%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM493+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 : n020.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 12:15:26 PM UTC 2026
% Result : Theorem 6.56s 1.98s
% Output : Refutation 8.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 13
% Syntax : Number of formulae : 81 ( 21 unt; 1 def)
% Number of atoms : 360 ( 57 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 489 ( 210 ~; 234 |; 30 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 93 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
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(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(f42,axiom,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(f43,axiom,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(f44,axiom,
( xr != xn
& sdtlseqdt0(xr,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1894) ).
fof(f45,axiom,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1913) ).
fof(f46,conjecture,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f50,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f51,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f50]) ).
fof(f77,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f78,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f77]) ).
fof(f86,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(f87,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,[],[f86]) ).
fof(f94,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f95,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f94]) ).
fof(f114,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(f115,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,[],[f114]) ).
fof(f116,plain,
( ~ doDivides0(xp,xr)
& ~ doDivides0(xp,xm) ),
inference(ennf_transformation,[],[f47]) ).
fof(f120,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f78]) ).
fof(f121,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f120]) ).
fof(f135,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f160,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f167,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,[],[f87]) ).
fof(f168,plain,
! [X2,X0,X1] :
( sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f178,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f200,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f201,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f202,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f203,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,[],[f115]) ).
fof(f205,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f206,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f207,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[],[f43]) ).
fof(f208,plain,
sdtlseqdt0(xr,xn),
inference(cnf_transformation,[],[f44]) ).
fof(f209,plain,
xn != xr,
inference(cnf_transformation,[],[f44]) ).
fof(f210,plain,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f45]) ).
fof(f211,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f116]) ).
fof(f212,plain,
~ doDivides0(xp,xr),
inference(cnf_transformation,[],[f116]) ).
fof(f215,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f160]) ).
fof(f246,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f215,f207]) ).
fof(f247,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f246,f206]) ).
fof(f248,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f247,f200]) ).
fof(f249,plain,
aNaturalNumber0(xr),
inference(forward_subsumption_resolution,[],[f248,f202]) ).
fof(f300,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,[],[f167,f178]) ).
fof(f308,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,[],[f300,f168]) ).
fof(f313,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,[],[f308,f135]) ).
fof(f317,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,[],[f313,f135]) ).
fof(f428,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,[],[f317,f203]) ).
fof(f431,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,[],[f428]) ).
fof(f434,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,[],[f431,f135]) ).
fof(f437,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,[],[f434,f200]) ).
fof(f440,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,[],[f437,f205]) ).
fof(f447,definition,
( spl4_14
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition]) ).
fof(f448,plain,
( aNaturalNumber0(sdtpldt0(xn,xm))
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f449,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl4_14 ),
inference(avatar_component_clause,[],[f447]) ).
fof(f454,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_14 ),
inference(resolution,[],[f449,f135]) ).
fof(f455,plain,
( ~ aNaturalNumber0(xm)
| spl4_14 ),
inference(forward_subsumption_resolution,[],[f454,f202]) ).
fof(f456,plain,
( $false
| spl4_14 ),
inference(forward_subsumption_resolution,[],[f455,f201]) ).
fof(f457,plain,
spl4_14,
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f627,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| doDivides0(xp,X1)
| doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) )
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f440,f448]) ).
fof(f640,plain,
( ! [X0] :
( sdtpldt0(xn,xm) = sdtpldt0(X0,xm)
| doDivides0(xp,xm)
| doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) )
| ~ spl4_14 ),
inference(resolution,[],[f627,f167]) ).
fof(f644,plain,
( ! [X0] :
( sdtpldt0(xn,xm) = sdtpldt0(X0,xm)
| doDivides0(xp,xm)
| doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl4_14 ),
inference(duplicate_literal_removal,[],[f640]) ).
fof(f647,plain,
( ! [X0] :
( doDivides0(xp,xm)
| doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f644,f168]) ).
fof(f650,plain,
( ! [X0] :
( doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f647,f211]) ).
fof(f653,plain,
( ! [X0] :
( doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f650,f201]) ).
fof(f679,plain,
( ! [X0] :
( ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| ~ aNaturalNumber0(X0)
| xn = X0
| ~ sdtlseqdt0(X0,xn) )
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f653,f202]) ).
fof(f681,plain,
( doDivides0(xp,xr)
| ~ aNaturalNumber0(xr)
| xn = xr
| ~ sdtlseqdt0(xr,xn)
| ~ spl4_14 ),
inference(resolution,[],[f679,f210]) ).
fof(f685,plain,
( ~ aNaturalNumber0(xr)
| xn = xr
| ~ sdtlseqdt0(xr,xn)
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f681,f212]) ).
fof(f687,plain,
( xn = xr
| ~ sdtlseqdt0(xr,xn)
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f685,f249]) ).
fof(f689,plain,
( ~ sdtlseqdt0(xr,xn)
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f687,f209]) ).
fof(f691,plain,
( $false
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f689,f208]) ).
fof(f692,plain,
~ spl4_14,
inference(avatar_contradiction_clause,[],[f691]) ).
cnf(s10,plain,
spl4_14,
inference(sat_conversion,[],[f457]) ).
cnf(s20,plain,
~ spl4_14,
inference(sat_conversion,[],[f692]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s10,s20]) ).
fof(f698,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM493+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n020.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
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 20:11:49 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
% 6.56/1.98 % (3711959)Detected formulas, will run a generic FOF schedule.
% 6.56/1.98 % (3711970)dis-21_1_sil=8000:lcm=predicate:random_seed=2354801010: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)
% 6.56/1.98 % (3711968)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1761078962:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.56/1.98 % (3711969)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=316448447:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.56/1.98 % (3711964)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=1667816592:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.56/1.98 % (3711967)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1081286805:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.56/1.98 % (3711965)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=1606851800:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.56/1.98 % (3711966)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=1088462106:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.56/1.98 % (3711970)Instruction limit reached!
% 6.56/1.98 % (3711970)------------------------------
% 6.56/1.98 % (3711970)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.98 % (3711970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.98 % (3711970)CaDiCaL version: 2.1.3
% 6.56/1.98 % (3711970)Termination reason: Instruction limit
% 6.56/1.98 % (3711970)Termination phase: Saturation
% 6.56/1.98 % (3711970)Time elapsed: 0.042 s
% 6.56/1.98 % (3711970)Peak memory usage: 90 MB
% 6.56/1.98 % (3711970)Instructions burned: 129 (million)
% 6.56/1.98 % (3711967)Instruction limit reached!
% 6.56/1.98 % (3711967)------------------------------
% 6.56/1.98 % (3711967)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.98 % (3711967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.98 % (3711967)CaDiCaL version: 2.1.3
% 6.56/1.98 % (3711967)Termination reason: Instruction limit
% 6.56/1.98 % (3711967)Termination phase: Saturation
% 6.56/1.98 % (3711967)Time elapsed: 0.066 s
% 6.56/1.98 % (3711967)Peak memory usage: 89 MB
% 6.56/1.98 % (3711967)Instructions burned: 110 (million)
% 6.56/1.98 % (3711968)Instruction limit reached!
% 6.56/1.98 % (3711968)------------------------------
% 6.56/1.98 % (3711968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.98 % (3711968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.98 % (3711968)CaDiCaL version: 2.1.3
% 6.56/1.98 % (3711968)Termination reason: Instruction limit
% 6.56/1.98 % (3711968)Termination phase: Saturation
% 6.56/1.98 % (3711968)Time elapsed: 0.071 s
% 6.56/1.98 % (3711968)Peak memory usage: 89 MB
% 6.56/1.98 % (3711968)Instructions burned: 119 (million)
% 6.56/1.98 % (3711969)Instruction limit reached!
% 6.56/1.98 % (3711969)------------------------------
% 6.56/1.98 % (3711969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.98 % (3711969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.98 % (3711969)CaDiCaL version: 2.1.3
% 6.56/1.98 % (3711969)Termination reason: Instruction limit
% 6.56/1.98 % (3711969)Termination phase: Saturation
% 6.56/1.98 % (3711969)Time elapsed: 0.093 s
% 6.56/1.98 % (3711969)Peak memory usage: 90 MB
% 6.56/1.98 % (3711969)Instructions burned: 140 (million)
% 6.56/1.98 % (3711978)lrs+10_1_sil=8000:sp=occurrence:random_seed=860624717:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.56/1.98 % (3711978)Instruction limit reached!
% 6.56/1.98 % (3711978)------------------------------
% 6.56/1.98 % (3711978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.98 % (3711978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.98 % (3711978)CaDiCaL version: 2.1.3
% 6.56/1.98 % (3711978)Termination reason: Instruction limit
% 6.56/1.98 % (3711978)Termination phase: Saturation
% 6.56/1.98 % (3711978)Time elapsed: 0.091 s
% 6.56/1.98 % (3711978)Peak memory usage: 92 MB
% 6.56/1.98 % (3711978)Instructions burned: 287 (million)
% 6.56/1.98 % (3711979)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2064518976:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.56/1.98 % (3711980)lrs+1011_1_sil=32000:sp=occurrence:random_seed=523276634:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.56/1.98 % (3711979)Refutation not found, incomplete strategy
% 6.56/1.98 % (3711979)------------------------------
% 6.56/1.98 % (3711979)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.98 % (3711979)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.98 % (3711979)CaDiCaL version: 2.1.3
% 6.56/1.98 % (3711979)Termination reason: Refutation not found, incomplete strategy
% 6.56/1.98 % (3711979)Time elapsed: 0.002 s
% 6.56/1.98 % (3711979)Peak memory usage: 88 MB
% 6.56/1.98 % (3711979)Instructions burned: 1 (million)
% 6.56/1.98 % (3711981)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=480732341:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.56/1.98 % (3711985)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=773400239:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.56/1.98 % (3711981)Instruction limit reached!
% 6.56/1.98 % (3711981)------------------------------
% 6.56/1.98 % (3711981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.98 % (3711981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.98 % (3711981)CaDiCaL version: 2.1.3
% 6.56/1.98 % (3711981)Termination reason: Instruction limit
% 6.56/1.98 % (3711981)Termination phase: Saturation
% 6.56/1.98 % (3711981)Time elapsed: 0.116 s
% 6.56/1.98 % (3711981)Peak memory usage: 93 MB
% 6.56/1.98 % (3711981)Instructions burned: 250 (million)
% 6.56/1.98 % (3711980)Instruction limit reached!
% 6.56/1.98 % (3711980)------------------------------
% 6.56/1.98 % (3711980)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.98 % (3711980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.98 % (3711980)CaDiCaL version: 2.1.3
% 6.56/1.98 % (3711980)Termination reason: Instruction limit
% 6.56/1.98 % (3711980)Termination phase: Saturation
% 6.56/1.98 % (3711980)Time elapsed: 0.195 s
% 6.56/1.98 % (3711980)Peak memory usage: 92 MB
% 6.56/1.98 % (3711980)Instructions burned: 325 (million)
% 6.56/1.98 % (3711985)Instruction limit reached!
% 6.56/1.98 % (3711985)------------------------------
% 6.56/1.98 % (3711985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.98 % (3711985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.98 % (3711985)CaDiCaL version: 2.1.3
% 6.56/1.98 % (3711985)Termination reason: Instruction limit
% 6.56/1.98 % (3711985)Termination phase: Saturation
% 6.56/1.98 % (3711985)Time elapsed: 0.088 s
% 6.56/1.98 % (3711985)Peak memory usage: 89 MB
% 6.56/1.98 % (3711985)Instructions burned: 298 (million)
% 6.56/1.98 % (3711979)------------------------------
% 6.56/1.98 % (3711979)------------------------------
% 6.56/1.98 % (3711988)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3371088635:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.56/1.98 % (3711990)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3345578329:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.56/1.98 % (3711989)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2377879821:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.56/1.98 % (3711990)Instruction limit reached!
% 6.56/1.98 % (3711990)------------------------------
% 6.56/1.98 % (3711990)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.98 % (3711990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.98 % (3711990)CaDiCaL version: 2.1.3
% 6.56/1.98 % (3711990)Termination reason: Instruction limit
% 6.56/1.98 % (3711990)Termination phase: Saturation
% 6.56/1.98 % (3711990)Time elapsed: 0.034 s
% 6.56/1.98 % (3711990)Peak memory usage: 89 MB
% 6.56/1.98 % (3711990)Instructions burned: 129 (million)
% 6.56/1.98 % (3711989)Instruction limit reached!
% 6.56/1.98 % (3711989)------------------------------
% 6.56/1.98 % (3711989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.98 % (3711989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.98 % (3711989)CaDiCaL version: 2.1.3
% 6.56/1.98 % (3711989)Termination reason: Instruction limit
% 6.56/1.98 % (3711989)Termination phase: Saturation
% 6.56/1.98 % (3711989)Time elapsed: 0.069 s
% 6.56/1.98 % (3711989)Peak memory usage: 90 MB
% 6.56/1.98 % (3711989)Instructions burned: 114 (million)
% 6.56/1.98 % (3711991)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1876031041:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.56/1.98 % (3711964)First to succeed.
% 6.56/1.98 % (3711964)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3711959"
% 6.56/1.98 % (3711995)lrs+10_1_sil=8000:sp=occurrence:random_seed=280239383:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.56/1.98 % (3711991)Instruction limit reached!
% 6.56/1.98 % (3711991)------------------------------
% 6.56/1.98 % (3711991)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.98 % (3711991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.98 % (3711991)CaDiCaL version: 2.1.3
% 6.56/1.98 % (3711991)Termination reason: Instruction limit
% 6.56/1.98 % (3711991)Termination phase: Saturation
% 6.56/1.98 % (3711991)Time elapsed: 0.073 s
% 6.56/1.98 % (3711991)Peak memory usage: 89 MB
% 6.56/1.98 % (3711991)Instructions burned: 114 (million)
% 6.56/1.98 % (3711996)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=919056648:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.56/1.98 % (3711999)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1267427023:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.56/1.98 % (3711964)Refutation found. Thanks to Tanya!
% 6.56/1.98 % SZS status Theorem for theBenchmark
% 6.56/1.98 % SZS output start Proof for theBenchmark
% See solution above
% 8.35/2.07 % (3711964)------------------------------
% 8.35/2.07 % (3711964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.35/2.07 % (3711964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.35/2.07 % (3711964)CaDiCaL version: 2.1.3
% 8.35/2.07 % (3711964)Termination reason: Refutation
% 8.35/2.07 % (3711964)Time elapsed: 0.675 s
% 8.35/2.07 % (3711964)Peak memory usage: 128 MB
% 8.35/2.07 % (3711964)Instructions burned: 1005 (million)
% 8.35/2.07 % (3711964)------------------------------
% 8.35/2.07 % (3711964)------------------------------
% 8.35/2.07 % (3711959)Success in time 1.109 s
% 8.35/2.07 % Vampire exiting
%------------------------------------------------------------------------------