%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM507+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 : n007.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 3.32s 1.34s
% Output : Refutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 19
% Syntax : Number of formulae : 112 ( 20 unt; 0 def)
% Number of atoms : 461 ( 143 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 614 ( 265 ~; 250 |; 75 &)
% ( 6 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 117 ( 114 !; 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(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
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(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(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X0,X1)
& X1 != sz00 )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
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(f46,axiom,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2315) ).
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,
( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f52,negated_conjecture,
~ ( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp)
& sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f57,plain,
( sz00 != xk
& sz10 != xk ),
inference(ennf_transformation,[],[f46]) ).
fof(f58,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(ennf_transformation,[],[f52]) ).
fof(f59,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(f60,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,[],[f59]) ).
fof(f65,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(f66,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,[],[f65]) ).
fof(f72,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f73,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f75,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f74]) ).
fof(f91,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f92,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f94,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f93]) ).
fof(f105,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(f106,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f105]) ).
fof(f109,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f110,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f112,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f111]) ).
fof(f116,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(f117,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,[],[f116]) ).
fof(f128,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,[],[f106]) ).
fof(f129,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,[],[f128]) ).
fof(f130,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,[],[f129]) ).
fof(f131,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ( sz10 != sK3(X0)
& sK3(X0) != X0
& aNaturalNumber0(sK3(X0))
& doDivides0(sK3(X0),X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f130]) ).
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(nnf_transformation,[],[f117]) ).
fof(f133,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,[],[f132]) ).
fof(f134,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f135,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f136,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f138,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f139,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f146,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f148,plain,
sz00 != xk,
inference(cnf_transformation,[],[f57]) ).
fof(f152,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f48]) ).
fof(f153,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f155,plain,
sdtlseqdt0(xr,xk),
inference(cnf_transformation,[],[f49]) ).
fof(f156,plain,
sdtlseqdt0(xk,xp),
inference(cnf_transformation,[],[f50]) ).
fof(f157,plain,
xp != xk,
inference(cnf_transformation,[],[f50]) ).
fof(f158,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) ),
inference(cnf_transformation,[],[f58]) ).
fof(f159,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,[],[f60]) ).
fof(f168,plain,
! [X2,X0,X1] :
( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| X1 = X2
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f175,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f176,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f190,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f191,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f203,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f210,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f110]) ).
fof(f211,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f215,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f217,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f226,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f203]) ).
fof(f230,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f215]) ).
fof(f234,plain,
~ isPrime0(sz00),
inference(forward_subsumption_resolution,[],[f226,f217]) ).
fof(f268,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(xp,sdtpldt0(xn,xm)))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(superposition,[],[f158,f175]) ).
fof(f279,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(xp,sdtpldt0(xn,xm)))
| sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f268,f134]) ).
fof(f293,plain,
( ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(xp,sdtpldt0(xn,xm)))
| sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xr) ),
inference(superposition,[],[f279,f175]) ).
fof(f294,plain,
( ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(xp,sdtpldt0(xn,xm)))
| sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xr) ),
inference(duplicate_literal_removal,[],[f293]) ).
fof(f296,plain,
( ~ sdtlseqdt0(sdtpldt0(xr,sdtpldt0(xn,xm)),sdtpldt0(xp,sdtpldt0(xn,xm)))
| sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f294,f153]) ).
fof(f418,plain,
( ~ sdtlseqdt0(xp,xk)
| xp = xk
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f211,f156]) ).
fof(f432,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f418,f157]) ).
fof(f435,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f432,f134]) ).
fof(f484,plain,
( ~ aNaturalNumber0(xk)
| ~ doDivides0(xp,xk)
| sz00 = xk
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f435,f191]) ).
fof(f487,plain,
( ~ aNaturalNumber0(xk)
| ~ doDivides0(xp,xk)
| sz00 = xk
| ~ aNaturalNumber0(xp) ),
inference(duplicate_literal_removal,[],[f484]) ).
fof(f488,plain,
( ~ aNaturalNumber0(xk)
| ~ doDivides0(xp,xk)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f487,f148]) ).
fof(f489,plain,
( ~ doDivides0(xp,xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f488,f134]) ).
fof(f508,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[],[f230,f146]) ).
fof(f509,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f508,f138]) ).
fof(f510,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f509,f134]) ).
fof(f1119,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(resolution,[],[f159,f296]) ).
fof(f1149,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| sdtpldt0(xr,sdtpldt0(xn,xm)) = sdtpldt0(xp,sdtpldt0(xn,xm)) ),
inference(duplicate_literal_removal,[],[f1119]) ).
fof(f1163,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f1149,f168]) ).
fof(f1166,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f1163,f153]) ).
fof(f1168,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = xr
| ~ sdtlseqdt0(xr,xp) ),
inference(forward_subsumption_resolution,[],[f1166,f134]) ).
fof(f1169,plain,
( xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f1168,f176]) ).
fof(f1170,plain,
( xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f1169,f136]) ).
fof(f1171,plain,
( ~ sdtlseqdt0(xr,xp)
| xp = xr ),
inference(forward_subsumption_resolution,[],[f1170,f135]) ).
fof(f1172,plain,
! [X0] :
( xp = xr
| ~ sdtlseqdt0(xr,X0)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f1171,f210]) ).
fof(f1177,plain,
! [X0] :
( xp = xr
| ~ sdtlseqdt0(xr,X0)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f1172,f153]) ).
fof(f1180,plain,
! [X0] :
( ~ sdtlseqdt0(xr,X0)
| xp = xr
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f1177,f134]) ).
fof(f1244,plain,
( xp = xr
| ~ sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f1180,f155]) ).
fof(f1249,plain,
( xp = xr
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f1244,f156]) ).
fof(f1276,plain,
( ~ doDivides0(xr,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xk) ),
inference(superposition,[],[f489,f1249]) ).
fof(f1282,plain,
( ~ doDivides0(xr,xk)
| ~ aNaturalNumber0(xk) ),
inference(duplicate_literal_removal,[],[f1276]) ).
fof(f1284,plain,
~ aNaturalNumber0(xk),
inference(forward_subsumption_resolution,[],[f1282,f152]) ).
fof(f2060,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp ),
inference(forward_subsumption_resolution,[],[f510,f1284]) ).
fof(f2062,plain,
( sz00 = xp
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f2060,f190]) ).
fof(f2063,plain,
( sz00 = xp
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f2062,f136]) ).
fof(f2064,plain,
sz00 = xp,
inference(forward_subsumption_resolution,[],[f2063,f135]) ).
fof(f2072,plain,
~ isPrime0(xp),
inference(superposition,[],[f234,f2064]) ).
fof(f2076,plain,
$false,
inference(forward_subsumption_resolution,[],[f2072,f139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM507+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 20:13:10 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.32/1.34 % (1753629)Detected formulas, will run a generic FOF schedule.
% 3.32/1.34 % (1753635)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=3900579304:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.32/1.34 % (1753634)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=403225665:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.32/1.34 % (1753640)dis-21_1_sil=8000:lcm=predicate:random_seed=1017039102: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)
% 3.32/1.34 % (1753638)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2862891030:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.32/1.34 % (1753637)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2820646416:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.32/1.34 % (1753636)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=1255265662:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.32/1.34 % (1753639)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1902462035:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.32/1.34 % (1753638)First to succeed.
% 3.32/1.34 % (1753638)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1753629"
% 3.32/1.34 % (1753637)Also succeeded, but the first one will report.
% 3.32/1.34 % (1753639)Also succeeded, but the first one will report.
% 3.32/1.34 % (1753640)Instruction limit reached!
% 3.32/1.34 % (1753640)------------------------------
% 3.32/1.34 % (1753640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.32/1.34 % (1753640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.32/1.34 % (1753640)CaDiCaL version: 2.1.3
% 3.32/1.34 % (1753640)Termination reason: Instruction limit
% 3.32/1.34 % (1753640)Termination phase: Saturation
% 3.32/1.34 % (1753640)Time elapsed: 0.080 s
% 3.32/1.34 % (1753640)Peak memory usage: 90 MB
% 3.32/1.34 % (1753640)Instructions burned: 131 (million)
% 3.32/1.34 % (1753648)lrs+10_1_sil=8000:sp=occurrence:random_seed=2455832926:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.32/1.34 % (1753638)Refutation found. Thanks to Tanya!
% 3.32/1.34 % SZS status Theorem for theBenchmark
% 3.32/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.93/1.53 % (1753638)------------------------------
% 3.93/1.53 % (1753638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.53 % (1753638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.53 % (1753638)CaDiCaL version: 2.1.3
% 3.93/1.53 % (1753638)Termination reason: Refutation
% 3.93/1.53 % (1753638)Time elapsed: 0.041 s
% 3.93/1.53 % (1753638)Peak memory usage: 89 MB
% 3.93/1.53 % (1753638)Instructions burned: 72 (million)
% 3.93/1.53 % (1753638)------------------------------
% 3.93/1.53 % (1753638)------------------------------
% 3.93/1.53 % (1753629)Success in time 0.473 s
% 3.93/1.53 % Vampire exiting
%------------------------------------------------------------------------------