%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM483+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 : n011.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 12:15:23 PM UTC 2026
% Result : Theorem 2.55s 1.31s
% Output : Refutation 3.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 12
% Syntax : Number of formulae : 90 ( 11 unt; 0 def)
% Number of atoms : 462 ( 157 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 607 ( 235 ~; 289 |; 65 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 105 ( 92 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != X1
& sdtlseqdt0(X0,X1) )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
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(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(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X0,X1)
& X1 != sz00 )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f38,axiom,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
fof(f39,axiom,
! [X0] :
( ( aNaturalNumber0(X0)
& X0 != sz00
& X0 != sz10 )
=> ( iLess0(X0,xk)
=> ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1700) ).
fof(f40,axiom,
( xk != sz00
& xk != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716_04) ).
fof(f41,axiom,
~ isPrime0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1725) ).
fof(f42,conjecture,
? [X0] :
( aNaturalNumber0(X0)
& doDivides0(X0,xk)
& isPrime0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
~ ? [X0] :
( aNaturalNumber0(X0)
& doDivides0(X0,xk)
& isPrime0(X0) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f46,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) )
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(ennf_transformation,[],[f39]) ).
fof(f47,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) )
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xk)
| ~ isPrime0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f52,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f53,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f55,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f54]) ).
fof(f60,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f61,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f63,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f65,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f64]) ).
fof(f85,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f105,plain,
! [X0] :
( ( aNaturalNumber0(sK0(X0))
& doDivides0(sK0(X0),X0)
& isPrime0(sK0(X0)) )
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f47]) ).
fof(f106,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,[],[f63]) ).
fof(f107,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,[],[f106]) ).
fof(f108,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))],[f107]) ).
fof(f109,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f110,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f110]) ).
fof(f112,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ( sz10 != sK2(X0)
& sK2(X0) != X0
& aNaturalNumber0(sK2(X0))
& doDivides0(sK2(X0),X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f111]) ).
fof(f116,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f38]) ).
fof(f117,plain,
! [X0] :
( isPrime0(sK0(X0))
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f105]) ).
fof(f118,plain,
! [X0] :
( doDivides0(sK0(X0),X0)
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f105]) ).
fof(f119,plain,
! [X0] :
( aNaturalNumber0(sK0(X0))
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f105]) ).
fof(f120,plain,
sz10 != xk,
inference(cnf_transformation,[],[f40]) ).
fof(f121,plain,
sz00 != xk,
inference(cnf_transformation,[],[f40]) ).
fof(f122,plain,
~ isPrime0(xk),
inference(cnf_transformation,[],[f41]) ).
fof(f123,plain,
! [X0] :
( ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f124,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f131,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f132,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f135,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f136,plain,
! [X0,X1] :
( sdtasdt0(X0,sK1(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f137,plain,
! [X0,X1] :
( aNaturalNumber0(sK1(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f142,plain,
! [X0] :
( doDivides0(sK2(X0),X0)
| sz00 = X0
| sz10 = X0
| isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f143,plain,
! [X0] :
( aNaturalNumber0(sK2(X0))
| sz00 = X0
| sz10 = X0
| isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f144,plain,
! [X0] :
( sK2(X0) != X0
| sz00 = X0
| sz10 = X0
| isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f145,plain,
! [X0] :
( sz10 != sK2(X0)
| sz00 = X0
| sz10 = X0
| isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f166,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f379,plain,
! [X0] :
( sz00 = X0
| ~ aNaturalNumber0(sK1(sz00,X0))
| ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f166,f136]) ).
fof(f384,plain,
! [X0] :
( sz00 = X0
| ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f379,f137]) ).
fof(f390,plain,
! [X0] :
( ~ doDivides0(sz00,X0)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f384,f124]) ).
fof(f466,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0) ),
inference(resolution,[],[f135,f123]) ).
fof(f469,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xk)
| ~ isPrime0(X0) ),
inference(duplicate_literal_removal,[],[f466]) ).
fof(f471,plain,
! [X0,X1] :
( ~ doDivides0(X1,xk)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ isPrime0(X0) ),
inference(forward_subsumption_resolution,[],[f469,f116]) ).
fof(f476,plain,
! [X0] :
( ~ doDivides0(X0,sK2(xk))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2(xk))
| ~ isPrime0(X0)
| sz00 = xk
| sz10 = xk
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f471,f142]) ).
fof(f481,plain,
! [X0] :
( ~ doDivides0(X0,sK2(xk))
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz00 = xk
| sz10 = xk
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f476,f143]) ).
fof(f484,plain,
! [X0] :
( ~ doDivides0(X0,sK2(xk))
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz10 = xk
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f481,f121]) ).
fof(f486,plain,
! [X0] :
( ~ doDivides0(X0,sK2(xk))
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f484,f120]) ).
fof(f487,plain,
! [X0] :
( ~ doDivides0(X0,sK2(xk))
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f486,f122]) ).
fof(f488,plain,
! [X0] :
( ~ doDivides0(X0,sK2(xk))
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0) ),
inference(forward_subsumption_resolution,[],[f487,f116]) ).
fof(f522,plain,
( ~ aNaturalNumber0(sK0(sK2(xk)))
| ~ isPrime0(sK0(sK2(xk)))
| ~ iLess0(sK2(xk),xk)
| ~ aNaturalNumber0(sK2(xk))
| sz00 = sK2(xk)
| sz10 = sK2(xk) ),
inference(resolution,[],[f488,f118]) ).
fof(f527,plain,
( ~ isPrime0(sK0(sK2(xk)))
| ~ iLess0(sK2(xk),xk)
| ~ aNaturalNumber0(sK2(xk))
| sz00 = sK2(xk)
| sz10 = sK2(xk) ),
inference(forward_subsumption_resolution,[],[f522,f119]) ).
fof(f529,plain,
( ~ iLess0(sK2(xk),xk)
| ~ aNaturalNumber0(sK2(xk))
| sz00 = sK2(xk)
| sz10 = sK2(xk) ),
inference(forward_subsumption_resolution,[],[f527,f117]) ).
fof(f560,plain,
( ~ aNaturalNumber0(sK2(xk))
| sz00 = sK2(xk)
| sz10 = sK2(xk)
| xk = sK2(xk)
| ~ sdtlseqdt0(sK2(xk),xk)
| ~ aNaturalNumber0(sK2(xk))
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f529,f131]) ).
fof(f561,plain,
( ~ aNaturalNumber0(sK2(xk))
| sz00 = sK2(xk)
| sz10 = sK2(xk)
| xk = sK2(xk)
| ~ sdtlseqdt0(sK2(xk),xk)
| ~ aNaturalNumber0(xk) ),
inference(duplicate_literal_removal,[],[f560]) ).
fof(f562,plain,
( ~ sdtlseqdt0(sK2(xk),xk)
| sz00 = sK2(xk)
| sz10 = sK2(xk)
| xk = sK2(xk)
| ~ aNaturalNumber0(sK2(xk)) ),
inference(forward_subsumption_resolution,[],[f561,f116]) ).
fof(f701,plain,
( sz00 = sK2(xk)
| sz10 = sK2(xk)
| xk = sK2(xk)
| ~ aNaturalNumber0(sK2(xk))
| ~ doDivides0(sK2(xk),xk)
| sz00 = xk
| ~ aNaturalNumber0(sK2(xk))
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f562,f132]) ).
fof(f704,plain,
( sz00 = sK2(xk)
| sz10 = sK2(xk)
| xk = sK2(xk)
| ~ aNaturalNumber0(sK2(xk))
| ~ doDivides0(sK2(xk),xk)
| sz00 = xk
| ~ aNaturalNumber0(xk) ),
inference(duplicate_literal_removal,[],[f701]) ).
fof(f707,plain,
( sz00 = sK2(xk)
| sz10 = sK2(xk)
| xk = sK2(xk)
| ~ aNaturalNumber0(sK2(xk))
| ~ doDivides0(sK2(xk),xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f704,f121]) ).
fof(f709,plain,
( ~ doDivides0(sK2(xk),xk)
| sz10 = sK2(xk)
| xk = sK2(xk)
| ~ aNaturalNumber0(sK2(xk))
| sz00 = sK2(xk) ),
inference(forward_subsumption_resolution,[],[f707,f116]) ).
fof(f801,plain,
( sz10 = sK2(xk)
| xk = sK2(xk)
| ~ aNaturalNumber0(sK2(xk))
| sz00 = sK2(xk)
| sz00 = xk
| sz10 = xk
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f709,f142]) ).
fof(f805,plain,
( xk = sK2(xk)
| ~ aNaturalNumber0(sK2(xk))
| sz00 = sK2(xk)
| sz00 = xk
| sz10 = xk
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f801,f145]) ).
fof(f806,plain,
( ~ aNaturalNumber0(sK2(xk))
| sz00 = sK2(xk)
| sz00 = xk
| sz10 = xk
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f805,f144]) ).
fof(f807,plain,
( sz00 = sK2(xk)
| sz00 = xk
| sz10 = xk
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f806,f143]) ).
fof(f808,plain,
( sz00 = sK2(xk)
| sz10 = xk
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f807,f121]) ).
fof(f809,plain,
( sz00 = sK2(xk)
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f808,f120]) ).
fof(f810,plain,
( sz00 = sK2(xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f809,f122]) ).
fof(f811,plain,
sz00 = sK2(xk),
inference(forward_subsumption_resolution,[],[f810,f116]) ).
fof(f818,plain,
( doDivides0(sz00,xk)
| sz00 = xk
| sz10 = xk
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(superposition,[],[f142,f811]) ).
fof(f820,plain,
( sz00 = xk
| sz10 = xk
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f818,f390]) ).
fof(f824,plain,
( sz10 = xk
| isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f820,f121]) ).
fof(f826,plain,
( isPrime0(xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f824,f120]) ).
fof(f827,plain,
~ aNaturalNumber0(xk),
inference(forward_subsumption_resolution,[],[f826,f122]) ).
fof(f828,plain,
$false,
inference(forward_subsumption_resolution,[],[f827,f116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM483+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n011.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 20:07:00 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.55/1.31 % (2726210)Detected formulas, will run a generic FOF schedule.
% 2.55/1.31 % (2726215)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=2506019270:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.55/1.31 % (2726219)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2812438854:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.55/1.31 % (2726217)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=1833580987:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.55/1.31 % (2726220)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3838816709:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.55/1.31 % (2726218)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1602001497:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.55/1.31 % (2726216)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=2130905978:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.55/1.31 % (2726219)First to succeed.
% 2.55/1.31 % (2726219)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2726210"
% 2.55/1.31 % (2726221)dis-21_1_sil=8000:lcm=predicate:random_seed=593653217: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)
% 2.55/1.31 % (2726218)Instruction limit reached!
% 2.55/1.31 % (2726218)------------------------------
% 2.55/1.31 % (2726218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.31 % (2726218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.31 % (2726218)CaDiCaL version: 2.1.3
% 2.55/1.31 % (2726218)Termination reason: Instruction limit
% 2.55/1.31 % (2726218)Termination phase: Saturation
% 2.55/1.31 % (2726218)Time elapsed: 0.054 s
% 2.55/1.31 % (2726218)Peak memory usage: 88 MB
% 2.55/1.31 % (2726218)Instructions burned: 110 (million)
% 2.55/1.31 % (2726220)Instruction limit reached!
% 2.55/1.31 % (2726220)------------------------------
% 2.55/1.31 % (2726220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.31 % (2726220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.31 % (2726220)CaDiCaL version: 2.1.3
% 2.55/1.31 % (2726220)Termination reason: Instruction limit
% 2.55/1.31 % (2726220)Termination phase: Saturation
% 2.55/1.31 % (2726220)Time elapsed: 0.088 s
% 2.55/1.31 % (2726220)Peak memory usage: 89 MB
% 2.55/1.31 % (2726220)Instructions burned: 140 (million)
% 2.55/1.31 % (2726221)Instruction limit reached!
% 2.55/1.31 % (2726221)------------------------------
% 2.55/1.31 % (2726221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.31 % (2726221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.31 % (2726221)CaDiCaL version: 2.1.3
% 2.55/1.31 % (2726221)Termination reason: Instruction limit
% 2.55/1.31 % (2726221)Termination phase: Saturation
% 2.55/1.31 % (2726221)Time elapsed: 0.078 s
% 2.55/1.31 % (2726221)Peak memory usage: 91 MB
% 2.55/1.31 % (2726221)Instructions burned: 129 (million)
% 2.55/1.31 % (2726229)lrs+10_1_sil=8000:sp=occurrence:random_seed=75276658:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.55/1.31 % (2726230)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2745291353:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.55/1.31 % (2726230)Refutation not found, incomplete strategy
% 2.55/1.31 % (2726230)------------------------------
% 2.55/1.31 % (2726230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.55/1.31 % (2726230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.55/1.31 % (2726230)CaDiCaL version: 2.1.3
% 2.55/1.31 % (2726230)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.31 % (2726230)Time elapsed: 0.003 s
% 2.55/1.31 % (2726230)Peak memory usage: 89 MB
% 2.55/1.31 % (2726230)Instructions burned: 3 (million)
% 2.55/1.31 % (2726231)lrs+1011_1_sil=32000:sp=occurrence:random_seed=939108284:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.55/1.31 % (2726219)Refutation found. Thanks to Tanya!
% 2.55/1.31 % SZS status Theorem for theBenchmark
% 2.55/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 3.78/1.51 % (2726219)------------------------------
% 3.78/1.51 % (2726219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.51 % (2726219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.51 % (2726219)CaDiCaL version: 2.1.3
% 3.78/1.51 % (2726219)Termination reason: Refutation
% 3.78/1.51 % (2726219)Time elapsed: 0.014 s
% 3.78/1.51 % (2726219)Peak memory usage: 88 MB
% 3.78/1.51 % (2726219)Instructions burned: 22 (million)
% 3.78/1.51 % (2726219)------------------------------
% 3.78/1.51 % (2726219)------------------------------
% 3.78/1.51 % (2726210)Success in time 0.443 s
% 3.78/1.51 % Vampire exiting
%------------------------------------------------------------------------------