%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM473+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:24:27 PM UTC 2026
% Result : Theorem 4.09s 1.09s
% Output : Refutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 22
% Syntax : Number of formulae : 193 ( 54 unt; 4 def)
% Number of atoms : 652 ( 202 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 795 ( 336 ~; 346 |; 83 &)
% ( 12 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-2 aty)
% Number of variables : 167 ( 0 sgn 155 !; 12 ?)
% 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(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
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(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(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(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(f34,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f35,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X0) )
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
fof(f36,axiom,
xl != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1347) ).
fof(f37,axiom,
( aNaturalNumber0(xp)
& xm = sdtasdt0(xl,xp)
& xp = sdtsldt0(xm,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1360) ).
fof(f38,axiom,
( aNaturalNumber0(xq)
& sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
& xq = sdtsldt0(sdtpldt0(xm,xn),xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1379) ).
fof(f39,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = sdtpldt0(xm,xn) )
& sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1409) ).
fof(f40,conjecture,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xq )
| sdtlseqdt0(xp,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f41,negated_conjecture,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xq )
| sdtlseqdt0(xp,xq) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f44,plain,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X1) )
& doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(rectify,[],[f35]) ).
fof(f46,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f47,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f46]) ).
fof(f54,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f65,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(f66,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,[],[f65]) ).
fof(f73,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f74,plain,
! [X0,X1] :
( ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f73]) ).
fof(f76,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f77,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(ennf_transformation,[],[f22]) ).
fof(f79,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f81,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f80]) ).
fof(f84,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(f85,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,[],[f84]) ).
fof(f90,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f91,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f90]) ).
fof(f92,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(f93,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,[],[f92]) ).
fof(f98,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xq != sdtpldt0(xp,X0) )
& ~ sdtlseqdt0(xp,xq) ),
inference(ennf_transformation,[],[f41]) ).
fof(f102,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f74]) ).
fof(f103,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtmndt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& sdtpldt0(X0,X2) = X1 )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f102]) ).
fof(f104,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,[],[f91]) ).
fof(f105,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,[],[f104]) ).
fof(f106,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))],[f105]) ).
fof(f107,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,[],[f93]) ).
fof(f108,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,[],[f107]) ).
fof(f109,plain,
( aNaturalNumber0(sK2)
& xm = sdtasdt0(xl,sK2)
& doDivides0(xl,xm)
& aNaturalNumber0(sK3)
& sdtpldt0(xm,xn) = sdtasdt0(xl,sK3)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f44]) ).
fof(f110,plain,
( aNaturalNumber0(sK4)
& sdtpldt0(xm,xn) = sdtpldt0(xm,sK4)
& sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f39]) ).
fof(f111,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f114,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f119,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f54]) ).
fof(f131,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f138,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X2) = X1
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f140,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| ~ aNaturalNumber0(X2)
| sdtpldt0(X0,X2) != X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f142,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| sdtlseqdt0(X0,X2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f79]) ).
fof(f144,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f145,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| X0 != X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f152,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,[],[f85]) ).
fof(f157,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sdtasdt0(X0,sK1(X0,X1)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f158,plain,
! [X0,X1] :
( aNaturalNumber0(sK1(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f162,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,[],[f108]) ).
fof(f165,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f166,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f167,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f169,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sK3),
inference(cnf_transformation,[],[f109]) ).
fof(f171,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f109]) ).
fof(f172,plain,
xm = sdtasdt0(xl,sK2),
inference(cnf_transformation,[],[f109]) ).
fof(f173,plain,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f109]) ).
fof(f174,plain,
sz00 != xl,
inference(cnf_transformation,[],[f36]) ).
fof(f175,plain,
xp = sdtsldt0(xm,xl),
inference(cnf_transformation,[],[f37]) ).
fof(f176,plain,
xm = sdtasdt0(xl,xp),
inference(cnf_transformation,[],[f37]) ).
fof(f177,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f37]) ).
fof(f178,plain,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
inference(cnf_transformation,[],[f38]) ).
fof(f179,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(cnf_transformation,[],[f38]) ).
fof(f180,plain,
aNaturalNumber0(xq),
inference(cnf_transformation,[],[f38]) ).
fof(f181,plain,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f110]) ).
fof(f184,plain,
~ sdtlseqdt0(xp,xq),
inference(cnf_transformation,[],[f98]) ).
fof(f185,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| xq != sdtpldt0(xp,X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f187,plain,
! [X2,X0] :
( ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f140]) ).
fof(f189,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f138]) ).
fof(f190,plain,
! [X1] :
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X1) ),
inference(equality_resolution,[],[f145]) ).
fof(f193,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,[],[f162]) ).
fof(f196,definition,
! [X0] : sF5(X0) = sdtpldt0(xp,X0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f197,plain,
! [X0] : sdtpldt0(xp,X0) = sF5(X0),
inference(reorient_equations,[],[f196]) ).
fof(f198,plain,
! [X0] :
( xq != sF5(X0)
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f185,f197]) ).
fof(f199,plain,
! [X1] :
( sdtlseqdt0(X1,X1)
| ~ aNaturalNumber0(X1) ),
inference(duplicate_literal_removal,[],[f190]) ).
fof(f200,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(forward_demodulation,[],[f176,f175]) ).
fof(f201,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(forward_demodulation,[],[f177,f175]) ).
fof(f203,plain,
! [X0] : sF5(X0) = sdtpldt0(sdtsldt0(xm,xl),X0),
inference(forward_demodulation,[],[f197,f175]) ).
fof(f204,plain,
~ sdtlseqdt0(sdtsldt0(xm,xl),xq),
inference(superposition,[],[f184,f175]) ).
fof(f205,plain,
sdtlseqdt0(xm,sdtasdt0(xl,sK3)),
inference(superposition,[],[f181,f169]) ).
fof(f206,plain,
xq = sdtsldt0(sdtasdt0(xl,sK3),xl),
inference(superposition,[],[f178,f169]) ).
fof(f209,plain,
sdtasdt0(xl,xq) = sdtasdt0(xl,sK3),
inference(superposition,[],[f169,f179]) ).
fof(f212,plain,
sdtasdt0(xl,sK3) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xl,sK3),xl)),
inference(forward_demodulation,[],[f209,f206]) ).
fof(f228,plain,
sdtsldt0(xm,xl) = sdtpldt0(sdtsldt0(xm,xl),sz00),
inference(resolution,[],[f119,f201]) ).
fof(f233,plain,
sK2 = sdtpldt0(sK2,sz00),
inference(resolution,[],[f119,f173]) ).
fof(f237,plain,
sdtsldt0(xm,xl) = sF5(sz00),
inference(forward_demodulation,[],[f228,f203]) ).
fof(f297,plain,
( aNaturalNumber0(sdtasdt0(xl,sK3))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[],[f114,f169]) ).
fof(f300,plain,
( aNaturalNumber0(sdtasdt0(xl,sK3))
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f297,f166]) ).
fof(f304,plain,
aNaturalNumber0(sdtasdt0(xl,sK3)),
inference(forward_subsumption_resolution,[],[f300,f165]) ).
fof(f546,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,sK3),xm)
| xm = sdtasdt0(xl,sK3)
| ~ aNaturalNumber0(sdtasdt0(xl,sK3))
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f142,f205]) ).
fof(f559,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,sK3),xm)
| xm = sdtasdt0(xl,sK3)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f546,f304]) ).
fof(f561,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,sK3),xm)
| xm = sdtasdt0(xl,sK3) ),
inference(forward_subsumption_resolution,[],[f559,f166]) ).
fof(f755,plain,
( xm = sdtasdt0(xl,sK1(xl,xm))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[],[f157,f171]) ).
fof(f758,plain,
( xm = sdtasdt0(xl,sK1(xl,xm))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f755,f167]) ).
fof(f760,plain,
xm = sdtasdt0(xl,sK1(xl,xm)),
inference(forward_subsumption_resolution,[],[f758,f166]) ).
fof(f769,plain,
! [X0] :
( sdtpldt0(X0,sdtmndt0(X0,X0)) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f189,f199]) ).
fof(f781,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sdtmndt0(X0,X0)) = X0 ),
inference(duplicate_literal_removal,[],[f769]) ).
fof(f1490,definition,
( spl6_21
<=> xm = sdtasdt0(xl,sK3) ),
introduced(definition,[new_symbols(definition,[spl6_21])],[avatar_definition]) ).
fof(f1492,plain,
( xm = sdtasdt0(xl,sK3)
| ~ spl6_21 ),
inference(avatar_component_clause,[],[f1490]) ).
fof(f1494,definition,
( spl6_22
<=> sdtlseqdt0(sdtasdt0(xl,sK3),xm) ),
introduced(definition,[new_symbols(definition,[spl6_22])],[avatar_definition]) ).
fof(f1496,plain,
( ~ sdtlseqdt0(sdtasdt0(xl,sK3),xm)
| spl6_22 ),
inference(avatar_component_clause,[],[f1494]) ).
fof(f1497,plain,
( spl6_21
| ~ spl6_22 ),
inference(avatar_split_clause,[],[f561,f1494,f1490]) ).
fof(f1591,plain,
! [X0] :
( xm != sdtasdt0(xl,X0)
| sK2 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2)
| sz00 = xl
| ~ aNaturalNumber0(xl) ),
inference(superposition,[],[f131,f172]) ).
fof(f1592,plain,
! [X0] :
( xm != sdtasdt0(xl,X0)
| sdtsldt0(xm,xl) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| sz00 = xl
| ~ aNaturalNumber0(xl) ),
inference(superposition,[],[f131,f200]) ).
fof(f1605,plain,
! [X0] :
( xm != sdtasdt0(xl,X0)
| sdtsldt0(xm,xl) = X0
| ~ aNaturalNumber0(X0)
| sz00 = xl
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f1592,f201]) ).
fof(f1606,plain,
! [X0] :
( xm != sdtasdt0(xl,X0)
| sK2 = X0
| ~ aNaturalNumber0(X0)
| sz00 = xl
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f1591,f173]) ).
fof(f1619,plain,
! [X0] :
( xm != sdtasdt0(xl,X0)
| sdtsldt0(xm,xl) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f1605,f174]) ).
fof(f1620,plain,
! [X0] :
( xm != sdtasdt0(xl,X0)
| sK2 = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xl) ),
inference(forward_subsumption_resolution,[],[f1606,f174]) ).
fof(f1633,plain,
! [X0] :
( xm != sdtasdt0(xl,X0)
| sdtsldt0(xm,xl) = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f1619,f167]) ).
fof(f1634,plain,
! [X0] :
( xm != sdtasdt0(xl,X0)
| sK2 = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f1620,f167]) ).
fof(f2222,plain,
( ~ sdtlseqdt0(sK2,sK2)
| ~ aNaturalNumber0(sz00)
| sz00 = sdtmndt0(sK2,sK2)
| ~ aNaturalNumber0(sK2)
| ~ aNaturalNumber0(sK2) ),
inference(superposition,[],[f187,f233]) ).
fof(f2227,plain,
( ~ sdtlseqdt0(sK2,sK2)
| ~ aNaturalNumber0(sz00)
| sz00 = sdtmndt0(sK2,sK2)
| ~ aNaturalNumber0(sK2) ),
inference(duplicate_literal_removal,[],[f2222]) ).
fof(f2242,plain,
( ~ aNaturalNumber0(sz00)
| sz00 = sdtmndt0(sK2,sK2)
| ~ aNaturalNumber0(sK2) ),
inference(forward_subsumption_resolution,[],[f2227,f199]) ).
fof(f2262,plain,
( sz00 = sdtmndt0(sK2,sK2)
| ~ aNaturalNumber0(sK2) ),
inference(forward_subsumption_resolution,[],[f2242,f111]) ).
fof(f2279,plain,
sz00 = sdtmndt0(sK2,sK2),
inference(forward_subsumption_resolution,[],[f2262,f173]) ).
fof(f2425,plain,
! [X0] :
( sdtlseqdt0(sdtasdt0(xl,X0),xm)
| sz00 = xl
| sK2 = X0
| ~ sdtlseqdt0(X0,sK2)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2) ),
inference(superposition,[],[f152,f172]) ).
fof(f2438,plain,
! [X0] :
( sdtlseqdt0(sdtasdt0(xl,X0),xm)
| sK2 = X0
| ~ sdtlseqdt0(X0,sK2)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2) ),
inference(forward_subsumption_resolution,[],[f2425,f174]) ).
fof(f2458,plain,
! [X0] :
( sdtlseqdt0(sdtasdt0(xl,X0),xm)
| sK2 = X0
| ~ sdtlseqdt0(X0,sK2)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK2) ),
inference(forward_subsumption_resolution,[],[f2438,f167]) ).
fof(f2478,plain,
! [X0] :
( sdtlseqdt0(sdtasdt0(xl,X0),xm)
| sK2 = X0
| ~ sdtlseqdt0(X0,sK2)
| ~ aNaturalNumber0(X0) ),
inference(forward_subsumption_resolution,[],[f2458,f173]) ).
fof(f2574,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(sK2)
| sz00 = xl
| sdtsldt0(xm,xl) = sK2
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f193,f172]) ).
fof(f2590,plain,
( ~ aNaturalNumber0(sK2)
| sz00 = xl
| sdtsldt0(xm,xl) = sK2
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f2574,f171]) ).
fof(f2597,plain,
( sz00 = xl
| sdtsldt0(xm,xl) = sK2
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f2590,f173]) ).
fof(f2604,plain,
( sdtsldt0(xm,xl) = sK2
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f2597,f174]) ).
fof(f2611,plain,
( sdtsldt0(xm,xl) = sK2
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f2604,f167]) ).
fof(f2615,plain,
sdtsldt0(xm,xl) = sK2,
inference(forward_subsumption_resolution,[],[f2611,f166]) ).
fof(f3888,plain,
( sdtsldt0(xm,xl) != xq
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[],[f198,f237]) ).
fof(f3889,plain,
sdtsldt0(xm,xl) != xq,
inference(forward_subsumption_resolution,[],[f3888,f111]) ).
fof(f3890,plain,
sdtsldt0(xm,xl) != sdtsldt0(sdtasdt0(xl,sK3),xl),
inference(forward_demodulation,[],[f3889,f206]) ).
fof(f3986,plain,
~ sdtlseqdt0(sdtsldt0(xm,xl),sdtsldt0(sdtasdt0(xl,sK3),xl)),
inference(superposition,[],[f204,f206]) ).
fof(f3987,plain,
aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK3),xl)),
inference(superposition,[],[f180,f206]) ).
fof(f4357,definition,
( spl6_56
<=> aNaturalNumber0(sK1(xl,xm)) ),
introduced(definition,[new_symbols(definition,[spl6_56])],[avatar_definition]) ).
fof(f4358,plain,
( aNaturalNumber0(sK1(xl,xm))
| ~ spl6_56 ),
inference(avatar_component_clause,[],[f4357]) ).
fof(f4359,plain,
( ~ aNaturalNumber0(sK1(xl,xm))
| spl6_56 ),
inference(avatar_component_clause,[],[f4357]) ).
fof(f4752,plain,
! [X0] : sF5(X0) = sdtpldt0(sK2,X0),
inference(superposition,[],[f203,f2615]) ).
fof(f4757,plain,
~ sdtlseqdt0(sK2,sdtsldt0(sdtasdt0(xl,sK3),xl)),
inference(superposition,[],[f3986,f2615]) ).
fof(f6029,plain,
( ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| spl6_56 ),
inference(resolution,[],[f4359,f158]) ).
fof(f6030,plain,
( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| spl6_56 ),
inference(forward_subsumption_resolution,[],[f6029,f171]) ).
fof(f6031,plain,
( ~ aNaturalNumber0(xm)
| spl6_56 ),
inference(forward_subsumption_resolution,[],[f6030,f167]) ).
fof(f6032,plain,
( $false
| spl6_56 ),
inference(forward_subsumption_resolution,[],[f6031,f166]) ).
fof(f6033,plain,
spl6_56,
inference(avatar_contradiction_clause,[],[f6032]) ).
fof(f6733,plain,
sK2 = sdtpldt0(sK2,sdtmndt0(sK2,sK2)),
inference(resolution,[],[f781,f173]) ).
fof(f6739,plain,
sK2 = sF5(sdtmndt0(sK2,sK2)),
inference(forward_demodulation,[],[f6733,f4752]) ).
fof(f6756,plain,
sK2 = sF5(sz00),
inference(forward_demodulation,[],[f6739,f2279]) ).
fof(f6897,plain,
( xq != sK2
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[],[f198,f6756]) ).
fof(f6898,plain,
xq != sK2,
inference(forward_subsumption_resolution,[],[f6897,f111]) ).
fof(f6900,plain,
sK2 != sdtsldt0(sdtasdt0(xl,sK3),xl),
inference(forward_demodulation,[],[f6898,f206]) ).
fof(f7036,plain,
( xm != xm
| sK2 = sK1(xl,xm)
| ~ aNaturalNumber0(sK1(xl,xm)) ),
inference(superposition,[],[f1634,f760]) ).
fof(f7037,plain,
( sK2 = sK1(xl,xm)
| ~ aNaturalNumber0(sK1(xl,xm)) ),
inference(trivial_inequality_removal,[],[f7036]) ).
fof(f7039,plain,
( sK2 = sK1(xl,xm)
| ~ spl6_56 ),
inference(forward_subsumption_resolution,[],[f7037,f4358]) ).
fof(f8252,plain,
( xm != sdtasdt0(xl,sK3)
| sdtsldt0(xm,xl) = sdtsldt0(sdtasdt0(xl,sK3),xl)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK3),xl)) ),
inference(superposition,[],[f1633,f212]) ).
fof(f8816,plain,
( sdtlseqdt0(sdtasdt0(xl,sK3),xm)
| sK2 = sdtsldt0(sdtasdt0(xl,sK3),xl)
| ~ sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK3),xl),sK2)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK3),xl)) ),
inference(superposition,[],[f2478,f212]) ).
fof(f8956,plain,
( sdtsldt0(sdtasdt0(xl,sK3),xl) != sK1(xl,xm)
| ~ spl6_56 ),
inference(forward_demodulation,[],[f6900,f7039]) ).
fof(f13551,plain,
( sdtlseqdt0(sdtasdt0(xl,sK3),xm)
| sK2 = sdtsldt0(sdtasdt0(xl,sK3),xl)
| ~ sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK3),xl),sK2) ),
inference(forward_subsumption_resolution,[],[f8816,f3987]) ).
fof(f13556,plain,
( sdtsldt0(xm,xl) = sdtsldt0(sdtasdt0(xl,sK3),xl)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK3),xl))
| ~ spl6_21 ),
inference(forward_subsumption_resolution,[],[f8252,f1492]) ).
fof(f13564,plain,
( ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK3),xl))
| ~ spl6_21 ),
inference(forward_subsumption_resolution,[],[f13556,f3890]) ).
fof(f13571,plain,
( $false
| ~ spl6_21 ),
inference(forward_subsumption_resolution,[],[f13564,f3987]) ).
fof(f13572,plain,
~ spl6_21,
inference(avatar_contradiction_clause,[],[f13571]) ).
fof(f13574,plain,
( sK2 = sdtsldt0(sdtasdt0(xl,sK3),xl)
| ~ sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK3),xl),sK2)
| spl6_22 ),
inference(forward_subsumption_resolution,[],[f13551,f1496]) ).
fof(f13575,plain,
( sdtsldt0(sdtasdt0(xl,sK3),xl) = sK1(xl,xm)
| ~ sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK3),xl),sK2)
| spl6_22
| ~ spl6_56 ),
inference(forward_demodulation,[],[f13574,f7039]) ).
fof(f13576,plain,
( ~ sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK3),xl),sK2)
| spl6_22
| ~ spl6_56 ),
inference(forward_subsumption_resolution,[],[f13575,f8956]) ).
fof(f13577,plain,
( ~ sdtlseqdt0(sdtsldt0(sdtasdt0(xl,sK3),xl),sK1(xl,xm))
| spl6_22
| ~ spl6_56 ),
inference(forward_demodulation,[],[f13576,f7039]) ).
fof(f13728,plain,
( sdtlseqdt0(sK1(xl,xm),sdtsldt0(sdtasdt0(xl,sK3),xl))
| ~ aNaturalNumber0(sK1(xl,xm))
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK3),xl))
| spl6_22
| ~ spl6_56 ),
inference(resolution,[],[f13577,f144]) ).
fof(f13729,plain,
( sdtlseqdt0(sK1(xl,xm),sdtsldt0(sdtasdt0(xl,sK3),xl))
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK3),xl))
| spl6_22
| ~ spl6_56 ),
inference(forward_subsumption_resolution,[],[f13728,f4358]) ).
fof(f13735,plain,
( sdtlseqdt0(sK1(xl,xm),sdtsldt0(sdtasdt0(xl,sK3),xl))
| spl6_22
| ~ spl6_56 ),
inference(forward_subsumption_resolution,[],[f13729,f3987]) ).
fof(f13859,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,sK1(xl,xm))
| sdtlseqdt0(X0,sdtsldt0(sdtasdt0(xl,sK3),xl))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sK1(xl,xm))
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK3),xl)) )
| spl6_22
| ~ spl6_56 ),
inference(resolution,[],[f13735,f143]) ).
fof(f13865,plain,
( ! [X0] :
( ~ sdtlseqdt0(X0,sK1(xl,xm))
| sdtlseqdt0(X0,sdtsldt0(sdtasdt0(xl,sK3),xl))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtsldt0(sdtasdt0(xl,sK3),xl)) )
| spl6_22
| ~ spl6_56 ),
inference(forward_subsumption_resolution,[],[f13859,f4358]) ).
fof(f13866,plain,
( ! [X0] :
( sdtlseqdt0(X0,sdtsldt0(sdtasdt0(xl,sK3),xl))
| ~ sdtlseqdt0(X0,sK1(xl,xm))
| ~ aNaturalNumber0(X0) )
| spl6_22
| ~ spl6_56 ),
inference(forward_subsumption_resolution,[],[f13865,f3987]) ).
fof(f17050,plain,
( ~ sdtlseqdt0(sK2,sK1(xl,xm))
| ~ aNaturalNumber0(sK2)
| spl6_22
| ~ spl6_56 ),
inference(resolution,[],[f13866,f4757]) ).
fof(f17075,plain,
( ~ sdtlseqdt0(sK2,sK1(xl,xm))
| spl6_22
| ~ spl6_56 ),
inference(forward_subsumption_resolution,[],[f17050,f173]) ).
fof(f17085,plain,
( ~ sdtlseqdt0(sK1(xl,xm),sK1(xl,xm))
| spl6_22
| ~ spl6_56 ),
inference(forward_demodulation,[],[f17075,f7039]) ).
fof(f17176,plain,
( ~ aNaturalNumber0(sK1(xl,xm))
| spl6_22
| ~ spl6_56 ),
inference(resolution,[],[f17085,f199]) ).
fof(f17185,plain,
( $false
| spl6_22
| ~ spl6_56 ),
inference(forward_subsumption_resolution,[],[f17176,f4358]) ).
fof(f17186,plain,
( spl6_22
| ~ spl6_56 ),
inference(avatar_contradiction_clause,[],[f17185]) ).
cnf(s19,plain,
( spl6_21
| ~ spl6_22 ),
inference(sat_conversion,[],[f1497]) ).
cnf(s84,plain,
spl6_56,
inference(sat_conversion,[],[f6033]) ).
cnf(s157,plain,
~ spl6_21,
inference(sat_conversion,[],[f13572]) ).
cnf(s194,plain,
( spl6_22
| ~ spl6_56 ),
inference(sat_conversion,[],[f17186]) ).
cnf(s201,plain,
spl6_22,
inference(rat,[],[s194,s84]) ).
cnf(s235,plain,
$false,
inference(rat,[],[s19,s201,s157]) ).
fof(f17187,plain,
$false,
inference(avatar_sat_refutation,[],[s235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM473+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:07:58 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.42 Running first-order model finding
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.09/1.09 % (3176842)Will run a generic schedule for satisfiability detection.
% 4.09/1.09 % (3176851)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3970105612:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.09/1.09 % (3176848)% WARNING: option uhcvi not known.
% 4.09/1.09 % (3176847)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=653133446_2999 on theBenchmark for (2999ds/0Mi)
% 4.09/1.09 % (3176848)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1026016934:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.09/1.09 % (3176849)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4086625624:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.09/1.09 % (3176850)dis+10_1_sil=32000:sp=arity:random_seed=1642456762:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.09/1.09 % (3176853)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1580752204:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.09/1.09 % (3176852)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4237854507:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.09/1.09 % TRYING [1]
% 4.09/1.09 % TRYING [2]
% 4.09/1.09 % TRYING [3]
% 4.09/1.09 % TRYING [4]
% 4.09/1.09 % (3176851)Instruction limit reached!
% 4.09/1.09 % (3176851)------------------------------
% 4.09/1.09 % (3176851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.09/1.09 % (3176851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.09 % (3176851)CaDiCaL version: 2.1.3
% 4.09/1.09 % (3176851)Termination reason: Instruction limit
% 4.09/1.09 % (3176851)Termination phase: Saturation
% 4.09/1.09 % (3176851)Time elapsed: 0.036 s
% 4.09/1.09 % (3176851)Peak memory usage: 13 MB
% 4.09/1.09 % (3176851)Instructions burned: 117 (million)
% 4.09/1.09 % TRYING [5]
% 4.09/1.09 % (3176861)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1389687507:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.09/1.09 % TRYING [1]
% 4.09/1.09 % TRYING [2]
% 4.09/1.09 % TRYING [3]
% 4.09/1.09 % TRYING [4]
% 4.09/1.09 % (3176850)Instruction limit reached!
% 4.09/1.09 % (3176850)------------------------------
% 4.09/1.09 % (3176850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.09/1.09 % (3176850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.09 % (3176850)CaDiCaL version: 2.1.3
% 4.09/1.09 % (3176850)Termination reason: Instruction limit
% 4.09/1.09 % (3176850)Termination phase: Saturation
% 4.09/1.09 % (3176850)Time elapsed: 0.059 s
% 4.09/1.09 % (3176850)Peak memory usage: 12 MB
% 4.09/1.09 % (3176850)Instructions burned: 104 (million)
% 4.09/1.09 % TRYING [5]
% 4.09/1.09 % (3176852)Instruction limit reached!
% 4.09/1.09 % (3176852)------------------------------
% 4.09/1.09 % (3176852)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.09/1.09 % (3176852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.09 % (3176852)CaDiCaL version: 2.1.3
% 4.09/1.09 % (3176852)Termination reason: Instruction limit
% 4.09/1.09 % (3176852)Termination phase: Saturation
% 4.09/1.09 % (3176852)Time elapsed: 0.074 s
% 4.09/1.09 % (3176852)Peak memory usage: 13 MB
% 4.09/1.09 % (3176852)Instructions burned: 131 (million)
% 4.09/1.09 % (3176863)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=63040886:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 4.09/1.09 % (3176853)Instruction limit reached!
% 4.09/1.09 % (3176853)------------------------------
% 4.09/1.09 % (3176853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.09/1.09 % (3176853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.09 % (3176853)CaDiCaL version: 2.1.3
% 4.09/1.09 % (3176853)Termination reason: Instruction limit
% 4.09/1.09 % (3176853)Termination phase: Saturation
% 4.09/1.09 % (3176853)Time elapsed: 0.095 s
% 4.09/1.09 % (3176853)Peak memory usage: 15 MB
% 4.09/1.09 % (3176853)Instructions burned: 160 (million)
% 4.09/1.09 % (3176864)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2117262802:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 4.09/1.09 % TRYING [6]
% 4.09/1.09 % TRYING [6]
% 4.09/1.09 % (3176867)ott-21_1_sil=16000:fs=off:random_seed=2815278281:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 4.09/1.09 % (3176863)Instruction limit reached!
% 4.09/1.09 % (3176863)------------------------------
% 4.09/1.09 % (3176863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.09/1.09 % (3176863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.09 % (3176863)CaDiCaL version: 2.1.3
% 4.09/1.09 % (3176863)Termination reason: Instruction limit
% 4.09/1.09 % (3176863)Termination phase: Saturation
% 4.09/1.09 % (3176863)Time elapsed: 0.064 s
% 4.09/1.09 % (3176863)Peak memory usage: 12 MB
% 4.09/1.09 % (3176863)Instructions burned: 133 (million)
% 4.09/1.09 % (3176869)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2585210684:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 4.09/1.09 % (3176861)Instruction limit reached!
% 4.09/1.09 % (3176861)------------------------------
% 4.09/1.09 % (3176861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.09/1.09 % (3176861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.09 % (3176861)CaDiCaL version: 2.1.3
% 4.09/1.09 % (3176861)Termination reason: Instruction limit
% 4.09/1.09 % (3176861)Termination phase: Finite model building SAT solving
% 4.09/1.09 % (3176861)Time elapsed: 0.148 s
% 4.09/1.09 % (3176861)Peak memory usage: 34 MB
% 4.09/1.09 % (3176861)Instructions burned: 716 (million)
% 4.09/1.09 % (3176871)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3371986050:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 4.09/1.09 % TRYING [1]
% 4.09/1.09 % TRYING [2]
% 4.09/1.09 % TRYING [3]
% 4.09/1.09 % (3176867)Instruction limit reached!
% 4.09/1.09 % (3176867)------------------------------
% 4.09/1.09 % (3176867)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.09/1.09 % (3176867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.09 % (3176867)CaDiCaL version: 2.1.3
% 4.09/1.09 % (3176867)Termination reason: Instruction limit
% 4.09/1.09 % (3176867)Termination phase: Saturation
% 4.09/1.09 % (3176867)Time elapsed: 0.090 s
% 4.09/1.09 % (3176867)Peak memory usage: 13 MB
% 4.09/1.09 % (3176867)Instructions burned: 181 (million)
% 4.09/1.09 % TRYING [4]
% 4.09/1.09 % (3176873)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3850329778:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 4.09/1.09 % TRYING [5]
% 4.09/1.09 % TRYING [7]
% 4.09/1.09 % TRYING [6]
% 4.09/1.09 % (3176871)Instruction limit reached!
% 4.09/1.09 % (3176871)------------------------------
% 4.09/1.09 % (3176871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.09/1.09 % (3176871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.09 % (3176871)CaDiCaL version: 2.1.3
% 4.09/1.09 % (3176871)Termination reason: Instruction limit
% 4.09/1.09 % (3176871)Termination phase: Finite model building constraint generation
% 4.09/1.09 % (3176871)Time elapsed: 0.179 s
% 4.09/1.09 % (3176871)Peak memory usage: 22 MB
% 4.09/1.09 % (3176871)Instructions burned: 868 (million)
% 4.09/1.09 % (3176875)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1410620778:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 4.09/1.09 % (3176864)Instruction limit reached!
% 4.09/1.09 % (3176864)------------------------------
% 4.09/1.09 % (3176864)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.09/1.09 % (3176864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.09 % (3176864)CaDiCaL version: 2.1.3
% 4.09/1.09 % (3176864)Termination reason: Instruction limit
% 4.09/1.09 % (3176864)Termination phase: Saturation
% 4.09/1.09 % (3176864)Time elapsed: 0.324 s
% 4.09/1.09 % (3176864)Peak memory usage: 19 MB
% 4.09/1.09 % (3176864)Instructions burned: 684 (million)
% 4.09/1.09 % (3176869)Instruction limit reached!
% 4.09/1.09 % (3176869)------------------------------
% 4.09/1.09 % (3176869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.09/1.09 % (3176869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.09 % (3176869)CaDiCaL version: 2.1.3
% 4.09/1.09 % (3176869)Termination reason: Instruction limit
% 4.09/1.09 % (3176869)Termination phase: Saturation
% 4.09/1.09 % (3176869)Time elapsed: 0.256 s
% 4.09/1.09 % (3176869)Peak memory usage: 15 MB
% 4.09/1.09 % (3176869)Instructions burned: 477 (million)
% 4.09/1.09 % (3176877)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1956072939:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2995 on theBenchmark for (2995ds/692Mi)
% 4.09/1.09 % (3176878)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3631296687:i=879:kws=inv_precedence:fsr=off_2995 on theBenchmark for (2995ds/879Mi)
% 4.09/1.09 % TRYING [14]
% 4.09/1.09 % (3176875)Instruction limit reached!
% 4.09/1.09 % (3176875)------------------------------
% 4.09/1.09 % (3176875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.09/1.09 % (3176875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.09 % (3176875)CaDiCaL version: 2.1.3
% 4.09/1.09 % (3176875)Termination reason: Instruction limit
% 4.09/1.09 % (3176875)Termination phase: Finite model building constraint generation
% 4.09/1.09 % (3176875)Time elapsed: 0.182 s
% 4.09/1.09 % (3176875)Peak memory usage: 73 MB
% 4.09/1.09 % (3176875)Instructions burned: 892 (million)
% 4.09/1.09 % (3176881)fmb+10_1_sil=64000:random_seed=1827386851:i=22061:nm=2:gsp=on_2993 on theBenchmark for (2993ds/22061Mi)
% 4.09/1.09 % TRYING [1]
% 4.09/1.09 % TRYING [2]
% 4.09/1.09 % TRYING [3]
% 4.09/1.09 % TRYING [4]
% 4.09/1.09 % (3176873) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3176842-3176873"...
% 4.09/1.09 % (3176873)...printing done.
% 4.09/1.09 % (3176873)Refutation found. Thanks to Tanya!
% 4.09/1.09 % SZS status Theorem for theBenchmark
% 4.09/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 4.09/1.09 % (3176873)------------------------------
% 4.09/1.09 % (3176873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.09/1.09 % (3176873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.09/1.09 % (3176873)CaDiCaL version: 2.1.3
% 4.09/1.09 % (3176873)Termination reason: Refutation
% 4.09/1.09 % (3176873)Time elapsed: 0.390 s
% 4.09/1.09 % (3176873)Peak memory usage: 19 MB
% 4.09/1.09 % (3176873)Instructions burned: 725 (million)
% 4.09/1.09 % (3176842)Success in time 0.663 s
% 4.09/1.09 % Vampire exiting
%------------------------------------------------------------------------------