%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM498+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 : 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 12:15:27 PM UTC 2026
% Result : Theorem 1.81s 1.74s
% Output : Refutation 5.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 28
% Syntax : Number of formulae : 201 ( 32 unt; 14 def)
% Number of atoms : 695 ( 204 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 845 ( 351 ~; 388 |; 68 &)
% ( 23 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 121 ( 0 sgn 113 !; 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(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X0 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
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(f44,axiom,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f46,conjecture,
( ( xk = sz00
| xk = sz10 )
=> ( doDivides0(xp,xn)
| doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
~ ( ( xk = sz00
| xk = sz10 )
=> ( doDivides0(xp,xn)
| doDivides0(xp,xm) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f52,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f53,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f52]) ).
fof(f63,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f64,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f73,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f74,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f73]) ).
fof(f96,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f97,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f96]) ).
fof(f98,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(f99,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,[],[f98]) ).
fof(f108,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(f109,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,[],[f108]) ).
fof(f110,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(f111,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f110]) ).
fof(f116,plain,
( ~ doDivides0(xp,xn)
& ~ doDivides0(xp,xm)
& ( xk = sz00
| xk = sz10 ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f117,plain,
( ~ doDivides0(xp,xn)
& ~ doDivides0(xp,xm)
& ( xk = sz00
| xk = sz10 ) ),
inference(flattening,[],[f116]) ).
fof(f123,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,[],[f97]) ).
fof(f124,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,[],[f123]) ).
fof(f125,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))],[f124]) ).
fof(f126,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,[],[f99]) ).
fof(f127,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,[],[f126]) ).
fof(f128,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,[],[f111]) ).
fof(f129,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,[],[f128]) ).
fof(f130,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,[],[f129]) ).
fof(f131,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))],[f130]) ).
fof(f133,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f137,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f144,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f145,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f147,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f156,plain,
! [X0,X1] :
( sz00 != sdtasdt0(X0,X1)
| sz00 = X1
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f182,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f183,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f185,plain,
! [X2,X0,X1] :
( sdtsldt0(X1,X0) = X2
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f190,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,[],[f109]) ).
fof(f191,plain,
! [X2,X0] :
( ~ isPrime0(X0)
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0)
| sz10 = X2
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f193,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f201,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f202,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f203,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f205,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f206,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f212,plain,
xn != xp,
inference(cnf_transformation,[],[f44]) ).
fof(f213,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f214,plain,
( sz00 = xk
| sz10 = xk ),
inference(cnf_transformation,[],[f117]) ).
fof(f215,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f117]) ).
fof(f216,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f117]) ).
fof(f223,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f182]) ).
fof(f224,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f185]) ).
fof(f226,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f183]) ).
fof(f227,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f193]) ).
fof(f231,definition,
( spl4_1
<=> sz10 = xk ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f233,plain,
( sz10 = xk
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f235,definition,
( spl4_2
<=> sz00 = xk ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f237,plain,
( sz00 = xk
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f238,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f214,f235,f231]) ).
fof(f249,definition,
( spl4_5
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f250,plain,
( aNaturalNumber0(sz00)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f253,definition,
( spl4_6
<=> isPrime0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f255,plain,
( ~ isPrime0(sz00)
| spl4_6 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f256,plain,
( ~ spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f227,f253,f249]) ).
fof(f258,plain,
spl4_5,
inference(avatar_split_clause,[],[f133,f249]) ).
fof(f312,definition,
( spl4_7
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f313,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f314,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_7 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f320,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_7 ),
inference(resolution,[],[f314,f137]) ).
fof(f321,plain,
( ~ aNaturalNumber0(xm)
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f320,f203]) ).
fof(f322,plain,
( $false
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f321,f202]) ).
fof(f323,plain,
spl4_7,
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f349,definition,
( spl4_9
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
fof(f351,plain,
( sz00 = xn
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f362,plain,
( ~ doDivides0(xp,sz00)
| ~ spl4_9 ),
inference(superposition,[],[f216,f351]) ).
fof(f442,definition,
( spl4_15
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[spl4_15])],[avatar_definition]) ).
fof(f483,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f223,f137]) ).
fof(f490,plain,
! [X0] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f483,f147]) ).
fof(f495,plain,
! [X0] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(duplicate_literal_removal,[],[f490]) ).
fof(f501,plain,
( ! [X0] :
( doDivides0(X0,sz00)
| ~ aNaturalNumber0(X0) )
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f495,f250]) ).
fof(f658,definition,
( spl4_24
<=> sz10 = xn ),
introduced(definition,[new_symbols(definition,[spl4_24])],[avatar_definition]) ).
fof(f659,plain,
( sz10 != xn
| spl4_24 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f660,plain,
( sz10 = xn
| ~ spl4_24 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f666,plain,
! [X0] :
( xp = X0
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xp)
| sz10 = X0
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f191,f206]) ).
fof(f673,plain,
! [X0] :
( ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0)
| xp = X0
| sz10 = X0 ),
inference(forward_subsumption_resolution,[],[f666,f201]) ).
fof(f853,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f226,f205]) ).
fof(f863,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f853,f201]) ).
fof(f867,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f863,f313]) ).
fof(f872,definition,
( spl4_28
<=> sz00 = xp ),
introduced(definition,[new_symbols(definition,[spl4_28])],[avatar_definition]) ).
fof(f873,plain,
( sz00 != xp
| spl4_28 ),
inference(avatar_component_clause,[],[f872]) ).
fof(f874,plain,
( sz00 = xp
| ~ spl4_28 ),
inference(avatar_component_clause,[],[f872]) ).
fof(f876,definition,
( spl4_29
<=> sdtasdt0(sz10,xm) = sdtasdt0(xp,sz00) ),
introduced(definition,[new_symbols(definition,[spl4_29])],[avatar_definition]) ).
fof(f877,plain,
( sdtasdt0(sz10,xm) != sdtasdt0(xp,sz00)
| spl4_29 ),
inference(avatar_component_clause,[],[f876]) ).
fof(f878,plain,
( sdtasdt0(sz10,xm) = sdtasdt0(xp,sz00)
| ~ spl4_29 ),
inference(avatar_component_clause,[],[f876]) ).
fof(f888,definition,
( spl4_31
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp)) ),
introduced(definition,[new_symbols(definition,[spl4_31])],[avatar_definition]) ).
fof(f890,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ spl4_31 ),
inference(avatar_component_clause,[],[f888]) ).
fof(f891,plain,
( spl4_31
| spl4_28
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f867,f312,f872,f888]) ).
fof(f895,plain,
( isPrime0(sz00)
| ~ spl4_28 ),
inference(superposition,[],[f206,f874]) ).
fof(f908,plain,
( $false
| spl4_6
| ~ spl4_28 ),
inference(forward_subsumption_resolution,[],[f895,f255]) ).
fof(f909,plain,
( spl4_6
| ~ spl4_28 ),
inference(avatar_contradiction_clause,[],[f908]) ).
fof(f910,plain,
( sz10 = sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ spl4_1 ),
inference(forward_demodulation,[],[f213,f233]) ).
fof(f1315,plain,
( ~ aNaturalNumber0(xp)
| ~ spl4_5
| ~ spl4_9 ),
inference(resolution,[],[f362,f501]) ).
fof(f1318,plain,
( $false
| ~ spl4_5
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f1315,f201]) ).
fof(f1319,plain,
( ~ spl4_5
| ~ spl4_9 ),
inference(avatar_contradiction_clause,[],[f1318]) ).
fof(f1328,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = xp
| sdtasdt0(X0,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtsldt0(sdtasdt0(X0,sdtasdt0(xn,xm)),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f190,f205]) ).
fof(f1338,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtsldt0(sdtasdt0(X0,sdtasdt0(xn,xm)),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) )
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f1328,f873]) ).
fof(f1342,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtsldt0(sdtasdt0(X0,sdtasdt0(xn,xm)),xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) )
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f1338,f201]) ).
fof(f1344,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(sdtasdt0(xn,xm),xp)) = sdtsldt0(sdtasdt0(X0,sdtasdt0(xn,xm)),xp) )
| ~ spl4_7
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f1342,f313]) ).
fof(f1345,plain,
( ! [X0] :
( sdtasdt0(X0,sz10) = sdtsldt0(sdtasdt0(X0,sdtasdt0(xn,xm)),xp)
| ~ aNaturalNumber0(X0) )
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(forward_demodulation,[],[f1344,f910]) ).
fof(f1353,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(forward_subsumption_resolution,[],[f224,f483]) ).
fof(f1354,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f1353,f137]) ).
fof(f1440,definition,
( spl4_53
<=> doDivides0(xp,sdtasdt0(sz10,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_53])],[avatar_definition]) ).
fof(f1441,plain,
( ~ doDivides0(xp,sdtasdt0(sz10,xm))
| spl4_53 ),
inference(avatar_component_clause,[],[f1440]) ).
fof(f1442,plain,
( doDivides0(xp,sdtasdt0(sz10,xm))
| ~ spl4_53 ),
inference(avatar_component_clause,[],[f1440]) ).
fof(f1479,definition,
( spl4_61
<=> sz00 = sdtasdt0(sz10,xm) ),
introduced(definition,[new_symbols(definition,[spl4_61])],[avatar_definition]) ).
fof(f1481,plain,
( sz00 != sdtasdt0(sz10,xm)
| spl4_61 ),
inference(avatar_component_clause,[],[f1479]) ).
fof(f1492,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz10)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp)
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(superposition,[],[f1354,f1345]) ).
fof(f1494,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz10)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(duplicate_literal_removal,[],[f1492]) ).
fof(f1497,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz10)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f1494,f313]) ).
fof(f1503,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz10)
| ~ aNaturalNumber0(xp)
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f1497,f873]) ).
fof(f1508,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz10)
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f1503,f201]) ).
fof(f1735,plain,
( doDivides0(xp,xm)
| ~ aNaturalNumber0(xm)
| ~ spl4_53 ),
inference(superposition,[],[f1442,f144]) ).
fof(f1736,plain,
( ~ aNaturalNumber0(xm)
| ~ spl4_53 ),
inference(forward_subsumption_resolution,[],[f1735,f215]) ).
fof(f1744,plain,
( $false
| ~ spl4_53 ),
inference(forward_subsumption_resolution,[],[f1736,f202]) ).
fof(f1745,plain,
~ spl4_53,
inference(avatar_contradiction_clause,[],[f1744]) ).
fof(f1926,plain,
( doDivides0(xn,sdtasdt0(xp,sz10))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(superposition,[],[f483,f1508]) ).
fof(f1929,plain,
( doDivides0(xn,sdtasdt0(xp,sz10))
| ~ aNaturalNumber0(xn)
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f1926,f202]) ).
fof(f1941,plain,
( doDivides0(xn,sdtasdt0(xp,sz10))
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f1929,f203]) ).
fof(f2228,plain,
( doDivides0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(superposition,[],[f1941,f145]) ).
fof(f2229,plain,
( doDivides0(xn,xp)
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f2228,f201]) ).
fof(f2615,plain,
( sz00 = sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ spl4_2 ),
inference(forward_demodulation,[],[f213,f237]) ).
fof(f2618,plain,
( doDivides0(xp,sdtasdt0(sz10,xm))
| ~ spl4_24 ),
inference(superposition,[],[f205,f660]) ).
fof(f2642,plain,
( $false
| ~ spl4_24
| spl4_53 ),
inference(forward_subsumption_resolution,[],[f2618,f1441]) ).
fof(f2643,plain,
( ~ spl4_24
| spl4_53 ),
inference(avatar_contradiction_clause,[],[f2642]) ).
fof(f2652,plain,
( doDivides0(xp,sdtasdt0(sz10,xm))
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ spl4_29 ),
inference(superposition,[],[f483,f878]) ).
fof(f2655,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ spl4_29
| spl4_53 ),
inference(forward_subsumption_resolution,[],[f2652,f1441]) ).
fof(f2664,plain,
( ~ aNaturalNumber0(xp)
| ~ spl4_5
| ~ spl4_29
| spl4_53 ),
inference(forward_subsumption_resolution,[],[f2655,f250]) ).
fof(f2672,plain,
( $false
| ~ spl4_5
| ~ spl4_29
| spl4_53 ),
inference(forward_subsumption_resolution,[],[f2664,f201]) ).
fof(f2673,plain,
( ~ spl4_5
| ~ spl4_29
| spl4_53 ),
inference(avatar_contradiction_clause,[],[f2672]) ).
fof(f2677,plain,
( sz00 != sdtasdt0(sz10,xm)
| ~ aNaturalNumber0(xp)
| spl4_29 ),
inference(superposition,[],[f877,f147]) ).
fof(f2678,plain,
( sz00 != sdtasdt0(sz10,xm)
| spl4_29 ),
inference(forward_subsumption_resolution,[],[f2677,f201]) ).
fof(f2679,plain,
( ~ spl4_61
| spl4_29 ),
inference(avatar_split_clause,[],[f2678,f876,f1479]) ).
fof(f2806,plain,
( sz00 != xm
| ~ aNaturalNumber0(xm)
| spl4_61 ),
inference(superposition,[],[f1481,f144]) ).
fof(f2807,plain,
( sz00 != xm
| spl4_61 ),
inference(forward_subsumption_resolution,[],[f2806,f202]) ).
fof(f2808,plain,
( ~ spl4_15
| spl4_61 ),
inference(avatar_split_clause,[],[f2807,f1479,f442]) ).
fof(f2967,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sz00)
| ~ spl4_2
| ~ spl4_31 ),
inference(forward_demodulation,[],[f890,f2615]) ).
fof(f3026,definition,
( spl4_123
<=> sz00 = sdtasdt0(xp,sz00) ),
introduced(definition,[new_symbols(definition,[spl4_123])],[avatar_definition]) ).
fof(f3028,plain,
( sz00 != sdtasdt0(xp,sz00)
| spl4_123 ),
inference(avatar_component_clause,[],[f3026]) ).
fof(f3116,plain,
( ~ aNaturalNumber0(xn)
| xn = xp
| sz10 = xn
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(resolution,[],[f2229,f673]) ).
fof(f3130,plain,
( xn = xp
| sz10 = xn
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f3116,f203]) ).
fof(f3137,plain,
( sz10 = xn
| ~ spl4_1
| ~ spl4_7
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f3130,f212]) ).
fof(f3140,plain,
( $false
| ~ spl4_1
| ~ spl4_7
| spl4_24
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f3137,f659]) ).
fof(f3141,plain,
( ~ spl4_1
| ~ spl4_7
| spl4_24
| spl4_28 ),
inference(avatar_contradiction_clause,[],[f3140]) ).
fof(f3184,plain,
( sz00 != sdtasdt0(xp,sz00)
| sz00 = xm
| sz00 = xn
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ spl4_2
| ~ spl4_31 ),
inference(superposition,[],[f156,f2967]) ).
fof(f3191,plain,
( sz00 != sdtasdt0(xp,sz00)
| sz00 = xm
| sz00 = xn
| ~ aNaturalNumber0(xm)
| ~ spl4_2
| ~ spl4_31 ),
inference(forward_subsumption_resolution,[],[f3184,f203]) ).
fof(f3202,plain,
( sz00 != sdtasdt0(xp,sz00)
| sz00 = xm
| sz00 = xn
| ~ spl4_2
| ~ spl4_31 ),
inference(forward_subsumption_resolution,[],[f3191,f202]) ).
fof(f3212,plain,
( spl4_9
| spl4_15
| ~ spl4_123
| ~ spl4_2
| ~ spl4_31 ),
inference(avatar_split_clause,[],[f3202,f888,f235,f3026,f442,f349]) ).
fof(f3235,plain,
( sz00 != sz00
| ~ aNaturalNumber0(xp)
| spl4_123 ),
inference(superposition,[],[f3028,f147]) ).
fof(f3236,plain,
( ~ aNaturalNumber0(xp)
| spl4_123 ),
inference(trivial_inequality_removal,[],[f3235]) ).
fof(f3237,plain,
( $false
| spl4_123 ),
inference(forward_subsumption_resolution,[],[f3236,f201]) ).
fof(f3238,plain,
spl4_123,
inference(avatar_contradiction_clause,[],[f3237]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f238]) ).
cnf(s3,plain,
( ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f256]) ).
cnf(s5,plain,
spl4_5,
inference(sat_conversion,[],[f258]) ).
cnf(s7,plain,
spl4_7,
inference(sat_conversion,[],[f323]) ).
cnf(s27,plain,
( ~ spl4_7
| spl4_28
| spl4_31 ),
inference(sat_conversion,[],[f891]) ).
cnf(s29,plain,
( spl4_6
| ~ spl4_28 ),
inference(sat_conversion,[],[f909]) ).
cnf(s48,plain,
( ~ spl4_5
| ~ spl4_9 ),
inference(sat_conversion,[],[f1319]) ).
cnf(s84,plain,
~ spl4_53,
inference(sat_conversion,[],[f1745]) ).
cnf(s146,plain,
( ~ spl4_24
| spl4_53 ),
inference(sat_conversion,[],[f2643]) ).
cnf(s149,plain,
( ~ spl4_5
| ~ spl4_29
| spl4_53 ),
inference(sat_conversion,[],[f2673]) ).
cnf(s151,plain,
( spl4_29
| ~ spl4_61 ),
inference(sat_conversion,[],[f2679]) ).
cnf(s169,plain,
( ~ spl4_15
| spl4_61 ),
inference(sat_conversion,[],[f2808]) ).
cnf(s205,plain,
( ~ spl4_1
| ~ spl4_7
| spl4_24
| spl4_28 ),
inference(sat_conversion,[],[f3141]) ).
cnf(s215,plain,
( ~ spl4_2
| spl4_9
| spl4_15
| ~ spl4_31
| ~ spl4_123 ),
inference(sat_conversion,[],[f3212]) ).
cnf(s220,plain,
spl4_123,
inference(sat_conversion,[],[f3238]) ).
cnf(s221,plain,
( ~ spl4_2
| spl4_9
| spl4_15
| ~ spl4_31 ),
inference(rat,[],[s215,s220]) ).
cnf(s230,plain,
~ spl4_24,
inference(rat,[],[s146,s84]) ).
cnf(s242,plain,
~ spl4_29,
inference(rat,[],[s149,s84,s5]) ).
cnf(s243,plain,
~ spl4_9,
inference(rat,[],[s48,s5]) ).
cnf(s245,plain,
~ spl4_61,
inference(rat,[],[s151,s242]) ).
cnf(s249,plain,
~ spl4_15,
inference(rat,[],[s169,s245]) ).
cnf(s255,plain,
~ spl4_6,
inference(rat,[],[s3,s5]) ).
cnf(s257,plain,
~ spl4_28,
inference(rat,[],[s29,s255]) ).
cnf(s259,plain,
spl4_31,
inference(rat,[],[s27,s7,s257]) ).
cnf(s260,plain,
~ spl4_1,
inference(rat,[],[s205,s7,s230,s257]) ).
cnf(s261,plain,
~ spl4_2,
inference(rat,[],[s221,s249,s243,s259]) ).
cnf(s270,plain,
$false,
inference(rat,[],[s1,s261,s260]) ).
fof(f3239,plain,
$false,
inference(avatar_sat_refutation,[],[s270]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM498+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.45 % Computer : n011.cluster.edu
% 0.16/0.45 % Model : x86_64 x86_64
% 0.16/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.45 % Memory : 8046.5625MB
% 0.16/0.45 % OS : Linux 6.8.0-71-generic
% 0.16/0.45 % CPULimit : 300
% 0.16/0.45 % WCLimit : 300
% 0.16/0.45 % DateTime : Sun Sep 27 20:12:45 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 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
% 1.81/1.73 % (2728859)Detected formulas, will run a generic FOF schedule.
% 1.81/1.73 % (2728867)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4185849268:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.81/1.73 % (2728869)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=659006010:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.81/1.73 % (2728867)Instruction limit reached!
% 1.81/1.73 % (2728867)------------------------------
% 1.81/1.73 % (2728867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.81/1.73 % (2728867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/1.73 % (2728867)CaDiCaL version: 2.1.3
% 1.81/1.73 % (2728867)Termination reason: Instruction limit
% 1.81/1.73 % (2728867)Termination phase: Saturation
% 1.81/1.73 % (2728867)Time elapsed: 0.052 s
% 1.81/1.73 % (2728867)Peak memory usage: 89 MB
% 1.81/1.73 % (2728867)Instructions burned: 109 (million)
% 1.81/1.73 % (2728869)First to succeed.
% 1.81/1.73 % (2728869)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2728859"
% 1.81/1.73 % (2728866)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=2849509388:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.81/1.73 % (2728865)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=1097096665:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.81/1.73 % (2728864)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=1559752651:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.81/1.73 % (2728870)dis-21_1_sil=8000:lcm=predicate:random_seed=3037588471: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)
% 1.81/1.73 % (2728868)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2973569140:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.81/1.73 % (2728868)Instruction limit reached!
% 1.81/1.73 % (2728868)------------------------------
% 1.81/1.73 % (2728868)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.81/1.73 % (2728868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/1.73 % (2728868)CaDiCaL version: 2.1.3
% 1.81/1.73 % (2728868)Termination reason: Instruction limit
% 1.81/1.73 % (2728868)Termination phase: Saturation
% 1.81/1.73 % (2728868)Time elapsed: 0.121 s
% 1.81/1.73 % (2728868)Peak memory usage: 88 MB
% 1.81/1.73 % (2728868)Instructions burned: 119 (million)
% 1.81/1.73 % (2728870)Instruction limit reached!
% 1.81/1.73 % (2728870)------------------------------
% 1.81/1.73 % (2728870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.81/1.73 % (2728870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.81/1.73 % (2728870)CaDiCaL version: 2.1.3
% 1.81/1.73 % (2728870)Termination reason: Instruction limit
% 1.81/1.73 % (2728870)Termination phase: Saturation
% 1.81/1.73 % (2728870)Time elapsed: 0.129 s
% 1.81/1.73 % (2728870)Peak memory usage: 90 MB
% 1.81/1.73 % (2728870)Instructions burned: 129 (million)
% 1.81/1.73 % (2728873)lrs+10_1_sil=8000:sp=occurrence:random_seed=1460405906:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 1.81/1.74 % (2728879)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3363691064:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 1.81/1.74 % (2728869)Refutation found. Thanks to Tanya!
% 1.81/1.74 % SZS status Theorem for theBenchmark
% 1.81/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 5.53/1.95 % (2728869)------------------------------
% 5.53/1.95 % (2728869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.53/1.95 % (2728869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.53/1.95 % (2728869)CaDiCaL version: 2.1.3
% 5.53/1.95 % (2728869)Termination reason: Refutation
% 5.53/1.95 % (2728869)Time elapsed: 0.083 s
% 5.53/1.95 % (2728869)Peak memory usage: 91 MB
% 5.53/1.95 % (2728869)Instructions burned: 98 (million)
% 5.53/1.95 % (2728869)------------------------------
% 5.53/1.95 % (2728869)------------------------------
% 5.53/1.95 % (2728859)Success in time 0.661 s
% 5.53/1.95 % Vampire exiting
%------------------------------------------------------------------------------