%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM483+3 : 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 2.99s 1.33s
% Output : Refutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 11
% Syntax : Number of formulae : 78 ( 12 unt; 2 def)
% Number of atoms : 436 ( 163 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 555 ( 197 ~; 194 |; 147 &)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 110 ( 74 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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)
& ? [X2] :
( aNaturalNumber0(X2)
& X0 = sdtasdt0(X1,X2) )
& doDivides0(X1,X0)
& X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& ( ? [X3] :
( aNaturalNumber0(X3)
& X1 = sdtasdt0(X2,X3) )
| doDivides0(X2,X1) ) )
=> ( X2 = sz10
| X2 = X1 ) )
& 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,
~ ( ! [X0] :
( ( aNaturalNumber0(X0)
& ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
& doDivides0(X0,xk) )
=> ( X0 = sz10
| X0 = xk ) )
| isPrime0(xk) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1725) ).
fof(f42,conjecture,
? [X0] :
( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
| doDivides0(X0,xk) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& X0 = sdtasdt0(X1,X2) )
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) )
| isPrime0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
~ ? [X0] :
( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
| doDivides0(X0,xk) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& X0 = sdtasdt0(X1,X2) )
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) )
| isPrime0(X0) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f44,plain,
! [X0] :
( ( aNaturalNumber0(X0)
& X0 != sz00
& X0 != sz10 )
=> ( iLess0(X0,xk)
=> ? [X1] :
( aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& X0 = sdtasdt0(X1,X2) )
& doDivides0(X1,X0)
& X1 != sz00
& X1 != sz10
& ! [X3] :
( ( aNaturalNumber0(X3)
& ( ? [X4] :
( aNaturalNumber0(X4)
& sdtasdt0(X3,X4) = X1 )
| doDivides0(X3,X1) ) )
=> ( sz10 = X3
| X1 = X3 ) )
& isPrime0(X1) ) ) ),
inference(rectify,[],[f39]) ).
fof(f45,plain,
~ ? [X0] :
( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
| doDivides0(X0,xk) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) )
=> ( sz10 = X2
| X0 = X2 ) ) )
| isPrime0(X0) ) ),
inference(rectify,[],[f43]) ).
fof(f48,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& X0 = sdtasdt0(X1,X2) )
& doDivides0(X1,X0)
& X1 != sz00
& X1 != sz10
& ! [X3] :
( sz10 = X3
| X1 = X3
| ~ aNaturalNumber0(X3)
| ( ! [X4] :
( ~ aNaturalNumber0(X4)
| sdtasdt0(X3,X4) != X1 )
& ~ doDivides0(X3,X1) ) )
& isPrime0(X1) )
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(ennf_transformation,[],[f44]) ).
fof(f49,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& X0 = sdtasdt0(X1,X2) )
& doDivides0(X1,X0)
& X1 != sz00
& X1 != sz10
& ! [X3] :
( sz10 = X3
| X1 = X3
| ~ aNaturalNumber0(X3)
| ( ! [X4] :
( ~ aNaturalNumber0(X4)
| sdtasdt0(X3,X4) != X1 )
& ~ doDivides0(X3,X1) ) )
& isPrime0(X1) )
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
( ? [X0] :
( sz10 != X0
& xk != X0
& aNaturalNumber0(X0)
& ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
& doDivides0(X0,xk) )
& ~ isPrime0(xk) ),
inference(ennf_transformation,[],[f41]) ).
fof(f51,plain,
( ? [X0] :
( sz10 != X0
& xk != X0
& aNaturalNumber0(X0)
& ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(X0,X1) )
& doDivides0(X0,xk) )
& ~ isPrime0(xk) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) )
| ( ( sz00 = X0
| sz10 = X0
| ? [X2] :
( sz10 != X2
& X0 != X2
& aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) ) )
& ~ isPrime0(X0) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f53,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) )
| ( ( sz00 = X0
| sz10 = X0
| ? [X2] :
( sz10 != X2
& X0 != X2
& aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) ) )
& ~ isPrime0(X0) ) ),
inference(flattening,[],[f52]) ).
fof(f57,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f58,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f57]) ).
fof(f63,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f70,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f71,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f70]) ).
fof(f76,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f77,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f76]) ).
fof(f110,definition,
! [X1] :
( ! [X3] :
( sz10 = X3
| X1 = X3
| ~ aNaturalNumber0(X3)
| ( ! [X4] :
( ~ aNaturalNumber0(X4)
| sdtasdt0(X3,X4) != X1 )
& ~ doDivides0(X3,X1) ) )
| ~ sP0(X1) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f111,plain,
! [X0] :
( ? [X1] :
( aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& X0 = sdtasdt0(X1,X2) )
& doDivides0(X1,X0)
& X1 != sz00
& X1 != sz10
& sP0(X1)
& isPrime0(X1) )
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(definition_folding,[],[f49,f110]) ).
fof(f112,definition,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ? [X2] :
( sz10 != X2
& X0 != X2
& aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) ) )
& ~ isPrime0(X0) )
| ~ sP1(X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f113,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xk )
& ~ doDivides0(X0,xk) )
| sP1(X0) ),
inference(definition_folding,[],[f53,f112]) ).
fof(f116,plain,
! [X0] :
( ( aNaturalNumber0(sK2(X0))
& aNaturalNumber0(sK3(X0))
& sdtasdt0(sK2(X0),sK3(X0)) = X0
& doDivides0(sK2(X0),X0)
& sz00 != sK2(X0)
& sz10 != sK2(X0)
& sP0(sK2(X0))
& isPrime0(sK2(X0)) )
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X1,sK2(X0)),skolemize(X2,sK3(X0))],[f111]) ).
fof(f117,plain,
( sz10 != sK4
& xk != sK4
& aNaturalNumber0(sK4)
& aNaturalNumber0(sK5)
& xk = sdtasdt0(sK4,sK5)
& doDivides0(sK4,xk)
& ~ isPrime0(xk) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f51]) ).
fof(f118,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ? [X2] :
( sz10 != X2
& X0 != X2
& aNaturalNumber0(X2)
& ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) ) )
& ~ isPrime0(X0) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f112]) ).
fof(f119,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
& doDivides0(X1,X0) ) )
& ~ isPrime0(X0) )
| ~ sP1(X0) ),
inference(rectify,[],[f118]) ).
fof(f120,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ( sz10 != sK6(X0)
& sK6(X0) != X0
& aNaturalNumber0(sK6(X0))
& aNaturalNumber0(sK7(X0))
& sdtasdt0(sK6(X0),sK7(X0)) = X0
& doDivides0(sK6(X0),X0) ) )
& ~ isPrime0(X0) )
| ~ sP1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X1,sK6(X0)),skolemize(X2,sK7(X0))],[f119]) ).
fof(f131,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f38]) ).
fof(f134,plain,
! [X0] :
( isPrime0(sK2(X0))
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f138,plain,
! [X0] :
( doDivides0(sK2(X0),X0)
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f141,plain,
! [X0] :
( aNaturalNumber0(sK2(X0))
| ~ iLess0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz10 = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f143,plain,
sz00 != xk,
inference(cnf_transformation,[],[f40]) ).
fof(f145,plain,
doDivides0(sK4,xk),
inference(cnf_transformation,[],[f117]) ).
fof(f146,plain,
xk = sdtasdt0(sK4,sK5),
inference(cnf_transformation,[],[f117]) ).
fof(f147,plain,
aNaturalNumber0(sK5),
inference(cnf_transformation,[],[f117]) ).
fof(f148,plain,
aNaturalNumber0(sK4),
inference(cnf_transformation,[],[f117]) ).
fof(f149,plain,
xk != sK4,
inference(cnf_transformation,[],[f117]) ).
fof(f150,plain,
sz10 != sK4,
inference(cnf_transformation,[],[f117]) ).
fof(f151,plain,
! [X0] :
( ~ sP1(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f158,plain,
! [X0] :
( ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0)
| sP1(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f167,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f171,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f176,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f179,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f681,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0)
| sP1(X0) ),
inference(resolution,[],[f179,f158]) ).
fof(f686,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xk)
| sP1(X0) ),
inference(duplicate_literal_removal,[],[f681]) ).
fof(f688,plain,
! [X0,X1] :
( ~ doDivides0(X1,xk)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sP1(X0) ),
inference(forward_subsumption_resolution,[],[f686,f131]) ).
fof(f693,plain,
! [X0] :
( ~ doDivides0(X0,sK4)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK4)
| sP1(X0) ),
inference(resolution,[],[f688,f145]) ).
fof(f704,plain,
! [X0] :
( ~ doDivides0(X0,sK4)
| ~ aNaturalNumber0(X0)
| sP1(X0) ),
inference(forward_subsumption_resolution,[],[f693,f148]) ).
fof(f718,plain,
( ~ aNaturalNumber0(sK2(sK4))
| sP1(sK2(sK4))
| ~ iLess0(sK4,xk)
| ~ aNaturalNumber0(sK4)
| sz00 = sK4
| sz10 = sK4 ),
inference(resolution,[],[f704,f138]) ).
fof(f725,plain,
( sP1(sK2(sK4))
| ~ iLess0(sK4,xk)
| ~ aNaturalNumber0(sK4)
| sz00 = sK4
| sz10 = sK4 ),
inference(forward_subsumption_resolution,[],[f718,f141]) ).
fof(f729,plain,
( sP1(sK2(sK4))
| ~ iLess0(sK4,xk)
| sz00 = sK4
| sz10 = sK4 ),
inference(forward_subsumption_resolution,[],[f725,f148]) ).
fof(f732,plain,
( sP1(sK2(sK4))
| ~ iLess0(sK4,xk)
| sz00 = sK4 ),
inference(forward_subsumption_resolution,[],[f729,f150]) ).
fof(f1022,plain,
( ~ isPrime0(sK2(sK4))
| sz00 = sK4
| ~ iLess0(sK4,xk) ),
inference(resolution,[],[f732,f151]) ).
fof(f1072,plain,
( sz00 = sK4
| ~ iLess0(sK4,xk)
| ~ iLess0(sK4,xk)
| ~ aNaturalNumber0(sK4)
| sz00 = sK4
| sz10 = sK4 ),
inference(resolution,[],[f1022,f134]) ).
fof(f1073,plain,
( sz00 = sK4
| ~ iLess0(sK4,xk)
| ~ aNaturalNumber0(sK4)
| sz10 = sK4 ),
inference(duplicate_literal_removal,[],[f1072]) ).
fof(f1074,plain,
( sz00 = sK4
| ~ iLess0(sK4,xk)
| sz10 = sK4 ),
inference(forward_subsumption_resolution,[],[f1073,f148]) ).
fof(f1075,plain,
( ~ iLess0(sK4,xk)
| sz00 = sK4 ),
inference(forward_subsumption_resolution,[],[f1074,f150]) ).
fof(f1148,plain,
( sz00 = sK4
| xk = sK4
| ~ sdtlseqdt0(sK4,xk)
| ~ aNaturalNumber0(sK4)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f1075,f167]) ).
fof(f1149,plain,
( sz00 = sK4
| ~ sdtlseqdt0(sK4,xk)
| ~ aNaturalNumber0(sK4)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f1148,f149]) ).
fof(f1150,plain,
( sz00 = sK4
| ~ sdtlseqdt0(sK4,xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f1149,f148]) ).
fof(f1151,plain,
( ~ sdtlseqdt0(sK4,xk)
| sz00 = sK4 ),
inference(forward_subsumption_resolution,[],[f1150,f131]) ).
fof(f1192,plain,
( sz00 = sK4
| ~ doDivides0(sK4,xk)
| sz00 = xk
| ~ aNaturalNumber0(sK4)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f1151,f176]) ).
fof(f1195,plain,
( sz00 = sK4
| sz00 = xk
| ~ aNaturalNumber0(sK4)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f1192,f145]) ).
fof(f1198,plain,
( sz00 = sK4
| ~ aNaturalNumber0(sK4)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f1195,f143]) ).
fof(f1200,plain,
( sz00 = sK4
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f1198,f148]) ).
fof(f1201,plain,
sz00 = sK4,
inference(forward_subsumption_resolution,[],[f1200,f131]) ).
fof(f1206,plain,
! [X0] :
( sK4 = sdtasdt0(sK4,X0)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f171,f1201]) ).
fof(f1432,plain,
( xk = sK4
| ~ aNaturalNumber0(sK5) ),
inference(superposition,[],[f146,f1206]) ).
fof(f1467,plain,
~ aNaturalNumber0(sK5),
inference(forward_subsumption_resolution,[],[f1432,f149]) ).
fof(f1473,plain,
$false,
inference(forward_subsumption_resolution,[],[f1467,f147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM483+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n011.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:07:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.99/1.33 % (2726630)Detected formulas, will run a generic FOF schedule.
% 2.99/1.33 % (2726636)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=2469754765:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.99/1.33 % (2726640)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=98726826:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.99/1.33 % (2726639)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=264869079:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.99/1.33 % (2726638)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1306443918:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.99/1.33 % (2726641)dis-21_1_sil=8000:lcm=predicate:random_seed=3717682809: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)
% 2.99/1.33 % (2726637)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=1558027327:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.99/1.33 % (2726635)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=3084744447:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.99/1.33 % (2726639)First to succeed.
% 2.99/1.33 % (2726639)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2726630"
% 2.99/1.33 % (2726638)Instruction limit reached!
% 2.99/1.33 % (2726638)------------------------------
% 2.99/1.33 % (2726638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.33 % (2726638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.33 % (2726638)CaDiCaL version: 2.1.3
% 2.99/1.33 % (2726638)Termination reason: Instruction limit
% 2.99/1.33 % (2726638)Termination phase: Saturation
% 2.99/1.33 % (2726638)Time elapsed: 0.063 s
% 2.99/1.33 % (2726638)Peak memory usage: 89 MB
% 2.99/1.33 % (2726638)Instructions burned: 111 (million)
% 2.99/1.33 % (2726641)Instruction limit reached!
% 2.99/1.33 % (2726641)------------------------------
% 2.99/1.33 % (2726641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.33 % (2726641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.33 % (2726641)CaDiCaL version: 2.1.3
% 2.99/1.33 % (2726641)Termination reason: Instruction limit
% 2.99/1.33 % (2726641)Termination phase: Saturation
% 2.99/1.33 % (2726641)Time elapsed: 0.079 s
% 2.99/1.33 % (2726641)Peak memory usage: 90 MB
% 2.99/1.33 % (2726641)Instructions burned: 130 (million)
% 2.99/1.33 % (2726640)Instruction limit reached!
% 2.99/1.33 % (2726640)------------------------------
% 2.99/1.33 % (2726640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.33 % (2726640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.33 % (2726640)CaDiCaL version: 2.1.3
% 2.99/1.33 % (2726640)Termination reason: Instruction limit
% 2.99/1.33 % (2726640)Termination phase: Saturation
% 2.99/1.33 % (2726640)Time elapsed: 0.089 s
% 2.99/1.33 % (2726640)Peak memory usage: 90 MB
% 2.99/1.33 % (2726640)Instructions burned: 139 (million)
% 2.99/1.33 % (2726649)lrs+10_1_sil=8000:sp=occurrence:random_seed=1882092365:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.99/1.33 % (2726650)lrs+10_1_sil=32000:urr=on:br=off:random_seed=295372542:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.99/1.33 % (2726651)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3265991511:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.99/1.33 % (2726639)Refutation found. Thanks to Tanya!
% 2.99/1.33 % SZS status Theorem for theBenchmark
% 2.99/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.87/1.53 % (2726639)------------------------------
% 3.87/1.53 % (2726639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.53 % (2726639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.53 % (2726639)CaDiCaL version: 2.1.3
% 3.87/1.53 % (2726639)Termination reason: Refutation
% 3.87/1.53 % (2726639)Time elapsed: 0.028 s
% 3.87/1.53 % (2726639)Peak memory usage: 88 MB
% 3.87/1.53 % (2726639)Instructions burned: 45 (million)
% 3.87/1.53 % (2726639)------------------------------
% 3.87/1.53 % (2726639)------------------------------
% 3.87/1.53 % (2726630)Success in time 0.464 s
% 3.87/1.53 % Vampire exiting
%------------------------------------------------------------------------------