%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM511+1 : 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 : n002.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 8.75s 2.07s
% Output : Refutation 9.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 24
% Syntax : Number of formulae : 165 ( 37 unt; 11 def)
% Number of atoms : 568 ( 141 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 672 ( 269 ~; 316 |; 59 &)
% ( 18 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 98 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
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(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f52,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(f54,conjecture,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f55,negated_conjecture,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f58,plain,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(flattening,[],[f55]) ).
fof(f61,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f62,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f61]) ).
fof(f68,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f69,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f68]) ).
fof(f105,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f106,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f105]) ).
fof(f107,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(f108,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,[],[f107]) ).
fof(f117,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(f118,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,[],[f117]) ).
fof(f119,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(f120,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f119]) ).
fof(f131,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,[],[f106]) ).
fof(f132,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,[],[f131]) ).
fof(f133,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))],[f132]) ).
fof(f134,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,[],[f108]) ).
fof(f135,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,[],[f134]) ).
fof(f136,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,[],[f120]) ).
fof(f137,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,[],[f136]) ).
fof(f138,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,[],[f137]) ).
fof(f139,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))],[f138]) ).
fof(f141,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f145,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f150,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f190,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f191,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f192,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f198,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,[],[f118]) ).
fof(f201,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f209,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f210,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f211,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f213,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f214,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f221,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f226,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f227,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f48]) ).
fof(f228,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f234,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f52]) ).
fof(f237,plain,
~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(cnf_transformation,[],[f58]) ).
fof(f244,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f190]) ).
fof(f246,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f192]) ).
fof(f247,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f191]) ).
fof(f248,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f201]) ).
fof(f250,definition,
sF4 = sdtsldt0(xn,xr),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f251,plain,
sdtsldt0(xn,xr) = sF4,
inference(reorient_equations,[],[f250]) ).
fof(f252,definition,
sF5 = sdtasdt0(sF4,xm),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f253,plain,
sdtasdt0(sF4,xm) = sF5,
inference(reorient_equations,[],[f252]) ).
fof(f254,plain,
~ doDivides0(xp,sF5),
inference(definition_folding,[],[f237,f253,f251]) ).
fof(f266,definition,
( spl6_3
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
fof(f270,definition,
( spl6_4
<=> isPrime0(sz00) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
fof(f272,plain,
( ~ isPrime0(sz00)
| spl6_4 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f273,plain,
( ~ spl6_3
| ~ spl6_4 ),
inference(avatar_split_clause,[],[f248,f270,f266]) ).
fof(f275,plain,
spl6_3,
inference(avatar_split_clause,[],[f141,f266]) ).
fof(f279,definition,
( spl6_5
<=> aNaturalNumber0(sF5) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
fof(f280,plain,
( aNaturalNumber0(sF5)
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f281,plain,
( ~ aNaturalNumber0(sF5)
| spl6_5 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f283,definition,
( spl6_6
<=> aNaturalNumber0(sF4) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f284,plain,
( aNaturalNumber0(sF4)
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f291,plain,
( aNaturalNumber0(sF4)
| sz00 = xr
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f246,f251]) ).
fof(f292,plain,
( aNaturalNumber0(sF4)
| sz00 = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f291,f234]) ).
fof(f293,plain,
( aNaturalNumber0(sF4)
| sz00 = xr
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f292,f228]) ).
fof(f294,plain,
( aNaturalNumber0(sF4)
| sz00 = xr ),
inference(forward_subsumption_resolution,[],[f293,f211]) ).
fof(f296,definition,
( spl6_8
<=> sz00 = xr ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
fof(f297,plain,
( sz00 != xr
| spl6_8 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f298,plain,
( sz00 = xr
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f299,plain,
( spl6_8
| spl6_6 ),
inference(avatar_split_clause,[],[f294,f283,f296]) ).
fof(f302,plain,
( aNaturalNumber0(sF5)
| ~ aNaturalNumber0(sF4)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f145,f253]) ).
fof(f303,plain,
( ~ aNaturalNumber0(sF4)
| ~ aNaturalNumber0(xm)
| spl6_5 ),
inference(forward_subsumption_resolution,[],[f302,f281]) ).
fof(f304,plain,
( ~ aNaturalNumber0(sF4)
| spl6_5 ),
inference(forward_subsumption_resolution,[],[f303,f210]) ).
fof(f305,plain,
( ~ spl6_6
| spl6_5 ),
inference(avatar_split_clause,[],[f304,f279,f283]) ).
fof(f306,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[],[f246,f221]) ).
fof(f307,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f306,f213]) ).
fof(f308,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f307,f209]) ).
fof(f310,definition,
( spl6_9
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
fof(f311,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f312,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl6_9 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f314,definition,
( spl6_10
<=> sz00 = xp ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
fof(f315,plain,
( sz00 != xp
| spl6_10 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f316,plain,
( sz00 = xp
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f318,definition,
( spl6_11
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition]) ).
fof(f320,plain,
( aNaturalNumber0(xk)
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f321,plain,
( ~ spl6_9
| spl6_10
| spl6_11 ),
inference(avatar_split_clause,[],[f308,f318,f314,f310]) ).
fof(f322,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl6_9 ),
inference(resolution,[],[f312,f145]) ).
fof(f323,plain,
( ~ aNaturalNumber0(xm)
| spl6_9 ),
inference(forward_subsumption_resolution,[],[f322,f211]) ).
fof(f324,plain,
( $false
| spl6_9 ),
inference(forward_subsumption_resolution,[],[f323,f210]) ).
fof(f325,plain,
spl6_9,
inference(avatar_contradiction_clause,[],[f324]) ).
fof(f327,plain,
( isPrime0(sz00)
| ~ spl6_10 ),
inference(superposition,[],[f214,f316]) ).
fof(f331,plain,
( $false
| spl6_4
| ~ spl6_10 ),
inference(forward_subsumption_resolution,[],[f327,f272]) ).
fof(f332,plain,
( spl6_4
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[],[f331]) ).
fof(f334,plain,
( isPrime0(sz00)
| ~ spl6_8 ),
inference(superposition,[],[f226,f298]) ).
fof(f335,plain,
( $false
| spl6_4
| ~ spl6_8 ),
inference(forward_subsumption_resolution,[],[f334,f272]) ).
fof(f336,plain,
( spl6_4
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f335]) ).
fof(f341,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = xr
| sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f198,f234]) ).
fof(f342,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = xr
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f198,f227]) ).
fof(f346,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) )
| spl6_8 ),
inference(forward_subsumption_resolution,[],[f342,f297]) ).
fof(f347,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) )
| spl6_8 ),
inference(forward_subsumption_resolution,[],[f341,f297]) ).
fof(f352,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr)
| ~ aNaturalNumber0(xk) )
| spl6_8 ),
inference(forward_subsumption_resolution,[],[f346,f228]) ).
fof(f353,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr)
| ~ aNaturalNumber0(xn) )
| spl6_8 ),
inference(forward_subsumption_resolution,[],[f347,f228]) ).
fof(f364,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr) )
| spl6_8
| ~ spl6_11 ),
inference(forward_subsumption_resolution,[],[f352,f320]) ).
fof(f365,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr) )
| spl6_8 ),
inference(forward_subsumption_resolution,[],[f353,f211]) ).
fof(f368,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtsldt0(sdtasdt0(X0,xn),xr) = sdtasdt0(X0,sF4) )
| spl6_8 ),
inference(forward_demodulation,[],[f365,f251]) ).
fof(f374,plain,
( sdtsldt0(sdtasdt0(xm,xn),xr) = sdtasdt0(xm,sF4)
| spl6_8 ),
inference(resolution,[],[f368,f210]) ).
fof(f395,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f247,f213]) ).
fof(f404,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl6_10 ),
inference(forward_subsumption_resolution,[],[f395,f315]) ).
fof(f409,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl6_10 ),
inference(forward_subsumption_resolution,[],[f404,f209]) ).
fof(f413,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ spl6_9
| spl6_10 ),
inference(forward_subsumption_resolution,[],[f409,f311]) ).
fof(f415,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| ~ spl6_9
| spl6_10 ),
inference(forward_demodulation,[],[f413,f221]) ).
fof(f635,plain,
( sdtasdt0(xp,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(xp,xk),xr)
| spl6_8
| ~ spl6_11 ),
inference(resolution,[],[f364,f209]) ).
fof(f655,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xm) = sdtasdt0(xm,X0) ),
inference(resolution,[],[f150,f210]) ).
fof(f665,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[],[f655,f211]) ).
fof(f670,plain,
( sdtasdt0(sF4,xm) = sdtasdt0(xm,sF4)
| ~ spl6_6 ),
inference(resolution,[],[f655,f284]) ).
fof(f672,plain,
( sF5 = sdtasdt0(xm,sF4)
| ~ spl6_6 ),
inference(forward_demodulation,[],[f670,f253]) ).
fof(f869,plain,
( sdtsldt0(sdtasdt0(xn,xm),xr) = sdtasdt0(xp,sdtsldt0(xk,xr))
| spl6_8
| ~ spl6_9
| spl6_10
| ~ spl6_11 ),
inference(forward_demodulation,[],[f635,f415]) ).
fof(f1852,plain,
( sdtsldt0(sdtasdt0(xn,xm),xr) = sdtasdt0(xm,sF4)
| spl6_8 ),
inference(superposition,[],[f374,f665]) ).
fof(f1884,plain,
( sF5 = sdtsldt0(sdtasdt0(xn,xm),xr)
| ~ spl6_6
| spl6_8 ),
inference(forward_demodulation,[],[f1852,f672]) ).
fof(f1900,plain,
( sF5 = sdtasdt0(xp,sdtsldt0(xk,xr))
| ~ spl6_6
| spl6_8
| ~ spl6_9
| spl6_10
| ~ spl6_11 ),
inference(forward_demodulation,[],[f1884,f869]) ).
fof(f1961,plain,
( doDivides0(xp,sF5)
| ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sF5)
| ~ spl6_6
| spl6_8
| ~ spl6_9
| spl6_10
| ~ spl6_11 ),
inference(superposition,[],[f244,f1900]) ).
fof(f1979,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sF5)
| ~ spl6_6
| spl6_8
| ~ spl6_9
| spl6_10
| ~ spl6_11 ),
inference(forward_subsumption_resolution,[],[f1961,f254]) ).
fof(f1994,definition,
( spl6_62
<=> aNaturalNumber0(sdtsldt0(xk,xr)) ),
introduced(definition,[new_symbols(definition,[spl6_62])],[avatar_definition]) ).
fof(f1996,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| spl6_62 ),
inference(avatar_component_clause,[],[f1994]) ).
fof(f2013,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(sF5)
| ~ spl6_6
| spl6_8
| ~ spl6_9
| spl6_10
| ~ spl6_11 ),
inference(forward_subsumption_resolution,[],[f1979,f209]) ).
fof(f2045,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ spl6_5
| ~ spl6_6
| spl6_8
| ~ spl6_9
| spl6_10
| ~ spl6_11 ),
inference(forward_subsumption_resolution,[],[f2013,f280]) ).
fof(f2054,plain,
( ~ spl6_62
| ~ spl6_5
| ~ spl6_6
| spl6_8
| ~ spl6_9
| spl6_10
| ~ spl6_11 ),
inference(avatar_split_clause,[],[f2045,f318,f314,f310,f296,f283,f279,f1994]) ).
fof(f2055,plain,
( sz00 = xr
| ~ doDivides0(xr,xk)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| spl6_62 ),
inference(resolution,[],[f1996,f246]) ).
fof(f2056,plain,
( ~ doDivides0(xr,xk)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| spl6_8
| spl6_62 ),
inference(forward_subsumption_resolution,[],[f2055,f297]) ).
fof(f2057,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| spl6_8
| spl6_62 ),
inference(forward_subsumption_resolution,[],[f2056,f227]) ).
fof(f2058,plain,
( ~ aNaturalNumber0(xk)
| spl6_8
| spl6_62 ),
inference(forward_subsumption_resolution,[],[f2057,f228]) ).
fof(f2059,plain,
( $false
| spl6_8
| ~ spl6_11
| spl6_62 ),
inference(forward_subsumption_resolution,[],[f2058,f320]) ).
fof(f2060,plain,
( spl6_8
| ~ spl6_11
| spl6_62 ),
inference(avatar_contradiction_clause,[],[f2059]) ).
cnf(s2,plain,
( ~ spl6_3
| ~ spl6_4 ),
inference(sat_conversion,[],[f273]) ).
cnf(s4,plain,
spl6_3,
inference(sat_conversion,[],[f275]) ).
cnf(s6,plain,
( spl6_6
| spl6_8 ),
inference(sat_conversion,[],[f299]) ).
cnf(s7,plain,
( spl6_5
| ~ spl6_6 ),
inference(sat_conversion,[],[f305]) ).
cnf(s8,plain,
( ~ spl6_9
| spl6_10
| spl6_11 ),
inference(sat_conversion,[],[f321]) ).
cnf(s9,plain,
spl6_9,
inference(sat_conversion,[],[f325]) ).
cnf(s10,plain,
( spl6_4
| ~ spl6_10 ),
inference(sat_conversion,[],[f332]) ).
cnf(s11,plain,
( spl6_4
| ~ spl6_8 ),
inference(sat_conversion,[],[f336]) ).
cnf(s67,plain,
( ~ spl6_5
| ~ spl6_6
| spl6_8
| ~ spl6_9
| spl6_10
| ~ spl6_11
| ~ spl6_62 ),
inference(sat_conversion,[],[f2054]) ).
cnf(s68,plain,
( spl6_8
| ~ spl6_11
| spl6_62 ),
inference(sat_conversion,[],[f2060]) ).
cnf(s72,plain,
( spl6_10
| spl6_11 ),
inference(rat,[],[s8,s9]) ).
cnf(s73,plain,
~ spl6_4,
inference(rat,[],[s2,s4]) ).
cnf(s74,plain,
~ spl6_8,
inference(rat,[],[s11,s73]) ).
cnf(s75,plain,
~ spl6_10,
inference(rat,[],[s10,s73]) ).
cnf(s78,plain,
spl6_6,
inference(rat,[],[s6,s74]) ).
cnf(s79,plain,
spl6_11,
inference(rat,[],[s72,s75]) ).
cnf(s83,plain,
spl6_5,
inference(rat,[],[s7,s78]) ).
cnf(s84,plain,
spl6_62,
inference(rat,[],[s68,s74,s79]) ).
cnf(s85,plain,
$false,
inference(rat,[],[s67,s78,s79,s75,s9,s74,s84,s83]) ).
fof(f2061,plain,
$false,
inference(avatar_sat_refutation,[],[s85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM511+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 20:18:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 8.75/2.07 % (3848570)Detected formulas, will run a generic FOF schedule.
% 8.75/2.07 % (3848576)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=3453291410:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.75/2.07 % (3848577)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=2554870587:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.75/2.07 % (3848578)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3731186211:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.75/2.07 % (3848581)dis-21_1_sil=8000:lcm=predicate:random_seed=3734933324: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)
% 8.75/2.07 % (3848580)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=334398278:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.75/2.07 % (3848575)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=2608314683:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.75/2.07 % (3848579)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=994969081:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.75/2.07 % (3848578)Instruction limit reached!
% 8.75/2.07 % (3848578)------------------------------
% 8.75/2.07 % (3848578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848578)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848578)Termination reason: Instruction limit
% 8.75/2.07 % (3848578)Termination phase: Saturation
% 8.75/2.07 % (3848578)Time elapsed: 0.065 s
% 8.75/2.07 % (3848578)Peak memory usage: 89 MB
% 8.75/2.07 % (3848578)Instructions burned: 110 (million)
% 8.75/2.07 % (3848579)Instruction limit reached!
% 8.75/2.07 % (3848579)------------------------------
% 8.75/2.07 % (3848579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848579)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848579)Termination reason: Instruction limit
% 8.75/2.07 % (3848579)Termination phase: Saturation
% 8.75/2.07 % (3848579)Time elapsed: 0.069 s
% 8.75/2.07 % (3848579)Peak memory usage: 88 MB
% 8.75/2.07 % (3848579)Instructions burned: 119 (million)
% 8.75/2.07 % (3848581)Instruction limit reached!
% 8.75/2.07 % (3848581)------------------------------
% 8.75/2.07 % (3848581)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848581)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848581)Termination reason: Instruction limit
% 8.75/2.07 % (3848581)Termination phase: Saturation
% 8.75/2.07 % (3848581)Time elapsed: 0.080 s
% 8.75/2.07 % (3848581)Peak memory usage: 90 MB
% 8.75/2.07 % (3848581)Instructions burned: 131 (million)
% 8.75/2.07 % (3848580)Instruction limit reached!
% 8.75/2.07 % (3848580)------------------------------
% 8.75/2.07 % (3848580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848580)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848580)Termination reason: Instruction limit
% 8.75/2.07 % (3848580)Termination phase: Saturation
% 8.75/2.07 % (3848580)Time elapsed: 0.091 s
% 8.75/2.07 % (3848580)Peak memory usage: 90 MB
% 8.75/2.07 % (3848580)Instructions burned: 140 (million)
% 8.75/2.07 % (3848589)lrs+10_1_sil=8000:sp=occurrence:random_seed=1211781856:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 8.75/2.07 % (3848591)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1354744206:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.75/2.07 % (3848590)lrs+10_1_sil=32000:urr=on:br=off:random_seed=563996938:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.75/2.07 % (3848592)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=3685553824:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 8.75/2.07 % (3848590)Instruction limit reached!
% 8.75/2.07 % (3848590)------------------------------
% 8.75/2.07 % (3848590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848590)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848590)Termination reason: Instruction limit
% 8.75/2.07 % (3848590)Termination phase: Saturation
% 8.75/2.07 % (3848590)Time elapsed: 0.069 s
% 8.75/2.07 % (3848590)Peak memory usage: 91 MB
% 8.75/2.07 % (3848590)Instructions burned: 157 (million)
% 8.75/2.07 % (3848592)Instruction limit reached!
% 8.75/2.07 % (3848592)------------------------------
% 8.75/2.07 % (3848592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848592)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848592)Termination reason: Instruction limit
% 8.75/2.07 % (3848592)Termination phase: Saturation
% 8.75/2.07 % (3848592)Time elapsed: 0.114 s
% 8.75/2.07 % (3848592)Peak memory usage: 94 MB
% 8.75/2.07 % (3848592)Instructions burned: 250 (million)
% 8.75/2.07 % (3848589)Instruction limit reached!
% 8.75/2.07 % (3848589)------------------------------
% 8.75/2.07 % (3848589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848589)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848589)Termination reason: Instruction limit
% 8.75/2.07 % (3848589)Termination phase: Saturation
% 8.75/2.07 % (3848589)Time elapsed: 0.167 s
% 8.75/2.07 % (3848589)Peak memory usage: 92 MB
% 8.75/2.07 % (3848589)Instructions burned: 286 (million)
% 8.75/2.07 % (3848597)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2580927799:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.75/2.07 % (3848591)Instruction limit reached!
% 8.75/2.07 % (3848591)------------------------------
% 8.75/2.07 % (3848591)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848591)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848591)Termination reason: Instruction limit
% 8.75/2.07 % (3848591)Termination phase: Saturation
% 8.75/2.07 % (3848591)Time elapsed: 0.196 s
% 8.75/2.07 % (3848591)Peak memory usage: 92 MB
% 8.75/2.07 % (3848591)Instructions burned: 325 (million)
% 8.75/2.07 % (3848597)Instruction limit reached!
% 8.75/2.07 % (3848597)------------------------------
% 8.75/2.07 % (3848597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848597)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848597)Termination reason: Instruction limit
% 8.75/2.07 % (3848597)Termination phase: Saturation
% 8.75/2.07 % (3848597)Time elapsed: 0.087 s
% 8.75/2.07 % (3848597)Peak memory usage: 90 MB
% 8.75/2.07 % (3848597)Instructions burned: 295 (million)
% 8.75/2.07 % (3848598)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2890034965:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 8.75/2.07 % (3848599)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=929573308:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 8.75/2.07 % (3848601)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3525349559:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 8.75/2.07 % (3848602)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4012825199:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 8.75/2.07 % (3848599)Instruction limit reached!
% 8.75/2.07 % (3848599)------------------------------
% 8.75/2.07 % (3848599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848599)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848599)Termination reason: Instruction limit
% 8.75/2.07 % (3848599)Termination phase: Saturation
% 8.75/2.07 % (3848599)Time elapsed: 0.070 s
% 8.75/2.07 % (3848599)Peak memory usage: 90 MB
% 8.75/2.07 % (3848599)Instructions burned: 114 (million)
% 8.75/2.07 % (3848602)Instruction limit reached!
% 8.75/2.07 % (3848602)------------------------------
% 8.75/2.07 % (3848602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848602)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848602)Termination reason: Instruction limit
% 8.75/2.07 % (3848602)Termination phase: Saturation
% 8.75/2.07 % (3848602)Time elapsed: 0.032 s
% 8.75/2.07 % (3848602)Peak memory usage: 89 MB
% 8.75/2.07 % (3848602)Instructions burned: 118 (million)
% 8.75/2.07 % (3848601)Instruction limit reached!
% 8.75/2.07 % (3848601)------------------------------
% 8.75/2.07 % (3848601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848601)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848601)Termination reason: Instruction limit
% 8.75/2.07 % (3848601)Termination phase: Saturation
% 8.75/2.07 % (3848601)Time elapsed: 0.065 s
% 8.75/2.07 % (3848601)Peak memory usage: 89 MB
% 8.75/2.07 % (3848601)Instructions burned: 128 (million)
% 8.75/2.07 % (3848608)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=923280110:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 8.75/2.07 % (3848607)lrs+10_1_sil=8000:sp=occurrence:random_seed=1501308632:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 8.75/2.07 % (3848609)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=132720610:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 8.75/2.07 % (3848608)Instruction limit reached!
% 8.75/2.07 % (3848608)------------------------------
% 8.75/2.07 % (3848608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848608)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848608)Termination reason: Instruction limit
% 8.75/2.07 % (3848608)Termination phase: Saturation
% 8.75/2.07 % (3848608)Time elapsed: 0.137 s
% 8.75/2.07 % (3848608)Peak memory usage: 92 MB
% 8.75/2.07 % (3848608)Instructions burned: 439 (million)
% 8.75/2.07 % (3848575)First to succeed.
% 8.75/2.07 % (3848575)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3848570"
% 8.75/2.07 % (3848613)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=425332426:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2990 on theBenchmark for (2990ds/134Mi)
% 8.75/2.07 % (3848613)Instruction limit reached!
% 8.75/2.07 % (3848613)------------------------------
% 8.75/2.07 % (3848613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.75/2.07 % (3848613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.75/2.07 % (3848613)CaDiCaL version: 2.1.3
% 8.75/2.07 % (3848613)Termination reason: Instruction limit
% 8.75/2.07 % (3848613)Termination phase: Saturation
% 8.75/2.07 % (3848613)Time elapsed: 0.034 s
% 8.75/2.07 % (3848613)Peak memory usage: 91 MB
% 8.75/2.07 % (3848613)Instructions burned: 135 (million)
% 8.75/2.07 % (3848615)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=317915222:st=8:i=592:sd=3:ep=RST:ss=axioms_2989 on theBenchmark for (2989ds/592Mi)
% 8.75/2.07 % (3848575)Refutation found. Thanks to Tanya!
% 8.75/2.07 % SZS status Theorem for theBenchmark
% 8.75/2.07 % SZS output start Proof for theBenchmark
% See solution above
% 9.13/2.16 % (3848575)------------------------------
% 9.13/2.16 % (3848575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.13/2.16 % (3848575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.13/2.16 % (3848575)CaDiCaL version: 2.1.3
% 9.13/2.16 % (3848575)Termination reason: Refutation
% 9.13/2.16 % (3848575)Time elapsed: 0.810 s
% 9.13/2.16 % (3848575)Peak memory usage: 132 MB
% 9.13/2.16 % (3848575)Instructions burned: 1214 (million)
% 9.13/2.16 % (3848575)------------------------------
% 9.13/2.16 % (3848575)------------------------------
% 9.13/2.16 % (3848570)Success in time 1.226 s
% 9.13/2.16 % Vampire exiting
%------------------------------------------------------------------------------