%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM503+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 : n010.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 12:15:29 PM UTC 2026
% Result : Theorem 3.18s 1.95s
% Output : Refutation 7.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 31
% Syntax : Number of formulae : 222 ( 34 unt; 12 def)
% Number of atoms : 859 ( 191 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1095 ( 458 ~; 500 |; 98 &)
% ( 24 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 175 ( 0 sgn 162 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
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(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
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(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(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(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& doDivides0(X1,X0) )
=> ( X1 = sz10
| X1 = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f41,axiom,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f43,axiom,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
fof(f44,axiom,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(f45,axiom,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f50,axiom,
sdtlseqdt0(xp,xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2389) ).
fof(f51,conjecture,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f52,negated_conjecture,
~ ( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f58,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(ennf_transformation,[],[f52]) ).
fof(f67,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f68,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f67]) ).
fof(f75,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f80,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f81,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f80]) ).
fof(f86,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(f87,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,[],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f89,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f88]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f25]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0)) )
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f92]) ).
fof(f98,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f104,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f105,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f104]) ).
fof(f108,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(f109,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f108]) ).
fof(f116,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f117,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f116]) ).
fof(f118,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f119,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f118]) ).
fof(f125,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,[],[f68]) ).
fof(f126,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,[],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK0(X0,X1))
& sdtpldt0(X0,sK0(X0,X1)) = X1 )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(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,[],[f87]) ).
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,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,[],[f89]) ).
fof(f131,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ? [X3] :
( aNaturalNumber0(X3)
& sdtasdt0(X0,X3) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(rectify,[],[f130]) ).
fof(f132,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 ) )
& ( ( aNaturalNumber0(sK1(X0,X1))
& sdtasdt0(X0,sK1(X0,X1)) = X1 )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f131]) ).
fof(f134,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,[],[f109]) ).
fof(f135,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ? [X1] :
( sz10 != X1
& X0 != X1
& aNaturalNumber0(X1)
& doDivides0(X1,X0) ) )
& ( ( X0 != sz00
& X0 != sz10
& ! [X1] :
( X1 = sz10
| X1 = X0
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,X0) ) )
| ~ isPrime0(X0) ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f134]) ).
fof(f136,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,[],[f135]) ).
fof(f137,plain,
! [X0] :
( ( ( isPrime0(X0)
| sz00 = X0
| sz10 = X0
| ( sz10 != sK3(X0)
& sK3(X0) != X0
& aNaturalNumber0(sK3(X0))
& doDivides0(sK3(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,[sK3]),skolemize(X1,sK3(X0))],[f136]) ).
fof(f138,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f139,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f140,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f142,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f41]) ).
fof(f143,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f145,plain,
~ sdtlseqdt0(xp,xm),
inference(cnf_transformation,[],[f43]) ).
fof(f148,plain,
sdtlseqdt0(xn,xp),
inference(cnf_transformation,[],[f44]) ).
fof(f149,plain,
xn != xp,
inference(cnf_transformation,[],[f44]) ).
fof(f150,plain,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(cnf_transformation,[],[f45]) ).
fof(f160,plain,
sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f50]) ).
fof(f161,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f173,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f180,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f184,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f187,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f188,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f189,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)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f194,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f196,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| sz00 = X0
| X1 = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f202,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f207,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f213,plain,
! [X0] :
( sz00 != X0
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f222,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f224,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f119]) ).
fof(f229,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f233,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f173]) ).
fof(f234,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f189]) ).
fof(f235,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f188]) ).
fof(f236,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sz00 = X0
| sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f187]) ).
fof(f237,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f192]) ).
fof(f238,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(equality_resolution,[],[f213]) ).
fof(f244,plain,
~ isPrime0(sz00),
inference(forward_subsumption_resolution,[],[f238,f229]) ).
fof(f245,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f237,f207]) ).
fof(f246,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f234,f207]) ).
fof(f247,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f233,f184]) ).
fof(f250,definition,
( spl4_1
<=> sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f252,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| spl4_1 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl4_2
<=> sdtasdt0(xp,xm) = sdtasdt0(xp,xk) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f256,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f258,definition,
( spl4_3
<=> sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f260,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| spl4_3 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f262,definition,
( spl4_4
<=> sdtasdt0(xn,xm) = sdtasdt0(xp,xm) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f264,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f265,plain,
( ~ spl4_1
| spl4_2
| ~ spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f161,f262,f258,f254,f250]) ).
fof(f266,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f246,f245]) ).
fof(f314,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[],[f247,f180]) ).
fof(f317,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sz00) ),
inference(duplicate_literal_removal,[],[f314]) ).
fof(f318,plain,
! [X0] :
( sdtlseqdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f317,f229]) ).
fof(f329,definition,
( spl4_8
<=> aNaturalNumber0(sdtasdt0(xp,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f330,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f331,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| spl4_8 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f458,definition,
( spl4_10
<=> sz00 = xm ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
fof(f460,plain,
( sz00 = xm
| ~ spl4_10 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f571,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(superposition,[],[f235,f150]) ).
fof(f576,definition,
( spl4_14
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition]) ).
fof(f577,plain,
( aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f578,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_14 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f580,definition,
( spl4_15
<=> sz00 = xp ),
introduced(definition,[new_symbols(definition,[spl4_15])],[avatar_definition]) ).
fof(f581,plain,
( sz00 != xp
| spl4_15 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f582,plain,
( sz00 = xp
| ~ spl4_15 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f584,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl4_14 ),
inference(resolution,[],[f578,f207]) ).
fof(f585,plain,
( ~ aNaturalNumber0(xm)
| spl4_14 ),
inference(forward_subsumption_resolution,[],[f584,f140]) ).
fof(f586,plain,
( $false
| spl4_14 ),
inference(forward_subsumption_resolution,[],[f585,f139]) ).
fof(f587,plain,
spl4_14,
inference(avatar_contradiction_clause,[],[f586]) ).
fof(f588,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f571,f142]) ).
fof(f589,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(forward_subsumption_resolution,[],[f588,f138]) ).
fof(f590,plain,
( aNaturalNumber0(xk)
| sz00 = xp
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f589,f577]) ).
fof(f592,definition,
( spl4_16
<=> aNaturalNumber0(xk) ),
introduced(definition,[new_symbols(definition,[spl4_16])],[avatar_definition]) ).
fof(f594,plain,
( aNaturalNumber0(xk)
| ~ spl4_16 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f595,plain,
( spl4_15
| spl4_16
| ~ spl4_14 ),
inference(avatar_split_clause,[],[f590,f576,f592,f580]) ).
fof(f613,plain,
( isPrime0(sz00)
| ~ spl4_15 ),
inference(superposition,[],[f143,f582]) ).
fof(f630,plain,
( $false
| ~ spl4_15 ),
inference(forward_subsumption_resolution,[],[f613,f244]) ).
fof(f631,plain,
~ spl4_15,
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f665,plain,
! [X0] :
( ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f224,f145]) ).
fof(f666,plain,
! [X0] :
( ~ sdtlseqdt0(xp,X0)
| ~ sdtlseqdt0(X0,xm)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f665,f138]) ).
fof(f668,plain,
! [X0] :
( ~ sdtlseqdt0(X0,xm)
| ~ sdtlseqdt0(xp,X0)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f666,f139]) ).
fof(f670,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| spl4_8 ),
inference(resolution,[],[f331,f207]) ).
fof(f671,plain,
( ~ aNaturalNumber0(xm)
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f670,f138]) ).
fof(f672,plain,
( $false
| spl4_8 ),
inference(forward_subsumption_resolution,[],[f671,f139]) ).
fof(f673,plain,
spl4_8,
inference(avatar_contradiction_clause,[],[f672]) ).
fof(f843,plain,
( sz00 = xp
| sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(resolution,[],[f236,f142]) ).
fof(f862,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_15 ),
inference(forward_subsumption_resolution,[],[f843,f581]) ).
fof(f869,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl4_15 ),
inference(forward_subsumption_resolution,[],[f862,f138]) ).
fof(f885,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,sdtsldt0(sdtasdt0(xn,xm),xp))
| ~ spl4_14
| spl4_15 ),
inference(forward_subsumption_resolution,[],[f869,f577]) ).
fof(f886,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| ~ spl4_14
| spl4_15 ),
inference(forward_demodulation,[],[f885,f150]) ).
fof(f1146,plain,
( sz00 = xp
| xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| spl4_1 ),
inference(resolution,[],[f196,f252]) ).
fof(f1180,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| spl4_1
| spl4_15 ),
inference(forward_subsumption_resolution,[],[f1146,f581]) ).
fof(f1185,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| spl4_1
| spl4_15 ),
inference(forward_subsumption_resolution,[],[f1180,f138]) ).
fof(f1188,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| ~ aNaturalNumber0(xk)
| spl4_1
| spl4_15 ),
inference(forward_subsumption_resolution,[],[f1185,f139]) ).
fof(f1189,plain,
( xm = xk
| ~ sdtlseqdt0(xm,xk)
| spl4_1
| spl4_15
| ~ spl4_16 ),
inference(forward_subsumption_resolution,[],[f1188,f594]) ).
fof(f1191,definition,
( spl4_26
<=> sdtlseqdt0(xm,xk) ),
introduced(definition,[new_symbols(definition,[spl4_26])],[avatar_definition]) ).
fof(f1193,plain,
( ~ sdtlseqdt0(xm,xk)
| spl4_26 ),
inference(avatar_component_clause,[],[f1191]) ).
fof(f1195,definition,
( spl4_27
<=> xm = xk ),
introduced(definition,[new_symbols(definition,[spl4_27])],[avatar_definition]) ).
fof(f1197,plain,
( xm = xk
| ~ spl4_27 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f1201,plain,
( sdtlseqdt0(xk,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xk)
| spl4_26 ),
inference(resolution,[],[f1193,f222]) ).
fof(f1202,plain,
( sdtlseqdt0(xk,xm)
| ~ aNaturalNumber0(xk)
| spl4_26 ),
inference(forward_subsumption_resolution,[],[f1201,f139]) ).
fof(f1205,plain,
( sdtlseqdt0(xk,xm)
| ~ spl4_16
| spl4_26 ),
inference(forward_subsumption_resolution,[],[f1202,f594]) ).
fof(f1311,plain,
( sz00 = xm
| xn = xp
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| spl4_3 ),
inference(resolution,[],[f260,f194]) ).
fof(f1317,plain,
( sz00 = xm
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f1311,f149]) ).
fof(f1320,plain,
( sz00 = xm
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f1317,f148]) ).
fof(f1322,definition,
( spl4_28
<=> sz00 = sdtasdt0(xp,xm) ),
introduced(definition,[new_symbols(definition,[spl4_28])],[avatar_definition]) ).
fof(f1323,plain,
( sz00 != sdtasdt0(xp,xm)
| spl4_28 ),
inference(avatar_component_clause,[],[f1322]) ).
fof(f1324,plain,
( sz00 = sdtasdt0(xp,xm)
| ~ spl4_28 ),
inference(avatar_component_clause,[],[f1322]) ).
fof(f1330,plain,
( sz00 = xm
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f1320,f139]) ).
fof(f1331,plain,
( sz00 = xm
| ~ aNaturalNumber0(xp)
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f1330,f140]) ).
fof(f1332,plain,
( sz00 = xm
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f1331,f138]) ).
fof(f1333,plain,
( spl4_10
| spl4_3 ),
inference(avatar_split_clause,[],[f1332,f258,f458]) ).
fof(f1493,plain,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| ~ spl4_2
| ~ spl4_14
| spl4_15 ),
inference(forward_demodulation,[],[f256,f886]) ).
fof(f1552,plain,
( spl4_4
| ~ spl4_2
| ~ spl4_14
| spl4_15 ),
inference(avatar_split_clause,[],[f1493,f580,f576,f254,f262]) ).
fof(f1574,plain,
( xm = sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ aNaturalNumber0(xm)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ spl4_4 ),
inference(superposition,[],[f266,f264]) ).
fof(f1575,plain,
( xm = sdtsldt0(sdtasdt0(xn,xm),xp)
| sz00 = xp
| ~ aNaturalNumber0(xp)
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f1574,f139]) ).
fof(f1587,plain,
( xm = sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ aNaturalNumber0(xp)
| ~ spl4_4
| spl4_15 ),
inference(forward_subsumption_resolution,[],[f1575,f581]) ).
fof(f1598,plain,
( xm = sdtsldt0(sdtasdt0(xn,xm),xp)
| ~ spl4_4
| spl4_15 ),
inference(forward_subsumption_resolution,[],[f1587,f138]) ).
fof(f1645,plain,
( xm = xk
| ~ spl4_4
| spl4_15 ),
inference(superposition,[],[f150,f1598]) ).
fof(f1648,plain,
( spl4_27
| ~ spl4_4
| spl4_15 ),
inference(avatar_split_clause,[],[f1645,f580,f262,f1195]) ).
fof(f1653,plain,
( sdtlseqdt0(xp,xm)
| ~ spl4_27 ),
inference(superposition,[],[f160,f1197]) ).
fof(f1668,plain,
( $false
| ~ spl4_27 ),
inference(forward_subsumption_resolution,[],[f1653,f145]) ).
fof(f1669,plain,
~ spl4_27,
inference(avatar_contradiction_clause,[],[f1668]) ).
fof(f1681,plain,
( sz00 = sdtasdt0(xp,sz00)
| ~ spl4_10
| ~ spl4_28 ),
inference(forward_demodulation,[],[f1324,f460]) ).
fof(f1685,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xn,xm),X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) )
| spl4_3 ),
inference(resolution,[],[f260,f224]) ).
fof(f1689,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xn,xm),X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) )
| spl4_3
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f1685,f577]) ).
fof(f1691,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xn,xm),X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0) )
| spl4_3
| ~ spl4_8
| ~ spl4_14 ),
inference(forward_subsumption_resolution,[],[f1689,f330]) ).
fof(f1693,plain,
( ! [X0] :
( ~ sdtlseqdt0(sdtasdt0(xn,sz00),X0)
| ~ sdtlseqdt0(X0,sdtasdt0(xp,xm))
| ~ aNaturalNumber0(X0) )
| spl4_3
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(forward_demodulation,[],[f1691,f460]) ).
fof(f1695,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,sdtasdt0(xp,sz00))
| ~ sdtlseqdt0(sdtasdt0(xn,sz00),X0)
| ~ aNaturalNumber0(X0) )
| spl4_3
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14 ),
inference(forward_demodulation,[],[f1693,f460]) ).
fof(f1697,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(sdtasdt0(xn,sz00),X0)
| ~ aNaturalNumber0(X0) )
| spl4_3
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_28 ),
inference(forward_demodulation,[],[f1695,f1681]) ).
fof(f1734,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,sz00),sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sz00)
| spl4_3
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_28 ),
inference(resolution,[],[f1697,f318]) ).
fof(f1743,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,sz00),sz00)
| ~ aNaturalNumber0(sz00)
| spl4_3
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_28 ),
inference(duplicate_literal_removal,[],[f1734]) ).
fof(f1746,plain,
( ~ sdtlseqdt0(sdtasdt0(xn,sz00),sz00)
| spl4_3
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_28 ),
inference(forward_subsumption_resolution,[],[f1743,f229]) ).
fof(f1751,plain,
( ~ sdtlseqdt0(sz00,sz00)
| ~ aNaturalNumber0(xn)
| spl4_3
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_28 ),
inference(superposition,[],[f1746,f202]) ).
fof(f1752,plain,
( ~ sdtlseqdt0(sz00,sz00)
| spl4_3
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_28 ),
inference(forward_subsumption_resolution,[],[f1751,f140]) ).
fof(f1801,plain,
( ~ aNaturalNumber0(sz00)
| spl4_3
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_28 ),
inference(resolution,[],[f1752,f318]) ).
fof(f1812,plain,
( $false
| spl4_3
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_28 ),
inference(forward_subsumption_resolution,[],[f1801,f229]) ).
fof(f1813,plain,
( spl4_3
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_28 ),
inference(avatar_contradiction_clause,[],[f1812]) ).
fof(f1815,plain,
( sz00 != sdtasdt0(xp,sz00)
| ~ spl4_10
| spl4_28 ),
inference(forward_demodulation,[],[f1323,f460]) ).
fof(f1817,plain,
( sz00 != sz00
| ~ aNaturalNumber0(xp)
| ~ spl4_10
| spl4_28 ),
inference(superposition,[],[f1815,f202]) ).
fof(f1818,plain,
( ~ aNaturalNumber0(xp)
| ~ spl4_10
| spl4_28 ),
inference(trivial_inequality_removal,[],[f1817]) ).
fof(f1819,plain,
( $false
| ~ spl4_10
| spl4_28 ),
inference(forward_subsumption_resolution,[],[f1818,f138]) ).
fof(f1820,plain,
( ~ spl4_10
| spl4_28 ),
inference(avatar_contradiction_clause,[],[f1819]) ).
fof(f1822,plain,
( ~ spl4_26
| spl4_27
| spl4_1
| spl4_15
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f1189,f592,f580,f250,f1195,f1191]) ).
fof(f1871,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk)
| ~ spl4_16
| spl4_26 ),
inference(resolution,[],[f668,f1205]) ).
fof(f1889,plain,
( ~ aNaturalNumber0(xk)
| ~ spl4_16
| spl4_26 ),
inference(forward_subsumption_resolution,[],[f1871,f160]) ).
fof(f1894,plain,
( $false
| ~ spl4_16
| spl4_26 ),
inference(forward_subsumption_resolution,[],[f1889,f594]) ).
fof(f1895,plain,
( ~ spl4_16
| spl4_26 ),
inference(avatar_contradiction_clause,[],[f1894]) ).
cnf(s1,plain,
( ~ spl4_1
| spl4_2
| ~ spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f265]) ).
cnf(s13,plain,
spl4_14,
inference(sat_conversion,[],[f587]) ).
cnf(s14,plain,
( ~ spl4_14
| spl4_15
| spl4_16 ),
inference(sat_conversion,[],[f595]) ).
cnf(s17,plain,
~ spl4_15,
inference(sat_conversion,[],[f631]) ).
cnf(s18,plain,
spl4_8,
inference(sat_conversion,[],[f673]) ).
cnf(s32,plain,
( spl4_3
| spl4_10 ),
inference(sat_conversion,[],[f1333]) ).
cnf(s61,plain,
( ~ spl4_2
| spl4_4
| ~ spl4_14
| spl4_15 ),
inference(sat_conversion,[],[f1552]) ).
cnf(s64,plain,
( ~ spl4_4
| spl4_15
| spl4_27 ),
inference(sat_conversion,[],[f1648]) ).
cnf(s67,plain,
~ spl4_27,
inference(sat_conversion,[],[f1669]) ).
cnf(s77,plain,
( spl4_3
| ~ spl4_8
| ~ spl4_10
| ~ spl4_14
| ~ spl4_28 ),
inference(sat_conversion,[],[f1813]) ).
cnf(s78,plain,
( ~ spl4_10
| spl4_28 ),
inference(sat_conversion,[],[f1820]) ).
cnf(s79,plain,
( spl4_1
| spl4_15
| ~ spl4_16
| ~ spl4_26
| spl4_27 ),
inference(sat_conversion,[],[f1822]) ).
cnf(s80,plain,
( ~ spl4_16
| spl4_26 ),
inference(sat_conversion,[],[f1895]) ).
cnf(s83,plain,
( ~ spl4_4
| spl4_15 ),
inference(rat,[],[s64,s67]) ).
cnf(s90,plain,
~ spl4_4,
inference(rat,[],[s83,s17]) ).
cnf(s91,plain,
( ~ spl4_14
| spl4_16 ),
inference(rat,[],[s14,s17]) ).
cnf(s93,plain,
~ spl4_2,
inference(rat,[],[s61,s17,s90,s13]) ).
cnf(s94,plain,
spl4_16,
inference(rat,[],[s91,s13]) ).
cnf(s95,plain,
spl4_26,
inference(rat,[],[s80,s94]) ).
cnf(s98,plain,
spl4_1,
inference(rat,[],[s79,s67,s95,s17,s94]) ).
cnf(s104,plain,
~ spl4_3,
inference(rat,[],[s1,s90,s93,s98]) ).
cnf(s105,plain,
spl4_10,
inference(rat,[],[s32,s104]) ).
cnf(s107,plain,
spl4_28,
inference(rat,[],[s78,s105]) ).
cnf(s110,plain,
$false,
inference(rat,[],[s77,s104,s13,s18,s107,s105]) ).
fof(f1908,plain,
$false,
inference(avatar_sat_refutation,[],[s110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM503+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 % Computer : n010.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sun Sep 27 20:14:18 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.48 Running first-order theorem proving
% 0.18/0.48 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
% 3.18/1.95 % (1280146)Detected formulas, will run a generic FOF schedule.
% 3.18/1.95 % (1280168)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=1492298871:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.18/1.95 % (1280169)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=272757966:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.18/1.95 % (1280172)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=383330642:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.18/1.95 % (1280171)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4128342988:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.18/1.95 % (1280170)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=3857145085:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.18/1.95 % (1280173)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=323875154:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.18/1.95 % (1280174)dis-21_1_sil=8000:lcm=predicate:random_seed=1574818289: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)
% 3.18/1.95 % (1280172)Instruction limit reached!
% 3.18/1.95 % (1280172)------------------------------
% 3.18/1.95 % (1280172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.95 % (1280172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.95 % (1280172)CaDiCaL version: 2.1.3
% 3.18/1.95 % (1280172)Termination reason: Instruction limit
% 3.18/1.95 % (1280172)Termination phase: Saturation
% 3.18/1.95 % (1280172)Time elapsed: 0.107 s
% 3.18/1.95 % (1280172)Peak memory usage: 88 MB
% 3.18/1.95 % (1280172)Instructions burned: 120 (million)
% 3.18/1.95 % (1280171)Instruction limit reached!
% 3.18/1.95 % (1280171)------------------------------
% 3.18/1.95 % (1280171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.95 % (1280171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.95 % (1280171)CaDiCaL version: 2.1.3
% 3.18/1.95 % (1280171)Termination reason: Instruction limit
% 3.18/1.95 % (1280171)Termination phase: Saturation
% 3.18/1.95 % (1280171)Time elapsed: 0.113 s
% 3.18/1.95 % (1280171)Peak memory usage: 89 MB
% 3.18/1.95 % (1280171)Instructions burned: 110 (million)
% 3.18/1.95 % (1280174)Instruction limit reached!
% 3.18/1.95 % (1280174)------------------------------
% 3.18/1.95 % (1280174)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.95 % (1280174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.95 % (1280174)CaDiCaL version: 2.1.3
% 3.18/1.95 % (1280174)Termination reason: Instruction limit
% 3.18/1.95 % (1280174)Termination phase: Saturation
% 3.18/1.95 % (1280174)Time elapsed: 0.135 s
% 3.18/1.95 % (1280174)Peak memory usage: 90 MB
% 3.18/1.95 % (1280174)Instructions burned: 130 (million)
% 3.18/1.95 % (1280173)Instruction limit reached!
% 3.18/1.95 % (1280173)------------------------------
% 3.18/1.95 % (1280173)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.95 % (1280173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.95 % (1280173)CaDiCaL version: 2.1.3
% 3.18/1.95 % (1280173)Termination reason: Instruction limit
% 3.18/1.95 % (1280173)Termination phase: Saturation
% 3.18/1.95 % (1280173)Time elapsed: 0.149 s
% 3.18/1.95 % (1280173)Peak memory usage: 90 MB
% 3.18/1.95 % (1280173)Instructions burned: 140 (million)
% 3.18/1.95 % (1280184)lrs+10_1_sil=8000:sp=occurrence:random_seed=3376332865:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 3.18/1.95 % (1280185)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1924760517:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.18/1.95 % (1280186)lrs+1011_1_sil=32000:sp=occurrence:random_seed=7924483:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.18/1.95 % (1280188)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=2092511222:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 3.18/1.95 % (1280185)Instruction limit reached!
% 3.18/1.95 % (1280185)------------------------------
% 3.18/1.95 % (1280185)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.95 % (1280185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.95 % (1280185)CaDiCaL version: 2.1.3
% 3.18/1.95 % (1280185)Termination reason: Instruction limit
% 3.18/1.95 % (1280185)Termination phase: Saturation
% 3.18/1.95 % (1280185)Time elapsed: 0.102 s
% 3.18/1.95 % (1280185)Peak memory usage: 90 MB
% 3.18/1.95 % (1280185)Instructions burned: 158 (million)
% 3.18/1.95 % (1280186)First to succeed.
% 3.18/1.95 % (1280186)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1280146"
% 3.18/1.95 % (1280184)Instruction limit reached!
% 3.18/1.95 % (1280184)------------------------------
% 3.18/1.95 % (1280184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.95 % (1280184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.95 % (1280184)CaDiCaL version: 2.1.3
% 3.18/1.95 % (1280184)Termination reason: Instruction limit
% 3.18/1.95 % (1280184)Termination phase: Saturation
% 3.18/1.95 % (1280184)Time elapsed: 0.211 s
% 3.18/1.95 % (1280184)Peak memory usage: 91 MB
% 3.18/1.95 % (1280184)Instructions burned: 287 (million)
% 3.18/1.95 % (1280188)Instruction limit reached!
% 3.18/1.95 % (1280188)------------------------------
% 3.18/1.95 % (1280188)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.95 % (1280188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.95 % (1280188)CaDiCaL version: 2.1.3
% 3.18/1.95 % (1280188)Termination reason: Instruction limit
% 3.18/1.95 % (1280188)Termination phase: Saturation
% 3.18/1.95 % (1280188)Time elapsed: 0.113 s
% 3.18/1.95 % (1280188)Peak memory usage: 94 MB
% 3.18/1.95 % (1280188)Instructions burned: 250 (million)
% 3.18/1.95 % (1280194)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=297009982:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 3.18/1.95 % (1280168)Also succeeded, but the first one will report.
% 3.18/1.95 % (1280195)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4085021684:i=2350_2992 on theBenchmark for (2992ds/2350Mi)
% 3.18/1.95 % (1280196)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2624324542:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 3.18/1.95 % (1280194)Also succeeded, but the first one will report.
% 3.18/1.95 % (1280186)Refutation found. Thanks to Tanya!
% 3.18/1.95 % SZS status Theorem for theBenchmark
% 3.18/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 7.14/2.14 % (1280186)------------------------------
% 7.14/2.14 % (1280186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.14/2.14 % (1280186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.14/2.14 % (1280186)CaDiCaL version: 2.1.3
% 7.14/2.14 % (1280186)Termination reason: Refutation
% 7.14/2.14 % (1280186)Time elapsed: 0.061 s
% 7.14/2.14 % (1280186)Peak memory usage: 90 MB
% 7.14/2.14 % (1280186)Instructions burned: 77 (million)
% 7.14/2.14 % (1280186)------------------------------
% 7.14/2.14 % (1280186)------------------------------
% 7.14/2.14 % (1280146)Success in time 0.908 s
% 7.14/2.14 % Vampire exiting
%------------------------------------------------------------------------------