%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM486+3 : 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 : n015.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 12:15:24 PM UTC 2026
% Result : Theorem 13.80s 3.06s
% Output : Refutation 16.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 40
% Syntax : Number of formulae : 293 ( 54 unt; 19 def)
% Number of atoms : 1234 ( 256 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 1569 ( 628 ~; 653 |; 229 &)
% ( 25 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 17 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 330 ( 0 sgn 275 !; 55 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
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(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/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != X1
& sdtlseqdt0(X0,X1) )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f33,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X0,X1)
& doDivides0(X0,X2) )
=> doDivides0(X0,sdtpldt0(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivSum) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( doDivides0(X0,X1)
& doDivides0(X0,sdtpldt0(X1,X2)) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivMin) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( ( ( X2 != sz00
& X2 != sz10
& ! [X3] :
( ( aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) )
=> ( X3 = sz10
| X3 = X2 ) ) )
| isPrime0(X2) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X0,X1) = sdtasdt0(X2,X3) )
| doDivides0(X2,sdtasdt0(X0,X1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [X3] :
( aNaturalNumber0(X3)
& X0 = sdtasdt0(X2,X3) )
& doDivides0(X2,X0) )
| ( ? [X3] :
( aNaturalNumber0(X3)
& X1 = sdtasdt0(X2,X3) )
& doDivides0(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
fof(f41,axiom,
( xp != sz00
& xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f42,conjecture,
( ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xn )
& sdtlseqdt0(xp,xn) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn)
| ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xp,X0) )
| doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
~ ( ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xn )
& sdtlseqdt0(xp,xn) )
=> ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
| doDivides0(xp,xn)
| ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xp,X0) )
| doDivides0(xp,xm) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( ( ( X2 != sz00
& X2 != sz10
& ! [X3] :
( ( aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) )
=> ( X3 = sz10
| X3 = X2 ) ) )
| isPrime0(X2) )
& ( ? [X5] :
( aNaturalNumber0(X5)
& sdtasdt0(X0,X1) = sdtasdt0(X2,X5) )
| doDivides0(X2,sdtasdt0(X0,X1)) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( ? [X6] :
( aNaturalNumber0(X6)
& sdtasdt0(X2,X6) = X0 )
& doDivides0(X2,X0) )
| ( ? [X7] :
( aNaturalNumber0(X7)
& sdtasdt0(X2,X7) = X1 )
& doDivides0(X2,X1) ) ) ) ) ),
inference(rectify,[],[f40]) ).
fof(f47,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(rectify,[],[f41]) ).
fof(f48,plain,
~ ( ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xn )
& sdtlseqdt0(xp,xn) )
=> ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
| doDivides0(xp,xn)
| ? [X2] :
( aNaturalNumber0(X2)
& xm = sdtasdt0(xp,X2) )
| doDivides0(xp,xm) ) ),
inference(rectify,[],[f43]) ).
fof(f49,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f50,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f54,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f53]) ).
fof(f57,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f58,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f59,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f58]) ).
fof(f62,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f13]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f64]) ).
fof(f74,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f75,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f77,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f76]) ).
fof(f83,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f84,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f83]) ).
fof(f85,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(f86,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,[],[f85]) ).
fof(f93,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f94,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f96,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f95]) ).
fof(f101,plain,
! [X0,X1,X2] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ doDivides0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f102,plain,
! [X0,X1,X2] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ doDivides0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f104,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f103]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ( ? [X6] :
( aNaturalNumber0(X6)
& sdtasdt0(X2,X6) = X0 )
& doDivides0(X2,X0) )
| ( ? [X7] :
( aNaturalNumber0(X7)
& sdtasdt0(X2,X7) = X1 )
& doDivides0(X2,X1) )
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ( sz00 = X2
| sz10 = X2
| ? [X3] :
( sz10 != X3
& X2 != X3
& aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) ) )
& ~ isPrime0(X2) )
| ( ! [X5] :
( ~ aNaturalNumber0(X5)
| sdtasdt0(X0,X1) != sdtasdt0(X2,X5) )
& ~ doDivides0(X2,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f46]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ( ? [X6] :
( aNaturalNumber0(X6)
& sdtasdt0(X2,X6) = X0 )
& doDivides0(X2,X0) )
| ( ? [X7] :
( aNaturalNumber0(X7)
& sdtasdt0(X2,X7) = X1 )
& doDivides0(X2,X1) )
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( ( sz00 = X2
| sz10 = X2
| ? [X3] :
( sz10 != X3
& X2 != X3
& aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) ) )
& ~ isPrime0(X2) )
| ( ! [X5] :
( ~ aNaturalNumber0(X5)
| sdtasdt0(X0,X1) != sdtasdt0(X2,X5) )
& ~ doDivides0(X2,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f116,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X2) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
( ! [X1] :
( ~ aNaturalNumber0(X1)
| xn != sdtasdt0(xp,X1) )
& ~ doDivides0(xp,xn)
& ! [X2] :
( ~ aNaturalNumber0(X2)
| xm != sdtasdt0(xp,X2) )
& ~ doDivides0(xp,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xn )
& sdtlseqdt0(xp,xn) ),
inference(ennf_transformation,[],[f48]) ).
fof(f118,plain,
( ! [X1] :
( ~ aNaturalNumber0(X1)
| xn != sdtasdt0(xp,X1) )
& ~ doDivides0(xp,xn)
& ! [X2] :
( ~ aNaturalNumber0(X2)
| xm != sdtasdt0(xp,X2) )
& ~ doDivides0(xp,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xn )
& sdtlseqdt0(xp,xn) ),
inference(flattening,[],[f117]) ).
fof(f119,definition,
! [X2] :
( ( ( sz00 = X2
| sz10 = X2
| ? [X3] :
( sz10 != X3
& X2 != X3
& aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) ) )
& ~ isPrime0(X2) )
| ~ sP0(X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f120,definition,
! [X1,X2] :
( ( ? [X7] :
( aNaturalNumber0(X7)
& sdtasdt0(X2,X7) = X1 )
& doDivides0(X2,X1) )
| ~ sP1(X1,X2) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( ? [X6] :
( aNaturalNumber0(X6)
& sdtasdt0(X2,X6) = X0 )
& doDivides0(X2,X0) )
| sP1(X1,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP0(X2)
| ( ! [X5] :
( ~ aNaturalNumber0(X5)
| sdtasdt0(X0,X1) != sdtasdt0(X2,X5) )
& ~ doDivides0(X2,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(definition_folding,[],[f114,f120,f119]) ).
fof(f122,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f75]) ).
fof(f123,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X0,X3) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f122]) ).
fof(f124,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK2(X0,X1))
& sdtpldt0(X0,sK2(X0,X1)) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1))],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f77]) ).
fof(f126,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f125]) ).
fof(f127,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,[],[f96]) ).
fof(f128,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,[],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK3(X0,X1))
& sdtasdt0(X0,sK3(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1))],[f128]) ).
fof(f137,plain,
! [X1,X2] :
( ( ? [X7] :
( aNaturalNumber0(X7)
& sdtasdt0(X2,X7) = X1 )
& doDivides0(X2,X1) )
| ~ sP1(X1,X2) ),
inference(nnf_transformation,[],[f120]) ).
fof(f138,plain,
! [X0,X1] :
( ( ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
& doDivides0(X1,X0) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f137]) ).
fof(f139,plain,
! [X0,X1] :
( ( aNaturalNumber0(sK6(X0,X1))
& sdtasdt0(X1,sK6(X0,X1)) = X0
& doDivides0(X1,X0) )
| ~ sP1(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f138]) ).
fof(f140,plain,
! [X2] :
( ( ( sz00 = X2
| sz10 = X2
| ? [X3] :
( sz10 != X3
& X2 != X3
& aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) ) )
& ~ isPrime0(X2) )
| ~ sP0(X2) ),
inference(nnf_transformation,[],[f119]) ).
fof(f141,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& ? [X2] :
( aNaturalNumber0(X2)
& sdtasdt0(X1,X2) = X0 )
& doDivides0(X1,X0) ) )
& ~ isPrime0(X0) )
| ~ sP0(X0) ),
inference(rectify,[],[f140]) ).
fof(f142,plain,
! [X0] :
( ( ( sz00 = X0
| sz10 = X0
| ( sz10 != sK7(X0)
& sK7(X0) != X0
& aNaturalNumber0(sK7(X0))
& aNaturalNumber0(sK8(X0))
& sdtasdt0(sK7(X0),sK8(X0)) = X0
& doDivides0(sK7(X0),X0) ) )
& ~ isPrime0(X0) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X1,sK7(X0)),skolemize(X2,sK8(X0))],[f141]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X2,X3) = X0 )
& doDivides0(X2,X0) )
| sP1(X1,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP0(X2)
| ( ! [X4] :
( ~ aNaturalNumber0(X4)
| sdtasdt0(X0,X1) != sdtasdt0(X2,X4) )
& ~ doDivides0(X2,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(rectify,[],[f121]) ).
fof(f144,plain,
! [X0,X1,X2] :
( ( aNaturalNumber0(sK9(X0,X2))
& sdtasdt0(X2,sK9(X0,X2)) = X0
& doDivides0(X2,X0) )
| sP1(X1,X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP0(X2)
| ( ! [X4] :
( ~ aNaturalNumber0(X4)
| sdtasdt0(X0,X1) != sdtasdt0(X2,X4) )
& ~ doDivides0(X2,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X2))],[f143]) ).
fof(f145,plain,
( xp != sz00
& xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp)
& aNaturalNumber0(sK10)
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK10)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10)],[f116]) ).
fof(f146,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xp,X0) )
& ~ doDivides0(xp,xn)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xp,X1) )
& ~ doDivides0(xp,xm)
& ? [X2] :
( aNaturalNumber0(X2)
& xn = sdtpldt0(xp,X2) )
& sdtlseqdt0(xp,xn) ),
inference(rectify,[],[f118]) ).
fof(f147,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xp,X0) )
& ~ doDivides0(xp,xn)
& ! [X1] :
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xp,X1) )
& ~ doDivides0(xp,xm)
& aNaturalNumber0(sK11)
& xn = sdtpldt0(xp,sK11)
& sdtlseqdt0(xp,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11)],[f146]) ).
fof(f148,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f150,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f151,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f152,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f153,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f156,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f57]) ).
fof(f157,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f160,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f62]) ).
fof(f163,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f174,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f177,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f182,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| X0 != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f183,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,[],[f86]) ).
fof(f184,plain,
! [X2,X0,X1] :
( sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f194,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f197,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f202,plain,
! [X2,X0,X1] :
( doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| ~ doDivides0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f203,plain,
! [X2,X0,X1] :
( ~ doDivides0(X0,sdtpldt0(X1,X2))
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f216,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f217,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f218,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f219,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| doDivides0(X1,X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f222,plain,
! [X0] :
( ~ sP0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f229,plain,
! [X2,X0,X1] :
( ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1(X1,X2)
| doDivides0(X2,X0)
| sP0(X2)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f144]) ).
fof(f236,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sK10),
inference(cnf_transformation,[],[f145]) ).
fof(f237,plain,
aNaturalNumber0(sK10),
inference(cnf_transformation,[],[f145]) ).
fof(f238,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f145]) ).
fof(f242,plain,
sz00 != xp,
inference(cnf_transformation,[],[f145]) ).
fof(f244,plain,
xn = sdtpldt0(xp,sK11),
inference(cnf_transformation,[],[f147]) ).
fof(f245,plain,
aNaturalNumber0(sK11),
inference(cnf_transformation,[],[f147]) ).
fof(f246,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f147]) ).
fof(f248,plain,
~ doDivides0(xp,xn),
inference(cnf_transformation,[],[f147]) ).
fof(f250,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f174]) ).
fof(f251,plain,
! [X2,X0] :
( ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f177]) ).
fof(f254,plain,
! [X1] :
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f182]) ).
fof(f256,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f197]) ).
fof(f262,definition,
sF12 = sdtpldt0(xp,sK11),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f263,plain,
sdtpldt0(xp,sK11) = sF12,
inference(reorient_equations,[],[f262]) ).
fof(f264,plain,
xn = sF12,
inference(definition_folding,[],[f244,f263]) ).
fof(f265,plain,
! [X1] :
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(duplicate_literal_removal,[],[f254]) ).
fof(f267,definition,
( spl13_1
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f268,plain,
( aNaturalNumber0(sz10)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f276,definition,
( spl13_3
<=> aNaturalNumber0(sz00) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f277,plain,
( aNaturalNumber0(sz00)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f284,plain,
spl13_1,
inference(avatar_split_clause,[],[f150,f267]) ).
fof(f285,plain,
spl13_3,
inference(avatar_split_clause,[],[f148,f276]) ).
fof(f286,plain,
xn = sdtpldt0(xp,sK11),
inference(forward_demodulation,[],[f263,f264]) ).
fof(f288,plain,
( aNaturalNumber0(sdtasdt0(xp,sK10))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f152,f236]) ).
fof(f289,plain,
( aNaturalNumber0(sdtasdt0(xp,sK10))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f288,f218]) ).
fof(f290,plain,
aNaturalNumber0(sdtasdt0(xp,sK10)),
inference(forward_subsumption_resolution,[],[f289,f217]) ).
fof(f301,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sK11) = sdtpldt0(sK11,X0) ),
inference(resolution,[],[f153,f245]) ).
fof(f320,plain,
sdtpldt0(xp,sK11) = sdtpldt0(sK11,xp),
inference(resolution,[],[f301,f216]) ).
fof(f324,plain,
xn = sdtpldt0(sK11,xp),
inference(forward_demodulation,[],[f320,f286]) ).
fof(f431,plain,
xp = sdtasdt0(xp,sz10),
inference(resolution,[],[f160,f216]) ).
fof(f453,plain,
( doDivides0(xp,xp)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f256,f431]) ).
fof(f455,plain,
( doDivides0(xp,xp)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(duplicate_literal_removal,[],[f453]) ).
fof(f456,plain,
( doDivides0(xp,xp)
| ~ aNaturalNumber0(xp)
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f455,f268]) ).
fof(f459,plain,
( doDivides0(xp,xp)
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f456,f216]) ).
fof(f464,plain,
( ~ sdtlseqdt0(sK11,xn)
| ~ aNaturalNumber0(xp)
| xp = sdtmndt0(xn,sK11)
| ~ aNaturalNumber0(sK11)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f251,f324]) ).
fof(f467,plain,
( ~ sdtlseqdt0(sK11,xn)
| xp = sdtmndt0(xn,sK11)
| ~ aNaturalNumber0(sK11)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f464,f216]) ).
fof(f471,plain,
( ~ sdtlseqdt0(sK11,xn)
| xp = sdtmndt0(xn,sK11)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f467,f245]) ).
fof(f474,plain,
( ~ sdtlseqdt0(sK11,xn)
| xp = sdtmndt0(xn,sK11) ),
inference(forward_subsumption_resolution,[],[f471,f218]) ).
fof(f478,definition,
( spl13_7
<=> xp = sdtmndt0(xn,sK11) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
fof(f480,plain,
( xp = sdtmndt0(xn,sK11)
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f482,definition,
( spl13_8
<=> sdtlseqdt0(sK11,xn) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f483,plain,
( sdtlseqdt0(sK11,xn)
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f484,plain,
( ~ sdtlseqdt0(sK11,xn)
| spl13_8 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f485,plain,
( spl13_7
| ~ spl13_8 ),
inference(avatar_split_clause,[],[f474,f482,f478]) ).
fof(f505,plain,
( sdtlseqdt0(sK11,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sK11)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f250,f324]) ).
fof(f509,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sK11)
| ~ aNaturalNumber0(xn)
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f505,f484]) ).
fof(f513,plain,
( ~ aNaturalNumber0(sK11)
| ~ aNaturalNumber0(xn)
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f509,f216]) ).
fof(f514,plain,
( ~ aNaturalNumber0(xn)
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f513,f245]) ).
fof(f515,plain,
( $false
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f514,f218]) ).
fof(f516,plain,
spl13_8,
inference(avatar_contradiction_clause,[],[f515]) ).
fof(f525,definition,
( spl13_11
<=> xn = sK11 ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f526,plain,
( xn != sK11
| spl13_11 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f527,plain,
( xn = sK11
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f551,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sK11) = sdtasdt0(sK11,X0) ),
inference(resolution,[],[f157,f245]) ).
fof(f556,plain,
sdtasdt0(xm,sK11) = sdtasdt0(sK11,xm),
inference(resolution,[],[f551,f217]) ).
fof(f632,plain,
xn = sdtpldt0(xn,sz00),
inference(resolution,[],[f156,f218]) ).
fof(f654,plain,
( ~ sdtlseqdt0(xn,xn)
| ~ aNaturalNumber0(sz00)
| sz00 = sdtmndt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f251,f632]) ).
fof(f659,plain,
( ~ sdtlseqdt0(xn,xn)
| ~ aNaturalNumber0(sz00)
| sz00 = sdtmndt0(xn,xn)
| ~ aNaturalNumber0(xn) ),
inference(duplicate_literal_removal,[],[f654]) ).
fof(f665,plain,
( ~ aNaturalNumber0(sz00)
| sz00 = sdtmndt0(xn,xn)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f659,f265]) ).
fof(f683,plain,
( sz00 = sdtmndt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f665,f277]) ).
fof(f697,plain,
( sz00 = sdtmndt0(xn,xn)
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f683,f218]) ).
fof(f906,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X2,X1)
| iLess0(sdtpldt0(X0,X1),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X1)
| X0 = X2
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2) ),
inference(resolution,[],[f194,f183]) ).
fof(f916,plain,
! [X2,X0,X1] :
( iLess0(sdtpldt0(X0,X1),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X1)
| X0 = X2
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2) ),
inference(forward_subsumption_resolution,[],[f906,f184]) ).
fof(f923,plain,
! [X2,X0,X1] :
( iLess0(sdtpldt0(X0,X1),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X1)
| X0 = X2
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2) ),
inference(forward_subsumption_resolution,[],[f916,f151]) ).
fof(f931,plain,
! [X2,X0,X1] :
( iLess0(sdtpldt0(X0,X1),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X1)
| X0 = X2
| ~ sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2) ),
inference(forward_subsumption_resolution,[],[f923,f151]) ).
fof(f1003,definition,
( spl13_14
<=> sP0(xp) ),
introduced(definition,[new_symbols(definition,[spl13_14])],[avatar_definition]) ).
fof(f1004,plain,
( ~ sP0(xp)
| spl13_14 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f1005,plain,
( sP0(xp)
| ~ spl13_14 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f1063,plain,
( ~ isPrime0(xp)
| ~ spl13_14 ),
inference(resolution,[],[f1005,f222]) ).
fof(f1064,plain,
( $false
| ~ spl13_14 ),
inference(forward_subsumption_resolution,[],[f1063,f238]) ).
fof(f1065,plain,
~ spl13_14,
inference(avatar_contradiction_clause,[],[f1064]) ).
fof(f1163,plain,
! [X0,X1] :
( ~ aNaturalNumber0(xp)
| sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sP1(X1,xp)
| doDivides0(xp,X0)
| sP0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[],[f931,f229]) ).
fof(f1180,plain,
! [X0,X1] :
( ~ aNaturalNumber0(xp)
| sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sP1(X1,xp)
| doDivides0(xp,X0)
| sP0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(duplicate_literal_removal,[],[f1163]) ).
fof(f1195,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sP1(X1,xp)
| doDivides0(xp,X0)
| sP0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f1180,f216]) ).
fof(f1210,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sP1(X1,xp)
| doDivides0(xp,X0)
| sP0(xp)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(forward_subsumption_resolution,[],[f1195,f151]) ).
fof(f1217,plain,
( ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| sP1(X1,xp)
| doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) )
| spl13_14 ),
inference(forward_subsumption_resolution,[],[f1210,f1004]) ).
fof(f1223,definition,
( spl13_30
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl13_30])],[avatar_definition]) ).
fof(f1225,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl13_30 ),
inference(avatar_component_clause,[],[f1223]) ).
fof(f1227,definition,
( spl13_31
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(xn,xm)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| doDivides0(xp,X0)
| sP1(X1,xp)
| ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm)) ) ),
introduced(definition,[new_symbols(definition,[spl13_31])],[avatar_definition]) ).
fof(f1228,plain,
( ! [X0,X1] :
( ~ sdtlseqdt0(sdtpldt0(X0,X1),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,X1))
| doDivides0(xp,X0)
| sP1(X1,xp)
| sdtpldt0(X0,X1) = sdtpldt0(xn,xm) )
| ~ spl13_31 ),
inference(avatar_component_clause,[],[f1227]) ).
fof(f1229,plain,
( ~ spl13_30
| spl13_31
| spl13_14 ),
inference(avatar_split_clause,[],[f1217,f1003,f1227,f1223]) ).
fof(f1232,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl13_30 ),
inference(resolution,[],[f1225,f151]) ).
fof(f1233,plain,
( ~ aNaturalNumber0(xm)
| spl13_30 ),
inference(forward_subsumption_resolution,[],[f1232,f218]) ).
fof(f1234,plain,
( $false
| spl13_30 ),
inference(forward_subsumption_resolution,[],[f1233,f217]) ).
fof(f1235,plain,
spl13_30,
inference(avatar_contradiction_clause,[],[f1234]) ).
fof(f1261,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtpldt0(X1,sK11),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(sK11,X0)) ),
inference(resolution,[],[f163,f245]) ).
fof(f1723,definition,
( spl13_53
<=> sP1(xm,xp) ),
introduced(definition,[new_symbols(definition,[spl13_53])],[avatar_definition]) ).
fof(f1725,plain,
( sP1(xm,xp)
| ~ spl13_53 ),
inference(avatar_component_clause,[],[f1723]) ).
fof(f1998,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| sdtpldt0(xn,xm) = sdtpldt0(X0,xm)
| ~ aNaturalNumber0(xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn) )
| ~ spl13_31 ),
inference(resolution,[],[f1228,f183]) ).
fof(f2007,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| sdtpldt0(xn,xm) = sdtpldt0(X0,xm)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl13_31 ),
inference(duplicate_literal_removal,[],[f1998]) ).
fof(f2013,plain,
( ! [X0] :
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl13_31 ),
inference(forward_subsumption_resolution,[],[f2007,f184]) ).
fof(f2019,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| xn = X0
| ~ sdtlseqdt0(X0,xn)
| ~ aNaturalNumber0(xn) )
| ~ spl13_31 ),
inference(forward_subsumption_resolution,[],[f2013,f217]) ).
fof(f2025,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm))
| doDivides0(xp,X0)
| sP1(xm,xp)
| xn = X0
| ~ sdtlseqdt0(X0,xn) )
| ~ spl13_31 ),
inference(forward_subsumption_resolution,[],[f2019,f218]) ).
fof(f2032,definition,
( spl13_62
<=> ! [X0] :
( ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xn)
| xn = X0
| doDivides0(xp,X0)
| ~ doDivides0(xp,sdtasdt0(X0,xm)) ) ),
introduced(definition,[new_symbols(definition,[spl13_62])],[avatar_definition]) ).
fof(f2033,plain,
( ! [X0] :
( ~ doDivides0(xp,sdtasdt0(X0,xm))
| ~ sdtlseqdt0(X0,xn)
| xn = X0
| doDivides0(xp,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl13_62 ),
inference(avatar_component_clause,[],[f2032]) ).
fof(f2034,plain,
( spl13_53
| spl13_62
| ~ spl13_31 ),
inference(avatar_split_clause,[],[f2025,f1227,f2032,f1723]) ).
fof(f2076,plain,
( doDivides0(xp,xm)
| ~ spl13_53 ),
inference(resolution,[],[f1725,f219]) ).
fof(f2077,plain,
( $false
| ~ spl13_53 ),
inference(forward_subsumption_resolution,[],[f2076,f246]) ).
fof(f2078,plain,
~ spl13_53,
inference(avatar_contradiction_clause,[],[f2077]) ).
fof(f2736,plain,
! [X0] :
( doDivides0(X0,xn)
| ~ doDivides0(X0,sK11)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK11)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f202,f324]) ).
fof(f2739,plain,
! [X0] :
( doDivides0(X0,xn)
| ~ doDivides0(X0,sK11)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f2736,f245]) ).
fof(f2742,plain,
! [X0] :
( ~ doDivides0(X0,sK11)
| doDivides0(X0,xn)
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f2739,f216]) ).
fof(f3692,plain,
( xp = sdtmndt0(xn,xn)
| ~ spl13_7
| ~ spl13_11 ),
inference(superposition,[],[f480,f527]) ).
fof(f3694,plain,
( sz00 = xp
| ~ spl13_3
| ~ spl13_7
| ~ spl13_11 ),
inference(forward_demodulation,[],[f3692,f697]) ).
fof(f3697,plain,
( $false
| ~ spl13_3
| ~ spl13_7
| ~ spl13_11 ),
inference(forward_subsumption_resolution,[],[f3694,f242]) ).
fof(f3698,plain,
( ~ spl13_3
| ~ spl13_7
| ~ spl13_11 ),
inference(avatar_contradiction_clause,[],[f3697]) ).
fof(f6010,definition,
( spl13_193
<=> aNaturalNumber0(sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[spl13_193])],[avatar_definition]) ).
fof(f6011,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ spl13_193 ),
inference(avatar_component_clause,[],[f6010]) ).
fof(f6012,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| spl13_193 ),
inference(avatar_component_clause,[],[f6010]) ).
fof(f6027,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| spl13_193 ),
inference(resolution,[],[f6012,f152]) ).
fof(f6028,plain,
( ~ aNaturalNumber0(xm)
| spl13_193 ),
inference(forward_subsumption_resolution,[],[f6027,f216]) ).
fof(f6029,plain,
( $false
| spl13_193 ),
inference(forward_subsumption_resolution,[],[f6028,f217]) ).
fof(f6030,plain,
spl13_193,
inference(avatar_contradiction_clause,[],[f6029]) ).
fof(f6801,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sdtpldt0(xp,sK11),X0) = sdtpldt0(sdtasdt0(xp,X0),sdtasdt0(sK11,X0)) ),
inference(resolution,[],[f1261,f216]) ).
fof(f6809,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xn,X0) = sdtpldt0(sdtasdt0(xp,X0),sdtasdt0(sK11,X0)) ),
inference(forward_demodulation,[],[f6801,f286]) ).
fof(f6827,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(sK11,xm)),
inference(resolution,[],[f6809,f217]) ).
fof(f6838,plain,
sdtasdt0(xn,xm) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xm,sK11)),
inference(forward_demodulation,[],[f6827,f556]) ).
fof(f6843,plain,
sdtasdt0(xp,sK10) = sdtpldt0(sdtasdt0(xp,xm),sdtasdt0(xm,sK11)),
inference(forward_demodulation,[],[f6838,f236]) ).
fof(f6862,plain,
! [X0] :
( ~ doDivides0(X0,sdtasdt0(xp,sK10))
| ~ doDivides0(X0,sdtasdt0(xp,xm))
| doDivides0(X0,sdtasdt0(xm,sK11))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xm,sK11)) ),
inference(superposition,[],[f203,f6843]) ).
fof(f6895,plain,
( ! [X0] :
( ~ doDivides0(X0,sdtasdt0(xp,sK10))
| ~ doDivides0(X0,sdtasdt0(xp,xm))
| doDivides0(X0,sdtasdt0(xm,sK11))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,sK11)) )
| ~ spl13_193 ),
inference(forward_subsumption_resolution,[],[f6862,f6011]) ).
fof(f6910,definition,
( spl13_204
<=> aNaturalNumber0(sdtasdt0(xm,sK11)) ),
introduced(definition,[new_symbols(definition,[spl13_204])],[avatar_definition]) ).
fof(f6912,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,sK11))
| spl13_204 ),
inference(avatar_component_clause,[],[f6910]) ).
fof(f6930,definition,
( spl13_209
<=> doDivides0(xp,sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[spl13_209])],[avatar_definition]) ).
fof(f6931,plain,
( ~ doDivides0(xp,sdtasdt0(xp,xm))
| spl13_209 ),
inference(avatar_component_clause,[],[f6930]) ).
fof(f6980,definition,
( spl13_220
<=> ! [X0] :
( ~ doDivides0(X0,sdtasdt0(xp,sK10))
| ~ aNaturalNumber0(X0)
| doDivides0(X0,sdtasdt0(xm,sK11))
| ~ doDivides0(X0,sdtasdt0(xp,xm)) ) ),
introduced(definition,[new_symbols(definition,[spl13_220])],[avatar_definition]) ).
fof(f6981,plain,
( ! [X0] :
( ~ doDivides0(X0,sdtasdt0(xp,sK10))
| ~ aNaturalNumber0(X0)
| doDivides0(X0,sdtasdt0(xm,sK11))
| ~ doDivides0(X0,sdtasdt0(xp,xm)) )
| ~ spl13_220 ),
inference(avatar_component_clause,[],[f6980]) ).
fof(f6982,plain,
( ~ spl13_204
| spl13_220
| ~ spl13_193 ),
inference(avatar_split_clause,[],[f6895,f6010,f6980,f6910]) ).
fof(f7064,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sK11)
| spl13_204 ),
inference(resolution,[],[f6912,f152]) ).
fof(f7065,plain,
( ~ aNaturalNumber0(sK11)
| spl13_204 ),
inference(forward_subsumption_resolution,[],[f7064,f217]) ).
fof(f7066,plain,
( $false
| spl13_204 ),
inference(forward_subsumption_resolution,[],[f7065,f245]) ).
fof(f7067,plain,
spl13_204,
inference(avatar_contradiction_clause,[],[f7066]) ).
fof(f7068,plain,
( ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtasdt0(xm,sK11))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sK10)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,sK10))
| ~ spl13_220 ),
inference(resolution,[],[f6981,f256]) ).
fof(f7073,plain,
( ~ aNaturalNumber0(xp)
| doDivides0(xp,sdtasdt0(xm,sK11))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sK10)
| ~ aNaturalNumber0(sdtasdt0(xp,sK10))
| ~ spl13_220 ),
inference(duplicate_literal_removal,[],[f7068]) ).
fof(f7078,plain,
( doDivides0(xp,sdtasdt0(xm,sK11))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sK10)
| ~ aNaturalNumber0(sdtasdt0(xp,sK10))
| ~ spl13_220 ),
inference(forward_subsumption_resolution,[],[f7073,f216]) ).
fof(f7089,definition,
( spl13_242
<=> doDivides0(xp,sdtasdt0(xm,sK11)) ),
introduced(definition,[new_symbols(definition,[spl13_242])],[avatar_definition]) ).
fof(f7091,plain,
( doDivides0(xp,sdtasdt0(xm,sK11))
| ~ spl13_242 ),
inference(avatar_component_clause,[],[f7089]) ).
fof(f7103,plain,
( doDivides0(xp,sdtasdt0(xm,sK11))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,sK10))
| ~ spl13_220 ),
inference(forward_subsumption_resolution,[],[f7078,f237]) ).
fof(f7104,plain,
( doDivides0(xp,sdtasdt0(xm,sK11))
| ~ doDivides0(xp,sdtasdt0(xp,xm))
| ~ spl13_220 ),
inference(forward_subsumption_resolution,[],[f7103,f290]) ).
fof(f7105,plain,
( ~ spl13_209
| spl13_242
| ~ spl13_220 ),
inference(avatar_split_clause,[],[f7104,f6980,f7089,f6930]) ).
fof(f7106,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| spl13_209 ),
inference(resolution,[],[f6931,f256]) ).
fof(f7107,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| spl13_209 ),
inference(forward_subsumption_resolution,[],[f7106,f217]) ).
fof(f7108,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| spl13_209 ),
inference(forward_subsumption_resolution,[],[f7107,f216]) ).
fof(f7109,plain,
( $false
| ~ spl13_193
| spl13_209 ),
inference(forward_subsumption_resolution,[],[f7108,f6011]) ).
fof(f7110,plain,
( ~ spl13_193
| spl13_209 ),
inference(avatar_contradiction_clause,[],[f7109]) ).
fof(f7427,definition,
( spl13_257
<=> doDivides0(xp,sK11) ),
introduced(definition,[new_symbols(definition,[spl13_257])],[avatar_definition]) ).
fof(f7429,plain,
( doDivides0(xp,sK11)
| ~ spl13_257 ),
inference(avatar_component_clause,[],[f7427]) ).
fof(f8062,plain,
( ~ doDivides0(xp,sdtasdt0(xm,sK11))
| ~ sdtlseqdt0(sK11,xn)
| xn = sK11
| doDivides0(xp,sK11)
| ~ aNaturalNumber0(sK11)
| ~ spl13_62 ),
inference(superposition,[],[f2033,f556]) ).
fof(f8115,plain,
( ~ sdtlseqdt0(sK11,xn)
| xn = sK11
| doDivides0(xp,sK11)
| ~ aNaturalNumber0(sK11)
| ~ spl13_62
| ~ spl13_242 ),
inference(forward_subsumption_resolution,[],[f8062,f7091]) ).
fof(f8139,plain,
( xn = sK11
| doDivides0(xp,sK11)
| ~ aNaturalNumber0(sK11)
| ~ spl13_8
| ~ spl13_62
| ~ spl13_242 ),
inference(forward_subsumption_resolution,[],[f8115,f483]) ).
fof(f8163,plain,
( doDivides0(xp,sK11)
| ~ aNaturalNumber0(sK11)
| ~ spl13_8
| spl13_11
| ~ spl13_62
| ~ spl13_242 ),
inference(forward_subsumption_resolution,[],[f8139,f526]) ).
fof(f8167,plain,
( doDivides0(xp,sK11)
| ~ spl13_8
| spl13_11
| ~ spl13_62
| ~ spl13_242 ),
inference(forward_subsumption_resolution,[],[f8163,f245]) ).
fof(f8169,plain,
( spl13_257
| ~ spl13_8
| spl13_11
| ~ spl13_62
| ~ spl13_242 ),
inference(avatar_split_clause,[],[f8167,f7089,f2032,f525,f482,f7427]) ).
fof(f8171,plain,
( doDivides0(xp,xn)
| ~ doDivides0(xp,xp)
| ~ aNaturalNumber0(xp)
| ~ spl13_257 ),
inference(resolution,[],[f7429,f2742]) ).
fof(f8175,plain,
( ~ doDivides0(xp,xp)
| ~ aNaturalNumber0(xp)
| ~ spl13_257 ),
inference(forward_subsumption_resolution,[],[f8171,f248]) ).
fof(f8177,plain,
( ~ aNaturalNumber0(xp)
| ~ spl13_1
| ~ spl13_257 ),
inference(forward_subsumption_resolution,[],[f8175,f459]) ).
fof(f8178,plain,
( $false
| ~ spl13_1
| ~ spl13_257 ),
inference(forward_subsumption_resolution,[],[f8177,f216]) ).
fof(f8179,plain,
( ~ spl13_1
| ~ spl13_257 ),
inference(avatar_contradiction_clause,[],[f8178]) ).
cnf(s3,plain,
spl13_1,
inference(sat_conversion,[],[f284]) ).
cnf(s4,plain,
spl13_3,
inference(sat_conversion,[],[f285]) ).
cnf(s7,plain,
( spl13_7
| ~ spl13_8 ),
inference(sat_conversion,[],[f485]) ).
cnf(s10,plain,
spl13_8,
inference(sat_conversion,[],[f516]) ).
cnf(s22,plain,
~ spl13_14,
inference(sat_conversion,[],[f1065]) ).
cnf(s26,plain,
( spl13_14
| ~ spl13_30
| spl13_31 ),
inference(sat_conversion,[],[f1229]) ).
cnf(s27,plain,
spl13_30,
inference(sat_conversion,[],[f1235]) ).
cnf(s57,plain,
( ~ spl13_31
| spl13_53
| spl13_62 ),
inference(sat_conversion,[],[f2034]) ).
cnf(s62,plain,
~ spl13_53,
inference(sat_conversion,[],[f2078]) ).
cnf(s98,plain,
( ~ spl13_3
| ~ spl13_7
| ~ spl13_11 ),
inference(sat_conversion,[],[f3698]) ).
cnf(s196,plain,
spl13_193,
inference(sat_conversion,[],[f6030]) ).
cnf(s216,plain,
( ~ spl13_193
| ~ spl13_204
| spl13_220 ),
inference(sat_conversion,[],[f6982]) ).
cnf(s235,plain,
spl13_204,
inference(sat_conversion,[],[f7067]) ).
cnf(s239,plain,
( ~ spl13_209
| ~ spl13_220
| spl13_242 ),
inference(sat_conversion,[],[f7105]) ).
cnf(s240,plain,
( ~ spl13_193
| spl13_209 ),
inference(sat_conversion,[],[f7110]) ).
cnf(s276,plain,
( ~ spl13_8
| spl13_11
| ~ spl13_62
| ~ spl13_242
| spl13_257 ),
inference(sat_conversion,[],[f8169]) ).
cnf(s277,plain,
( ~ spl13_1
| ~ spl13_257 ),
inference(sat_conversion,[],[f8179]) ).
cnf(s296,plain,
( ~ spl13_193
| spl13_220 ),
inference(rat,[],[s216,s235]) ).
cnf(s308,plain,
spl13_209,
inference(rat,[],[s240,s196]) ).
cnf(s322,plain,
spl13_220,
inference(rat,[],[s296,s196]) ).
cnf(s333,plain,
spl13_242,
inference(rat,[],[s239,s308,s322]) ).
cnf(s374,plain,
( ~ spl13_31
| spl13_62 ),
inference(rat,[],[s57,s62]) ).
cnf(s405,plain,
( spl13_14
| spl13_31 ),
inference(rat,[],[s26,s27]) ).
cnf(s407,plain,
spl13_31,
inference(rat,[],[s405,s22]) ).
cnf(s408,plain,
spl13_62,
inference(rat,[],[s374,s407]) ).
cnf(s415,plain,
spl13_7,
inference(rat,[],[s7,s10]) ).
cnf(s422,plain,
~ spl13_11,
inference(rat,[],[s98,s415,s4]) ).
cnf(s431,plain,
spl13_257,
inference(rat,[],[s276,s10,s333,s408,s422]) ).
cnf(s439,plain,
~ spl13_1,
inference(rat,[],[s277,s431]) ).
cnf(s451,plain,
$false,
inference(rat,[],[s3,s439]) ).
fof(f8180,plain,
$false,
inference(avatar_sat_refutation,[],[s451]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM486+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:13:16 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 12.69/2.72 % (1981945)Detected formulas, will run a generic FOF schedule.
% 12.69/2.72 % (1981955)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4232835875:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.69/2.72 % (1981953)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1226288057:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.69/2.72 % (1981950)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=636556100:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.69/2.72 % (1981951)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=2254238122:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.69/2.72 % (1981952)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=1202773021:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.69/2.72 % (1981954)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2353793753:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.69/2.72 % (1981955)Instruction limit reached!
% 12.69/2.72 % (1981955)------------------------------
% 12.69/2.72 % (1981955)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.69/2.72 % (1981955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.69/2.72 % (1981955)CaDiCaL version: 2.1.3
% 12.69/2.72 % (1981955)Termination reason: Instruction limit
% 12.69/2.72 % (1981955)Termination phase: Saturation
% 12.69/2.72 % (1981955)Time elapsed: 0.050 s
% 12.69/2.72 % (1981955)Peak memory usage: 90 MB
% 12.69/2.72 % (1981955)Instructions burned: 142 (million)
% 12.69/2.72 % (1981956)dis-21_1_sil=8000:lcm=predicate:random_seed=944239545: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)
% 12.69/2.72 % (1981953)Instruction limit reached!
% 12.69/2.72 % (1981953)------------------------------
% 12.69/2.72 % (1981953)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.69/2.72 % (1981953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.69/2.72 % (1981953)CaDiCaL version: 2.1.3
% 12.69/2.72 % (1981953)Termination reason: Instruction limit
% 12.69/2.72 % (1981953)Termination phase: Saturation
% 12.69/2.72 % (1981953)Time elapsed: 0.064 s
% 12.69/2.72 % (1981953)Peak memory usage: 89 MB
% 12.69/2.72 % (1981953)Instructions burned: 109 (million)
% 12.69/2.72 % (1981954)Instruction limit reached!
% 12.69/2.72 % (1981954)------------------------------
% 12.69/2.72 % (1981954)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.69/2.72 % (1981954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.69/2.72 % (1981954)CaDiCaL version: 2.1.3
% 12.69/2.72 % (1981954)Termination reason: Instruction limit
% 12.69/2.72 % (1981954)Termination phase: Saturation
% 12.69/2.72 % (1981954)Time elapsed: 0.072 s
% 12.69/2.72 % (1981954)Peak memory usage: 89 MB
% 12.69/2.72 % (1981954)Instructions burned: 120 (million)
% 12.69/2.72 % (1981956)Instruction limit reached!
% 12.69/2.72 % (1981956)------------------------------
% 12.69/2.72 % (1981956)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.69/2.72 % (1981956)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.69/2.72 % (1981956)CaDiCaL version: 2.1.3
% 12.69/2.72 % (1981956)Termination reason: Instruction limit
% 12.69/2.72 % (1981956)Termination phase: Saturation
% 12.69/2.72 % (1981956)Time elapsed: 0.080 s
% 12.69/2.72 % (1981956)Peak memory usage: 90 MB
% 12.69/2.72 % (1981956)Instructions burned: 129 (million)
% 12.69/2.72 % (1981963)lrs+10_1_sil=8000:sp=occurrence:random_seed=668116800:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 12.69/2.72 % (1981965)lrs+10_1_sil=32000:urr=on:br=off:random_seed=94723962:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.69/2.72 % (1981966)lrs+1011_1_sil=32000:sp=occurrence:random_seed=904734898:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 12.69/2.72 % (1981963)Instruction limit reached!
% 12.69/2.72 % (1981963)------------------------------
% 12.69/2.72 % (1981963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.69/2.72 % (1981963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981963)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981963)Termination reason: Instruction limit
% 13.80/3.06 % (1981963)Termination phase: Saturation
% 13.80/3.06 % (1981963)Time elapsed: 0.088 s
% 13.80/3.06 % (1981963)Peak memory usage: 91 MB
% 13.80/3.06 % (1981963)Instructions burned: 287 (million)
% 13.80/3.06 % (1981967)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=1559649478:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 13.80/3.06 % (1981965)Instruction limit reached!
% 13.80/3.06 % (1981965)------------------------------
% 13.80/3.06 % (1981965)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1981965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981965)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981965)Termination reason: Instruction limit
% 13.80/3.06 % (1981965)Termination phase: Saturation
% 13.80/3.06 % (1981965)Time elapsed: 0.076 s
% 13.80/3.06 % (1981965)Peak memory usage: 91 MB
% 13.80/3.06 % (1981965)Instructions burned: 157 (million)
% 13.80/3.06 % (1981971)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2052157590:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 13.80/3.06 % (1981967)Instruction limit reached!
% 13.80/3.06 % (1981967)------------------------------
% 13.80/3.06 % (1981967)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1981967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981967)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981967)Termination reason: Instruction limit
% 13.80/3.06 % (1981967)Termination phase: Saturation
% 13.80/3.06 % (1981967)Time elapsed: 0.118 s
% 13.80/3.06 % (1981967)Peak memory usage: 95 MB
% 13.80/3.06 % (1981967)Instructions burned: 248 (million)
% 13.80/3.06 % (1981966)Instruction limit reached!
% 13.80/3.06 % (1981966)------------------------------
% 13.80/3.06 % (1981966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1981966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981966)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981966)Termination reason: Instruction limit
% 13.80/3.06 % (1981966)Termination phase: Saturation
% 13.80/3.06 % (1981966)Time elapsed: 0.201 s
% 13.80/3.06 % (1981966)Peak memory usage: 92 MB
% 13.80/3.06 % (1981966)Instructions burned: 325 (million)
% 13.80/3.06 % (1981971)Instruction limit reached!
% 13.80/3.06 % (1981971)------------------------------
% 13.80/3.06 % (1981971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1981971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981971)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981971)Termination reason: Instruction limit
% 13.80/3.06 % (1981971)Termination phase: Saturation
% 13.80/3.06 % (1981971)Time elapsed: 0.093 s
% 13.80/3.06 % (1981971)Peak memory usage: 91 MB
% 13.80/3.06 % (1981971)Instructions burned: 295 (million)
% 13.80/3.06 % (1981973)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4148641859:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 13.80/3.06 % (1981975)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3541569289:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 13.80/3.06 % (1981977)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2216295903:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 13.80/3.06 % (1981976)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1962181927:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 13.80/3.06 % (1981977)Instruction limit reached!
% 13.80/3.06 % (1981977)------------------------------
% 13.80/3.06 % (1981977)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1981977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981977)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981977)Termination reason: Instruction limit
% 13.80/3.06 % (1981977)Termination phase: Saturation
% 13.80/3.06 % (1981977)Time elapsed: 0.034 s
% 13.80/3.06 % (1981977)Peak memory usage: 89 MB
% 13.80/3.06 % (1981977)Instructions burned: 117 (million)
% 13.80/3.06 % (1981975)Instruction limit reached!
% 13.80/3.06 % (1981975)------------------------------
% 13.80/3.06 % (1981975)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1981975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981975)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981975)Termination reason: Instruction limit
% 13.80/3.06 % (1981975)Termination phase: Saturation
% 13.80/3.06 % (1981975)Time elapsed: 0.071 s
% 13.80/3.06 % (1981975)Peak memory usage: 90 MB
% 13.80/3.06 % (1981975)Instructions burned: 114 (million)
% 13.80/3.06 % (1981976)Instruction limit reached!
% 13.80/3.06 % (1981976)------------------------------
% 13.80/3.06 % (1981976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1981976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981976)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981976)Termination reason: Instruction limit
% 13.80/3.06 % (1981976)Termination phase: Saturation
% 13.80/3.06 % (1981976)Time elapsed: 0.065 s
% 13.80/3.06 % (1981976)Peak memory usage: 89 MB
% 13.80/3.06 % (1981976)Instructions burned: 128 (million)
% 13.80/3.06 % (1981982)lrs+10_1_sil=8000:sp=occurrence:random_seed=2173424853:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 13.80/3.06 % (1981983)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3676321480:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 13.80/3.06 % (1981984)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1652514307:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 13.80/3.06 % (1981982)Instruction limit reached!
% 13.80/3.06 % (1981982)------------------------------
% 13.80/3.06 % (1981982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1981982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981982)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981982)Termination reason: Instruction limit
% 13.80/3.06 % (1981982)Termination phase: Saturation
% 13.80/3.06 % (1981982)Time elapsed: 0.269 s
% 13.80/3.06 % (1981982)Peak memory usage: 97 MB
% 13.80/3.06 % (1981982)Instructions burned: 909 (million)
% 13.80/3.06 % (1981983)Instruction limit reached!
% 13.80/3.06 % (1981983)------------------------------
% 13.80/3.06 % (1981983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1981983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981983)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981983)Termination reason: Instruction limit
% 13.80/3.06 % (1981983)Termination phase: Saturation
% 13.80/3.06 % (1981983)Time elapsed: 0.255 s
% 13.80/3.06 % (1981983)Peak memory usage: 92 MB
% 13.80/3.06 % (1981983)Instructions burned: 438 (million)
% 13.80/3.06 % (1981989)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1255829934:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 13.80/3.06 % (1981989)Instruction limit reached!
% 13.80/3.06 % (1981989)------------------------------
% 13.80/3.06 % (1981989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1981989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981989)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981989)Termination reason: Instruction limit
% 13.80/3.06 % (1981989)Termination phase: Saturation
% 13.80/3.06 % (1981989)Time elapsed: 0.035 s
% 13.80/3.06 % (1981989)Peak memory usage: 91 MB
% 13.80/3.06 % (1981989)Instructions burned: 135 (million)
% 13.80/3.06 % (1981993)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2944086476:st=8:i=592:sd=3:ep=RST:ss=axioms_2988 on theBenchmark for (2988ds/592Mi)
% 13.80/3.06 % (1981996)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=4097305854:st=3:i=13193:sd=3:ss=axioms_2987 on theBenchmark for (2987ds/13193Mi)
% 13.80/3.06 % (1981993)Instruction limit reached!
% 13.80/3.06 % (1981993)------------------------------
% 13.80/3.06 % (1981993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1981993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981993)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981993)Termination reason: Instruction limit
% 13.80/3.06 % (1981993)Termination phase: Saturation
% 13.80/3.06 % (1981993)Time elapsed: 0.356 s
% 13.80/3.06 % (1981993)Peak memory usage: 95 MB
% 13.80/3.06 % (1981993)Instructions burned: 594 (million)
% 13.80/3.06 % (1981999)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=2138698648:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2983 on theBenchmark for (2983ds/125Mi)
% 13.80/3.06 % (1981973)First to succeed.
% 13.80/3.06 % (1981999)Instruction limit reached!
% 13.80/3.06 % (1981999)------------------------------
% 13.80/3.06 % (1981999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1981999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1981999)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1981999)Termination reason: Instruction limit
% 13.80/3.06 % (1981999)Termination phase: Saturation
% 13.80/3.06 % (1981999)Time elapsed: 0.069 s
% 13.80/3.06 % (1981999)Peak memory usage: 91 MB
% 13.80/3.06 % (1981999)Instructions burned: 125 (million)
% 13.80/3.06 % (1981973)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1981945"
% 13.80/3.06 % (1982001)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=72570355:i=134:gtgl=5:slsql=off:gtg=exists_sym_2980 on theBenchmark for (2980ds/134Mi)
% 13.80/3.06 % (1982001)Instruction limit reached!
% 13.80/3.06 % (1982001)------------------------------
% 13.80/3.06 % (1982001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.80/3.06 % (1982001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.80/3.06 % (1982001)CaDiCaL version: 2.1.3
% 13.80/3.06 % (1982001)Termination reason: Instruction limit
% 13.80/3.06 % (1982001)Termination phase: Saturation
% 13.80/3.06 % (1982001)Time elapsed: 0.078 s
% 13.80/3.06 % (1982001)Peak memory usage: 90 MB
% 13.80/3.06 % (1982001)Instructions burned: 134 (million)
% 13.80/3.06 % (1981973)Refutation found. Thanks to Tanya!
% 13.80/3.06 % SZS status Theorem for theBenchmark
% 13.80/3.06 % SZS output start Proof for theBenchmark
% See solution above
% 16.06/3.26 % (1981973)------------------------------
% 16.06/3.26 % (1981973)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.06/3.26 % (1981973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.06/3.26 % (1981973)CaDiCaL version: 2.1.3
% 16.06/3.26 % (1981973)Termination reason: Refutation
% 16.06/3.26 % (1981973)Time elapsed: 1.311 s
% 16.06/3.26 % (1981973)Peak memory usage: 140 MB
% 16.06/3.26 % (1981973)Instructions burned: 2074 (million)
% 16.06/3.26 % (1981973)------------------------------
% 16.06/3.26 % (1981973)------------------------------
% 16.06/3.26 % (1981945)Success in time 2.196 s
% 16.06/3.26 % Vampire exiting
%------------------------------------------------------------------------------