%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM498+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:27 PM UTC 2026
% Result : Theorem 2.91s 1.05s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 93 ( 17 unt; 0 def)
% Number of atoms : 350 ( 158 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 404 ( 147 ~; 149 |; 93 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 93 ( 72 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X0 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( xp != sz00
& xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f44,axiom,
( xn != xp
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = xp )
& sdtlseqdt0(xn,xp)
& xm != xp
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xp )
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(f45,axiom,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f46,conjecture,
( ( xk = sz00
| xk = sz10 )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn)
| ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xp,X0) )
| doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ( ( xk = sz00
| xk = sz10 )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn)
| ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xp,X0) )
| doDivides0(xp,xm) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f49,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(rectify,[],[f41]) ).
fof(f50,plain,
( xn != xp
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xn,X0) = xp )
& sdtlseqdt0(xn,xp)
& xm != xp
& ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtpldt0(xm,X1) )
& sdtlseqdt0(xm,xp) ),
inference(rectify,[],[f44]) ).
fof(f51,plain,
~ ( ( xk = sz00
| xk = sz10 )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn)
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xp,X1) )
| doDivides0(xp,xm) ) ),
inference(rectify,[],[f47]) ).
fof(f56,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f57,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(flattening,[],[f56]) ).
fof(f60,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xp,X0) )
& ~ doDivides0(xp,xn)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xp,X1) )
& ~ doDivides0(xp,xm)
& ( xk = sz00
| xk = sz10 ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f61,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xp,X0) )
& ~ doDivides0(xp,xn)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xp,X1) )
& ~ doDivides0(xp,xm)
& ( xk = sz00
| xk = sz10 ) ),
inference(flattening,[],[f60]) ).
fof(f64,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f80,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f81,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f80]) ).
fof(f84,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f87,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f88,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f90,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f89]) ).
fof(f99,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f100,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f99]) ).
fof(f135,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& aNaturalNumber0(sK6)
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK6)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6)],[f57]) ).
fof(f136,plain,
( xn != xp
& aNaturalNumber0(sK7)
& xp = sdtpldt0(xn,sK7)
& sdtlseqdt0(xn,xp)
& xm != xp
& aNaturalNumber0(sK8)
& xp = sdtpldt0(xm,sK8)
& sdtlseqdt0(xm,xp) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f50]) ).
fof(f137,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,[],[f100]) ).
fof(f138,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,[],[f137]) ).
fof(f139,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK9(X0,X1))
& sdtasdt0(X0,sK9(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X1))],[f138]) ).
fof(f150,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f151,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f152,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f169,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f135]) ).
fof(f173,plain,
! [X0] :
( ~ doDivides0(X0,xp)
| xp = X0
| ~ aNaturalNumber0(X0)
| sz10 = X0 ),
inference(cnf_transformation,[],[f135]) ).
fof(f188,plain,
xn != xp,
inference(cnf_transformation,[],[f136]) ).
fof(f190,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f191,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f192,plain,
( sz10 = xk
| sz00 = xk ),
inference(cnf_transformation,[],[f61]) ).
fof(f193,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f61]) ).
fof(f194,plain,
! [X1] :
( xm != sdtasdt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f196,plain,
! [X0] :
( xn != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f197,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f200,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f201,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f216,plain,
! [X0,X1] :
( sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f219,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f220,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f222,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f223,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f230,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f139]) ).
fof(f263,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f230]) ).
fof(f289,plain,
! [X0] :
( sdtasdt0(xk,X0) = X0
| ~ aNaturalNumber0(X0)
| sz00 = xk ),
inference(superposition,[],[f200,f192]) ).
fof(f290,plain,
! [X0] :
( sdtasdt0(X0,xk) = X0
| ~ aNaturalNumber0(X0)
| sz00 = xk ),
inference(superposition,[],[f201,f192]) ).
fof(f298,plain,
( xp = sdtasdt0(xn,xm)
| ~ aNaturalNumber0(xp)
| sz00 = xk ),
inference(superposition,[],[f190,f290]) ).
fof(f301,plain,
( xp = sdtasdt0(xn,xm)
| sz00 = xk ),
inference(forward_subsumption_resolution,[],[f298,f150]) ).
fof(f313,plain,
( sz00 != xn
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f196,f220]) ).
fof(f314,plain,
( sz00 != xm
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f194,f220]) ).
fof(f315,plain,
( sz00 != xm
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f314,f197]) ).
fof(f316,plain,
( sz00 != xn
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f313,f197]) ).
fof(f317,plain,
sz00 != xm,
inference(forward_subsumption_resolution,[],[f315,f150]) ).
fof(f318,plain,
sz00 != xn,
inference(forward_subsumption_resolution,[],[f316,f150]) ).
fof(f478,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xk,xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f190,f222]) ).
fof(f511,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xk,xp)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f478,f191]) ).
fof(f523,plain,
sdtasdt0(xn,xm) = sdtasdt0(xk,xp),
inference(forward_subsumption_resolution,[],[f511,f150]) ).
fof(f684,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f263,f223]) ).
fof(f704,plain,
( doDivides0(xn,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| sz00 = xk ),
inference(superposition,[],[f684,f301]) ).
fof(f721,plain,
( doDivides0(xn,xp)
| ~ aNaturalNumber0(xn)
| sz00 = xk ),
inference(forward_subsumption_resolution,[],[f704,f151]) ).
fof(f729,plain,
( doDivides0(xn,xp)
| sz00 = xk ),
inference(forward_subsumption_resolution,[],[f721,f152]) ).
fof(f731,plain,
( sz00 = xk
| xn = xp
| ~ aNaturalNumber0(xn)
| sz10 = xn ),
inference(resolution,[],[f729,f173]) ).
fof(f732,plain,
( sz00 = xk
| ~ aNaturalNumber0(xn)
| sz10 = xn ),
inference(forward_subsumption_resolution,[],[f731,f188]) ).
fof(f733,plain,
( sz10 = xn
| sz00 = xk ),
inference(forward_subsumption_resolution,[],[f732,f152]) ).
fof(f737,plain,
( xn = xk
| sz00 = xk
| sz00 = xk ),
inference(superposition,[],[f192,f733]) ).
fof(f743,plain,
( xn = xk
| sz00 = xk ),
inference(duplicate_literal_removal,[],[f737]) ).
fof(f809,plain,
( doDivides0(xp,sdtasdt0(xk,xm))
| sz00 = xk ),
inference(superposition,[],[f169,f743]) ).
fof(f920,plain,
( sz00 != sdtasdt0(xk,xp)
| sz00 = xm
| sz00 = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f216,f523]) ).
fof(f939,plain,
( sz00 != sdtasdt0(xk,xp)
| sz00 = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f920,f317]) ).
fof(f944,plain,
( sz00 != sdtasdt0(xk,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f939,f318]) ).
fof(f947,plain,
( sz00 != sdtasdt0(xk,xp)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f944,f152]) ).
fof(f950,plain,
sz00 != sdtasdt0(xk,xp),
inference(forward_subsumption_resolution,[],[f947,f151]) ).
fof(f1404,plain,
( doDivides0(xp,xm)
| sz00 = xk
| ~ aNaturalNumber0(xm)
| sz00 = xk ),
inference(superposition,[],[f809,f289]) ).
fof(f1405,plain,
( doDivides0(xp,xm)
| sz00 = xk
| ~ aNaturalNumber0(xm) ),
inference(duplicate_literal_removal,[],[f1404]) ).
fof(f1407,plain,
( sz00 = xk
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f1405,f193]) ).
fof(f1412,plain,
sz00 = xk,
inference(forward_subsumption_resolution,[],[f1407,f151]) ).
fof(f1420,plain,
! [X0] :
( xk = sdtasdt0(xk,X0)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f219,f1412]) ).
fof(f2016,plain,
( sz00 != xk
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f950,f1420]) ).
fof(f2075,plain,
~ aNaturalNumber0(xp),
inference(forward_subsumption_resolution,[],[f2016,f1412]) ).
fof(f2082,plain,
$false,
inference(forward_subsumption_resolution,[],[f2075,f150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM498+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 20:11:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.91/1.05 % (521573)Detected formulas, will run a generic FOF schedule.
% 2.91/1.05 % (521579)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=1371709172:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.91/1.05 % (521578)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=2333802490:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.91/1.05 % (521581)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=801763636:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.91/1.05 % (521580)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=786474955:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.91/1.05 % (521583)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2765120359:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.91/1.05 % (521582)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3539758607:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.91/1.05 % (521584)dis-21_1_sil=8000:lcm=predicate:random_seed=1249609116: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)
% 2.91/1.05 % (521582)First to succeed.
% 2.91/1.05 % (521582)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-521573"
% 2.91/1.05 % (521583)Also succeeded, but the first one will report.
% 2.91/1.05 % (521581)Instruction limit reached!
% 2.91/1.05 % (521581)------------------------------
% 2.91/1.05 % (521581)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.05 % (521581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.05 % (521581)CaDiCaL version: 2.1.3
% 2.91/1.05 % (521581)Termination reason: Instruction limit
% 2.91/1.05 % (521581)Termination phase: Saturation
% 2.91/1.05 % (521581)Time elapsed: 0.062 s
% 2.91/1.05 % (521581)Peak memory usage: 89 MB
% 2.91/1.05 % (521581)Instructions burned: 110 (million)
% 2.91/1.05 % (521584)Instruction limit reached!
% 2.91/1.05 % (521584)------------------------------
% 2.91/1.05 % (521584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.05 % (521584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.05 % (521584)CaDiCaL version: 2.1.3
% 2.91/1.05 % (521584)Termination reason: Instruction limit
% 2.91/1.05 % (521584)Termination phase: Saturation
% 2.91/1.05 % (521584)Time elapsed: 0.078 s
% 2.91/1.05 % (521584)Peak memory usage: 90 MB
% 2.91/1.05 % (521584)Instructions burned: 131 (million)
% 2.91/1.05 % (521593)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1390185930:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.91/1.05 % (521592)lrs+10_1_sil=8000:sp=occurrence:random_seed=1816482853:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.91/1.05 % (521582)Refutation found. Thanks to Tanya!
% 2.91/1.05 % SZS status Theorem for theBenchmark
% 2.91/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.25 % (521582)------------------------------
% 3.57/1.25 % (521582)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.25 % (521582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.25 % (521582)CaDiCaL version: 2.1.3
% 3.57/1.25 % (521582)Termination reason: Refutation
% 3.57/1.25 % (521582)Time elapsed: 0.034 s
% 3.57/1.25 % (521582)Peak memory usage: 88 MB
% 3.57/1.25 % (521582)Instructions burned: 57 (million)
% 3.57/1.25 % (521582)------------------------------
% 3.57/1.25 % (521582)------------------------------
% 3.57/1.25 % (521573)Success in time 0.453 s
% 3.57/1.25 % Vampire exiting
%------------------------------------------------------------------------------