%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM495+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 : n019.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 12:15:27 PM UTC 2026
% Result : Theorem 2.94s 1.36s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 120 ( 32 unt; 8 def)
% Number of atoms : 335 ( 33 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 392 ( 177 ~; 176 |; 20 &)
% ( 10 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
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(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(f45,axiom,
doDivides0(xp,sdtasdt0(xr,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1913) ).
fof(f46,axiom,
( sdtpldt0(sdtpldt0(xr,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2062) ).
fof(f47,conjecture,
( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f48,negated_conjecture,
~ ( doDivides0(xp,xr)
| doDivides0(xp,xm) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f51,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(f52,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,[],[f51]) ).
fof(f53,plain,
( ~ doDivides0(xp,xr)
& ~ doDivides0(xp,xm) ),
inference(ennf_transformation,[],[f48]) ).
fof(f67,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f68,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f70,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f72,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f71]) ).
fof(f104,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(f105,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f104]) ).
fof(f117,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,[],[f105]) ).
fof(f118,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,[],[f117]) ).
fof(f119,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f120,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f121,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f122,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,[],[f52]) ).
fof(f124,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f125,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f126,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[],[f43]) ).
fof(f129,plain,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f45]) ).
fof(f130,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f46]) ).
fof(f131,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xr,xm),xp),
inference(cnf_transformation,[],[f46]) ).
fof(f132,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f53]) ).
fof(f133,plain,
~ doDivides0(xp,xr),
inference(cnf_transformation,[],[f53]) ).
fof(f150,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f151,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f152,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f184,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f188,definition,
~ sP5(sdtpldt0(sdtpldt0(xn,xm),xp)),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f189,plain,
sP5(sdtpldt0(sdtpldt0(xr,xm),xp)),
inference(inequality_splitting,[],[f131,f188]) ).
fof(f204,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f184]) ).
fof(f330,plain,
~ doDivides0(xp,sdtmndt0(xn,xp)),
inference(superposition,[],[f133,f126]) ).
fof(f338,plain,
doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm)),
inference(superposition,[],[f129,f126]) ).
fof(f414,definition,
( spl11_22
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl11_22])],[avatar_definition]) ).
fof(f415,plain,
( aNaturalNumber0(sdtpldt0(xn,xm))
| ~ spl11_22 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f416,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl11_22 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f425,plain,
sP5(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)),
inference(superposition,[],[f189,f126]) ).
fof(f476,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xr,xm),xp)
| iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(resolution,[],[f130,f152]) ).
fof(f688,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl11_22 ),
inference(resolution,[],[f416,f151]) ).
fof(f689,plain,
( ~ aNaturalNumber0(xm)
| spl11_22 ),
inference(forward_subsumption_resolution,[],[f688,f121]) ).
fof(f690,plain,
( $false
| spl11_22 ),
inference(forward_subsumption_resolution,[],[f689,f120]) ).
fof(f691,plain,
spl11_22,
inference(avatar_contradiction_clause,[],[f690]) ).
fof(f1171,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)
| iLess0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(forward_demodulation,[],[f476,f126]) ).
fof(f1190,definition,
( spl11_63
<=> aNaturalNumber0(sdtmndt0(xn,xp)) ),
introduced(definition,[new_symbols(definition,[spl11_63])],[avatar_definition]) ).
fof(f1191,plain,
( aNaturalNumber0(sdtmndt0(xn,xp))
| ~ spl11_63 ),
inference(avatar_component_clause,[],[f1190]) ).
fof(f1192,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| spl11_63 ),
inference(avatar_component_clause,[],[f1190]) ).
fof(f1212,definition,
( spl11_66
<=> aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm)) ),
introduced(definition,[new_symbols(definition,[spl11_66])],[avatar_definition]) ).
fof(f1213,plain,
( aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| ~ spl11_66 ),
inference(avatar_component_clause,[],[f1212]) ).
fof(f1214,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| spl11_66 ),
inference(avatar_component_clause,[],[f1212]) ).
fof(f1218,plain,
( iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(forward_demodulation,[],[f1171,f126]) ).
fof(f1282,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp))
| iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(forward_demodulation,[],[f1218,f126]) ).
fof(f1284,definition,
( spl11_79
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
introduced(definition,[new_symbols(definition,[spl11_79])],[avatar_definition]) ).
fof(f1286,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| spl11_79 ),
inference(avatar_component_clause,[],[f1284]) ).
fof(f1291,definition,
( spl11_81
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)) ),
introduced(definition,[new_symbols(definition,[spl11_81])],[avatar_definition]) ).
fof(f1293,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp))
| spl11_81 ),
inference(avatar_component_clause,[],[f1291]) ).
fof(f1314,definition,
( spl11_85
<=> sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp) ),
introduced(definition,[new_symbols(definition,[spl11_85])],[avatar_definition]) ).
fof(f1316,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp)
| ~ spl11_85 ),
inference(avatar_component_clause,[],[f1314]) ).
fof(f1318,definition,
( spl11_86
<=> iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
introduced(definition,[new_symbols(definition,[spl11_86])],[avatar_definition]) ).
fof(f1320,plain,
( iLess0(sdtpldt0(sdtpldt0(sdtmndt0(xn,xp),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ spl11_86 ),
inference(avatar_component_clause,[],[f1318]) ).
fof(f1321,plain,
( ~ spl11_79
| spl11_85
| spl11_86
| ~ spl11_81 ),
inference(avatar_split_clause,[],[f1282,f1291,f1318,f1314,f1284]) ).
fof(f1328,plain,
( ~ sdtlseqdt0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| spl11_63 ),
inference(resolution,[],[f1192,f204]) ).
fof(f1329,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| spl11_63 ),
inference(forward_subsumption_resolution,[],[f1328,f125]) ).
fof(f1330,plain,
( ~ aNaturalNumber0(xn)
| spl11_63 ),
inference(forward_subsumption_resolution,[],[f1329,f119]) ).
fof(f1331,plain,
( $false
| spl11_63 ),
inference(forward_subsumption_resolution,[],[f1330,f121]) ).
fof(f1332,plain,
spl11_63,
inference(avatar_contradiction_clause,[],[f1331]) ).
fof(f1517,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| spl11_66 ),
inference(resolution,[],[f1214,f151]) ).
fof(f1519,plain,
( ~ aNaturalNumber0(xm)
| ~ spl11_63
| spl11_66 ),
inference(forward_subsumption_resolution,[],[f1517,f1191]) ).
fof(f1520,plain,
( $false
| ~ spl11_63
| spl11_66 ),
inference(forward_subsumption_resolution,[],[f1519,f120]) ).
fof(f1521,plain,
( ~ spl11_63
| spl11_66 ),
inference(avatar_contradiction_clause,[],[f1520]) ).
fof(f1537,plain,
( ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl11_79 ),
inference(superposition,[],[f1286,f150]) ).
fof(f1540,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl11_79 ),
inference(forward_subsumption_resolution,[],[f1537,f151]) ).
fof(f1544,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl11_79 ),
inference(forward_subsumption_resolution,[],[f1540,f119]) ).
fof(f1550,plain,
( $false
| ~ spl11_22
| spl11_79 ),
inference(forward_subsumption_resolution,[],[f1544,f415]) ).
fof(f1551,plain,
( ~ spl11_22
| spl11_79 ),
inference(avatar_contradiction_clause,[],[f1550]) ).
fof(f1929,plain,
( ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(sdtmndt0(xn,xp),xm)))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| spl11_81 ),
inference(superposition,[],[f1293,f150]) ).
fof(f1932,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| spl11_81 ),
inference(forward_subsumption_resolution,[],[f1929,f151]) ).
fof(f1936,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xp),xm))
| spl11_81 ),
inference(forward_subsumption_resolution,[],[f1932,f119]) ).
fof(f1942,plain,
( $false
| ~ spl11_66
| spl11_81 ),
inference(forward_subsumption_resolution,[],[f1936,f1213]) ).
fof(f1943,plain,
( ~ spl11_66
| spl11_81 ),
inference(avatar_contradiction_clause,[],[f1942]) ).
fof(f2385,plain,
( sP5(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ spl11_85 ),
inference(superposition,[],[f425,f1316]) ).
fof(f2439,plain,
( $false
| ~ spl11_85 ),
inference(forward_subsumption_resolution,[],[f2385,f188]) ).
fof(f2440,plain,
~ spl11_85,
inference(avatar_contradiction_clause,[],[f2439]) ).
fof(f2864,plain,
( doDivides0(xp,xm)
| doDivides0(xp,sdtmndt0(xn,xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl11_86 ),
inference(resolution,[],[f1320,f122]) ).
fof(f2875,plain,
( doDivides0(xp,sdtmndt0(xn,xp))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl11_86 ),
inference(forward_subsumption_resolution,[],[f2864,f132]) ).
fof(f2880,plain,
( ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl11_86 ),
inference(forward_subsumption_resolution,[],[f2875,f330]) ).
fof(f2883,plain,
( ~ doDivides0(xp,sdtasdt0(sdtmndt0(xn,xp),xm))
| ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl11_86 ),
inference(forward_subsumption_resolution,[],[f2880,f124]) ).
fof(f2886,plain,
( ~ aNaturalNumber0(sdtmndt0(xn,xp))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl11_86 ),
inference(forward_subsumption_resolution,[],[f2883,f338]) ).
fof(f2887,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl11_63
| ~ spl11_86 ),
inference(forward_subsumption_resolution,[],[f2886,f1191]) ).
fof(f2888,plain,
( ~ aNaturalNumber0(xp)
| ~ spl11_63
| ~ spl11_86 ),
inference(forward_subsumption_resolution,[],[f2887,f120]) ).
fof(f2889,plain,
( $false
| ~ spl11_63
| ~ spl11_86 ),
inference(forward_subsumption_resolution,[],[f2888,f119]) ).
fof(f2890,plain,
( ~ spl11_63
| ~ spl11_86 ),
inference(avatar_contradiction_clause,[],[f2889]) ).
cnf(s25,plain,
spl11_22,
inference(sat_conversion,[],[f691]) ).
cnf(s81,plain,
( ~ spl11_79
| ~ spl11_81
| spl11_85
| spl11_86 ),
inference(sat_conversion,[],[f1321]) ).
cnf(s83,plain,
spl11_63,
inference(sat_conversion,[],[f1332]) ).
cnf(s90,plain,
( ~ spl11_63
| spl11_66 ),
inference(sat_conversion,[],[f1521]) ).
cnf(s94,plain,
( ~ spl11_22
| spl11_79 ),
inference(sat_conversion,[],[f1551]) ).
cnf(s125,plain,
( ~ spl11_66
| spl11_81 ),
inference(sat_conversion,[],[f1943]) ).
cnf(s152,plain,
~ spl11_85,
inference(sat_conversion,[],[f2440]) ).
cnf(s179,plain,
( ~ spl11_63
| ~ spl11_86 ),
inference(sat_conversion,[],[f2890]) ).
cnf(s180,plain,
~ spl11_86,
inference(rat,[],[s179,s83]) ).
cnf(s184,plain,
spl11_66,
inference(rat,[],[s90,s83]) ).
cnf(s185,plain,
spl11_81,
inference(rat,[],[s125,s184]) ).
cnf(s187,plain,
~ spl11_79,
inference(rat,[],[s81,s180,s152,s185]) ).
cnf(s188,plain,
~ spl11_22,
inference(rat,[],[s94,s187]) ).
cnf(s205,plain,
$false,
inference(rat,[],[s25,s188]) ).
fof(f2891,plain,
$false,
inference(avatar_sat_refutation,[],[s205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM495+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:12:08 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.94/1.36 % (3376193)Detected formulas, will run a generic FOF schedule.
% 2.94/1.36 % (3376200)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=2462008670:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.94/1.36 % (3376203)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4085231758:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.94/1.36 % (3376198)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=3960042600:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.94/1.36 % (3376199)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=3992855906:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.94/1.36 % (3376202)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1633524590:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.94/1.36 % (3376204)dis-21_1_sil=8000:lcm=predicate:random_seed=621035041: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)
% 2.94/1.36 % (3376201)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=125075727:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.94/1.36 % (3376201)First to succeed.
% 2.94/1.36 % (3376201)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3376193"
% 2.94/1.36 % (3376202)Instruction limit reached!
% 2.94/1.36 % (3376202)------------------------------
% 2.94/1.36 % (3376202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.36 % (3376202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.36 % (3376202)CaDiCaL version: 2.1.3
% 2.94/1.36 % (3376202)Termination reason: Instruction limit
% 2.94/1.36 % (3376202)Termination phase: Saturation
% 2.94/1.36 % (3376202)Time elapsed: 0.073 s
% 2.94/1.36 % (3376202)Peak memory usage: 88 MB
% 2.94/1.36 % (3376202)Instructions burned: 121 (million)
% 2.94/1.36 % (3376204)Instruction limit reached!
% 2.94/1.36 % (3376204)------------------------------
% 2.94/1.36 % (3376204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.36 % (3376204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.36 % (3376204)CaDiCaL version: 2.1.3
% 2.94/1.36 % (3376204)Termination reason: Instruction limit
% 2.94/1.36 % (3376204)Termination phase: Saturation
% 2.94/1.36 % (3376204)Time elapsed: 0.076 s
% 2.94/1.36 % (3376204)Peak memory usage: 89 MB
% 2.94/1.36 % (3376204)Instructions burned: 129 (million)
% 2.94/1.36 % (3376203)Instruction limit reached!
% 2.94/1.36 % (3376203)------------------------------
% 2.94/1.36 % (3376203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.36 % (3376203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.36 % (3376203)CaDiCaL version: 2.1.3
% 2.94/1.36 % (3376203)Termination reason: Instruction limit
% 2.94/1.36 % (3376203)Termination phase: Saturation
% 2.94/1.36 % (3376203)Time elapsed: 0.092 s
% 2.94/1.36 % (3376203)Peak memory usage: 90 MB
% 2.94/1.36 % (3376203)Instructions burned: 140 (million)
% 2.94/1.36 % (3376212)lrs+10_1_sil=8000:sp=occurrence:random_seed=878793493:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.94/1.36 % (3376213)lrs+10_1_sil=32000:urr=on:br=off:random_seed=976806978:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.94/1.36 % (3376213)Refutation not found, incomplete strategy
% 2.94/1.36 % (3376213)------------------------------
% 2.94/1.36 % (3376213)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.36 % (3376213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.36 % (3376213)CaDiCaL version: 2.1.3
% 2.94/1.36 % (3376213)Termination reason: Refutation not found, incomplete strategy
% 2.94/1.36 % (3376213)Time elapsed: 0.002 s
% 2.94/1.36 % (3376213)Peak memory usage: 88 MB
% 2.94/1.36 % (3376213)Instructions burned: 2 (million)
% 2.94/1.36 % (3376214)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1708314064:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.94/1.36 % (3376212)Also succeeded, but the first one will report.
% 2.94/1.36 % (3376201)Refutation found. Thanks to Tanya!
% 2.94/1.36 % SZS status Theorem for theBenchmark
% 2.94/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.46 % (3376201)------------------------------
% 3.94/1.46 % (3376201)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.46 % (3376201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.46 % (3376201)CaDiCaL version: 2.1.3
% 3.94/1.46 % (3376201)Termination reason: Refutation
% 3.94/1.46 % (3376201)Time elapsed: 0.053 s
% 3.94/1.46 % (3376201)Peak memory usage: 91 MB
% 3.94/1.46 % (3376201)Instructions burned: 85 (million)
% 3.94/1.46 % (3376201)------------------------------
% 3.94/1.46 % (3376201)------------------------------
% 3.94/1.46 % (3376193)Success in time 0.493 s
% 3.94/1.46 % Vampire exiting
%------------------------------------------------------------------------------