%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM529+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:36 PM UTC 2026
% Result : ContradictoryAxioms 3.00s 1.41s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 110 ( 29 unt; 3 def)
% Number of atoms : 424 ( 160 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 511 ( 197 ~; 218 |; 79 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn 67 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != X1
& sdtlseqdt0(X0,X1) )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( X0 != sz00
& doDivides0(X0,X1) )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f40,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& xn != sz00
& xm != sz00
& xp != sz00 ),
file('/export/starexec/sandbox/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)
=> ~ ( ( X2 != sz10
& ! [X3] :
( ( aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,X2) )
=> ( X3 = sz10
| X3 = X2 ) ) )
| isPrime0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2963) ).
fof(f42,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3014) ).
fof(f43,axiom,
( xp != sz10
& ! [X0] :
( ( aNaturalNumber0(X0)
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtasdt0(X0,X1) )
| doDivides0(X0,xp) ) )
=> ( X0 = sz10
| X0 = xp ) )
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3025) ).
fof(f44,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xp,X0) )
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3046) ).
fof(f45,axiom,
( aNaturalNumber0(xq)
& xn = sdtasdt0(xp,xq)
& xq = sdtsldt0(xn,xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3059) ).
fof(f46,axiom,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3082) ).
fof(f47,axiom,
( xm != xn
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,X0) = xn )
& sdtlseqdt0(xm,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3124) ).
fof(f50,plain,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xn) = sdtasdt0(xp,X0) )
& doDivides0(xp,sdtasdt0(xn,xn))
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
& doDivides0(xp,xn) ),
inference(rectify,[],[f44]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( ( sz10 = X2
| ? [X3] :
( sz10 != X3
& X2 != X3
& aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,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(f55,plain,
! [X0,X1,X2] :
( ( ( sz10 = X2
| ? [X3] :
( sz10 != X3
& X2 != X3
& aNaturalNumber0(X3)
& ? [X4] :
( aNaturalNumber0(X4)
& X2 = sdtasdt0(X3,X4) )
& doDivides0(X3,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,[],[f54]) ).
fof(f56,plain,
( xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp) ),
inference(ennf_transformation,[],[f43]) ).
fof(f57,plain,
( xp != sz10
& ! [X0] :
( X0 = sz10
| X0 = xp
| ~ aNaturalNumber0(X0)
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != xp )
& ~ doDivides0(X0,xp) ) )
& isPrime0(xp) ),
inference(flattening,[],[f56]) ).
fof(f62,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f70,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f71,plain,
! [X0,X1] :
( iLess0(X0,X1)
| X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f70]) ).
fof(f76,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f77,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f76]) ).
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(f122,plain,
! [X0,X1,X2] :
( ( ( sz10 = X2
| ( sz10 != sK0(X2)
& sK0(X2) != X2
& aNaturalNumber0(sK0(X2))
& aNaturalNumber0(sK1(X2))
& sdtasdt0(sK0(X2),sK1(X2)) = X2
& doDivides0(sK0(X2),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(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X2)),skolemize(X4,sK1(X2))],[f55]) ).
fof(f123,plain,
( aNaturalNumber0(sK2)
& sdtasdt0(xn,xn) = sdtasdt0(xp,sK2)
& doDivides0(xp,sdtasdt0(xn,xn))
& aNaturalNumber0(sK3)
& xn = sdtasdt0(xp,sK3)
& doDivides0(xp,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f50]) ).
fof(f124,plain,
( xm != xn
& aNaturalNumber0(sK4)
& xn = sdtpldt0(xm,sK4)
& sdtlseqdt0(xm,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f47]) ).
fof(f133,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(nnf_transformation,[],[f93]) ).
fof(f134,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = sdtsldt0(X1,X0)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1 )
& ( ( aNaturalNumber0(X2)
& X1 = sdtasdt0(X0,X2) )
| sdtsldt0(X1,X0) != X2 ) )
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f133]) ).
fof(f138,plain,
sz00 != xp,
inference(cnf_transformation,[],[f40]) ).
fof(f139,plain,
sz00 != xm,
inference(cnf_transformation,[],[f40]) ).
fof(f140,plain,
sz00 != xn,
inference(cnf_transformation,[],[f40]) ).
fof(f141,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f142,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f143,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f40]) ).
fof(f144,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,[],[f122]) ).
fof(f151,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f152,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f57]) ).
fof(f159,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(cnf_transformation,[],[f123]) ).
fof(f160,plain,
sdtasdt0(xn,xn) = sdtasdt0(xp,sK2),
inference(cnf_transformation,[],[f123]) ).
fof(f161,plain,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f123]) ).
fof(f163,plain,
xn = sdtasdt0(xp,xq),
inference(cnf_transformation,[],[f45]) ).
fof(f164,plain,
aNaturalNumber0(xq),
inference(cnf_transformation,[],[f45]) ).
fof(f165,plain,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(cnf_transformation,[],[f46]) ).
fof(f166,plain,
sdtlseqdt0(xm,xn),
inference(cnf_transformation,[],[f124]) ).
fof(f169,plain,
xn != xm,
inference(cnf_transformation,[],[f124]) ).
fof(f174,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f62]) ).
fof(f192,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f195,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f207,plain,
! [X2,X0,X1] :
( sdtsldt0(X1,X0) = X2
| ~ aNaturalNumber0(X2)
| sdtasdt0(X0,X2) != X1
| sz00 = X0
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f240,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,[],[f207]) ).
fof(f271,plain,
sz00 = sdtasdt0(xp,sz00),
inference(resolution,[],[f174,f141]) ).
fof(f320,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sK2) ),
inference(superposition,[],[f195,f160]) ).
fof(f327,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sK2) ),
inference(forward_subsumption_resolution,[],[f320,f141]) ).
fof(f328,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(forward_subsumption_resolution,[],[f327,f161]) ).
fof(f345,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(superposition,[],[f195,f165]) ).
fof(f346,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
inference(forward_subsumption_resolution,[],[f345,f141]) ).
fof(f348,definition,
( spl9_3
<=> aNaturalNumber0(sdtasdt0(xq,xq)) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f350,plain,
( ~ aNaturalNumber0(sdtasdt0(xq,xq))
| spl9_3 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f352,definition,
( spl9_4
<=> aNaturalNumber0(sdtasdt0(xm,xm)) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f354,plain,
( aNaturalNumber0(sdtasdt0(xm,xm))
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f355,plain,
( ~ spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f346,f352,f348]) ).
fof(f356,plain,
( ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xq)
| spl9_3 ),
inference(resolution,[],[f350,f195]) ).
fof(f357,plain,
( ~ aNaturalNumber0(xq)
| spl9_3 ),
inference(duplicate_literal_removal,[],[f356]) ).
fof(f358,plain,
( $false
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f357,f164]) ).
fof(f359,plain,
spl9_3,
inference(avatar_contradiction_clause,[],[f358]) ).
fof(f502,definition,
( spl9_11
<=> sz00 = xq ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
fof(f503,plain,
( sz00 != xq
| spl9_11 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f504,plain,
( sz00 = xq
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f541,plain,
( xn = xm
| iLess0(xm,xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[],[f192,f166]) ).
fof(f550,plain,
( iLess0(xm,xn)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f541,f169]) ).
fof(f557,plain,
( iLess0(xm,xn)
| ~ aNaturalNumber0(xn) ),
inference(forward_subsumption_resolution,[],[f550,f142]) ).
fof(f569,plain,
iLess0(xm,xn),
inference(forward_subsumption_resolution,[],[f557,f143]) ).
fof(f722,plain,
( xn = sdtasdt0(xp,sz00)
| ~ spl9_11 ),
inference(superposition,[],[f163,f504]) ).
fof(f730,plain,
( sz00 = xn
| ~ spl9_11 ),
inference(forward_demodulation,[],[f722,f271]) ).
fof(f732,plain,
( $false
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f730,f140]) ).
fof(f733,plain,
~ spl9_11,
inference(avatar_contradiction_clause,[],[f732]) ).
fof(f1946,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,[],[f240,f151]) ).
fof(f1949,plain,
( ~ doDivides0(xp,sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sK2)
| sz00 = xp
| sK2 = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(superposition,[],[f240,f160]) ).
fof(f1971,plain,
( ~ aNaturalNumber0(sK2)
| sz00 = xp
| sK2 = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(forward_subsumption_resolution,[],[f1949,f159]) ).
fof(f1973,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,[],[f1946,f159]) ).
fof(f1986,plain,
( sz00 = xp
| sK2 = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(forward_subsumption_resolution,[],[f1971,f161]) ).
fof(f1988,plain,
( sz00 = xp
| sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f1973,f354]) ).
fof(f2000,plain,
( sK2 = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(forward_subsumption_resolution,[],[f1986,f138]) ).
fof(f2002,plain,
( sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f1988,f138]) ).
fof(f2014,plain,
( sK2 = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn)) ),
inference(forward_subsumption_resolution,[],[f2000,f141]) ).
fof(f2016,plain,
( sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xn))
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f2002,f141]) ).
fof(f2025,plain,
sK2 = sdtsldt0(sdtasdt0(xn,xn),xp),
inference(forward_subsumption_resolution,[],[f2014,f328]) ).
fof(f2027,plain,
( sdtasdt0(xm,xm) = sdtsldt0(sdtasdt0(xn,xn),xp)
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f2016,f328]) ).
fof(f2030,plain,
( sdtasdt0(xm,xm) = sK2
| ~ spl9_4 ),
inference(forward_demodulation,[],[f2027,f2025]) ).
fof(f2042,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,[],[f144,f165]) ).
fof(f2045,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,[],[f2042,f152]) ).
fof(f2047,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,[],[f2045,f164]) ).
fof(f2049,plain,
! [X0] :
( sdtasdt0(X0,X0) != sdtasdt0(xm,xm)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz00 = xq
| sz00 = xp ),
inference(forward_subsumption_resolution,[],[f2047,f141]) ).
fof(f2051,plain,
( ! [X0] :
( sdtasdt0(X0,X0) != sdtasdt0(xm,xm)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sz00 = xp )
| spl9_11 ),
inference(forward_subsumption_resolution,[],[f2049,f503]) ).
fof(f2053,plain,
( ! [X0] :
( sdtasdt0(X0,X0) != sdtasdt0(xm,xm)
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| sz00 = X0 )
| spl9_11 ),
inference(forward_subsumption_resolution,[],[f2051,f138]) ).
fof(f3632,plain,
( ! [X0] :
( sdtasdt0(X0,X0) != sK2
| ~ iLess0(X0,xn)
| ~ aNaturalNumber0(X0)
| sz00 = X0 )
| ~ spl9_4
| spl9_11 ),
inference(forward_demodulation,[],[f2053,f2030]) ).
fof(f6858,plain,
( sK2 != sK2
| ~ iLess0(xm,xn)
| ~ aNaturalNumber0(xm)
| sz00 = xm
| ~ spl9_4
| spl9_11 ),
inference(superposition,[],[f3632,f2030]) ).
fof(f6859,plain,
( ~ iLess0(xm,xn)
| ~ aNaturalNumber0(xm)
| sz00 = xm
| ~ spl9_4
| spl9_11 ),
inference(trivial_inequality_removal,[],[f6858]) ).
fof(f6860,plain,
( ~ aNaturalNumber0(xm)
| sz00 = xm
| ~ spl9_4
| spl9_11 ),
inference(forward_subsumption_resolution,[],[f6859,f569]) ).
fof(f6862,plain,
( sz00 = xm
| ~ spl9_4
| spl9_11 ),
inference(forward_subsumption_resolution,[],[f6860,f142]) ).
fof(f6864,plain,
( $false
| ~ spl9_4
| spl9_11 ),
inference(forward_subsumption_resolution,[],[f6862,f139]) ).
fof(f6865,plain,
( ~ spl9_4
| spl9_11 ),
inference(avatar_contradiction_clause,[],[f6864]) ).
cnf(s3,plain,
( ~ spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f355]) ).
cnf(s4,plain,
spl9_3,
inference(sat_conversion,[],[f359]) ).
cnf(s18,plain,
~ spl9_11,
inference(sat_conversion,[],[f733]) ).
cnf(s155,plain,
( ~ spl9_4
| spl9_11 ),
inference(sat_conversion,[],[f6865]) ).
cnf(s193,plain,
~ spl9_4,
inference(rat,[],[s155,s18]) ).
cnf(s201,plain,
$false,
inference(rat,[],[s3,s193,s4]) ).
fof(f6869,plain,
$false,
inference(avatar_sat_refutation,[],[s201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM529+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:27:31 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.00/1.41 % (3927332)Detected formulas, will run a generic FOF schedule.
% 3.00/1.41 % (3927341)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=927817549:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.00/1.41 % (3927342)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=116603219:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.00/1.41 % (3927338)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=3690380511:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.00/1.41 % (3927343)dis-21_1_sil=8000:lcm=predicate:random_seed=1846435861: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)
% 3.00/1.41 % (3927337)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=3631004522:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.00/1.41 % (3927339)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=3116502878:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.00/1.41 % (3927340)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3951980838:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.00/1.41 % (3927341)Instruction limit reached!
% 3.00/1.41 % (3927341)------------------------------
% 3.00/1.41 % (3927341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.41 % (3927341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.41 % (3927341)CaDiCaL version: 2.1.3
% 3.00/1.41 % (3927341)Termination reason: Instruction limit
% 3.00/1.41 % (3927341)Termination phase: Saturation
% 3.00/1.41 % (3927341)Time elapsed: 0.037 s
% 3.00/1.41 % (3927341)Peak memory usage: 88 MB
% 3.00/1.41 % (3927341)Instructions burned: 121 (million)
% 3.00/1.41 % (3927340)Instruction limit reached!
% 3.00/1.41 % (3927340)------------------------------
% 3.00/1.41 % (3927340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.41 % (3927340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.41 % (3927340)CaDiCaL version: 2.1.3
% 3.00/1.41 % (3927340)Termination reason: Instruction limit
% 3.00/1.41 % (3927340)Termination phase: Saturation
% 3.00/1.41 % (3927340)Time elapsed: 0.058 s
% 3.00/1.41 % (3927340)Peak memory usage: 89 MB
% 3.00/1.41 % (3927340)Instructions burned: 109 (million)
% 3.00/1.41 % (3927343)Instruction limit reached!
% 3.00/1.41 % (3927343)------------------------------
% 3.00/1.41 % (3927343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.41 % (3927343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.41 % (3927343)CaDiCaL version: 2.1.3
% 3.00/1.41 % (3927343)Termination reason: Instruction limit
% 3.00/1.41 % (3927343)Termination phase: Saturation
% 3.00/1.41 % (3927343)Time elapsed: 0.078 s
% 3.00/1.41 % (3927343)Peak memory usage: 91 MB
% 3.00/1.41 % (3927343)Instructions burned: 131 (million)
% 3.00/1.41 % (3927342)Instruction limit reached!
% 3.00/1.41 % (3927342)------------------------------
% 3.00/1.41 % (3927342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.41 % (3927342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.41 % (3927342)CaDiCaL version: 2.1.3
% 3.00/1.41 % (3927342)Termination reason: Instruction limit
% 3.00/1.41 % (3927342)Termination phase: Saturation
% 3.00/1.41 % (3927342)Time elapsed: 0.090 s
% 3.00/1.41 % (3927342)Peak memory usage: 90 MB
% 3.00/1.41 % (3927342)Instructions burned: 139 (million)
% 3.00/1.41 % (3927351)lrs+10_1_sil=8000:sp=occurrence:random_seed=331495807:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.00/1.41 % (3927351)First to succeed.
% 3.00/1.41 % (3927351)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3927332"
% 3.00/1.41 % (3927352)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2221461181:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.00/1.41 % (3927352)Refutation not found, incomplete strategy
% 3.00/1.41 % (3927352)------------------------------
% 3.00/1.41 % (3927352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.41 % (3927352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.41 % (3927352)CaDiCaL version: 2.1.3
% 3.00/1.41 % (3927352)Termination reason: Refutation not found, incomplete strategy
% 3.00/1.41 % (3927352)Time elapsed: 0.001 s
% 3.00/1.41 % (3927352)Peak memory usage: 87 MB
% 3.00/1.41 % (3927353)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2033018152:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.00/1.41 % (3927354)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=3225979065:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 3.00/1.41 % (3927351)Refutation found. Thanks to Tanya!
% 3.00/1.41 % SZS status ContradictoryAxioms for theBenchmark
% 3.00/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.60 % (3927351)------------------------------
% 0.17/1.60 % (3927351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.60 % (3927351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.60 % (3927351)CaDiCaL version: 2.1.3
% 0.17/1.60 % (3927351)Termination reason: Refutation
% 0.17/1.60 % (3927351)Time elapsed: 0.076 s
% 0.17/1.60 % (3927351)Peak memory usage: 92 MB
% 0.17/1.60 % (3927351)Instructions burned: 240 (million)
% 0.17/1.60 % (3927351)------------------------------
% 0.17/1.60 % (3927351)------------------------------
% 0.17/1.60 % (3927332)Success in time 0.538 s
% 0.17/1.60 % Vampire exiting
%------------------------------------------------------------------------------