,plain,
( ~ list_succeeds(rev(sK156))
| spl162_20 ),
inference(avatar_component_clause,[],[f2029]) ).
fof(f2036,plain,
( ~ list_succeeds(sK156)
| spl162_20 ),
inference(resolution,[],[f2031,f1668]) ).
fof(f2037,plain,
( $false
| ~ spl162_5
| spl162_20 ),
inference(forward_subsumption_resolution,[],[f2036,f1865]) ).
fof(f2038,plain,
( ~ spl162_5
| spl162_20 ),
inference(avatar_contradiction_clause,[],[f2037]) ).
fof(f2115,plain,
! [X0,X1] : '**'(cons(X0,nil),X1) = cons(X0,'**'(nil,X1)),
inference(resolution,[],[f1751,f1526]) ).
fof(f2118,plain,
! [X0,X1] : cons(X0,X1) = '**'(cons(X0,nil),X1),
inference(forward_demodulation,[],[f2115,f1525]) ).
fof(f2348,plain,
! [X2,X0,X1] :
( ~ list_succeeds(X0)
| '**'('**'(X0,cons(X1,nil)),X2) = '**'(X0,'**'(cons(X1,nil),X2)) ),
inference(resolution,[],[f1504,f1532]) ).
fof(f2357,plain,
! [X2,X0,X1] :
( ~ list_succeeds(X0)
| '**'('**'(X0,cons(X1,nil)),X2) = '**'(X0,cons(X1,X2)) ),
inference(forward_demodulation,[],[f2348,f2118]) ).
fof(f2372,plain,
( ! [X0,X1] : '**'('**'(rev(sK156),cons(X0,nil)),X1) = '**'(rev(sK156),cons(X0,X1))
| ~ spl162_20 ),
inference(resolution,[],[f2357,f2030]) ).
fof(f2380,plain,
( ! [X0,X1] : '**'(rev(cons(X0,sK156)),X1) = '**'(rev(sK156),cons(X0,X1))
| ~ spl162_5
| ~ spl162_20 ),
inference(forward_demodulation,[],[f2372,f1919]) ).
fof(f2392,plain,
( ! [X0] : '**'(rev(sK152),X0) = '**'(rev(sK156),cons(sK155,X0))
| ~ spl162_5
| ~ spl162_6
| ~ spl162_20 ),
inference(superposition,[],[f2380,f1841]) ).
fof(f2404,plain,
( sK154 = '**'(rev(sK152),sK153)
| ~ spl162_2
| ~ spl162_5
| ~ spl162_6
| ~ spl162_20 ),
inference(superposition,[],[f2392,f1822]) ).
fof(f2420,plain,
( $false
| ~ spl162_2
| ~ spl162_5
| ~ spl162_6
| spl162_7
| ~ spl162_20 ),
inference(forward_subsumption_resolution,[],[f2404,f1847]) ).
fof(f2421,plain,
( ~ spl162_2
| ~ spl162_5
| ~ spl162_6
| spl162_7
| ~ spl162_20 ),
inference(avatar_contradiction_clause,[],[f2420]) ).
cnf(s1,plain,
( spl162_1
| spl162_2
| spl162_3 ),
inference(sat_conversion,[],[f1826]) ).
cnf(s2,plain,
( spl162_2
| spl162_3
| spl162_4 ),
inference(sat_conversion,[],[f1831]) ).
cnf(s3,plain,
( spl162_1
| spl162_3
| spl162_5 ),
inference(sat_conversion,[],[f1836]) ).
cnf(s4,plain,
( spl162_3
| spl162_4
| spl162_5 ),
inference(sat_conversion,[],[f1837]) ).
cnf(s5,plain,
( spl162_1
| spl162_3
| spl162_6 ),
inference(sat_conversion,[],[f1842]) ).
cnf(s6,plain,
( spl162_3
| spl162_4
| spl162_6 ),
inference(sat_conversion,[],[f1843]) ).
cnf(s7,plain,
( spl162_3
| ~ spl162_7 ),
inference(sat_conversion,[],[f1848]) ).
cnf(s8,plain,
~ spl162_3,
inference(sat_conversion,[],[f1855]) ).
cnf(s9,plain,
( ~ spl162_1
| ~ spl162_4
| spl162_7 ),
inference(sat_conversion,[],[f1860]) ).
cnf(s21,plain,
( ~ spl162_5
| spl162_20 ),
inference(sat_conversion,[],[f2038]) ).
cnf(s41,plain,
( ~ spl162_2
| ~ spl162_5
| ~ spl162_6
| spl162_7
| ~ spl162_20 ),
inference(sat_conversion,[],[f2421]) ).
cnf(s44,plain,
~ spl162_7,
inference(rat,[],[s7,s8]) ).
cnf(s45,plain,
( spl162_4
| spl162_6 ),
inference(rat,[],[s6,s8]) ).
cnf(s46,plain,
( spl162_1
| spl162_6 ),
inference(rat,[],[s5,s8]) ).
cnf(s47,plain,
( spl162_4
| spl162_5 ),
inference(rat,[],[s4,s8]) ).
cnf(s48,plain,
( spl162_1
| spl162_5 ),
inference(rat,[],[s3,s8]) ).
cnf(s49,plain,
( spl162_2
| spl162_4 ),
inference(rat,[],[s2,s8]) ).
cnf(s50,plain,
( spl162_1
| spl162_2 ),
inference(rat,[],[s1,s8]) ).
cnf(s51,plain,
spl162_1,
inference(rat,[],[s41,s21,s50,s48,s46,s44]) ).
cnf(s52,plain,
~ spl162_4,
inference(rat,[],[s9,s44,s51]) ).
cnf(s53,plain,
spl162_6,
inference(rat,[],[s45,s52]) ).
cnf(s54,plain,
spl162_5,
inference(rat,[],[s47,s52]) ).
cnf(s55,plain,
spl162_2,
inference(rat,[],[s49,s52]) ).
cnf(s59,plain,
spl162_20,
inference(rat,[],[s21,s54]) ).
cnf(s60,plain,
$false,
inference(rat,[],[s41,s59,s44,s53,s54,s55]) ).
fof(f2423,plain,
$false,
inference(avatar_sat_refutation,[],[s60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX061+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 14:56:43 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.22/1.92 % (1984138)Detected formulas, will run a generic FOF schedule.
% 6.22/1.92 % (1984147)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=12574635:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.22/1.92 % (1984147)Instruction limit reached!
% 6.22/1.92 % (1984147)------------------------------
% 6.22/1.92 % (1984147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/1.92 % (1984147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.92 % (1984147)CaDiCaL version: 2.1.3
% 6.22/1.92 % (1984147)Termination reason: Instruction limit
% 6.22/1.92 % (1984147)Termination phase: Saturation
% 6.22/1.92 % (1984147)Time elapsed: 0.040 s
% 6.22/1.92 % (1984147)Peak memory usage: 89 MB
% 6.22/1.92 % (1984147)Instructions burned: 120 (million)
% 6.22/1.92 % (1984143)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3618169538:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.22/1.92 % (1984146)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4098002573:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.22/1.92 % (1984148)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3848762022:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.22/1.92 % (1984144)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3867581248:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.22/1.92 % (1984149)dis-21_1_sil=8000:lcm=predicate:random_seed=2556798608:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 6.22/1.92 % (1984145)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1762272595:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.22/1.92 % (1984146)Refutation not found, incomplete strategy
% 6.22/1.92 % (1984146)------------------------------
% 6.22/1.92 % (1984146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/1.92 % (1984146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.92 % (1984146)CaDiCaL version: 2.1.3
% 6.22/1.92 % (1984146)Termination reason: Refutation not found, incomplete strategy
% 6.22/1.92 % (1984146)Time elapsed: 0.005 s
% 6.22/1.92 % (1984146)Peak memory usage: 89 MB
% 6.22/1.92 % (1984146)Instructions burned: 5 (million)
% 6.22/1.92 % (1984149)Instruction limit reached!
% 6.22/1.92 % (1984149)------------------------------
% 6.22/1.92 % (1984149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/1.92 % (1984149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.92 % (1984149)CaDiCaL version: 2.1.3
% 6.22/1.92 % (1984149)Termination reason: Instruction limit
% 6.22/1.92 % (1984149)Termination phase: Saturation
% 6.22/1.92 % (1984149)Time elapsed: 0.079 s
% 6.22/1.92 % (1984149)Peak memory usage: 89 MB
% 6.22/1.92 % (1984149)Instructions burned: 129 (million)
% 6.22/1.92 % (1984148)Instruction limit reached!
% 6.22/1.92 % (1984148)------------------------------
% 6.22/1.92 % (1984148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/1.92 % (1984148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.92 % (1984148)CaDiCaL version: 2.1.3
% 6.22/1.92 % (1984148)Termination reason: Instruction limit
% 6.22/1.92 % (1984148)Termination phase: Saturation
% 6.22/1.92 % (1984148)Time elapsed: 0.098 s
% 6.22/1.92 % (1984148)Peak memory usage: 90 MB
% 6.22/1.92 % (1984148)Instructions burned: 140 (million)
% 6.22/1.92 % (1984157)lrs+10_1_sil=8000:sp=occurrence:random_seed=2944687256:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.22/1.92 % (1984157)Instruction limit reached!
% 6.22/1.92 % (1984157)------------------------------
% 6.22/1.92 % (1984157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/1.92 % (1984157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.92 % (1984157)CaDiCaL version: 2.1.3
% 6.22/1.92 % (1984157)Termination reason: Instruction limit
% 6.22/1.92 % (1984157)Termination phase: Saturation
% 6.22/1.92 % (1984157)Time elapsed: 0.099 s
% 6.22/1.92 % (1984157)Peak memory usage: 92 MB
% 6.22/1.92 % (1984157)Instructions burned: 285 (million)
% 6.22/1.92 % (1984158)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3039723302:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.22/1.92 % (1984146)------------------------------
% 6.22/1.92 % (1984146)------------------------------
% 6.22/1.92 % (1984159)lrs+1011_1_sil=32000:sp=occurrence:random_seed=515261717:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.22/1.92 % (1984158)Instruction limit reached!
% 6.22/1.92 % (1984158)------------------------------
% 6.22/1.92 % (1984158)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/1.92 % (1984158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.92 % (1984158)CaDiCaL version: 2.1.3
% 6.22/1.92 % (1984158)Termination reason: Instruction limit
% 6.22/1.92 % (1984158)Termination phase: Saturation
% 6.22/1.92 % (1984158)Time elapsed: 0.085 s
% 6.22/1.92 % (1984158)Peak memory usage: 91 MB
% 6.22/1.92 % (1984158)Instructions burned: 158 (million)
% 6.22/1.92 % (1984161)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1236040474:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.22/1.92 % (1984163)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=253747176:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.22/1.92 % (1984163)Refutation not found, incomplete strategy
% 6.22/1.92 % (1984163)------------------------------
% 6.22/1.92 % (1984163)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/1.92 % (1984163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.92 % (1984163)CaDiCaL version: 2.1.3
% 6.22/1.92 % (1984163)Termination reason: Refutation not found, incomplete strategy
% 6.22/1.92 % (1984163)Time elapsed: 0.010 s
% 6.22/1.92 % (1984163)Peak memory usage: 89 MB
% 6.22/1.92 % (1984163)Instructions burned: 16 (million)
% 6.22/1.92 % (1984161)Instruction limit reached!
% 6.22/1.92 % (1984161)------------------------------
% 6.22/1.92 % (1984161)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/1.92 % (1984161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.92 % (1984161)CaDiCaL version: 2.1.3
% 6.22/1.92 % (1984161)Termination reason: Instruction limit
% 6.22/1.92 % (1984161)Termination phase: Saturation
% 6.22/1.92 % (1984161)Time elapsed: 0.079 s
% 6.22/1.92 % (1984161)Peak memory usage: 93 MB
% 6.22/1.92 % (1984161)Instructions burned: 249 (million)
% 6.22/1.92 % (1984159)Instruction limit reached!
% 6.22/1.92 % (1984159)------------------------------
% 6.22/1.92 % (1984159)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/1.92 % (1984159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.92 % (1984159)CaDiCaL version: 2.1.3
% 6.22/1.92 % (1984159)Termination reason: Instruction limit
% 6.22/1.92 % (1984159)Termination phase: Saturation
% 6.22/1.92 % (1984159)Time elapsed: 0.229 s
% 6.22/1.92 % (1984159)Peak memory usage: 93 MB
% 6.22/1.92 % (1984159)Instructions burned: 326 (million)
% 6.22/1.92 % (1984165)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1670179092:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.22/1.92 % (1984168)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1217508705:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.22/1.92 % (1984168)Instruction limit reached!
% 6.22/1.92 % (1984168)------------------------------
% 6.22/1.92 % (1984168)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/1.92 % (1984168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.92 % (1984168)CaDiCaL version: 2.1.3
% 6.22/1.92 % (1984168)Termination reason: Instruction limit
% 6.22/1.92 % (1984168)Termination phase: Saturation
% 6.22/1.92 % (1984168)Time elapsed: 0.038 s
% 6.22/1.92 % (1984168)Peak memory usage: 91 MB
% 6.22/1.92 % (1984168)Instructions burned: 113 (million)
% 6.22/1.92 % (1984163)------------------------------
% 6.22/1.92 % (1984163)------------------------------
% 6.22/1.92 % (1984170)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4180952344:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.22/1.92 % (1984172)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1593587521:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.22/1.92 % (1984170)Instruction limit reached!
% 6.22/1.92 % (1984170)------------------------------
% 6.22/1.92 % (1984170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/1.92 % (1984170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.92 % (1984170)CaDiCaL version: 2.1.3
% 6.22/1.92 % (1984170)Termination reason: Instruction limit
% 6.22/1.92 % (1984170)Termination phase: Saturation
% 6.22/1.92 % (1984170)Time elapsed: 0.067 s
% 6.22/1.92 % (1984170)Peak memory usage: 90 MB
% 6.22/1.92 % (1984170)Instructions burned: 128 (million)
% 6.22/1.92 % (1984172)Instruction limit reached!
% 6.22/1.92 % (1984172)------------------------------
% 6.22/1.92 % (1984172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.22/1.92 % (1984172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.22/1.92 % (1984172)CaDiCaL version: 2.1.3
% 6.22/1.92 % (1984172)Termination reason: Instruction limit
% 6.22/1.92 % (1984172)Termination phase: Saturation
% 6.22/1.92 % (1984172)Time elapsed: 0.035 s
% 6.22/1.92 % (1984172)Peak memory usage: 89 MB
% 6.22/1.92 % (1984172)Instructions burned: 115 (million)
% 6.22/1.92 % (1984143)First to succeed.
% 6.22/1.92 % (1984143)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1984138"
% 6.22/1.92 % (1984173)lrs+10_1_sil=8000:sp=occurrence:random_seed=1691389609:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.22/1.92 % (1984176)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2344223887:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 6.22/1.92 % (1984177)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4065118192:i=5202:ss=axioms:sgt=16_2990 on theBenchmark for (2990ds/5202Mi)
% 6.22/1.92 % (1984143)Refutation found. Thanks to Tanya!
% 6.22/1.92 % SZS status Theorem for theBenchmark
% 6.22/1.92 % SZS output start Proof for theBenchmark
% See solution above
% 9.42/2.12 % (1984143)------------------------------
% 9.42/2.12 % (1984143)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.42/2.12 % (1984143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.42/2.12 % (1984143)CaDiCaL version: 2.1.3
% 9.42/2.12 % (1984143)Termination reason: Refutation
% 9.42/2.12 % (1984143)Time elapsed: 0.809 s
% 9.42/2.12 % (1984143)Peak memory usage: 134 MB
% 9.42/2.12 % (1984143)Instructions burned: 1240 (million)
% 9.42/2.12 % (1984143)------------------------------
% 9.42/2.12 % (1984143)------------------------------
% 9.42/2.12 % (1984138)Success in time 1.254 s
% 9.42/2.12 % Vampire exiting
%------------------------------------------------------------------------------