%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM507+3 : 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 12:15:30 PM UTC 2026
% Result : Theorem 2.86s 6.37s
% Output : Refutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 98 ( 17 unt; 0 def)
% Number of atoms : 420 ( 122 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 543 ( 221 ~; 199 |; 104 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 120 ( 102 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
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(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
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(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(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f45,axiom,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& 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)
& ? [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/sandbox/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/sandbox/benchmark/theBenchmark.p',m__2362) ).
fof(f50,axiom,
( xk != xp
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xk,X0) = 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)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0) = 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)
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0) = sdtpldt0(sdtpldt0(xn,xm),xp) )
| sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f56,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(f57,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(f66,plain,
( sz00 != xk
& sz10 != xk ),
inference(ennf_transformation,[],[f46]) ).
fof(f67,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,[],[f56]) ).
fof(f68,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,[],[f67]) ).
fof(f69,plain,
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr)
| ( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0) )
& ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f75,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(f76,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,[],[f75]) ).
fof(f80,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f81,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f83,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f82]) ).
fof(f99,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f100,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f99]) ).
fof(f117,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(f118,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,[],[f117]) ).
fof(f121,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f122,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f124,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f123]) ).
fof(f126,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f127,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f126]) ).
fof(f145,plain,
( aNaturalNumber0(xr)
& aNaturalNumber0(sK9)
& xk = sdtasdt0(xr,sK9)
& 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,[sK9]),skolemize(X0,sK9)],[f68]) ).
fof(f146,plain,
( aNaturalNumber0(sK10)
& xk = sdtpldt0(xr,sK10)
& aNaturalNumber0(sK11)
& sdtasdt0(xn,xm) = sdtasdt0(xr,sK11)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f57]) ).
fof(f147,plain,
( xk != xp
& aNaturalNumber0(sK12)
& xp = sdtpldt0(xk,sK12)
& sdtlseqdt0(xk,xp) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f50]) ).
fof(f156,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f127]) ).
fof(f157,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X0,X3) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f156]) ).
fof(f158,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK16(X0,X1))
& sdtpldt0(X0,sK16(X0,X1)) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X3,sK16(X0,X1))],[f157]) ).
fof(f161,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f162,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f163,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f202,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f204,plain,
sz00 != xk,
inference(cnf_transformation,[],[f66]) ).
fof(f212,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f145]) ).
fof(f215,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f145]) ).
fof(f219,plain,
xk = sdtpldt0(xr,sK10),
inference(cnf_transformation,[],[f146]) ).
fof(f220,plain,
aNaturalNumber0(sK10),
inference(cnf_transformation,[],[f146]) ).
fof(f221,plain,
sdtlseqdt0(xk,xp),
inference(cnf_transformation,[],[f147]) ).
fof(f224,plain,
xp != xk,
inference(cnf_transformation,[],[f147]) ).
fof(f225,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,[],[f69]) ).
fof(f236,plain,
! [X2,X0,X1] :
( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| X1 = X2
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f241,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f242,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f254,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f276,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,[],[f118]) ).
fof(f282,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f122]) ).
fof(f283,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f287,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f158]) ).
fof(f297,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f287]) ).
fof(f394,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,[],[f225,f241]) ).
fof(f424,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,[],[f394,f161]) ).
fof(f566,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,[],[f424,f241]) ).
fof(f567,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,[],[f566]) ).
fof(f569,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,[],[f567,f215]) ).
fof(f703,plain,
( ~ sdtlseqdt0(xp,xk)
| xp = xk
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f283,f221]) ).
fof(f715,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f703,f224]) ).
fof(f718,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f715,f161]) ).
fof(f719,plain,
~ sdtlseqdt0(xp,xk),
inference(forward_subsumption_resolution,[],[f718,f202]) ).
fof(f720,plain,
( ~ doDivides0(xp,xk)
| sz00 = xk
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f719,f254]) ).
fof(f722,plain,
( ~ doDivides0(xp,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f720,f204]) ).
fof(f723,plain,
( ~ doDivides0(xp,xk)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f722,f161]) ).
fof(f724,plain,
~ doDivides0(xp,xk),
inference(forward_subsumption_resolution,[],[f723,f202]) ).
fof(f751,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f297,f242]) ).
fof(f774,plain,
( sdtlseqdt0(xr,xk)
| ~ aNaturalNumber0(sK10)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[],[f751,f219]) ).
fof(f780,plain,
( sdtlseqdt0(xr,xk)
| ~ aNaturalNumber0(xr) ),
inference(forward_subsumption_resolution,[],[f774,f220]) ).
fof(f783,plain,
sdtlseqdt0(xr,xk),
inference(forward_subsumption_resolution,[],[f780,f215]) ).
fof(f2244,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,[],[f276,f569]) ).
fof(f2288,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,[],[f2244]) ).
fof(f2314,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f2288,f236]) ).
fof(f2328,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f2314,f215]) ).
fof(f2330,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| xp = xr
| ~ sdtlseqdt0(xr,xp) ),
inference(forward_subsumption_resolution,[],[f2328,f161]) ).
fof(f2331,plain,
( xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f2330,f242]) ).
fof(f2332,plain,
( xp = xr
| ~ sdtlseqdt0(xr,xp)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f2331,f163]) ).
fof(f2333,plain,
( ~ sdtlseqdt0(xr,xp)
| xp = xr ),
inference(forward_subsumption_resolution,[],[f2332,f162]) ).
fof(f2334,plain,
! [X0] :
( xp = xr
| ~ sdtlseqdt0(xr,X0)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f2333,f282]) ).
fof(f2339,plain,
! [X0] :
( xp = xr
| ~ sdtlseqdt0(xr,X0)
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f2334,f215]) ).
fof(f2342,plain,
! [X0] :
( ~ sdtlseqdt0(xr,X0)
| xp = xr
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f2339,f161]) ).
fof(f2448,plain,
( xp = xr
| ~ sdtlseqdt0(xk,xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f2342,f783]) ).
fof(f2453,plain,
( xp = xr
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f2448,f221]) ).
fof(f2459,plain,
xp = xr,
inference(forward_subsumption_resolution,[],[f2453,f202]) ).
fof(f2580,plain,
~ doDivides0(xr,xk),
inference(superposition,[],[f724,f2459]) ).
fof(f2595,plain,
$false,
inference(forward_subsumption_resolution,[],[f2580,f212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM507+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.41 % Computer : n010.cluster.edu
% 0.11/5.41 % Model : x86_64 x86_64
% 0.11/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.41 % Memory : 8046.5625MB
% 0.11/5.41 % OS : Linux 6.8.0-71-generic
% 0.11/5.41 % CPULimit : 300
% 0.11/5.41 % WCLimit : 300
% 0.11/5.41 % DateTime : Sun Sep 27 20:15:22 UTC 2026
% 0.11/5.41 % CPUTime :
% 0.11/5.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.45 Running first-order theorem proving
% 0.11/5.45 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
% 2.86/6.37 % (1281832)Detected formulas, will run a generic FOF schedule.
% 2.86/6.37 % (1281837)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=4152981756:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.86/6.37 % (1281838)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=377833059:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.86/6.37 % (1281840)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3972784343:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.86/6.37 % (1281843)dis-21_1_sil=8000:lcm=predicate:random_seed=3670552911: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)
% 2.86/6.37 % (1281842)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=189005362:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.86/6.37 % (1281839)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=1662846198:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.86/6.37 % (1281841)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4156635591:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.86/6.37 % (1281841)First to succeed.
% 2.86/6.37 % (1281841)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1281832"
% 2.86/6.37 % (1281840)Instruction limit reached!
% 2.86/6.37 % (1281840)------------------------------
% 2.86/6.37 % (1281840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/6.37 % (1281840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/6.37 % (1281840)CaDiCaL version: 2.1.3
% 2.86/6.37 % (1281840)Termination reason: Instruction limit
% 2.86/6.37 % (1281840)Termination phase: Saturation
% 2.86/6.37 % (1281840)Time elapsed: 0.061 s
% 2.86/6.37 % (1281840)Peak memory usage: 89 MB
% 2.86/6.37 % (1281840)Instructions burned: 109 (million)
% 2.86/6.37 % (1281843)Instruction limit reached!
% 2.86/6.37 % (1281843)------------------------------
% 2.86/6.37 % (1281843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/6.37 % (1281843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/6.37 % (1281843)CaDiCaL version: 2.1.3
% 2.86/6.37 % (1281843)Termination reason: Instruction limit
% 2.86/6.37 % (1281843)Termination phase: Saturation
% 2.86/6.37 % (1281843)Time elapsed: 0.078 s
% 2.86/6.37 % (1281843)Peak memory usage: 91 MB
% 2.86/6.37 % (1281843)Instructions burned: 130 (million)
% 2.86/6.37 % (1281842)Instruction limit reached!
% 2.86/6.37 % (1281842)------------------------------
% 2.86/6.37 % (1281842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/6.37 % (1281842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/6.37 % (1281842)CaDiCaL version: 2.1.3
% 2.86/6.37 % (1281842)Termination reason: Instruction limit
% 2.86/6.37 % (1281842)Termination phase: Saturation
% 2.86/6.37 % (1281842)Time elapsed: 0.085 s
% 2.86/6.37 % (1281842)Peak memory usage: 90 MB
% 2.86/6.37 % (1281842)Instructions burned: 139 (million)
% 2.86/6.37 % (1281851)lrs+10_1_sil=8000:sp=occurrence:random_seed=1069449271:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.86/6.37 % (1281852)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1911700230:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.86/6.37 % (1281853)lrs+1011_1_sil=32000:sp=occurrence:random_seed=83882930:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.86/6.37 % (1281841)Refutation found. Thanks to Tanya!
% 2.86/6.37 % SZS status Theorem for theBenchmark
% 2.86/6.37 % SZS output start Proof for theBenchmark
% See solution above
% 4.00/6.57 % (1281841)------------------------------
% 4.00/6.57 % (1281841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/6.57 % (1281841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/6.57 % (1281841)CaDiCaL version: 2.1.3
% 4.00/6.57 % (1281841)Termination reason: Refutation
% 4.00/6.57 % (1281841)Time elapsed: 0.050 s
% 4.00/6.57 % (1281841)Peak memory usage: 89 MB
% 4.00/6.57 % (1281841)Instructions burned: 89 (million)
% 4.00/6.57 % (1281841)------------------------------
% 4.00/6.57 % (1281841)------------------------------
% 4.00/6.57 % (1281832)Success in time 0.482 s
% 4.00/6.57 % Vampire exiting
%------------------------------------------------------------------------------