%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM501+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 : n011.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 12:15:28 PM UTC 2026
% Result : Theorem 6.08s 2.02s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 19
% Syntax : Number of formulae : 121 ( 28 unt; 7 def)
% Number of atoms : 446 ( 114 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 558 ( 233 ~; 241 |; 60 &)
% ( 15 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 92 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X0,X1)
& doDivides0(X1,X2) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(f49,conjecture,
doDivides0(xr,sdtasdt0(xn,xm)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f50,negated_conjecture,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(negated_conjecture,[status(cth)],[f49]) ).
fof(f53,plain,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(flattening,[],[f50]) ).
fof(f56,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f57,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f56]) ).
fof(f63,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f64,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f63]) ).
fof(f100,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f101,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f100]) ).
fof(f102,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(f103,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,[],[f102]) ).
fof(f104,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f105,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f104]) ).
fof(f114,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(f115,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f114]) ).
fof(f126,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,[],[f101]) ).
fof(f127,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,[],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtasdt0(X0,sK1(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f127]) ).
fof(f129,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,[],[f103]) ).
fof(f130,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,[],[f129]) ).
fof(f131,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f115]) ).
fof(f132,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f131]) ).
fof(f133,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f132]) ).
fof(f134,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ( sz10 != sK2(X0)
& sK2(X0) != X0
& aNaturalNumber0(sK2(X0))
& doDivides0(sK2(X0),X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f133]) ).
fof(f136,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f140,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f145,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f185,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f128]) ).
fof(f186,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f187,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f105]) ).
fof(f196,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f204,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f205,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f206,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f208,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f209,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f216,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f222,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f48]) ).
fof(f223,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f224,plain,
~ doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f53]) ).
fof(f231,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f185]) ).
fof(f233,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f187]) ).
fof(f234,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f186]) ).
fof(f235,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f196]) ).
fof(f237,definition,
sF4 = sdtasdt0(xn,xm),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f238,plain,
sdtasdt0(xn,xm) = sF4,
inference(reorient_equations,[],[f237]) ).
fof(f239,plain,
~ doDivides0(xr,sF4),
inference(definition_folding,[],[f224,f238]) ).
fof(f251,definition,
( spl5_3
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f255,definition,
( spl5_4
<=> isPrime0(sz00) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f257,plain,
( ~ isPrime0(sz00)
| spl5_4 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f258,plain,
( ~ spl5_3
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f235,f255,f251]) ).
fof(f260,plain,
spl5_3,
inference(avatar_split_clause,[],[f136,f251]) ).
fof(f266,definition,
( spl5_5
<=> aNaturalNumber0(sF4) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f267,plain,
( aNaturalNumber0(sF4)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f268,plain,
( ~ aNaturalNumber0(sF4)
| spl5_5 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f275,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[],[f233,f216]) ).
fof(f276,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f275,f208]) ).
fof(f277,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f276,f204]) ).
fof(f278,plain,
( ~ aNaturalNumber0(sF4)
| aNaturalNumber0(xk)
| sz00 = xp ),
inference(forward_demodulation,[],[f277,f238]) ).
fof(f279,plain,
( aNaturalNumber0(sF4)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f140,f238]) ).
fof(f280,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f279,f268]) ).
fof(f281,plain,
( ~ aNaturalNumber0(xm)
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f280,f206]) ).
fof(f282,plain,
( $false
| spl5_5 ),
inference(forward_subsumption_resolution,[],[f281,f205]) ).
fof(f283,plain,
spl5_5,
inference(avatar_contradiction_clause,[],[f282]) ).
fof(f284,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ spl5_5 ),
inference(forward_subsumption_resolution,[],[f278,f267]) ).
fof(f286,definition,
( spl5_7
<=> sz00 = xp ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
fof(f288,plain,
( sz00 = xp
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f290,definition,
( spl5_8
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f292,plain,
( aNaturalNumber0(xk)
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f293,plain,
( spl5_7
| spl5_8
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f284,f266,f290,f286]) ).
fof(f359,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f234,f208]) ).
fof(f365,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f359,f204]) ).
fof(f370,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_demodulation,[],[f365,f216]) ).
fof(f382,plain,
( sF4 = sdtasdt0(xp,xk)
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_demodulation,[],[f370,f238]) ).
fof(f393,definition,
( spl5_21
<=> sF4 = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[spl5_21])],[avatar_definition]) ).
fof(f395,plain,
( sF4 = sdtasdt0(xp,xk)
| ~ spl5_21 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f397,plain,
( ~ aNaturalNumber0(sF4)
| sF4 = sdtasdt0(xp,xk)
| sz00 = xp ),
inference(forward_demodulation,[],[f382,f238]) ).
fof(f398,plain,
( sF4 = sdtasdt0(xp,xk)
| sz00 = xp
| ~ spl5_5 ),
inference(forward_subsumption_resolution,[],[f397,f267]) ).
fof(f399,plain,
( spl5_7
| spl5_21
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f398,f266,f393,f286]) ).
fof(f464,plain,
( isPrime0(sz00)
| ~ spl5_7 ),
inference(superposition,[],[f209,f288]) ).
fof(f470,plain,
( $false
| spl5_4
| ~ spl5_7 ),
inference(forward_subsumption_resolution,[],[f464,f257]) ).
fof(f471,plain,
( spl5_4
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[],[f470]) ).
fof(f662,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xp) = sdtasdt0(xp,X0) ),
inference(resolution,[],[f145,f204]) ).
fof(f788,plain,
( sdtasdt0(xp,xk) = sdtasdt0(xk,xp)
| ~ spl5_8 ),
inference(resolution,[],[f662,f292]) ).
fof(f791,plain,
( sF4 = sdtasdt0(xk,xp)
| ~ spl5_8
| ~ spl5_21 ),
inference(forward_demodulation,[],[f788,f395]) ).
fof(f795,plain,
( doDivides0(xk,sF4)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sF4)
| ~ spl5_8
| ~ spl5_21 ),
inference(superposition,[],[f231,f791]) ).
fof(f796,plain,
( doDivides0(xk,sF4)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sF4)
| ~ spl5_8
| ~ spl5_21 ),
inference(forward_subsumption_resolution,[],[f795,f204]) ).
fof(f798,plain,
( doDivides0(xk,sF4)
| ~ aNaturalNumber0(sF4)
| ~ spl5_8
| ~ spl5_21 ),
inference(forward_subsumption_resolution,[],[f796,f292]) ).
fof(f800,plain,
( doDivides0(xk,sF4)
| ~ spl5_5
| ~ spl5_8
| ~ spl5_21 ),
inference(forward_subsumption_resolution,[],[f798,f267]) ).
fof(f806,plain,
( ! [X0] :
( ~ doDivides0(X0,xk)
| doDivides0(X0,sF4)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(sF4) )
| ~ spl5_5
| ~ spl5_8
| ~ spl5_21 ),
inference(resolution,[],[f800,f189]) ).
fof(f810,plain,
( ! [X0] :
( ~ doDivides0(X0,xk)
| doDivides0(X0,sF4)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sF4) )
| ~ spl5_5
| ~ spl5_8
| ~ spl5_21 ),
inference(forward_subsumption_resolution,[],[f806,f292]) ).
fof(f814,plain,
( ! [X0] :
( ~ doDivides0(X0,xk)
| doDivides0(X0,sF4)
| ~ aNaturalNumber0(X0) )
| ~ spl5_5
| ~ spl5_8
| ~ spl5_21 ),
inference(forward_subsumption_resolution,[],[f810,f267]) ).
fof(f1555,plain,
( doDivides0(xr,sF4)
| ~ aNaturalNumber0(xr)
| ~ spl5_5
| ~ spl5_8
| ~ spl5_21 ),
inference(resolution,[],[f814,f222]) ).
fof(f1556,plain,
( ~ aNaturalNumber0(xr)
| ~ spl5_5
| ~ spl5_8
| ~ spl5_21 ),
inference(forward_subsumption_resolution,[],[f1555,f239]) ).
fof(f1557,plain,
( $false
| ~ spl5_5
| ~ spl5_8
| ~ spl5_21 ),
inference(forward_subsumption_resolution,[],[f1556,f223]) ).
fof(f1558,plain,
( ~ spl5_5
| ~ spl5_8
| ~ spl5_21 ),
inference(avatar_contradiction_clause,[],[f1557]) ).
cnf(s2,plain,
( ~ spl5_3
| ~ spl5_4 ),
inference(sat_conversion,[],[f258]) ).
cnf(s4,plain,
spl5_3,
inference(sat_conversion,[],[f260]) ).
cnf(s6,plain,
spl5_5,
inference(sat_conversion,[],[f283]) ).
cnf(s7,plain,
( ~ spl5_5
| spl5_7
| spl5_8 ),
inference(sat_conversion,[],[f293]) ).
cnf(s15,plain,
( ~ spl5_5
| spl5_7
| spl5_21 ),
inference(sat_conversion,[],[f399]) ).
cnf(s21,plain,
( spl5_4
| ~ spl5_7 ),
inference(sat_conversion,[],[f471]) ).
cnf(s47,plain,
( ~ spl5_5
| ~ spl5_8
| ~ spl5_21 ),
inference(sat_conversion,[],[f1558]) ).
cnf(s56,plain,
~ spl5_4,
inference(rat,[],[s2,s4]) ).
cnf(s57,plain,
~ spl5_7,
inference(rat,[],[s21,s56]) ).
cnf(s60,plain,
spl5_21,
inference(rat,[],[s15,s6,s57]) ).
cnf(s61,plain,
spl5_8,
inference(rat,[],[s7,s6,s57]) ).
cnf(s62,plain,
$false,
inference(rat,[],[s47,s6,s60,s61]) ).
fof(f1559,plain,
$false,
inference(avatar_sat_refutation,[],[s62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM501+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n011.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 20:13:46 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 6.08/2.02 % (2730160)Detected formulas, will run a generic FOF schedule.
% 6.08/2.02 % (2730271)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2888536477:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.08/2.02 % (2730268)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1460283247:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.08/2.02 % (2730266)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=2279989797:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.08/2.02 % (2730264)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=2930372888:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.08/2.02 % (2730262)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=1620852153:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.08/2.02 % (2730271)Instruction limit reached!
% 6.08/2.02 % (2730271)------------------------------
% 6.08/2.02 % (2730271)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730271)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730271)Termination reason: Instruction limit
% 6.08/2.02 % (2730271)Termination phase: Saturation
% 6.08/2.02 % (2730271)Time elapsed: 0.049 s
% 6.08/2.02 % (2730271)Peak memory usage: 90 MB
% 6.08/2.02 % (2730271)Instructions burned: 140 (million)
% 6.08/2.02 % (2730273)dis-21_1_sil=8000:lcm=predicate:random_seed=3693099817: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)
% 6.08/2.02 % (2730270)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1725954385:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.08/2.02 % (2730268)Instruction limit reached!
% 6.08/2.02 % (2730268)------------------------------
% 6.08/2.02 % (2730268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730268)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730268)Termination reason: Instruction limit
% 6.08/2.02 % (2730268)Termination phase: Saturation
% 6.08/2.02 % (2730268)Time elapsed: 0.064 s
% 6.08/2.02 % (2730268)Peak memory usage: 89 MB
% 6.08/2.02 % (2730268)Instructions burned: 111 (million)
% 6.08/2.02 % (2730270)Instruction limit reached!
% 6.08/2.02 % (2730270)------------------------------
% 6.08/2.02 % (2730270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730270)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730270)Termination reason: Instruction limit
% 6.08/2.02 % (2730270)Termination phase: Saturation
% 6.08/2.02 % (2730270)Time elapsed: 0.074 s
% 6.08/2.02 % (2730270)Peak memory usage: 89 MB
% 6.08/2.02 % (2730270)Instructions burned: 119 (million)
% 6.08/2.02 % (2730273)Instruction limit reached!
% 6.08/2.02 % (2730273)------------------------------
% 6.08/2.02 % (2730273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730273)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730273)Termination reason: Instruction limit
% 6.08/2.02 % (2730273)Termination phase: Saturation
% 6.08/2.02 % (2730273)Time elapsed: 0.081 s
% 6.08/2.02 % (2730273)Peak memory usage: 90 MB
% 6.08/2.02 % (2730273)Instructions burned: 130 (million)
% 6.08/2.02 % (2730290)lrs+10_1_sil=8000:sp=occurrence:random_seed=1802211670:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.08/2.02 % (2730292)lrs+10_1_sil=32000:urr=on:br=off:random_seed=838958113:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 6.08/2.02 % (2730290)Instruction limit reached!
% 6.08/2.02 % (2730290)------------------------------
% 6.08/2.02 % (2730290)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730290)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730290)Termination reason: Instruction limit
% 6.08/2.02 % (2730290)Termination phase: Saturation
% 6.08/2.02 % (2730290)Time elapsed: 0.089 s
% 6.08/2.02 % (2730290)Peak memory usage: 92 MB
% 6.08/2.02 % (2730290)Instructions burned: 285 (million)
% 6.08/2.02 % (2730293)lrs+1011_1_sil=32000:sp=occurrence:random_seed=328308909:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.08/2.02 % (2730295)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=1538889363:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.08/2.02 % (2730292)Instruction limit reached!
% 6.08/2.02 % (2730292)------------------------------
% 6.08/2.02 % (2730292)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730292)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730292)Termination reason: Instruction limit
% 6.08/2.02 % (2730292)Termination phase: Saturation
% 6.08/2.02 % (2730292)Time elapsed: 0.072 s
% 6.08/2.02 % (2730292)Peak memory usage: 90 MB
% 6.08/2.02 % (2730292)Instructions burned: 158 (million)
% 6.08/2.02 % (2730297)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1304737525:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.08/2.02 % (2730295)Instruction limit reached!
% 6.08/2.02 % (2730295)------------------------------
% 6.08/2.02 % (2730295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730295)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730295)Termination reason: Instruction limit
% 6.08/2.02 % (2730295)Termination phase: Saturation
% 6.08/2.02 % (2730295)Time elapsed: 0.114 s
% 6.08/2.02 % (2730295)Peak memory usage: 94 MB
% 6.08/2.02 % (2730295)Instructions burned: 249 (million)
% 6.08/2.02 % (2730297)Instruction limit reached!
% 6.08/2.02 % (2730297)------------------------------
% 6.08/2.02 % (2730297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730297)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730297)Termination reason: Instruction limit
% 6.08/2.02 % (2730297)Termination phase: Saturation
% 6.08/2.02 % (2730297)Time elapsed: 0.084 s
% 6.08/2.02 % (2730297)Peak memory usage: 89 MB
% 6.08/2.02 % (2730297)Instructions burned: 296 (million)
% 6.08/2.02 % (2730300)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3558912247:i=2350_2996 on theBenchmark for (2996ds/2350Mi)
% 6.08/2.02 % (2730293)Instruction limit reached!
% 6.08/2.02 % (2730293)------------------------------
% 6.08/2.02 % (2730293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730293)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730293)Termination reason: Instruction limit
% 6.08/2.02 % (2730293)Termination phase: Saturation
% 6.08/2.02 % (2730293)Time elapsed: 0.206 s
% 6.08/2.02 % (2730293)Peak memory usage: 92 MB
% 6.08/2.02 % (2730293)Instructions burned: 326 (million)
% 6.08/2.02 % (2730303)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2427640801:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.08/2.02 % (2730302)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2807237025:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 6.08/2.02 % (2730303)Instruction limit reached!
% 6.08/2.02 % (2730303)------------------------------
% 6.08/2.02 % (2730303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730303)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730303)Termination reason: Instruction limit
% 6.08/2.02 % (2730303)Termination phase: Saturation
% 6.08/2.02 % (2730303)Time elapsed: 0.034 s
% 6.08/2.02 % (2730303)Peak memory usage: 89 MB
% 6.08/2.02 % (2730303)Instructions burned: 128 (million)
% 6.08/2.02 % (2730302)Instruction limit reached!
% 6.08/2.02 % (2730302)------------------------------
% 6.08/2.02 % (2730302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730302)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730302)Termination reason: Instruction limit
% 6.08/2.02 % (2730302)Termination phase: Saturation
% 6.08/2.02 % (2730302)Time elapsed: 0.069 s
% 6.08/2.02 % (2730302)Peak memory usage: 90 MB
% 6.08/2.02 % (2730302)Instructions burned: 114 (million)
% 6.08/2.02 % (2730305)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4097437939:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 6.08/2.02 % (2730305)Instruction limit reached!
% 6.08/2.02 % (2730305)------------------------------
% 6.08/2.02 % (2730305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730305)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730305)Termination reason: Instruction limit
% 6.08/2.02 % (2730305)Termination phase: Saturation
% 6.08/2.02 % (2730305)Time elapsed: 0.031 s
% 6.08/2.02 % (2730305)Peak memory usage: 89 MB
% 6.08/2.02 % (2730305)Instructions burned: 115 (million)
% 6.08/2.02 % (2730308)lrs+10_1_sil=8000:sp=occurrence:random_seed=1221272296:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 6.08/2.02 % (2730311)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2419936170:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 6.08/2.02 % (2730309)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3768640257:i=437:sd=1:aac=none:ss=included_2993 on theBenchmark for (2993ds/437Mi)
% 6.08/2.02 % (2730262)First to succeed.
% 6.08/2.02 % (2730262)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2730160"
% 6.08/2.02 % (2730264)Also succeeded, but the first one will report.
% 6.08/2.02 % (2730309)Instruction limit reached!
% 6.08/2.02 % (2730309)------------------------------
% 6.08/2.02 % (2730309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/2.02 % (2730309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/2.02 % (2730309)CaDiCaL version: 2.1.3
% 6.08/2.02 % (2730309)Termination reason: Instruction limit
% 6.08/2.02 % (2730309)Termination phase: Saturation
% 6.08/2.02 % (2730309)Time elapsed: 0.259 s
% 6.08/2.02 % (2730309)Peak memory usage: 92 MB
% 6.08/2.02 % (2730309)Instructions burned: 439 (million)
% 6.08/2.02 % (2730311)Also succeeded, but the first one will report.
% 6.08/2.02 % (2730262)Refutation found. Thanks to Tanya!
% 6.08/2.02 % SZS status Theorem for theBenchmark
% 6.08/2.02 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/2.21 % (2730262)------------------------------
% 0.17/2.21 % (2730262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/2.21 % (2730262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/2.21 % (2730262)CaDiCaL version: 2.1.3
% 0.17/2.21 % (2730262)Termination reason: Refutation
% 0.17/2.21 % (2730262)Time elapsed: 0.763 s
% 0.17/2.21 % (2730262)Peak memory usage: 131 MB
% 0.17/2.21 % (2730262)Instructions burned: 1146 (million)
% 0.17/2.21 % (2730262)------------------------------
% 0.17/2.21 % (2730262)------------------------------
% 0.17/2.21 % (2730160)Success in time 1.158 s
% 0.17/2.21 % Vampire exiting
%------------------------------------------------------------------------------