%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM517+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 : n003.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 12:15:33 PM UTC 2026
% Result : Theorem 6.55s 1.73s
% Output : Refutation 8.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 108 ( 21 unt; 7 def)
% Number of atoms : 630 ( 166 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 802 ( 280 ~; 301 |; 196 &)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 6 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 163 ( 0 sgn 120 !; 43 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != X1
& sdtlseqdt0(X0,X1) )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtpldt0(X2,X0) != sdtpldt0(X2,X1)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
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(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( ( ( X2 != sz00
& X2 != sz10
& ! [X3] :
( ( aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) )
=> ( X3 = sz10
| X3 = X2 ) ) )
| isPrime0(X2) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X0,X1) = sdtasdt0(X2,X3) )
| doDivides0(X2,sdtasdt0(X0,X1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [X3] :
( aNaturalNumber0(X3)
& X0 = sdtasdt0(X2,X3) )
& doDivides0(X2,X0) )
| ( ? [X3] :
( aNaturalNumber0(X3)
& X1 = sdtasdt0(X2,X3) )
& doDivides0(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
fof(f41,axiom,
( xp != sz00
& xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f53,axiom,
( ~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> sdtsldt0(xn,xr) = xn )
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtsldt0(xn,xr),X0) = xn )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2504) ).
fof(f54,axiom,
( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2529) ).
fof(f56,conjecture,
( ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtsldt0(xn,xr) = sdtasdt0(xp,X0) )
| doDivides0(xp,sdtsldt0(xn,xr)) ) )
| ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xp,X0) )
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ( ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtsldt0(xn,xr) = sdtasdt0(xp,X0) )
| doDivides0(xp,sdtsldt0(xn,xr)) ) )
| ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xp,X0) )
| doDivides0(xp,xm) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( ( ( X2 != sz00
& X2 != sz10
& ! [X3] :
( ( aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) )
=> ( X3 = sz10
| X3 = X2 ) ) )
| isPrime0(X2) )
& ( ? [X5] :
( aNaturalNumber0(X5)
& sdtasdt0(X0,X1) = sdtasdt0(X2,X5) )
| doDivides0(X2,sdtasdt0(X0,X1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [X6] :
( aNaturalNumber0(X6)
& sdtasdt0(X2,X6) = X0 )
& doDivides0(X2,X0) )
| ( ? [X7] :
( aNaturalNumber0(X7)
& sdtasdt0(X2,X7) = X1 )
& doDivides0(X2,X1) ) ) ) ) ),
inference(rectify,[],[f40]) ).
fof(f61,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(rectify,[],[f41]) ).
fof(f66,plain,
~ ( ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtsldt0(xn,xr) = sdtasdt0(xp,X0) )
| doDivides0(xp,sdtsldt0(xn,xr)) ) )
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xp,X1) )
| doDivides0(xp,xm) ),
inference(rectify,[],[f57]) ).
fof(f67,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f68,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f67]) ).
fof(f103,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt0(X2,X0) != sdtpldt0(X2,X1)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) )
| ~ aNaturalNumber0(X2) )
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt0(X2,X0) != sdtpldt0(X2,X1)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) )
| ~ aNaturalNumber0(X2) )
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f103]) ).
fof(f111,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f112,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f111]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ( ? [X6] :
( aNaturalNumber0(X6)
& sdtasdt0(X2,X6) = X0 )
& doDivides0(X2,X0) )
| ( ? [X7] :
( aNaturalNumber0(X7)
& sdtasdt0(X2,X7) = X1 )
& doDivides0(X2,X1) )
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ( sz00 = X2
| sz10 = X2
| ? [X3] :
( sz10 != X3
& X2 != X3
& aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) ) )
& ~ isPrime0(X2) )
| ( ! [X5] :
( ~ aNaturalNumber0(X5)
| sdtasdt0(X0,X1) != sdtasdt0(X2,X5) )
& ~ doDivides0(X2,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f60]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ( ? [X6] :
( aNaturalNumber0(X6)
& sdtasdt0(X2,X6) = X0 )
& doDivides0(X2,X0) )
| ( ? [X7] :
( aNaturalNumber0(X7)
& sdtasdt0(X2,X7) = X1 )
& doDivides0(X2,X1) )
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ( sz00 = X2
| sz10 = X2
| ? [X3] :
( sz10 != X3
& X2 != X3
& aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) ) )
& ~ isPrime0(X2) )
| ( ! [X5] :
( ~ aNaturalNumber0(X5)
| sdtasdt0(X0,X1) != sdtasdt0(X2,X5) )
& ~ doDivides0(X2,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f131]) ).
fof(f133,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(ennf_transformation,[],[f61]) ).
fof(f134,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(flattening,[],[f133]) ).
fof(f140,plain,
( xn != sdtsldt0(xn,xr)
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtsldt0(xn,xr),X0) = xn )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(ennf_transformation,[],[f53]) ).
fof(f141,plain,
( xn != sdtsldt0(xn,xr)
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtsldt0(xn,xr),X0) = xn )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(flattening,[],[f140]) ).
fof(f144,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xp,X0) != sdtsldt0(xn,xr) )
& ~ doDivides0(xp,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ! [X1] :
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xp,X1) )
& ~ doDivides0(xp,xm) ),
inference(ennf_transformation,[],[f66]) ).
fof(f145,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xp,X0) != sdtsldt0(xn,xr) )
& ~ doDivides0(xp,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ! [X1] :
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xp,X1) )
& ~ doDivides0(xp,xm) ),
inference(flattening,[],[f144]) ).
fof(f146,definition,
! [X2] :
( ( ( sz00 = X2
| sz10 = X2
| ? [X3] :
( sz10 != X3
& X2 != X3
& aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) ) )
& ~ isPrime0(X2) )
| ~ sP0(X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f147,definition,
! [X1,X2] :
( ( ? [X7] :
( aNaturalNumber0(X7)
& sdtasdt0(X2,X7) = X1 )
& doDivides0(X2,X1) )
| ~ sP1(X1,X2) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f148,plain,
! [X0,X1,X2] :
( ( ? [X6] :
( aNaturalNumber0(X6)
& sdtasdt0(X2,X6) = X0 )
& doDivides0(X2,X0) )
| sP1(X1,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP0(X2)
| ( ! [X5] :
( ~ aNaturalNumber0(X5)
| sdtasdt0(X0,X1) != sdtasdt0(X2,X5) )
& ~ doDivides0(X2,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(definition_folding,[],[f132,f147,f146]) ).
fof(f164,plain,
! [X1,X2] :
( ( ? [X7] :
( aNaturalNumber0(X7)
& sdtasdt0(X2,X7) = X1 )
& doDivides0(X2,X1) )
| ~ sP1(X1,X2) ),
inference(nnf_transformation,[],[f147]) ).
fof(f165,plain,
! [X0,X1] :
( ( ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
& doDivides0(X1,X0) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f164]) ).
fof(f166,plain,
! [X0,X1] :
( ( aNaturalNumber0(sK6(X0,X1))
& sdtasdt0(X1,sK6(X0,X1)) = X0
& doDivides0(X1,X0) )
| ~ sP1(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f165]) ).
fof(f167,plain,
! [X2] :
( ( ( sz00 = X2
| sz10 = X2
| ? [X3] :
( sz10 != X3
& X2 != X3
& aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) ) )
& ~ isPrime0(X2) )
| ~ sP0(X2) ),
inference(nnf_transformation,[],[f146]) ).
fof(f168,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) )
| ~ sP0(X0) ),
inference(rectify,[],[f167]) ).
fof(f169,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ( sz10 != sK7(X0)
& sK7(X0) != X0
& aNaturalNumber0(sK7(X0))
& aNaturalNumber0(sK8(X0))
& sdtasdt0(sK7(X0),sK8(X0)) = X0
& doDivides0(sK7(X0),X0) ) )
& ~ isPrime0(X0) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X1,sK7(X0)),skolemize(X2,sK8(X0))],[f168]) ).
fof(f170,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) )
| sP1(X1,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP0(X2)
| ( ! [X4] :
( ~ aNaturalNumber0(X4)
| sdtasdt0(X0,X1) != sdtasdt0(X2,X4) )
& ~ doDivides0(X2,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(rectify,[],[f148]) ).
fof(f171,plain,
! [X0,X1,X2] :
( ( aNaturalNumber0(sK9(X0,X2))
& sdtasdt0(X2,sK9(X0,X2)) = X0
& doDivides0(X2,X0) )
| sP1(X1,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP0(X2)
| ( ! [X4] :
( ~ aNaturalNumber0(X4)
| sdtasdt0(X0,X1) != sdtasdt0(X2,X4) )
& ~ doDivides0(X2,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X2))],[f170]) ).
fof(f172,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& aNaturalNumber0(sK10)
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK10)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10)],[f134]) ).
fof(f179,plain,
( xn != sdtsldt0(xn,xr)
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sK20)
& xn = sdtpldt0(sdtsldt0(xn,xr),sK20)
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X0,sK20)],[f141]) ).
fof(f180,plain,
( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sK21)
& sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sK21)
& doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X0,sK21)],[f54]) ).
fof(f185,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f217,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f218,plain,
! [X2,X0,X1] :
( sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f228,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f250,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f251,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f252,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f253,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| doDivides0(X1,X0) ),
inference(cnf_transformation,[],[f166]) ).
fof(f256,plain,
! [X0] :
( ~ sP0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f169]) ).
fof(f263,plain,
! [X2,X0,X1] :
( ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1(X1,X2)
| doDivides0(X2,X0)
| sP0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f171]) ).
fof(f272,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f172]) ).
fof(f326,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f179]) ).
fof(f333,plain,
xn != sdtsldt0(xn,xr),
inference(cnf_transformation,[],[f179]) ).
fof(f334,plain,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(cnf_transformation,[],[f180]) ).
fof(f347,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f145]) ).
fof(f350,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f145]) ).
fof(f351,plain,
~ doDivides0(xp,sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f145]) ).
fof(f649,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| iLess0(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| ~ aNaturalNumber0(sdtpldt0(X1,X0))
| ~ aNaturalNumber0(sdtpldt0(X2,X0)) ),
inference(resolution,[],[f217,f228]) ).
fof(f650,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| iLess0(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| ~ aNaturalNumber0(sdtpldt0(X1,X0))
| ~ aNaturalNumber0(sdtpldt0(X2,X0)) ),
inference(forward_subsumption_resolution,[],[f649,f218]) ).
fof(f652,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| iLess0(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| ~ aNaturalNumber0(sdtpldt0(X2,X0)) ),
inference(forward_subsumption_resolution,[],[f650,f185]) ).
fof(f654,plain,
! [X2,X0,X1] :
( iLess0(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f652,f185]) ).
fof(f657,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sP1(X1,xp)
| doDivides0(xp,X0)
| sP0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f654,f263]) ).
fof(f658,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sP1(X1,xp)
| doDivides0(xp,X0)
| sP0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(duplicate_literal_removal,[],[f657]) ).
fof(f660,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| sP1(X1,xp)
| doDivides0(xp,X0)
| sP0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f658,f185]) ).
fof(f662,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sP1(X1,xp)
| doDivides0(xp,X0)
| sP0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f660,f250]) ).
fof(f665,definition,
( spl23_25
<=> sP0(xp) ),
introduced(definition,[new_symbols(definition,[spl23_25])],[avatar_definition]) ).
fof(f666,plain,
( sP0(xp)
| ~ spl23_25 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f668,definition,
( spl23_26
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl23_26])],[avatar_definition]) ).
fof(f669,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl23_26 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f671,definition,
( spl23_27
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| doDivides0(xp,X0)
| sP1(X1,xp)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm)) ) ),
introduced(definition,[new_symbols(definition,[spl23_27])],[avatar_definition]) ).
fof(f672,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| doDivides0(xp,X0)
| sP1(X1,xp)
| sdtpldt0(X0,X1) = sdtpldt0(xn,xm) )
| ~ spl23_27 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f673,plain,
( spl23_25
| ~ spl23_26
| spl23_27 ),
inference(avatar_split_clause,[],[f662,f671,f668,f665]) ).
fof(f683,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl23_26 ),
inference(resolution,[],[f185,f669]) ).
fof(f688,plain,
( ~ aNaturalNumber0(xm)
| spl23_26 ),
inference(forward_subsumption_resolution,[],[f683,f252]) ).
fof(f689,plain,
( $false
| spl23_26 ),
inference(forward_subsumption_resolution,[],[f688,f251]) ).
fof(f690,plain,
spl23_26,
inference(avatar_contradiction_clause,[],[f689]) ).
fof(f729,plain,
( ~ isPrime0(xp)
| ~ spl23_25 ),
inference(resolution,[],[f666,f256]) ).
fof(f731,plain,
( $false
| ~ spl23_25 ),
inference(forward_subsumption_resolution,[],[f729,f272]) ).
fof(f732,plain,
~ spl23_25,
inference(avatar_contradiction_clause,[],[f731]) ).
fof(f733,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| sdtpldt0(xn,xm) = sdtpldt0(X0,xm)
| ~ aNaturalNumber0(xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) )
| ~ spl23_27 ),
inference(resolution,[],[f672,f217]) ).
fof(f734,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| sdtpldt0(xn,xm) = sdtpldt0(X0,xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl23_27 ),
inference(duplicate_literal_removal,[],[f733]) ).
fof(f735,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl23_27 ),
inference(forward_subsumption_resolution,[],[f734,f218]) ).
fof(f736,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl23_27 ),
inference(forward_subsumption_resolution,[],[f735,f251]) ).
fof(f737,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| xn = X0
| ~ sdtlseqdt0(X0,xn) )
| ~ spl23_27 ),
inference(forward_subsumption_resolution,[],[f736,f252]) ).
fof(f739,definition,
( spl23_34
<=> sP1(xm,xp) ),
introduced(definition,[new_symbols(definition,[spl23_34])],[avatar_definition]) ).
fof(f740,plain,
( sP1(xm,xp)
| ~ spl23_34 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f742,definition,
( spl23_35
<=> ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| xn = X0
| doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm)) ) ),
introduced(definition,[new_symbols(definition,[spl23_35])],[avatar_definition]) ).
fof(f743,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| xn = X0
| doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm)) )
| ~ spl23_35 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f744,plain,
( spl23_34
| spl23_35
| ~ spl23_27 ),
inference(avatar_split_clause,[],[f737,f671,f742,f739]) ).
fof(f746,plain,
( doDivides0(xp,xm)
| ~ spl23_34 ),
inference(resolution,[],[f740,f253]) ).
fof(f748,plain,
( $false
| ~ spl23_34 ),
inference(forward_subsumption_resolution,[],[f746,f347]) ).
fof(f749,plain,
~ spl23_34,
inference(avatar_contradiction_clause,[],[f748]) ).
fof(f751,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| xn = sdtsldt0(xn,xr)
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ spl23_35 ),
inference(resolution,[],[f743,f326]) ).
fof(f755,plain,
( xn = sdtsldt0(xn,xr)
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ spl23_35 ),
inference(forward_subsumption_resolution,[],[f751,f350]) ).
fof(f757,plain,
( doDivides0(xp,sdtsldt0(xn,xr))
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ spl23_35 ),
inference(forward_subsumption_resolution,[],[f755,f333]) ).
fof(f759,plain,
( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ spl23_35 ),
inference(forward_subsumption_resolution,[],[f757,f351]) ).
fof(f762,plain,
( $false
| ~ spl23_35 ),
inference(forward_subsumption_resolution,[],[f759,f334]) ).
fof(f763,plain,
~ spl23_35,
inference(avatar_contradiction_clause,[],[f762]) ).
cnf(s22,plain,
( spl23_25
| ~ spl23_26
| spl23_27 ),
inference(sat_conversion,[],[f673]) ).
cnf(s25,plain,
spl23_26,
inference(sat_conversion,[],[f690]) ).
cnf(s33,plain,
~ spl23_25,
inference(sat_conversion,[],[f732]) ).
cnf(s34,plain,
( ~ spl23_27
| spl23_34
| spl23_35 ),
inference(sat_conversion,[],[f744]) ).
cnf(s36,plain,
~ spl23_34,
inference(sat_conversion,[],[f749]) ).
cnf(s39,plain,
~ spl23_35,
inference(sat_conversion,[],[f763]) ).
cnf(s40,plain,
~ spl23_27,
inference(rat,[],[s34,s39,s36]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s22,s40,s25,s33]) ).
fof(f764,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM517+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:19:26 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 6.55/1.73 % (894262)Detected formulas, will run a generic FOF schedule.
% 6.55/1.73 % (894268)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=363095818:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.55/1.73 % (894267)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=2859882638:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.55/1.73 % (894273)dis-21_1_sil=8000:lcm=predicate:random_seed=1900420419: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)
% 6.55/1.73 % (894269)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=4026087367:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.55/1.73 % (894271)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=145450531:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.55/1.73 % (894270)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1521016362:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.55/1.73 % (894272)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3095981909:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.55/1.73 % (894270)Instruction limit reached!
% 6.55/1.73 % (894270)------------------------------
% 6.55/1.73 % (894270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.73 % (894270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.73 % (894270)CaDiCaL version: 2.1.3
% 6.55/1.73 % (894270)Termination reason: Instruction limit
% 6.55/1.73 % (894270)Termination phase: Saturation
% 6.55/1.73 % (894270)Time elapsed: 0.064 s
% 6.55/1.73 % (894270)Peak memory usage: 89 MB
% 6.55/1.73 % (894270)Instructions burned: 111 (million)
% 6.55/1.73 % (894271)Instruction limit reached!
% 6.55/1.73 % (894271)------------------------------
% 6.55/1.73 % (894271)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.73 % (894271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.73 % (894271)CaDiCaL version: 2.1.3
% 6.55/1.73 % (894271)Termination reason: Instruction limit
% 6.55/1.73 % (894271)Termination phase: Saturation
% 6.55/1.73 % (894271)Time elapsed: 0.065 s
% 6.55/1.73 % (894271)Peak memory usage: 88 MB
% 6.55/1.73 % (894271)Instructions burned: 121 (million)
% 6.55/1.73 % (894273)Instruction limit reached!
% 6.55/1.73 % (894273)------------------------------
% 6.55/1.73 % (894273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.73 % (894273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.73 % (894273)CaDiCaL version: 2.1.3
% 6.55/1.73 % (894273)Termination reason: Instruction limit
% 6.55/1.73 % (894273)Termination phase: Saturation
% 6.55/1.73 % (894273)Time elapsed: 0.077 s
% 6.55/1.73 % (894273)Peak memory usage: 91 MB
% 6.55/1.73 % (894273)Instructions burned: 129 (million)
% 6.55/1.73 % (894272)Instruction limit reached!
% 6.55/1.73 % (894272)------------------------------
% 6.55/1.73 % (894272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.73 % (894272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.73 % (894272)CaDiCaL version: 2.1.3
% 6.55/1.73 % (894272)Termination reason: Instruction limit
% 6.55/1.73 % (894272)Termination phase: Saturation
% 6.55/1.73 % (894272)Time elapsed: 0.111 s
% 6.55/1.73 % (894272)Peak memory usage: 90 MB
% 6.55/1.73 % (894272)Instructions burned: 140 (million)
% 6.55/1.73 % (894281)lrs+10_1_sil=8000:sp=occurrence:random_seed=400485093:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.55/1.73 % (894282)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3465966404:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.55/1.73 % (894284)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1759736010:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.55/1.73 % (894283)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4041590826:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.55/1.73 % (894282)Instruction limit reached!
% 6.55/1.73 % (894282)------------------------------
% 6.55/1.73 % (894282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.73 % (894282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.73 % (894282)CaDiCaL version: 2.1.3
% 6.55/1.73 % (894282)Termination reason: Instruction limit
% 6.55/1.73 % (894282)Termination phase: Saturation
% 6.55/1.73 % (894282)Time elapsed: 0.076 s
% 6.55/1.73 % (894282)Peak memory usage: 94 MB
% 6.55/1.73 % (894282)Instructions burned: 159 (million)
% 6.55/1.73 % (894284)Instruction limit reached!
% 6.55/1.73 % (894284)------------------------------
% 6.55/1.73 % (894284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.73 % (894284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.73 % (894284)CaDiCaL version: 2.1.3
% 6.55/1.73 % (894284)Termination reason: Instruction limit
% 6.55/1.73 % (894284)Termination phase: Saturation
% 6.55/1.73 % (894284)Time elapsed: 0.061 s
% 6.55/1.73 % (894284)Peak memory usage: 95 MB
% 6.55/1.73 % (894284)Instructions burned: 250 (million)
% 6.55/1.73 % (894281)Instruction limit reached!
% 6.55/1.73 % (894281)------------------------------
% 6.55/1.73 % (894281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.73 % (894281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.73 % (894281)CaDiCaL version: 2.1.3
% 6.55/1.73 % (894281)Termination reason: Instruction limit
% 6.55/1.73 % (894281)Termination phase: Saturation
% 6.55/1.73 % (894281)Time elapsed: 0.157 s
% 6.55/1.73 % (894281)Peak memory usage: 91 MB
% 6.55/1.73 % (894281)Instructions burned: 286 (million)
% 6.55/1.73 % (894290)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2055443002:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.55/1.73 % (894283)Instruction limit reached!
% 6.55/1.73 % (894283)------------------------------
% 6.55/1.73 % (894283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.73 % (894283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.73 % (894283)CaDiCaL version: 2.1.3
% 6.55/1.73 % (894283)Termination reason: Instruction limit
% 6.55/1.73 % (894283)Termination phase: Saturation
% 6.55/1.73 % (894283)Time elapsed: 0.197 s
% 6.55/1.73 % (894283)Peak memory usage: 92 MB
% 6.55/1.73 % (894283)Instructions burned: 325 (million)
% 6.55/1.73 % (894289)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1822680336:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.55/1.73 % (894291)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2401494625:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.55/1.73 % (894291)Instruction limit reached!
% 6.55/1.73 % (894291)------------------------------
% 6.55/1.73 % (894291)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.73 % (894291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.73 % (894291)CaDiCaL version: 2.1.3
% 6.55/1.73 % (894291)Termination reason: Instruction limit
% 6.55/1.73 % (894291)Termination phase: Saturation
% 6.55/1.73 % (894291)Time elapsed: 0.066 s
% 6.55/1.73 % (894291)Peak memory usage: 91 MB
% 6.55/1.73 % (894291)Instructions burned: 113 (million)
% 6.55/1.73 % (894293)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3732879237:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.55/1.73 % (894289)Instruction limit reached!
% 6.55/1.73 % (894289)------------------------------
% 6.55/1.73 % (894289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.73 % (894289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.73 % (894289)CaDiCaL version: 2.1.3
% 6.55/1.73 % (894289)Termination reason: Instruction limit
% 6.55/1.73 % (894289)Termination phase: Saturation
% 6.55/1.73 % (894289)Time elapsed: 0.167 s
% 6.55/1.73 % (894289)Peak memory usage: 90 MB
% 6.55/1.73 % (894289)Instructions burned: 294 (million)
% 6.55/1.73 % (894293)Instruction limit reached!
% 6.55/1.73 % (894293)------------------------------
% 6.55/1.73 % (894293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.73 % (894293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.73 % (894293)CaDiCaL version: 2.1.3
% 6.55/1.73 % (894293)Termination reason: Instruction limit
% 6.55/1.73 % (894293)Termination phase: Saturation
% 6.55/1.73 % (894293)Time elapsed: 0.063 s
% 6.55/1.73 % (894293)Peak memory usage: 89 MB
% 6.55/1.73 % (894293)Instructions burned: 127 (million)
% 6.55/1.73 % (894268)First to succeed.
% 6.55/1.73 % (894268)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-894262"
% 6.55/1.73 % (894297)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=973939298:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.55/1.73 % (894298)lrs+10_1_sil=8000:sp=occurrence:random_seed=3367931444:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.55/1.73 % (894290)Also succeeded, but the first one will report.
% 6.55/1.73 % (894267)Also succeeded, but the first one will report.
% 6.55/1.73 % (894297)Instruction limit reached!
% 6.55/1.73 % (894297)------------------------------
% 6.55/1.73 % (894297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.55/1.73 % (894297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.55/1.73 % (894297)CaDiCaL version: 2.1.3
% 6.55/1.73 % (894297)Termination reason: Instruction limit
% 6.55/1.73 % (894297)Termination phase: Saturation
% 6.55/1.73 % (894297)Time elapsed: 0.060 s
% 6.55/1.73 % (894297)Peak memory usage: 89 MB
% 6.55/1.73 % (894297)Instructions burned: 115 (million)
% 6.55/1.73 % (894299)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=337181578:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.55/1.73 % (894268)Refutation found. Thanks to Tanya!
% 6.55/1.73 % SZS status Theorem for theBenchmark
% 6.55/1.73 % SZS output start Proof for theBenchmark
% See solution above
% 8.11/1.82 % (894268)------------------------------
% 8.11/1.82 % (894268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.11/1.82 % (894268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.11/1.82 % (894268)CaDiCaL version: 2.1.3
% 8.11/1.82 % (894268)Termination reason: Refutation
% 8.11/1.82 % (894268)Time elapsed: 0.678 s
% 8.11/1.82 % (894268)Peak memory usage: 129 MB
% 8.11/1.82 % (894268)Instructions burned: 1021 (million)
% 8.11/1.82 % (894268)------------------------------
% 8.11/1.82 % (894268)------------------------------
% 8.11/1.82 % (894262)Success in time 1.11 s
% 8.11/1.82 % Vampire exiting
%------------------------------------------------------------------------------