%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM471+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 12:15:20 PM UTC 2026
% Result : Theorem 2.51s 1.32s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 21
% Syntax : Number of formulae : 147 ( 41 unt; 7 def)
% Number of atoms : 439 ( 108 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 492 ( 200 ~; 213 |; 59 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 82 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
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(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X0,X1) = sdtasdt0(X0,X2)
| sdtasdt0(X1,X0) = sdtasdt0(X2,X0) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X0 != sz00
& X1 != X2
& sdtlseqdt0(X1,X2) )
=> ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(f34,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f35,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X0) )
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
fof(f36,axiom,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1347) ).
fof(f37,axiom,
( aNaturalNumber0(xp)
& xm = sdtasdt0(xl,xp)
& xp = sdtsldt0(xm,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
fof(f38,axiom,
( aNaturalNumber0(xq)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& xq = sdtsldt0(sdtpldt0(xm,xn),xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
fof(f39,conjecture,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xq )
| sdtlseqdt0(xp,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xq )
| sdtlseqdt0(xp,xq) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f41,plain,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X1) )
& doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(rectify,[],[f35]) ).
fof(f43,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xq != sdtpldt0(xp,X0) )
& ~ sdtlseqdt0(xp,xq) ),
inference(ennf_transformation,[],[f40]) ).
fof(f58,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f59,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f58]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f68]) ).
fof(f74,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f75,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f74]) ).
fof(f77,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f82,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f83,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f82]) ).
fof(f86,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f87,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f86]) ).
fof(f89,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f90,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
( aNaturalNumber0(sK0)
& xm = sdtasdt0(xl,sK0)
& doDivides0(xl,xm)
& aNaturalNumber0(sK1)
& sdtpldt0(xm,xn) = sdtasdt0(xl,sK1)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f41]) ).
fof(f97,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f90]) ).
fof(f98,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X0,X3) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK3(X0,X1))
& sdtpldt0(X0,sK3(X0,X1)) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1))],[f98]) ).
fof(f100,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f101,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f102,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f104,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sK1),
inference(cnf_transformation,[],[f91]) ).
fof(f105,plain,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f91]) ).
fof(f109,plain,
sz00 != xl,
inference(cnf_transformation,[],[f36]) ).
fof(f110,plain,
xp = sdtsldt0(xm,xl),
inference(cnf_transformation,[],[f37]) ).
fof(f111,plain,
xm = sdtasdt0(xl,xp),
inference(cnf_transformation,[],[f37]) ).
fof(f112,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f37]) ).
fof(f113,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(cnf_transformation,[],[f38]) ).
fof(f114,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(cnf_transformation,[],[f38]) ).
fof(f115,plain,
aNaturalNumber0(xq),
inference(cnf_transformation,[],[f38]) ).
fof(f116,plain,
~ sdtlseqdt0(xp,xq),
inference(cnf_transformation,[],[f43]) ).
fof(f117,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| xq != sdtpldt0(xp,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f127,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f136,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f142,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f146,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f147,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f155,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f158,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f162,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f163,definition,
~ sP4(sz00),
introduced(definition,[new_symbols(definition,[sP4])],[inequality_splitting_name_introduction]) ).
fof(f164,plain,
sP4(xl),
inference(inequality_splitting,[],[f109,f163]) ).
fof(f165,definition,
~ sP5(xq),
introduced(definition,[new_symbols(definition,[sP5])],[inequality_splitting_name_introduction]) ).
fof(f166,plain,
! [X0] :
( sP5(sdtpldt0(xp,X0))
| ~ aNaturalNumber0(X0) ),
inference(inequality_splitting,[],[f117,f165]) ).
fof(f178,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f162]) ).
fof(f180,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sdtsldt0(sdtpldt0(xm,xn),xl)),
inference(forward_demodulation,[],[f114,f113]) ).
fof(f181,plain,
aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl)),
inference(forward_demodulation,[],[f115,f113]) ).
fof(f182,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(forward_demodulation,[],[f111,f110]) ).
fof(f183,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(forward_demodulation,[],[f112,f110]) ).
fof(f184,plain,
sdtasdt0(xl,sK1) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xl,sK1),xl)),
inference(forward_demodulation,[],[f180,f104]) ).
fof(f185,plain,
aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK1),xl)),
inference(forward_demodulation,[],[f181,f104]) ).
fof(f186,plain,
( sdtlseqdt0(xq,xp)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f116,f155]) ).
fof(f187,plain,
( sdtlseqdt0(xq,sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(forward_demodulation,[],[f186,f110]) ).
fof(f188,plain,
( sdtlseqdt0(sdtsldt0(sdtpldt0(xm,xn),xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(forward_demodulation,[],[f187,f113]) ).
fof(f189,plain,
( sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK1),xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(forward_demodulation,[],[f188,f104]) ).
fof(f190,plain,
( ~ aNaturalNumber0(sdtsldt0(sdtpldt0(xm,xn),xl))
| sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK1),xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xp) ),
inference(forward_demodulation,[],[f189,f113]) ).
fof(f191,plain,
( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK1),xl))
| sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK1),xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xp) ),
inference(forward_demodulation,[],[f190,f104]) ).
fof(f192,plain,
( sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK1),xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f191,f185]) ).
fof(f193,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK1),xl),sdtsldt0(xm,xl)) ),
inference(forward_demodulation,[],[f192,f110]) ).
fof(f194,plain,
sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK1),xl),sdtsldt0(xm,xl)),
inference(forward_subsumption_resolution,[],[f193,f183]) ).
fof(f197,plain,
( sP5(xp)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f166,f146]) ).
fof(f202,plain,
( sP5(xp)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f197,f147]) ).
fof(f206,plain,
( sP5(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xp) ),
inference(forward_demodulation,[],[f202,f110]) ).
fof(f210,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| sP5(sdtsldt0(xm,xl)) ),
inference(forward_demodulation,[],[f206,f110]) ).
fof(f214,plain,
sP5(sdtsldt0(xm,xl)),
inference(forward_subsumption_resolution,[],[f210,f183]) ).
fof(f241,definition,
( spl9_1
<=> aNaturalNumber0(sdtasdt0(xl,sK1)) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f242,plain,
( aNaturalNumber0(sdtasdt0(xl,sK1))
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f243,plain,
( ~ aNaturalNumber0(sdtasdt0(xl,sK1))
| spl9_1 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f249,definition,
( spl9_3
<=> sz00 = xl ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f250,plain,
( sz00 != xl
| spl9_3 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f251,plain,
( sz00 = xl
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f266,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sK1)
| spl9_1 ),
inference(resolution,[],[f243,f127]) ).
fof(f267,plain,
( ~ aNaturalNumber0(sK1)
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f266,f102]) ).
fof(f268,plain,
( $false
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f267,f105]) ).
fof(f269,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f268]) ).
fof(f288,definition,
( spl9_7
<=> sdtsldt0(xm,xl) = sK1 ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
fof(f289,plain,
( sdtsldt0(xm,xl) != sK1
| spl9_7 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f290,plain,
( sdtsldt0(xm,xl) = sK1
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f429,plain,
( sP4(sz00)
| ~ spl9_3 ),
inference(superposition,[],[f164,f251]) ).
fof(f439,plain,
( $false
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f429,f163]) ).
fof(f440,plain,
~ spl9_3,
inference(avatar_contradiction_clause,[],[f439]) ).
fof(f491,plain,
( sdtlseqdt0(xm,sdtasdt0(xl,sK1))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,sK1)) ),
inference(superposition,[],[f178,f104]) ).
fof(f492,plain,
( sdtlseqdt0(xm,sdtasdt0(xl,sK1))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,sK1)) ),
inference(forward_subsumption_resolution,[],[f491,f100]) ).
fof(f509,plain,
( sdtlseqdt0(xm,sdtasdt0(xl,sK1))
| ~ aNaturalNumber0(sdtasdt0(xl,sK1)) ),
inference(forward_subsumption_resolution,[],[f492,f101]) ).
fof(f526,plain,
( sdtlseqdt0(xm,sdtasdt0(xl,sK1))
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f509,f242]) ).
fof(f545,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,sK1),xm)
| xm = sdtasdt0(xl,sK1)
| ~ aNaturalNumber0(sdtasdt0(xl,sK1))
| ~ aNaturalNumber0(xm)
| ~ spl9_1 ),
inference(resolution,[],[f526,f158]) ).
fof(f548,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,sK1),xm)
| xm = sdtasdt0(xl,sK1)
| ~ aNaturalNumber0(xm)
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f545,f242]) ).
fof(f550,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,sK1),xm)
| xm = sdtasdt0(xl,sK1)
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f548,f101]) ).
fof(f564,plain,
~ sP5(sdtsldt0(sdtpldt0(xm,xn),xl)),
inference(superposition,[],[f165,f113]) ).
fof(f565,plain,
~ sP5(sdtsldt0(sdtasdt0(xl,sK1),xl)),
inference(forward_demodulation,[],[f564,f104]) ).
fof(f656,plain,
! [X0] :
( sdtlseqdt0(sdtasdt0(xl,sK1),sdtasdt0(xl,X0))
| sz00 = xl
| sdtsldt0(sdtasdt0(xl,sK1),xl) = X0
| ~ sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK1),xl),X0)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK1),xl))
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f136,f184]) ).
fof(f663,plain,
! [X0] :
( sdtasdt0(xl,X0) != sdtasdt0(xl,sK1)
| sdtsldt0(sdtasdt0(xl,sK1),xl) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK1),xl))
| sz00 = xl
| ~ aNaturalNumber0(xl) ),
inference(superposition,[],[f142,f184]) ).
fof(f667,plain,
! [X0] :
( sdtasdt0(xl,X0) != sdtasdt0(xl,sK1)
| sdtsldt0(sdtasdt0(xl,sK1),xl) = X0
| ~ aNaturalNumber0(X0)
| sz00 = xl
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f663,f185]) ).
fof(f674,plain,
( ! [X0] :
( sdtlseqdt0(sdtasdt0(xl,sK1),sdtasdt0(xl,X0))
| sdtsldt0(sdtasdt0(xl,sK1),xl) = X0
| ~ sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK1),xl),X0)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK1),xl))
| ~ aNaturalNumber0(X0) )
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f656,f250]) ).
fof(f686,plain,
( ! [X0] :
( sdtasdt0(xl,X0) != sdtasdt0(xl,sK1)
| sdtsldt0(sdtasdt0(xl,sK1),xl) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl) )
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f667,f250]) ).
fof(f693,plain,
( ! [X0] :
( sdtlseqdt0(sdtasdt0(xl,sK1),sdtasdt0(xl,X0))
| sdtsldt0(sdtasdt0(xl,sK1),xl) = X0
| ~ sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK1),xl),X0)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK1),xl))
| ~ aNaturalNumber0(X0) )
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f674,f102]) ).
fof(f705,plain,
( ! [X0] :
( sdtasdt0(xl,X0) != sdtasdt0(xl,sK1)
| sdtsldt0(sdtasdt0(xl,sK1),xl) = X0
| ~ aNaturalNumber0(X0) )
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f686,f102]) ).
fof(f719,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK1),xl),X0)
| sdtsldt0(sdtasdt0(xl,sK1),xl) = X0
| sdtlseqdt0(sdtasdt0(xl,sK1),sdtasdt0(xl,X0))
| ~ aNaturalNumber0(X0) )
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f693,f185]) ).
fof(f829,plain,
( sK1 = sdtsldt0(sdtasdt0(xl,sK1),xl)
| ~ aNaturalNumber0(sK1)
| spl9_3 ),
inference(equality_resolution,[],[f705]) ).
fof(f832,plain,
( sK1 = sdtsldt0(sdtasdt0(xl,sK1),xl)
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f829,f105]) ).
fof(f871,plain,
( sdtsldt0(xm,xl) = sdtsldt0(sdtasdt0(xl,sK1),xl)
| sdtlseqdt0(sdtasdt0(xl,sK1),sdtasdt0(xl,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| spl9_3 ),
inference(resolution,[],[f719,f194]) ).
fof(f877,plain,
( sdtsldt0(xm,xl) = sdtsldt0(sdtasdt0(xl,sK1),xl)
| sdtlseqdt0(sdtasdt0(xl,sK1),sdtasdt0(xl,sdtsldt0(xm,xl)))
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f871,f183]) ).
fof(f881,plain,
( sdtsldt0(xm,xl) = sK1
| sdtlseqdt0(sdtasdt0(xl,sK1),sdtasdt0(xl,sdtsldt0(xm,xl)))
| spl9_3 ),
inference(forward_demodulation,[],[f877,f832]) ).
fof(f896,definition,
( spl9_39
<=> xm = sdtasdt0(xl,sK1) ),
introduced(definition,[new_symbols(definition,[spl9_39])],[avatar_definition]) ).
fof(f898,plain,
( xm = sdtasdt0(xl,sK1)
| ~ spl9_39 ),
inference(avatar_component_clause,[],[f896]) ).
fof(f900,definition,
( spl9_40
<=> sdtlseqdt0(sdtasdt0(xl,sK1),xm) ),
introduced(definition,[new_symbols(definition,[spl9_40])],[avatar_definition]) ).
fof(f902,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,sK1),xm)
| spl9_40 ),
inference(avatar_component_clause,[],[f900]) ).
fof(f903,plain,
( spl9_39
| ~ spl9_40
| ~ spl9_1 ),
inference(avatar_split_clause,[],[f550,f241,f900,f896]) ).
fof(f1233,plain,
( ~ sP5(sdtsldt0(xm,xl))
| ~ spl9_39 ),
inference(superposition,[],[f565,f898]) ).
fof(f1286,plain,
( $false
| ~ spl9_39 ),
inference(forward_subsumption_resolution,[],[f1233,f214]) ).
fof(f1287,plain,
~ spl9_39,
inference(avatar_contradiction_clause,[],[f1286]) ).
fof(f1352,plain,
( sdtlseqdt0(sdtasdt0(xl,sK1),xm)
| sdtsldt0(xm,xl) = sK1
| spl9_3 ),
inference(forward_demodulation,[],[f881,f182]) ).
fof(f1388,plain,
( sdtsldt0(xm,xl) = sK1
| spl9_3
| spl9_40 ),
inference(forward_subsumption_resolution,[],[f1352,f902]) ).
fof(f1390,plain,
( $false
| spl9_3
| spl9_7
| spl9_40 ),
inference(forward_subsumption_resolution,[],[f1388,f289]) ).
fof(f1391,plain,
( spl9_3
| spl9_7
| spl9_40 ),
inference(avatar_contradiction_clause,[],[f1390]) ).
fof(f1454,plain,
( ~ sP5(sdtsldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),xl))
| ~ spl9_7 ),
inference(superposition,[],[f565,f290]) ).
fof(f1478,plain,
( ~ sP5(sdtsldt0(xm,xl))
| ~ spl9_7 ),
inference(forward_demodulation,[],[f1454,f182]) ).
fof(f1492,plain,
( $false
| ~ spl9_7 ),
inference(forward_subsumption_resolution,[],[f1478,f214]) ).
fof(f1493,plain,
~ spl9_7,
inference(avatar_contradiction_clause,[],[f1492]) ).
cnf(s3,plain,
spl9_1,
inference(sat_conversion,[],[f269]) ).
cnf(s21,plain,
~ spl9_3,
inference(sat_conversion,[],[f440]) ).
cnf(s37,plain,
( ~ spl9_1
| spl9_39
| ~ spl9_40 ),
inference(sat_conversion,[],[f903]) ).
cnf(s57,plain,
~ spl9_39,
inference(sat_conversion,[],[f1287]) ).
cnf(s67,plain,
( spl9_3
| spl9_7
| spl9_40 ),
inference(sat_conversion,[],[f1391]) ).
cnf(s72,plain,
~ spl9_7,
inference(sat_conversion,[],[f1493]) ).
cnf(s75,plain,
( spl9_3
| spl9_40 ),
inference(rat,[],[s67,s72]) ).
cnf(s76,plain,
( ~ spl9_1
| ~ spl9_40 ),
inference(rat,[],[s37,s57]) ).
cnf(s77,plain,
spl9_40,
inference(rat,[],[s75,s21]) ).
cnf(s78,plain,
~ spl9_1,
inference(rat,[],[s76,s77]) ).
cnf(s87,plain,
$false,
inference(rat,[],[s3,s78]) ).
fof(f1504,plain,
$false,
inference(avatar_sat_refutation,[],[s87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM471+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:04:31 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.51/1.32 % (1128733)Detected formulas, will run a generic FOF schedule.
% 2.51/1.32 % (1128744)dis-21_1_sil=8000:lcm=predicate:random_seed=3702608709: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)
% 2.51/1.32 % (1128738)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=1739968363:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.51/1.32 % (1128742)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=356918672:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.51/1.32 % (1128741)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=283534970:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.51/1.32 % (1128740)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=3487463534:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.51/1.32 % (1128739)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=695130767:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.51/1.32 % (1128743)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2253299228:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.51/1.32 % (1128744)Instruction limit reached!
% 2.51/1.32 % (1128744)------------------------------
% 2.51/1.32 % (1128744)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.32 % (1128744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.32 % (1128744)CaDiCaL version: 2.1.3
% 2.51/1.32 % (1128744)Termination reason: Instruction limit
% 2.51/1.32 % (1128744)Termination phase: Saturation
% 2.51/1.32 % (1128744)Time elapsed: 0.043 s
% 2.51/1.32 % (1128744)Peak memory usage: 90 MB
% 2.51/1.32 % (1128744)Instructions burned: 132 (million)
% 2.51/1.32 % (1128741)First to succeed.
% 2.51/1.32 % (1128741)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1128733"
% 2.51/1.32 % (1128742)Instruction limit reached!
% 2.51/1.32 % (1128742)------------------------------
% 2.51/1.32 % (1128742)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.32 % (1128742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.32 % (1128742)CaDiCaL version: 2.1.3
% 2.51/1.32 % (1128742)Termination reason: Instruction limit
% 2.51/1.32 % (1128742)Termination phase: Saturation
% 2.51/1.32 % (1128742)Time elapsed: 0.070 s
% 2.51/1.32 % (1128742)Peak memory usage: 88 MB
% 2.51/1.32 % (1128742)Instructions burned: 121 (million)
% 2.51/1.32 % (1128743)Instruction limit reached!
% 2.51/1.32 % (1128743)------------------------------
% 2.51/1.32 % (1128743)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.32 % (1128743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.32 % (1128743)CaDiCaL version: 2.1.3
% 2.51/1.32 % (1128743)Termination reason: Instruction limit
% 2.51/1.32 % (1128743)Termination phase: Saturation
% 2.51/1.32 % (1128743)Time elapsed: 0.090 s
% 2.51/1.32 % (1128743)Peak memory usage: 90 MB
% 2.51/1.32 % (1128743)Instructions burned: 141 (million)
% 2.51/1.32 % (1128752)lrs+10_1_sil=8000:sp=occurrence:random_seed=3036614326:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.51/1.32 % (1128752)Also succeeded, but the first one will report.
% 2.51/1.32 % (1128753)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3687323576:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.51/1.32 % (1128754)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4133610123:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.51/1.32 % (1128741)Refutation found. Thanks to Tanya!
% 2.51/1.32 % SZS status Theorem for theBenchmark
% 2.51/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.41 % (1128741)------------------------------
% 3.77/1.41 % (1128741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.41 % (1128741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.41 % (1128741)CaDiCaL version: 2.1.3
% 3.77/1.41 % (1128741)Termination reason: Refutation
% 3.77/1.41 % (1128741)Time elapsed: 0.030 s
% 3.77/1.41 % (1128741)Peak memory usage: 89 MB
% 3.77/1.41 % (1128741)Instructions burned: 47 (million)
% 3.77/1.41 % (1128741)------------------------------
% 3.77/1.41 % (1128741)------------------------------
% 3.77/1.41 % (1128733)Success in time 0.468 s
% 3.77/1.41 % Vampire exiting
%------------------------------------------------------------------------------