%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM511+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:15:31 PM UTC 2026
% Result : Theorem 5.63s 1.73s
% Output : Refutation 6.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 109 ( 32 unt; 2 def)
% Number of atoms : 399 ( 130 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 464 ( 174 ~; 175 |; 95 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 93 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f36,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( aNaturalNumber0(X2)
=> sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( aNaturalNumber0(xr)
& ? [X0] :
( aNaturalNumber0(X0)
& xk = sdtasdt0(xr,X0) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xr = sdtasdt0(X0,X1) )
| doDivides0(X0,xr) ) )
=> ( X0 = sz10
| X0 = xr ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xr,X0) = xk )
& ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X0) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(f52,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xr,X0) )
& doDivides0(xr,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(f54,conjecture,
( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,X0) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f55,negated_conjecture,
~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,X0) )
| doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)) ) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f61,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(f62,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,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f67,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f66]) ).
fof(f73,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f74,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f73]) ).
fof(f110,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f111,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f110]) ).
fof(f112,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(f113,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,[],[f112]) ).
fof(f122,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f123,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f122]) ).
fof(f135,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,[],[f61]) ).
fof(f136,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,[],[f135]) ).
fof(f139,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xp,X0) != sdtasdt0(sdtsldt0(xn,xr),xm) )
& ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ),
inference(ennf_transformation,[],[f55]) ).
fof(f140,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xp,X0) != sdtasdt0(sdtsldt0(xn,xr),xm) )
& ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ),
inference(flattening,[],[f139]) ).
fof(f149,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f111]) ).
fof(f150,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X0,X3) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f149]) ).
fof(f151,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK3(X0,X1))
& sdtasdt0(X0,sK3(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1))],[f150]) ).
fof(f152,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,[],[f113]) ).
fof(f153,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,[],[f152]) ).
fof(f169,plain,
( aNaturalNumber0(xr)
& aNaturalNumber0(sK13)
& xk = sdtasdt0(xr,sK13)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( sz10 = X1
| xr = X1
| ~ aNaturalNumber0(X1)
| ( ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != xr )
& ~ doDivides0(X1,xr) ) )
& isPrime0(xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f136]) ).
fof(f170,plain,
( aNaturalNumber0(sK14)
& xk = sdtpldt0(xr,sK14)
& aNaturalNumber0(sK15)
& sdtasdt0(xn,xm) = sdtasdt0(xr,sK15)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f62]) ).
fof(f173,plain,
( aNaturalNumber0(sK19)
& xn = sdtasdt0(xr,sK19)
& doDivides0(xr,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(X0,sK19)],[f52]) ).
fof(f179,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f184,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f224,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f151]) ).
fof(f226,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f153]) ).
fof(f227,plain,
! [X2,X0,X1] :
( sdtsldt0(X1,X0) = X2
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f153]) ).
fof(f232,plain,
! [X2,X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f243,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f244,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f245,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f283,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f284,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f293,plain,
sz00 != xr,
inference(cnf_transformation,[],[f169]) ).
fof(f294,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f169]) ).
fof(f297,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f169]) ).
fof(f298,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f170]) ).
fof(f299,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,sK15),
inference(cnf_transformation,[],[f170]) ).
fof(f300,plain,
aNaturalNumber0(sK15),
inference(cnf_transformation,[],[f170]) ).
fof(f316,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f173]) ).
fof(f328,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f140]) ).
fof(f329,plain,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(cnf_transformation,[],[f140]) ).
fof(f337,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f224]) ).
fof(f338,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| sdtsldt0(sdtasdt0(X0,X2),X0) = X2 ),
inference(equality_resolution,[],[f227]) ).
fof(f339,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f226]) ).
fof(f387,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(superposition,[],[f179,f283]) ).
fof(f389,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f387,f243]) ).
fof(f391,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(forward_subsumption_resolution,[],[f389,f284]) ).
fof(f475,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sK15)
| sz00 = xr
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| sK15 = sdtsldt0(sdtasdt0(xn,xm),xr) ),
inference(superposition,[],[f338,f299]) ).
fof(f479,plain,
( ~ aNaturalNumber0(sK15)
| sz00 = xr
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| sK15 = sdtsldt0(sdtasdt0(xn,xm),xr) ),
inference(forward_subsumption_resolution,[],[f475,f391]) ).
fof(f480,plain,
( sz00 = xr
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| sK15 = sdtsldt0(sdtasdt0(xn,xm),xr) ),
inference(forward_subsumption_resolution,[],[f479,f300]) ).
fof(f481,plain,
( ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xr)
| sK15 = sdtsldt0(sdtasdt0(xn,xm),xr) ),
inference(forward_subsumption_resolution,[],[f480,f293]) ).
fof(f482,plain,
( ~ aNaturalNumber0(xr)
| sK15 = sdtsldt0(sdtasdt0(xn,xm),xr) ),
inference(forward_subsumption_resolution,[],[f481,f298]) ).
fof(f483,plain,
sK15 = sdtsldt0(sdtasdt0(xn,xm),xr),
inference(forward_subsumption_resolution,[],[f482,f297]) ).
fof(f518,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtsldt0(xn,xr),X0) = sdtasdt0(X0,sdtsldt0(xn,xr)) ),
inference(resolution,[],[f184,f328]) ).
fof(f520,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xm,X0) = sdtasdt0(X0,xm) ),
inference(resolution,[],[f184,f244]) ).
fof(f527,plain,
sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xm,sdtsldt0(xn,xr)),
inference(resolution,[],[f518,f244]) ).
fof(f532,plain,
~ doDivides0(xp,sdtasdt0(xm,sdtsldt0(xn,xr))),
inference(superposition,[],[f329,f527]) ).
fof(f566,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[],[f520,f245]) ).
fof(f579,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = xr
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f294,f232]) ).
fof(f582,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f579,f293]) ).
fof(f584,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f582,f297]) ).
fof(f586,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr) ),
inference(forward_subsumption_resolution,[],[f584,f284]) ).
fof(f591,plain,
sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(xp,xk),xr),
inference(resolution,[],[f586,f243]) ).
fof(f595,plain,
sdtsldt0(sdtasdt0(xn,xm),xr) = sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(forward_demodulation,[],[f591,f283]) ).
fof(f597,plain,
sK15 = sdtasdt0(xp,sdtsldt0(xk,xr)),
inference(forward_demodulation,[],[f595,f483]) ).
fof(f603,plain,
( ~ aNaturalNumber0(sK15)
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sK15) ),
inference(superposition,[],[f337,f597]) ).
fof(f604,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,sK15) ),
inference(forward_subsumption_resolution,[],[f603,f300]) ).
fof(f608,definition,
( spl21_17
<=> aNaturalNumber0(sdtsldt0(xk,xr)) ),
introduced(definition,[new_symbols(definition,[spl21_17])],[avatar_definition]) ).
fof(f609,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| spl21_17 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f614,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| doDivides0(xp,sK15) ),
inference(forward_subsumption_resolution,[],[f604,f243]) ).
fof(f616,definition,
( spl21_19
<=> doDivides0(xp,sK15) ),
introduced(definition,[new_symbols(definition,[spl21_19])],[avatar_definition]) ).
fof(f617,plain,
( doDivides0(xp,sK15)
| ~ spl21_19 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f620,plain,
( spl21_19
| ~ spl21_17 ),
inference(avatar_split_clause,[],[f614,f608,f616]) ).
fof(f627,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = xr
| sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f316,f232]) ).
fof(f629,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f627,f293]) ).
fof(f630,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f629,f297]) ).
fof(f631,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr) ),
inference(forward_subsumption_resolution,[],[f630,f245]) ).
fof(f669,plain,
( sz00 = xr
| aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f339,f294]) ).
fof(f672,plain,
( aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) ),
inference(forward_subsumption_resolution,[],[f669,f293]) ).
fof(f677,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| spl21_17 ),
inference(forward_subsumption_resolution,[],[f672,f609]) ).
fof(f680,plain,
( ~ aNaturalNumber0(xk)
| spl21_17 ),
inference(forward_subsumption_resolution,[],[f677,f297]) ).
fof(f683,plain,
( $false
| spl21_17 ),
inference(forward_subsumption_resolution,[],[f680,f284]) ).
fof(f684,plain,
spl21_17,
inference(avatar_contradiction_clause,[],[f683]) ).
fof(f694,plain,
sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(xm,xn),xr),
inference(resolution,[],[f631,f244]) ).
fof(f701,plain,
sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(xn,xm),xr),
inference(forward_demodulation,[],[f694,f566]) ).
fof(f704,plain,
sK15 = sdtasdt0(xm,sdtsldt0(xn,xr)),
inference(forward_demodulation,[],[f701,f483]) ).
fof(f728,plain,
~ doDivides0(xp,sK15),
inference(superposition,[],[f532,f704]) ).
fof(f737,plain,
( $false
| ~ spl21_19 ),
inference(forward_subsumption_resolution,[],[f728,f617]) ).
fof(f738,plain,
~ spl21_19,
inference(avatar_contradiction_clause,[],[f737]) ).
cnf(s16,plain,
( ~ spl21_17
| spl21_19 ),
inference(sat_conversion,[],[f620]) ).
cnf(s18,plain,
spl21_17,
inference(sat_conversion,[],[f684]) ).
cnf(s21,plain,
~ spl21_19,
inference(sat_conversion,[],[f738]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s16,s21,s18]) ).
fof(f749,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM511+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:22:01 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.63/1.73 % (3924754)Detected formulas, will run a generic FOF schedule.
% 5.63/1.73 % (3924760)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=3598591884:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.63/1.73 % (3924762)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3403442442:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.63/1.73 % (3924761)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=3208756522:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.63/1.73 % (3924759)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=659505986:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.63/1.73 % (3924763)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2218382374:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.63/1.73 % (3924765)dis-21_1_sil=8000:lcm=predicate:random_seed=2873227256: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)
% 5.63/1.73 % (3924764)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3145675669:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.63/1.73 % (3924762)Instruction limit reached!
% 5.63/1.73 % (3924762)------------------------------
% 5.63/1.73 % (3924762)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.73 % (3924762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.73 % (3924762)CaDiCaL version: 2.1.3
% 5.63/1.73 % (3924762)Termination reason: Instruction limit
% 5.63/1.73 % (3924762)Termination phase: Saturation
% 5.63/1.73 % (3924762)Time elapsed: 0.064 s
% 5.63/1.73 % (3924762)Peak memory usage: 89 MB
% 5.63/1.73 % (3924762)Instructions burned: 109 (million)
% 5.63/1.73 % (3924763)Instruction limit reached!
% 5.63/1.73 % (3924763)------------------------------
% 5.63/1.73 % (3924763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.73 % (3924763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.73 % (3924763)CaDiCaL version: 2.1.3
% 5.63/1.73 % (3924763)Termination reason: Instruction limit
% 5.63/1.73 % (3924763)Termination phase: Saturation
% 5.63/1.73 % (3924763)Time elapsed: 0.068 s
% 5.63/1.73 % (3924763)Peak memory usage: 88 MB
% 5.63/1.73 % (3924763)Instructions burned: 121 (million)
% 5.63/1.73 % (3924765)Instruction limit reached!
% 5.63/1.73 % (3924765)------------------------------
% 5.63/1.73 % (3924765)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.73 % (3924765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.73 % (3924765)CaDiCaL version: 2.1.3
% 5.63/1.73 % (3924765)Termination reason: Instruction limit
% 5.63/1.73 % (3924765)Termination phase: Saturation
% 5.63/1.73 % (3924765)Time elapsed: 0.109 s
% 5.63/1.73 % (3924765)Peak memory usage: 90 MB
% 5.63/1.73 % (3924765)Instructions burned: 130 (million)
% 5.63/1.73 % (3924764)Instruction limit reached!
% 5.63/1.73 % (3924764)------------------------------
% 5.63/1.73 % (3924764)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.73 % (3924764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.73 % (3924764)CaDiCaL version: 2.1.3
% 5.63/1.73 % (3924764)Termination reason: Instruction limit
% 5.63/1.73 % (3924764)Termination phase: Saturation
% 5.63/1.73 % (3924764)Time elapsed: 0.122 s
% 5.63/1.73 % (3924764)Peak memory usage: 90 MB
% 5.63/1.73 % (3924764)Instructions burned: 140 (million)
% 5.63/1.73 % (3924773)lrs+10_1_sil=8000:sp=occurrence:random_seed=2928118282:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.63/1.73 % (3924774)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2121662759:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.63/1.73 % (3924775)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3258865687:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.63/1.73 % (3924776)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=1150047701:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.63/1.73 % (3924774)Instruction limit reached!
% 5.63/1.73 % (3924774)------------------------------
% 5.63/1.73 % (3924774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.73 % (3924774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.73 % (3924774)CaDiCaL version: 2.1.3
% 5.63/1.73 % (3924774)Termination reason: Instruction limit
% 5.63/1.73 % (3924774)Termination phase: Saturation
% 5.63/1.73 % (3924774)Time elapsed: 0.075 s
% 5.63/1.73 % (3924774)Peak memory usage: 93 MB
% 5.63/1.73 % (3924774)Instructions burned: 157 (million)
% 5.63/1.73 % (3924773)Instruction limit reached!
% 5.63/1.73 % (3924773)------------------------------
% 5.63/1.73 % (3924773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.73 % (3924773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.73 % (3924773)CaDiCaL version: 2.1.3
% 5.63/1.73 % (3924773)Termination reason: Instruction limit
% 5.63/1.73 % (3924773)Termination phase: Saturation
% 5.63/1.73 % (3924773)Time elapsed: 0.152 s
% 5.63/1.73 % (3924773)Peak memory usage: 91 MB
% 5.63/1.73 % (3924773)Instructions burned: 286 (million)
% 5.63/1.73 % (3924776)Instruction limit reached!
% 5.63/1.73 % (3924776)------------------------------
% 5.63/1.73 % (3924776)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.73 % (3924776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.73 % (3924776)CaDiCaL version: 2.1.3
% 5.63/1.73 % (3924776)Termination reason: Instruction limit
% 5.63/1.73 % (3924776)Termination phase: Saturation
% 5.63/1.73 % (3924776)Time elapsed: 0.112 s
% 5.63/1.73 % (3924776)Peak memory usage: 94 MB
% 5.63/1.73 % (3924776)Instructions burned: 248 (million)
% 5.63/1.73 % (3924760)First to succeed.
% 5.63/1.73 % (3924760)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3924754"
% 5.63/1.73 % (3924781)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1252201439:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.63/1.73 % (3924775)Instruction limit reached!
% 5.63/1.73 % (3924775)------------------------------
% 5.63/1.73 % (3924775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.73 % (3924775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.73 % (3924775)CaDiCaL version: 2.1.3
% 5.63/1.73 % (3924775)Termination reason: Instruction limit
% 5.63/1.73 % (3924775)Termination phase: Saturation
% 5.63/1.73 % (3924775)Time elapsed: 0.193 s
% 5.63/1.73 % (3924775)Peak memory usage: 91 MB
% 5.63/1.73 % (3924775)Instructions burned: 326 (million)
% 5.63/1.73 % (3924782)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3220477160:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.63/1.73 % (3924783)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1844465064:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.63/1.73 % (3924781)Instruction limit reached!
% 5.63/1.73 % (3924781)------------------------------
% 5.63/1.73 % (3924781)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.73 % (3924781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.73 % (3924781)CaDiCaL version: 2.1.3
% 5.63/1.73 % (3924781)Termination reason: Instruction limit
% 5.63/1.73 % (3924781)Termination phase: Saturation
% 5.63/1.73 % (3924781)Time elapsed: 0.161 s
% 5.63/1.73 % (3924781)Peak memory usage: 89 MB
% 5.63/1.73 % (3924781)Instructions burned: 295 (million)
% 5.63/1.73 % (3924783)Instruction limit reached!
% 5.63/1.73 % (3924783)------------------------------
% 5.63/1.73 % (3924783)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.63/1.73 % (3924783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.63/1.73 % (3924783)CaDiCaL version: 2.1.3
% 5.63/1.73 % (3924783)Termination reason: Instruction limit
% 5.63/1.73 % (3924783)Termination phase: Saturation
% 5.63/1.73 % (3924783)Time elapsed: 0.066 s
% 5.63/1.73 % (3924783)Peak memory usage: 91 MB
% 5.63/1.73 % (3924783)Instructions burned: 114 (million)
% 5.63/1.73 % (3924785)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2139437640:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.63/1.73 % (3924759)Also succeeded, but the first one will report.
% 5.63/1.73 % (3924760)Refutation found. Thanks to Tanya!
% 5.63/1.73 % SZS status Theorem for theBenchmark
% 5.63/1.73 % SZS output start Proof for theBenchmark
% See solution above
% 6.51/1.82 % (3924760)------------------------------
% 6.51/1.82 % (3924760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.51/1.82 % (3924760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.51/1.82 % (3924760)CaDiCaL version: 2.1.3
% 6.51/1.82 % (3924760)Termination reason: Refutation
% 6.51/1.82 % (3924760)Time elapsed: 0.460 s
% 6.51/1.82 % (3924760)Peak memory usage: 131 MB
% 6.51/1.82 % (3924760)Instructions burned: 1033 (million)
% 6.51/1.82 % (3924760)------------------------------
% 6.51/1.82 % (3924760)------------------------------
% 6.51/1.82 % (3924754)Success in time 0.862 s
% 6.51/1.82 % Vampire exiting
%------------------------------------------------------------------------------