%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM509+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 12:15:30 PM UTC 2026
% Result : Theorem 12.81s 2.90s
% Output : Refutation 12.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 49
% Syntax : Number of formulae : 376 ( 52 unt; 24 def)
% Number of atoms : 1423 ( 260 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1818 ( 771 ~; 886 |; 97 &)
% ( 33 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 25 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 233 ( 0 sgn 225 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != X1
& sdtlseqdt0(X0,X1) )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtpldt0(X2,X0) != sdtpldt0(X2,X1)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( X0 != sz00
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != X1
& sdtlseqdt0(X0,X1) )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( doDivides0(X0,X1)
& X1 != sz00 )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivLE) ).
fof(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/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( isPrime0(X2)
& doDivides0(X2,sdtasdt0(X0,X1)) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X2,X0)
| doDivides0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1799) ).
fof(f41,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f44,axiom,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f48,axiom,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( sdtlseqdt0(xr,xk)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
fof(f52,conjecture,
( doDivides0(xr,xn)
=> ( doDivides0(xp,xn)
| doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f53,negated_conjecture,
~ ( doDivides0(xr,xn)
=> ( doDivides0(xp,xn)
| doDivides0(xp,xm) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f57,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f59,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f58]) ).
fof(f65,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f66,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f65]) ).
fof(f69,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f70,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f86,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f87,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f89,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f88]) ).
fof(f92,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt0(X2,X0) != sdtpldt0(X2,X1)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) )
| ~ aNaturalNumber0(X2) )
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f93,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtpldt0(X2,X0) != sdtpldt0(X2,X1)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) )
| ~ aNaturalNumber0(X2) )
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f92]) ).
fof(f98,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f99,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f101,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f103,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f102]) ).
fof(f104,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(f105,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,[],[f104]) ).
fof(f112,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f113,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ doDivides0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f112]) ).
fof(f114,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(f115,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,[],[f114]) ).
fof(f116,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(f117,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f116]) ).
fof(f120,plain,
! [X0,X1,X2] :
( doDivides0(X2,X0)
| doDivides0(X2,X1)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f40]) ).
fof(f121,plain,
! [X0,X1,X2] :
( doDivides0(X2,X0)
| doDivides0(X2,X1)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f120]) ).
fof(f123,plain,
( ~ doDivides0(xp,xn)
& ~ doDivides0(xp,xm)
& doDivides0(xr,xn) ),
inference(ennf_transformation,[],[f53]) ).
fof(f124,plain,
( ~ doDivides0(xp,xn)
& ~ doDivides0(xp,xm)
& doDivides0(xr,xn) ),
inference(flattening,[],[f123]) ).
fof(f130,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,[],[f103]) ).
fof(f131,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,[],[f130]) ).
fof(f132,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))],[f131]) ).
fof(f133,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,[],[f105]) ).
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(flattening,[],[f133]) ).
fof(f135,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,[],[f117]) ).
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(flattening,[],[f135]) ).
fof(f137,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,[],[f136]) ).
fof(f138,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))],[f137]) ).
fof(f140,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f142,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f143,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f144,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f149,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f152,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f69]) ).
fof(f154,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f70]) ).
fof(f171,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f175,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f176,plain,
! [X2,X0,X1] :
( sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f185,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f186,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f189,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f190,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f191,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f192,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,[],[f134]) ).
fof(f196,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f197,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,[],[f115]) ).
fof(f199,plain,
! [X0] :
( sz10 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f200,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f208,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f209,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f210,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f211,plain,
! [X2,X0,X1] :
( ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ isPrime0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f121]) ).
fof(f212,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f213,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f218,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f44]) ).
fof(f220,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f225,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f226,plain,
doDivides0(xr,xk),
inference(cnf_transformation,[],[f48]) ).
fof(f227,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f228,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f49]) ).
fof(f233,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f124]) ).
fof(f234,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f124]) ).
fof(f235,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f124]) ).
fof(f242,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f189]) ).
fof(f243,plain,
! [X2,X0] :
( ~ doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| sz00 = X0
| sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f192]) ).
fof(f244,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f191]) ).
fof(f245,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f190]) ).
fof(f246,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f200]) ).
fof(f247,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(equality_resolution,[],[f199]) ).
fof(f250,definition,
( spl4_1
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f251,plain,
( aNaturalNumber0(sz10)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl4_2
<=> isPrime0(sz10) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f256,plain,
( ~ isPrime0(sz10)
| spl4_2 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f257,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f247,f254,f250]) ).
fof(f259,definition,
( spl4_3
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f260,plain,
( aNaturalNumber0(sz00)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f263,definition,
( spl4_4
<=> isPrime0(sz00) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f265,plain,
( ~ isPrime0(sz00)
| spl4_4 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f266,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f246,f263,f259]) ).
fof(f267,plain,
spl4_1,
inference(avatar_split_clause,[],[f142,f250]) ).
fof(f268,plain,
spl4_3,
inference(avatar_split_clause,[],[f140,f259]) ).
fof(f281,definition,
( spl4_5
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
fof(f282,plain,
( aNaturalNumber0(xk)
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f283,plain,
( ~ aNaturalNumber0(xk)
| spl4_5 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f305,definition,
( spl4_7
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f306,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f307,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_7 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f322,definition,
( spl4_11
<=> sz10 = xr ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
fof(f324,plain,
( sz10 = xr
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f347,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| iLess0(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| ~ aNaturalNumber0(sdtpldt0(X1,X0))
| ~ aNaturalNumber0(sdtpldt0(X2,X0)) ),
inference(resolution,[],[f175,f186]) ).
fof(f348,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| iLess0(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| ~ aNaturalNumber0(sdtpldt0(X1,X0))
| ~ aNaturalNumber0(sdtpldt0(X2,X0)) ),
inference(forward_subsumption_resolution,[],[f347,f176]) ).
fof(f350,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| iLess0(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| ~ aNaturalNumber0(sdtpldt0(X2,X0)) ),
inference(forward_subsumption_resolution,[],[f348,f143]) ).
fof(f352,plain,
! [X2,X0,X1] :
( iLess0(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f350,f143]) ).
fof(f362,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_7 ),
inference(resolution,[],[f144,f307]) ).
fof(f363,plain,
( ~ aNaturalNumber0(xm)
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f362,f210]) ).
fof(f364,plain,
( $false
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f363,f209]) ).
fof(f365,plain,
spl4_7,
inference(avatar_contradiction_clause,[],[f364]) ).
fof(f366,plain,
( sz00 = xr
| xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f245,f233]) ).
fof(f371,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f245,f212]) ).
fof(f374,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f371,f208]) ).
fof(f378,plain,
( sz00 = xr
| xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f366,f227]) ).
fof(f379,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f374,f306]) ).
fof(f381,plain,
( sz00 = xr
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ),
inference(forward_subsumption_resolution,[],[f378,f210]) ).
fof(f382,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| sz00 = xp
| ~ spl4_7 ),
inference(forward_demodulation,[],[f379,f220]) ).
fof(f388,definition,
( spl4_16
<=> sz00 = xr ),
introduced(definition,[new_symbols(definition,[spl4_16])],[avatar_definition]) ).
fof(f389,plain,
( sz00 != xr
| spl4_16 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f390,plain,
( sz00 = xr
| ~ spl4_16 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f393,definition,
( spl4_17
<=> xn = sdtasdt0(xr,sdtsldt0(xn,xr)) ),
introduced(definition,[new_symbols(definition,[spl4_17])],[avatar_definition]) ).
fof(f395,plain,
( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
| ~ spl4_17 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f396,plain,
( spl4_17
| spl4_16 ),
inference(avatar_split_clause,[],[f381,f388,f393]) ).
fof(f398,definition,
( spl4_18
<=> sz00 = xp ),
introduced(definition,[new_symbols(definition,[spl4_18])],[avatar_definition]) ).
fof(f399,plain,
( sz00 != xp
| spl4_18 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f400,plain,
( sz00 = xp
| ~ spl4_18 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f402,definition,
( spl4_19
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[spl4_19])],[avatar_definition]) ).
fof(f404,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| ~ spl4_19 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f405,plain,
( spl4_18
| spl4_19
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f382,f305,f402,f398]) ).
fof(f409,plain,
( isPrime0(sz00)
| ~ spl4_18 ),
inference(superposition,[],[f213,f400]) ).
fof(f417,plain,
( $false
| spl4_4
| ~ spl4_18 ),
inference(forward_subsumption_resolution,[],[f409,f265]) ).
fof(f418,plain,
( spl4_4
| ~ spl4_18 ),
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f419,plain,
( isPrime0(sz00)
| ~ spl4_16 ),
inference(superposition,[],[f225,f390]) ).
fof(f425,plain,
( $false
| spl4_4
| ~ spl4_16 ),
inference(forward_subsumption_resolution,[],[f419,f265]) ).
fof(f426,plain,
( spl4_4
| ~ spl4_16 ),
inference(avatar_contradiction_clause,[],[f425]) ).
fof(f428,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = xr
| sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f197,f233]) ).
fof(f430,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = xr
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[],[f197,f226]) ).
fof(f440,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn) )
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f428,f389]) ).
fof(f443,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr)
| ~ aNaturalNumber0(xn) )
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f440,f227]) ).
fof(f446,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(X0,xn),xr) )
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f443,f210]) ).
fof(f449,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[],[f244,f220]) ).
fof(f450,plain,
( sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f449,f283]) ).
fof(f451,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_5
| spl4_18 ),
inference(forward_subsumption_resolution,[],[f450,f399]) ).
fof(f452,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_5
| spl4_18 ),
inference(forward_subsumption_resolution,[],[f451,f212]) ).
fof(f453,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_5
| spl4_18 ),
inference(forward_subsumption_resolution,[],[f452,f208]) ).
fof(f454,plain,
( $false
| spl4_5
| ~ spl4_7
| spl4_18 ),
inference(forward_subsumption_resolution,[],[f453,f306]) ).
fof(f455,plain,
( spl4_5
| ~ spl4_7
| spl4_18 ),
inference(avatar_contradiction_clause,[],[f454]) ).
fof(f459,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) )
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f430,f389]) ).
fof(f463,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr)
| ~ aNaturalNumber0(xk) )
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f459,f227]) ).
fof(f475,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xk,xr)) = sdtsldt0(sdtasdt0(X0,xk),xr) )
| ~ spl4_5
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f463,f282]) ).
fof(f479,plain,
( doDivides0(xr,sdtasdt0(xp,xk))
| ~ spl4_19 ),
inference(superposition,[],[f228,f404]) ).
fof(f480,plain,
( aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ spl4_19 ),
inference(superposition,[],[f144,f404]) ).
fof(f485,plain,
( aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xm)
| ~ spl4_19 ),
inference(forward_subsumption_resolution,[],[f480,f210]) ).
fof(f488,plain,
( aNaturalNumber0(sdtasdt0(xp,xk))
| ~ spl4_19 ),
inference(forward_subsumption_resolution,[],[f485,f209]) ).
fof(f490,definition,
( spl4_22
<=> aNaturalNumber0(sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[spl4_22])],[avatar_definition]) ).
fof(f491,plain,
( aNaturalNumber0(sdtasdt0(xp,xk))
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f503,definition,
( spl4_25
<=> sz00 = xn ),
introduced(definition,[new_symbols(definition,[spl4_25])],[avatar_definition]) ).
fof(f504,plain,
( sz00 != xn
| spl4_25 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f505,plain,
( sz00 = xn
| ~ spl4_25 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f507,plain,
( spl4_22
| ~ spl4_19 ),
inference(avatar_split_clause,[],[f488,f402,f490]) ).
fof(f510,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,X1)
| doDivides0(xp,X0)
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f352,f211]) ).
fof(f511,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,X1)
| doDivides0(xp,X0)
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(duplicate_literal_removal,[],[f510]) ).
fof(f512,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| doDivides0(xp,X1)
| doDivides0(xp,X0)
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f511,f143]) ).
fof(f513,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| doDivides0(xp,X1)
| doDivides0(xp,X0)
| ~ isPrime0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f512,f208]) ).
fof(f514,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| doDivides0(xp,X1)
| doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f513,f213]) ).
fof(f516,definition,
( spl4_26
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_26])],[avatar_definition]) ).
fof(f518,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl4_26 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f520,definition,
( spl4_27
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| doDivides0(xp,X0)
| doDivides0(xp,X1)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm)) ) ),
introduced(definition,[new_symbols(definition,[spl4_27])],[avatar_definition]) ).
fof(f521,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| doDivides0(xp,X0)
| doDivides0(xp,X1)
| sdtpldt0(X0,X1) = sdtpldt0(xn,xm) )
| ~ spl4_27 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f522,plain,
( ~ spl4_26
| spl4_27 ),
inference(avatar_split_clause,[],[f514,f520,f516]) ).
fof(f523,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_26 ),
inference(resolution,[],[f518,f143]) ).
fof(f524,plain,
( ~ aNaturalNumber0(xm)
| spl4_26 ),
inference(forward_subsumption_resolution,[],[f523,f210]) ).
fof(f525,plain,
( $false
| spl4_26 ),
inference(forward_subsumption_resolution,[],[f524,f209]) ).
fof(f526,plain,
spl4_26,
inference(avatar_contradiction_clause,[],[f525]) ).
fof(f527,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| doDivides0(xp,xm)
| sdtpldt0(xn,xm) = sdtpldt0(X0,xm)
| ~ aNaturalNumber0(xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) )
| ~ spl4_27 ),
inference(resolution,[],[f521,f175]) ).
fof(f530,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| doDivides0(xp,xm)
| sdtpldt0(xn,xm) = sdtpldt0(X0,xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl4_27 ),
inference(duplicate_literal_removal,[],[f527]) ).
fof(f532,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| doDivides0(xp,xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl4_27 ),
inference(forward_subsumption_resolution,[],[f530,f176]) ).
fof(f534,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| doDivides0(xp,xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl4_27 ),
inference(forward_subsumption_resolution,[],[f532,f209]) ).
fof(f536,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl4_27 ),
inference(forward_subsumption_resolution,[],[f534,f234]) ).
fof(f538,plain,
( ! [X0] :
( ~ doDivides0(xp,sdtasdt0(X0,xm))
| ~ aNaturalNumber0(X0)
| doDivides0(xp,X0)
| xn = X0
| ~ sdtlseqdt0(X0,xn) )
| ~ spl4_27 ),
inference(forward_subsumption_resolution,[],[f536,f210]) ).
fof(f611,plain,
( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtsldt0(sdtasdt0(xm,xn),xr)
| spl4_16 ),
inference(resolution,[],[f446,f209]) ).
fof(f660,plain,
( ~ doDivides0(xp,sz00)
| ~ spl4_25 ),
inference(superposition,[],[f235,f505]) ).
fof(f685,plain,
( sdtsldt0(sdtasdt0(xp,xk),xr) = sdtasdt0(xp,sdtsldt0(xk,xr))
| ~ spl4_5
| spl4_16 ),
inference(resolution,[],[f475,f208]) ).
fof(f1121,plain,
xn = sdtasdt0(xn,sz10),
inference(resolution,[],[f152,f210]) ).
fof(f1215,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xn)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f172,f218]) ).
fof(f1224,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xn)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f1215,f210]) ).
fof(f1234,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xn)
| sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f1224,f208]) ).
fof(f1258,plain,
sz00 = sdtasdt0(xp,sz00),
inference(resolution,[],[f154,f208]) ).
fof(f1260,plain,
sz00 = sdtasdt0(xr,sz00),
inference(resolution,[],[f154,f227]) ).
fof(f1597,plain,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[],[f242,f1258]) ).
fof(f1604,plain,
( doDivides0(xp,sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(duplicate_literal_removal,[],[f1597]) ).
fof(f1609,plain,
( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp)
| ~ spl4_25 ),
inference(forward_subsumption_resolution,[],[f1604,f660]) ).
fof(f1616,plain,
( ~ aNaturalNumber0(xp)
| ~ spl4_3
| ~ spl4_25 ),
inference(forward_subsumption_resolution,[],[f1609,f260]) ).
fof(f1623,plain,
( $false
| ~ spl4_3
| ~ spl4_25 ),
inference(forward_subsumption_resolution,[],[f1616,f208]) ).
fof(f1624,plain,
( ~ spl4_3
| ~ spl4_25 ),
inference(avatar_contradiction_clause,[],[f1623]) ).
fof(f1641,definition,
( spl4_54
<=> aNaturalNumber0(sdtsldt0(xn,xr)) ),
introduced(definition,[new_symbols(definition,[spl4_54])],[avatar_definition]) ).
fof(f1642,plain,
( aNaturalNumber0(sdtsldt0(xn,xr))
| ~ spl4_54 ),
inference(avatar_component_clause,[],[f1641]) ).
fof(f1643,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| spl4_54 ),
inference(avatar_component_clause,[],[f1641]) ).
fof(f1645,definition,
( spl4_55
<=> sz00 = sdtsldt0(xn,xr) ),
introduced(definition,[new_symbols(definition,[spl4_55])],[avatar_definition]) ).
fof(f1646,plain,
( sz00 != sdtsldt0(xn,xr)
| spl4_55 ),
inference(avatar_component_clause,[],[f1645]) ).
fof(f1647,plain,
( sz00 = sdtsldt0(xn,xr)
| ~ spl4_55 ),
inference(avatar_component_clause,[],[f1645]) ).
fof(f1801,plain,
( sz00 = xr
| ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| spl4_54 ),
inference(resolution,[],[f1643,f244]) ).
fof(f1802,plain,
( ~ doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| spl4_16
| spl4_54 ),
inference(forward_subsumption_resolution,[],[f1801,f389]) ).
fof(f1803,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| spl4_16
| spl4_54 ),
inference(forward_subsumption_resolution,[],[f1802,f233]) ).
fof(f1804,plain,
( ~ aNaturalNumber0(xn)
| spl4_16
| spl4_54 ),
inference(forward_subsumption_resolution,[],[f1803,f227]) ).
fof(f1805,plain,
( $false
| spl4_16
| spl4_54 ),
inference(forward_subsumption_resolution,[],[f1804,f210]) ).
fof(f1806,plain,
( spl4_16
| spl4_54 ),
inference(avatar_contradiction_clause,[],[f1805]) ).
fof(f1838,plain,
( xn = sdtasdt0(xr,sz00)
| ~ spl4_17
| ~ spl4_55 ),
inference(superposition,[],[f395,f1647]) ).
fof(f1840,plain,
( sz00 = xn
| ~ spl4_17
| ~ spl4_55 ),
inference(forward_demodulation,[],[f1838,f1260]) ).
fof(f1841,plain,
( $false
| ~ spl4_17
| spl4_25
| ~ spl4_55 ),
inference(forward_subsumption_resolution,[],[f1840,f504]) ).
fof(f1842,plain,
( ~ spl4_17
| spl4_25
| ~ spl4_55 ),
inference(avatar_contradiction_clause,[],[f1841]) ).
fof(f1860,plain,
( doDivides0(xn,xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f242,f1121]) ).
fof(f1861,plain,
( ~ doDivides0(xn,xn)
| ~ aNaturalNumber0(sz10)
| sz00 = xn
| sz10 = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f243,f1121]) ).
fof(f1870,plain,
( ~ doDivides0(xn,xn)
| ~ aNaturalNumber0(sz10)
| sz00 = xn
| sz10 = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn) ),
inference(duplicate_literal_removal,[],[f1861]) ).
fof(f1871,plain,
( doDivides0(xn,xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(duplicate_literal_removal,[],[f1860]) ).
fof(f1880,plain,
( ~ doDivides0(xn,xn)
| sz00 = xn
| sz10 = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f1870,f251]) ).
fof(f1881,plain,
( doDivides0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f1871,f251]) ).
fof(f1893,plain,
( ~ doDivides0(xn,xn)
| sz10 = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl4_1
| spl4_25 ),
inference(forward_subsumption_resolution,[],[f1880,f504]) ).
fof(f1894,plain,
( doDivides0(xn,xn)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f1881,f210]) ).
fof(f1906,plain,
( ~ doDivides0(xn,xn)
| sz10 = sdtsldt0(xn,xn)
| ~ spl4_1
| spl4_25 ),
inference(forward_subsumption_resolution,[],[f1893,f210]) ).
fof(f1910,plain,
( sz10 = sdtsldt0(xn,xn)
| ~ spl4_1
| spl4_25 ),
inference(forward_subsumption_resolution,[],[f1906,f1894]) ).
fof(f2081,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xn) = sdtasdt0(xn,X0) ),
inference(resolution,[],[f149,f210]) ).
fof(f2082,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xm) = sdtasdt0(xm,X0) ),
inference(resolution,[],[f149,f209]) ).
fof(f2085,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xr,X0) = sdtasdt0(X0,xr) ),
inference(resolution,[],[f149,f227]) ).
fof(f2278,definition,
( spl4_74
<=> aNaturalNumber0(sdtsldt0(xk,xr)) ),
introduced(definition,[new_symbols(definition,[spl4_74])],[avatar_definition]) ).
fof(f2279,plain,
( aNaturalNumber0(sdtsldt0(xk,xr))
| ~ spl4_74 ),
inference(avatar_component_clause,[],[f2278]) ).
fof(f2280,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| spl4_74 ),
inference(avatar_component_clause,[],[f2278]) ).
fof(f2331,plain,
( sz00 = xr
| ~ doDivides0(xr,xk)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| spl4_74 ),
inference(resolution,[],[f2280,f244]) ).
fof(f2332,plain,
( ~ doDivides0(xr,xk)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| spl4_16
| spl4_74 ),
inference(forward_subsumption_resolution,[],[f2331,f389]) ).
fof(f2333,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk)
| spl4_16
| spl4_74 ),
inference(forward_subsumption_resolution,[],[f2332,f226]) ).
fof(f2334,plain,
( ~ aNaturalNumber0(xk)
| spl4_16
| spl4_74 ),
inference(forward_subsumption_resolution,[],[f2333,f227]) ).
fof(f2335,plain,
( $false
| ~ spl4_5
| spl4_16
| spl4_74 ),
inference(forward_subsumption_resolution,[],[f2334,f282]) ).
fof(f2336,plain,
( ~ spl4_5
| spl4_16
| spl4_74 ),
inference(avatar_contradiction_clause,[],[f2335]) ).
fof(f2375,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[],[f2081,f209]) ).
fof(f2380,plain,
( sdtasdt0(xp,xk) = sdtasdt0(xm,xn)
| ~ spl4_19 ),
inference(forward_demodulation,[],[f2375,f404]) ).
fof(f2400,plain,
( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xm)
| ~ spl4_54 ),
inference(resolution,[],[f2082,f1642]) ).
fof(f4242,plain,
( ~ doDivides0(xp,sdtasdt0(xm,sdtsldt0(xn,xr)))
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| doDivides0(xp,sdtsldt0(xn,xr))
| xn = sdtsldt0(xn,xr)
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ~ spl4_27
| ~ spl4_54 ),
inference(superposition,[],[f538,f2400]) ).
fof(f4282,plain,
( ~ doDivides0(xp,sdtasdt0(xm,sdtsldt0(xn,xr)))
| doDivides0(xp,sdtsldt0(xn,xr))
| xn = sdtsldt0(xn,xr)
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ~ spl4_27
| ~ spl4_54 ),
inference(forward_subsumption_resolution,[],[f4242,f1642]) ).
fof(f4303,definition,
( spl4_219
<=> sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
introduced(definition,[new_symbols(definition,[spl4_219])],[avatar_definition]) ).
fof(f4304,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ~ spl4_219 ),
inference(avatar_component_clause,[],[f4303]) ).
fof(f4307,definition,
( spl4_220
<=> xn = sdtsldt0(xn,xr) ),
introduced(definition,[new_symbols(definition,[spl4_220])],[avatar_definition]) ).
fof(f4309,plain,
( xn = sdtsldt0(xn,xr)
| ~ spl4_220 ),
inference(avatar_component_clause,[],[f4307]) ).
fof(f4311,definition,
( spl4_221
<=> doDivides0(xp,sdtsldt0(xn,xr)) ),
introduced(definition,[new_symbols(definition,[spl4_221])],[avatar_definition]) ).
fof(f4313,plain,
( doDivides0(xp,sdtsldt0(xn,xr))
| ~ spl4_221 ),
inference(avatar_component_clause,[],[f4311]) ).
fof(f4315,definition,
( spl4_222
<=> doDivides0(xp,sdtasdt0(xm,sdtsldt0(xn,xr))) ),
introduced(definition,[new_symbols(definition,[spl4_222])],[avatar_definition]) ).
fof(f4317,plain,
( ~ doDivides0(xp,sdtasdt0(xm,sdtsldt0(xn,xr)))
| spl4_222 ),
inference(avatar_component_clause,[],[f4315]) ).
fof(f4318,plain,
( ~ spl4_219
| spl4_220
| spl4_221
| ~ spl4_222
| ~ spl4_27
| ~ spl4_54 ),
inference(avatar_split_clause,[],[f4282,f1641,f520,f4315,f4311,f4307,f4303]) ).
fof(f4364,plain,
( sdtasdt0(xr,sdtsldt0(xn,xr)) = sdtasdt0(sdtsldt0(xn,xr),xr)
| ~ spl4_54 ),
inference(resolution,[],[f2085,f1642]) ).
fof(f4375,plain,
( xn = sdtasdt0(sdtsldt0(xn,xr),xr)
| ~ spl4_17
| ~ spl4_54 ),
inference(forward_demodulation,[],[f4364,f395]) ).
fof(f4394,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
| sz00 = xr
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ spl4_17
| ~ spl4_54 ),
inference(superposition,[],[f185,f4375]) ).
fof(f4395,plain,
( doDivides0(sdtsldt0(xn,xr),xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| ~ spl4_17
| ~ spl4_54 ),
inference(superposition,[],[f242,f4375]) ).
fof(f4414,plain,
( doDivides0(sdtsldt0(xn,xr),xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ aNaturalNumber0(xn)
| ~ spl4_17
| ~ spl4_54 ),
inference(forward_subsumption_resolution,[],[f4395,f227]) ).
fof(f4415,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| spl4_16
| ~ spl4_17
| ~ spl4_54 ),
inference(forward_subsumption_resolution,[],[f4394,f389]) ).
fof(f4433,plain,
( doDivides0(sdtsldt0(xn,xr),xn)
| ~ aNaturalNumber0(xn)
| ~ spl4_17
| ~ spl4_54 ),
inference(forward_subsumption_resolution,[],[f4414,f1642]) ).
fof(f4434,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| spl4_16
| ~ spl4_17
| ~ spl4_54 ),
inference(forward_subsumption_resolution,[],[f4415,f227]) ).
fof(f4452,plain,
( doDivides0(sdtsldt0(xn,xr),xn)
| ~ spl4_17
| ~ spl4_54 ),
inference(forward_subsumption_resolution,[],[f4433,f210]) ).
fof(f4453,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
| spl4_16
| ~ spl4_17
| ~ spl4_54 ),
inference(forward_subsumption_resolution,[],[f4434,f1642]) ).
fof(f4463,plain,
( spl4_219
| spl4_16
| ~ spl4_17
| ~ spl4_54 ),
inference(avatar_split_clause,[],[f4453,f1641,f393,f388,f4303]) ).
fof(f4465,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ spl4_219 ),
inference(resolution,[],[f4304,f1234]) ).
fof(f4474,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xp)
| ~ spl4_54
| ~ spl4_219 ),
inference(forward_subsumption_resolution,[],[f4465,f1642]) ).
fof(f4498,plain,
( xn = sdtasdt0(xn,xr)
| ~ spl4_17
| ~ spl4_54
| ~ spl4_220 ),
inference(superposition,[],[f4375,f4309]) ).
fof(f4530,plain,
( ~ doDivides0(xn,xn)
| ~ aNaturalNumber0(xr)
| sz00 = xn
| xr = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn)
| ~ spl4_17
| ~ spl4_54
| ~ spl4_220 ),
inference(superposition,[],[f243,f4498]) ).
fof(f4539,plain,
( ~ doDivides0(xn,xn)
| ~ aNaturalNumber0(xr)
| sz00 = xn
| xr = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl4_17
| ~ spl4_54
| ~ spl4_220 ),
inference(duplicate_literal_removal,[],[f4530]) ).
fof(f4549,plain,
( ~ aNaturalNumber0(xr)
| sz00 = xn
| xr = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl4_1
| ~ spl4_17
| ~ spl4_54
| ~ spl4_220 ),
inference(forward_subsumption_resolution,[],[f4539,f1894]) ).
fof(f4565,plain,
( sz00 = xn
| xr = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl4_1
| ~ spl4_17
| ~ spl4_54
| ~ spl4_220 ),
inference(forward_subsumption_resolution,[],[f4549,f227]) ).
fof(f4581,plain,
( xr = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl4_1
| ~ spl4_17
| spl4_25
| ~ spl4_54
| ~ spl4_220 ),
inference(forward_subsumption_resolution,[],[f4565,f504]) ).
fof(f4589,plain,
( xr = sdtsldt0(xn,xn)
| ~ spl4_1
| ~ spl4_17
| spl4_25
| ~ spl4_54
| ~ spl4_220 ),
inference(forward_subsumption_resolution,[],[f4581,f210]) ).
fof(f4590,plain,
( sz10 = xr
| ~ spl4_1
| ~ spl4_17
| spl4_25
| ~ spl4_54
| ~ spl4_220 ),
inference(forward_demodulation,[],[f4589,f1910]) ).
fof(f4591,plain,
( spl4_11
| ~ spl4_1
| ~ spl4_17
| spl4_25
| ~ spl4_54
| ~ spl4_220 ),
inference(avatar_split_clause,[],[f4590,f4307,f1641,f503,f393,f250,f322]) ).
fof(f4592,plain,
( isPrime0(sz10)
| ~ spl4_11 ),
inference(superposition,[],[f225,f324]) ).
fof(f4645,plain,
( $false
| spl4_2
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f4592,f256]) ).
fof(f4646,plain,
( spl4_2
| ~ spl4_11 ),
inference(avatar_contradiction_clause,[],[f4645]) ).
fof(f4699,plain,
( ~ sdtlseqdt0(xp,sdtsldt0(xn,xr))
| xp = sdtsldt0(xn,xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ spl4_54
| ~ spl4_219 ),
inference(resolution,[],[f4474,f171]) ).
fof(f4702,plain,
( ~ sdtlseqdt0(xp,sdtsldt0(xn,xr))
| xp = sdtsldt0(xn,xr)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ spl4_54
| ~ spl4_219 ),
inference(forward_subsumption_resolution,[],[f4699,f208]) ).
fof(f4706,plain,
( ~ sdtlseqdt0(xp,sdtsldt0(xn,xr))
| xp = sdtsldt0(xn,xr)
| ~ spl4_54
| ~ spl4_219 ),
inference(forward_subsumption_resolution,[],[f4702,f1642]) ).
fof(f4714,definition,
( spl4_232
<=> xp = sdtsldt0(xn,xr) ),
introduced(definition,[new_symbols(definition,[spl4_232])],[avatar_definition]) ).
fof(f4716,plain,
( xp = sdtsldt0(xn,xr)
| ~ spl4_232 ),
inference(avatar_component_clause,[],[f4714]) ).
fof(f4719,definition,
( spl4_233
<=> sdtlseqdt0(xp,sdtsldt0(xn,xr)) ),
introduced(definition,[new_symbols(definition,[spl4_233])],[avatar_definition]) ).
fof(f4721,plain,
( ~ sdtlseqdt0(xp,sdtsldt0(xn,xr))
| spl4_233 ),
inference(avatar_component_clause,[],[f4719]) ).
fof(f4722,plain,
( spl4_232
| ~ spl4_233
| ~ spl4_54
| ~ spl4_219 ),
inference(avatar_split_clause,[],[f4706,f4303,f1641,f4719,f4714]) ).
fof(f8448,plain,
( aNaturalNumber0(sdtasdt0(xp,sdtsldt0(xk,xr)))
| sz00 = xr
| ~ doDivides0(xr,sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ spl4_5
| spl4_16 ),
inference(superposition,[],[f244,f685]) ).
fof(f8449,plain,
( aNaturalNumber0(sdtasdt0(xp,sdtsldt0(xk,xr)))
| ~ doDivides0(xr,sdtasdt0(xp,xk))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ spl4_5
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f8448,f389]) ).
fof(f8450,plain,
( aNaturalNumber0(sdtasdt0(xp,sdtsldt0(xk,xr)))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ spl4_5
| spl4_16
| ~ spl4_19 ),
inference(forward_subsumption_resolution,[],[f8449,f479]) ).
fof(f8451,plain,
( aNaturalNumber0(sdtasdt0(xp,sdtsldt0(xk,xr)))
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ spl4_5
| spl4_16
| ~ spl4_19 ),
inference(forward_subsumption_resolution,[],[f8450,f227]) ).
fof(f8452,plain,
( aNaturalNumber0(sdtasdt0(xp,sdtsldt0(xk,xr)))
| ~ spl4_5
| spl4_16
| ~ spl4_19
| ~ spl4_22 ),
inference(forward_subsumption_resolution,[],[f8451,f491]) ).
fof(f9865,plain,
( doDivides0(xp,xn)
| ~ spl4_17
| ~ spl4_54
| ~ spl4_232 ),
inference(superposition,[],[f4452,f4716]) ).
fof(f9875,plain,
( $false
| ~ spl4_17
| ~ spl4_54
| ~ spl4_232 ),
inference(forward_subsumption_resolution,[],[f9865,f235]) ).
fof(f9876,plain,
( ~ spl4_17
| ~ spl4_54
| ~ spl4_232 ),
inference(avatar_contradiction_clause,[],[f9875]) ).
fof(f10761,plain,
( sdtsldt0(sdtasdt0(xp,xk),xr) = sdtasdt0(xm,sdtsldt0(xn,xr))
| spl4_16
| ~ spl4_19 ),
inference(superposition,[],[f611,f2380]) ).
fof(f10763,plain,
( sdtasdt0(xm,sdtsldt0(xn,xr)) = sdtasdt0(xp,sdtsldt0(xk,xr))
| ~ spl4_5
| spl4_16
| ~ spl4_19 ),
inference(forward_demodulation,[],[f10761,f685]) ).
fof(f10764,plain,
( ~ doDivides0(xp,sdtasdt0(xp,sdtsldt0(xk,xr)))
| ~ spl4_5
| spl4_16
| ~ spl4_19
| spl4_222 ),
inference(superposition,[],[f4317,f10763]) ).
fof(f11157,plain,
( ~ aNaturalNumber0(sdtsldt0(xk,xr))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,sdtsldt0(xk,xr)))
| ~ spl4_5
| spl4_16
| ~ spl4_19
| spl4_222 ),
inference(resolution,[],[f10764,f242]) ).
fof(f11159,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,sdtsldt0(xk,xr)))
| ~ spl4_5
| spl4_16
| ~ spl4_19
| ~ spl4_74
| spl4_222 ),
inference(forward_subsumption_resolution,[],[f11157,f2279]) ).
fof(f11160,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,sdtsldt0(xk,xr)))
| ~ spl4_5
| spl4_16
| ~ spl4_19
| ~ spl4_74
| spl4_222 ),
inference(forward_subsumption_resolution,[],[f11159,f208]) ).
fof(f11161,plain,
( $false
| ~ spl4_5
| spl4_16
| ~ spl4_19
| ~ spl4_22
| ~ spl4_74
| spl4_222 ),
inference(forward_subsumption_resolution,[],[f11160,f8452]) ).
fof(f11162,plain,
( ~ spl4_5
| spl4_16
| ~ spl4_19
| ~ spl4_22
| ~ spl4_74
| spl4_222 ),
inference(avatar_contradiction_clause,[],[f11161]) ).
fof(f11183,plain,
( sdtlseqdt0(xp,sdtsldt0(xn,xr))
| sz00 = sdtsldt0(xn,xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ spl4_221 ),
inference(resolution,[],[f4313,f196]) ).
fof(f11192,plain,
( sz00 = sdtsldt0(xn,xr)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ spl4_221
| spl4_233 ),
inference(forward_subsumption_resolution,[],[f11183,f4721]) ).
fof(f11198,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| spl4_55
| ~ spl4_221
| spl4_233 ),
inference(forward_subsumption_resolution,[],[f11192,f1646]) ).
fof(f11203,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xr))
| spl4_55
| ~ spl4_221
| spl4_233 ),
inference(forward_subsumption_resolution,[],[f11198,f208]) ).
fof(f11205,plain,
( $false
| ~ spl4_54
| spl4_55
| ~ spl4_221
| spl4_233 ),
inference(forward_subsumption_resolution,[],[f11203,f1642]) ).
fof(f11206,plain,
( ~ spl4_54
| spl4_55
| ~ spl4_221
| spl4_233 ),
inference(avatar_contradiction_clause,[],[f11205]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f257]) ).
cnf(s2,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f266]) ).
cnf(s3,plain,
spl4_1,
inference(sat_conversion,[],[f267]) ).
cnf(s4,plain,
spl4_3,
inference(sat_conversion,[],[f268]) ).
cnf(s9,plain,
spl4_7,
inference(sat_conversion,[],[f365]) ).
cnf(s11,plain,
( spl4_16
| spl4_17 ),
inference(sat_conversion,[],[f396]) ).
cnf(s12,plain,
( ~ spl4_7
| spl4_18
| spl4_19 ),
inference(sat_conversion,[],[f405]) ).
cnf(s13,plain,
( spl4_4
| ~ spl4_18 ),
inference(sat_conversion,[],[f418]) ).
cnf(s14,plain,
( spl4_4
| ~ spl4_16 ),
inference(sat_conversion,[],[f426]) ).
cnf(s15,plain,
( spl4_5
| ~ spl4_7
| spl4_18 ),
inference(sat_conversion,[],[f455]) ).
cnf(s19,plain,
( ~ spl4_19
| spl4_22 ),
inference(sat_conversion,[],[f507]) ).
cnf(s20,plain,
( ~ spl4_26
| spl4_27 ),
inference(sat_conversion,[],[f522]) ).
cnf(s21,plain,
spl4_26,
inference(sat_conversion,[],[f526]) ).
cnf(s48,plain,
( ~ spl4_3
| ~ spl4_25 ),
inference(sat_conversion,[],[f1624]) ).
cnf(s69,plain,
( spl4_16
| spl4_54 ),
inference(sat_conversion,[],[f1806]) ).
cnf(s72,plain,
( ~ spl4_17
| spl4_25
| ~ spl4_55 ),
inference(sat_conversion,[],[f1842]) ).
cnf(s87,plain,
( ~ spl4_5
| spl4_16
| spl4_74 ),
inference(sat_conversion,[],[f2336]) ).
cnf(s219,plain,
( ~ spl4_27
| ~ spl4_54
| ~ spl4_219
| spl4_220
| spl4_221
| ~ spl4_222 ),
inference(sat_conversion,[],[f4318]) ).
cnf(s223,plain,
( spl4_16
| ~ spl4_17
| ~ spl4_54
| spl4_219 ),
inference(sat_conversion,[],[f4463]) ).
cnf(s229,plain,
( ~ spl4_1
| spl4_11
| ~ spl4_17
| spl4_25
| ~ spl4_54
| ~ spl4_220 ),
inference(sat_conversion,[],[f4591]) ).
cnf(s231,plain,
( spl4_2
| ~ spl4_11 ),
inference(sat_conversion,[],[f4646]) ).
cnf(s235,plain,
( ~ spl4_54
| ~ spl4_219
| spl4_232
| ~ spl4_233 ),
inference(sat_conversion,[],[f4722]) ).
cnf(s360,plain,
( ~ spl4_17
| ~ spl4_54
| ~ spl4_232 ),
inference(sat_conversion,[],[f9876]) ).
cnf(s385,plain,
( ~ spl4_5
| spl4_16
| ~ spl4_19
| ~ spl4_22
| ~ spl4_74
| spl4_222 ),
inference(sat_conversion,[],[f11162]) ).
cnf(s388,plain,
( ~ spl4_54
| spl4_55
| ~ spl4_221
| spl4_233 ),
inference(sat_conversion,[],[f11206]) ).
cnf(s459,plain,
spl4_27,
inference(rat,[],[s20,s21]) ).
cnf(s472,plain,
~ spl4_25,
inference(rat,[],[s48,s4]) ).
cnf(s478,plain,
~ spl4_4,
inference(rat,[],[s2,s4]) ).
cnf(s479,plain,
~ spl4_16,
inference(rat,[],[s14,s478]) ).
cnf(s480,plain,
~ spl4_18,
inference(rat,[],[s13,s478]) ).
cnf(s483,plain,
spl4_54,
inference(rat,[],[s69,s479]) ).
cnf(s484,plain,
spl4_17,
inference(rat,[],[s11,s479]) ).
cnf(s487,plain,
spl4_19,
inference(rat,[],[s12,s9,s480]) ).
cnf(s488,plain,
spl4_5,
inference(rat,[],[s15,s9,s480]) ).
cnf(s494,plain,
~ spl4_232,
inference(rat,[],[s360,s483,s484]) ).
cnf(s495,plain,
spl4_219,
inference(rat,[],[s223,s483,s479,s484]) ).
cnf(s496,plain,
~ spl4_55,
inference(rat,[],[s72,s472,s484]) ).
cnf(s505,plain,
spl4_22,
inference(rat,[],[s19,s487]) ).
cnf(s515,plain,
spl4_74,
inference(rat,[],[s87,s479,s488]) ).
cnf(s532,plain,
~ spl4_233,
inference(rat,[],[s235,s494,s483,s495]) ).
cnf(s534,plain,
~ spl4_221,
inference(rat,[],[s388,s532,s483,s496]) ).
cnf(s610,plain,
spl4_222,
inference(rat,[],[s385,s488,s487,s505,s479,s515]) ).
cnf(s614,plain,
spl4_220,
inference(rat,[],[s219,s610,s495,s483,s459,s534]) ).
cnf(s641,plain,
spl4_11,
inference(rat,[],[s229,s484,s483,s472,s3,s614]) ).
cnf(s644,plain,
spl4_2,
inference(rat,[],[s231,s641]) ).
cnf(s645,plain,
$false,
inference(rat,[],[s1,s644,s3]) ).
fof(f11207,plain,
$false,
inference(avatar_sat_refutation,[],[s645]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM509+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 20:21:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.81/2.90 % (3923501)Detected formulas, will run a generic FOF schedule.
% 12.81/2.90 % (3923508)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=1484809453:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.81/2.90 % (3923506)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=869659001:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.81/2.90 % (3923507)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=4105156334:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.81/2.90 % (3923509)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=246856903:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.81/2.90 % (3923512)dis-21_1_sil=8000:lcm=predicate:random_seed=3594246668: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)
% 12.81/2.90 % (3923510)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2092067978:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.81/2.90 % (3923511)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1585244306:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.81/2.90 % (3923509)Instruction limit reached!
% 12.81/2.90 % (3923509)------------------------------
% 12.81/2.90 % (3923509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923509)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923509)Termination reason: Instruction limit
% 12.81/2.90 % (3923509)Termination phase: Saturation
% 12.81/2.90 % (3923509)Time elapsed: 0.063 s
% 12.81/2.90 % (3923509)Peak memory usage: 89 MB
% 12.81/2.90 % (3923509)Instructions burned: 110 (million)
% 12.81/2.90 % (3923510)Instruction limit reached!
% 12.81/2.90 % (3923510)------------------------------
% 12.81/2.90 % (3923510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923510)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923510)Termination reason: Instruction limit
% 12.81/2.90 % (3923510)Termination phase: Saturation
% 12.81/2.90 % (3923510)Time elapsed: 0.072 s
% 12.81/2.90 % (3923510)Peak memory usage: 88 MB
% 12.81/2.90 % (3923510)Instructions burned: 120 (million)
% 12.81/2.90 % (3923512)Instruction limit reached!
% 12.81/2.90 % (3923512)------------------------------
% 12.81/2.90 % (3923512)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923512)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923512)Termination reason: Instruction limit
% 12.81/2.90 % (3923512)Termination phase: Saturation
% 12.81/2.90 % (3923512)Time elapsed: 0.078 s
% 12.81/2.90 % (3923512)Peak memory usage: 90 MB
% 12.81/2.90 % (3923512)Instructions burned: 130 (million)
% 12.81/2.90 % (3923511)Instruction limit reached!
% 12.81/2.90 % (3923511)------------------------------
% 12.81/2.90 % (3923511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923511)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923511)Termination reason: Instruction limit
% 12.81/2.90 % (3923511)Termination phase: Saturation
% 12.81/2.90 % (3923511)Time elapsed: 0.093 s
% 12.81/2.90 % (3923511)Peak memory usage: 90 MB
% 12.81/2.90 % (3923511)Instructions burned: 140 (million)
% 12.81/2.90 % (3923520)lrs+10_1_sil=8000:sp=occurrence:random_seed=420297471:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 12.81/2.90 % (3923521)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3935292741:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.81/2.90 % (3923521)Refutation not found, incomplete strategy
% 12.81/2.90 % (3923521)------------------------------
% 12.81/2.90 % (3923521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923521)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923521)Termination reason: Refutation not found, incomplete strategy
% 12.81/2.90 % (3923521)Time elapsed: 0.003 s
% 12.81/2.90 % (3923521)Peak memory usage: 89 MB
% 12.81/2.90 % (3923521)Instructions burned: 2 (million)
% 12.81/2.90 % (3923522)lrs+1011_1_sil=32000:sp=occurrence:random_seed=653020013:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 12.81/2.90 % (3923523)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=2421413563:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 12.81/2.90 % (3923523)Instruction limit reached!
% 12.81/2.90 % (3923523)------------------------------
% 12.81/2.90 % (3923523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923523)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923523)Termination reason: Instruction limit
% 12.81/2.90 % (3923523)Termination phase: Saturation
% 12.81/2.90 % (3923523)Time elapsed: 0.116 s
% 12.81/2.90 % (3923523)Peak memory usage: 93 MB
% 12.81/2.90 % (3923523)Instructions burned: 250 (million)
% 12.81/2.90 % (3923520)Instruction limit reached!
% 12.81/2.90 % (3923520)------------------------------
% 12.81/2.90 % (3923520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923520)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923520)Termination reason: Instruction limit
% 12.81/2.90 % (3923520)Termination phase: Saturation
% 12.81/2.90 % (3923520)Time elapsed: 0.168 s
% 12.81/2.90 % (3923520)Peak memory usage: 92 MB
% 12.81/2.90 % (3923520)Instructions burned: 285 (million)
% 12.81/2.90 % (3923522)Instruction limit reached!
% 12.81/2.90 % (3923522)------------------------------
% 12.81/2.90 % (3923522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923522)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923522)Termination reason: Instruction limit
% 12.81/2.90 % (3923522)Termination phase: Saturation
% 12.81/2.90 % (3923522)Time elapsed: 0.197 s
% 12.81/2.90 % (3923522)Peak memory usage: 91 MB
% 12.81/2.90 % (3923522)Instructions burned: 326 (million)
% 12.81/2.90 % (3923521)------------------------------
% 12.81/2.90 % (3923521)------------------------------
% 12.81/2.90 % (3923528)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2128269764:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 12.81/2.90 % (3923529)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4167693556:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 12.81/2.90 % (3923530)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3339233213:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 12.81/2.90 % (3923531)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1888836531:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 12.81/2.90 % (3923530)Instruction limit reached!
% 12.81/2.90 % (3923530)------------------------------
% 12.81/2.90 % (3923530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923530)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923530)Termination reason: Instruction limit
% 12.81/2.90 % (3923530)Termination phase: Saturation
% 12.81/2.90 % (3923530)Time elapsed: 0.070 s
% 12.81/2.90 % (3923530)Peak memory usage: 91 MB
% 12.81/2.90 % (3923530)Instructions burned: 115 (million)
% 12.81/2.90 % (3923531)Instruction limit reached!
% 12.81/2.90 % (3923531)------------------------------
% 12.81/2.90 % (3923531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923531)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923531)Termination reason: Instruction limit
% 12.81/2.90 % (3923531)Termination phase: Saturation
% 12.81/2.90 % (3923531)Time elapsed: 0.063 s
% 12.81/2.90 % (3923531)Peak memory usage: 89 MB
% 12.81/2.90 % (3923531)Instructions burned: 129 (million)
% 12.81/2.90 % (3923528)Instruction limit reached!
% 12.81/2.90 % (3923528)------------------------------
% 12.81/2.90 % (3923528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923528)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923528)Termination reason: Instruction limit
% 12.81/2.90 % (3923528)Termination phase: Saturation
% 12.81/2.90 % (3923528)Time elapsed: 0.163 s
% 12.81/2.90 % (3923528)Peak memory usage: 89 MB
% 12.81/2.90 % (3923528)Instructions burned: 294 (million)
% 12.81/2.90 % (3923536)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2520106151:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 12.81/2.90 % (3923537)lrs+10_1_sil=8000:sp=occurrence:random_seed=188402268:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 12.81/2.90 % (3923538)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2099201275:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 12.81/2.90 % (3923536)Instruction limit reached!
% 12.81/2.90 % (3923536)------------------------------
% 12.81/2.90 % (3923536)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923536)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923536)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923536)Termination reason: Instruction limit
% 12.81/2.90 % (3923536)Termination phase: Saturation
% 12.81/2.90 % (3923536)Time elapsed: 0.064 s
% 12.81/2.90 % (3923536)Peak memory usage: 89 MB
% 12.81/2.90 % (3923536)Instructions burned: 115 (million)
% 12.81/2.90 % (3923542)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1549253125:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 12.81/2.90 % (3923538)Instruction limit reached!
% 12.81/2.90 % (3923538)------------------------------
% 12.81/2.90 % (3923538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923538)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923538)Termination reason: Instruction limit
% 12.81/2.90 % (3923538)Termination phase: Saturation
% 12.81/2.90 % (3923538)Time elapsed: 0.258 s
% 12.81/2.90 % (3923538)Peak memory usage: 92 MB
% 12.81/2.90 % (3923538)Instructions burned: 438 (million)
% 12.81/2.90 % (3923544)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1057859670:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 12.81/2.90 % (3923537)Instruction limit reached!
% 12.81/2.90 % (3923537)------------------------------
% 12.81/2.90 % (3923537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923537)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923537)Termination reason: Instruction limit
% 12.81/2.90 % (3923537)Termination phase: Saturation
% 12.81/2.90 % (3923537)Time elapsed: 0.504 s
% 12.81/2.90 % (3923537)Peak memory usage: 97 MB
% 12.81/2.90 % (3923537)Instructions burned: 908 (million)
% 12.81/2.90 % (3923544)Instruction limit reached!
% 12.81/2.90 % (3923544)------------------------------
% 12.81/2.90 % (3923544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923544)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923544)Termination reason: Instruction limit
% 12.81/2.90 % (3923544)Termination phase: Saturation
% 12.81/2.90 % (3923544)Time elapsed: 0.063 s
% 12.81/2.90 % (3923544)Peak memory usage: 91 MB
% 12.81/2.90 % (3923544)Instructions burned: 135 (million)
% 12.81/2.90 % (3923546)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3439477375:st=8:i=592:sd=3:ep=RST:ss=axioms_2984 on theBenchmark for (2984ds/592Mi)
% 12.81/2.90 % (3923547)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2180587486:st=3:i=13193:sd=3:ss=axioms_2984 on theBenchmark for (2984ds/13193Mi)
% 12.81/2.90 % (3923506)First to succeed.
% 12.81/2.90 % (3923506)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3923501"
% 12.81/2.90 % (3923546)Instruction limit reached!
% 12.81/2.90 % (3923546)------------------------------
% 12.81/2.90 % (3923546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/2.90 % (3923546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/2.90 % (3923546)CaDiCaL version: 2.1.3
% 12.81/2.90 % (3923546)Termination reason: Instruction limit
% 12.81/2.90 % (3923546)Termination phase: Saturation
% 12.81/2.90 % (3923546)Time elapsed: 0.287 s
% 12.81/2.90 % (3923546)Peak memory usage: 91 MB
% 12.81/2.90 % (3923546)Instructions burned: 593 (million)
% 12.81/2.90 % (3923506)Refutation found. Thanks to Tanya!
% 12.81/2.90 % SZS status Theorem for theBenchmark
% 12.81/2.90 % SZS output start Proof for theBenchmark
% See solution above
% 12.81/3.00 % (3923506)------------------------------
% 12.81/3.00 % (3923506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.81/3.00 % (3923506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.81/3.00 % (3923506)CaDiCaL version: 2.1.3
% 12.81/3.00 % (3923506)Termination reason: Refutation
% 12.81/3.00 % (3923506)Time elapsed: 1.614 s
% 12.81/3.00 % (3923506)Peak memory usage: 143 MB
% 12.81/3.00 % (3923506)Instructions burned: 2576 (million)
% 12.81/3.00 % (3923506)------------------------------
% 12.81/3.00 % (3923506)------------------------------
% 12.81/3.00 % (3923501)Success in time 2.04 s
% 12.81/3.00 % Vampire exiting
%------------------------------------------------------------------------------