%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM502+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 : n007.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 7.62s 1.94s
% Output : Refutation 7.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 29
% Syntax : Number of formulae : 231 ( 30 unt; 12 def)
% Number of atoms : 1070 ( 234 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 1434 ( 595 ~; 731 |; 75 &)
% ( 18 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 150 ( 0 sgn 147 !; 3 ?)
% 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(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X0 != sz00
& X1 != X2
& sdtlseqdt0(X1,X2) )
=> ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( X0 != sz00
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
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(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(f42,axiom,
~ sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
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(f47,axiom,
( xk != sz00
& xk != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2327) ).
fof(f50,conjecture,
( xk != xp
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f51,negated_conjecture,
~ ( xk != xp
& sdtlseqdt0(xk,xp) ),
inference(negated_conjecture,[status(cth)],[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(f68,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f84,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f85,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f87,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f89,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f88]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f92]) ).
fof(f96,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f97,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f96]) ).
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(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(f121,plain,
( xp = xk
| ~ sdtlseqdt0(xk,xp) ),
inference(ennf_transformation,[],[f51]) ).
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(nnf_transformation,[],[f103]) ).
fof(f131,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,[],[f130]) ).
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(nnf_transformation,[],[f115]) ).
fof(f133,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,[],[f132]) ).
fof(f134,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,[],[f133]) ).
fof(f135,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))],[f134]) ).
fof(f137,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f141,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f151,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f68]) ).
fof(f168,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f87]) ).
fof(f170,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f176,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f177,plain,
! [X2,X0,X1] :
( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f178,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f179,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f182,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f187,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f188,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f197,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f205,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f206,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f207,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f209,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f210,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f211,plain,
~ sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f213,plain,
sdtlseqdt0(xm,xp),
inference(cnf_transformation,[],[f44]) ).
fof(f214,plain,
xm != xp,
inference(cnf_transformation,[],[f44]) ).
fof(f215,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f44]) ).
fof(f216,plain,
xn != xp,
inference(cnf_transformation,[],[f44]) ).
fof(f217,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f221,plain,
sz00 != xk,
inference(cnf_transformation,[],[f47]) ).
fof(f227,plain,
( xp = xk
| ~ sdtlseqdt0(xk,xp) ),
inference(cnf_transformation,[],[f121]) ).
fof(f236,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f188]) ).
fof(f237,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f187]) ).
fof(f238,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f197]) ).
fof(f242,definition,
( spl4_1
<=> sdtlseqdt0(xk,xp) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f244,plain,
( ~ sdtlseqdt0(xk,xp)
| spl4_1 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f246,definition,
( spl4_2
<=> xp = xk ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f248,plain,
( xp = xk
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f249,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f227,f246,f242]) ).
fof(f260,definition,
( spl4_5
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f264,definition,
( spl4_6
<=> isPrime0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f266,plain,
( ~ isPrime0(sz00)
| spl4_6 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f267,plain,
( ~ spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f238,f264,f260]) ).
fof(f269,plain,
spl4_5,
inference(avatar_split_clause,[],[f137,f260]) ).
fof(f270,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[],[f236,f217]) ).
fof(f271,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f270,f209]) ).
fof(f272,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f271,f205]) ).
fof(f274,definition,
( spl4_7
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f275,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f276,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_7 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f278,definition,
( spl4_8
<=> sz00 = xp ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f279,plain,
( sz00 != xp
| spl4_8 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f280,plain,
( sz00 = xp
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f282,definition,
( spl4_9
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
fof(f284,plain,
( aNaturalNumber0(xk)
| ~ spl4_9 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f285,plain,
( ~ spl4_7
| spl4_8
| spl4_9 ),
inference(avatar_split_clause,[],[f272,f282,f278,f274]) ).
fof(f287,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f237,f209]) ).
fof(f312,plain,
sz00 = sdtasdt0(xn,sz00),
inference(resolution,[],[f151,f207]) ).
fof(f319,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_7 ),
inference(resolution,[],[f141,f276]) ).
fof(f321,plain,
( ~ aNaturalNumber0(xm)
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f319,f207]) ).
fof(f322,plain,
( $false
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f321,f206]) ).
fof(f323,plain,
spl4_7,
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f358,plain,
( isPrime0(sz00)
| ~ spl4_8 ),
inference(superposition,[],[f210,f280]) ).
fof(f365,plain,
( $false
| spl4_6
| ~ spl4_8 ),
inference(forward_subsumption_resolution,[],[f358,f266]) ).
fof(f366,plain,
( spl4_6
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f365]) ).
fof(f370,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f287,f279]) ).
fof(f374,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f370,f205]) ).
fof(f378,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ spl4_7
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f374,f275]) ).
fof(f382,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| ~ spl4_7
| spl4_8 ),
inference(forward_demodulation,[],[f378,f217]) ).
fof(f489,definition,
( spl4_24
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl4_24])],[avatar_definition]) ).
fof(f490,plain,
( sz00 != xn
| spl4_24 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f491,plain,
( sz00 = xn
| ~ spl4_24 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f507,definition,
( spl4_27
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[spl4_27])],[avatar_definition]) ).
fof(f508,plain,
( sz00 != xm
| spl4_27 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f509,plain,
( sz00 = xm
| ~ spl4_27 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f518,plain,
( sdtlseqdt0(xp,sdtasdt0(xn,xm))
| sz00 = xk
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ spl4_7
| spl4_8 ),
inference(superposition,[],[f182,f382]) ).
fof(f522,plain,
( sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| ~ spl4_7
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f518,f221]) ).
fof(f526,plain,
( sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f522,f284]) ).
fof(f527,plain,
( sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f526,f205]) ).
fof(f564,plain,
! [X2,X0,X1] :
( sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X1,X0))
| sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| ~ aNaturalNumber0(sdtasdt0(X2,X0))
| ~ aNaturalNumber0(sdtasdt0(X1,X0)) ),
inference(resolution,[],[f176,f168]) ).
fof(f567,plain,
( ! [X0] :
( sdtlseqdt0(sdtasdt0(X0,xk),sdtasdt0(xn,xm))
| sz00 = xk
| xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) )
| ~ spl4_7
| spl4_8 ),
inference(superposition,[],[f176,f382]) ).
fof(f570,plain,
( ! [X0] :
( sdtlseqdt0(sdtasdt0(X0,xk),sdtasdt0(xn,xm))
| xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) )
| ~ spl4_7
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f567,f221]) ).
fof(f573,plain,
! [X2,X0,X1] :
( sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X1,X0))
| ~ aNaturalNumber0(sdtasdt0(X2,X0))
| ~ aNaturalNumber0(sdtasdt0(X1,X0)) ),
inference(forward_subsumption_resolution,[],[f564,f177]) ).
fof(f577,plain,
( ! [X0] :
( sdtlseqdt0(sdtasdt0(X0,xk),sdtasdt0(xn,xm))
| xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) )
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f570,f284]) ).
fof(f580,plain,
! [X2,X0,X1] :
( sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X1,X0))
| ~ aNaturalNumber0(sdtasdt0(X1,X0)) ),
inference(forward_subsumption_resolution,[],[f573,f141]) ).
fof(f584,plain,
( ! [X0] :
( sdtlseqdt0(sdtasdt0(X0,xk),sdtasdt0(xn,xm))
| xp = X0
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) )
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f577,f205]) ).
fof(f587,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(sdtasdt0(X2,X0),sdtasdt0(X1,X0))
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0 ),
inference(forward_subsumption_resolution,[],[f580,f141]) ).
fof(f613,plain,
! [X2,X0,X1] :
( sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X0,X1))
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(resolution,[],[f178,f168]) ).
fof(f622,plain,
( ! [X0] :
( sdtlseqdt0(sdtasdt0(xp,X0),sdtasdt0(xn,xm))
| sz00 = xp
| xk = X0
| ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk) )
| ~ spl4_7
| spl4_8 ),
inference(superposition,[],[f178,f382]) ).
fof(f629,plain,
( ! [X0] :
( sdtlseqdt0(sdtasdt0(xp,X0),sdtasdt0(xn,xm))
| xk = X0
| ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk) )
| ~ spl4_7
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f622,f279]) ).
fof(f638,plain,
! [X2,X0,X1] :
( sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f613,f179]) ).
fof(f644,plain,
( ! [X0] :
( sdtlseqdt0(sdtasdt0(xp,X0),sdtasdt0(xn,xm))
| xk = X0
| ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk) )
| ~ spl4_7
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f629,f205]) ).
fof(f653,plain,
! [X2,X0,X1] :
( sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f638,f141]) ).
fof(f659,plain,
( ! [X0] :
( sdtlseqdt0(sdtasdt0(xp,X0),sdtasdt0(xn,xm))
| xk = X0
| ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) )
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f644,f284]) ).
fof(f680,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(sdtasdt0(X0,X2),sdtasdt0(X0,X1))
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0 ),
inference(forward_subsumption_resolution,[],[f653,f141]) ).
fof(f696,plain,
( ~ sdtlseqdt0(xp,sz00)
| ~ spl4_24 ),
inference(superposition,[],[f211,f491]) ).
fof(f729,plain,
( sdtlseqdt0(xp,sdtasdt0(xn,sz00))
| ~ spl4_7
| spl4_8
| ~ spl4_9
| ~ spl4_27 ),
inference(forward_demodulation,[],[f527,f509]) ).
fof(f744,plain,
( sdtlseqdt0(xp,sz00)
| ~ spl4_7
| spl4_8
| ~ spl4_9
| ~ spl4_27 ),
inference(forward_demodulation,[],[f729,f312]) ).
fof(f753,plain,
( $false
| ~ spl4_7
| spl4_8
| ~ spl4_9
| ~ spl4_24
| ~ spl4_27 ),
inference(forward_subsumption_resolution,[],[f744,f696]) ).
fof(f754,plain,
( ~ spl4_7
| spl4_8
| ~ spl4_9
| ~ spl4_24
| ~ spl4_27 ),
inference(avatar_contradiction_clause,[],[f753]) ).
fof(f787,plain,
( sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp)
| spl4_1 ),
inference(resolution,[],[f170,f244]) ).
fof(f809,plain,
( sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xp)
| spl4_1
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f787,f284]) ).
fof(f814,plain,
( sdtlseqdt0(xp,xk)
| spl4_1
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f809,f205]) ).
fof(f855,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,X0))
| xk = X0
| ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| sz00 = xp )
| ~ spl4_7
| spl4_8 ),
inference(superposition,[],[f680,f382]) ).
fof(f875,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,X0))
| xk = X0
| ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk)
| sz00 = xp )
| ~ spl4_7
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f855,f205]) ).
fof(f885,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,X0))
| xk = X0
| ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0)
| sz00 = xp )
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f875,f284]) ).
fof(f895,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,X0))
| xk = X0
| ~ sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) )
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f885,f279]) ).
fof(f1080,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,xp)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) )
| spl4_1
| ~ spl4_9 ),
inference(resolution,[],[f814,f169]) ).
fof(f1084,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,xp)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xk) )
| spl4_1
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f1080,f205]) ).
fof(f1086,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,xp)
| sdtlseqdt0(X0,xk)
| ~ aNaturalNumber0(X0) )
| spl4_1
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f1084,f284]) ).
fof(f1257,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm)
| xn = xp
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| sz00 = xm
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(resolution,[],[f659,f587]) ).
fof(f1265,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm)
| xn = xp
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| sz00 = xm
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(duplicate_literal_removal,[],[f1257]) ).
fof(f1270,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| xn = xp
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| sz00 = xm
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f1265,f206]) ).
fof(f1272,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| sz00 = xm
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f1270,f216]) ).
fof(f1274,definition,
( spl4_58
<=> sdtlseqdt0(sz00,xk) ),
introduced(definition,[new_symbols(definition,[spl4_58])],[avatar_definition]) ).
fof(f1275,plain,
( sdtlseqdt0(sz00,xk)
| ~ spl4_58 ),
inference(avatar_component_clause,[],[f1274]) ).
fof(f1276,plain,
( ~ sdtlseqdt0(sz00,xk)
| spl4_58 ),
inference(avatar_component_clause,[],[f1274]) ).
fof(f1282,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| sz00 = xm
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f1272,f215]) ).
fof(f1283,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xp)
| sz00 = xm
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f1282,f207]) ).
fof(f1284,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| sz00 = xm
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f1283,f205]) ).
fof(f1285,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(forward_subsumption_resolution,[],[f1284,f508]) ).
fof(f1287,definition,
( spl4_60
<=> sdtlseqdt0(xm,xk) ),
introduced(definition,[new_symbols(definition,[spl4_60])],[avatar_definition]) ).
fof(f1288,plain,
( sdtlseqdt0(xm,xk)
| ~ spl4_60 ),
inference(avatar_component_clause,[],[f1287]) ).
fof(f1289,plain,
( ~ sdtlseqdt0(xm,xk)
| spl4_60 ),
inference(avatar_component_clause,[],[f1287]) ).
fof(f1291,definition,
( spl4_61
<=> xm = xk ),
introduced(definition,[new_symbols(definition,[spl4_61])],[avatar_definition]) ).
fof(f1293,plain,
( xm = xk
| ~ spl4_61 ),
inference(avatar_component_clause,[],[f1291]) ).
fof(f1294,plain,
( ~ spl4_60
| spl4_61
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(avatar_split_clause,[],[f1285,f507,f282,f278,f274,f1291,f1287]) ).
fof(f2037,plain,
( xn = xp
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sz00 = xn
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(resolution,[],[f584,f680]) ).
fof(f2043,plain,
( xn = xp
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sz00 = xn
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(duplicate_literal_removal,[],[f2037]) ).
fof(f2598,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm)
| sz00 = xm
| xn = xp
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(resolution,[],[f895,f176]) ).
fof(f2601,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm)
| sz00 = xm
| xn = xp
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(duplicate_literal_removal,[],[f2598]) ).
fof(f3043,plain,
( sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm)
| spl4_1
| ~ spl4_9 ),
inference(resolution,[],[f1086,f213]) ).
fof(f3047,plain,
( ~ aNaturalNumber0(xm)
| spl4_1
| ~ spl4_9
| spl4_60 ),
inference(forward_subsumption_resolution,[],[f3043,f1289]) ).
fof(f3049,plain,
( $false
| spl4_1
| ~ spl4_9
| spl4_60 ),
inference(forward_subsumption_resolution,[],[f3047,f206]) ).
fof(f3050,plain,
( spl4_1
| ~ spl4_9
| spl4_60 ),
inference(avatar_contradiction_clause,[],[f3049]) ).
fof(f3055,plain,
( ~ sdtlseqdt0(xm,xp)
| spl4_1
| ~ spl4_61 ),
inference(superposition,[],[f244,f1293]) ).
fof(f3098,plain,
( $false
| spl4_1
| ~ spl4_61 ),
inference(forward_subsumption_resolution,[],[f3055,f213]) ).
fof(f3099,plain,
( spl4_1
| ~ spl4_61 ),
inference(avatar_contradiction_clause,[],[f3098]) ).
fof(f3102,plain,
( ~ sdtlseqdt0(xm,xp)
| ~ spl4_2
| spl4_60 ),
inference(forward_demodulation,[],[f1289,f248]) ).
fof(f3105,plain,
( ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sz00 = xn
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f2043,f216]) ).
fof(f3106,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| sz00 = xm
| xn = xp
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f2601,f206]) ).
fof(f3108,plain,
( $false
| ~ spl4_2
| spl4_60 ),
inference(forward_subsumption_resolution,[],[f3102,f213]) ).
fof(f3109,plain,
( ~ spl4_2
| spl4_60 ),
inference(avatar_contradiction_clause,[],[f3108]) ).
fof(f3111,plain,
( ~ aNaturalNumber0(xn)
| xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sz00 = xn
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f3105,f215]) ).
fof(f3112,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| xn = xp
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(forward_subsumption_resolution,[],[f3106,f508]) ).
fof(f3115,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| sz00 = xn
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f3111,f207]) ).
fof(f3116,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(forward_subsumption_resolution,[],[f3112,f216]) ).
fof(f3119,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xk)
| sz00 = xn
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f3115,f206]) ).
fof(f3120,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(forward_subsumption_resolution,[],[f3116,f215]) ).
fof(f3123,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| sz00 = xn
| ~ spl4_7
| spl4_8
| ~ spl4_9 ),
inference(forward_subsumption_resolution,[],[f3119,f284]) ).
fof(f3124,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xp)
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(forward_subsumption_resolution,[],[f3120,f207]) ).
fof(f3127,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_24 ),
inference(forward_subsumption_resolution,[],[f3123,f490]) ).
fof(f3128,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(forward_subsumption_resolution,[],[f3124,f205]) ).
fof(f3132,plain,
( xm = xp
| ~ sdtlseqdt0(xm,xk)
| ~ spl4_2
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(forward_demodulation,[],[f3128,f248]) ).
fof(f3136,plain,
( ~ sdtlseqdt0(xm,xk)
| ~ spl4_2
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(forward_subsumption_resolution,[],[f3132,f214]) ).
fof(f3140,plain,
( ~ sdtlseqdt0(xm,xp)
| ~ spl4_2
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(forward_demodulation,[],[f3136,f248]) ).
fof(f3154,plain,
( $false
| ~ spl4_2
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(forward_subsumption_resolution,[],[f3140,f213]) ).
fof(f3155,plain,
( ~ spl4_2
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(avatar_contradiction_clause,[],[f3154]) ).
fof(f3157,plain,
( sdtlseqdt0(sz00,xk)
| ~ spl4_27
| ~ spl4_60 ),
inference(forward_demodulation,[],[f1288,f509]) ).
fof(f3161,plain,
( sz00 = xk
| ~ sdtlseqdt0(xm,xk)
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_24
| ~ spl4_27 ),
inference(forward_demodulation,[],[f3127,f509]) ).
fof(f3162,plain,
( $false
| ~ spl4_27
| spl4_58
| ~ spl4_60 ),
inference(forward_subsumption_resolution,[],[f3157,f1276]) ).
fof(f3163,plain,
( ~ spl4_27
| spl4_58
| ~ spl4_60 ),
inference(avatar_contradiction_clause,[],[f3162]) ).
fof(f3166,plain,
( ~ sdtlseqdt0(xm,xk)
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_24
| ~ spl4_27 ),
inference(forward_subsumption_resolution,[],[f3161,f221]) ).
fof(f3177,plain,
( ~ sdtlseqdt0(sz00,xk)
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_24
| ~ spl4_27 ),
inference(forward_demodulation,[],[f3166,f509]) ).
fof(f3183,plain,
( $false
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_24
| ~ spl4_27
| ~ spl4_58 ),
inference(forward_subsumption_resolution,[],[f3177,f1275]) ).
fof(f3184,plain,
( ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_24
| ~ spl4_27
| ~ spl4_58 ),
inference(avatar_contradiction_clause,[],[f3183]) ).
cnf(s1,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f249]) ).
cnf(s3,plain,
( ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f267]) ).
cnf(s5,plain,
spl4_5,
inference(sat_conversion,[],[f269]) ).
cnf(s6,plain,
( ~ spl4_7
| spl4_8
| spl4_9 ),
inference(sat_conversion,[],[f285]) ).
cnf(s8,plain,
spl4_7,
inference(sat_conversion,[],[f323]) ).
cnf(s12,plain,
( spl4_6
| ~ spl4_8 ),
inference(sat_conversion,[],[f366]) ).
cnf(s36,plain,
( ~ spl4_7
| spl4_8
| ~ spl4_9
| ~ spl4_24
| ~ spl4_27 ),
inference(sat_conversion,[],[f754]) ).
cnf(s58,plain,
( ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27
| ~ spl4_60
| spl4_61 ),
inference(sat_conversion,[],[f1294]) ).
cnf(s113,plain,
( spl4_1
| ~ spl4_9
| spl4_60 ),
inference(sat_conversion,[],[f3050]) ).
cnf(s115,plain,
( spl4_1
| ~ spl4_61 ),
inference(sat_conversion,[],[f3099]) ).
cnf(s117,plain,
( ~ spl4_2
| spl4_60 ),
inference(sat_conversion,[],[f3109]) ).
cnf(s121,plain,
( ~ spl4_2
| ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_27 ),
inference(sat_conversion,[],[f3155]) ).
cnf(s122,plain,
( ~ spl4_27
| spl4_58
| ~ spl4_60 ),
inference(sat_conversion,[],[f3163]) ).
cnf(s125,plain,
( ~ spl4_7
| spl4_8
| ~ spl4_9
| spl4_24
| ~ spl4_27
| ~ spl4_58 ),
inference(sat_conversion,[],[f3184]) ).
cnf(s140,plain,
( spl4_8
| spl4_9 ),
inference(rat,[],[s6,s8]) ).
cnf(s146,plain,
~ spl4_6,
inference(rat,[],[s3,s5]) ).
cnf(s148,plain,
~ spl4_8,
inference(rat,[],[s12,s146]) ).
cnf(s151,plain,
spl4_9,
inference(rat,[],[s140,s148]) ).
cnf(s190,plain,
( ~ spl4_27
| ~ spl4_58 ),
inference(rat,[],[s36,s125,s151,s148,s8]) ).
cnf(s191,plain,
( ~ spl4_27
| ~ spl4_60 ),
inference(rat,[],[s190,s122]) ).
cnf(s192,plain,
( ~ spl4_60
| spl4_61 ),
inference(rat,[],[s191,s58,s151,s148,s8]) ).
cnf(s193,plain,
spl4_1,
inference(rat,[],[s192,s113,s115,s151]) ).
cnf(s194,plain,
spl4_2,
inference(rat,[],[s1,s193]) ).
cnf(s195,plain,
spl4_27,
inference(rat,[],[s121,s151,s148,s8,s194]) ).
cnf(s197,plain,
spl4_60,
inference(rat,[],[s117,s194]) ).
cnf(s201,plain,
$false,
inference(rat,[],[s191,s197,s195]) ).
fof(f3194,plain,
$false,
inference(avatar_sat_refutation,[],[s201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM502+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n007.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 20:11:41 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 7.62/1.94 % (1751515)Detected formulas, will run a generic FOF schedule.
% 7.62/1.94 % (1751525)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=947703402:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 7.62/1.94 % (1751524)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2530767849:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 7.62/1.94 % (1751526)dis-21_1_sil=8000:lcm=predicate:random_seed=1805501231: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)
% 7.62/1.94 % (1751522)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=842718281:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 7.62/1.94 % (1751520)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=2145920329:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 7.62/1.94 % (1751523)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1205664267:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 7.62/1.94 % (1751521)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=3154341420:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 7.62/1.94 % (1751523)Instruction limit reached!
% 7.62/1.94 % (1751523)------------------------------
% 7.62/1.94 % (1751523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751523)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751523)Termination reason: Instruction limit
% 7.62/1.94 % (1751523)Termination phase: Saturation
% 7.62/1.94 % (1751523)Time elapsed: 0.061 s
% 7.62/1.94 % (1751523)Peak memory usage: 89 MB
% 7.62/1.94 % (1751523)Instructions burned: 109 (million)
% 7.62/1.94 % (1751524)Instruction limit reached!
% 7.62/1.94 % (1751524)------------------------------
% 7.62/1.94 % (1751524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751524)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751524)Termination reason: Instruction limit
% 7.62/1.94 % (1751524)Termination phase: Saturation
% 7.62/1.94 % (1751524)Time elapsed: 0.068 s
% 7.62/1.94 % (1751524)Peak memory usage: 88 MB
% 7.62/1.94 % (1751524)Instructions burned: 120 (million)
% 7.62/1.94 % (1751526)Instruction limit reached!
% 7.62/1.94 % (1751526)------------------------------
% 7.62/1.94 % (1751526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751526)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751526)Termination reason: Instruction limit
% 7.62/1.94 % (1751526)Termination phase: Saturation
% 7.62/1.94 % (1751526)Time elapsed: 0.077 s
% 7.62/1.94 % (1751526)Peak memory usage: 90 MB
% 7.62/1.94 % (1751526)Instructions burned: 130 (million)
% 7.62/1.94 % (1751525)Instruction limit reached!
% 7.62/1.94 % (1751525)------------------------------
% 7.62/1.94 % (1751525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751525)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751525)Termination reason: Instruction limit
% 7.62/1.94 % (1751525)Termination phase: Saturation
% 7.62/1.94 % (1751525)Time elapsed: 0.115 s
% 7.62/1.94 % (1751525)Peak memory usage: 90 MB
% 7.62/1.94 % (1751525)Instructions burned: 140 (million)
% 7.62/1.94 % (1751534)lrs+10_1_sil=8000:sp=occurrence:random_seed=2928961387:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 7.62/1.94 % (1751535)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3370850007:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 7.62/1.94 % (1751535)Refutation not found, incomplete strategy
% 7.62/1.94 % (1751535)------------------------------
% 7.62/1.94 % (1751535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751535)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751535)Termination reason: Refutation not found, incomplete strategy
% 7.62/1.94 % (1751535)Time elapsed: 0.003 s
% 7.62/1.94 % (1751535)Peak memory usage: 89 MB
% 7.62/1.94 % (1751535)Instructions burned: 3 (million)
% 7.62/1.94 % (1751536)lrs+1011_1_sil=32000:sp=occurrence:random_seed=807838355:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 7.62/1.94 % (1751537)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=3483800923:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 7.62/1.94 % (1751537)Instruction limit reached!
% 7.62/1.94 % (1751537)------------------------------
% 7.62/1.94 % (1751537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751537)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751537)Termination reason: Instruction limit
% 7.62/1.94 % (1751537)Termination phase: Saturation
% 7.62/1.94 % (1751537)Time elapsed: 0.065 s
% 7.62/1.94 % (1751537)Peak memory usage: 94 MB
% 7.62/1.94 % (1751537)Instructions burned: 251 (million)
% 7.62/1.94 % (1751534)Instruction limit reached!
% 7.62/1.94 % (1751534)------------------------------
% 7.62/1.94 % (1751534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751534)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751534)Termination reason: Instruction limit
% 7.62/1.94 % (1751534)Termination phase: Saturation
% 7.62/1.94 % (1751534)Time elapsed: 0.165 s
% 7.62/1.94 % (1751534)Peak memory usage: 92 MB
% 7.62/1.94 % (1751534)Instructions burned: 286 (million)
% 7.62/1.94 % (1751542)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=529313496:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 7.62/1.94 % (1751536)Instruction limit reached!
% 7.62/1.94 % (1751536)------------------------------
% 7.62/1.94 % (1751536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751536)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751536)Termination reason: Instruction limit
% 7.62/1.94 % (1751536)Termination phase: Saturation
% 7.62/1.94 % (1751536)Time elapsed: 0.197 s
% 7.62/1.94 % (1751536)Peak memory usage: 92 MB
% 7.62/1.94 % (1751536)Instructions burned: 325 (million)
% 7.62/1.94 % (1751535)------------------------------
% 7.62/1.94 % (1751535)------------------------------
% 7.62/1.94 % (1751542)Instruction limit reached!
% 7.62/1.94 % (1751542)------------------------------
% 7.62/1.94 % (1751542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751542)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751542)Termination reason: Instruction limit
% 7.62/1.94 % (1751542)Termination phase: Saturation
% 7.62/1.94 % (1751542)Time elapsed: 0.088 s
% 7.62/1.94 % (1751542)Peak memory usage: 89 MB
% 7.62/1.94 % (1751542)Instructions burned: 295 (million)
% 7.62/1.94 % (1751543)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1242620932:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 7.62/1.94 % (1751545)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2653570621:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 7.62/1.94 % (1751547)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1048487864:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 7.62/1.94 % (1751546)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1805062486:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 7.62/1.94 % (1751547)Instruction limit reached!
% 7.62/1.94 % (1751547)------------------------------
% 7.62/1.94 % (1751547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751547)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751547)Termination reason: Instruction limit
% 7.62/1.94 % (1751547)Termination phase: Saturation
% 7.62/1.94 % (1751547)Time elapsed: 0.034 s
% 7.62/1.94 % (1751547)Peak memory usage: 89 MB
% 7.62/1.94 % (1751547)Instructions burned: 117 (million)
% 7.62/1.94 % (1751545)Instruction limit reached!
% 7.62/1.94 % (1751545)------------------------------
% 7.62/1.94 % (1751545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751545)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751545)Termination reason: Instruction limit
% 7.62/1.94 % (1751545)Termination phase: Saturation
% 7.62/1.94 % (1751545)Time elapsed: 0.069 s
% 7.62/1.94 % (1751545)Peak memory usage: 90 MB
% 7.62/1.94 % (1751545)Instructions burned: 114 (million)
% 7.62/1.94 % (1751546)Instruction limit reached!
% 7.62/1.94 % (1751546)------------------------------
% 7.62/1.94 % (1751546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751546)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751546)Termination reason: Instruction limit
% 7.62/1.94 % (1751546)Termination phase: Saturation
% 7.62/1.94 % (1751546)Time elapsed: 0.063 s
% 7.62/1.94 % (1751546)Peak memory usage: 89 MB
% 7.62/1.94 % (1751546)Instructions burned: 127 (million)
% 7.62/1.94 % (1751552)lrs+10_1_sil=8000:sp=occurrence:random_seed=837575252:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 7.62/1.94 % (1751553)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4012626318:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 7.62/1.94 % (1751554)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3304594862:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 7.62/1.94 % (1751520)First to succeed.
% 7.62/1.94 % (1751521)Also succeeded, but the first one will report.
% 7.62/1.94 % (1751520)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1751515"
% 7.62/1.94 % (1751553)Instruction limit reached!
% 7.62/1.94 % (1751553)------------------------------
% 7.62/1.94 % (1751553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751553)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751553)Termination reason: Instruction limit
% 7.62/1.94 % (1751553)Termination phase: Saturation
% 7.62/1.94 % (1751553)Time elapsed: 0.256 s
% 7.62/1.94 % (1751553)Peak memory usage: 92 MB
% 7.62/1.94 % (1751553)Instructions burned: 438 (million)
% 7.62/1.94 % (1751552)Instruction limit reached!
% 7.62/1.94 % (1751552)------------------------------
% 7.62/1.94 % (1751552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/1.94 % (1751552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/1.94 % (1751552)CaDiCaL version: 2.1.3
% 7.62/1.94 % (1751552)Termination reason: Instruction limit
% 7.62/1.94 % (1751552)Termination phase: Saturation
% 7.62/1.94 % (1751552)Time elapsed: 0.272 s
% 7.62/1.94 % (1751552)Peak memory usage: 97 MB
% 7.62/1.94 % (1751552)Instructions burned: 908 (million)
% 7.62/1.94 % (1751559)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3587036714:st=8:i=592:sd=3:ep=RST:ss=axioms_2988 on theBenchmark for (2988ds/592Mi)
% 7.62/1.94 % (1751558)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1724360545:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 7.62/1.94 % (1751520)Refutation found. Thanks to Tanya!
% 7.62/1.94 % SZS status Theorem for theBenchmark
% 7.62/1.94 % SZS output start Proof for theBenchmark
% See solution above
% 7.62/2.03 % (1751520)------------------------------
% 7.62/2.03 % (1751520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.62/2.03 % (1751520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.62/2.03 % (1751520)CaDiCaL version: 2.1.3
% 7.62/2.03 % (1751520)Termination reason: Refutation
% 7.62/2.03 % (1751520)Time elapsed: 0.912 s
% 7.62/2.03 % (1751520)Peak memory usage: 132 MB
% 7.62/2.03 % (1751520)Instructions burned: 1395 (million)
% 7.62/2.03 % (1751520)------------------------------
% 7.62/2.03 % (1751520)------------------------------
% 7.62/2.03 % (1751515)Success in time 1.305 s
% 7.62/2.03 % Vampire exiting
%------------------------------------------------------------------------------