%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM506+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:29 PM UTC 2026
% Result : Theorem 8.69s 2.07s
% Output : Refutation 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 27
% Syntax : Number of formulae : 157 ( 30 unt; 9 def)
% Number of atoms : 625 ( 138 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 798 ( 330 ~; 358 |; 75 &)
% ( 15 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 142 ( 0 sgn 139 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
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/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != X1
& sdtlseqdt0(X0,X1) )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( isPrime0(X2)
& doDivides0(X2,sdtasdt0(X0,X1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X2,X0)
| doDivides0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1799) ).
fof(f41,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( sdtlseqdt0(xr,xk)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
fof(f50,axiom,
( xk != xp
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2377) ).
fof(f51,conjecture,
( doDivides0(xr,xn)
| doDivides0(xr,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f52,negated_conjecture,
~ ( doDivides0(xr,xn)
| doDivides0(xr,xm) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f56,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f58,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f57]) ).
fof(f72,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(f73,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,[],[f72]) ).
fof(f85,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f86,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f88,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f87]) ).
fof(f91,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(f92,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,[],[f91]) ).
fof(f99,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f100,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f99]) ).
fof(f103,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f103]) ).
fof(f115,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f116,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f115]) ).
fof(f119,plain,
! [X0,X1,X2] :
( doDivides0(X2,X0)
| doDivides0(X2,X1)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f120,plain,
! [X0,X1,X2] :
( doDivides0(X2,X0)
| doDivides0(X2,X1)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f119]) ).
fof(f122,plain,
( ~ doDivides0(xr,xn)
& ~ doDivides0(xr,xm) ),
inference(ennf_transformation,[],[f52]) ).
fof(f131,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f104]) ).
fof(f132,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f131]) ).
fof(f133,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f116]) ).
fof(f134,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f134]) ).
fof(f136,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ( sz10 != sK2(X0)
& sK2(X0) != X0
& aNaturalNumber0(sK2(X0))
& doDivides0(sK2(X0),X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f135]) ).
fof(f138,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f141,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f142,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f156,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f169,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f175,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,[],[f92]) ).
fof(f184,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f188,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f189,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f198,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f206,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f207,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f208,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f209,plain,
! [X2,X0,X1] :
( ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f120]) ).
fof(f210,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f211,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f218,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f223,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f225,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f226,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f49]) ).
fof(f227,plain,
sdtlseqdt0(xr,xk),
inference(cnf_transformation,[],[f49]) ).
fof(f228,plain,
sdtlseqdt0(xk,xp),
inference(cnf_transformation,[],[f50]) ).
fof(f229,plain,
xp != xk,
inference(cnf_transformation,[],[f50]) ).
fof(f230,plain,
~ doDivides0(xr,xm),
inference(cnf_transformation,[],[f122]) ).
fof(f231,plain,
~ doDivides0(xr,xn),
inference(cnf_transformation,[],[f122]) ).
fof(f240,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f189]) ).
fof(f241,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f188]) ).
fof(f242,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f198]) ).
fof(f253,definition,
( spl4_3
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f254,plain,
( ~ aNaturalNumber0(sz00)
| spl4_3 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f256,definition,
( spl4_4
<=> isPrime0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f257,plain,
( ~ isPrime0(sz00)
| spl4_4 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f258,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f242,f256,f253]) ).
fof(f264,definition,
( spl4_5
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f284,plain,
( xp = xk
| ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f169,f228]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2)
| iLess0(sdtpldt0(X0,X1),sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(resolution,[],[f175,f184]) ).
fof(f304,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| iLess0(sdtpldt0(X0,X1),sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(forward_subsumption_resolution,[],[f302,f156]) ).
fof(f306,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| iLess0(sdtpldt0(X0,X1),sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(forward_subsumption_resolution,[],[f304,f141]) ).
fof(f308,plain,
! [X2,X0,X1] :
( iLess0(sdtpldt0(X0,X1),sdtpldt0(X0,X2))
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f306,f141]) ).
fof(f314,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[],[f240,f218]) ).
fof(f319,definition,
( spl4_8
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f320,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_8 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f322,definition,
( spl4_9
<=> sz00 = xp ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
fof(f323,plain,
( sz00 = xp
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f326,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_8 ),
inference(resolution,[],[f320,f142]) ).
fof(f328,plain,
( ~ aNaturalNumber0(xm)
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f326,f208]) ).
fof(f329,plain,
( $false
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f328,f207]) ).
fof(f330,plain,
spl4_8,
inference(avatar_contradiction_clause,[],[f329]) ).
fof(f333,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f284,f229]) ).
fof(f334,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f314,f210]) ).
fof(f340,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f333,f206]) ).
fof(f341,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f334,f206]) ).
fof(f347,definition,
( spl4_12
<=> sdtlseqdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition]) ).
fof(f348,plain,
( ~ sdtlseqdt0(xp,xk)
| spl4_12 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f349,plain,
( ~ spl4_5
| ~ spl4_12 ),
inference(avatar_split_clause,[],[f340,f347,f264]) ).
fof(f350,plain,
( aNaturalNumber0(xk)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f351,plain,
( ~ spl4_8
| spl4_9
| spl4_5 ),
inference(avatar_split_clause,[],[f341,f264,f322,f319]) ).
fof(f355,plain,
( isPrime0(sz00)
| ~ spl4_9 ),
inference(superposition,[],[f211,f323]) ).
fof(f362,plain,
( $false
| spl4_4
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f355,f257]) ).
fof(f363,plain,
( spl4_4
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f362]) ).
fof(f399,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f241,f210]) ).
fof(f403,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f399,f206]) ).
fof(f406,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_demodulation,[],[f403,f218]) ).
fof(f416,definition,
( spl4_17
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[spl4_17])],[avatar_definition]) ).
fof(f417,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f418,plain,
( ~ spl4_8
| spl4_9
| spl4_17 ),
inference(avatar_split_clause,[],[f406,f416,f322,f319]) ).
fof(f436,plain,
( doDivides0(xr,sdtasdt0(xp,xk))
| ~ spl4_17 ),
inference(superposition,[],[f226,f417]) ).
fof(f481,plain,
( $false
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f254,f138]) ).
fof(f482,plain,
spl4_3,
inference(avatar_contradiction_clause,[],[f481]) ).
fof(f1028,plain,
! [X0] :
( xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| doDivides0(X0,xm)
| doDivides0(X0,xn)
| ~ isPrime0(X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f308,f209]) ).
fof(f1029,plain,
! [X0] :
( xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| doDivides0(X0,xm)
| doDivides0(X0,xn)
| ~ isPrime0(X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(duplicate_literal_removal,[],[f1028]) ).
fof(f1030,plain,
! [X0] :
( xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| doDivides0(X0,xm)
| doDivides0(X0,xn)
| ~ isPrime0(X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f1029,f206]) ).
fof(f1031,plain,
! [X0] :
( xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| doDivides0(X0,xm)
| doDivides0(X0,xn)
| ~ isPrime0(X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f1030,f141]) ).
fof(f1032,plain,
! [X0] :
( xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| doDivides0(X0,xm)
| doDivides0(X0,xn)
| ~ isPrime0(X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f1031,f208]) ).
fof(f1033,plain,
! [X0] :
( xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| doDivides0(X0,xm)
| doDivides0(X0,xn)
| ~ isPrime0(X0)
| ~ doDivides0(X0,sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f1032,f207]) ).
fof(f1572,plain,
( ! [X0] :
( ~ isPrime0(X0)
| xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| doDivides0(X0,xm)
| doDivides0(X0,xn)
| ~ doDivides0(X0,sdtasdt0(xp,xk)) )
| ~ spl4_17 ),
inference(forward_demodulation,[],[f1033,f417]) ).
fof(f1602,plain,
( xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xr)
| doDivides0(xr,xm)
| doDivides0(xr,xn)
| ~ doDivides0(xr,sdtasdt0(xp,xk))
| ~ spl4_17 ),
inference(resolution,[],[f1572,f223]) ).
fof(f1603,plain,
( xp = xr
| ~ sdtlseqdt0(xr,xp)
| doDivides0(xr,xm)
| doDivides0(xr,xn)
| ~ doDivides0(xr,sdtasdt0(xp,xk))
| ~ spl4_17 ),
inference(forward_subsumption_resolution,[],[f1602,f225]) ).
fof(f1604,plain,
( xp = xr
| ~ sdtlseqdt0(xr,xp)
| doDivides0(xr,xn)
| ~ doDivides0(xr,sdtasdt0(xp,xk))
| ~ spl4_17 ),
inference(forward_subsumption_resolution,[],[f1603,f230]) ).
fof(f1605,plain,
( xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ doDivides0(xr,sdtasdt0(xp,xk))
| ~ spl4_17 ),
inference(forward_subsumption_resolution,[],[f1604,f231]) ).
fof(f1606,plain,
( xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ spl4_17 ),
inference(forward_subsumption_resolution,[],[f1605,f436]) ).
fof(f1608,definition,
( spl4_119
<=> sdtlseqdt0(xr,xp) ),
introduced(definition,[new_symbols(definition,[spl4_119])],[avatar_definition]) ).
fof(f1609,plain,
( ~ sdtlseqdt0(xr,xp)
| spl4_119 ),
inference(avatar_component_clause,[],[f1608]) ).
fof(f1611,definition,
( spl4_120
<=> xp = xr ),
introduced(definition,[new_symbols(definition,[spl4_120])],[avatar_definition]) ).
fof(f1612,plain,
( xp = xr
| ~ spl4_120 ),
inference(avatar_component_clause,[],[f1611]) ).
fof(f1613,plain,
( ~ spl4_119
| spl4_120
| ~ spl4_17 ),
inference(avatar_split_clause,[],[f1606,f416,f1611,f1608]) ).
fof(f2371,plain,
( $false
| ~ spl4_5
| spl4_119 ),
inference(unit_resulting_resolution,[],[f170,f206,f350,f225,f228,f1609,f227]) ).
fof(f2380,plain,
( ~ spl4_5
| spl4_119 ),
inference(avatar_contradiction_clause,[],[f2371]) ).
fof(f2401,plain,
( sdtlseqdt0(xp,xk)
| ~ spl4_120 ),
inference(superposition,[],[f227,f1612]) ).
fof(f2416,plain,
( $false
| spl4_12
| ~ spl4_120 ),
inference(forward_subsumption_resolution,[],[f2401,f348]) ).
fof(f2417,plain,
( spl4_12
| ~ spl4_120 ),
inference(avatar_contradiction_clause,[],[f2416]) ).
cnf(s2,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f258]) ).
cnf(s7,plain,
spl4_8,
inference(sat_conversion,[],[f330]) ).
cnf(s10,plain,
( ~ spl4_5
| ~ spl4_12 ),
inference(sat_conversion,[],[f349]) ).
cnf(s11,plain,
( spl4_5
| ~ spl4_8
| spl4_9 ),
inference(sat_conversion,[],[f351]) ).
cnf(s12,plain,
( spl4_4
| ~ spl4_9 ),
inference(sat_conversion,[],[f363]) ).
cnf(s17,plain,
( ~ spl4_8
| spl4_9
| spl4_17 ),
inference(sat_conversion,[],[f418]) ).
cnf(s25,plain,
spl4_3,
inference(sat_conversion,[],[f482]) ).
cnf(s122,plain,
( ~ spl4_17
| ~ spl4_119
| spl4_120 ),
inference(sat_conversion,[],[f1613]) ).
cnf(s182,plain,
( ~ spl4_5
| spl4_119 ),
inference(sat_conversion,[],[f2380]) ).
cnf(s184,plain,
( spl4_12
| ~ spl4_120 ),
inference(sat_conversion,[],[f2417]) ).
cnf(s224,plain,
~ spl4_4,
inference(rat,[],[s2,s25]) ).
cnf(s226,plain,
~ spl4_9,
inference(rat,[],[s12,s224]) ).
cnf(s242,plain,
spl4_17,
inference(rat,[],[s17,s7,s226]) ).
cnf(s243,plain,
spl4_5,
inference(rat,[],[s11,s7,s226]) ).
cnf(s262,plain,
spl4_119,
inference(rat,[],[s182,s243]) ).
cnf(s266,plain,
~ spl4_12,
inference(rat,[],[s10,s243]) ).
cnf(s276,plain,
spl4_120,
inference(rat,[],[s122,s242,s262]) ).
cnf(s283,plain,
$false,
inference(rat,[],[s184,s276,s266]) ).
fof(f2418,plain,
$false,
inference(avatar_sat_refutation,[],[s283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM506+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 20:15:02 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.69/2.07 % (1281371)Detected formulas, will run a generic FOF schedule.
% 8.69/2.07 % (1281382)dis-21_1_sil=8000:lcm=predicate:random_seed=14089433: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)
% 8.69/2.07 % (1281376)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=2294065795:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.69/2.07 % (1281378)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=1387927033:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.69/2.07 % (1281379)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1799464016:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.69/2.07 % (1281377)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=2906893876:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.69/2.07 % (1281380)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3113350229:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.69/2.07 % (1281381)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=286077022:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.69/2.07 % (1281382)Instruction limit reached!
% 8.69/2.07 % (1281382)------------------------------
% 8.69/2.07 % (1281382)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281382)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281382)Termination reason: Instruction limit
% 8.69/2.07 % (1281382)Termination phase: Saturation
% 8.69/2.07 % (1281382)Time elapsed: 0.044 s
% 8.69/2.07 % (1281382)Peak memory usage: 90 MB
% 8.69/2.07 % (1281382)Instructions burned: 131 (million)
% 8.69/2.07 % (1281379)Instruction limit reached!
% 8.69/2.07 % (1281379)------------------------------
% 8.69/2.07 % (1281379)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281379)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281379)Termination reason: Instruction limit
% 8.69/2.07 % (1281379)Termination phase: Saturation
% 8.69/2.07 % (1281379)Time elapsed: 0.066 s
% 8.69/2.07 % (1281379)Peak memory usage: 89 MB
% 8.69/2.07 % (1281379)Instructions burned: 110 (million)
% 8.69/2.07 % (1281380)Instruction limit reached!
% 8.69/2.07 % (1281380)------------------------------
% 8.69/2.07 % (1281380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281380)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281380)Termination reason: Instruction limit
% 8.69/2.07 % (1281380)Termination phase: Saturation
% 8.69/2.07 % (1281380)Time elapsed: 0.072 s
% 8.69/2.07 % (1281380)Peak memory usage: 89 MB
% 8.69/2.07 % (1281380)Instructions burned: 119 (million)
% 8.69/2.07 % (1281381)Instruction limit reached!
% 8.69/2.07 % (1281381)------------------------------
% 8.69/2.07 % (1281381)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281381)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281381)Termination reason: Instruction limit
% 8.69/2.07 % (1281381)Termination phase: Saturation
% 8.69/2.07 % (1281381)Time elapsed: 0.094 s
% 8.69/2.07 % (1281381)Peak memory usage: 90 MB
% 8.69/2.07 % (1281381)Instructions burned: 139 (million)
% 8.69/2.07 % (1281390)lrs+10_1_sil=8000:sp=occurrence:random_seed=717362995:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.69/2.07 % (1281390)Instruction limit reached!
% 8.69/2.07 % (1281390)------------------------------
% 8.69/2.07 % (1281390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281390)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281390)Termination reason: Instruction limit
% 8.69/2.07 % (1281390)Termination phase: Saturation
% 8.69/2.07 % (1281390)Time elapsed: 0.089 s
% 8.69/2.07 % (1281390)Peak memory usage: 92 MB
% 8.69/2.07 % (1281390)Instructions burned: 286 (million)
% 8.69/2.07 % (1281391)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3602299890:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.69/2.07 % (1281391)Refutation not found, incomplete strategy
% 8.69/2.07 % (1281391)------------------------------
% 8.69/2.07 % (1281391)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281391)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281391)Termination reason: Refutation not found, incomplete strategy
% 8.69/2.07 % (1281391)Time elapsed: 0.002 s
% 8.69/2.07 % (1281391)Peak memory usage: 89 MB
% 8.69/2.07 % (1281391)Instructions burned: 2 (million)
% 8.69/2.07 % (1281392)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1587490001:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.69/2.07 % (1281393)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=2977033822:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 8.69/2.07 % (1281396)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=922362353:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 8.69/2.07 % (1281393)Instruction limit reached!
% 8.69/2.07 % (1281393)------------------------------
% 8.69/2.07 % (1281393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281393)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281393)Termination reason: Instruction limit
% 8.69/2.07 % (1281393)Termination phase: Saturation
% 8.69/2.07 % (1281393)Time elapsed: 0.117 s
% 8.69/2.07 % (1281393)Peak memory usage: 93 MB
% 8.69/2.07 % (1281393)Instructions burned: 250 (million)
% 8.69/2.07 % (1281396)Instruction limit reached!
% 8.69/2.07 % (1281396)------------------------------
% 8.69/2.07 % (1281396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281396)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281396)Termination reason: Instruction limit
% 8.69/2.07 % (1281396)Termination phase: Saturation
% 8.69/2.07 % (1281396)Time elapsed: 0.087 s
% 8.69/2.07 % (1281396)Peak memory usage: 89 MB
% 8.69/2.07 % (1281396)Instructions burned: 297 (million)
% 8.69/2.07 % (1281392)Instruction limit reached!
% 8.69/2.07 % (1281392)------------------------------
% 8.69/2.07 % (1281392)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281392)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281392)Termination reason: Instruction limit
% 8.69/2.07 % (1281392)Termination phase: Saturation
% 8.69/2.07 % (1281392)Time elapsed: 0.199 s
% 8.69/2.07 % (1281392)Peak memory usage: 92 MB
% 8.69/2.07 % (1281392)Instructions burned: 326 (million)
% 8.69/2.07 % (1281391)------------------------------
% 8.69/2.07 % (1281391)------------------------------
% 8.69/2.07 % (1281400)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=202220828:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.69/2.07 % (1281401)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4105167693:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 8.69/2.07 % (1281402)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1812563554:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 8.69/2.07 % (1281401)Instruction limit reached!
% 8.69/2.07 % (1281401)------------------------------
% 8.69/2.07 % (1281401)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281401)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281401)Termination reason: Instruction limit
% 8.69/2.07 % (1281401)Termination phase: Saturation
% 8.69/2.07 % (1281401)Time elapsed: 0.037 s
% 8.69/2.07 % (1281401)Peak memory usage: 91 MB
% 8.69/2.07 % (1281401)Instructions burned: 114 (million)
% 8.69/2.07 % (1281403)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2916756611:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 8.69/2.07 % (1281402)Instruction limit reached!
% 8.69/2.07 % (1281402)------------------------------
% 8.69/2.07 % (1281402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281402)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281402)Termination reason: Instruction limit
% 8.69/2.07 % (1281402)Termination phase: Saturation
% 8.69/2.07 % (1281402)Time elapsed: 0.065 s
% 8.69/2.07 % (1281402)Peak memory usage: 89 MB
% 8.69/2.07 % (1281402)Instructions burned: 128 (million)
% 8.69/2.07 % (1281403)Instruction limit reached!
% 8.69/2.07 % (1281403)------------------------------
% 8.69/2.07 % (1281403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281403)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281403)Termination reason: Instruction limit
% 8.69/2.07 % (1281403)Termination phase: Saturation
% 8.69/2.07 % (1281403)Time elapsed: 0.064 s
% 8.69/2.07 % (1281403)Peak memory usage: 89 MB
% 8.69/2.07 % (1281403)Instructions burned: 114 (million)
% 8.69/2.07 % (1281407)lrs+10_1_sil=8000:sp=occurrence:random_seed=3097066804:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 8.69/2.07 % (1281377)First to succeed.
% 8.69/2.07 % (1281377)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1281371"
% 8.69/2.07 % (1281409)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1035544911:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 8.69/2.07 % (1281376)Also succeeded, but the first one will report.
% 8.69/2.07 % (1281411)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2132343190:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 8.69/2.07 % (1281407)Instruction limit reached!
% 8.69/2.07 % (1281407)------------------------------
% 8.69/2.07 % (1281407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.07 % (1281407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.07 % (1281407)CaDiCaL version: 2.1.3
% 8.69/2.07 % (1281407)Termination reason: Instruction limit
% 8.69/2.07 % (1281407)Termination phase: Saturation
% 8.69/2.07 % (1281407)Time elapsed: 0.267 s
% 8.69/2.07 % (1281407)Peak memory usage: 98 MB
% 8.69/2.07 % (1281407)Instructions burned: 908 (million)
% 8.69/2.07 % (1281377)Refutation found. Thanks to Tanya!
% 8.69/2.07 % SZS status Theorem for theBenchmark
% 8.69/2.07 % SZS output start Proof for theBenchmark
% See solution above
% 9.15/2.24 % (1281377)------------------------------
% 9.15/2.24 % (1281377)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.24 % (1281377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.24 % (1281377)CaDiCaL version: 2.1.3
% 9.15/2.24 % (1281377)Termination reason: Refutation
% 9.15/2.24 % (1281377)Time elapsed: 0.790 s
% 9.15/2.24 % (1281377)Peak memory usage: 129 MB
% 9.15/2.24 % (1281377)Instructions burned: 1184 (million)
% 9.15/2.24 % (1281377)------------------------------
% 9.15/2.24 % (1281377)------------------------------
% 9.15/2.24 % (1281371)Success in time 1.216 s
% 9.15/2.24 % Vampire exiting
%------------------------------------------------------------------------------