%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM518+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 : n017.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 12:15:33 PM UTC 2026
% Result : Theorem 3.33s 1.30s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 20
% Syntax : Number of formulae : 112 ( 27 unt; 7 def)
% Number of atoms : 385 ( 103 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 471 ( 198 ~; 200 |; 53 &)
% ( 11 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 67 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
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(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X0,X1)
& X1 != sz00 )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
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(f42,axiom,
~ sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
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(f55,axiom,
( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2645) ).
fof(f56,conjecture,
( doDivides0(xp,xn)
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ( doDivides0(xp,xn)
| doDivides0(xp,xm) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f63,plain,
( ~ doDivides0(xp,xn)
& ~ doDivides0(xp,xm) ),
inference(ennf_transformation,[],[f57]) ).
fof(f99,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(f100,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f99]) ).
fof(f103,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f104,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f103]) ).
fof(f110,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(f111,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,[],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f113,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f112]) ).
fof(f122,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f133,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,[],[f100]) ).
fof(f134,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,[],[f133]) ).
fof(f135,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,[],[f134]) ).
fof(f136,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ( sz10 != sK3(X0)
& sK3(X0) != X0
& aNaturalNumber0(sK3(X0))
& doDivides0(sK3(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,[sK3]),skolemize(X1,sK3(X0))],[f135]) ).
fof(f137,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,[],[f111]) ).
fof(f138,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,[],[f137]) ).
fof(f139,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f141,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f145,plain,
~ sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f156,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f158,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f164,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f52]) ).
fof(f165,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f53]) ).
fof(f166,plain,
xn != sdtsldt0(xn,xr),
inference(cnf_transformation,[],[f53]) ).
fof(f168,plain,
( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm) ),
inference(cnf_transformation,[],[f55]) ).
fof(f169,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f63]) ).
fof(f204,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f211,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f215,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f216,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f218,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f228,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f229,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f250,definition,
~ sP11(xn),
introduced(definition,[new_symbols(definition,[sP11])],[inequality_splitting_name_introduction]) ).
fof(f251,plain,
sP11(sdtsldt0(xn,xr)),
inference(inequality_splitting,[],[f166,f250]) ).
fof(f258,definition,
~ sP15(sz00),
introduced(definition,[new_symbols(definition,[sP15])],[inequality_splitting_name_introduction]) ).
fof(f259,plain,
! [X0] :
( ~ isPrime0(X0)
| sP15(X0)
| ~ aNaturalNumber0(X0) ),
inference(inequality_splitting,[],[f204,f258]) ).
fof(f272,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f216]) ).
fof(f273,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f215]) ).
fof(f275,plain,
doDivides0(xp,sdtsldt0(xn,xr)),
inference(forward_subsumption_resolution,[],[f168,f169]) ).
fof(f276,plain,
( sdtlseqdt0(xp,sdtsldt0(xn,xr))
| sz00 = sdtsldt0(xn,xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(resolution,[],[f275,f218]) ).
fof(f281,plain,
( sdtlseqdt0(xp,sdtsldt0(xn,xr))
| sz00 = sdtsldt0(xn,xr)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(forward_subsumption_resolution,[],[f276,f139]) ).
fof(f283,definition,
( spl20_1
<=> aNaturalNumber0(sdtsldt0(xn,xr)) ),
introduced(definition,[new_symbols(definition,[spl20_1])],[avatar_definition]) ).
fof(f284,plain,
( aNaturalNumber0(sdtsldt0(xn,xr))
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f285,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| spl20_1 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f304,definition,
( spl20_6
<=> sz00 = sdtsldt0(xn,xr) ),
introduced(definition,[new_symbols(definition,[spl20_6])],[avatar_definition]) ).
fof(f306,plain,
( sz00 = sdtsldt0(xn,xr)
| ~ spl20_6 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f308,definition,
( spl20_7
<=> sdtlseqdt0(xp,sdtsldt0(xn,xr)) ),
introduced(definition,[new_symbols(definition,[spl20_7])],[avatar_definition]) ).
fof(f310,plain,
( sdtlseqdt0(xp,sdtsldt0(xn,xr))
| ~ spl20_7 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f311,plain,
( ~ spl20_1
| spl20_6
| spl20_7 ),
inference(avatar_split_clause,[],[f281,f308,f304,f283]) ).
fof(f312,plain,
( sz00 = xr
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| spl20_1 ),
inference(resolution,[],[f285,f272]) ).
fof(f313,plain,
( sz00 = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| spl20_1 ),
inference(forward_subsumption_resolution,[],[f312,f164]) ).
fof(f314,plain,
( sz00 = xr
| ~ aNaturalNumber0(xn)
| spl20_1 ),
inference(forward_subsumption_resolution,[],[f313,f158]) ).
fof(f315,plain,
( sz00 = xr
| spl20_1 ),
inference(forward_subsumption_resolution,[],[f314,f141]) ).
fof(f327,plain,
( sP15(xr)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[],[f156,f259]) ).
fof(f329,plain,
sP15(xr),
inference(forward_subsumption_resolution,[],[f327,f158]) ).
fof(f331,plain,
( sP15(sz00)
| spl20_1 ),
inference(forward_demodulation,[],[f329,f315]) ).
fof(f333,plain,
( $false
| spl20_1 ),
inference(forward_subsumption_resolution,[],[f331,f258]) ).
fof(f334,plain,
spl20_1,
inference(avatar_contradiction_clause,[],[f333]) ).
fof(f338,plain,
( xn = sdtasdt0(xr,sz00)
| sz00 = xr
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ spl20_6 ),
inference(superposition,[],[f273,f306]) ).
fof(f340,plain,
( xn = sdtasdt0(xr,sz00)
| sz00 = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ spl20_6 ),
inference(forward_subsumption_resolution,[],[f338,f164]) ).
fof(f341,plain,
( xn = sdtasdt0(xr,sz00)
| sz00 = xr
| ~ aNaturalNumber0(xn)
| ~ spl20_6 ),
inference(forward_subsumption_resolution,[],[f340,f158]) ).
fof(f342,plain,
( xn = sdtasdt0(xr,sz00)
| sz00 = xr
| ~ spl20_6 ),
inference(forward_subsumption_resolution,[],[f341,f141]) ).
fof(f344,definition,
( spl20_8
<=> sz00 = xr ),
introduced(definition,[new_symbols(definition,[spl20_8])],[avatar_definition]) ).
fof(f346,plain,
( sz00 = xr
| ~ spl20_8 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f348,definition,
( spl20_9
<=> xn = sdtasdt0(xr,sz00) ),
introduced(definition,[new_symbols(definition,[spl20_9])],[avatar_definition]) ).
fof(f350,plain,
( xn = sdtasdt0(xr,sz00)
| ~ spl20_9 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f351,plain,
( spl20_8
| spl20_9
| ~ spl20_6 ),
inference(avatar_split_clause,[],[f342,f304,f348,f344]) ).
fof(f381,plain,
( isPrime0(sz00)
| ~ spl20_8 ),
inference(superposition,[],[f156,f346]) ).
fof(f390,plain,
( sP15(sz00)
| ~ aNaturalNumber0(sz00)
| ~ spl20_8 ),
inference(resolution,[],[f381,f259]) ).
fof(f391,plain,
( ~ aNaturalNumber0(sz00)
| ~ spl20_8 ),
inference(forward_subsumption_resolution,[],[f390,f258]) ).
fof(f393,plain,
( $false
| ~ spl20_8 ),
inference(forward_subsumption_resolution,[],[f391,f229]) ).
fof(f394,plain,
~ spl20_8,
inference(avatar_contradiction_clause,[],[f393]) ).
fof(f657,plain,
! [X0] :
( ~ sdtlseqdt0(X0,sdtsldt0(xn,xr))
| sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f165,f211]) ).
fof(f660,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,sdtsldt0(xn,xr))
| sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) )
| ~ spl20_1 ),
inference(forward_subsumption_resolution,[],[f657,f284]) ).
fof(f663,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,sdtsldt0(xn,xr))
| sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0) )
| ~ spl20_1 ),
inference(forward_subsumption_resolution,[],[f660,f141]) ).
fof(f855,plain,
( sP11(sz00)
| ~ spl20_6 ),
inference(superposition,[],[f251,f306]) ).
fof(f901,plain,
( ~ sP11(sdtasdt0(xr,sz00))
| ~ spl20_9 ),
inference(superposition,[],[f250,f350]) ).
fof(f933,plain,
( ~ sP11(sz00)
| ~ aNaturalNumber0(xr)
| ~ spl20_9 ),
inference(superposition,[],[f901,f228]) ).
fof(f938,plain,
( ~ aNaturalNumber0(xr)
| ~ spl20_6
| ~ spl20_9 ),
inference(forward_subsumption_resolution,[],[f933,f855]) ).
fof(f941,plain,
( $false
| ~ spl20_6
| ~ spl20_9 ),
inference(forward_subsumption_resolution,[],[f938,f158]) ).
fof(f942,plain,
( ~ spl20_6
| ~ spl20_9 ),
inference(avatar_contradiction_clause,[],[f941]) ).
fof(f1030,plain,
( sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ spl20_1
| ~ spl20_7 ),
inference(resolution,[],[f310,f663]) ).
fof(f1035,plain,
( ~ aNaturalNumber0(xp)
| ~ spl20_1
| ~ spl20_7 ),
inference(forward_subsumption_resolution,[],[f1030,f145]) ).
fof(f1037,plain,
( $false
| ~ spl20_1
| ~ spl20_7 ),
inference(forward_subsumption_resolution,[],[f1035,f139]) ).
fof(f1038,plain,
( ~ spl20_1
| ~ spl20_7 ),
inference(avatar_contradiction_clause,[],[f1037]) ).
cnf(s3,plain,
( ~ spl20_1
| spl20_6
| spl20_7 ),
inference(sat_conversion,[],[f311]) ).
cnf(s4,plain,
spl20_1,
inference(sat_conversion,[],[f334]) ).
cnf(s5,plain,
( ~ spl20_6
| spl20_8
| spl20_9 ),
inference(sat_conversion,[],[f351]) ).
cnf(s9,plain,
~ spl20_8,
inference(sat_conversion,[],[f394]) ).
cnf(s42,plain,
( ~ spl20_6
| ~ spl20_9 ),
inference(sat_conversion,[],[f942]) ).
cnf(s49,plain,
( ~ spl20_1
| ~ spl20_7 ),
inference(sat_conversion,[],[f1038]) ).
cnf(s50,plain,
( ~ spl20_6
| spl20_9 ),
inference(rat,[],[s5,s9]) ).
cnf(s51,plain,
~ spl20_7,
inference(rat,[],[s49,s4]) ).
cnf(s52,plain,
spl20_6,
inference(rat,[],[s3,s51,s4]) ).
cnf(s53,plain,
~ spl20_9,
inference(rat,[],[s42,s52]) ).
cnf(s55,plain,
$false,
inference(rat,[],[s50,s53,s52]) ).
fof(f1041,plain,
$false,
inference(avatar_sat_refutation,[],[s55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM518+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 20:13:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.33/1.30 % (2908785)Detected formulas, will run a generic FOF schedule.
% 3.33/1.30 % (2908794)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2587285835:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.33/1.30 % (2908794)Instruction limit reached!
% 3.33/1.30 % (2908794)------------------------------
% 3.33/1.30 % (2908794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.30 % (2908794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.30 % (2908794)CaDiCaL version: 2.1.3
% 3.33/1.30 % (2908794)Termination reason: Instruction limit
% 3.33/1.30 % (2908794)Termination phase: Saturation
% 3.33/1.30 % (2908794)Time elapsed: 0.039 s
% 3.33/1.30 % (2908794)Peak memory usage: 89 MB
% 3.33/1.30 % (2908794)Instructions burned: 119 (million)
% 3.33/1.30 % (2908796)dis-21_1_sil=8000:lcm=predicate:random_seed=1204995221: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)
% 3.33/1.30 % (2908791)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=1078635312:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.33/1.30 % (2908790)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=1018080791:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.33/1.30 % (2908793)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3547417488:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.33/1.30 % (2908792)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=3175585774:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.33/1.30 % (2908795)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=909890199:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.33/1.30 % (2908793)First to succeed.
% 3.33/1.30 % (2908793)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2908785"
% 3.33/1.30 % (2908795)Also succeeded, but the first one will report.
% 3.33/1.30 % (2908796)Instruction limit reached!
% 3.33/1.30 % (2908796)------------------------------
% 3.33/1.30 % (2908796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.30 % (2908796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.30 % (2908796)CaDiCaL version: 2.1.3
% 3.33/1.30 % (2908796)Termination reason: Instruction limit
% 3.33/1.30 % (2908796)Termination phase: Saturation
% 3.33/1.30 % (2908796)Time elapsed: 0.081 s
% 3.33/1.30 % (2908796)Peak memory usage: 90 MB
% 3.33/1.30 % (2908796)Instructions burned: 130 (million)
% 3.33/1.30 % (2908804)lrs+10_1_sil=8000:sp=occurrence:random_seed=1339541717:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.33/1.30 % (2908804)Also succeeded, but the first one will report.
% 3.33/1.30 % (2908805)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3070644369:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.33/1.30 % (2908805)Refutation not found, incomplete strategy
% 3.33/1.30 % (2908805)------------------------------
% 3.33/1.30 % (2908805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.33/1.30 % (2908805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.33/1.30 % (2908805)CaDiCaL version: 2.1.3
% 3.33/1.30 % (2908805)Termination reason: Refutation not found, incomplete strategy
% 3.33/1.30 % (2908805)Time elapsed: 0.002 s
% 3.33/1.30 % (2908805)Peak memory usage: 88 MB
% 3.33/1.30 % (2908805)Instructions burned: 1 (million)
% 3.33/1.30 % (2908793)Refutation found. Thanks to Tanya!
% 3.33/1.30 % SZS status Theorem for theBenchmark
% 3.33/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (2908793)------------------------------
% 0.17/1.50 % (2908793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (2908793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (2908793)CaDiCaL version: 2.1.3
% 0.17/1.50 % (2908793)Termination reason: Refutation
% 0.17/1.50 % (2908793)Time elapsed: 0.020 s
% 0.17/1.50 % (2908793)Peak memory usage: 90 MB
% 0.17/1.50 % (2908793)Instructions burned: 27 (million)
% 0.17/1.50 % (2908793)------------------------------
% 0.17/1.50 % (2908793)------------------------------
% 0.17/1.50 % (2908785)Success in time 0.454 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------