%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX053+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 : n004.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 01:45:46 PM UTC 2026
% Result : Theorem 7.15s 1.93s
% Output : Refutation 8.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 109 ( 27 unt; 11 def)
% Number of atoms : 348 ( 121 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 398 ( 159 ~; 171 |; 43 &)
% ( 10 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-3 aty)
% Number of variables : 196 ( 0 sgn 152 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : '0' != s(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id2) ).
fof(f61,axiom,
! [X0,X1,X2] :
( delete_succeeds(X0,X1,X2)
<=> ( ? [X3,X4,X5] :
( X1 = cons(X3,X4)
& X2 = cons(X3,X5)
& delete_succeeds(X0,X4,X5) )
| X1 = cons(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id61) ).
fof(f286,axiom,
! [X0] : occ(X0,nil) = '0',
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(occ:nil)') ).
fof(f287,axiom,
! [X0,X1,X2] :
( ( list_succeeds(X2)
& X0 != X1 )
=> occ(X0,cons(X1,X2)) = occ(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(occ:cons:diff)') ).
fof(f296,axiom,
( ! [X0] :
( ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2)
& ! [X3,X4] :
( occ(X3,X2) = s(X4)
=> ? [X5] : delete_succeeds(X3,X2,X5) ) )
| X0 = nil )
=> ! [X3,X4] :
( occ(X3,X0) = s(X4)
=> ? [X5] : delete_succeeds(X3,X0,X5) ) )
=> ! [X0] :
( list_succeeds(X0)
=> ! [X3,X4] :
( occ(X3,X0) = s(X4)
=> ? [X5] : delete_succeeds(X3,X0,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction) ).
fof(f297,conjecture,
! [X0,X1,X2] :
( ( list_succeeds(X1)
& occ(X0,X1) = s(X2) )
=> ? [X3] : delete_succeeds(X0,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(occ:successor)') ).
fof(f298,negated_conjecture,
~ ! [X0,X1,X2] :
( ( list_succeeds(X1)
& occ(X0,X1) = s(X2) )
=> ? [X3] : delete_succeeds(X0,X1,X3) ),
inference(negated_conjecture,[status(cth)],[f297]) ).
fof(f323,plain,
( ! [X0] :
( ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2)
& ! [X3,X4] :
( occ(X3,X2) = s(X4)
=> ? [X5] : delete_succeeds(X3,X2,X5) ) )
| X0 = nil )
=> ! [X6,X7] :
( s(X7) = occ(X6,X0)
=> ? [X8] : delete_succeeds(X6,X0,X8) ) )
=> ! [X9] :
( list_succeeds(X9)
=> ! [X10,X11] :
( s(X11) = occ(X10,X9)
=> ? [X12] : delete_succeeds(X10,X9,X12) ) ) ),
inference(rectify,[],[f296]) ).
fof(f665,plain,
! [X0,X1,X2] :
( occ(X0,cons(X1,X2)) = occ(X0,X2)
| ~ list_succeeds(X2)
| X0 = X1 ),
inference(ennf_transformation,[],[f287]) ).
fof(f666,plain,
! [X0,X1,X2] :
( occ(X0,cons(X1,X2)) = occ(X0,X2)
| ~ list_succeeds(X2)
| X0 = X1 ),
inference(flattening,[],[f665]) ).
fof(f680,plain,
( ! [X9] :
( ! [X10,X11] :
( ? [X12] : delete_succeeds(X10,X9,X12)
| s(X11) != occ(X10,X9) )
| ~ list_succeeds(X9) )
| ? [X0] :
( ? [X6,X7] :
( ! [X8] : ~ delete_succeeds(X6,X0,X8)
& s(X7) = occ(X6,X0) )
& ( ? [X1,X2] :
( X0 = cons(X1,X2)
& list_succeeds(X2)
& ! [X3,X4] :
( ? [X5] : delete_succeeds(X3,X2,X5)
| s(X4) != occ(X3,X2) ) )
| X0 = nil ) ) ),
inference(ennf_transformation,[],[f323]) ).
fof(f681,plain,
? [X0,X1,X2] :
( ! [X3] : ~ delete_succeeds(X0,X1,X3)
& list_succeeds(X1)
& occ(X0,X1) = s(X2) ),
inference(ennf_transformation,[],[f298]) ).
fof(f682,plain,
? [X0,X1,X2] :
( ! [X3] : ~ delete_succeeds(X0,X1,X3)
& list_succeeds(X1)
& occ(X0,X1) = s(X2) ),
inference(flattening,[],[f681]) ).
fof(f750,plain,
! [X0,X1,X2] :
( ( delete_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X1
| cons(X3,X5) != X2
| ~ delete_succeeds(X0,X4,X5) )
& cons(X0,X2) != X1 ) )
& ( ? [X3,X4,X5] :
( X1 = cons(X3,X4)
& X2 = cons(X3,X5)
& delete_succeeds(X0,X4,X5) )
| X1 = cons(X0,X2)
| ~ delete_succeeds(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f751,plain,
! [X0,X1,X2] :
( ( delete_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X1
| cons(X3,X5) != X2
| ~ delete_succeeds(X0,X4,X5) )
& cons(X0,X2) != X1 ) )
& ( ? [X3,X4,X5] :
( X1 = cons(X3,X4)
& X2 = cons(X3,X5)
& delete_succeeds(X0,X4,X5) )
| X1 = cons(X0,X2)
| ~ delete_succeeds(X0,X1,X2) ) ),
inference(flattening,[],[f750]) ).
fof(f752,plain,
! [X0,X1,X2] :
( ( delete_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X1
| cons(X3,X5) != X2
| ~ delete_succeeds(X0,X4,X5) )
& cons(X0,X2) != X1 ) )
& ( ? [X6,X7,X8] :
( cons(X6,X7) = X1
& cons(X6,X8) = X2
& delete_succeeds(X0,X7,X8) )
| X1 = cons(X0,X2)
| ~ delete_succeeds(X0,X1,X2) ) ),
inference(rectify,[],[f751]) ).
fof(f753,plain,
! [X0,X1,X2] :
( ( delete_succeeds(X0,X1,X2)
| ( ! [X3,X4,X5] :
( cons(X3,X4) != X1
| cons(X3,X5) != X2
| ~ delete_succeeds(X0,X4,X5) )
& cons(X0,X2) != X1 ) )
& ( ( cons(sK36(X0,X1,X2),sK37(X0,X1,X2)) = X1
& cons(sK36(X0,X1,X2),sK38(X0,X1,X2)) = X2
& delete_succeeds(X0,sK37(X0,X1,X2),sK38(X0,X1,X2)) )
| X1 = cons(X0,X2)
| ~ delete_succeeds(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36,sK37,sK38]),skolemize(X6,sK36(X0,X1,X2)),skolemize(X7,sK37(X0,X1,X2)),skolemize(X8,sK38(X0,X1,X2))],[f752]) ).
fof(f895,plain,
( ! [X0] :
( ! [X1,X2] :
( ? [X3] : delete_succeeds(X1,X0,X3)
| s(X2) != occ(X1,X0) )
| ~ list_succeeds(X0) )
| ? [X4] :
( ? [X5,X6] :
( ! [X7] : ~ delete_succeeds(X5,X4,X7)
& s(X6) = occ(X5,X4) )
& ( ? [X8,X9] :
( cons(X8,X9) = X4
& list_succeeds(X9)
& ! [X10,X11] :
( ? [X12] : delete_succeeds(X10,X9,X12)
| s(X11) != occ(X10,X9) ) )
| nil = X4 ) ) ),
inference(rectify,[],[f680]) ).
fof(f896,plain,
( ! [X0] :
( ! [X1,X2] :
( delete_succeeds(X1,X0,sK131(X0,X1))
| s(X2) != occ(X1,X0) )
| ~ list_succeeds(X0) )
| ( ! [X7] : ~ delete_succeeds(sK133,sK132,X7)
& s(sK134) = occ(sK133,sK132)
& ( ( sK132 = cons(sK135,sK136)
& list_succeeds(sK136)
& ! [X10,X11] :
( delete_succeeds(X10,sK136,sK137(X10))
| s(X11) != occ(X10,sK136) ) )
| nil = sK132 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131,sK132,sK133,sK134,sK135,sK136,sK137]),skolemize(X3,sK131(X0,X1)),skolemize(X4,sK132),skolemize(X5,sK133),skolemize(X6,sK134),skolemize(X8,sK135),skolemize(X9,sK136),skolemize(X12,sK137(X10))],[f895]) ).
fof(f897,plain,
( ! [X3] : ~ delete_succeeds(sK138,sK139,X3)
& list_succeeds(sK139)
& s(sK140) = occ(sK138,sK139) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138,sK139,sK140]),skolemize(X0,sK138),skolemize(X1,sK139),skolemize(X2,sK140)],[f682]) ).
fof(f899,plain,
! [X0] : '0' != s(X0),
inference(cnf_transformation,[],[f2]) ).
fof(f1049,plain,
! [X2,X0,X1] :
( delete_succeeds(X0,X1,X2)
| cons(X0,X2) != X1 ),
inference(cnf_transformation,[],[f753]) ).
fof(f1050,plain,
! [X2,X3,X0,X1,X4,X5] :
( delete_succeeds(X0,X1,X2)
| cons(X3,X4) != X1
| cons(X3,X5) != X2
| ~ delete_succeeds(X0,X4,X5) ),
inference(cnf_transformation,[],[f753]) ).
fof(f1432,plain,
! [X0] : '0' = occ(X0,nil),
inference(cnf_transformation,[],[f286]) ).
fof(f1433,plain,
! [X2,X0,X1] :
( ~ list_succeeds(X2)
| occ(X0,cons(X1,X2)) = occ(X0,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f666]) ).
fof(f1442,plain,
! [X2,X10,X0,X11,X1] :
( delete_succeeds(X1,X0,sK131(X0,X1))
| s(X2) != occ(X1,X0)
| ~ list_succeeds(X0)
| delete_succeeds(X10,sK136,sK137(X10))
| s(X11) != occ(X10,sK136)
| nil = sK132 ),
inference(cnf_transformation,[],[f896]) ).
fof(f1443,plain,
! [X2,X0,X1] :
( delete_succeeds(X1,X0,sK131(X0,X1))
| s(X2) != occ(X1,X0)
| ~ list_succeeds(X0)
| list_succeeds(sK136)
| nil = sK132 ),
inference(cnf_transformation,[],[f896]) ).
fof(f1444,plain,
! [X2,X0,X1] :
( delete_succeeds(X1,X0,sK131(X0,X1))
| s(X2) != occ(X1,X0)
| ~ list_succeeds(X0)
| sK132 = cons(sK135,sK136)
| nil = sK132 ),
inference(cnf_transformation,[],[f896]) ).
fof(f1445,plain,
! [X2,X0,X1] :
( delete_succeeds(X1,X0,sK131(X0,X1))
| s(X2) != occ(X1,X0)
| ~ list_succeeds(X0)
| s(sK134) = occ(sK133,sK132) ),
inference(cnf_transformation,[],[f896]) ).
fof(f1446,plain,
! [X2,X0,X1,X7] :
( delete_succeeds(X1,X0,sK131(X0,X1))
| s(X2) != occ(X1,X0)
| ~ list_succeeds(X0)
| ~ delete_succeeds(sK133,sK132,X7) ),
inference(cnf_transformation,[],[f896]) ).
fof(f1447,plain,
s(sK140) = occ(sK138,sK139),
inference(cnf_transformation,[],[f897]) ).
fof(f1448,plain,
list_succeeds(sK139),
inference(cnf_transformation,[],[f897]) ).
fof(f1449,plain,
! [X3] : ~ delete_succeeds(sK138,sK139,X3),
inference(cnf_transformation,[],[f897]) ).
fof(f1473,plain,
! [X2,X3,X0,X4,X5] :
( delete_succeeds(X0,cons(X3,X4),X2)
| cons(X3,X5) != X2
| ~ delete_succeeds(X0,X4,X5) ),
inference(equality_resolution,[],[f1050]) ).
fof(f1474,plain,
! [X3,X0,X4,X5] :
( delete_succeeds(X0,cons(X3,X4),cons(X3,X5))
| ~ delete_succeeds(X0,X4,X5) ),
inference(equality_resolution,[],[f1473]) ).
fof(f1475,plain,
! [X2,X0] : delete_succeeds(X0,cons(X0,X2),X2),
inference(equality_resolution,[],[f1049]) ).
fof(f1565,definition,
sF141 = s(sK140),
introduced(definition,[new_symbols(definition,[sF141])],[function_definition]) ).
fof(f1566,plain,
s(sK140) = sF141,
inference(reorient_equations,[],[f1565]) ).
fof(f1567,definition,
sF142 = occ(sK138,sK139),
introduced(definition,[new_symbols(definition,[sF142])],[function_definition]) ).
fof(f1568,plain,
occ(sK138,sK139) = sF142,
inference(reorient_equations,[],[f1567]) ).
fof(f1569,plain,
sF141 = sF142,
inference(definition_folding,[],[f1447,f1568,f1566]) ).
fof(f1571,definition,
( spl143_1
<=> nil = sK132 ),
introduced(definition,[new_symbols(definition,[spl143_1])],[avatar_definition]) ).
fof(f1573,plain,
( nil = sK132
| ~ spl143_1 ),
inference(avatar_component_clause,[],[f1571]) ).
fof(f1575,definition,
( spl143_2
<=> ! [X11,X10] :
( delete_succeeds(X10,sK136,sK137(X10))
| s(X11) != occ(X10,sK136) ) ),
introduced(definition,[new_symbols(definition,[spl143_2])],[avatar_definition]) ).
fof(f1576,plain,
( ! [X10,X11] :
( s(X11) != occ(X10,sK136)
| delete_succeeds(X10,sK136,sK137(X10)) )
| ~ spl143_2 ),
inference(avatar_component_clause,[],[f1575]) ).
fof(f1578,definition,
( spl143_3
<=> ! [X2,X0,X1] :
( delete_succeeds(X1,X0,sK131(X0,X1))
| ~ list_succeeds(X0)
| s(X2) != occ(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl143_3])],[avatar_definition]) ).
fof(f1579,plain,
( ! [X2,X0,X1] :
( s(X2) != occ(X1,X0)
| ~ list_succeeds(X0)
| delete_succeeds(X1,X0,sK131(X0,X1)) )
| ~ spl143_3 ),
inference(avatar_component_clause,[],[f1578]) ).
fof(f1580,plain,
( spl143_1
| spl143_2
| spl143_3 ),
inference(avatar_split_clause,[],[f1442,f1578,f1575,f1571]) ).
fof(f1582,definition,
( spl143_4
<=> list_succeeds(sK136) ),
introduced(definition,[new_symbols(definition,[spl143_4])],[avatar_definition]) ).
fof(f1584,plain,
( list_succeeds(sK136)
| ~ spl143_4 ),
inference(avatar_component_clause,[],[f1582]) ).
fof(f1585,plain,
( spl143_1
| spl143_4
| spl143_3 ),
inference(avatar_split_clause,[],[f1443,f1578,f1582,f1571]) ).
fof(f1587,definition,
( spl143_5
<=> sK132 = cons(sK135,sK136) ),
introduced(definition,[new_symbols(definition,[spl143_5])],[avatar_definition]) ).
fof(f1589,plain,
( sK132 = cons(sK135,sK136)
| ~ spl143_5 ),
inference(avatar_component_clause,[],[f1587]) ).
fof(f1590,plain,
( spl143_1
| spl143_5
| spl143_3 ),
inference(avatar_split_clause,[],[f1444,f1578,f1587,f1571]) ).
fof(f1592,definition,
( spl143_6
<=> s(sK134) = occ(sK133,sK132) ),
introduced(definition,[new_symbols(definition,[spl143_6])],[avatar_definition]) ).
fof(f1594,plain,
( s(sK134) = occ(sK133,sK132)
| ~ spl143_6 ),
inference(avatar_component_clause,[],[f1592]) ).
fof(f1595,plain,
( spl143_6
| spl143_3 ),
inference(avatar_split_clause,[],[f1445,f1578,f1592]) ).
fof(f1597,definition,
( spl143_7
<=> ! [X7] : ~ delete_succeeds(sK133,sK132,X7) ),
introduced(definition,[new_symbols(definition,[spl143_7])],[avatar_definition]) ).
fof(f1598,plain,
( ! [X7] : ~ delete_succeeds(sK133,sK132,X7)
| ~ spl143_7 ),
inference(avatar_component_clause,[],[f1597]) ).
fof(f1599,plain,
( spl143_7
| spl143_3 ),
inference(avatar_split_clause,[],[f1446,f1578,f1597]) ).
fof(f1601,plain,
occ(sK138,sK139) = sF141,
inference(forward_demodulation,[],[f1568,f1569]) ).
fof(f1603,plain,
( ! [X0] :
( s(X0) != sF141
| ~ list_succeeds(sK139)
| delete_succeeds(sK138,sK139,sK131(sK139,sK138)) )
| ~ spl143_3 ),
inference(superposition,[],[f1579,f1601]) ).
fof(f1604,plain,
( ! [X0] :
( s(X0) != sF141
| delete_succeeds(sK138,sK139,sK131(sK139,sK138)) )
| ~ spl143_3 ),
inference(forward_subsumption_resolution,[],[f1603,f1448]) ).
fof(f1605,plain,
( ! [X0] : s(X0) != sF141
| ~ spl143_3 ),
inference(forward_subsumption_resolution,[],[f1604,f1449]) ).
fof(f1606,plain,
( sF141 != sF141
| ~ spl143_3 ),
inference(superposition,[],[f1605,f1566]) ).
fof(f1607,plain,
( $false
| ~ spl143_3 ),
inference(trivial_inequality_removal,[],[f1606]) ).
fof(f1608,plain,
~ spl143_3,
inference(avatar_contradiction_clause,[],[f1607]) ).
fof(f1609,plain,
( s(sK134) = occ(sK133,nil)
| ~ spl143_1
| ~ spl143_6 ),
inference(forward_demodulation,[],[f1594,f1573]) ).
fof(f1611,plain,
( '0' = s(sK134)
| ~ spl143_1
| ~ spl143_6 ),
inference(forward_demodulation,[],[f1609,f1432]) ).
fof(f1612,plain,
( $false
| ~ spl143_1
| ~ spl143_6 ),
inference(forward_subsumption_resolution,[],[f1611,f899]) ).
fof(f1613,plain,
( ~ spl143_1
| ~ spl143_6 ),
inference(avatar_contradiction_clause,[],[f1612]) ).
fof(f1616,plain,
( delete_succeeds(sK135,sK132,sK136)
| ~ spl143_5 ),
inference(superposition,[],[f1475,f1589]) ).
fof(f1619,plain,
( ! [X0,X1] :
( occ(X0,sK136) = occ(X0,cons(X1,sK136))
| X0 = X1 )
| ~ spl143_4 ),
inference(resolution,[],[f1433,f1584]) ).
fof(f1620,plain,
( ! [X0] :
( occ(X0,sK136) = occ(X0,sK132)
| sK135 = X0 )
| ~ spl143_4
| ~ spl143_5 ),
inference(superposition,[],[f1619,f1589]) ).
fof(f1622,plain,
( ! [X0,X1] :
( s(X1) != occ(X0,sK132)
| delete_succeeds(X0,sK136,sK137(X0))
| sK135 = X0 )
| ~ spl143_2
| ~ spl143_4
| ~ spl143_5 ),
inference(superposition,[],[f1576,f1620]) ).
fof(f1623,plain,
( ! [X0,X1] :
( delete_succeeds(X0,sK132,cons(sK135,X1))
| ~ delete_succeeds(X0,sK136,X1) )
| ~ spl143_5 ),
inference(superposition,[],[f1474,f1589]) ).
fof(f1625,plain,
( ! [X0] : ~ delete_succeeds(sK133,sK136,X0)
| ~ spl143_5
| ~ spl143_7 ),
inference(resolution,[],[f1623,f1598]) ).
fof(f1629,plain,
( ! [X0] :
( s(X0) != s(sK134)
| delete_succeeds(sK133,sK136,sK137(sK133))
| sK133 = sK135 )
| ~ spl143_2
| ~ spl143_4
| ~ spl143_5
| ~ spl143_6 ),
inference(superposition,[],[f1622,f1594]) ).
fof(f1630,plain,
( ! [X0] :
( s(X0) != s(sK134)
| sK133 = sK135 )
| ~ spl143_2
| ~ spl143_4
| ~ spl143_5
| ~ spl143_6
| ~ spl143_7 ),
inference(forward_subsumption_resolution,[],[f1629,f1625]) ).
fof(f1632,definition,
( spl143_8
<=> sK133 = sK135 ),
introduced(definition,[new_symbols(definition,[spl143_8])],[avatar_definition]) ).
fof(f1634,plain,
( sK133 = sK135
| ~ spl143_8 ),
inference(avatar_component_clause,[],[f1632]) ).
fof(f1636,definition,
( spl143_9
<=> ! [X0] : s(X0) != s(sK134) ),
introduced(definition,[new_symbols(definition,[spl143_9])],[avatar_definition]) ).
fof(f1637,plain,
( ! [X0] : s(X0) != s(sK134)
| ~ spl143_9 ),
inference(avatar_component_clause,[],[f1636]) ).
fof(f1638,plain,
( spl143_8
| spl143_9
| ~ spl143_2
| ~ spl143_4
| ~ spl143_5
| ~ spl143_6
| ~ spl143_7 ),
inference(avatar_split_clause,[],[f1630,f1597,f1592,f1587,f1582,f1575,f1636,f1632]) ).
fof(f1641,plain,
( $false
| ~ spl143_9 ),
inference(equality_resolution,[],[f1637]) ).
fof(f1642,plain,
~ spl143_9,
inference(avatar_contradiction_clause,[],[f1641]) ).
fof(f1645,plain,
( delete_succeeds(sK133,sK132,sK136)
| ~ spl143_5
| ~ spl143_8 ),
inference(superposition,[],[f1616,f1634]) ).
fof(f1650,plain,
( $false
| ~ spl143_5
| ~ spl143_7
| ~ spl143_8 ),
inference(forward_subsumption_resolution,[],[f1645,f1598]) ).
fof(f1651,plain,
( ~ spl143_5
| ~ spl143_7
| ~ spl143_8 ),
inference(avatar_contradiction_clause,[],[f1650]) ).
cnf(s1,plain,
( spl143_1
| spl143_2
| spl143_3 ),
inference(sat_conversion,[],[f1580]) ).
cnf(s2,plain,
( spl143_1
| spl143_3
| spl143_4 ),
inference(sat_conversion,[],[f1585]) ).
cnf(s3,plain,
( spl143_1
| spl143_3
| spl143_5 ),
inference(sat_conversion,[],[f1590]) ).
cnf(s4,plain,
( spl143_3
| spl143_6 ),
inference(sat_conversion,[],[f1595]) ).
cnf(s5,plain,
( spl143_3
| spl143_7 ),
inference(sat_conversion,[],[f1599]) ).
cnf(s6,plain,
~ spl143_3,
inference(sat_conversion,[],[f1608]) ).
cnf(s7,plain,
( ~ spl143_1
| ~ spl143_6 ),
inference(sat_conversion,[],[f1613]) ).
cnf(s8,plain,
( ~ spl143_2
| ~ spl143_4
| ~ spl143_5
| ~ spl143_6
| ~ spl143_7
| spl143_8
| spl143_9 ),
inference(sat_conversion,[],[f1638]) ).
cnf(s9,plain,
~ spl143_9,
inference(sat_conversion,[],[f1642]) ).
cnf(s10,plain,
( ~ spl143_5
| ~ spl143_7
| ~ spl143_8 ),
inference(sat_conversion,[],[f1651]) ).
cnf(s11,plain,
( ~ spl143_2
| ~ spl143_4
| ~ spl143_5
| ~ spl143_6
| ~ spl143_7
| spl143_8 ),
inference(rat,[],[s8,s9]) ).
cnf(s12,plain,
spl143_7,
inference(rat,[],[s5,s6]) ).
cnf(s13,plain,
spl143_6,
inference(rat,[],[s4,s6]) ).
cnf(s14,plain,
~ spl143_1,
inference(rat,[],[s7,s13]) ).
cnf(s15,plain,
spl143_5,
inference(rat,[],[s3,s6,s14]) ).
cnf(s16,plain,
~ spl143_8,
inference(rat,[],[s10,s12,s15]) ).
cnf(s17,plain,
spl143_4,
inference(rat,[],[s2,s6,s14]) ).
cnf(s18,plain,
~ spl143_2,
inference(rat,[],[s11,s16,s12,s13,s15,s17]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s1,s6,s18,s14]) ).
fof(f1653,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX053+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.26 % Computer : n004.cluster.edu
% 0.13/0.26 % Model : x86_64 x86_64
% 0.13/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.26 % Memory : 8046.5625MB
% 0.13/0.26 % OS : Linux 6.8.0-71-generic
% 0.13/0.26 % CPULimit : 300
% 0.13/0.26 % WCLimit : 300
% 0.13/0.26 % DateTime : Mon Sep 28 14:54:37 UTC 2026
% 0.13/0.26 % CPUTime :
% 0.13/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.29/0.31 Running first-order theorem proving
% 0.29/0.31 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
% 7.15/1.93 % (435829)Detected formulas, will run a generic FOF schedule.
% 7.15/1.93 % (435844)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=3522599902:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.15/1.93 % (435845)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=3624669923:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.15/1.93 % (435846)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=2903384596:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.15/1.93 % (435847)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=902999125:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.15/1.93 % (435848)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1885293934:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.15/1.93 % (435849)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=317986180:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.15/1.93 % (435850)dis-21_1_sil=8000:lcm=predicate:random_seed=4183331916: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)
% 7.15/1.93 % (435847)Instruction limit reached!
% 7.15/1.93 % (435847)------------------------------
% 7.15/1.93 % (435847)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/1.93 % (435847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/1.93 % (435847)CaDiCaL version: 2.1.3
% 7.15/1.93 % (435847)Termination reason: Instruction limit
% 7.15/1.93 % (435847)Termination phase: Saturation
% 7.15/1.93 % (435847)Time elapsed: 0.119 s
% 7.15/1.93 % (435847)Peak memory usage: 89 MB
% 7.15/1.93 % (435847)Instructions burned: 109 (million)
% 7.15/1.93 % (435848)Instruction limit reached!
% 7.15/1.93 % (435848)------------------------------
% 7.15/1.93 % (435848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/1.93 % (435848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/1.93 % (435848)CaDiCaL version: 2.1.3
% 7.15/1.93 % (435848)Termination reason: Instruction limit
% 7.15/1.93 % (435848)Termination phase: Saturation
% 7.15/1.93 % (435848)Time elapsed: 0.118 s
% 7.15/1.93 % (435848)Peak memory usage: 89 MB
% 7.15/1.93 % (435848)Instructions burned: 120 (million)
% 7.15/1.93 % (435850)Instruction limit reached!
% 7.15/1.93 % (435850)------------------------------
% 7.15/1.93 % (435850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/1.93 % (435850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/1.93 % (435850)CaDiCaL version: 2.1.3
% 7.15/1.93 % (435850)Termination reason: Instruction limit
% 7.15/1.93 % (435850)Termination phase: Saturation
% 7.15/1.93 % (435850)Time elapsed: 0.134 s
% 7.15/1.93 % (435850)Peak memory usage: 90 MB
% 7.15/1.93 % (435850)Instructions burned: 129 (million)
% 7.15/1.93 % (435849)Instruction limit reached!
% 7.15/1.93 % (435849)------------------------------
% 7.15/1.93 % (435849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/1.93 % (435849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/1.93 % (435849)CaDiCaL version: 2.1.3
% 7.15/1.93 % (435849)Termination reason: Instruction limit
% 7.15/1.93 % (435849)Termination phase: Saturation
% 7.15/1.93 % (435849)Time elapsed: 0.163 s
% 7.15/1.93 % (435849)Peak memory usage: 91 MB
% 7.15/1.93 % (435849)Instructions burned: 139 (million)
% 7.15/1.93 % (435862)lrs+10_1_sil=8000:sp=occurrence:random_seed=291758384:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 7.15/1.93 % (435863)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2016916572:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 7.15/1.93 % (435864)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3395292336:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 7.15/1.93 % (435865)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=2420922121:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 7.15/1.93 % (435863)Instruction limit reached!
% 7.15/1.93 % (435863)------------------------------
% 7.15/1.93 % (435863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/1.93 % (435863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/1.93 % (435863)CaDiCaL version: 2.1.3
% 7.15/1.93 % (435863)Termination reason: Instruction limit
% 7.15/1.93 % (435863)Termination phase: Saturation
% 7.15/1.93 % (435863)Time elapsed: 0.146 s
% 7.15/1.93 % (435863)Peak memory usage: 91 MB
% 7.15/1.93 % (435863)Instructions burned: 157 (million)
% 7.15/1.93 % (435844)First to succeed.
% 7.15/1.93 % (435844)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-435829"
% 7.15/1.93 % (435865)Instruction limit reached!
% 7.15/1.93 % (435865)------------------------------
% 7.15/1.93 % (435865)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/1.93 % (435865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/1.93 % (435865)CaDiCaL version: 2.1.3
% 7.15/1.93 % (435865)Termination reason: Instruction limit
% 7.15/1.93 % (435865)Termination phase: Saturation
% 7.15/1.93 % (435865)Time elapsed: 0.232 s
% 7.15/1.93 % (435865)Peak memory usage: 93 MB
% 7.15/1.93 % (435865)Instructions burned: 248 (million)
% 7.15/1.93 % (435862)Instruction limit reached!
% 7.15/1.93 % (435862)------------------------------
% 7.15/1.93 % (435862)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/1.93 % (435862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/1.93 % (435862)CaDiCaL version: 2.1.3
% 7.15/1.93 % (435862)Termination reason: Instruction limit
% 7.15/1.93 % (435862)Termination phase: Saturation
% 7.15/1.93 % (435862)Time elapsed: 0.315 s
% 7.15/1.93 % (435862)Peak memory usage: 92 MB
% 7.15/1.93 % (435862)Instructions burned: 285 (million)
% 7.15/1.93 % (435870)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3418134672:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2992 on theBenchmark for (2992ds/294Mi)
% 7.15/1.93 % (435864)Instruction limit reached!
% 7.15/1.93 % (435864)------------------------------
% 7.15/1.93 % (435864)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/1.93 % (435864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/1.93 % (435864)CaDiCaL version: 2.1.3
% 7.15/1.93 % (435864)Termination reason: Instruction limit
% 7.15/1.93 % (435864)Termination phase: Saturation
% 7.15/1.93 % (435864)Time elapsed: 0.341 s
% 7.15/1.93 % (435864)Peak memory usage: 92 MB
% 7.15/1.93 % (435864)Instructions burned: 325 (million)
% 7.15/1.93 % (435844)Refutation found. Thanks to Tanya!
% 7.15/1.93 % SZS status Theorem for theBenchmark
% 7.15/1.93 % SZS output start Proof for theBenchmark
% See solution above
% 8.26/2.23 % (435844)------------------------------
% 8.26/2.23 % (435844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.26/2.23 % (435844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.26/2.23 % (435844)CaDiCaL version: 2.1.3
% 8.26/2.23 % (435844)Termination reason: Refutation
% 8.26/2.23 % (435844)Time elapsed: 0.619 s
% 8.26/2.23 % (435844)Peak memory usage: 138 MB
% 8.26/2.23 % (435844)Instructions burned: 1101 (million)
% 8.26/2.23 % (435844)------------------------------
% 8.26/2.23 % (435844)------------------------------
% 8.26/2.23 % (435829)Success in time 1.036 s
% 8.26/2.23 % Vampire exiting
%------------------------------------------------------------------------------