%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM481+1 : 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 : 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 12:15:23 PM UTC 2026
% Result : Theorem 2.86s 1.32s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 11
% Syntax : Number of formulae : 104 ( 10 unt; 0 def)
% Number of atoms : 561 ( 182 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 748 ( 291 ~; 325 |; 102 &)
% ( 6 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 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 : 142 ( 122 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
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(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != X1
& sdtlseqdt0(X0,X1) )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X0,X1)
& X1 != sz00 )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f38,conjecture,
! [X0] :
( ( aNaturalNumber0(X0)
& X0 != sz00
& X0 != sz10 )
=> ( ! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00
& X1 != sz10 )
=> ( iLess0(X1,X0)
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ) )
=> ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( ( aNaturalNumber0(X0)
& X0 != sz00
& X0 != sz10 )
=> ( ! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00
& X1 != sz10 )
=> ( iLess0(X1,X0)
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ) )
=> ? [X1] :
( aNaturalNumber0(X1)
& doDivides0(X1,X0)
& isPrime0(X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f40,plain,
~ ! [X0] :
( ( aNaturalNumber0(X0)
& X0 != sz00
& X0 != sz10 )
=> ( ! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00
& X1 != sz10 )
=> ( iLess0(X1,X0)
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ) )
=> ? [X3] :
( aNaturalNumber0(X3)
& doDivides0(X3,X0)
& isPrime0(X3) ) ) ),
inference(rectify,[],[f39]) ).
fof(f43,plain,
? [X0] :
( ! [X3] :
( ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X0)
| ~ isPrime0(X3) )
& ! [X1] :
( ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) )
| ~ iLess0(X1,X0)
| ~ aNaturalNumber0(X1)
| sz00 = X1
| sz10 = X1 )
& aNaturalNumber0(X0)
& X0 != sz00
& X0 != sz10 ),
inference(ennf_transformation,[],[f40]) ).
fof(f44,plain,
? [X0] :
( ! [X3] :
( ~ aNaturalNumber0(X3)
| ~ doDivides0(X3,X0)
| ~ isPrime0(X3) )
& ! [X1] :
( ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) )
| ~ iLess0(X1,X0)
| ~ aNaturalNumber0(X1)
| sz00 = X1
| sz10 = X1 )
& aNaturalNumber0(X0)
& X0 != sz00
& X0 != sz10 ),
inference(flattening,[],[f43]) ).
fof(f47,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f48,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f49,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f51,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f50]) ).
fof(f56,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f57,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f59,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f58]) ).
fof(f60,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(f61,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f60]) ).
fof(f81,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f86,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f87,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f86]) ).
fof(f101,plain,
? [X0] :
( ! [X1] :
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0)
| ~ isPrime0(X1) )
& ! [X2] :
( ? [X3] :
( aNaturalNumber0(X3)
& doDivides0(X3,X2)
& isPrime0(X3) )
| ~ iLess0(X2,X0)
| ~ aNaturalNumber0(X2)
| sz00 = X2
| sz10 = X2 )
& aNaturalNumber0(X0)
& X0 != sz00
& X0 != sz10 ),
inference(rectify,[],[f44]) ).
fof(f102,plain,
( ! [X1] :
( ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,sK0)
| ~ isPrime0(X1) )
& ! [X2] :
( ( aNaturalNumber0(sK1(X2))
& doDivides0(sK1(X2),X2)
& isPrime0(sK1(X2)) )
| ~ iLess0(X2,sK0)
| ~ aNaturalNumber0(X2)
| sz00 = X2
| sz10 = X2 )
& aNaturalNumber0(sK0)
& sz00 != sK0
& sz10 != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X3,sK1(X2))],[f101]) ).
fof(f103,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,[],[f59]) ).
fof(f104,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,[],[f103]) ).
fof(f105,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK2(X0,X1))
& sdtasdt0(X0,sK2(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1))],[f104]) ).
fof(f106,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,[],[f61]) ).
fof(f107,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,[],[f106]) ).
fof(f108,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,[],[f107]) ).
fof(f109,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ( sz10 != sK3(X0)
& sK3(X0) != X0
& aNaturalNumber0(sK3(X0))
& doDivides0(sK3(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,[sK3]),skolemize(X1,sK3(X0))],[f108]) ).
fof(f113,plain,
sz10 != sK0,
inference(cnf_transformation,[],[f102]) ).
fof(f114,plain,
sz00 != sK0,
inference(cnf_transformation,[],[f102]) ).
fof(f115,plain,
aNaturalNumber0(sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f116,plain,
! [X2] :
( isPrime0(sK1(X2))
| ~ iLess0(X2,sK0)
| ~ aNaturalNumber0(X2)
| sz00 = X2
| sz10 = X2 ),
inference(cnf_transformation,[],[f102]) ).
fof(f117,plain,
! [X2] :
( doDivides0(sK1(X2),X2)
| ~ iLess0(X2,sK0)
| ~ aNaturalNumber0(X2)
| sz00 = X2
| sz10 = X2 ),
inference(cnf_transformation,[],[f102]) ).
fof(f118,plain,
! [X2] :
( aNaturalNumber0(sK1(X2))
| ~ iLess0(X2,sK0)
| ~ aNaturalNumber0(X2)
| sz00 = X2
| sz10 = X2 ),
inference(cnf_transformation,[],[f102]) ).
fof(f119,plain,
! [X1] :
( ~ doDivides0(X1,sK0)
| ~ aNaturalNumber0(X1)
| ~ isPrime0(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f120,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f124,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f126,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f127,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f128,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f131,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f132,plain,
! [X0,X1] :
( sdtasdt0(X0,sK2(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f133,plain,
! [X0,X1] :
( aNaturalNumber0(sK2(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f134,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f138,plain,
! [X0] :
( doDivides0(sK3(X0),X0)
| sz00 = X0
| sz10 = X0
| isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f139,plain,
! [X0] :
( aNaturalNumber0(sK3(X0))
| sz00 = X0
| sz10 = X0
| isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f140,plain,
! [X0] :
( sK3(X0) != X0
| sz00 = X0
| sz10 = X0
| isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f141,plain,
! [X0] :
( sz10 != sK3(X0)
| sz00 = X0
| sz10 = X0
| isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f162,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f166,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f179,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f134]) ).
fof(f316,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f179,f166]) ).
fof(f318,plain,
! [X0] :
( doDivides0(X0,X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f316,f124]) ).
fof(f327,plain,
! [X0] :
( doDivides0(X0,X0)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literal_removal,[],[f318]) ).
fof(f331,plain,
! [X0] :
( doDivides0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f327,f126]) ).
fof(f346,plain,
( ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(sK0)
| ~ isPrime0(sK0) ),
inference(resolution,[],[f331,f119]) ).
fof(f347,plain,
( ~ aNaturalNumber0(sK0)
| ~ isPrime0(sK0) ),
inference(duplicate_literal_removal,[],[f346]) ).
fof(f348,plain,
~ isPrime0(sK0),
inference(forward_subsumption_resolution,[],[f347,f115]) ).
fof(f356,plain,
! [X0] :
( sz00 = X0
| ~ aNaturalNumber0(sK2(sz00,X0))
| ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f162,f132]) ).
fof(f361,plain,
! [X0] :
( sz00 = X0
| ~ doDivides0(sz00,X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f356,f133]) ).
fof(f367,plain,
! [X0] :
( ~ doDivides0(sz00,X0)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f361,f120]) ).
fof(f430,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,sK0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sK0)
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0) ),
inference(resolution,[],[f131,f119]) ).
fof(f433,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ doDivides0(X1,sK0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(sK0)
| ~ isPrime0(X0) ),
inference(duplicate_literal_removal,[],[f430]) ).
fof(f435,plain,
! [X0,X1] :
( ~ doDivides0(X1,sK0)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ isPrime0(X0) ),
inference(forward_subsumption_resolution,[],[f433,f115]) ).
fof(f440,plain,
! [X0] :
( ~ doDivides0(X0,sK3(sK0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK3(sK0))
| ~ isPrime0(X0)
| sz00 = sK0
| sz10 = sK0
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(resolution,[],[f435,f138]) ).
fof(f445,plain,
! [X0] :
( ~ doDivides0(X0,sK3(sK0))
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz00 = sK0
| sz10 = sK0
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f440,f139]) ).
fof(f448,plain,
! [X0] :
( ~ doDivides0(X0,sK3(sK0))
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz10 = sK0
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f445,f114]) ).
fof(f450,plain,
! [X0] :
( ~ doDivides0(X0,sK3(sK0))
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f448,f113]) ).
fof(f451,plain,
! [X0] :
( ~ doDivides0(X0,sK3(sK0))
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f450,f348]) ).
fof(f452,plain,
! [X0] :
( ~ doDivides0(X0,sK3(sK0))
| ~ aNaturalNumber0(X0)
| ~ isPrime0(X0) ),
inference(forward_subsumption_resolution,[],[f451,f115]) ).
fof(f486,plain,
( ~ aNaturalNumber0(sK1(sK3(sK0)))
| ~ isPrime0(sK1(sK3(sK0)))
| ~ iLess0(sK3(sK0),sK0)
| ~ aNaturalNumber0(sK3(sK0))
| sz00 = sK3(sK0)
| sz10 = sK3(sK0) ),
inference(resolution,[],[f452,f117]) ).
fof(f491,plain,
( ~ isPrime0(sK1(sK3(sK0)))
| ~ iLess0(sK3(sK0),sK0)
| ~ aNaturalNumber0(sK3(sK0))
| sz00 = sK3(sK0)
| sz10 = sK3(sK0) ),
inference(forward_subsumption_resolution,[],[f486,f118]) ).
fof(f493,plain,
( ~ iLess0(sK3(sK0),sK0)
| ~ aNaturalNumber0(sK3(sK0))
| sz00 = sK3(sK0)
| sz10 = sK3(sK0) ),
inference(forward_subsumption_resolution,[],[f491,f116]) ).
fof(f521,plain,
( ~ aNaturalNumber0(sK3(sK0))
| sz00 = sK3(sK0)
| sz10 = sK3(sK0)
| sK0 = sK3(sK0)
| ~ sdtlseqdt0(sK3(sK0),sK0)
| ~ aNaturalNumber0(sK3(sK0))
| ~ aNaturalNumber0(sK0) ),
inference(resolution,[],[f493,f127]) ).
fof(f522,plain,
( ~ aNaturalNumber0(sK3(sK0))
| sz00 = sK3(sK0)
| sz10 = sK3(sK0)
| sK0 = sK3(sK0)
| ~ sdtlseqdt0(sK3(sK0),sK0)
| ~ aNaturalNumber0(sK0) ),
inference(duplicate_literal_removal,[],[f521]) ).
fof(f523,plain,
( ~ sdtlseqdt0(sK3(sK0),sK0)
| sz00 = sK3(sK0)
| sz10 = sK3(sK0)
| sK0 = sK3(sK0)
| ~ aNaturalNumber0(sK3(sK0)) ),
inference(forward_subsumption_resolution,[],[f522,f115]) ).
fof(f662,plain,
( sz00 = sK3(sK0)
| sz10 = sK3(sK0)
| sK0 = sK3(sK0)
| ~ aNaturalNumber0(sK3(sK0))
| ~ doDivides0(sK3(sK0),sK0)
| sz00 = sK0
| ~ aNaturalNumber0(sK3(sK0))
| ~ aNaturalNumber0(sK0) ),
inference(resolution,[],[f523,f128]) ).
fof(f665,plain,
( sz00 = sK3(sK0)
| sz10 = sK3(sK0)
| sK0 = sK3(sK0)
| ~ aNaturalNumber0(sK3(sK0))
| ~ doDivides0(sK3(sK0),sK0)
| sz00 = sK0
| ~ aNaturalNumber0(sK0) ),
inference(duplicate_literal_removal,[],[f662]) ).
fof(f668,plain,
( sz00 = sK3(sK0)
| sz10 = sK3(sK0)
| sK0 = sK3(sK0)
| ~ aNaturalNumber0(sK3(sK0))
| ~ doDivides0(sK3(sK0),sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f665,f114]) ).
fof(f670,plain,
( ~ doDivides0(sK3(sK0),sK0)
| sz10 = sK3(sK0)
| sK0 = sK3(sK0)
| ~ aNaturalNumber0(sK3(sK0))
| sz00 = sK3(sK0) ),
inference(forward_subsumption_resolution,[],[f668,f115]) ).
fof(f762,plain,
( sz10 = sK3(sK0)
| sK0 = sK3(sK0)
| ~ aNaturalNumber0(sK3(sK0))
| sz00 = sK3(sK0)
| sz00 = sK0
| sz10 = sK0
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(resolution,[],[f670,f138]) ).
fof(f766,plain,
( sK0 = sK3(sK0)
| ~ aNaturalNumber0(sK3(sK0))
| sz00 = sK3(sK0)
| sz00 = sK0
| sz10 = sK0
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f762,f141]) ).
fof(f767,plain,
( ~ aNaturalNumber0(sK3(sK0))
| sz00 = sK3(sK0)
| sz00 = sK0
| sz10 = sK0
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f766,f140]) ).
fof(f768,plain,
( sz00 = sK3(sK0)
| sz00 = sK0
| sz10 = sK0
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f767,f139]) ).
fof(f769,plain,
( sz00 = sK3(sK0)
| sz10 = sK0
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f768,f114]) ).
fof(f770,plain,
( sz00 = sK3(sK0)
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f769,f113]) ).
fof(f771,plain,
( sz00 = sK3(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f770,f348]) ).
fof(f772,plain,
sz00 = sK3(sK0),
inference(forward_subsumption_resolution,[],[f771,f115]) ).
fof(f779,plain,
( doDivides0(sz00,sK0)
| sz00 = sK0
| sz10 = sK0
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(superposition,[],[f138,f772]) ).
fof(f781,plain,
( sz00 = sK0
| sz10 = sK0
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f779,f367]) ).
fof(f785,plain,
( sz10 = sK0
| isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f781,f114]) ).
fof(f787,plain,
( isPrime0(sK0)
| ~ aNaturalNumber0(sK0) ),
inference(forward_subsumption_resolution,[],[f785,f113]) ).
fof(f788,plain,
~ aNaturalNumber0(sK0),
inference(forward_subsumption_resolution,[],[f787,f348]) ).
fof(f789,plain,
$false,
inference(forward_subsumption_resolution,[],[f788,f115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM481+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n010.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 20:06:32 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 2.86/1.32 % (1273760)Detected formulas, will run a generic FOF schedule.
% 2.86/1.32 % (1273771)dis-21_1_sil=8000:lcm=predicate:random_seed=838927770: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)
% 2.86/1.32 % (1273769)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=296381203:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.86/1.32 % (1273768)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2448649631:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.86/1.32 % (1273770)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3065013898:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.86/1.32 % (1273767)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=2141859573:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.86/1.32 % (1273765)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=980128531:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.86/1.32 % (1273766)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=2775339810:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.86/1.32 % (1273771)Instruction limit reached!
% 2.86/1.32 % (1273771)------------------------------
% 2.86/1.32 % (1273771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.32 % (1273771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.32 % (1273771)CaDiCaL version: 2.1.3
% 2.86/1.32 % (1273771)Termination reason: Instruction limit
% 2.86/1.32 % (1273771)Termination phase: Saturation
% 2.86/1.32 % (1273771)Time elapsed: 0.043 s
% 2.86/1.32 % (1273771)Peak memory usage: 90 MB
% 2.86/1.32 % (1273771)Instructions burned: 131 (million)
% 2.86/1.32 % (1273769)First to succeed.
% 2.86/1.32 % (1273769)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1273760"
% 2.86/1.32 % (1273768)Instruction limit reached!
% 2.86/1.32 % (1273768)------------------------------
% 2.86/1.32 % (1273768)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.32 % (1273768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.32 % (1273768)CaDiCaL version: 2.1.3
% 2.86/1.32 % (1273768)Termination reason: Instruction limit
% 2.86/1.32 % (1273768)Termination phase: Saturation
% 2.86/1.32 % (1273768)Time elapsed: 0.055 s
% 2.86/1.32 % (1273768)Peak memory usage: 88 MB
% 2.86/1.32 % (1273768)Instructions burned: 111 (million)
% 2.86/1.32 % (1273770)Instruction limit reached!
% 2.86/1.32 % (1273770)------------------------------
% 2.86/1.32 % (1273770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.32 % (1273770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.32 % (1273770)CaDiCaL version: 2.1.3
% 2.86/1.32 % (1273770)Termination reason: Instruction limit
% 2.86/1.32 % (1273770)Termination phase: Saturation
% 2.86/1.32 % (1273770)Time elapsed: 0.090 s
% 2.86/1.32 % (1273770)Peak memory usage: 90 MB
% 2.86/1.32 % (1273770)Instructions burned: 140 (million)
% 2.86/1.32 % (1273779)lrs+10_1_sil=8000:sp=occurrence:random_seed=2890672177:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.86/1.32 % (1273780)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1004791098:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.86/1.32 % (1273781)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2980591771:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.86/1.32 % (1273769)Refutation found. Thanks to Tanya!
% 2.86/1.32 % SZS status Theorem for theBenchmark
% 2.86/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.42 % (1273769)------------------------------
% 3.68/1.42 % (1273769)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.42 % (1273769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.42 % (1273769)CaDiCaL version: 2.1.3
% 3.68/1.42 % (1273769)Termination reason: Refutation
% 3.68/1.42 % (1273769)Time elapsed: 0.014 s
% 3.68/1.42 % (1273769)Peak memory usage: 88 MB
% 3.68/1.42 % (1273769)Instructions burned: 21 (million)
% 3.68/1.42 % (1273769)------------------------------
% 3.68/1.42 % (1273769)------------------------------
% 3.68/1.42 % (1273760)Success in time 0.444 s
% 3.68/1.42 % Vampire exiting
%------------------------------------------------------------------------------