%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM506+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 : n002.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 12:15:30 PM UTC 2026
% Result : Theorem 10.65s 2.17s
% Output : Refutation 11.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 22
% Syntax : Number of formulae : 147 ( 34 unt; 7 def)
% Number of atoms : 711 ( 174 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 878 ( 314 ~; 348 |; 188 &)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 193 ( 0 sgn 149 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtpldt0(X0,X1) = sdtpldt0(X0,X2)
| sdtpldt0(X1,X0) = sdtpldt0(X2,X0) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
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(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X0,X1)
& X1 != sz00 )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivLE) ).
fof(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(f45,axiom,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f47,axiom,
( xk != sz00
& xk != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
fof(f48,axiom,
( aNaturalNumber0(xr)
& ? [X0] :
( aNaturalNumber0(X0)
& xk = sdtasdt0(xr,X0) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xr = sdtasdt0(X0,X1) )
| doDivides0(X0,xr) ) )
=> ( X0 = sz10
| X0 = xr ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xr,X0) = xk )
& ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X0) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(f50,axiom,
( xk != xp
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xk,X0) = xp )
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2377) ).
fof(f51,conjecture,
( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xr,X0) )
| doDivides0(xr,xn)
| ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xr,X0) )
| doDivides0(xr,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f52,negated_conjecture,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xr,X0) )
| doDivides0(xr,xn)
| ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xr,X0) )
| doDivides0(xr,xm) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f55,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(f58,plain,
( aNaturalNumber0(xr)
& ? [X0] :
( aNaturalNumber0(X0)
& xk = sdtasdt0(xr,X0) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = xr )
| doDivides0(X1,xr) ) )
=> ( sz10 = X1
| xr = X1 ) )
& isPrime0(xr) ),
inference(rectify,[],[f48]) ).
fof(f59,plain,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xr,X0) = xk )
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(rectify,[],[f49]) ).
fof(f60,plain,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xr,X0) )
| doDivides0(xr,xn)
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xr,X1) )
| doDivides0(xr,xm) ),
inference(rectify,[],[f52]) ).
fof(f61,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f62,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f61]) ).
fof(f78,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
& sdtpldt0(X1,X0) != sdtpldt0(X2,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f79,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
& sdtpldt0(X1,X0) != sdtpldt0(X2,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f78]) ).
fof(f91,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f92,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f94,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f93]) ).
fof(f97,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(f98,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,[],[f97]) ).
fof(f105,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f106,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f105]) ).
fof(f117,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f118,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f117]) ).
fof(f125,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,[],[f55]) ).
fof(f126,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,[],[f125]) ).
fof(f132,plain,
( aNaturalNumber0(xr)
& ? [X0] :
( aNaturalNumber0(X0)
& xk = sdtasdt0(xr,X0) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( sz10 = X1
| xr = X1
| ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != xr )
& ~ doDivides0(X1,xr) ) )
& isPrime0(xr) ),
inference(ennf_transformation,[],[f58]) ).
fof(f133,plain,
( aNaturalNumber0(xr)
& ? [X0] :
( aNaturalNumber0(X0)
& xk = sdtasdt0(xr,X0) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( sz10 = X1
| xr = X1
| ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != xr )
& ~ doDivides0(X1,xr) ) )
& isPrime0(xr) ),
inference(flattening,[],[f132]) ).
fof(f134,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xr,X0) )
& ~ doDivides0(xr,xn)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xr,X1) )
& ~ doDivides0(xr,xm) ),
inference(ennf_transformation,[],[f60]) ).
fof(f135,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(f136,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(f137,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,[],[f126,f136,f135]) ).
fof(f153,plain,
! [X1,X2] :
( ( ? [X7] :
( aNaturalNumber0(X7)
& sdtasdt0(X2,X7) = X1 )
& doDivides0(X2,X1) )
| ~ sP1(X1,X2) ),
inference(nnf_transformation,[],[f136]) ).
fof(f154,plain,
! [X0,X1] :
( ( ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
& doDivides0(X1,X0) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f153]) ).
fof(f155,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))],[f154]) ).
fof(f156,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,[],[f135]) ).
fof(f157,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,[],[f156]) ).
fof(f158,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))],[f157]) ).
fof(f159,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,[],[f137]) ).
fof(f160,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))],[f159]) ).
fof(f163,plain,
( aNaturalNumber0(xr)
& aNaturalNumber0(sK13)
& xk = sdtasdt0(xr,sK13)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( sz10 = X1
| xr = X1
| ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != xr )
& ~ doDivides0(X1,xr) ) )
& isPrime0(xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f133]) ).
fof(f164,plain,
( aNaturalNumber0(sK14)
& xk = sdtpldt0(xr,sK14)
& aNaturalNumber0(sK15)
& sdtasdt0(xn,xm) = sdtasdt0(xr,sK15)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f59]) ).
fof(f165,plain,
( xk != xp
& aNaturalNumber0(sK16)
& xp = sdtpldt0(xk,sK16)
& sdtlseqdt0(xk,xp) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f50]) ).
fof(f169,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f184,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f197,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f203,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f212,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f222,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f234,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f235,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f236,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f237,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| doDivides0(X1,X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f240,plain,
! [X0] :
( ~ sP0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f247,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,[],[f160]) ).
fof(f274,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f275,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f279,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f280,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f163]) ).
fof(f285,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f163]) ).
fof(f288,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f163]) ).
fof(f289,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f164]) ).
fof(f290,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,sK15),
inference(cnf_transformation,[],[f164]) ).
fof(f294,plain,
sdtlseqdt0(xk,xp),
inference(cnf_transformation,[],[f165]) ).
fof(f297,plain,
xp != xk,
inference(cnf_transformation,[],[f165]) ).
fof(f298,plain,
~ doDivides0(xr,xm),
inference(cnf_transformation,[],[f134]) ).
fof(f300,plain,
~ doDivides0(xr,xn),
inference(cnf_transformation,[],[f134]) ).
fof(f314,definition,
! [X0] : sF17(X0) = sdtasdt0(xr,X0),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f315,plain,
! [X0] : sdtasdt0(xr,X0) = sF17(X0),
inference(reorient_equations,[],[f314]) ).
fof(f357,plain,
sdtasdt0(xn,xm) = sF17(sK15),
inference(superposition,[],[f315,f290]) ).
fof(f359,plain,
sdtasdt0(xp,xk) = sF17(sK15),
inference(forward_demodulation,[],[f357,f274]) ).
fof(f365,plain,
doDivides0(xr,sdtasdt0(xp,xk)),
inference(superposition,[],[f289,f274]) ).
fof(f366,plain,
doDivides0(xr,sF17(sK15)),
inference(forward_demodulation,[],[f365,f359]) ).
fof(f499,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X0,X2)
| iLess0(sdtpldt0(X0,X1),sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(resolution,[],[f212,f203]) ).
fof(f500,plain,
! [X2,X0,X1] :
( iLess0(sdtpldt0(X0,X1),sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(forward_subsumption_resolution,[],[f499,f184]) ).
fof(f504,plain,
! [X2,X0,X1] :
( iLess0(sdtpldt0(X0,X1),sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(forward_subsumption_resolution,[],[f500,f169]) ).
fof(f508,plain,
! [X2,X0,X1] :
( iLess0(sdtpldt0(X0,X1),sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(forward_subsumption_resolution,[],[f504,f169]) ).
fof(f516,plain,
( sdtlseqdt0(xr,xk)
| sz00 = xk
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f222,f285]) ).
fof(f528,plain,
( sdtlseqdt0(xr,xk)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f516,f279]) ).
fof(f537,plain,
( sdtlseqdt0(xr,xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f528,f288]) ).
fof(f559,plain,
sdtlseqdt0(xr,xk),
inference(forward_subsumption_resolution,[],[f537,f275]) ).
fof(f831,definition,
( spl18_25
<=> sP0(xr) ),
introduced(definition,[new_symbols(definition,[spl18_25])],[avatar_definition]) ).
fof(f832,plain,
( ~ sP0(xr)
| spl18_25 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f833,plain,
( sP0(xr)
| ~ spl18_25 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f931,plain,
( ~ isPrime0(xr)
| ~ spl18_25 ),
inference(resolution,[],[f833,f240]) ).
fof(f932,plain,
( $false
| ~ spl18_25 ),
inference(forward_subsumption_resolution,[],[f931,f280]) ).
fof(f933,plain,
~ spl18_25,
inference(avatar_contradiction_clause,[],[f932]) ).
fof(f1024,definition,
( spl18_50
<=> sP1(xm,xr) ),
introduced(definition,[new_symbols(definition,[spl18_50])],[avatar_definition]) ).
fof(f1026,plain,
( sP1(xm,xr)
| ~ spl18_50 ),
inference(avatar_component_clause,[],[f1024]) ).
fof(f1295,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| sP1(xm,X0)
| doDivides0(X0,xn)
| sP0(X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f508,f247]) ).
fof(f1296,plain,
! [X0] :
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| sP1(xm,X0)
| doDivides0(X0,xn)
| sP0(X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(duplicate_literal_removal,[],[f1295]) ).
fof(f1297,plain,
! [X0] :
( xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| sP1(xm,X0)
| doDivides0(X0,xn)
| sP0(X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f1296,f169]) ).
fof(f1298,plain,
! [X0] :
( xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| sP1(xm,X0)
| doDivides0(X0,xn)
| sP0(X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f1297,f234]) ).
fof(f1299,plain,
! [X0] :
( xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| sP1(xm,X0)
| doDivides0(X0,xn)
| sP0(X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f1298,f236]) ).
fof(f1300,plain,
! [X0] :
( xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| sP1(xm,X0)
| doDivides0(X0,xn)
| sP0(X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f1299,f235]) ).
fof(f1301,plain,
! [X0] :
( ~ doDivides0(X0,sdtasdt0(xp,xk))
| xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| sP1(xm,X0)
| doDivides0(X0,xn)
| sP0(X0) ),
inference(forward_demodulation,[],[f1300,f274]) ).
fof(f1302,plain,
! [X0] :
( ~ doDivides0(X0,sF17(sK15))
| xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| sP1(xm,X0)
| doDivides0(X0,xn)
| sP0(X0) ),
inference(forward_demodulation,[],[f1301,f359]) ).
fof(f1532,definition,
( spl18_78
<=> xp = xr ),
introduced(definition,[new_symbols(definition,[spl18_78])],[avatar_definition]) ).
fof(f1533,plain,
( xp != xr
| spl18_78 ),
inference(avatar_component_clause,[],[f1532]) ).
fof(f1534,plain,
( xp = xr
| ~ spl18_78 ),
inference(avatar_component_clause,[],[f1532]) ).
fof(f2051,definition,
( spl18_111
<=> sdtlseqdt0(xr,xp) ),
introduced(definition,[new_symbols(definition,[spl18_111])],[avatar_definition]) ).
fof(f2052,plain,
( sdtlseqdt0(xr,xp)
| ~ spl18_111 ),
inference(avatar_component_clause,[],[f2051]) ).
fof(f2053,plain,
( ~ sdtlseqdt0(xr,xp)
| spl18_111 ),
inference(avatar_component_clause,[],[f2051]) ).
fof(f2581,plain,
( xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xr)
| sP1(xm,xr)
| doDivides0(xr,xn)
| sP0(xr) ),
inference(resolution,[],[f1302,f366]) ).
fof(f4591,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xk)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f294,f198]) ).
fof(f4593,plain,
( ~ sdtlseqdt0(xp,xk)
| xp = xk
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f294,f197]) ).
fof(f4594,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f4593,f297]) ).
fof(f4596,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xk)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f4591,f275]) ).
fof(f4597,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f4594,f234]) ).
fof(f4599,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xk)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f4596,f234]) ).
fof(f4600,plain,
~ sdtlseqdt0(xp,xk),
inference(forward_subsumption_resolution,[],[f4597,f275]) ).
fof(f5443,plain,
( sdtlseqdt0(xp,xk)
| ~ spl18_78 ),
inference(superposition,[],[f559,f1534]) ).
fof(f5475,plain,
( $false
| ~ spl18_78 ),
inference(forward_subsumption_resolution,[],[f5443,f4600]) ).
fof(f5476,plain,
~ spl18_78,
inference(avatar_contradiction_clause,[],[f5475]) ).
fof(f5745,plain,
( sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[],[f4599,f559]) ).
fof(f5748,plain,
( ~ aNaturalNumber0(xr)
| spl18_111 ),
inference(forward_subsumption_resolution,[],[f5745,f2053]) ).
fof(f5749,plain,
( $false
| spl18_111 ),
inference(forward_subsumption_resolution,[],[f5748,f288]) ).
fof(f5750,plain,
spl18_111,
inference(avatar_contradiction_clause,[],[f5749]) ).
fof(f5755,plain,
( ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xr)
| sP1(xm,xr)
| doDivides0(xr,xn)
| sP0(xr)
| spl18_78 ),
inference(forward_subsumption_resolution,[],[f2581,f1533]) ).
fof(f5765,plain,
( ~ aNaturalNumber0(xr)
| sP1(xm,xr)
| doDivides0(xr,xn)
| sP0(xr)
| spl18_78
| ~ spl18_111 ),
inference(forward_subsumption_resolution,[],[f5755,f2052]) ).
fof(f5774,plain,
( sP1(xm,xr)
| doDivides0(xr,xn)
| sP0(xr)
| spl18_78
| ~ spl18_111 ),
inference(forward_subsumption_resolution,[],[f5765,f288]) ).
fof(f5781,plain,
( sP1(xm,xr)
| sP0(xr)
| spl18_78
| ~ spl18_111 ),
inference(forward_subsumption_resolution,[],[f5774,f300]) ).
fof(f5788,plain,
( sP1(xm,xr)
| spl18_25
| spl18_78
| ~ spl18_111 ),
inference(forward_subsumption_resolution,[],[f5781,f832]) ).
fof(f5795,plain,
( spl18_50
| spl18_25
| spl18_78
| ~ spl18_111 ),
inference(avatar_split_clause,[],[f5788,f2051,f1532,f831,f1024]) ).
fof(f5801,plain,
( doDivides0(xr,xm)
| ~ spl18_50 ),
inference(resolution,[],[f1026,f237]) ).
fof(f5802,plain,
( $false
| ~ spl18_50 ),
inference(forward_subsumption_resolution,[],[f5801,f298]) ).
fof(f5803,plain,
~ spl18_50,
inference(avatar_contradiction_clause,[],[f5802]) ).
cnf(s37,plain,
~ spl18_25,
inference(sat_conversion,[],[f933]) ).
cnf(s192,plain,
~ spl18_78,
inference(sat_conversion,[],[f5476]) ).
cnf(s198,plain,
spl18_111,
inference(sat_conversion,[],[f5750]) ).
cnf(s199,plain,
( spl18_25
| spl18_50
| spl18_78
| ~ spl18_111 ),
inference(sat_conversion,[],[f5795]) ).
cnf(s202,plain,
~ spl18_50,
inference(sat_conversion,[],[f5803]) ).
cnf(s205,plain,
( spl18_25
| spl18_78
| ~ spl18_111 ),
inference(rat,[],[s199,s202]) ).
cnf(s206,plain,
spl18_25,
inference(rat,[],[s205,s198,s192]) ).
cnf(s246,plain,
$false,
inference(rat,[],[s37,s206]) ).
fof(f5804,plain,
$false,
inference(avatar_sat_refutation,[],[s246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM506+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n002.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 20:18:07 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 10.65/2.17 % (3848115)Detected formulas, will run a generic FOF schedule.
% 10.65/2.17 % (3848125)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3948540046:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.65/2.17 % (3848126)dis-21_1_sil=8000:lcm=predicate:random_seed=1038923783: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)
% 10.65/2.17 % (3848124)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1887771070:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.65/2.17 % (3848121)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=2291763492:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.65/2.17 % (3848120)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=1067990865:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.65/2.17 % (3848123)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=308468323:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.65/2.17 % (3848122)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=3046828397:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.65/2.17 % (3848125)Instruction limit reached!
% 10.65/2.17 % (3848125)------------------------------
% 10.65/2.17 % (3848125)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848125)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848125)Termination reason: Instruction limit
% 10.65/2.17 % (3848125)Termination phase: Saturation
% 10.65/2.17 % (3848125)Time elapsed: 0.047 s
% 10.65/2.17 % (3848125)Peak memory usage: 90 MB
% 10.65/2.17 % (3848125)Instructions burned: 139 (million)
% 10.65/2.17 % (3848123)Instruction limit reached!
% 10.65/2.17 % (3848123)------------------------------
% 10.65/2.17 % (3848123)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848123)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848123)Termination reason: Instruction limit
% 10.65/2.17 % (3848123)Termination phase: Saturation
% 10.65/2.17 % (3848123)Time elapsed: 0.064 s
% 10.65/2.17 % (3848123)Peak memory usage: 89 MB
% 10.65/2.17 % (3848123)Instructions burned: 109 (million)
% 10.65/2.17 % (3848124)Instruction limit reached!
% 10.65/2.17 % (3848124)------------------------------
% 10.65/2.17 % (3848124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848124)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848124)Termination reason: Instruction limit
% 10.65/2.17 % (3848124)Termination phase: Saturation
% 10.65/2.17 % (3848124)Time elapsed: 0.069 s
% 10.65/2.17 % (3848124)Peak memory usage: 89 MB
% 10.65/2.17 % (3848124)Instructions burned: 120 (million)
% 10.65/2.17 % (3848126)Instruction limit reached!
% 10.65/2.17 % (3848126)------------------------------
% 10.65/2.17 % (3848126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848126)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848126)Termination reason: Instruction limit
% 10.65/2.17 % (3848126)Termination phase: Saturation
% 10.65/2.17 % (3848126)Time elapsed: 0.078 s
% 10.65/2.17 % (3848126)Peak memory usage: 91 MB
% 10.65/2.17 % (3848126)Instructions burned: 129 (million)
% 10.65/2.17 % (3848134)lrs+10_1_sil=8000:sp=occurrence:random_seed=707581742:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 10.65/2.17 % (3848135)lrs+10_1_sil=32000:urr=on:br=off:random_seed=63741046:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 10.65/2.17 % (3848136)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3689411243:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 10.65/2.17 % (3848137)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=1493909749:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 10.65/2.17 % (3848134)Instruction limit reached!
% 10.65/2.17 % (3848134)------------------------------
% 10.65/2.17 % (3848134)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848134)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848134)Termination reason: Instruction limit
% 10.65/2.17 % (3848134)Termination phase: Saturation
% 10.65/2.17 % (3848134)Time elapsed: 0.084 s
% 10.65/2.17 % (3848134)Peak memory usage: 91 MB
% 10.65/2.17 % (3848134)Instructions burned: 287 (million)
% 10.65/2.17 % (3848135)Instruction limit reached!
% 10.65/2.17 % (3848135)------------------------------
% 10.65/2.17 % (3848135)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848135)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848135)Termination reason: Instruction limit
% 10.65/2.17 % (3848135)Termination phase: Saturation
% 10.65/2.17 % (3848135)Time elapsed: 0.074 s
% 10.65/2.17 % (3848135)Peak memory usage: 92 MB
% 10.65/2.17 % (3848135)Instructions burned: 160 (million)
% 10.65/2.17 % (3848137)Instruction limit reached!
% 10.65/2.17 % (3848137)------------------------------
% 10.65/2.17 % (3848137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848137)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848137)Termination reason: Instruction limit
% 10.65/2.17 % (3848137)Termination phase: Saturation
% 10.65/2.17 % (3848137)Time elapsed: 0.115 s
% 10.65/2.17 % (3848137)Peak memory usage: 94 MB
% 10.65/2.17 % (3848137)Instructions burned: 249 (million)
% 10.65/2.17 % (3848142)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=198910896:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 10.65/2.17 % (3848136)Instruction limit reached!
% 10.65/2.17 % (3848136)------------------------------
% 10.65/2.17 % (3848136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848136)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848136)Termination reason: Instruction limit
% 10.65/2.17 % (3848136)Termination phase: Saturation
% 10.65/2.17 % (3848136)Time elapsed: 0.203 s
% 10.65/2.17 % (3848136)Peak memory usage: 92 MB
% 10.65/2.17 % (3848136)Instructions burned: 325 (million)
% 10.65/2.17 % (3848143)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2862798371:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 10.65/2.17 % (3848142)Instruction limit reached!
% 10.65/2.17 % (3848142)------------------------------
% 10.65/2.17 % (3848142)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848142)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848142)Termination reason: Instruction limit
% 10.65/2.17 % (3848142)Termination phase: Saturation
% 10.65/2.17 % (3848142)Time elapsed: 0.087 s
% 10.65/2.17 % (3848142)Peak memory usage: 90 MB
% 10.65/2.17 % (3848142)Instructions burned: 296 (million)
% 10.65/2.17 % (3848144)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2859973053:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 10.65/2.17 % (3848146)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2120734454:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 10.65/2.17 % (3848148)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3359531268:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 10.65/2.17 % (3848144)Instruction limit reached!
% 10.65/2.17 % (3848144)------------------------------
% 10.65/2.17 % (3848144)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848144)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848144)Termination reason: Instruction limit
% 10.65/2.17 % (3848144)Termination phase: Saturation
% 10.65/2.17 % (3848144)Time elapsed: 0.071 s
% 10.65/2.17 % (3848144)Peak memory usage: 91 MB
% 10.65/2.17 % (3848144)Instructions burned: 113 (million)
% 10.65/2.17 % (3848148)Instruction limit reached!
% 10.65/2.17 % (3848148)------------------------------
% 10.65/2.17 % (3848148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848148)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848148)Termination reason: Instruction limit
% 10.65/2.17 % (3848148)Termination phase: Saturation
% 10.65/2.17 % (3848148)Time elapsed: 0.030 s
% 10.65/2.17 % (3848148)Peak memory usage: 89 MB
% 10.65/2.17 % (3848148)Instructions burned: 115 (million)
% 10.65/2.17 % (3848146)Instruction limit reached!
% 10.65/2.17 % (3848146)------------------------------
% 10.65/2.17 % (3848146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848146)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848146)Termination reason: Instruction limit
% 10.65/2.17 % (3848146)Termination phase: Saturation
% 10.65/2.17 % (3848146)Time elapsed: 0.064 s
% 10.65/2.17 % (3848146)Peak memory usage: 89 MB
% 10.65/2.17 % (3848146)Instructions burned: 127 (million)
% 10.65/2.17 % (3848153)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3113225315:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 10.65/2.17 % (3848152)lrs+10_1_sil=8000:sp=occurrence:random_seed=328415376:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 10.65/2.17 % (3848154)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2449535513:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 10.65/2.17 % (3848153)Instruction limit reached!
% 10.65/2.17 % (3848153)------------------------------
% 10.65/2.17 % (3848153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848153)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848153)Termination reason: Instruction limit
% 10.65/2.17 % (3848153)Termination phase: Saturation
% 10.65/2.17 % (3848153)Time elapsed: 0.139 s
% 10.65/2.17 % (3848153)Peak memory usage: 92 MB
% 10.65/2.17 % (3848153)Instructions burned: 439 (million)
% 10.65/2.17 % (3848158)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2487787799:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2989 on theBenchmark for (2989ds/134Mi)
% 10.65/2.17 % (3848158)Instruction limit reached!
% 10.65/2.17 % (3848158)------------------------------
% 10.65/2.17 % (3848158)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848158)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848158)Termination reason: Instruction limit
% 10.65/2.17 % (3848158)Termination phase: Saturation
% 10.65/2.17 % (3848158)Time elapsed: 0.034 s
% 10.65/2.17 % (3848158)Peak memory usage: 91 MB
% 10.65/2.17 % (3848158)Instructions burned: 138 (million)
% 10.65/2.17 % (3848120)First to succeed.
% 10.65/2.17 % (3848120)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3848115"
% 10.65/2.17 % (3848143)Also succeeded, but the first one will report.
% 10.65/2.17 % (3848160)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=4077575141:st=8:i=592:sd=3:ep=RST:ss=axioms_2988 on theBenchmark for (2988ds/592Mi)
% 10.65/2.17 % (3848152)Instruction limit reached!
% 10.65/2.17 % (3848152)------------------------------
% 10.65/2.17 % (3848152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.65/2.17 % (3848152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.65/2.17 % (3848152)CaDiCaL version: 2.1.3
% 10.65/2.17 % (3848152)Termination reason: Instruction limit
% 10.65/2.17 % (3848152)Termination phase: Saturation
% 10.65/2.17 % (3848152)Time elapsed: 0.505 s
% 10.65/2.17 % (3848152)Peak memory usage: 97 MB
% 10.65/2.17 % (3848152)Instructions burned: 908 (million)
% 10.65/2.17 % (3848120)Refutation found. Thanks to Tanya!
% 10.65/2.17 % SZS status Theorem for theBenchmark
% 10.65/2.17 % SZS output start Proof for theBenchmark
% See solution above
% 11.21/2.37 % (3848120)------------------------------
% 11.21/2.37 % (3848120)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.21/2.37 % (3848120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.21/2.37 % (3848120)CaDiCaL version: 2.1.3
% 11.21/2.37 % (3848120)Termination reason: Refutation
% 11.21/2.37 % (3848120)Time elapsed: 1.115 s
% 11.21/2.37 % (3848120)Peak memory usage: 135 MB
% 11.21/2.37 % (3848120)Instructions burned: 1706 (million)
% 11.21/2.37 % (3848120)------------------------------
% 11.21/2.37 % (3848120)------------------------------
% 11.21/2.37 % (3848115)Success in time 1.534 s
% 11.21/2.37 % Vampire exiting
%------------------------------------------------------------------------------