%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM518+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 12:24:38 PM UTC 2026
% Result : Theorem 1.98s 0.82s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 25
% Syntax : Number of formulae : 141 ( 32 unt; 10 def)
% Number of atoms : 388 ( 75 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 427 ( 180 ~; 189 |; 31 &)
% ( 16 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
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(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(f44,axiom,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(f48,axiom,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(f52,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2487) ).
fof(f53,axiom,
( sdtsldt0(xn,xr) != xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2504) ).
fof(f55,axiom,
( doDivides0(xp,sdtsldt0(xn,xr))
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2645) ).
fof(f56,conjecture,
( doDivides0(xp,xn)
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ( doDivides0(xp,xn)
| doDivides0(xp,xm) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f73,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f89,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f90,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f92,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f91]) ).
fof(f109,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(f110,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,[],[f109]) ).
fof(f117,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f118,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f117]) ).
fof(f121,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(f122,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f121]) ).
fof(f128,plain,
( ~ doDivides0(xp,xn)
& ~ doDivides0(xp,xm) ),
inference(ennf_transformation,[],[f57]) ).
fof(f129,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f142,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f143,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f73]) ).
fof(f160,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f90]) ).
fof(f161,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f178,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2 ),
inference(cnf_transformation,[],[f110]) ).
fof(f179,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2 ),
inference(cnf_transformation,[],[f110]) ).
fof(f184,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| sz00 = X1
| ~ aNaturalNumber0(X1)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f192,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 != X0
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f196,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f197,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f198,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f200,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f206,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f44]) ).
fof(f213,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f215,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f221,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f52]) ).
fof(f222,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f53]) ).
fof(f223,plain,
xn != sdtsldt0(xn,xr),
inference(cnf_transformation,[],[f53]) ).
fof(f225,plain,
( doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f226,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f128]) ).
fof(f227,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f128]) ).
fof(f235,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f179]) ).
fof(f236,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1 ),
inference(equality_resolution,[],[f178]) ).
fof(f237,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(equality_resolution,[],[f192]) ).
fof(f241,definition,
( spl4_1
<=> doDivides0(xp,sdtsldt0(xn,xr)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f243,plain,
( doDivides0(xp,sdtsldt0(xn,xr))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f245,definition,
( spl4_2
<=> doDivides0(xp,xm) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f247,plain,
( doDivides0(xp,xm)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f225,f245,f241]) ).
fof(f268,definition,
( spl4_7
<=> isPrime0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f270,plain,
( ~ isPrime0(sz00)
| spl4_7 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f272,definition,
( spl4_8
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f274,plain,
( ~ aNaturalNumber0(sz00)
| spl4_8 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,plain,
( ~ spl4_7
| ~ spl4_8 ),
inference(avatar_split_clause,[],[f237,f272,f268]) ).
fof(f302,plain,
( $false
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f274,f129]) ).
fof(f303,plain,
spl4_8,
inference(avatar_contradiction_clause,[],[f302]) ).
fof(f311,definition,
( spl4_13
<=> aNaturalNumber0(sdtsldt0(xn,xr)) ),
introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition]) ).
fof(f312,plain,
( aNaturalNumber0(sdtsldt0(xn,xr))
| ~ spl4_13 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f313,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| spl4_13 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f460,plain,
sz00 = sdtasdt0(sz00,xm),
inference(resolution,[],[f142,f197]) ).
fof(f469,plain,
sz00 = sdtasdt0(xr,sz00),
inference(resolution,[],[f143,f215]) ).
fof(f1564,definition,
( spl4_94
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl4_94])],[avatar_definition]) ).
fof(f1565,plain,
( sz00 != xn
| spl4_94 ),
inference(avatar_component_clause,[],[f1564]) ).
fof(f1566,plain,
( sz00 = xn
| ~ spl4_94 ),
inference(avatar_component_clause,[],[f1564]) ).
fof(f1574,definition,
( spl4_96
<=> sz00 = xr ),
introduced(definition,[new_symbols(definition,[spl4_96])],[avatar_definition]) ).
fof(f1575,plain,
( sz00 != xr
| spl4_96 ),
inference(avatar_component_clause,[],[f1574]) ).
fof(f1576,plain,
( sz00 = xr
| ~ spl4_96 ),
inference(avatar_component_clause,[],[f1574]) ).
fof(f1763,plain,
( ~ doDivides0(xp,sz00)
| ~ spl4_94 ),
inference(superposition,[],[f227,f1566]) ).
fof(f1846,plain,
( isPrime0(sz00)
| ~ spl4_96 ),
inference(superposition,[],[f213,f1576]) ).
fof(f1947,plain,
( $false
| spl4_7
| ~ spl4_96 ),
inference(forward_subsumption_resolution,[],[f1846,f270]) ).
fof(f1948,plain,
( spl4_7
| ~ spl4_96 ),
inference(avatar_contradiction_clause,[],[f1947]) ).
fof(f1971,plain,
( doDivides0(xp,sdtasdt0(sz00,xm))
| ~ spl4_94 ),
inference(superposition,[],[f200,f1566]) ).
fof(f2056,plain,
( doDivides0(xp,sz00)
| ~ spl4_94 ),
inference(forward_demodulation,[],[f1971,f460]) ).
fof(f2057,plain,
( $false
| ~ spl4_94 ),
inference(forward_subsumption_resolution,[],[f2056,f1763]) ).
fof(f2058,plain,
~ spl4_94,
inference(avatar_contradiction_clause,[],[f2057]) ).
fof(f2439,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ sdtlseqdt0(xn,sdtsldt0(xn,xr))
| xn = sdtsldt0(xn,xr) ),
inference(resolution,[],[f160,f222]) ).
fof(f2465,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ sdtlseqdt0(xn,sdtsldt0(xn,xr))
| xn = sdtsldt0(xn,xr) ),
inference(forward_subsumption_resolution,[],[f2439,f198]) ).
fof(f2487,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
inference(forward_subsumption_resolution,[],[f2465,f223]) ).
fof(f2644,definition,
( spl4_163
<=> sdtlseqdt0(xn,sdtsldt0(xn,xr)) ),
introduced(definition,[new_symbols(definition,[spl4_163])],[avatar_definition]) ).
fof(f2646,plain,
( ~ sdtlseqdt0(xn,sdtsldt0(xn,xr))
| spl4_163 ),
inference(avatar_component_clause,[],[f2644]) ).
fof(f2647,plain,
( ~ spl4_163
| ~ spl4_13 ),
inference(avatar_split_clause,[],[f2487,f311,f2644]) ).
fof(f2887,definition,
( spl4_180
<=> sdtlseqdt0(xp,sdtsldt0(xn,xr)) ),
introduced(definition,[new_symbols(definition,[spl4_180])],[avatar_definition]) ).
fof(f2889,plain,
( sdtlseqdt0(xp,sdtsldt0(xn,xr))
| ~ spl4_180 ),
inference(avatar_component_clause,[],[f2887]) ).
fof(f2891,definition,
( spl4_181
<=> sz00 = sdtsldt0(xn,xr) ),
introduced(definition,[new_symbols(definition,[spl4_181])],[avatar_definition]) ).
fof(f2893,plain,
( sz00 = sdtsldt0(xn,xr)
| ~ spl4_181 ),
inference(avatar_component_clause,[],[f2891]) ).
fof(f6975,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f247,f226]) ).
fof(f6976,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f6975]) ).
fof(f7398,plain,
( ~ aNaturalNumber0(xr)
| ~ doDivides0(xr,xn)
| sz00 = xr
| ~ aNaturalNumber0(xn)
| spl4_13 ),
inference(resolution,[],[f313,f235]) ).
fof(f7399,plain,
( ~ doDivides0(xr,xn)
| sz00 = xr
| ~ aNaturalNumber0(xn)
| spl4_13 ),
inference(forward_subsumption_resolution,[],[f7398,f215]) ).
fof(f7400,plain,
( sz00 = xr
| ~ aNaturalNumber0(xn)
| spl4_13 ),
inference(forward_subsumption_resolution,[],[f7399,f221]) ).
fof(f7401,plain,
( ~ aNaturalNumber0(xn)
| spl4_13
| spl4_96 ),
inference(forward_subsumption_resolution,[],[f7400,f1575]) ).
fof(f7402,plain,
( $false
| spl4_13
| spl4_96 ),
inference(forward_subsumption_resolution,[],[f7401,f198]) ).
fof(f7403,plain,
( spl4_13
| spl4_96 ),
inference(avatar_contradiction_clause,[],[f7402]) ).
fof(f7703,plain,
( ~ aNaturalNumber0(xp)
| sz00 = sdtsldt0(xn,xr)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtlseqdt0(xp,sdtsldt0(xn,xr))
| ~ spl4_1 ),
inference(resolution,[],[f243,f184]) ).
fof(f7706,plain,
( sz00 = sdtsldt0(xn,xr)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtlseqdt0(xp,sdtsldt0(xn,xr))
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f7703,f196]) ).
fof(f7709,plain,
( sz00 = sdtsldt0(xn,xr)
| sdtlseqdt0(xp,sdtsldt0(xn,xr))
| ~ spl4_1
| ~ spl4_13 ),
inference(forward_subsumption_resolution,[],[f7706,f312]) ).
fof(f7711,plain,
( spl4_180
| spl4_181
| ~ spl4_1
| ~ spl4_13 ),
inference(avatar_split_clause,[],[f7709,f311,f241,f2891,f2887]) ).
fof(f8753,plain,
! [X0] :
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(xn,X0) ),
inference(resolution,[],[f161,f206]) ).
fof(f8776,plain,
! [X0] :
( ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(xn,X0) ),
inference(forward_subsumption_resolution,[],[f8753,f196]) ).
fof(f8815,plain,
! [X0] :
( ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(xn,X0) ),
inference(forward_subsumption_resolution,[],[f8776,f198]) ).
fof(f10967,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| sz00 = xr
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ),
inference(resolution,[],[f236,f221]) ).
fof(f10993,plain,
( ~ aNaturalNumber0(xn)
| sz00 = xr
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ),
inference(forward_subsumption_resolution,[],[f10967,f215]) ).
fof(f11038,plain,
( sz00 = xr
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ),
inference(forward_subsumption_resolution,[],[f10993,f198]) ).
fof(f11084,plain,
( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| spl4_96 ),
inference(forward_subsumption_resolution,[],[f11038,f1575]) ).
fof(f13541,plain,
( xn = sdtasdt0(xr,sz00)
| spl4_96
| ~ spl4_181 ),
inference(forward_demodulation,[],[f11084,f2893]) ).
fof(f13542,plain,
( sz00 = xn
| spl4_96
| ~ spl4_181 ),
inference(forward_demodulation,[],[f13541,f469]) ).
fof(f13543,plain,
( $false
| spl4_94
| spl4_96
| ~ spl4_181 ),
inference(forward_subsumption_resolution,[],[f13542,f1565]) ).
fof(f13544,plain,
( spl4_94
| spl4_96
| ~ spl4_181 ),
inference(avatar_contradiction_clause,[],[f13543]) ).
fof(f13545,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ spl4_180 ),
inference(resolution,[],[f2889,f8815]) ).
fof(f13558,plain,
( sdtlseqdt0(xn,sdtsldt0(xn,xr))
| ~ spl4_13
| ~ spl4_180 ),
inference(forward_subsumption_resolution,[],[f13545,f312]) ).
fof(f13564,plain,
( $false
| ~ spl4_13
| spl4_163
| ~ spl4_180 ),
inference(forward_subsumption_resolution,[],[f13558,f2646]) ).
fof(f13565,plain,
( ~ spl4_13
| spl4_163
| ~ spl4_180 ),
inference(avatar_contradiction_clause,[],[f13564]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f248]) ).
cnf(s4,plain,
( ~ spl4_7
| ~ spl4_8 ),
inference(sat_conversion,[],[f275]) ).
cnf(s8,plain,
spl4_8,
inference(sat_conversion,[],[f303]) ).
cnf(s54,plain,
( spl4_7
| ~ spl4_96 ),
inference(sat_conversion,[],[f1948]) ).
cnf(s56,plain,
~ spl4_94,
inference(sat_conversion,[],[f2058]) ).
cnf(s93,plain,
( ~ spl4_13
| ~ spl4_163 ),
inference(sat_conversion,[],[f2647]) ).
cnf(s299,plain,
~ spl4_2,
inference(sat_conversion,[],[f6976]) ).
cnf(s340,plain,
( spl4_13
| spl4_96 ),
inference(sat_conversion,[],[f7403]) ).
cnf(s356,plain,
( ~ spl4_1
| ~ spl4_13
| spl4_180
| spl4_181 ),
inference(sat_conversion,[],[f7711]) ).
cnf(s570,plain,
( spl4_94
| spl4_96
| ~ spl4_181 ),
inference(sat_conversion,[],[f13544]) ).
cnf(s571,plain,
( ~ spl4_13
| spl4_163
| ~ spl4_180 ),
inference(sat_conversion,[],[f13565]) ).
cnf(s903,plain,
~ spl4_7,
inference(rat,[],[s4,s8]) ).
cnf(s904,plain,
~ spl4_96,
inference(rat,[],[s54,s903]) ).
cnf(s905,plain,
~ spl4_181,
inference(rat,[],[s570,s56,s904]) ).
cnf(s907,plain,
spl4_13,
inference(rat,[],[s340,s904]) ).
cnf(s915,plain,
~ spl4_163,
inference(rat,[],[s93,s907]) ).
cnf(s921,plain,
~ spl4_180,
inference(rat,[],[s571,s907,s915]) ).
cnf(s923,plain,
~ spl4_1,
inference(rat,[],[s356,s905,s907,s921]) ).
cnf(s928,plain,
$false,
inference(rat,[],[s1,s299,s923]) ).
fof(f13568,plain,
$false,
inference(avatar_sat_refutation,[],[s928]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM518+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:19:19 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.98/0.82 % (3716015)Will run a generic schedule for satisfiability detection.
% 1.98/0.82 % (3716027)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2393752898:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.98/0.82 % (3716024)% WARNING: option uhcvi not known.
% 1.98/0.82 % (3716025)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=792507284:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.98/0.82 % (3716024)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2486907784:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.98/0.82 % (3716026)dis+10_1_sil=32000:sp=arity:random_seed=2346794226:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.98/0.82 % (3716023)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=757687586_2999 on theBenchmark for (2999ds/0Mi)
% 1.98/0.82 % (3716028)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=453313117:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.98/0.82 % (3716029)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3981513034:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.98/0.82 % Detected minimum model sizes of [3]
% 1.98/0.82 % Detected maximum model sizes of [max]
% 1.98/0.82 % TRYING [3]
% 1.98/0.82 % TRYING [4]
% 1.98/0.82 % (3716027)Instruction limit reached!
% 1.98/0.82 % (3716027)------------------------------
% 1.98/0.82 % (3716027)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.82 % (3716027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.82 % (3716027)CaDiCaL version: 2.1.3
% 1.98/0.82 % (3716027)Termination reason: Instruction limit
% 1.98/0.82 % (3716027)Termination phase: Saturation
% 1.98/0.82 % (3716027)Time elapsed: 0.037 s
% 1.98/0.82 % (3716027)Peak memory usage: 13 MB
% 1.98/0.82 % (3716027)Instructions burned: 119 (million)
% 1.98/0.82 % (3716051)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=976433813:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.98/0.82 % TRYING [5]
% 1.98/0.82 % Detected minimum model sizes of [3]
% 1.98/0.82 % Detected maximum model sizes of [max]
% 1.98/0.82 % TRYING [3]
% 1.98/0.82 % TRYING [4]
% 1.98/0.82 % (3716026)Instruction limit reached!
% 1.98/0.82 % (3716026)------------------------------
% 1.98/0.82 % (3716026)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.82 % (3716026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.82 % (3716026)CaDiCaL version: 2.1.3
% 1.98/0.82 % (3716026)Termination reason: Instruction limit
% 1.98/0.82 % (3716026)Termination phase: Saturation
% 1.98/0.82 % (3716026)Time elapsed: 0.061 s
% 1.98/0.82 % (3716026)Peak memory usage: 13 MB
% 1.98/0.82 % (3716026)Instructions burned: 104 (million)
% 1.98/0.82 % TRYING [5]
% 1.98/0.82 % (3716028)Instruction limit reached!
% 1.98/0.82 % (3716028)------------------------------
% 1.98/0.82 % (3716028)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.82 % (3716028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.82 % (3716028)CaDiCaL version: 2.1.3
% 1.98/0.82 % (3716028)Termination reason: Instruction limit
% 1.98/0.82 % (3716028)Termination phase: Saturation
% 1.98/0.82 % (3716028)Time elapsed: 0.077 s
% 1.98/0.82 % (3716028)Peak memory usage: 14 MB
% 1.98/0.82 % (3716028)Instructions burned: 131 (million)
% 1.98/0.82 % (3716064)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3770333236:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.98/0.82 % (3716029)Instruction limit reached!
% 1.98/0.82 % (3716029)------------------------------
% 1.98/0.82 % (3716029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.82 % (3716029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.82 % (3716029)CaDiCaL version: 2.1.3
% 1.98/0.82 % (3716029)Termination reason: Instruction limit
% 1.98/0.82 % (3716029)Termination phase: Saturation
% 1.98/0.82 % (3716029)Time elapsed: 0.097 s
% 1.98/0.82 % (3716029)Peak memory usage: 14 MB
% 1.98/0.82 % (3716029)Instructions burned: 160 (million)
% 1.98/0.82 % (3716072)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2901272871:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.98/0.82 % TRYING [6]
% 1.98/0.82 % (3716084)ott-21_1_sil=16000:fs=off:random_seed=289685930:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.98/0.82 % TRYING [6]
% 1.98/0.82 % (3716064)Instruction limit reached!
% 1.98/0.82 % (3716064)------------------------------
% 1.98/0.82 % (3716064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.82 % (3716064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.82 % (3716064)CaDiCaL version: 2.1.3
% 1.98/0.82 % (3716064)Termination reason: Instruction limit
% 1.98/0.82 % (3716064)Termination phase: Saturation
% 1.98/0.82 % (3716064)Time elapsed: 0.069 s
% 1.98/0.82 % (3716064)Peak memory usage: 12 MB
% 1.98/0.82 % (3716064)Instructions burned: 131 (million)
% 1.98/0.82 % (3716108)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3674622173:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.98/0.82 % (3716051)Instruction limit reached!
% 1.98/0.82 % (3716051)------------------------------
% 1.98/0.82 % (3716051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.82 % (3716051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.82 % (3716051)CaDiCaL version: 2.1.3
% 1.98/0.82 % (3716051)Termination reason: Instruction limit
% 1.98/0.82 % (3716051)Termination phase: Finite model building constraint generation
% 1.98/0.82 % (3716051)Time elapsed: 0.149 s
% 1.98/0.82 % (3716051)Peak memory usage: 34 MB
% 1.98/0.82 % (3716051)Instructions burned: 718 (million)
% 1.98/0.82 % (3716084)Instruction limit reached!
% 1.98/0.82 % (3716084)------------------------------
% 1.98/0.82 % (3716084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.82 % (3716084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.82 % (3716084)CaDiCaL version: 2.1.3
% 1.98/0.82 % (3716084)Termination reason: Instruction limit
% 1.98/0.82 % (3716084)Termination phase: Saturation
% 1.98/0.82 % (3716084)Time elapsed: 0.096 s
% 1.98/0.82 % (3716084)Peak memory usage: 13 MB
% 1.98/0.82 % (3716084)Instructions burned: 181 (million)
% 1.98/0.82 % (3716121)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3532423544:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.98/0.82 % Detected minimum model sizes of [3]
% 1.98/0.82 % Detected maximum model sizes of [max]
% 1.98/0.82 % TRYING [3]
% 1.98/0.82 % (3716127)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=637912572:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.98/0.82 % TRYING [4]
% 1.98/0.82 % TRYING [7]
% 1.98/0.82 % TRYING [5]
% 1.98/0.82 % (3716072) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3716015-3716072"...
% 1.98/0.82 % (3716072)...printing done.
% 1.98/0.82 % (3716072)Refutation found. Thanks to Tanya!
% 1.98/0.82 % SZS status Theorem for theBenchmark
% 1.98/0.82 % SZS output start Proof for theBenchmark
% See solution above
% 1.98/0.82 % (3716072)------------------------------
% 1.98/0.82 % (3716072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.98/0.82 % (3716072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.98/0.82 % (3716072)CaDiCaL version: 2.1.3
% 1.98/0.82 % (3716072)Termination reason: Refutation
% 1.98/0.82 % (3716072)Time elapsed: 0.259 s
% 1.98/0.82 % (3716072)Peak memory usage: 18 MB
% 1.98/0.82 % (3716072)Instructions burned: 430 (million)
% 1.98/0.82 % (3716015)Success in time 0.397 s
% 1.98/0.82 % Vampire exiting
%------------------------------------------------------------------------------