%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM517+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 3.13s 1.35s
% Output : Refutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 134 ( 31 unt; 10 def)
% Number of atoms : 442 ( 86 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 535 ( 227 ~; 229 |; 54 &)
% ( 14 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 9 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 72 !; 3 ?)
% 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(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(f54,axiom,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2529) ).
fof(f55,axiom,
( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2686) ).
fof(f56,conjecture,
( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f60,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(f61,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,[],[f60]) ).
fof(f63,plain,
( ~ doDivides0(xp,sdtsldt0(xn,xr))
& ~ doDivides0(xp,xm) ),
inference(ennf_transformation,[],[f57]) ).
fof(f81,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f82,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f84,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f86,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f85]) ).
fof(f101,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(f102,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f101]) ).
fof(f112,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(f113,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,[],[f112]) ).
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,[],[f102]) ).
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,[],[f113]) ).
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(f140,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f141,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f142,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,[],[f61]) ).
fof(f144,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
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(f167,plain,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(cnf_transformation,[],[f54]) ).
fof(f168,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f55]) ).
fof(f169,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),
inference(cnf_transformation,[],[f55]) ).
fof(f170,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f63]) ).
fof(f171,plain,
~ doDivides0(xp,sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f63]) ).
fof(f190,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f191,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f192,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f206,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f218,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f253,definition,
~ sP12(sdtpldt0(sdtpldt0(xn,xm),xp)),
introduced(definition,[new_symbols(definition,[sP12])],[inequality_splitting_name_introduction]) ).
fof(f254,plain,
sP12(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)),
inference(inequality_splitting,[],[f169,f253]) ).
fof(f261,definition,
~ sP16(sz00),
introduced(definition,[new_symbols(definition,[sP16])],[inequality_splitting_name_introduction]) ).
fof(f262,plain,
! [X0] :
( ~ isPrime0(X0)
| sP16(X0)
| ~ aNaturalNumber0(X0) ),
inference(inequality_splitting,[],[f206,f261]) ).
fof(f275,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f218]) ).
fof(f283,plain,
( sP16(xr)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[],[f156,f262]) ).
fof(f284,plain,
sP16(xr),
inference(forward_subsumption_resolution,[],[f283,f158]) ).
fof(f618,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)
| iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(resolution,[],[f168,f192]) ).
fof(f813,definition,
( spl21_52
<=> aNaturalNumber0(sdtsldt0(xn,xr)) ),
introduced(definition,[new_symbols(definition,[spl21_52])],[avatar_definition]) ).
fof(f814,plain,
( aNaturalNumber0(sdtsldt0(xn,xr))
| ~ spl21_52 ),
inference(avatar_component_clause,[],[f813]) ).
fof(f815,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| spl21_52 ),
inference(avatar_component_clause,[],[f813]) ).
fof(f835,definition,
( spl21_57
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl21_57])],[avatar_definition]) ).
fof(f836,plain,
( aNaturalNumber0(sdtpldt0(xn,xm))
| ~ spl21_57 ),
inference(avatar_component_clause,[],[f835]) ).
fof(f837,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl21_57 ),
inference(avatar_component_clause,[],[f835]) ).
fof(f887,definition,
( spl21_68
<=> aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
introduced(definition,[new_symbols(definition,[spl21_68])],[avatar_definition]) ).
fof(f888,plain,
( aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ spl21_68 ),
inference(avatar_component_clause,[],[f887]) ).
fof(f889,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| spl21_68 ),
inference(avatar_component_clause,[],[f887]) ).
fof(f908,definition,
( spl21_72
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
introduced(definition,[new_symbols(definition,[spl21_72])],[avatar_definition]) ).
fof(f910,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| spl21_72 ),
inference(avatar_component_clause,[],[f908]) ).
fof(f912,definition,
( spl21_73
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
introduced(definition,[new_symbols(definition,[spl21_73])],[avatar_definition]) ).
fof(f914,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| spl21_73 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f916,definition,
( spl21_74
<=> iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
introduced(definition,[new_symbols(definition,[spl21_74])],[avatar_definition]) ).
fof(f918,plain,
( iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ spl21_74 ),
inference(avatar_component_clause,[],[f916]) ).
fof(f920,definition,
( spl21_75
<=> sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) ),
introduced(definition,[new_symbols(definition,[spl21_75])],[avatar_definition]) ).
fof(f922,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)
| ~ spl21_75 ),
inference(avatar_component_clause,[],[f920]) ).
fof(f923,plain,
( ~ spl21_72
| ~ spl21_73
| spl21_74
| spl21_75 ),
inference(avatar_split_clause,[],[f618,f920,f916,f912,f908]) ).
fof(f1290,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl21_57 ),
inference(resolution,[],[f837,f191]) ).
fof(f1294,plain,
( ~ aNaturalNumber0(xm)
| spl21_57 ),
inference(forward_subsumption_resolution,[],[f1290,f141]) ).
fof(f1295,plain,
( $false
| spl21_57 ),
inference(forward_subsumption_resolution,[],[f1294,f140]) ).
fof(f1296,plain,
spl21_57,
inference(avatar_contradiction_clause,[],[f1295]) ).
fof(f1722,definition,
( spl21_113
<=> sz00 = xr ),
introduced(definition,[new_symbols(definition,[spl21_113])],[avatar_definition]) ).
fof(f1724,plain,
( sz00 = xr
| ~ spl21_113 ),
inference(avatar_component_clause,[],[f1722]) ).
fof(f1749,plain,
( sz00 = xr
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| spl21_52 ),
inference(resolution,[],[f815,f275]) ).
fof(f1750,plain,
( sz00 = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| spl21_52 ),
inference(forward_subsumption_resolution,[],[f1749,f164]) ).
fof(f1751,plain,
( sz00 = xr
| ~ aNaturalNumber0(xn)
| spl21_52 ),
inference(forward_subsumption_resolution,[],[f1750,f158]) ).
fof(f1752,plain,
( sz00 = xr
| spl21_52 ),
inference(forward_subsumption_resolution,[],[f1751,f141]) ).
fof(f1753,plain,
( spl21_113
| spl21_52 ),
inference(avatar_split_clause,[],[f1752,f813,f1722]) ).
fof(f1755,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,sdtsldt0(xn,xr)))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| spl21_68 ),
inference(superposition,[],[f889,f190]) ).
fof(f1769,plain,
( sP16(sz00)
| ~ spl21_113 ),
inference(superposition,[],[f284,f1724]) ).
fof(f1795,plain,
( $false
| ~ spl21_113 ),
inference(forward_subsumption_resolution,[],[f1769,f261]) ).
fof(f1796,plain,
~ spl21_113,
inference(avatar_contradiction_clause,[],[f1795]) ).
fof(f1803,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| spl21_68 ),
inference(forward_subsumption_resolution,[],[f1755,f191]) ).
fof(f1806,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| spl21_68 ),
inference(forward_subsumption_resolution,[],[f1803,f140]) ).
fof(f1811,plain,
( $false
| ~ spl21_52
| spl21_68 ),
inference(forward_subsumption_resolution,[],[f1806,f814]) ).
fof(f1812,plain,
( ~ spl21_52
| spl21_68 ),
inference(avatar_contradiction_clause,[],[f1811]) ).
fof(f2354,plain,
( ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(sdtsldt0(xn,xr),xm)))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| spl21_73 ),
inference(superposition,[],[f914,f190]) ).
fof(f2357,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| spl21_73 ),
inference(forward_subsumption_resolution,[],[f2354,f191]) ).
fof(f2363,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| spl21_73 ),
inference(forward_subsumption_resolution,[],[f2357,f139]) ).
fof(f2371,plain,
( $false
| ~ spl21_68
| spl21_73 ),
inference(forward_subsumption_resolution,[],[f2363,f888]) ).
fof(f2372,plain,
( ~ spl21_68
| spl21_73 ),
inference(avatar_contradiction_clause,[],[f2371]) ).
fof(f3103,plain,
( doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl21_74 ),
inference(resolution,[],[f918,f142]) ).
fof(f3119,plain,
( doDivides0(xp,sdtsldt0(xn,xr))
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl21_74 ),
inference(forward_subsumption_resolution,[],[f3103,f170]) ).
fof(f3127,plain,
( ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl21_74 ),
inference(forward_subsumption_resolution,[],[f3119,f171]) ).
fof(f3129,plain,
( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl21_74 ),
inference(forward_subsumption_resolution,[],[f3127,f144]) ).
fof(f3130,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl21_74 ),
inference(forward_subsumption_resolution,[],[f3129,f167]) ).
fof(f3131,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ spl21_52
| ~ spl21_74 ),
inference(forward_subsumption_resolution,[],[f3130,f814]) ).
fof(f3132,plain,
( ~ aNaturalNumber0(xp)
| ~ spl21_52
| ~ spl21_74 ),
inference(forward_subsumption_resolution,[],[f3131,f140]) ).
fof(f3133,plain,
( $false
| ~ spl21_52
| ~ spl21_74 ),
inference(forward_subsumption_resolution,[],[f3132,f139]) ).
fof(f3134,plain,
( ~ spl21_52
| ~ spl21_74 ),
inference(avatar_contradiction_clause,[],[f3133]) ).
fof(f3146,plain,
( ~ aNaturalNumber0(sdtpldt0(xp,sdtpldt0(xn,xm)))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl21_72 ),
inference(superposition,[],[f910,f190]) ).
fof(f3149,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl21_72 ),
inference(forward_subsumption_resolution,[],[f3146,f191]) ).
fof(f3152,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl21_72 ),
inference(forward_subsumption_resolution,[],[f3149,f139]) ).
fof(f3157,plain,
( $false
| ~ spl21_57
| spl21_72 ),
inference(forward_subsumption_resolution,[],[f3152,f836]) ).
fof(f3158,plain,
( ~ spl21_57
| spl21_72 ),
inference(avatar_contradiction_clause,[],[f3157]) ).
fof(f3238,plain,
( sP12(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ spl21_75 ),
inference(superposition,[],[f254,f922]) ).
fof(f3286,plain,
( $false
| ~ spl21_75 ),
inference(forward_subsumption_resolution,[],[f3238,f253]) ).
fof(f3287,plain,
~ spl21_75,
inference(avatar_contradiction_clause,[],[f3286]) ).
cnf(s52,plain,
( ~ spl21_72
| ~ spl21_73
| spl21_74
| spl21_75 ),
inference(sat_conversion,[],[f923]) ).
cnf(s94,plain,
spl21_57,
inference(sat_conversion,[],[f1296]) ).
cnf(s121,plain,
( spl21_52
| spl21_113 ),
inference(sat_conversion,[],[f1753]) ).
cnf(s123,plain,
~ spl21_113,
inference(sat_conversion,[],[f1796]) ).
cnf(s127,plain,
( ~ spl21_52
| spl21_68 ),
inference(sat_conversion,[],[f1812]) ).
cnf(s163,plain,
( ~ spl21_68
| spl21_73 ),
inference(sat_conversion,[],[f2372]) ).
cnf(s199,plain,
( ~ spl21_52
| ~ spl21_74 ),
inference(sat_conversion,[],[f3134]) ).
cnf(s203,plain,
( ~ spl21_57
| spl21_72 ),
inference(sat_conversion,[],[f3158]) ).
cnf(s209,plain,
~ spl21_75,
inference(sat_conversion,[],[f3287]) ).
cnf(s213,plain,
spl21_52,
inference(rat,[],[s121,s123]) ).
cnf(s214,plain,
~ spl21_74,
inference(rat,[],[s199,s213]) ).
cnf(s215,plain,
spl21_68,
inference(rat,[],[s127,s213]) ).
cnf(s217,plain,
spl21_73,
inference(rat,[],[s163,s215]) ).
cnf(s226,plain,
spl21_72,
inference(rat,[],[s203,s94]) ).
cnf(s239,plain,
$false,
inference(rat,[],[s52,s209,s214,s217,s226]) ).
fof(f3333,plain,
$false,
inference(avatar_sat_refutation,[],[s239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM517+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n017.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 20:13:05 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 3.13/1.35 % (2907496)Detected formulas, will run a generic FOF schedule.
% 3.13/1.35 % (2907506)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=512728025:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.13/1.35 % (2907504)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2730212485:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.13/1.35 % (2907503)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=1537859621:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.13/1.35 % (2907502)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=2230000290:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.13/1.35 % (2907505)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2974919803:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.13/1.35 % (2907507)dis-21_1_sil=8000:lcm=predicate:random_seed=3915628358: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)
% 3.13/1.35 % (2907501)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=3091169226:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.13/1.35 % (2907506)Instruction limit reached!
% 3.13/1.35 % (2907506)------------------------------
% 3.13/1.35 % (2907506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2907506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2907506)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2907506)Termination reason: Instruction limit
% 3.13/1.35 % (2907506)Termination phase: Saturation
% 3.13/1.35 % (2907506)Time elapsed: 0.051 s
% 3.13/1.35 % (2907506)Peak memory usage: 90 MB
% 3.13/1.35 % (2907506)Instructions burned: 139 (million)
% 3.13/1.35 % (2907504)First to succeed.
% 3.13/1.35 % (2907504)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2907496"
% 3.13/1.35 % (2907505)Instruction limit reached!
% 3.13/1.35 % (2907505)------------------------------
% 3.13/1.35 % (2907505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2907505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2907505)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2907505)Termination reason: Instruction limit
% 3.13/1.35 % (2907505)Termination phase: Saturation
% 3.13/1.35 % (2907505)Time elapsed: 0.073 s
% 3.13/1.35 % (2907505)Peak memory usage: 88 MB
% 3.13/1.35 % (2907505)Instructions burned: 120 (million)
% 3.13/1.35 % (2907507)Instruction limit reached!
% 3.13/1.35 % (2907507)------------------------------
% 3.13/1.35 % (2907507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2907507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2907507)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2907507)Termination reason: Instruction limit
% 3.13/1.35 % (2907507)Termination phase: Saturation
% 3.13/1.35 % (2907507)Time elapsed: 0.082 s
% 3.13/1.35 % (2907507)Peak memory usage: 90 MB
% 3.13/1.35 % (2907507)Instructions burned: 130 (million)
% 3.13/1.35 % (2907515)lrs+10_1_sil=8000:sp=occurrence:random_seed=2576313343:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.13/1.35 % (2907516)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1222646182:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.13/1.35 % (2907515)Instruction limit reached!
% 3.13/1.35 % (2907515)------------------------------
% 3.13/1.35 % (2907515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2907515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2907515)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2907515)Termination reason: Instruction limit
% 3.13/1.35 % (2907515)Termination phase: Saturation
% 3.13/1.35 % (2907515)Time elapsed: 0.094 s
% 3.13/1.35 % (2907515)Peak memory usage: 92 MB
% 3.13/1.35 % (2907515)Instructions burned: 287 (million)
% 3.13/1.35 % (2907516)Refutation not found, incomplete strategy
% 3.13/1.35 % (2907516)------------------------------
% 3.13/1.35 % (2907516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2907516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2907516)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2907516)Termination reason: Refutation not found, incomplete strategy
% 3.13/1.35 % (2907516)Time elapsed: 0.004 s
% 3.13/1.35 % (2907516)Peak memory usage: 89 MB
% 3.13/1.35 % (2907516)Instructions burned: 4 (million)
% 3.13/1.35 % (2907517)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2396076904:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.13/1.35 % (2907504)Refutation found. Thanks to Tanya!
% 3.13/1.35 % SZS status Theorem for theBenchmark
% 3.13/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.07/1.54 % (2907504)------------------------------
% 4.07/1.54 % (2907504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.54 % (2907504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.54 % (2907504)CaDiCaL version: 2.1.3
% 4.07/1.54 % (2907504)Termination reason: Refutation
% 4.07/1.54 % (2907504)Time elapsed: 0.062 s
% 4.07/1.54 % (2907504)Peak memory usage: 90 MB
% 4.07/1.54 % (2907504)Instructions burned: 97 (million)
% 4.07/1.54 % (2907504)------------------------------
% 4.07/1.54 % (2907504)------------------------------
% 4.07/1.54 % (2907496)Success in time 0.489 s
% 4.07/1.54 % Vampire exiting
%------------------------------------------------------------------------------