%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM476+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 : n012.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 12:15:21 PM UTC 2026
% Result : Theorem 0.76s 0.80s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 21
% Syntax : Number of formulae : 141 ( 23 unt; 10 def)
% Number of atoms : 440 ( 114 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 488 ( 189 ~; 209 |; 58 &)
% ( 19 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 88 !; 14 ?)
% 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(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(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(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(f34,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f35,axiom,
( doDivides0(xl,xm)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
fof(f36,conjecture,
( ( xl != sz00
=> ? [X0] :
( X0 = sdtsldt0(xm,xl)
& ? [X1] :
( X1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtlseqdt0(X0,X1)
& ? [X2] :
( X2 = sdtmndt0(X1,X0)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& xn = sdtasdt0(xl,X2) ) ) ) )
=> doDivides0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f37,negated_conjecture,
~ ( ( xl != sz00
=> ? [X0] :
( X0 = sdtsldt0(xm,xl)
& ? [X1] :
( X1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtlseqdt0(X0,X1)
& ? [X2] :
( X2 = sdtmndt0(X1,X0)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& xn = sdtasdt0(xl,X2) ) ) ) )
=> doDivides0(xl,xn) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f41,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f42,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f43]) ).
fof(f49,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f55,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f68,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(f69,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f68]) ).
fof(f85,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f86,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f85]) ).
fof(f87,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(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(flattening,[],[f87]) ).
fof(f93,plain,
( ~ doDivides0(xl,xn)
& ( ? [X0] :
( X0 = sdtsldt0(xm,xl)
& ? [X1] :
( X1 = sdtsldt0(sdtpldt0(xm,xn),xl)
& sdtlseqdt0(X0,X1)
& ? [X2] :
( X2 = sdtmndt0(X1,X0)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& xn = sdtasdt0(xl,X2) ) ) )
| sz00 = xl ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f97,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,[],[f69]) ).
fof(f98,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,[],[f97]) ).
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,[],[f86]) ).
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,[],[f88]) ).
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,
( ~ doDivides0(xl,xn)
& ( ( sdtsldt0(xm,xl) = sK2
& sdtsldt0(sdtpldt0(xm,xn),xl) = sK3
& sdtlseqdt0(sK2,sK3)
& sK4 = sdtmndt0(sK3,sK2)
& sdtpldt0(sdtasdt0(xl,sK2),sdtasdt0(xl,sK4)) = sdtpldt0(sdtasdt0(xl,sK2),xn)
& xn = sdtasdt0(xl,sK4) )
| sz00 = xl ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f93]) ).
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,[],[f42]) ).
fof(f109,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f112,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f118,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f133,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f151,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sdtasdt0(X0,sK1(X0,X1)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f152,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| aNaturalNumber0(sK1(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f153,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f155,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f159,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f160,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f161,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f162,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f35]) ).
fof(f163,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f35]) ).
fof(f164,plain,
( xn = sdtasdt0(xl,sK4)
| sz00 = xl ),
inference(cnf_transformation,[],[f104]) ).
fof(f166,plain,
( sK4 = sdtmndt0(sK3,sK2)
| sz00 = xl ),
inference(cnf_transformation,[],[f104]) ).
fof(f167,plain,
( sdtlseqdt0(sK2,sK3)
| sz00 = xl ),
inference(cnf_transformation,[],[f104]) ).
fof(f168,plain,
( sdtsldt0(sdtpldt0(xm,xn),xl) = sK3
| sz00 = xl ),
inference(cnf_transformation,[],[f104]) ).
fof(f169,plain,
( sdtsldt0(xm,xl) = sK2
| sz00 = xl ),
inference(cnf_transformation,[],[f104]) ).
fof(f170,plain,
~ doDivides0(xl,xn),
inference(cnf_transformation,[],[f104]) ).
fof(f173,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f133]) ).
fof(f177,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f153]) ).
fof(f179,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f155]) ).
fof(f183,definition,
( spl5_1
<=> sz00 = xl ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f185,plain,
( sz00 = xl
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f187,definition,
( spl5_2
<=> xn = sdtasdt0(xl,sK4) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f189,plain,
( xn = sdtasdt0(xl,sK4)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f190,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f164,f187,f183]) ).
fof(f197,definition,
( spl5_4
<=> sK4 = sdtmndt0(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f199,plain,
( sK4 = sdtmndt0(sK3,sK2)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f200,plain,
( spl5_1
| spl5_4 ),
inference(avatar_split_clause,[],[f166,f197,f183]) ).
fof(f202,definition,
( spl5_5
<=> sdtlseqdt0(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f204,plain,
( sdtlseqdt0(sK2,sK3)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f205,plain,
( spl5_1
| spl5_5 ),
inference(avatar_split_clause,[],[f167,f202,f183]) ).
fof(f207,definition,
( spl5_6
<=> sdtsldt0(sdtpldt0(xm,xn),xl) = sK3 ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f209,plain,
( sdtsldt0(sdtpldt0(xm,xn),xl) = sK3
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f210,plain,
( spl5_1
| spl5_6 ),
inference(avatar_split_clause,[],[f168,f207,f183]) ).
fof(f212,definition,
( spl5_7
<=> sdtsldt0(xm,xl) = sK2 ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
fof(f214,plain,
( sdtsldt0(xm,xl) = sK2
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f215,plain,
( spl5_1
| spl5_7 ),
inference(avatar_split_clause,[],[f169,f212,f183]) ).
fof(f264,plain,
( aNaturalNumber0(sK1(xl,xm))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f152,f163]) ).
fof(f267,plain,
( aNaturalNumber0(sK1(xl,xm))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f264,f161]) ).
fof(f269,definition,
( spl5_8
<=> aNaturalNumber0(sdtpldt0(xm,xn)) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f270,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f271,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| spl5_8 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f277,plain,
aNaturalNumber0(sK1(xl,xm)),
inference(forward_subsumption_resolution,[],[f267,f160]) ).
fof(f278,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl5_8 ),
inference(resolution,[],[f271,f108]) ).
fof(f279,plain,
( ~ aNaturalNumber0(xn)
| spl5_8 ),
inference(forward_subsumption_resolution,[],[f278,f160]) ).
fof(f280,plain,
( $false
| spl5_8 ),
inference(forward_subsumption_resolution,[],[f279,f159]) ).
fof(f281,plain,
spl5_8,
inference(avatar_contradiction_clause,[],[f280]) ).
fof(f285,plain,
( aNaturalNumber0(sK4)
| ~ sdtlseqdt0(sK2,sK3)
| ~ aNaturalNumber0(sK2)
| ~ aNaturalNumber0(sK3)
| ~ spl5_4 ),
inference(superposition,[],[f173,f199]) ).
fof(f286,plain,
( aNaturalNumber0(sK4)
| ~ aNaturalNumber0(sK2)
| ~ aNaturalNumber0(sK3)
| ~ spl5_4
| ~ spl5_5 ),
inference(forward_subsumption_resolution,[],[f285,f204]) ).
fof(f288,definition,
( spl5_10
<=> aNaturalNumber0(sK3) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
fof(f292,definition,
( spl5_11
<=> aNaturalNumber0(sK2) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
fof(f296,definition,
( spl5_12
<=> aNaturalNumber0(sK4) ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
fof(f299,plain,
( ~ spl5_10
| ~ spl5_11
| spl5_12
| ~ spl5_4
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f286,f202,f197,f296,f292,f288]) ).
fof(f314,plain,
( doDivides0(sz00,xm)
| ~ spl5_1 ),
inference(superposition,[],[f163,f185]) ).
fof(f315,plain,
( ~ doDivides0(sz00,xn)
| ~ spl5_1 ),
inference(superposition,[],[f170,f185]) ).
fof(f412,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f177,f109]) ).
fof(f433,plain,
( doDivides0(xl,xn)
| ~ aNaturalNumber0(sK4)
| ~ aNaturalNumber0(xl)
| ~ spl5_2 ),
inference(superposition,[],[f412,f189]) ).
fof(f542,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f179,f163]) ).
fof(f543,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolution,[],[f179,f162]) ).
fof(f560,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f543,f161]) ).
fof(f561,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f542,f161]) ).
fof(f562,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f560,f270]) ).
fof(f563,plain,
( sz00 = xl
| aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(forward_subsumption_resolution,[],[f561,f160]) ).
fof(f564,plain,
( aNaturalNumber0(sK3)
| sz00 = xl
| ~ spl5_6
| ~ spl5_8 ),
inference(forward_demodulation,[],[f562,f209]) ).
fof(f565,plain,
( aNaturalNumber0(sK2)
| sz00 = xl
| ~ spl5_7 ),
inference(forward_demodulation,[],[f563,f214]) ).
fof(f567,plain,
( spl5_1
| spl5_11
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f565,f212,f292,f183]) ).
fof(f570,plain,
( doDivides0(sz00,sdtpldt0(xm,xn))
| ~ spl5_1 ),
inference(superposition,[],[f162,f185]) ).
fof(f579,plain,
( aNaturalNumber0(sK1(sz00,xm))
| ~ spl5_1 ),
inference(superposition,[],[f277,f185]) ).
fof(f588,plain,
( xm = sdtasdt0(sz00,sK1(sz00,xm))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ spl5_1 ),
inference(resolution,[],[f314,f151]) ).
fof(f591,plain,
( xm = sdtasdt0(sz00,sK1(sz00,xm))
| ~ aNaturalNumber0(xm)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f588,f105]) ).
fof(f593,plain,
( xm = sdtasdt0(sz00,sK1(sz00,xm))
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f591,f160]) ).
fof(f717,plain,
( sz00 = xm
| ~ aNaturalNumber0(sK1(sz00,xm))
| ~ spl5_1 ),
inference(superposition,[],[f118,f593]) ).
fof(f722,plain,
( sz00 = xm
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f717,f579]) ).
fof(f803,plain,
( doDivides0(sz00,sdtpldt0(sz00,xn))
| ~ spl5_1 ),
inference(superposition,[],[f570,f722]) ).
fof(f1065,plain,
( doDivides0(sz00,xn)
| ~ aNaturalNumber0(xn)
| ~ spl5_1 ),
inference(superposition,[],[f803,f112]) ).
fof(f1066,plain,
( ~ aNaturalNumber0(xn)
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f1065,f315]) ).
fof(f1070,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f1066,f159]) ).
fof(f1071,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f1070]) ).
fof(f1076,plain,
( ~ aNaturalNumber0(sK4)
| ~ aNaturalNumber0(xl)
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f433,f170]) ).
fof(f1095,plain,
( spl5_1
| spl5_10
| ~ spl5_6
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f564,f269,f207,f288,f183]) ).
fof(f1108,plain,
( ~ aNaturalNumber0(sK4)
| ~ spl5_2 ),
inference(forward_subsumption_resolution,[],[f1076,f161]) ).
fof(f1126,plain,
( ~ spl5_12
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f1108,f187,f296]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f190]) ).
cnf(s3,plain,
( spl5_1
| spl5_4 ),
inference(sat_conversion,[],[f200]) ).
cnf(s4,plain,
( spl5_1
| spl5_5 ),
inference(sat_conversion,[],[f205]) ).
cnf(s5,plain,
( spl5_1
| spl5_6 ),
inference(sat_conversion,[],[f210]) ).
cnf(s6,plain,
( spl5_1
| spl5_7 ),
inference(sat_conversion,[],[f215]) ).
cnf(s8,plain,
spl5_8,
inference(sat_conversion,[],[f281]) ).
cnf(s9,plain,
( ~ spl5_4
| ~ spl5_5
| ~ spl5_10
| ~ spl5_11
| spl5_12 ),
inference(sat_conversion,[],[f299]) ).
cnf(s29,plain,
( spl5_1
| ~ spl5_7
| spl5_11 ),
inference(sat_conversion,[],[f567]) ).
cnf(s40,plain,
~ spl5_1,
inference(sat_conversion,[],[f1071]) ).
cnf(s45,plain,
( spl5_1
| ~ spl5_6
| ~ spl5_8
| spl5_10 ),
inference(sat_conversion,[],[f1095]) ).
cnf(s52,plain,
( ~ spl5_2
| ~ spl5_12 ),
inference(sat_conversion,[],[f1126]) ).
cnf(s56,plain,
( ~ spl5_7
| spl5_11 ),
inference(rat,[],[s29,s40]) ).
cnf(s65,plain,
spl5_7,
inference(rat,[],[s6,s40]) ).
cnf(s67,plain,
spl5_11,
inference(rat,[],[s56,s65]) ).
cnf(s68,plain,
spl5_6,
inference(rat,[],[s5,s40]) ).
cnf(s70,plain,
spl5_10,
inference(rat,[],[s45,s8,s40,s68]) ).
cnf(s71,plain,
spl5_5,
inference(rat,[],[s4,s40]) ).
cnf(s73,plain,
spl5_4,
inference(rat,[],[s3,s40]) ).
cnf(s75,plain,
spl5_12,
inference(rat,[],[s9,s71,s67,s70,s73]) ).
cnf(s76,plain,
~ spl5_2,
inference(rat,[],[s52,s75]) ).
cnf(s78,plain,
$false,
inference(rat,[],[s1,s76,s40]) ).
fof(f1139,plain,
$false,
inference(avatar_sat_refutation,[],[s78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM476+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sun Sep 27 20:05:20 UTC 2026
% 0.03/0.32 % CPUTime :
% 0.03/0.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 0.76/0.80 % (2700364)Detected formulas, will run a generic FOF schedule.
% 0.76/0.80 % (2700374)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2790676589:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.76/0.80 % (2700372)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=848214483:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.76/0.80 % (2700373)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3626379003:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.76/0.80 % (2700369)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=4121829664:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.76/0.80 % (2700370)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=1002388066:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.76/0.80 % (2700371)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=2852127073:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.76/0.80 % (2700374)First to succeed.
% 0.76/0.80 % (2700374)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2700364"
% 0.76/0.80 % (2700375)dis-21_1_sil=8000:lcm=predicate:random_seed=405595827: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)
% 0.76/0.80 % (2700372)Instruction limit reached!
% 0.76/0.80 % (2700372)------------------------------
% 0.76/0.80 % (2700372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.76/0.80 % (2700372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.80 % (2700372)CaDiCaL version: 2.1.3
% 0.76/0.80 % (2700372)Termination reason: Instruction limit
% 0.76/0.80 % (2700372)Termination phase: Saturation
% 0.76/0.80 % (2700372)Time elapsed: 0.025 s
% 0.76/0.80 % (2700372)Peak memory usage: 88 MB
% 0.76/0.80 % (2700372)Instructions burned: 113 (million)
% 0.76/0.80 % (2700373)Also succeeded, but the first one will report.
% 0.76/0.80 % (2700375)Instruction limit reached!
% 0.76/0.80 % (2700375)------------------------------
% 0.76/0.80 % (2700375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.76/0.80 % (2700375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.80 % (2700375)CaDiCaL version: 2.1.3
% 0.76/0.80 % (2700375)Termination reason: Instruction limit
% 0.76/0.80 % (2700375)Termination phase: Saturation
% 0.76/0.80 % (2700375)Time elapsed: 0.041 s
% 0.76/0.80 % (2700375)Peak memory usage: 89 MB
% 0.76/0.80 % (2700375)Instructions burned: 129 (million)
% 0.76/0.80 % (2700383)lrs+10_1_sil=8000:sp=occurrence:random_seed=2863846899:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 0.76/0.80 % (2700383)Also succeeded, but the first one will report.
% 0.76/0.80 % (2700384)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4017553236:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 0.76/0.80 % (2700374)Refutation found. Thanks to Tanya!
% 0.76/0.80 % SZS status Theorem for theBenchmark
% 0.76/0.80 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.90 % (2700374)------------------------------
% 0.07/0.90 % (2700374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.07/0.90 % (2700374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.90 % (2700374)CaDiCaL version: 2.1.3
% 0.07/0.90 % (2700374)Termination reason: Refutation
% 0.07/0.90 % (2700374)Time elapsed: 0.012 s
% 0.07/0.90 % (2700374)Peak memory usage: 90 MB
% 0.07/0.90 % (2700374)Instructions burned: 33 (million)
% 0.07/0.90 % (2700374)------------------------------
% 0.07/0.90 % (2700374)------------------------------
% 0.07/0.90 % (2700364)Success in time 0.269 s
% 0.07/0.90 % Vampire exiting
%------------------------------------------------------------------------------