%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM479+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 : n010.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 12:15:22 PM UTC 2026
% Result : Theorem 4.08s 1.58s
% Output : Refutation 5.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 13 unt; 0 def)
% Number of atoms : 296 ( 65 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 422 ( 199 ~; 181 |; 28 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 99 ( 94 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
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(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X0,X1)
& doDivides0(X1,X2) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivTrans) ).
fof(f36,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524) ).
fof(f37,axiom,
( xl != sz00
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524_04) ).
fof(f38,axiom,
aNaturalNumber0(xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1553) ).
fof(f39,conjecture,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f41,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(flattening,[],[f40]) ).
fof(f54,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f55,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f57,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f59,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f61,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f63,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f62]) ).
fof(f64,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(f65,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,[],[f64]) ).
fof(f94,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,[],[f57]) ).
fof(f95,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,[],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK0(X0,X1))
& sdtasdt0(X0,sK0(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f95]) ).
fof(f97,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,[],[f65]) ).
fof(f98,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,[],[f97]) ).
fof(f102,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f36]) ).
fof(f103,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f36]) ).
fof(f104,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f37]) ).
fof(f105,plain,
sz00 != xl,
inference(cnf_transformation,[],[f37]) ).
fof(f106,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f38]) ).
fof(f107,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) != sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)),
inference(cnf_transformation,[],[f41]) ).
fof(f117,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f120,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f121,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f122,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f123,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f124,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f125,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f155,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f120]) ).
fof(f157,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f125]) ).
fof(f158,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f124]) ).
fof(f183,plain,
( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) != sdtasdt0(sdtasdt0(xn,xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[],[f107,f122]) ).
fof(f194,plain,
( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) != sdtasdt0(sdtasdt0(xn,xl),sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f183,f106]) ).
fof(f196,plain,
sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) != sdtasdt0(sdtasdt0(xn,xl),sdtsldt0(xm,xl)),
inference(forward_subsumption_resolution,[],[f194,f103]) ).
fof(f266,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f155,f123]) ).
fof(f270,plain,
! [X0,X1] :
( doDivides0(X1,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f266,f122]) ).
fof(f271,plain,
! [X0,X1] :
( doDivides0(X1,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(duplicate_literal_removal,[],[f270]) ).
fof(f500,plain,
( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) != sdtasdt0(xn,sdtasdt0(xl,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(superposition,[],[f196,f121]) ).
fof(f537,plain,
( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) != sdtasdt0(xn,sdtasdt0(xl,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(forward_subsumption_resolution,[],[f500,f106]) ).
fof(f548,plain,
( sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) != sdtasdt0(xn,sdtasdt0(xl,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(forward_subsumption_resolution,[],[f537,f103]) ).
fof(f679,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xn,sdtasdt0(xl,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| sz00 = xl
| ~ doDivides0(xl,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[],[f548,f158]) ).
fof(f687,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xn,sdtasdt0(xl,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ doDivides0(xl,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f679,f105]) ).
fof(f695,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xn,sdtasdt0(xl,sdtsldt0(xm,xl)))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ doDivides0(xl,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f687,f103]) ).
fof(f698,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xn,xm)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ doDivides0(xl,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xl
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f695,f158]) ).
fof(f699,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ doDivides0(xl,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xl
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(trivial_inequality_removal,[],[f698]) ).
fof(f700,plain,
( ~ doDivides0(xl,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xl
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f699,f157]) ).
fof(f701,plain,
( ~ doDivides0(xl,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f700,f105]) ).
fof(f702,plain,
( ~ doDivides0(xl,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f701,f104]) ).
fof(f703,plain,
( ~ doDivides0(xl,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f702,f103]) ).
fof(f704,plain,
( ~ doDivides0(xl,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f703,f102]) ).
fof(f705,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xl,X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f704,f117]) ).
fof(f706,plain,
! [X0] :
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ doDivides0(xl,X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literal_removal,[],[f705]) ).
fof(f707,plain,
! [X0] :
( ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ doDivides0(xl,X0)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f706,f103]) ).
fof(f745,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f707,f271]) ).
fof(f748,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(duplicate_literal_removal,[],[f745]) ).
fof(f750,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f748,f104]) ).
fof(f752,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f750,f123]) ).
fof(f754,plain,
~ aNaturalNumber0(xn),
inference(forward_subsumption_resolution,[],[f752,f102]) ).
fof(f756,plain,
$false,
inference(forward_subsumption_resolution,[],[f754,f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM479+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n010.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 20:07:02 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 4.08/1.58 % (1274937)Detected formulas, will run a generic FOF schedule.
% 4.08/1.58 % (1274996)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=473187430:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.08/1.58 % (1274996)Instruction limit reached!
% 4.08/1.58 % (1274996)------------------------------
% 4.08/1.58 % (1274996)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.58 % (1274996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.58 % (1274996)CaDiCaL version: 2.1.3
% 4.08/1.58 % (1274996)Termination reason: Instruction limit
% 4.08/1.58 % (1274996)Termination phase: Saturation
% 4.08/1.58 % (1274996)Time elapsed: 0.050 s
% 4.08/1.58 % (1274996)Peak memory usage: 90 MB
% 4.08/1.58 % (1274996)Instructions burned: 142 (million)
% 4.08/1.58 % (1274991)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=2283162095:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.08/1.58 % (1274993)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=2811660774:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.08/1.58 % (1274992)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=75457953:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.08/1.58 % (1274997)dis-21_1_sil=8000:lcm=predicate:random_seed=322089307: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)
% 4.08/1.58 % (1274995)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3230448247:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.08/1.58 % (1274994)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=203261196:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.08/1.58 % (1274994)Refutation not found, incomplete strategy
% 4.08/1.58 % (1274994)------------------------------
% 4.08/1.58 % (1274994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.58 % (1274994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.58 % (1274994)CaDiCaL version: 2.1.3
% 4.08/1.58 % (1274994)Termination reason: Refutation not found, incomplete strategy
% 4.08/1.58 % (1274994)Time elapsed: 0.006 s
% 4.08/1.58 % (1274994)Peak memory usage: 89 MB
% 4.08/1.58 % (1274994)Instructions burned: 3 (million)
% 4.08/1.58 % (1274995)First to succeed.
% 4.08/1.58 % (1274995)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1274937"
% 4.08/1.58 % (1274997)Instruction limit reached!
% 4.08/1.58 % (1274997)------------------------------
% 4.08/1.58 % (1274997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.58 % (1274997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.58 % (1274997)CaDiCaL version: 2.1.3
% 4.08/1.58 % (1274997)Termination reason: Instruction limit
% 4.08/1.58 % (1274997)Termination phase: Saturation
% 4.08/1.58 % (1274997)Time elapsed: 0.131 s
% 4.08/1.58 % (1274997)Peak memory usage: 90 MB
% 4.08/1.58 % (1274997)Instructions burned: 129 (million)
% 4.08/1.58 % (1275006)lrs+10_1_sil=8000:sp=occurrence:random_seed=251037496:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.08/1.58 % (1275015)lrs+10_1_sil=32000:urr=on:br=off:random_seed=456481751:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 4.08/1.58 % (1275015)Instruction limit reached!
% 4.08/1.58 % (1275015)------------------------------
% 4.08/1.58 % (1275015)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.58 % (1275015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.58 % (1275015)CaDiCaL version: 2.1.3
% 4.08/1.58 % (1275015)Termination reason: Instruction limit
% 4.08/1.58 % (1275015)Termination phase: Saturation
% 4.08/1.58 % (1275015)Time elapsed: 0.068 s
% 4.08/1.58 % (1275015)Peak memory usage: 90 MB
% 4.08/1.58 % (1275015)Instructions burned: 159 (million)
% 4.08/1.58 % (1274995)Refutation found. Thanks to Tanya!
% 4.08/1.58 % SZS status Theorem for theBenchmark
% 4.08/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 5.42/1.82 % (1274995)------------------------------
% 5.42/1.82 % (1274995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.42/1.82 % (1274995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.42/1.82 % (1274995)CaDiCaL version: 2.1.3
% 5.42/1.82 % (1274995)Termination reason: Refutation
% 5.42/1.82 % (1274995)Time elapsed: 0.023 s
% 5.42/1.82 % (1274995)Peak memory usage: 88 MB
% 5.42/1.82 % (1274995)Instructions burned: 20 (million)
% 5.42/1.82 % (1274995)------------------------------
% 5.42/1.82 % (1274995)------------------------------
% 5.42/1.82 % (1274937)Success in time 0.671 s
% 5.42/1.82 % Vampire exiting
%------------------------------------------------------------------------------