%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM475+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 12:15:21 PM UTC 2026
% Result : Theorem 2.69s 1.29s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 92 ( 28 unt; 0 def)
% Number of atoms : 312 ( 84 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 394 ( 174 ~; 172 |; 32 &)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 97 ( 92 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
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(f34,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
fof(f35,axiom,
( doDivides0(xl,xm)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).
fof(f36,axiom,
xl != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1347) ).
fof(f37,axiom,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
fof(f38,axiom,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
fof(f39,axiom,
sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1395) ).
fof(f40,axiom,
xr = sdtmndt0(xq,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1422) ).
fof(f41,axiom,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1459) ).
fof(f42,conjecture,
xn = sdtasdt0(xl,xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
xn != sdtasdt0(xl,xr),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f44,plain,
xn != sdtasdt0(xl,xr),
inference(flattening,[],[f43]) ).
fof(f54,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f55,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f54]) ).
fof(f74,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(f75,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,[],[f74]) ).
fof(f85,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f86,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f88,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f87]) ).
fof(f93,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f94,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f93]) ).
fof(f98,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,[],[f75]) ).
fof(f99,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,[],[f98]) ).
fof(f100,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,[],[f86]) ).
fof(f101,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,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtpldt0(X0,sK1(X0,X1)) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f101]) ).
fof(f103,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f88]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f103]) ).
fof(f105,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f106,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f107,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f108,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f35]) ).
fof(f109,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f35]) ).
fof(f110,plain,
sz00 != xl,
inference(cnf_transformation,[],[f36]) ).
fof(f111,plain,
xp = sdtsldt0(xm,xl),
inference(cnf_transformation,[],[f37]) ).
fof(f112,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(cnf_transformation,[],[f38]) ).
fof(f113,plain,
sdtlseqdt0(xp,xq),
inference(cnf_transformation,[],[f39]) ).
fof(f114,plain,
xr = sdtmndt0(xq,xp),
inference(cnf_transformation,[],[f40]) ).
fof(f115,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnf_transformation,[],[f41]) ).
fof(f116,plain,
xn != sdtasdt0(xl,xr),
inference(cnf_transformation,[],[f44]) ).
fof(f123,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f144,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f145,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f158,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f160,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f161,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f164,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f167,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f145]) ).
fof(f168,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f144]) ).
fof(f170,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f158]) ).
fof(f171,plain,
! [X2,X0] :
( sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f161]) ).
fof(f172,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f160]) ).
fof(f227,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq) ),
inference(superposition,[],[f172,f114]) ).
fof(f228,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq) ),
inference(forward_subsumption_resolution,[],[f227,f113]) ).
fof(f294,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f170,f123]) ).
fof(f373,plain,
( aNaturalNumber0(xp)
| sz00 = xl
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f167,f111]) ).
fof(f374,plain,
( aNaturalNumber0(xq)
| sz00 = xl
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(superposition,[],[f167,f112]) ).
fof(f375,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f374,f110]) ).
fof(f376,plain,
( aNaturalNumber0(xp)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f373,f110]) ).
fof(f377,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(forward_subsumption_resolution,[],[f375,f108]) ).
fof(f378,plain,
( aNaturalNumber0(xp)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f376,f109]) ).
fof(f379,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| aNaturalNumber0(xq) ),
inference(forward_subsumption_resolution,[],[f377,f107]) ).
fof(f380,plain,
( aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f378,f107]) ).
fof(f381,plain,
aNaturalNumber0(xp),
inference(forward_subsumption_resolution,[],[f380,f106]) ).
fof(f404,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f379,f123]) ).
fof(f405,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f404,f106]) ).
fof(f406,plain,
aNaturalNumber0(xq),
inference(forward_subsumption_resolution,[],[f405,f105]) ).
fof(f712,plain,
( xm = sdtasdt0(xl,xp)
| sz00 = xl
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f168,f111]) ).
fof(f738,plain,
( xm = sdtasdt0(xl,xp)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f712,f110]) ).
fof(f742,plain,
( xm = sdtasdt0(xl,xp)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f738,f109]) ).
fof(f744,plain,
( xm = sdtasdt0(xl,xp)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f742,f107]) ).
fof(f745,plain,
xm = sdtasdt0(xl,xp),
inference(forward_subsumption_resolution,[],[f744,f106]) ).
fof(f1301,plain,
! [X2,X0] :
( sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(forward_subsumption_resolution,[],[f171,f294]) ).
fof(f1302,plain,
! [X2,X0] :
( sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f1301,f123]) ).
fof(f1310,plain,
( sdtasdt0(xl,xr) = sdtmndt0(sdtpldt0(sdtasdt0(xl,xp),xn),sdtasdt0(xl,xp))
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(superposition,[],[f1302,f115]) ).
fof(f1327,plain,
( sdtasdt0(xl,xr) = sdtmndt0(sdtpldt0(xm,xn),xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(forward_demodulation,[],[f1310,f745]) ).
fof(f1334,plain,
( ~ aNaturalNumber0(xm)
| sdtasdt0(xl,xr) = sdtmndt0(sdtpldt0(xm,xn),xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xr)) ),
inference(forward_demodulation,[],[f1327,f745]) ).
fof(f1335,plain,
( sdtasdt0(xl,xr) = sdtmndt0(sdtpldt0(xm,xn),xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xr)) ),
inference(forward_subsumption_resolution,[],[f1334,f106]) ).
fof(f2332,plain,
( xn = sdtasdt0(xl,xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xr)) ),
inference(superposition,[],[f1302,f1335]) ).
fof(f2335,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xr)) ),
inference(forward_subsumption_resolution,[],[f2332,f116]) ).
fof(f2337,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xl,xr)) ),
inference(forward_subsumption_resolution,[],[f2335,f105]) ).
fof(f2339,plain,
~ aNaturalNumber0(sdtasdt0(xl,xr)),
inference(forward_subsumption_resolution,[],[f2337,f106]) ).
fof(f2341,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[],[f2339,f164]) ).
fof(f2346,plain,
~ aNaturalNumber0(xr),
inference(forward_subsumption_resolution,[],[f2341,f107]) ).
fof(f2350,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq) ),
inference(resolution,[],[f2346,f228]) ).
fof(f2351,plain,
~ aNaturalNumber0(xq),
inference(forward_subsumption_resolution,[],[f2350,f381]) ).
fof(f2352,plain,
$false,
inference(forward_subsumption_resolution,[],[f2351,f406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM475+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.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 20:06:02 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.69/1.29 % (1272915)Detected formulas, will run a generic FOF schedule.
% 2.69/1.29 % (1272923)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2025184427:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.29 % (1272925)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1439606374:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.29 % (1272924)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=752414564:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.29 % (1272920)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=1088491763:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.29 % (1272926)dis-21_1_sil=8000:lcm=predicate:random_seed=2794795797: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)
% 2.69/1.29 % (1272921)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=3004002769:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.29 % (1272922)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=3186135862:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.29 % (1272923)Instruction limit reached!
% 2.69/1.29 % (1272923)------------------------------
% 2.69/1.29 % (1272923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.29 % (1272923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.29 % (1272923)CaDiCaL version: 2.1.3
% 2.69/1.29 % (1272923)Termination reason: Instruction limit
% 2.69/1.29 % (1272923)Termination phase: Saturation
% 2.69/1.29 % (1272923)Time elapsed: 0.033 s
% 2.69/1.29 % (1272923)Peak memory usage: 89 MB
% 2.69/1.29 % (1272923)Instructions burned: 110 (million)
% 2.69/1.29 % (1272924)First to succeed.
% 2.69/1.29 % (1272924)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1272915"
% 2.69/1.29 % (1272926)Instruction limit reached!
% 2.69/1.29 % (1272926)------------------------------
% 2.69/1.29 % (1272926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.29 % (1272926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.29 % (1272926)CaDiCaL version: 2.1.3
% 2.69/1.29 % (1272926)Termination reason: Instruction limit
% 2.69/1.29 % (1272926)Termination phase: Saturation
% 2.69/1.29 % (1272926)Time elapsed: 0.080 s
% 2.69/1.29 % (1272926)Peak memory usage: 91 MB
% 2.69/1.29 % (1272926)Instructions burned: 130 (million)
% 2.69/1.29 % (1272925)Instruction limit reached!
% 2.69/1.29 % (1272925)------------------------------
% 2.69/1.29 % (1272925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.29 % (1272925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.29 % (1272925)CaDiCaL version: 2.1.3
% 2.69/1.29 % (1272925)Termination reason: Instruction limit
% 2.69/1.29 % (1272925)Termination phase: Saturation
% 2.69/1.29 % (1272925)Time elapsed: 0.086 s
% 2.69/1.29 % (1272925)Peak memory usage: 90 MB
% 2.69/1.29 % (1272925)Instructions burned: 139 (million)
% 2.69/1.29 % (1272934)lrs+10_1_sil=8000:sp=occurrence:random_seed=1695629094:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.69/1.29 % (1272934)Also succeeded, but the first one will report.
% 2.69/1.29 % (1272936)lrs+1011_1_sil=32000:sp=occurrence:random_seed=806762076:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.69/1.29 % (1272935)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1949691576:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.69/1.29 % (1272936)Also succeeded, but the first one will report.
% 2.69/1.29 % (1272924)Refutation found. Thanks to Tanya!
% 2.69/1.29 % SZS status Theorem for theBenchmark
% 2.69/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.72/1.48 % (1272924)------------------------------
% 3.72/1.48 % (1272924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.48 % (1272924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.48 % (1272924)CaDiCaL version: 2.1.3
% 3.72/1.48 % (1272924)Termination reason: Refutation
% 3.72/1.48 % (1272924)Time elapsed: 0.041 s
% 3.72/1.48 % (1272924)Peak memory usage: 89 MB
% 3.72/1.48 % (1272924)Instructions burned: 70 (million)
% 3.72/1.48 % (1272924)------------------------------
% 3.72/1.48 % (1272924)------------------------------
% 3.72/1.48 % (1272915)Success in time 0.447 s
% 3.72/1.48 % Vampire exiting
%------------------------------------------------------------------------------