%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM515+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 : n012.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 12:15:32 PM UTC 2026
% Result : Theorem 4.47s 1.22s
% Output : Refutation 5.00s
% 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(f55,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(f56,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)],[f55]) ).
fof(f59,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(f60,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(f65,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,[],[f56]) ).
fof(f66,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f67,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f66]) ).
fof(f102,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(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(flattening,[],[f102]) ).
fof(f110,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f111,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f110]) ).
fof(f130,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,[],[f59]) ).
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(flattening,[],[f130]) ).
fof(f132,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,[],[f60]) ).
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(flattening,[],[f132]) ).
fof(f139,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(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(flattening,[],[f139]) ).
fof(f141,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,[],[f65]) ).
fof(f142,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,[],[f141]) ).
fof(f143,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(f144,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(f145,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,[],[f131,f144,f143]) ).
fof(f161,plain,
! [X1,X2] :
( ( ? [X7] :
( aNaturalNumber0(X7)
& sdtasdt0(X2,X7) = X1 )
& doDivides0(X2,X1) )
| ~ sP1(X1,X2) ),
inference(nnf_transformation,[],[f144]) ).
fof(f162,plain,
! [X0,X1] :
( ( ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
& doDivides0(X1,X0) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f161]) ).
fof(f163,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))],[f162]) ).
fof(f164,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,[],[f143]) ).
fof(f165,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,[],[f164]) ).
fof(f166,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))],[f165]) ).
fof(f167,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,[],[f145]) ).
fof(f168,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))],[f167]) ).
fof(f169,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)],[f133]) ).
fof(f176,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)],[f140]) ).
fof(f177,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(f181,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f213,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,[],[f103]) ).
fof(f214,plain,
! [X2,X0,X1] :
( sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f224,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f246,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f247,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f248,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f249,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| doDivides0(X1,X0) ),
inference(cnf_transformation,[],[f163]) ).
fof(f252,plain,
! [X0] :
( ~ sP0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f166]) ).
fof(f259,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,[],[f168]) ).
fof(f268,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f169]) ).
fof(f322,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f176]) ).
fof(f329,plain,
xn != sdtsldt0(xn,xr),
inference(cnf_transformation,[],[f176]) ).
fof(f330,plain,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(cnf_transformation,[],[f177]) ).
fof(f335,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f142]) ).
fof(f338,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f142]) ).
fof(f339,plain,
~ doDivides0(xp,sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f142]) ).
fof(f661,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,[],[f213,f224]) ).
fof(f664,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,[],[f661,f214]) ).
fof(f666,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,[],[f664,f181]) ).
fof(f668,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,[],[f666,f181]) ).
fof(f988,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,[],[f668,f259]) ).
fof(f995,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,[],[f988]) ).
fof(f1002,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,[],[f995,f181]) ).
fof(f1009,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,[],[f1002,f246]) ).
fof(f1013,definition,
( spl22_27
<=> sP0(xp) ),
introduced(definition,[new_symbols(definition,[spl22_27])],[avatar_definition]) ).
fof(f1014,plain,
( sP0(xp)
| ~ spl22_27 ),
inference(avatar_component_clause,[],[f1013]) ).
fof(f1016,definition,
( spl22_28
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl22_28])],[avatar_definition]) ).
fof(f1017,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl22_28 ),
inference(avatar_component_clause,[],[f1016]) ).
fof(f1019,definition,
( spl22_29
<=> ! [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,[spl22_29])],[avatar_definition]) ).
fof(f1020,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) )
| ~ spl22_29 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f1021,plain,
( spl22_27
| ~ spl22_28
| spl22_29 ),
inference(avatar_split_clause,[],[f1009,f1019,f1016,f1013]) ).
fof(f1025,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl22_28 ),
inference(resolution,[],[f181,f1017]) ).
fof(f1037,plain,
( ~ aNaturalNumber0(xm)
| spl22_28 ),
inference(forward_subsumption_resolution,[],[f1025,f248]) ).
fof(f1038,plain,
( $false
| spl22_28 ),
inference(forward_subsumption_resolution,[],[f1037,f247]) ).
fof(f1039,plain,
spl22_28,
inference(avatar_contradiction_clause,[],[f1038]) ).
fof(f1041,plain,
( ~ isPrime0(xp)
| ~ spl22_27 ),
inference(resolution,[],[f1014,f252]) ).
fof(f1043,plain,
( $false
| ~ spl22_27 ),
inference(forward_subsumption_resolution,[],[f1041,f268]) ).
fof(f1044,plain,
~ spl22_27,
inference(avatar_contradiction_clause,[],[f1043]) ).
fof(f1045,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) )
| ~ spl22_29 ),
inference(resolution,[],[f1020,f213]) ).
fof(f1051,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) )
| ~ spl22_29 ),
inference(duplicate_literal_removal,[],[f1045]) ).
fof(f1056,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl22_29 ),
inference(forward_subsumption_resolution,[],[f1051,f214]) ).
fof(f1061,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl22_29 ),
inference(forward_subsumption_resolution,[],[f1056,f247]) ).
fof(f1081,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| xn = X0
| ~ sdtlseqdt0(X0,xn) )
| ~ spl22_29 ),
inference(forward_subsumption_resolution,[],[f1061,f248]) ).
fof(f1101,definition,
( spl22_40
<=> sP1(xm,xp) ),
introduced(definition,[new_symbols(definition,[spl22_40])],[avatar_definition]) ).
fof(f1102,plain,
( sP1(xm,xp)
| ~ spl22_40 ),
inference(avatar_component_clause,[],[f1101]) ).
fof(f1104,definition,
( spl22_41
<=> ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| xn = X0
| doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm)) ) ),
introduced(definition,[new_symbols(definition,[spl22_41])],[avatar_definition]) ).
fof(f1105,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| xn = X0
| doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm)) )
| ~ spl22_41 ),
inference(avatar_component_clause,[],[f1104]) ).
fof(f1106,plain,
( spl22_40
| spl22_41
| ~ spl22_29 ),
inference(avatar_split_clause,[],[f1081,f1019,f1104,f1101]) ).
fof(f1109,plain,
( doDivides0(xp,xm)
| ~ spl22_40 ),
inference(resolution,[],[f1102,f249]) ).
fof(f1111,plain,
( $false
| ~ spl22_40 ),
inference(forward_subsumption_resolution,[],[f1109,f335]) ).
fof(f1112,plain,
~ spl22_40,
inference(avatar_contradiction_clause,[],[f1111]) ).
fof(f1114,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| xn = sdtsldt0(xn,xr)
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ spl22_41 ),
inference(resolution,[],[f1105,f322]) ).
fof(f1118,plain,
( xn = sdtsldt0(xn,xr)
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ spl22_41 ),
inference(forward_subsumption_resolution,[],[f1114,f338]) ).
fof(f1120,plain,
( doDivides0(xp,sdtsldt0(xn,xr))
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ spl22_41 ),
inference(forward_subsumption_resolution,[],[f1118,f329]) ).
fof(f1122,plain,
( ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ spl22_41 ),
inference(forward_subsumption_resolution,[],[f1120,f339]) ).
fof(f1125,plain,
( $false
| ~ spl22_41 ),
inference(forward_subsumption_resolution,[],[f1122,f330]) ).
fof(f1126,plain,
~ spl22_41,
inference(avatar_contradiction_clause,[],[f1125]) ).
cnf(s25,plain,
( spl22_27
| ~ spl22_28
| spl22_29 ),
inference(sat_conversion,[],[f1021]) ).
cnf(s27,plain,
spl22_28,
inference(sat_conversion,[],[f1039]) ).
cnf(s29,plain,
~ spl22_27,
inference(sat_conversion,[],[f1044]) ).
cnf(s33,plain,
( ~ spl22_29
| spl22_40
| spl22_41 ),
inference(sat_conversion,[],[f1106]) ).
cnf(s36,plain,
~ spl22_40,
inference(sat_conversion,[],[f1112]) ).
cnf(s39,plain,
~ spl22_41,
inference(sat_conversion,[],[f1126]) ).
cnf(s40,plain,
~ spl22_29,
inference(rat,[],[s33,s39,s36]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s25,s40,s27,s29]) ).
fof(f1127,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM515+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 20:17:05 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.47/1.22 % (2704506)Detected formulas, will run a generic FOF schedule.
% 4.47/1.22 % (2704513)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=2661191028:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.47/1.22 % (2704517)dis-21_1_sil=8000:lcm=predicate:random_seed=641456171:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.47/1.22 % (2704514)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1109700012:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.47/1.22 % (2704516)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=391313:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.47/1.22 % (2704511)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=2651291067:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.47/1.22 % (2704515)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2935447025:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.47/1.22 % (2704512)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=1508259754:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.47/1.22 % (2704514)Instruction limit reached!
% 4.47/1.22 % (2704514)------------------------------
% 4.47/1.22 % (2704514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.47/1.22 % (2704514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.47/1.22 % (2704514)CaDiCaL version: 2.1.3
% 4.47/1.22 % (2704514)Termination reason: Instruction limit
% 4.47/1.22 % (2704514)Termination phase: Saturation
% 4.47/1.22 % (2704514)Time elapsed: 0.034 s
% 4.47/1.22 % (2704514)Peak memory usage: 89 MB
% 4.47/1.22 % (2704514)Instructions burned: 110 (million)
% 4.47/1.22 % (2704515)Instruction limit reached!
% 4.47/1.22 % (2704515)------------------------------
% 4.47/1.22 % (2704515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.47/1.22 % (2704515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.47/1.22 % (2704515)CaDiCaL version: 2.1.3
% 4.47/1.22 % (2704515)Termination reason: Instruction limit
% 4.47/1.22 % (2704515)Termination phase: Saturation
% 4.47/1.22 % (2704515)Time elapsed: 0.035 s
% 4.47/1.22 % (2704515)Peak memory usage: 88 MB
% 4.47/1.22 % (2704515)Instructions burned: 120 (million)
% 4.47/1.22 % (2704517)Instruction limit reached!
% 4.47/1.22 % (2704517)------------------------------
% 4.47/1.22 % (2704517)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.47/1.22 % (2704517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.47/1.22 % (2704517)CaDiCaL version: 2.1.3
% 4.47/1.22 % (2704517)Termination reason: Instruction limit
% 4.47/1.22 % (2704517)Termination phase: Saturation
% 4.47/1.22 % (2704517)Time elapsed: 0.042 s
% 4.47/1.22 % (2704517)Peak memory usage: 91 MB
% 4.47/1.22 % (2704517)Instructions burned: 131 (million)
% 4.47/1.22 % (2704516)Instruction limit reached!
% 4.47/1.22 % (2704516)------------------------------
% 4.47/1.22 % (2704516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.47/1.22 % (2704516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.47/1.22 % (2704516)CaDiCaL version: 2.1.3
% 4.47/1.22 % (2704516)Termination reason: Instruction limit
% 4.47/1.22 % (2704516)Termination phase: Saturation
% 4.47/1.22 % (2704516)Time elapsed: 0.049 s
% 4.47/1.22 % (2704516)Peak memory usage: 90 MB
% 4.47/1.22 % (2704516)Instructions burned: 142 (million)
% 4.47/1.22 % (2704526)lrs+10_1_sil=32000:urr=on:br=off:random_seed=113745468:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 4.47/1.22 % (2704525)lrs+10_1_sil=8000:sp=occurrence:random_seed=813872705:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.47/1.22 % (2704528)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=1454970888:s2a=on:i=248:s2at=1.23:gtg=position_2998 on theBenchmark for (2998ds/248Mi)
% 4.47/1.22 % (2704527)lrs+1011_1_sil=32000:sp=occurrence:random_seed=802244736:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 4.47/1.22 % (2704526)Instruction limit reached!
% 4.47/1.22 % (2704526)------------------------------
% 4.47/1.22 % (2704526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.47/1.22 % (2704526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.47/1.22 % (2704526)CaDiCaL version: 2.1.3
% 4.47/1.22 % (2704526)Termination reason: Instruction limit
% 4.47/1.22 % (2704526)Termination phase: Saturation
% 4.47/1.22 % (2704526)Time elapsed: 0.041 s
% 4.47/1.22 % (2704526)Peak memory usage: 94 MB
% 4.47/1.22 % (2704526)Instructions burned: 159 (million)
% 4.47/1.22 % (2704528)Instruction limit reached!
% 4.47/1.22 % (2704528)------------------------------
% 4.47/1.22 % (2704528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.47/1.22 % (2704528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.47/1.22 % (2704528)CaDiCaL version: 2.1.3
% 4.47/1.22 % (2704528)Termination reason: Instruction limit
% 4.47/1.22 % (2704528)Termination phase: Saturation
% 4.47/1.22 % (2704528)Time elapsed: 0.063 s
% 4.47/1.22 % (2704528)Peak memory usage: 95 MB
% 4.47/1.22 % (2704528)Instructions burned: 250 (million)
% 4.47/1.22 % (2704525)Instruction limit reached!
% 4.47/1.22 % (2704525)------------------------------
% 4.47/1.22 % (2704525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.47/1.22 % (2704525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.47/1.22 % (2704525)CaDiCaL version: 2.1.3
% 4.47/1.22 % (2704525)Termination reason: Instruction limit
% 4.47/1.22 % (2704525)Termination phase: Saturation
% 4.47/1.22 % (2704525)Time elapsed: 0.081 s
% 4.47/1.22 % (2704525)Peak memory usage: 91 MB
% 4.47/1.22 % (2704525)Instructions burned: 285 (million)
% 4.47/1.22 % (2704527)Instruction limit reached!
% 4.47/1.22 % (2704527)------------------------------
% 4.47/1.22 % (2704527)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.47/1.22 % (2704527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.47/1.22 % (2704527)CaDiCaL version: 2.1.3
% 4.47/1.22 % (2704527)Termination reason: Instruction limit
% 4.47/1.22 % (2704527)Termination phase: Saturation
% 4.47/1.22 % (2704527)Time elapsed: 0.111 s
% 4.47/1.22 % (2704527)Peak memory usage: 92 MB
% 4.47/1.22 % (2704527)Instructions burned: 326 (million)
% 4.47/1.22 % (2704533)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3391893378:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2997 on theBenchmark for (2997ds/294Mi)
% 4.47/1.22 % (2704534)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4167885557:i=2350_2996 on theBenchmark for (2996ds/2350Mi)
% 4.47/1.22 % (2704535)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1036039115:cts=off:i=113:fsr=off:ss=included:sgt=4_2996 on theBenchmark for (2996ds/113Mi)
% 4.47/1.22 % (2704536)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2061111239:i=127:av=off:fsr=off:sup=off_2996 on theBenchmark for (2996ds/127Mi)
% 4.47/1.22 % (2704535)Instruction limit reached!
% 4.47/1.22 % (2704535)------------------------------
% 4.47/1.22 % (2704535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.47/1.22 % (2704535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.47/1.22 % (2704535)CaDiCaL version: 2.1.3
% 4.47/1.22 % (2704535)Termination reason: Instruction limit
% 4.47/1.22 % (2704535)Termination phase: Saturation
% 4.47/1.22 % (2704535)Time elapsed: 0.036 s
% 4.47/1.22 % (2704535)Peak memory usage: 91 MB
% 4.47/1.22 % (2704535)Instructions burned: 115 (million)
% 4.47/1.22 % (2704533)Instruction limit reached!
% 4.47/1.22 % (2704533)------------------------------
% 4.47/1.22 % (2704533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.47/1.22 % (2704533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.47/1.22 % (2704533)CaDiCaL version: 2.1.3
% 4.47/1.22 % (2704533)Termination reason: Instruction limit
% 4.47/1.22 % (2704533)Termination phase: Saturation
% 4.47/1.22 % (2704533)Time elapsed: 0.091 s
% 4.47/1.22 % (2704533)Peak memory usage: 90 MB
% 4.47/1.22 % (2704533)Instructions burned: 297 (million)
% 4.47/1.22 % (2704536)Instruction limit reached!
% 4.47/1.22 % (2704536)------------------------------
% 4.47/1.22 % (2704536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.47/1.22 % (2704536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.47/1.22 % (2704536)CaDiCaL version: 2.1.3
% 4.47/1.22 % (2704536)Termination reason: Instruction limit
% 4.47/1.22 % (2704536)Termination phase: Saturation
% 4.47/1.22 % (2704536)Time elapsed: 0.034 s
% 4.47/1.22 % (2704536)Peak memory usage: 89 MB
% 4.47/1.22 % (2704536)Instructions burned: 130 (million)
% 4.47/1.22 % (2704512)First to succeed.
% 4.47/1.22 % (2704512)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2704506"
% 4.47/1.22 % (2704541)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=301998533:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2995 on theBenchmark for (2995ds/114Mi)
% 4.47/1.22 % (2704542)lrs+10_1_sil=8000:sp=occurrence:random_seed=1034776817:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2995 on theBenchmark for (2995ds/907Mi)
% 4.47/1.22 % (2704543)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3505736426:i=437:sd=1:aac=none:ss=included_2995 on theBenchmark for (2995ds/437Mi)
% 4.47/1.22 % (2704541)Instruction limit reached!
% 4.47/1.22 % (2704541)------------------------------
% 4.47/1.22 % (2704541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.47/1.22 % (2704541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.47/1.22 % (2704541)CaDiCaL version: 2.1.3
% 4.47/1.22 % (2704541)Termination reason: Instruction limit
% 4.47/1.22 % (2704541)Termination phase: Saturation
% 4.47/1.22 % (2704541)Time elapsed: 0.032 s
% 4.47/1.22 % (2704541)Peak memory usage: 89 MB
% 4.47/1.22 % (2704541)Instructions burned: 115 (million)
% 4.47/1.22 % (2704547)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2925371152:i=5202:ss=axioms:sgt=16_2994 on theBenchmark for (2994ds/5202Mi)
% 4.47/1.22 % (2704512)Refutation found. Thanks to Tanya!
% 4.47/1.22 % SZS status Theorem for theBenchmark
% 4.47/1.22 % SZS output start Proof for theBenchmark
% See solution above
% 5.00/1.32 % (2704512)------------------------------
% 5.00/1.32 % (2704512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.00/1.32 % (2704512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.00/1.32 % (2704512)CaDiCaL version: 2.1.3
% 5.00/1.32 % (2704512)Termination reason: Refutation
% 5.00/1.32 % (2704512)Time elapsed: 0.406 s
% 5.00/1.32 % (2704512)Peak memory usage: 130 MB
% 5.00/1.32 % (2704512)Instructions burned: 1096 (million)
% 5.00/1.32 % (2704512)------------------------------
% 5.00/1.32 % (2704512)------------------------------
% 5.00/1.32 % (2704506)Success in time 0.681 s
% 5.00/1.32 % Vampire exiting
%------------------------------------------------------------------------------