%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM526+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:35 PM UTC 2026
% Result : Theorem 9.68s 2.52s
% Output : Refutation 12.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 39
% Syntax : Number of formulae : 356 ( 50 unt; 15 def)
% Number of atoms : 1384 ( 375 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1802 ( 774 ~; 874 |; 100 &)
% ( 24 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 233 ( 0 sgn 225 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtasdt0(X0,X1) = sdtasdt0(X0,X2)
| sdtasdt0(X1,X0) = sdtasdt0(X2,X0) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X2) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X0 != sz00
& X1 != X2
& sdtlseqdt0(X1,X2) )
=> ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( X0 != sz00
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(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(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f36,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( aNaturalNumber0(X2)
=> sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f40,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(f41,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& X0 != sz00
& X1 != sz00
& X2 != sz00 )
=> ( sdtasdt0(X2,sdtasdt0(X1,X1)) = sdtasdt0(X0,X0)
=> ( iLess0(X0,xn)
=> ~ isPrime0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2963) ).
fof(f42,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(f43,axiom,
isPrime0(xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3025) ).
fof(f44,axiom,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
fof(f45,axiom,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(f46,axiom,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3082) ).
fof(f47,conjecture,
( xm != xn
& sdtlseqdt0(xm,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f48,negated_conjecture,
~ ( xm != xn
& sdtlseqdt0(xm,xn) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f53,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f54,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f53]) ).
fof(f60,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f61,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f60]) ).
fof(f64,plain,
! [X0] :
( ( sdtasdt0(X0,sz10) = X0
& X0 = sdtasdt0(sz10,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f65,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f70,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f71,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f70]) ).
fof(f81,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f82,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f84,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f86,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f85]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f89]) ).
fof(f93,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f94,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f96,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f98,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f100,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,[],[f99]) ).
fof(f109,plain,
! [X0,X1] :
( ! [X2] :
( sdtasdt0(X2,sdtsldt0(X1,X0)) = sdtsldt0(sdtasdt0(X2,X1),X0)
| ~ aNaturalNumber0(X2) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f110,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,[],[f109]) ).
fof(f111,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(f112,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f111]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ~ isPrime0(X2)
| ~ iLess0(X0,xn)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| sz00 = X1
| sz00 = X2 ),
inference(ennf_transformation,[],[f41]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ~ isPrime0(X2)
| ~ iLess0(X0,xn)
| sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| sz00 = X1
| sz00 = X2 ),
inference(flattening,[],[f117]) ).
fof(f119,plain,
( xn = xm
| ~ sdtlseqdt0(xm,xn) ),
inference(ennf_transformation,[],[f48]) ).
fof(f125,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,[],[f98]) ).
fof(f126,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,[],[f125]) ).
fof(f127,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))],[f126]) ).
fof(f128,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,[],[f100]) ).
fof(f129,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,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f112]) ).
fof(f131,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,[],[f130]) ).
fof(f132,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X2] :
( sz10 = X2
| X0 = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X2,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f131]) ).
fof(f133,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))],[f132]) ).
fof(f137,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f139,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f144,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f147,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 ),
inference(cnf_transformation,[],[f64]) ).
fof(f149,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f65]) ).
fof(f155,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f166,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f84]) ).
fof(f168,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f174,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f175,plain,
! [X2,X0,X1] :
( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f176,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f90]) ).
fof(f180,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f181,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f184,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f185,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f186,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f187,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,[],[f129]) ).
fof(f192,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,[],[f110]) ).
fof(f194,plain,
! [X0] :
( sz10 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f204,plain,
sz00 != xp,
inference(cnf_transformation,[],[f40]) ).
fof(f205,plain,
sz00 != xm,
inference(cnf_transformation,[],[f40]) ).
fof(f206,plain,
sz00 != xn,
inference(cnf_transformation,[],[f40]) ).
fof(f207,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f208,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f209,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f210,plain,
! [X2,X0,X1] :
( sdtasdt0(X2,sdtasdt0(X1,X1)) != sdtasdt0(X0,X0)
| ~ iLess0(X0,xn)
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| sz00 = X1
| sz00 = X2 ),
inference(cnf_transformation,[],[f118]) ).
fof(f211,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f212,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f43]) ).
fof(f213,plain,
doDivides0(xp,xn),
inference(cnf_transformation,[],[f44]) ).
fof(f214,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(cnf_transformation,[],[f44]) ).
fof(f215,plain,
xq = sdtsldt0(xn,xp),
inference(cnf_transformation,[],[f45]) ).
fof(f216,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(cnf_transformation,[],[f46]) ).
fof(f217,plain,
( xn = xm
| ~ sdtlseqdt0(xm,xn) ),
inference(cnf_transformation,[],[f119]) ).
fof(f224,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f184]) ).
fof(f225,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,[],[f187]) ).
fof(f226,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f186]) ).
fof(f227,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f185]) ).
fof(f229,plain,
( ~ isPrime0(sz10)
| ~ aNaturalNumber0(sz10) ),
inference(equality_resolution,[],[f194]) ).
fof(f232,definition,
( spl4_1
<=> sdtlseqdt0(xm,xn) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f234,plain,
( ~ sdtlseqdt0(xm,xn)
| spl4_1 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f236,definition,
( spl4_2
<=> xn = xm ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f237,plain,
( xn != xm
| spl4_2 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f238,plain,
( xn = xm
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f239,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f217,f236,f232]) ).
fof(f241,definition,
( spl4_3
<=> aNaturalNumber0(sz10) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f242,plain,
( aNaturalNumber0(sz10)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f245,definition,
( spl4_4
<=> isPrime0(sz10) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f247,plain,
( ~ isPrime0(sz10)
| spl4_4 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f248,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f229,f245,f241]) ).
fof(f258,plain,
spl4_3,
inference(avatar_split_clause,[],[f137,f241]) ).
fof(f263,definition,
( spl4_7
<=> aNaturalNumber0(sdtasdt0(xm,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f264,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f265,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| spl4_7 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f278,definition,
( spl4_10
<=> aNaturalNumber0(sdtasdt0(xq,xq)) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
fof(f279,plain,
( aNaturalNumber0(sdtasdt0(xq,xq))
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f280,plain,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| spl4_10 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f291,plain,
( sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl4_1 ),
inference(resolution,[],[f168,f234]) ).
fof(f294,plain,
( sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f291,f208]) ).
fof(f296,plain,
( sdtlseqdt0(xn,xm)
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f294,f209]) ).
fof(f298,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sz00 = xp
| sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(superposition,[],[f225,f211]) ).
fof(f300,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xq)
| spl4_10 ),
inference(resolution,[],[f139,f280]) ).
fof(f301,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| spl4_7 ),
inference(resolution,[],[f139,f265]) ).
fof(f302,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(superposition,[],[f139,f211]) ).
fof(f304,plain,
( ~ aNaturalNumber0(xm)
| spl4_7 ),
inference(duplicate_literal_removal,[],[f301]) ).
fof(f305,plain,
( ~ aNaturalNumber0(xq)
| spl4_10 ),
inference(duplicate_literal_removal,[],[f300]) ).
fof(f306,plain,
( $false
| spl4_7 ),
inference(forward_subsumption_resolution,[],[f304,f208]) ).
fof(f307,plain,
spl4_7,
inference(avatar_contradiction_clause,[],[f306]) ).
fof(f308,plain,
( ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sz00 = xp
| sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(forward_subsumption_resolution,[],[f298,f214]) ).
fof(f309,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(forward_subsumption_resolution,[],[f302,f207]) ).
fof(f310,plain,
( sz00 = xp
| sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f308,f264]) ).
fof(f311,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f309,f264]) ).
fof(f312,plain,
( sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f310,f204]) ).
fof(f313,plain,
( sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f312,f207]) ).
fof(f314,plain,
( sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f313,f311]) ).
fof(f316,plain,
( aNaturalNumber0(xq)
| sz00 = xp
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f226,f215]) ).
fof(f317,plain,
( sz00 = xp
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| spl4_10 ),
inference(forward_subsumption_resolution,[],[f316,f305]) ).
fof(f318,plain,
( ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| spl4_10 ),
inference(forward_subsumption_resolution,[],[f317,f204]) ).
fof(f319,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| spl4_10 ),
inference(forward_subsumption_resolution,[],[f318,f213]) ).
fof(f320,plain,
( ~ aNaturalNumber0(xn)
| spl4_10 ),
inference(forward_subsumption_resolution,[],[f319,f207]) ).
fof(f321,plain,
( $false
| spl4_10 ),
inference(forward_subsumption_resolution,[],[f320,f209]) ).
fof(f322,plain,
spl4_10,
inference(avatar_contradiction_clause,[],[f321]) ).
fof(f324,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f316,f204]) ).
fof(f326,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f324,f213]) ).
fof(f328,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f326,f207]) ).
fof(f330,plain,
aNaturalNumber0(xq),
inference(forward_subsumption_resolution,[],[f328,f209]) ).
fof(f344,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = xp
| sdtasdt0(X0,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(X0,xn),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f192,f213]) ).
fof(f345,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(X0,xn),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f344,f204]) ).
fof(f347,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(X0,xn),xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f345,f207]) ).
fof(f349,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sdtsldt0(xn,xp)) = sdtsldt0(sdtasdt0(X0,xn),xp) ),
inference(forward_subsumption_resolution,[],[f347,f209]) ).
fof(f351,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtsldt0(sdtasdt0(X0,xn),xp) = sdtasdt0(X0,xq) ),
inference(forward_demodulation,[],[f349,f215]) ).
fof(f356,plain,
sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xn,xq),
inference(resolution,[],[f351,f209]) ).
fof(f383,definition,
( spl4_16
<=> sz00 = xq ),
introduced(definition,[new_symbols(definition,[spl4_16])],[avatar_definition]) ).
fof(f384,plain,
( sz00 != xq
| spl4_16 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f385,plain,
( sz00 = xq
| ~ spl4_16 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f404,plain,
( sdtasdt0(xm,xm) = sdtasdt0(xn,xq)
| ~ spl4_7 ),
inference(forward_demodulation,[],[f356,f314]) ).
fof(f417,plain,
( aNaturalNumber0(sdtasdt0(xn,xq))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ spl4_7 ),
inference(superposition,[],[f139,f404]) ).
fof(f418,plain,
( ~ doDivides0(xm,sdtasdt0(xn,xq))
| ~ aNaturalNumber0(xm)
| sz00 = xm
| xm = sdtsldt0(sdtasdt0(xn,xq),xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xq))
| ~ spl4_7 ),
inference(superposition,[],[f225,f404]) ).
fof(f421,plain,
( ~ doDivides0(xm,sdtasdt0(xn,xq))
| ~ aNaturalNumber0(xm)
| sz00 = xm
| xm = sdtsldt0(sdtasdt0(xn,xq),xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xq))
| ~ spl4_7 ),
inference(duplicate_literal_removal,[],[f418]) ).
fof(f422,plain,
( aNaturalNumber0(sdtasdt0(xn,xq))
| ~ aNaturalNumber0(xm)
| ~ spl4_7 ),
inference(duplicate_literal_removal,[],[f417]) ).
fof(f424,plain,
( ~ doDivides0(xm,sdtasdt0(xn,xq))
| sz00 = xm
| xm = sdtsldt0(sdtasdt0(xn,xq),xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xq))
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f421,f208]) ).
fof(f425,plain,
( aNaturalNumber0(sdtasdt0(xn,xq))
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f422,f208]) ).
fof(f427,plain,
( ~ doDivides0(xm,sdtasdt0(xn,xq))
| xm = sdtsldt0(sdtasdt0(xn,xq),xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xq))
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f424,f205]) ).
fof(f428,plain,
( ~ doDivides0(xm,sdtasdt0(xn,xq))
| xm = sdtsldt0(sdtasdt0(xn,xq),xm)
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f427,f425]) ).
fof(f430,definition,
( spl4_22
<=> xm = sdtsldt0(sdtasdt0(xn,xq),xm) ),
introduced(definition,[new_symbols(definition,[spl4_22])],[avatar_definition]) ).
fof(f432,plain,
( xm = sdtsldt0(sdtasdt0(xn,xq),xm)
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f434,definition,
( spl4_23
<=> doDivides0(xm,sdtasdt0(xn,xq)) ),
introduced(definition,[new_symbols(definition,[spl4_23])],[avatar_definition]) ).
fof(f436,plain,
( ~ doDivides0(xm,sdtasdt0(xn,xq))
| spl4_23 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f437,plain,
( spl4_22
| ~ spl4_23
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f428,f263,f434,f430]) ).
fof(f439,plain,
( sz00 = xp
| xn = sdtasdt0(xp,sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f227,f213]) ).
fof(f440,plain,
( xn = sdtasdt0(xp,sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f439,f204]) ).
fof(f442,plain,
( xn = sdtasdt0(xp,sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f440,f207]) ).
fof(f444,plain,
xn = sdtasdt0(xp,sdtsldt0(xn,xp)),
inference(forward_subsumption_resolution,[],[f442,f209]) ).
fof(f446,plain,
xn = sdtasdt0(xp,xq),
inference(forward_demodulation,[],[f444,f215]) ).
fof(f485,plain,
( xn = sdtasdt0(xp,sz00)
| ~ spl4_16 ),
inference(superposition,[],[f446,f385]) ).
fof(f514,plain,
( ~ sdtlseqdt0(xn,xn)
| spl4_1
| ~ spl4_2 ),
inference(superposition,[],[f234,f238]) ).
fof(f516,plain,
( sdtlseqdt0(xn,xn)
| spl4_1
| ~ spl4_2 ),
inference(superposition,[],[f296,f238]) ).
fof(f519,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f514,f516]) ).
fof(f520,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f519]) ).
fof(f529,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,xq) = sdtasdt0(xq,X0) ),
inference(resolution,[],[f144,f330]) ).
fof(f541,plain,
sz00 = sdtasdt0(xp,sz00),
inference(resolution,[],[f149,f207]) ).
fof(f544,plain,
( sz00 = xn
| ~ spl4_16 ),
inference(forward_demodulation,[],[f541,f485]) ).
fof(f548,plain,
( $false
| ~ spl4_16 ),
inference(forward_subsumption_resolution,[],[f544,f206]) ).
fof(f549,plain,
~ spl4_16,
inference(avatar_contradiction_clause,[],[f548]) ).
fof(f566,plain,
( doDivides0(xm,sdtasdt0(xn,xq))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xq))
| ~ spl4_7 ),
inference(superposition,[],[f224,f404]) ).
fof(f568,plain,
( doDivides0(xm,sdtasdt0(xn,xq))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xq))
| ~ spl4_7 ),
inference(duplicate_literal_removal,[],[f566]) ).
fof(f573,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xn,xq))
| ~ spl4_7
| spl4_23 ),
inference(forward_subsumption_resolution,[],[f568,f436]) ).
fof(f579,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xq))
| ~ spl4_7
| spl4_23 ),
inference(forward_subsumption_resolution,[],[f573,f208]) ).
fof(f581,plain,
( $false
| ~ spl4_7
| spl4_23 ),
inference(forward_subsumption_resolution,[],[f579,f425]) ).
fof(f582,plain,
( ~ spl4_7
| spl4_23 ),
inference(avatar_contradiction_clause,[],[f581]) ).
fof(f594,plain,
sdtasdt0(xn,xq) = sdtasdt0(xq,xn),
inference(resolution,[],[f529,f209]) ).
fof(f595,plain,
sdtasdt0(xm,xq) = sdtasdt0(xq,xm),
inference(resolution,[],[f529,f208]) ).
fof(f596,plain,
sdtasdt0(xp,xq) = sdtasdt0(xq,xp),
inference(resolution,[],[f529,f207]) ).
fof(f598,plain,
xn = sdtasdt0(xq,xp),
inference(forward_demodulation,[],[f596,f446]) ).
fof(f601,plain,
( doDivides0(xq,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f224,f598]) ).
fof(f603,plain,
( ~ doDivides0(xq,xn)
| ~ aNaturalNumber0(xp)
| sz00 = xq
| xp = sdtsldt0(xn,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f225,f598]) ).
fof(f604,plain,
( sdtlseqdt0(xq,xn)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq) ),
inference(superposition,[],[f180,f598]) ).
fof(f605,plain,
( sdtlseqdt0(xq,xn)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xq) ),
inference(forward_subsumption_resolution,[],[f604,f204]) ).
fof(f606,plain,
( ~ doDivides0(xq,xn)
| sz00 = xq
| xp = sdtsldt0(xn,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f603,f207]) ).
fof(f607,plain,
( doDivides0(xq,xn)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f601,f207]) ).
fof(f608,plain,
( sdtlseqdt0(xq,xn)
| ~ aNaturalNumber0(xq) ),
inference(forward_subsumption_resolution,[],[f605,f207]) ).
fof(f609,plain,
( ~ doDivides0(xq,xn)
| xp = sdtsldt0(xn,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn)
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f606,f384]) ).
fof(f610,plain,
( doDivides0(xq,xn)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f607,f330]) ).
fof(f611,plain,
sdtlseqdt0(xq,xn),
inference(forward_subsumption_resolution,[],[f608,f330]) ).
fof(f612,plain,
( ~ doDivides0(xq,xn)
| xp = sdtsldt0(xn,xq)
| ~ aNaturalNumber0(xn)
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f609,f330]) ).
fof(f613,plain,
doDivides0(xq,xn),
inference(forward_subsumption_resolution,[],[f610,f209]) ).
fof(f614,plain,
( ~ doDivides0(xq,xn)
| xp = sdtsldt0(xn,xq)
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f612,f209]) ).
fof(f615,plain,
( xp = sdtsldt0(xn,xq)
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f614,f613]) ).
fof(f769,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,xn)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
| spl4_1 ),
inference(resolution,[],[f167,f296]) ).
fof(f778,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,xn)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) )
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f769,f209]) ).
fof(f782,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,xn)
| sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) )
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f778,f208]) ).
fof(f860,definition,
( spl4_34
<=> sz10 = xp ),
introduced(definition,[new_symbols(definition,[spl4_34])],[avatar_definition]) ).
fof(f862,plain,
( sz10 = xp
| ~ spl4_34 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f1024,plain,
! [X0] :
( sdtasdt0(xn,xn) != sdtasdt0(xp,X0)
| sdtasdt0(xm,xm) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| sz00 = xp
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f155,f211]) ).
fof(f1041,plain,
( ! [X0] :
( sdtasdt0(xn,xn) != sdtasdt0(xp,X0)
| sdtasdt0(xm,xm) = X0
| ~ aNaturalNumber0(X0)
| sz00 = xp
| ~ aNaturalNumber0(xp) )
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f1024,f264]) ).
fof(f1053,plain,
( ! [X0] :
( sdtasdt0(xn,xn) != sdtasdt0(xp,X0)
| sdtasdt0(xm,xm) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp) )
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f1041,f204]) ).
fof(f1064,plain,
( ! [X0] :
( sdtasdt0(xn,xn) != sdtasdt0(xp,X0)
| sdtasdt0(xm,xm) = X0
| ~ aNaturalNumber0(X0) )
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f1053,f207]) ).
fof(f1120,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X2,X1))
| sdtasdt0(X0,X1) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X2,X1))
| sz00 = X1
| X0 = X2
| ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f166,f174]) ).
fof(f1131,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X2,X1))
| ~ aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(sdtasdt0(X2,X1))
| sz00 = X1
| X0 = X2
| ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f1120,f175]) ).
fof(f1135,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X2,X1))
| ~ aNaturalNumber0(sdtasdt0(X2,X1))
| sz00 = X1
| X0 = X2
| ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f1131,f139]) ).
fof(f1138,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X2,X1))
| sz00 = X1
| X0 = X2
| ~ sdtlseqdt0(X2,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f1135,f139]) ).
fof(f1141,plain,
( ! [X0] :
( sdtasdt0(xn,xq) = X0
| sdtasdt0(xn,xn) != sdtasdt0(xp,X0)
| ~ aNaturalNumber0(X0) )
| ~ spl4_7 ),
inference(forward_demodulation,[],[f1064,f404]) ).
fof(f1146,plain,
( ! [X0] :
( sdtasdt0(xn,xn) != sdtasdt0(xp,X0)
| sdtasdt0(xq,xn) = X0
| ~ aNaturalNumber0(X0) )
| ~ spl4_7 ),
inference(forward_demodulation,[],[f1141,f594]) ).
fof(f1166,plain,
xn = sdtasdt0(xn,sz10),
inference(resolution,[],[f147,f209]) ).
fof(f1223,plain,
( doDivides0(xn,xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f224,f1166]) ).
fof(f1224,plain,
( ~ doDivides0(xn,xn)
| ~ aNaturalNumber0(sz10)
| sz00 = xn
| sz10 = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f225,f1166]) ).
fof(f1225,plain,
( ~ doDivides0(xn,xn)
| ~ aNaturalNumber0(sz10)
| sz00 = xn
| sz10 = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn) ),
inference(duplicate_literal_removal,[],[f1224]) ).
fof(f1226,plain,
( doDivides0(xn,xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(duplicate_literal_removal,[],[f1223]) ).
fof(f1227,plain,
( ~ doDivides0(xn,xn)
| sz00 = xn
| sz10 = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f1225,f242]) ).
fof(f1228,plain,
( doDivides0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f1226,f242]) ).
fof(f1236,plain,
( ~ doDivides0(xn,xn)
| sz10 = sdtsldt0(xn,xn)
| ~ aNaturalNumber0(xn)
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f1227,f206]) ).
fof(f1237,plain,
( doDivides0(xn,xn)
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f1228,f209]) ).
fof(f1245,plain,
( ~ doDivides0(xn,xn)
| sz10 = sdtsldt0(xn,xn)
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f1236,f209]) ).
fof(f1253,plain,
( sz10 = sdtsldt0(xn,xn)
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f1245,f1237]) ).
fof(f1350,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xn,xq),sdtasdt0(X0,xm))
| sz00 = xm
| xm = X0
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) )
| ~ spl4_7 ),
inference(superposition,[],[f1138,f404]) ).
fof(f1361,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xn,xq),sdtasdt0(X0,xm))
| sz00 = xm
| xm = X0
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) )
| ~ spl4_7 ),
inference(duplicate_literal_removal,[],[f1350]) ).
fof(f1375,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xn,xq),sdtasdt0(X0,xm))
| xm = X0
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(X0) )
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f1361,f205]) ).
fof(f1389,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xn,xq),sdtasdt0(X0,xm))
| xm = X0
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) )
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f1375,f208]) ).
fof(f1403,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xq,xn),sdtasdt0(X0,xm))
| xm = X0
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0) )
| ~ spl4_7 ),
inference(forward_demodulation,[],[f1389,f594]) ).
fof(f1568,plain,
( sdtasdt0(xm,xm) != sdtasdt0(xn,xn)
| sdtasdt0(xq,xq) = sdtasdt0(xq,xn)
| ~ aNaturalNumber0(sdtasdt0(xq,xq))
| ~ spl4_7 ),
inference(superposition,[],[f1146,f216]) ).
fof(f1570,plain,
( sdtasdt0(xm,xm) != sdtasdt0(xn,xn)
| sdtasdt0(xq,xq) = sdtasdt0(xq,xn)
| ~ spl4_7
| ~ spl4_10 ),
inference(forward_subsumption_resolution,[],[f1568,f279]) ).
fof(f1572,plain,
( sdtasdt0(xn,xn) != sdtasdt0(xn,xq)
| sdtasdt0(xq,xq) = sdtasdt0(xq,xn)
| ~ spl4_7
| ~ spl4_10 ),
inference(forward_demodulation,[],[f1570,f404]) ).
fof(f1574,plain,
( sdtasdt0(xn,xn) != sdtasdt0(xq,xn)
| sdtasdt0(xq,xq) = sdtasdt0(xq,xn)
| ~ spl4_7
| ~ spl4_10 ),
inference(forward_demodulation,[],[f1572,f594]) ).
fof(f1576,definition,
( spl4_50
<=> sdtasdt0(xq,xq) = sdtasdt0(xq,xn) ),
introduced(definition,[new_symbols(definition,[spl4_50])],[avatar_definition]) ).
fof(f1578,plain,
( sdtasdt0(xq,xq) = sdtasdt0(xq,xn)
| ~ spl4_50 ),
inference(avatar_component_clause,[],[f1576]) ).
fof(f1580,definition,
( spl4_51
<=> sdtasdt0(xn,xn) = sdtasdt0(xq,xn) ),
introduced(definition,[new_symbols(definition,[spl4_51])],[avatar_definition]) ).
fof(f1582,plain,
( sdtasdt0(xn,xn) != sdtasdt0(xq,xn)
| spl4_51 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f1583,plain,
( spl4_50
| ~ spl4_51
| ~ spl4_7
| ~ spl4_10 ),
inference(avatar_split_clause,[],[f1574,f278,f263,f1580,f1576]) ).
fof(f1587,plain,
( xn = xq
| iLess0(xq,xn)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f611,f181]) ).
fof(f1588,plain,
( xn = xq
| iLess0(xq,xn)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f1587,f330]) ).
fof(f1591,plain,
( xn = xq
| iLess0(xq,xn) ),
inference(forward_subsumption_resolution,[],[f1588,f209]) ).
fof(f1595,definition,
( spl4_52
<=> iLess0(xq,xn) ),
introduced(definition,[new_symbols(definition,[spl4_52])],[avatar_definition]) ).
fof(f1597,plain,
( iLess0(xq,xn)
| ~ spl4_52 ),
inference(avatar_component_clause,[],[f1595]) ).
fof(f1599,definition,
( spl4_53
<=> xn = xq ),
introduced(definition,[new_symbols(definition,[spl4_53])],[avatar_definition]) ).
fof(f1600,plain,
( xn != xq
| spl4_53 ),
inference(avatar_component_clause,[],[f1599]) ).
fof(f1601,plain,
( xn = xq
| ~ spl4_53 ),
inference(avatar_component_clause,[],[f1599]) ).
fof(f1602,plain,
( spl4_52
| spl4_53 ),
inference(avatar_split_clause,[],[f1591,f1599,f1595]) ).
fof(f1627,plain,
( xp = sdtsldt0(xq,xq)
| spl4_16
| ~ spl4_53 ),
inference(superposition,[],[f615,f1601]) ).
fof(f1736,plain,
( sz10 = sdtsldt0(xq,xq)
| ~ spl4_3
| ~ spl4_53 ),
inference(superposition,[],[f1253,f1601]) ).
fof(f1739,plain,
( sz10 = xp
| ~ spl4_3
| spl4_16
| ~ spl4_53 ),
inference(forward_demodulation,[],[f1736,f1627]) ).
fof(f1740,plain,
( spl4_34
| ~ spl4_3
| spl4_16
| ~ spl4_53 ),
inference(avatar_split_clause,[],[f1739,f1599,f383,f241,f860]) ).
fof(f1744,plain,
( isPrime0(sz10)
| ~ spl4_34 ),
inference(superposition,[],[f212,f862]) ).
fof(f1787,plain,
( $false
| spl4_4
| ~ spl4_34 ),
inference(forward_subsumption_resolution,[],[f1744,f247]) ).
fof(f1788,plain,
( spl4_4
| ~ spl4_34 ),
inference(avatar_contradiction_clause,[],[f1787]) ).
fof(f1871,plain,
! [X0] :
( sdtasdt0(X0,X0) != sdtasdt0(xm,xm)
| ~ iLess0(X0,xn)
| ~ isPrime0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| sz00 = X0
| sz00 = xq
| sz00 = xp ),
inference(superposition,[],[f210,f216]) ).
fof(f1874,plain,
! [X0] :
( sdtasdt0(X0,X0) != sdtasdt0(xm,xm)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp)
| sz00 = X0
| sz00 = xq
| sz00 = xp ),
inference(forward_subsumption_resolution,[],[f1871,f212]) ).
fof(f1877,plain,
! [X0] :
( sdtasdt0(X0,X0) != sdtasdt0(xm,xm)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xp)
| sz00 = X0
| sz00 = xq
| sz00 = xp ),
inference(forward_subsumption_resolution,[],[f1874,f330]) ).
fof(f1880,plain,
! [X0] :
( sdtasdt0(X0,X0) != sdtasdt0(xm,xm)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz00 = xq
| sz00 = xp ),
inference(forward_subsumption_resolution,[],[f1877,f207]) ).
fof(f1883,plain,
( ! [X0] :
( sdtasdt0(X0,X0) != sdtasdt0(xm,xm)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz00 = xp )
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f1880,f384]) ).
fof(f1885,plain,
( ! [X0] :
( sdtasdt0(X0,X0) != sdtasdt0(xm,xm)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| sz00 = X0 )
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f1883,f204]) ).
fof(f1887,plain,
( ! [X0] :
( sdtasdt0(X0,X0) != sdtasdt0(xn,xq)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| sz00 = X0 )
| ~ spl4_7
| spl4_16 ),
inference(forward_demodulation,[],[f1885,f404]) ).
fof(f1888,plain,
( ! [X0] :
( sdtasdt0(X0,X0) != sdtasdt0(xq,xn)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| sz00 = X0 )
| ~ spl4_7
| spl4_16 ),
inference(forward_demodulation,[],[f1887,f594]) ).
fof(f1896,plain,
( sdtasdt0(xn,xq) != sdtasdt0(xq,xn)
| ~ iLess0(xm,xn)
| ~ aNaturalNumber0(xm)
| sz00 = xm
| ~ spl4_7
| spl4_16 ),
inference(superposition,[],[f1888,f404]) ).
fof(f1897,plain,
( ~ iLess0(xm,xn)
| ~ aNaturalNumber0(xm)
| sz00 = xm
| ~ spl4_7
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f1896,f594]) ).
fof(f1898,plain,
( ~ iLess0(xm,xn)
| sz00 = xm
| ~ spl4_7
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f1897,f208]) ).
fof(f1899,plain,
( ~ iLess0(xm,xn)
| ~ spl4_7
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f1898,f205]) ).
fof(f1904,plain,
( sdtlseqdt0(xq,xm)
| ~ aNaturalNumber0(xq)
| spl4_1 ),
inference(resolution,[],[f782,f611]) ).
fof(f1908,plain,
( sdtlseqdt0(xq,xm)
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f1904,f330]) ).
fof(f1966,plain,
( sdtasdt0(xn,xn) = sdtasdt0(xn,xq)
| ~ spl4_2
| ~ spl4_7 ),
inference(superposition,[],[f404,f238]) ).
fof(f1968,plain,
( xn = sdtsldt0(sdtasdt0(xn,xq),xn)
| ~ spl4_2
| ~ spl4_22 ),
inference(superposition,[],[f432,f238]) ).
fof(f1976,plain,
( xn = sdtsldt0(sdtasdt0(xq,xn),xn)
| ~ spl4_2
| ~ spl4_22 ),
inference(forward_demodulation,[],[f1968,f594]) ).
fof(f1978,plain,
( sdtasdt0(xn,xn) = sdtasdt0(xq,xn)
| ~ spl4_2
| ~ spl4_7 ),
inference(forward_demodulation,[],[f1966,f594]) ).
fof(f1980,plain,
( $false
| ~ spl4_2
| ~ spl4_7
| spl4_51 ),
inference(forward_subsumption_resolution,[],[f1978,f1582]) ).
fof(f1981,plain,
( ~ spl4_2
| ~ spl4_7
| spl4_51 ),
inference(avatar_contradiction_clause,[],[f1980]) ).
fof(f2288,plain,
( doDivides0(xm,sdtasdt0(xq,xm))
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xq,xm)) ),
inference(superposition,[],[f224,f595]) ).
fof(f2289,plain,
( ~ doDivides0(xm,sdtasdt0(xq,xm))
| ~ aNaturalNumber0(xq)
| sz00 = xm
| xq = sdtsldt0(sdtasdt0(xq,xm),xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xq,xm)) ),
inference(superposition,[],[f225,f595]) ).
fof(f2298,plain,
( ~ doDivides0(xm,sdtasdt0(xq,xm))
| sz00 = xm
| xq = sdtsldt0(sdtasdt0(xq,xm),xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xq,xm)) ),
inference(forward_subsumption_resolution,[],[f2289,f330]) ).
fof(f2299,plain,
( doDivides0(xm,sdtasdt0(xq,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xq,xm)) ),
inference(forward_subsumption_resolution,[],[f2288,f330]) ).
fof(f2317,plain,
( ~ doDivides0(xm,sdtasdt0(xq,xm))
| xq = sdtsldt0(sdtasdt0(xq,xm),xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xq,xm)) ),
inference(forward_subsumption_resolution,[],[f2298,f205]) ).
fof(f2318,plain,
( doDivides0(xm,sdtasdt0(xq,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xm)) ),
inference(forward_subsumption_resolution,[],[f2299,f208]) ).
fof(f2336,plain,
( ~ doDivides0(xm,sdtasdt0(xq,xm))
| xq = sdtsldt0(sdtasdt0(xq,xm),xm)
| ~ aNaturalNumber0(sdtasdt0(xq,xm)) ),
inference(forward_subsumption_resolution,[],[f2317,f208]) ).
fof(f2337,plain,
( doDivides0(xn,sdtasdt0(xq,xn))
| ~ aNaturalNumber0(sdtasdt0(xq,xm))
| ~ spl4_2 ),
inference(forward_demodulation,[],[f2318,f238]) ).
fof(f2355,plain,
( ~ doDivides0(xn,sdtasdt0(xq,xn))
| xq = sdtsldt0(sdtasdt0(xq,xm),xm)
| ~ aNaturalNumber0(sdtasdt0(xq,xm))
| ~ spl4_2 ),
inference(forward_demodulation,[],[f2336,f238]) ).
fof(f2356,plain,
( doDivides0(xn,sdtasdt0(xq,xq))
| ~ aNaturalNumber0(sdtasdt0(xq,xm))
| ~ spl4_2
| ~ spl4_50 ),
inference(forward_demodulation,[],[f2337,f1578]) ).
fof(f2374,plain,
( ~ doDivides0(xn,sdtasdt0(xq,xq))
| xq = sdtsldt0(sdtasdt0(xq,xm),xm)
| ~ aNaturalNumber0(sdtasdt0(xq,xm))
| ~ spl4_2
| ~ spl4_50 ),
inference(forward_demodulation,[],[f2355,f1578]) ).
fof(f2375,plain,
( ~ aNaturalNumber0(sdtasdt0(xq,xn))
| doDivides0(xn,sdtasdt0(xq,xq))
| ~ spl4_2
| ~ spl4_50 ),
inference(forward_demodulation,[],[f2356,f238]) ).
fof(f2390,plain,
( xq = sdtsldt0(sdtasdt0(xq,xn),xn)
| ~ doDivides0(xn,sdtasdt0(xq,xq))
| ~ aNaturalNumber0(sdtasdt0(xq,xm))
| ~ spl4_2
| ~ spl4_50 ),
inference(forward_demodulation,[],[f2374,f238]) ).
fof(f2391,plain,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| doDivides0(xn,sdtasdt0(xq,xq))
| ~ spl4_2
| ~ spl4_50 ),
inference(forward_demodulation,[],[f2375,f1578]) ).
fof(f2400,plain,
( xn = xq
| ~ doDivides0(xn,sdtasdt0(xq,xq))
| ~ aNaturalNumber0(sdtasdt0(xq,xm))
| ~ spl4_2
| ~ spl4_22
| ~ spl4_50 ),
inference(forward_demodulation,[],[f2390,f1976]) ).
fof(f2401,plain,
( doDivides0(xn,sdtasdt0(xq,xq))
| ~ spl4_2
| ~ spl4_10
| ~ spl4_50 ),
inference(forward_subsumption_resolution,[],[f2391,f279]) ).
fof(f2406,plain,
( ~ doDivides0(xn,sdtasdt0(xq,xq))
| ~ aNaturalNumber0(sdtasdt0(xq,xm))
| ~ spl4_2
| ~ spl4_22
| ~ spl4_50
| spl4_53 ),
inference(forward_subsumption_resolution,[],[f2400,f1600]) ).
fof(f2407,plain,
( ~ aNaturalNumber0(sdtasdt0(xq,xm))
| ~ spl4_2
| ~ spl4_10
| ~ spl4_22
| ~ spl4_50
| spl4_53 ),
inference(forward_subsumption_resolution,[],[f2406,f2401]) ).
fof(f2408,plain,
( ~ aNaturalNumber0(sdtasdt0(xq,xn))
| ~ spl4_2
| ~ spl4_10
| ~ spl4_22
| ~ spl4_50
| spl4_53 ),
inference(forward_demodulation,[],[f2407,f238]) ).
fof(f2409,plain,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| ~ spl4_2
| ~ spl4_10
| ~ spl4_22
| ~ spl4_50
| spl4_53 ),
inference(forward_demodulation,[],[f2408,f1578]) ).
fof(f2410,plain,
( $false
| ~ spl4_2
| ~ spl4_10
| ~ spl4_22
| ~ spl4_50
| spl4_53 ),
inference(forward_subsumption_resolution,[],[f2409,f279]) ).
fof(f2411,plain,
( ~ spl4_2
| ~ spl4_10
| ~ spl4_22
| ~ spl4_50
| spl4_53 ),
inference(avatar_contradiction_clause,[],[f2410]) ).
fof(f2448,definition,
( spl4_62
<=> xm = xq ),
introduced(definition,[new_symbols(definition,[spl4_62])],[avatar_definition]) ).
fof(f2450,plain,
( xm = xq
| ~ spl4_62 ),
inference(avatar_component_clause,[],[f2448]) ).
fof(f7236,plain,
( xm = xq
| ~ sdtlseqdt0(xq,xm)
| ~ aNaturalNumber0(xq)
| sz00 = xq
| xn = xm
| ~ sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ spl4_7 ),
inference(resolution,[],[f1403,f176]) ).
fof(f7247,plain,
( xm = xq
| ~ sdtlseqdt0(xq,xm)
| ~ aNaturalNumber0(xq)
| sz00 = xq
| xn = xm
| ~ sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ spl4_7 ),
inference(duplicate_literal_removal,[],[f7236]) ).
fof(f7251,plain,
( xm = xq
| ~ aNaturalNumber0(xq)
| sz00 = xq
| xn = xm
| ~ sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_1
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f7247,f1908]) ).
fof(f7253,plain,
( xm = xq
| sz00 = xq
| xn = xm
| ~ sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_1
| ~ spl4_7 ),
inference(forward_subsumption_resolution,[],[f7251,f330]) ).
fof(f7255,plain,
( xm = xq
| xn = xm
| ~ sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_1
| ~ spl4_7
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f7253,f384]) ).
fof(f7257,plain,
( xm = xq
| ~ sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_1
| spl4_2
| ~ spl4_7
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f7255,f237]) ).
fof(f7259,plain,
( xm = xq
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_1
| spl4_2
| ~ spl4_7
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f7257,f296]) ).
fof(f7269,plain,
( xm = xq
| ~ aNaturalNumber0(xm)
| spl4_1
| spl4_2
| ~ spl4_7
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f7259,f209]) ).
fof(f7270,plain,
( xm = xq
| spl4_1
| spl4_2
| ~ spl4_7
| spl4_16 ),
inference(forward_subsumption_resolution,[],[f7269,f208]) ).
fof(f7271,plain,
( spl4_62
| spl4_1
| spl4_2
| ~ spl4_7
| spl4_16 ),
inference(avatar_split_clause,[],[f7270,f383,f263,f236,f232,f2448]) ).
fof(f7299,plain,
( ~ iLess0(xq,xn)
| ~ spl4_7
| spl4_16
| ~ spl4_62 ),
inference(superposition,[],[f1899,f2450]) ).
fof(f7325,plain,
( $false
| ~ spl4_7
| spl4_16
| ~ spl4_52
| ~ spl4_62 ),
inference(forward_subsumption_resolution,[],[f7299,f1597]) ).
fof(f7326,plain,
( ~ spl4_7
| spl4_16
| ~ spl4_52
| ~ spl4_62 ),
inference(avatar_contradiction_clause,[],[f7325]) ).
cnf(s1,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f239]) ).
cnf(s2,plain,
( ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f248]) ).
cnf(s4,plain,
spl4_3,
inference(sat_conversion,[],[f258]) ).
cnf(s8,plain,
spl4_7,
inference(sat_conversion,[],[f307]) ).
cnf(s9,plain,
spl4_10,
inference(sat_conversion,[],[f322]) ).
cnf(s15,plain,
( ~ spl4_7
| spl4_22
| ~ spl4_23 ),
inference(sat_conversion,[],[f437]) ).
cnf(s19,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f520]) ).
cnf(s20,plain,
~ spl4_16,
inference(sat_conversion,[],[f549]) ).
cnf(s23,plain,
( ~ spl4_7
| spl4_23 ),
inference(sat_conversion,[],[f582]) ).
cnf(s44,plain,
( ~ spl4_7
| ~ spl4_10
| spl4_50
| ~ spl4_51 ),
inference(sat_conversion,[],[f1583]) ).
cnf(s45,plain,
( spl4_52
| spl4_53 ),
inference(sat_conversion,[],[f1602]) ).
cnf(s47,plain,
( ~ spl4_3
| spl4_16
| spl4_34
| ~ spl4_53 ),
inference(sat_conversion,[],[f1740]) ).
cnf(s48,plain,
( spl4_4
| ~ spl4_34 ),
inference(sat_conversion,[],[f1788]) ).
cnf(s56,plain,
( ~ spl4_2
| ~ spl4_7
| spl4_51 ),
inference(sat_conversion,[],[f1981]) ).
cnf(s57,plain,
( ~ spl4_2
| ~ spl4_10
| ~ spl4_22
| ~ spl4_50
| spl4_53 ),
inference(sat_conversion,[],[f2411]) ).
cnf(s176,plain,
( spl4_1
| spl4_2
| ~ spl4_7
| spl4_16
| spl4_62 ),
inference(sat_conversion,[],[f7271]) ).
cnf(s181,plain,
( ~ spl4_7
| spl4_16
| ~ spl4_52
| ~ spl4_62 ),
inference(sat_conversion,[],[f7326]) ).
cnf(s243,plain,
spl4_23,
inference(rat,[],[s23,s8]) ).
cnf(s244,plain,
spl4_22,
inference(rat,[],[s15,s243,s8]) ).
cnf(s276,plain,
~ spl4_4,
inference(rat,[],[s2,s4]) ).
cnf(s277,plain,
~ spl4_34,
inference(rat,[],[s48,s276]) ).
cnf(s278,plain,
~ spl4_53,
inference(rat,[],[s47,s4,s20,s277]) ).
cnf(s280,plain,
spl4_52,
inference(rat,[],[s45,s278]) ).
cnf(s281,plain,
~ spl4_62,
inference(rat,[],[s181,s8,s20,s280]) ).
cnf(s282,plain,
spl4_1,
inference(rat,[],[s19,s176,s8,s20,s281]) ).
cnf(s283,plain,
spl4_2,
inference(rat,[],[s1,s282]) ).
cnf(s284,plain,
~ spl4_50,
inference(rat,[],[s57,s278,s244,s9,s283]) ).
cnf(s285,plain,
spl4_51,
inference(rat,[],[s56,s8,s283]) ).
cnf(s288,plain,
$false,
inference(rat,[],[s44,s8,s9,s285,s284]) ).
fof(f7344,plain,
$false,
inference(avatar_sat_refutation,[],[s288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM526+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 20:18:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.68/2.52 % (1755716)Detected formulas, will run a generic FOF schedule.
% 9.68/2.52 % (1755725)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3987257358:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 9.68/2.52 % (1755725)Instruction limit reached!
% 9.68/2.52 % (1755725)------------------------------
% 9.68/2.52 % (1755725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755725)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755725)Termination reason: Instruction limit
% 9.68/2.52 % (1755725)Termination phase: Saturation
% 9.68/2.52 % (1755725)Time elapsed: 0.039 s
% 9.68/2.52 % (1755725)Peak memory usage: 89 MB
% 9.68/2.52 % (1755725)Instructions burned: 120 (million)
% 9.68/2.52 % (1755723)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=1102472791:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 9.68/2.52 % (1755721)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=2991677925:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 9.68/2.52 % (1755722)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=4218563168:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 9.68/2.52 % (1755724)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3344861578:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 9.68/2.52 % (1755727)dis-21_1_sil=8000:lcm=predicate:random_seed=3824812850: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)
% 9.68/2.52 % (1755726)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=324939036:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 9.68/2.52 % (1755724)Instruction limit reached!
% 9.68/2.52 % (1755724)------------------------------
% 9.68/2.52 % (1755724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755724)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755724)Termination reason: Instruction limit
% 9.68/2.52 % (1755724)Termination phase: Saturation
% 9.68/2.52 % (1755724)Time elapsed: 0.064 s
% 9.68/2.52 % (1755724)Peak memory usage: 89 MB
% 9.68/2.52 % (1755724)Instructions burned: 111 (million)
% 9.68/2.52 % (1755727)Instruction limit reached!
% 9.68/2.52 % (1755727)------------------------------
% 9.68/2.52 % (1755727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755727)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755727)Termination reason: Instruction limit
% 9.68/2.52 % (1755727)Termination phase: Saturation
% 9.68/2.52 % (1755727)Time elapsed: 0.077 s
% 9.68/2.52 % (1755727)Peak memory usage: 91 MB
% 9.68/2.52 % (1755727)Instructions burned: 131 (million)
% 9.68/2.52 % (1755726)Instruction limit reached!
% 9.68/2.52 % (1755726)------------------------------
% 9.68/2.52 % (1755726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755726)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755726)Termination reason: Instruction limit
% 9.68/2.52 % (1755726)Termination phase: Saturation
% 9.68/2.52 % (1755726)Time elapsed: 0.090 s
% 9.68/2.52 % (1755726)Peak memory usage: 90 MB
% 9.68/2.52 % (1755726)Instructions burned: 140 (million)
% 9.68/2.52 % (1755729)lrs+10_1_sil=8000:sp=occurrence:random_seed=155350536:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 9.68/2.52 % (1755729)Instruction limit reached!
% 9.68/2.52 % (1755729)------------------------------
% 9.68/2.52 % (1755729)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755729)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755729)Termination reason: Instruction limit
% 9.68/2.52 % (1755729)Termination phase: Saturation
% 9.68/2.52 % (1755729)Time elapsed: 0.090 s
% 9.68/2.52 % (1755729)Peak memory usage: 91 MB
% 9.68/2.52 % (1755729)Instructions burned: 288 (million)
% 9.68/2.52 % (1755737)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2247134981:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 9.68/2.52 % (1755736)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3228149123:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 9.68/2.52 % (1755736)Refutation not found, incomplete strategy
% 9.68/2.52 % (1755736)------------------------------
% 9.68/2.52 % (1755736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755736)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755736)Termination reason: Refutation not found, incomplete strategy
% 9.68/2.52 % (1755736)Time elapsed: 0.005 s
% 9.68/2.52 % (1755736)Peak memory usage: 89 MB
% 9.68/2.52 % (1755736)Instructions burned: 7 (million)
% 9.68/2.52 % (1755738)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=96135761:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 9.68/2.52 % (1755740)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=325410611:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 9.68/2.52 % (1755738)Instruction limit reached!
% 9.68/2.52 % (1755738)------------------------------
% 9.68/2.52 % (1755738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755738)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755738)Termination reason: Instruction limit
% 9.68/2.52 % (1755738)Termination phase: Saturation
% 9.68/2.52 % (1755738)Time elapsed: 0.129 s
% 9.68/2.52 % (1755738)Peak memory usage: 92 MB
% 9.68/2.52 % (1755738)Instructions burned: 249 (million)
% 9.68/2.52 % (1755740)Instruction limit reached!
% 9.68/2.52 % (1755740)------------------------------
% 9.68/2.52 % (1755740)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755740)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755740)Termination reason: Instruction limit
% 9.68/2.52 % (1755740)Termination phase: Saturation
% 9.68/2.52 % (1755740)Time elapsed: 0.089 s
% 9.68/2.52 % (1755740)Peak memory usage: 90 MB
% 9.68/2.52 % (1755740)Instructions burned: 296 (million)
% 9.68/2.52 % (1755737)Instruction limit reached!
% 9.68/2.52 % (1755737)------------------------------
% 9.68/2.52 % (1755737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755737)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755737)Termination reason: Instruction limit
% 9.68/2.52 % (1755737)Termination phase: Saturation
% 9.68/2.52 % (1755737)Time elapsed: 0.201 s
% 9.68/2.52 % (1755737)Peak memory usage: 91 MB
% 9.68/2.52 % (1755737)Instructions burned: 326 (million)
% 9.68/2.52 % (1755736)------------------------------
% 9.68/2.52 % (1755736)------------------------------
% 9.68/2.52 % (1755745)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3308349921:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 9.68/2.52 % (1755746)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1687162533:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 9.68/2.52 % (1755746)Instruction limit reached!
% 9.68/2.52 % (1755746)------------------------------
% 9.68/2.52 % (1755746)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755746)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755746)Termination reason: Instruction limit
% 9.68/2.52 % (1755746)Termination phase: Saturation
% 9.68/2.52 % (1755746)Time elapsed: 0.038 s
% 9.68/2.52 % (1755746)Peak memory usage: 91 MB
% 9.68/2.52 % (1755746)Instructions burned: 116 (million)
% 9.68/2.52 % (1755747)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3892319420:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 9.68/2.52 % (1755748)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1189458888:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 9.68/2.52 % (1755747)Instruction limit reached!
% 9.68/2.52 % (1755747)------------------------------
% 9.68/2.52 % (1755747)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755747)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755747)Termination reason: Instruction limit
% 9.68/2.52 % (1755747)Termination phase: Saturation
% 9.68/2.52 % (1755747)Time elapsed: 0.065 s
% 9.68/2.52 % (1755747)Peak memory usage: 89 MB
% 9.68/2.52 % (1755747)Instructions burned: 129 (million)
% 9.68/2.52 % (1755752)lrs+10_1_sil=8000:sp=occurrence:random_seed=1085374243:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 9.68/2.52 % (1755748)Instruction limit reached!
% 9.68/2.52 % (1755748)------------------------------
% 9.68/2.52 % (1755748)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755748)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755748)Termination reason: Instruction limit
% 9.68/2.52 % (1755748)Termination phase: Saturation
% 9.68/2.52 % (1755748)Time elapsed: 0.064 s
% 9.68/2.52 % (1755748)Peak memory usage: 89 MB
% 9.68/2.52 % (1755748)Instructions burned: 115 (million)
% 9.68/2.52 % (1755754)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=479561522:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 9.68/2.52 % (1755756)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1411284098:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 9.68/2.52 % (1755752)Instruction limit reached!
% 9.68/2.52 % (1755752)------------------------------
% 9.68/2.52 % (1755752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755752)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755752)Termination reason: Instruction limit
% 9.68/2.52 % (1755752)Termination phase: Saturation
% 9.68/2.52 % (1755752)Time elapsed: 0.272 s
% 9.68/2.52 % (1755752)Peak memory usage: 98 MB
% 9.68/2.52 % (1755752)Instructions burned: 911 (million)
% 9.68/2.52 % (1755754)Instruction limit reached!
% 9.68/2.52 % (1755754)------------------------------
% 9.68/2.52 % (1755754)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755754)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755754)Termination reason: Instruction limit
% 9.68/2.52 % (1755754)Termination phase: Saturation
% 9.68/2.52 % (1755754)Time elapsed: 0.250 s
% 9.68/2.52 % (1755754)Peak memory usage: 92 MB
% 9.68/2.52 % (1755754)Instructions burned: 437 (million)
% 9.68/2.52 % (1755759)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3670869464:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 9.68/2.52 % (1755759)Instruction limit reached!
% 9.68/2.52 % (1755759)------------------------------
% 9.68/2.52 % (1755759)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.52 % (1755759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.52 % (1755759)CaDiCaL version: 2.1.3
% 9.68/2.52 % (1755759)Termination reason: Instruction limit
% 9.68/2.52 % (1755759)Termination phase: Saturation
% 9.68/2.52 % (1755759)Time elapsed: 0.034 s
% 9.68/2.52 % (1755759)Peak memory usage: 91 MB
% 9.68/2.52 % (1755759)Instructions burned: 136 (million)
% 9.68/2.52 % (1755760)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1657929740:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 9.68/2.52 % (1755721)First to succeed.
% 9.68/2.52 % (1755721)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1755716"
% 9.68/2.52 % (1755762)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1615306511:st=3:i=13193:sd=3:ss=axioms_2987 on theBenchmark for (2987ds/13193Mi)
% 9.68/2.52 % (1755721)Refutation found. Thanks to Tanya!
% 9.68/2.52 % SZS status Theorem for theBenchmark
% 9.68/2.52 % SZS output start Proof for theBenchmark
% See solution above
% 12.44/2.72 % (1755721)------------------------------
% 12.44/2.72 % (1755721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.44/2.72 % (1755721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.44/2.72 % (1755721)CaDiCaL version: 2.1.3
% 12.44/2.72 % (1755721)Termination reason: Refutation
% 12.44/2.72 % (1755721)Time elapsed: 1.234 s
% 12.44/2.72 % (1755721)Peak memory usage: 136 MB
% 12.44/2.72 % (1755721)Instructions burned: 1895 (million)
% 12.44/2.72 % (1755721)------------------------------
% 12.44/2.72 % (1755721)------------------------------
% 12.44/2.72 % (1755716)Success in time 1.671 s
% 12.44/2.72 % Vampire exiting
%------------------------------------------------------------------------------