%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM469+2 : 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 : n014.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 12:15:19 PM UTC 2026
% Result : Theorem 2.27s 1.19s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 114 ( 15 unt; 6 def)
% Number of atoms : 361 ( 100 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 410 ( 163 ~; 172 |; 54 &)
% ( 12 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 78 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
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(f33,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240) ).
fof(f34,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xl,X0) )
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240_04) ).
fof(f35,axiom,
( xl != sz00
=> ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1298) ).
fof(f36,conjecture,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X0) )
| doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f37,negated_conjecture,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X0) )
| doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xl,X1) )
& doDivides0(xl,xn) ),
inference(rectify,[],[f34]) ).
fof(f42,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f43,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f45,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f47,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f46]) ).
fof(f50,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f56,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f86,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f87,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f86]) ).
fof(f88,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(f89,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,[],[f88]) ).
fof(f92,plain,
( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) )
| sz00 = xl ),
inference(ennf_transformation,[],[f35]) ).
fof(f93,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xl,X0) != sdtpldt0(xm,xn) )
& ~ doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f99,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f87]) ).
fof(f100,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X0,X3) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtasdt0(X0,sK1(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f100]) ).
fof(f102,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,[],[f89]) ).
fof(f103,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,[],[f102]) ).
fof(f104,plain,
( aNaturalNumber0(sK2)
& xm = sdtasdt0(xl,sK2)
& doDivides0(xl,xm)
& aNaturalNumber0(sK3)
& xn = sdtasdt0(xl,sK3)
& doDivides0(xl,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f40]) ).
fof(f105,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f108,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f109,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f110,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f112,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f118,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f153,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f156,plain,
! [X2,X0,X1] :
( sdtsldt0(X1,X0) = X2
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f159,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f33]) ).
fof(f160,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f33]) ).
fof(f162,plain,
xn = sdtasdt0(xl,sK3),
inference(cnf_transformation,[],[f104]) ).
fof(f163,plain,
aNaturalNumber0(sK3),
inference(cnf_transformation,[],[f104]) ).
fof(f164,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f104]) ).
fof(f165,plain,
xm = sdtasdt0(xl,sK2),
inference(cnf_transformation,[],[f104]) ).
fof(f166,plain,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f104]) ).
fof(f167,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| sz00 = xl ),
inference(cnf_transformation,[],[f92]) ).
fof(f172,plain,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f93]) ).
fof(f180,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f153]) ).
fof(f181,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f156]) ).
fof(f186,definition,
( spl4_1
<=> sz00 = xl ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f188,plain,
( sz00 = xl
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f190,definition,
( spl4_2
<=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f192,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f167,f190,f186]) ).
fof(f241,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xm,X0) = sdtpldt0(X0,xm) ),
inference(resolution,[],[f110,f159]) ).
fof(f264,plain,
sdtpldt0(xm,sz00) = sdtpldt0(sz00,xm),
inference(resolution,[],[f241,f105]) ).
fof(f318,plain,
( doDivides0(sz00,xm)
| ~ spl4_1 ),
inference(superposition,[],[f164,f188]) ).
fof(f414,plain,
( xn = sdtasdt0(sz00,sK3)
| ~ spl4_1 ),
inference(superposition,[],[f162,f188]) ).
fof(f417,plain,
( ~ doDivides0(sz00,sdtpldt0(xm,xn))
| ~ spl4_1 ),
inference(superposition,[],[f172,f188]) ).
fof(f432,definition,
( spl4_19
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl4_19])],[avatar_definition]) ).
fof(f433,plain,
( sz00 = xn
| ~ spl4_19 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f434,plain,
( sz00 != xn
| spl4_19 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f533,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f180,f109]) ).
fof(f1207,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(forward_subsumption_resolution,[],[f181,f533]) ).
fof(f1208,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f1207,f109]) ).
fof(f1214,plain,
( sdtsldt0(xn,xl) = sK3
| ~ aNaturalNumber0(sK3)
| sz00 = xl
| ~ aNaturalNumber0(xl) ),
inference(superposition,[],[f1208,f162]) ).
fof(f1215,plain,
( sdtsldt0(xm,xl) = sK2
| ~ aNaturalNumber0(sK2)
| sz00 = xl
| ~ aNaturalNumber0(xl) ),
inference(superposition,[],[f1208,f165]) ).
fof(f1275,plain,
( ~ doDivides0(sz00,sdtpldt0(xm,sz00))
| ~ spl4_1
| ~ spl4_19 ),
inference(superposition,[],[f417,f433]) ).
fof(f1302,plain,
( ~ doDivides0(sz00,sdtpldt0(sz00,xm))
| ~ spl4_1
| ~ spl4_19 ),
inference(forward_demodulation,[],[f1275,f264]) ).
fof(f1312,plain,
( ~ doDivides0(sz00,xm)
| ~ aNaturalNumber0(xm)
| ~ spl4_1
| ~ spl4_19 ),
inference(superposition,[],[f1302,f112]) ).
fof(f1313,plain,
( ~ aNaturalNumber0(xm)
| ~ spl4_1
| ~ spl4_19 ),
inference(forward_subsumption_resolution,[],[f1312,f318]) ).
fof(f1315,plain,
( $false
| ~ spl4_1
| ~ spl4_19 ),
inference(forward_subsumption_resolution,[],[f1313,f159]) ).
fof(f1316,plain,
( ~ spl4_1
| ~ spl4_19 ),
inference(avatar_contradiction_clause,[],[f1315]) ).
fof(f1408,plain,
( sz00 = xn
| ~ aNaturalNumber0(sK3)
| ~ spl4_1 ),
inference(superposition,[],[f414,f118]) ).
fof(f1416,plain,
( ~ aNaturalNumber0(sK3)
| ~ spl4_1
| spl4_19 ),
inference(forward_subsumption_resolution,[],[f1408,f434]) ).
fof(f1420,plain,
( $false
| ~ spl4_1
| spl4_19 ),
inference(forward_subsumption_resolution,[],[f1416,f163]) ).
fof(f1421,plain,
( ~ spl4_1
| spl4_19 ),
inference(avatar_contradiction_clause,[],[f1420]) ).
fof(f1449,plain,
( sdtsldt0(xm,xl) = sK2
| sz00 = xl
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f1215,f166]) ).
fof(f1450,plain,
( sdtsldt0(xn,xl) = sK3
| sz00 = xl
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f1214,f163]) ).
fof(f1466,plain,
( sdtsldt0(xm,xl) = sK2
| sz00 = xl ),
inference(forward_subsumption_resolution,[],[f1449,f160]) ).
fof(f1467,plain,
( sdtsldt0(xn,xl) = sK3
| sz00 = xl ),
inference(forward_subsumption_resolution,[],[f1450,f160]) ).
fof(f1480,definition,
( spl4_48
<=> sdtsldt0(xn,xl) = sK3 ),
introduced(definition,[new_symbols(definition,[spl4_48])],[avatar_definition]) ).
fof(f1482,plain,
( sdtsldt0(xn,xl) = sK3
| ~ spl4_48 ),
inference(avatar_component_clause,[],[f1480]) ).
fof(f1483,plain,
( spl4_1
| spl4_48 ),
inference(avatar_split_clause,[],[f1467,f1480,f186]) ).
fof(f1572,definition,
( spl4_67
<=> sdtsldt0(xm,xl) = sK2 ),
introduced(definition,[new_symbols(definition,[spl4_67])],[avatar_definition]) ).
fof(f1574,plain,
( sdtsldt0(xm,xl) = sK2
| ~ spl4_67 ),
inference(avatar_component_clause,[],[f1572]) ).
fof(f1575,plain,
( spl4_1
| spl4_67 ),
inference(avatar_split_clause,[],[f1466,f1572,f186]) ).
fof(f1613,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ aNaturalNumber0(xl)
| ~ spl4_2 ),
inference(superposition,[],[f533,f192]) ).
fof(f1618,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ aNaturalNumber0(xl)
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f1613,f172]) ).
fof(f1622,definition,
( spl4_68
<=> aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
introduced(definition,[new_symbols(definition,[spl4_68])],[avatar_definition]) ).
fof(f1624,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| spl4_68 ),
inference(avatar_component_clause,[],[f1622]) ).
fof(f1634,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f1618,f160]) ).
fof(f1640,plain,
( ~ spl4_68
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f1634,f190,f1622]) ).
fof(f2088,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sK3))
| ~ spl4_48
| spl4_68 ),
inference(forward_demodulation,[],[f1624,f1482]) ).
fof(f2146,plain,
( ~ aNaturalNumber0(sdtpldt0(sK2,sK3))
| ~ spl4_48
| ~ spl4_67
| spl4_68 ),
inference(forward_demodulation,[],[f2088,f1574]) ).
fof(f2168,plain,
( ~ aNaturalNumber0(sK2)
| ~ aNaturalNumber0(sK3)
| ~ spl4_48
| ~ spl4_67
| spl4_68 ),
inference(resolution,[],[f2146,f108]) ).
fof(f2169,plain,
( ~ aNaturalNumber0(sK3)
| ~ spl4_48
| ~ spl4_67
| spl4_68 ),
inference(forward_subsumption_resolution,[],[f2168,f166]) ).
fof(f2170,plain,
( $false
| ~ spl4_48
| ~ spl4_67
| spl4_68 ),
inference(forward_subsumption_resolution,[],[f2169,f163]) ).
fof(f2171,plain,
( ~ spl4_48
| ~ spl4_67
| spl4_68 ),
inference(avatar_contradiction_clause,[],[f2170]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f193]) ).
cnf(s52,plain,
( ~ spl4_1
| ~ spl4_19 ),
inference(sat_conversion,[],[f1316]) ).
cnf(s61,plain,
( ~ spl4_1
| spl4_19 ),
inference(sat_conversion,[],[f1421]) ).
cnf(s63,plain,
( spl4_1
| spl4_48 ),
inference(sat_conversion,[],[f1483]) ).
cnf(s81,plain,
( spl4_1
| spl4_67 ),
inference(sat_conversion,[],[f1575]) ).
cnf(s87,plain,
( ~ spl4_2
| ~ spl4_68 ),
inference(sat_conversion,[],[f1640]) ).
cnf(s120,plain,
( ~ spl4_48
| ~ spl4_67
| spl4_68 ),
inference(sat_conversion,[],[f2171]) ).
cnf(s124,plain,
spl4_1,
inference(rat,[],[s87,s120,s1,s63,s81]) ).
cnf(s125,plain,
spl4_19,
inference(rat,[],[s61,s124]) ).
cnf(s126,plain,
$false,
inference(rat,[],[s52,s125,s124]) ).
fof(f2172,plain,
$false,
inference(avatar_sat_refutation,[],[s126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM469+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n014.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
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:04:01 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
% 2.27/1.19 % (1127872)Detected formulas, will run a generic FOF schedule.
% 2.27/1.19 % (1127882)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=97755913:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.27/1.19 % (1127882)First to succeed.
% 2.27/1.19 % (1127882)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1127872"
% 2.27/1.19 % (1127880)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=86696438:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.27/1.19 % (1127881)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1699011888:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.27/1.19 % (1127878)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=2804353664:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.27/1.19 % (1127877)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=2507284387:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.27/1.19 % (1127879)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=3384767668:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.27/1.19 % (1127883)dis-21_1_sil=8000:lcm=predicate:random_seed=2317689517: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)
% 2.27/1.19 % (1127880)Also succeeded, but the first one will report.
% 2.27/1.19 % (1127881)Also succeeded, but the first one will report.
% 2.27/1.19 % (1127883)Instruction limit reached!
% 2.27/1.19 % (1127883)------------------------------
% 2.27/1.19 % (1127883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.27/1.19 % (1127883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.27/1.19 % (1127883)CaDiCaL version: 2.1.3
% 2.27/1.19 % (1127883)Termination reason: Instruction limit
% 2.27/1.19 % (1127883)Termination phase: Saturation
% 2.27/1.19 % (1127883)Time elapsed: 0.079 s
% 2.27/1.19 % (1127883)Peak memory usage: 90 MB
% 2.27/1.19 % (1127883)Instructions burned: 129 (million)
% 2.27/1.19 % (1127882)Refutation found. Thanks to Tanya!
% 2.27/1.19 % SZS status Theorem for theBenchmark
% 2.27/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.28 % (1127882)------------------------------
% 2.72/1.28 % (1127882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.28 % (1127882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.28 % (1127882)CaDiCaL version: 2.1.3
% 2.72/1.28 % (1127882)Termination reason: Refutation
% 2.72/1.28 % (1127882)Time elapsed: 0.025 s
% 2.72/1.28 % (1127882)Peak memory usage: 90 MB
% 2.72/1.28 % (1127882)Instructions burned: 69 (million)
% 2.72/1.28 % (1127882)------------------------------
% 2.72/1.28 % (1127882)------------------------------
% 2.72/1.28 % (1127872)Success in time 0.32 s
% 2.72/1.28 % Vampire exiting
%------------------------------------------------------------------------------