%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM515+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:15:32 PM UTC 2026
% Result : Theorem 4.31s 1.54s
% Output : Refutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 21
% Syntax : Number of formulae : 121 ( 29 unt; 7 def)
% Number of atoms : 525 ( 114 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 688 ( 284 ~; 315 |; 64 &)
% ( 12 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn 110 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != X1
& sdtlseqdt0(X0,X1) )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtpldt0(X2,X0) != sdtpldt0(X2,X1)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != X1
& sdtlseqdt0(X0,X1) )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( isPrime0(X2)
& doDivides0(X2,sdtasdt0(X0,X1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X2,X0)
| doDivides0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
fof(f41,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f48,axiom,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f52,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(f53,axiom,
( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2504) ).
fof(f54,axiom,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2529) ).
fof(f55,conjecture,
( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f56,negated_conjecture,
~ ( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f59,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f60,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f59]) ).
fof(f95,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt0(X2,X0) != sdtpldt0(X2,X1)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) )
| ~ aNaturalNumber0(X2) )
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f96,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt0(X2,X0) != sdtpldt0(X2,X1)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) )
| ~ aNaturalNumber0(X2) )
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f95]) ).
fof(f103,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f104,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f103]) ).
fof(f107,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f108,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f107]) ).
fof(f119,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f120,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f119]) ).
fof(f123,plain,
! [X0,X1,X2] :
( doDivides0(X2,X0)
| doDivides0(X2,X1)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f124,plain,
! [X0,X1,X2] :
( doDivides0(X2,X0)
| doDivides0(X2,X1)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f123]) ).
fof(f126,plain,
( ~ doDivides0(xp,sdtsldt0(xn,xr))
& ~ doDivides0(xp,xm) ),
inference(ennf_transformation,[],[f56]) ).
fof(f135,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f108]) ).
fof(f136,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f135]) ).
fof(f137,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f120]) ).
fof(f138,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f137]) ).
fof(f139,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f138]) ).
fof(f140,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ( sz10 != sK2(X0)
& sK2(X0) != X0
& aNaturalNumber0(sK2(X0))
& doDivides0(sK2(X0),X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f139]) ).
fof(f142,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f145,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f177,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f178,plain,
! [X2,X0,X1] :
( sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f188,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f193,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f202,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f210,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f211,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f212,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f213,plain,
! [X2,X0,X1] :
( ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f124]) ).
fof(f215,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f227,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f229,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f235,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f52]) ).
fof(f236,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f53]) ).
fof(f237,plain,
xn != sdtsldt0(xn,xr),
inference(cnf_transformation,[],[f53]) ).
fof(f238,plain,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(cnf_transformation,[],[f54]) ).
fof(f239,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f126]) ).
fof(f240,plain,
~ doDivides0(xp,sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f126]) ).
fof(f249,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f193]) ).
fof(f251,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f202]) ).
fof(f253,definition,
sF4 = sdtsldt0(xn,xr),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f254,plain,
sdtsldt0(xn,xr) = sF4,
inference(reorient_equations,[],[f253]) ).
fof(f255,plain,
~ doDivides0(xp,sF4),
inference(definition_folding,[],[f240,f254]) ).
fof(f267,definition,
( spl5_3
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f271,definition,
( spl5_4
<=> isPrime0(sz00) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f273,plain,
( ~ isPrime0(sz00)
| spl5_4 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f274,plain,
( ~ spl5_3
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f251,f271,f267]) ).
fof(f276,plain,
spl5_3,
inference(avatar_split_clause,[],[f142,f267]) ).
fof(f278,plain,
( aNaturalNumber0(sF4)
| sz00 = xr
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f249,f254]) ).
fof(f279,plain,
( aNaturalNumber0(sF4)
| sz00 = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f278,f235]) ).
fof(f280,plain,
( aNaturalNumber0(sF4)
| sz00 = xr
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f279,f229]) ).
fof(f281,plain,
( aNaturalNumber0(sF4)
| sz00 = xr ),
inference(forward_subsumption_resolution,[],[f280,f212]) ).
fof(f283,definition,
( spl5_5
<=> sz00 = xr ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f285,plain,
( sz00 = xr
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f287,definition,
( spl5_6
<=> aNaturalNumber0(sF4) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f289,plain,
( aNaturalNumber0(sF4)
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f290,plain,
( spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f281,f287,f283]) ).
fof(f381,plain,
( isPrime0(sz00)
| ~ spl5_5 ),
inference(superposition,[],[f227,f285]) ).
fof(f393,plain,
( $false
| spl5_4
| ~ spl5_5 ),
inference(forward_subsumption_resolution,[],[f381,f273]) ).
fof(f394,plain,
( spl5_4
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f393]) ).
fof(f765,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| iLess0(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| ~ aNaturalNumber0(sdtpldt0(X1,X0))
| ~ aNaturalNumber0(sdtpldt0(X2,X0)) ),
inference(resolution,[],[f177,f188]) ).
fof(f766,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| iLess0(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| ~ aNaturalNumber0(sdtpldt0(X1,X0))
| ~ aNaturalNumber0(sdtpldt0(X2,X0)) ),
inference(forward_subsumption_resolution,[],[f765,f178]) ).
fof(f768,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| iLess0(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| ~ aNaturalNumber0(sdtpldt0(X2,X0)) ),
inference(forward_subsumption_resolution,[],[f766,f145]) ).
fof(f770,plain,
! [X2,X0,X1] :
( iLess0(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f768,f145]) ).
fof(f842,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,X1)
| doDivides0(xp,X0)
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f770,f213]) ).
fof(f843,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,X1)
| doDivides0(xp,X0)
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(duplicate_literal_removal,[],[f842]) ).
fof(f844,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,X1)
| doDivides0(xp,X0)
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f843,f145]) ).
fof(f845,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| doDivides0(xp,X1)
| doDivides0(xp,X0)
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f844,f210]) ).
fof(f846,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| doDivides0(xp,X1)
| doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f845,f215]) ).
fof(f848,definition,
( spl5_38
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl5_38])],[avatar_definition]) ).
fof(f850,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl5_38 ),
inference(avatar_component_clause,[],[f848]) ).
fof(f852,definition,
( spl5_39
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| doDivides0(xp,X0)
| doDivides0(xp,X1)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm)) ) ),
introduced(definition,[new_symbols(definition,[spl5_39])],[avatar_definition]) ).
fof(f853,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| doDivides0(xp,X0)
| doDivides0(xp,X1)
| sdtpldt0(X0,X1) = sdtpldt0(xn,xm) )
| ~ spl5_39 ),
inference(avatar_component_clause,[],[f852]) ).
fof(f854,plain,
( ~ spl5_38
| spl5_39 ),
inference(avatar_split_clause,[],[f846,f852,f848]) ).
fof(f855,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl5_38 ),
inference(resolution,[],[f850,f145]) ).
fof(f856,plain,
( ~ aNaturalNumber0(xm)
| spl5_38 ),
inference(forward_subsumption_resolution,[],[f855,f212]) ).
fof(f857,plain,
( $false
| spl5_38 ),
inference(forward_subsumption_resolution,[],[f856,f211]) ).
fof(f858,plain,
spl5_38,
inference(avatar_contradiction_clause,[],[f857]) ).
fof(f859,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| doDivides0(xp,xm)
| sdtpldt0(xn,xm) = sdtpldt0(X0,xm)
| ~ aNaturalNumber0(xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) )
| ~ spl5_39 ),
inference(resolution,[],[f853,f177]) ).
fof(f860,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| doDivides0(xp,xm)
| sdtpldt0(xn,xm) = sdtpldt0(X0,xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl5_39 ),
inference(duplicate_literal_removal,[],[f859]) ).
fof(f861,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| doDivides0(xp,xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl5_39 ),
inference(forward_subsumption_resolution,[],[f860,f178]) ).
fof(f862,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| doDivides0(xp,xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl5_39 ),
inference(forward_subsumption_resolution,[],[f861,f211]) ).
fof(f863,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl5_39 ),
inference(forward_subsumption_resolution,[],[f862,f239]) ).
fof(f864,plain,
( ! [X0] :
( ~ doDivides0(xp,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| doDivides0(xp,X0)
| xn = X0
| ~ sdtlseqdt0(X0,xn) )
| ~ spl5_39 ),
inference(forward_subsumption_resolution,[],[f863,f212]) ).
fof(f865,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| doDivides0(xp,sdtsldt0(xn,xr))
| xn = sdtsldt0(xn,xr)
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ~ spl5_39 ),
inference(resolution,[],[f864,f238]) ).
fof(f871,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ~ spl5_39 ),
inference(forward_subsumption_resolution,[],[f865,f237]) ).
fof(f873,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ spl5_39 ),
inference(forward_subsumption_resolution,[],[f871,f236]) ).
fof(f875,plain,
( ~ aNaturalNumber0(sF4)
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ spl5_39 ),
inference(forward_demodulation,[],[f873,f254]) ).
fof(f878,plain,
( doDivides0(xp,sdtsldt0(xn,xr))
| ~ spl5_6
| ~ spl5_39 ),
inference(forward_subsumption_resolution,[],[f875,f289]) ).
fof(f879,plain,
( doDivides0(xp,sF4)
| ~ spl5_6
| ~ spl5_39 ),
inference(forward_demodulation,[],[f878,f254]) ).
fof(f880,plain,
( $false
| ~ spl5_6
| ~ spl5_39 ),
inference(forward_subsumption_resolution,[],[f879,f255]) ).
fof(f881,plain,
( ~ spl5_6
| ~ spl5_39 ),
inference(avatar_contradiction_clause,[],[f880]) ).
cnf(s2,plain,
( ~ spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f274]) ).
cnf(s4,plain,
spl5_3,
inference(sat_conversion,[],[f276]) ).
cnf(s5,plain,
( spl5_5
| spl5_6 ),
inference(sat_conversion,[],[f290]) ).
cnf(s15,plain,
( spl5_4
| ~ spl5_5 ),
inference(sat_conversion,[],[f394]) ).
cnf(s36,plain,
( ~ spl5_38
| spl5_39 ),
inference(sat_conversion,[],[f854]) ).
cnf(s37,plain,
spl5_38,
inference(sat_conversion,[],[f858]) ).
cnf(s39,plain,
( ~ spl5_6
| ~ spl5_39 ),
inference(sat_conversion,[],[f881]) ).
cnf(s40,plain,
spl5_39,
inference(rat,[],[s36,s37]) ).
cnf(s41,plain,
~ spl5_6,
inference(rat,[],[s39,s40]) ).
cnf(s44,plain,
spl5_5,
inference(rat,[],[s5,s41]) ).
cnf(s45,plain,
spl5_4,
inference(rat,[],[s15,s44]) ).
cnf(s46,plain,
$false,
inference(rat,[],[s2,s45,s4]) ).
fof(f882,plain,
$false,
inference(avatar_sat_refutation,[],[s46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM515+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:19:11 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.31/1.54 % (893836)Detected formulas, will run a generic FOF schedule.
% 4.31/1.54 % (893841)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=1625082551:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.31/1.54 % (893844)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1640133018:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.31/1.54 % (893842)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=3562985419:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.31/1.54 % (893843)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=2742637806:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.31/1.54 % (893847)dis-21_1_sil=8000:lcm=predicate:random_seed=3287140654: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)
% 4.31/1.54 % (893845)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3604548983:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.31/1.54 % (893846)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3051636129:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.31/1.54 % (893844)Instruction limit reached!
% 4.31/1.54 % (893844)------------------------------
% 4.31/1.54 % (893844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.54 % (893844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.54 % (893844)CaDiCaL version: 2.1.3
% 4.31/1.54 % (893844)Termination reason: Instruction limit
% 4.31/1.54 % (893844)Termination phase: Saturation
% 4.31/1.54 % (893844)Time elapsed: 0.068 s
% 4.31/1.54 % (893844)Peak memory usage: 89 MB
% 4.31/1.54 % (893844)Instructions burned: 110 (million)
% 4.31/1.54 % (893845)Instruction limit reached!
% 4.31/1.54 % (893845)------------------------------
% 4.31/1.54 % (893845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.54 % (893845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.54 % (893845)CaDiCaL version: 2.1.3
% 4.31/1.54 % (893845)Termination reason: Instruction limit
% 4.31/1.54 % (893845)Termination phase: Saturation
% 4.31/1.54 % (893845)Time elapsed: 0.071 s
% 4.31/1.54 % (893845)Peak memory usage: 88 MB
% 4.31/1.54 % (893845)Instructions burned: 120 (million)
% 4.31/1.54 % (893847)Instruction limit reached!
% 4.31/1.54 % (893847)------------------------------
% 4.31/1.54 % (893847)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.54 % (893847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.54 % (893847)CaDiCaL version: 2.1.3
% 4.31/1.54 % (893847)Termination reason: Instruction limit
% 4.31/1.54 % (893847)Termination phase: Saturation
% 4.31/1.54 % (893847)Time elapsed: 0.079 s
% 4.31/1.54 % (893847)Peak memory usage: 90 MB
% 4.31/1.54 % (893847)Instructions burned: 129 (million)
% 4.31/1.54 % (893846)Instruction limit reached!
% 4.31/1.54 % (893846)------------------------------
% 4.31/1.54 % (893846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.54 % (893846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.54 % (893846)CaDiCaL version: 2.1.3
% 4.31/1.54 % (893846)Termination reason: Instruction limit
% 4.31/1.54 % (893846)Termination phase: Saturation
% 4.31/1.54 % (893846)Time elapsed: 0.091 s
% 4.31/1.54 % (893846)Peak memory usage: 90 MB
% 4.31/1.54 % (893846)Instructions burned: 140 (million)
% 4.31/1.54 % (893855)lrs+10_1_sil=8000:sp=occurrence:random_seed=2482124316:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.31/1.54 % (893857)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3864026677:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.31/1.54 % (893856)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1503043019:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.31/1.54 % (893856)Refutation not found, incomplete strategy
% 4.31/1.54 % (893856)------------------------------
% 4.31/1.54 % (893856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.54 % (893856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.54 % (893856)CaDiCaL version: 2.1.3
% 4.31/1.54 % (893856)Termination reason: Refutation not found, incomplete strategy
% 4.31/1.54 % (893856)Time elapsed: 0.004 s
% 4.31/1.54 % (893856)Peak memory usage: 89 MB
% 4.31/1.54 % (893856)Instructions burned: 4 (million)
% 4.31/1.54 % (893858)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=2317601803:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.31/1.54 % (893841)First to succeed.
% 4.31/1.54 % (893841)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-893836"
% 4.31/1.54 % (893855)Instruction limit reached!
% 4.31/1.54 % (893855)------------------------------
% 4.31/1.54 % (893855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.54 % (893855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.54 % (893855)CaDiCaL version: 2.1.3
% 4.31/1.54 % (893855)Termination reason: Instruction limit
% 4.31/1.54 % (893855)Termination phase: Saturation
% 4.31/1.54 % (893855)Time elapsed: 0.167 s
% 4.31/1.54 % (893855)Peak memory usage: 92 MB
% 4.31/1.54 % (893855)Instructions burned: 285 (million)
% 4.31/1.54 % (893858)Instruction limit reached!
% 4.31/1.54 % (893858)------------------------------
% 4.31/1.54 % (893858)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.54 % (893858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.54 % (893858)CaDiCaL version: 2.1.3
% 4.31/1.54 % (893858)Termination reason: Instruction limit
% 4.31/1.54 % (893858)Termination phase: Saturation
% 4.31/1.54 % (893858)Time elapsed: 0.119 s
% 4.31/1.54 % (893858)Peak memory usage: 93 MB
% 4.31/1.54 % (893858)Instructions burned: 249 (million)
% 4.31/1.54 % (893857)Instruction limit reached!
% 4.31/1.54 % (893857)------------------------------
% 4.31/1.54 % (893857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.54 % (893857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.54 % (893857)CaDiCaL version: 2.1.3
% 4.31/1.54 % (893857)Termination reason: Instruction limit
% 4.31/1.54 % (893857)Termination phase: Saturation
% 4.31/1.54 % (893857)Time elapsed: 0.198 s
% 4.31/1.54 % (893857)Peak memory usage: 91 MB
% 4.31/1.54 % (893857)Instructions burned: 325 (million)
% 4.31/1.54 % (893856)------------------------------
% 4.31/1.54 % (893856)------------------------------
% 4.31/1.54 % (893841)Refutation found. Thanks to Tanya!
% 4.31/1.54 % SZS status Theorem for theBenchmark
% 4.31/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 5.38/1.74 % (893841)------------------------------
% 5.38/1.74 % (893841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.38/1.74 % (893841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.38/1.74 % (893841)CaDiCaL version: 2.1.3
% 5.38/1.74 % (893841)Termination reason: Refutation
% 5.38/1.74 % (893841)Time elapsed: 0.390 s
% 5.38/1.74 % (893841)Peak memory usage: 130 MB
% 5.38/1.74 % (893841)Instructions burned: 1028 (million)
% 5.38/1.74 % (893841)------------------------------
% 5.38/1.74 % (893841)------------------------------
% 5.38/1.74 % (893836)Success in time 0.674 s
% 5.38/1.74 % Vampire exiting
%------------------------------------------------------------------------------