%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG049+2 : 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 : n004.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 12:35:17 PM UTC 2026
% Result : Theorem 5.85s 1.67s
% Output : Refutation 7.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 97 ( 26 unt; 6 def)
% Number of atoms : 253 ( 41 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 264 ( 108 ~; 107 |; 28 &)
% ( 5 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> iLess0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X0)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(f26,axiom,
! [X0,X1] :
( ( aScalar0(X0)
& aScalar0(X1) )
=> ( ( sdtlseqdt0(sz0z00,X0)
& sdtlseqdt0(sz0z00,X1) )
=> ( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
& sdtlseqdt0(sz0z00,sdtasdt0(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPosMon) ).
fof(f30,axiom,
! [X0] :
( aVector0(X0)
=> aNaturalNumber0(aDimensionOf0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(f31,axiom,
! [X0,X1] :
( ( aVector0(X0)
& aNaturalNumber0(X1) )
=> aScalar0(sdtlbdtrb0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mElmSc) ).
fof(f34,axiom,
! [X0,X1] :
( ( aVector0(X0)
& aVector0(X1) )
=> ( aDimensionOf0(X0) = aDimensionOf0(X1)
=> aScalar0(sdtasasdt0(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mScPr) ).
fof(f36,axiom,
! [X0,X1] :
( ( aVector0(X0)
& aVector0(X1) )
=> ( ( aDimensionOf0(X0) = aDimensionOf0(X1)
& aDimensionOf0(X1) != sz00 )
=> sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSPN) ).
fof(f37,axiom,
aVector0(xs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542) ).
fof(f38,axiom,
! [X0] :
( aVector0(X0)
=> ( iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
=> sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1516) ).
fof(f39,axiom,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1542_01) ).
fof(f41,axiom,
( aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
& aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
& sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1590) ).
fof(f42,conjecture,
sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f50,plain,
( aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) )
& aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(sziznziztdt0(xs),X1) = sdtlbdtrb0(xs,X1) )
& sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(rectify,[],[f41]) ).
fof(f51,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(flattening,[],[f43]) ).
fof(f57,plain,
! [X0] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f60,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f61,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(flattening,[],[f60]) ).
fof(f85,plain,
! [X0,X1] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
& sdtlseqdt0(sz0z00,sdtasdt0(X0,X1)) )
| ~ sdtlseqdt0(sz0z00,X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f86,plain,
! [X0,X1] :
( ( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
& sdtlseqdt0(sz0z00,sdtasdt0(X0,X1)) )
| ~ sdtlseqdt0(sz0z00,X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(flattening,[],[f85]) ).
fof(f90,plain,
! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f91,plain,
! [X0,X1] :
( aScalar0(sdtlbdtrb0(X0,X1))
| ~ aVector0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f92,plain,
! [X0,X1] :
( aScalar0(sdtlbdtrb0(X0,X1))
| ~ aVector0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f91]) ).
fof(f97,plain,
! [X0,X1] :
( aScalar0(sdtasasdt0(X0,X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f98,plain,
! [X0,X1] :
( aScalar0(sdtasasdt0(X0,X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(flattening,[],[f97]) ).
fof(f101,plain,
! [X0,X1] :
( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sz00 = aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f102,plain,
! [X0,X1] :
( sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sz00 = aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(flattening,[],[f101]) ).
fof(f103,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f104,plain,
! [X0] :
( sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| ~ aVector0(X0) ),
inference(flattening,[],[f103]) ).
fof(f106,plain,
( aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X0] :
( sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0)
| ~ aNaturalNumber0(X0) )
& aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X1] :
( sdtlbdtrb0(sziznziztdt0(xs),X1) = sdtlbdtrb0(xs,X1)
| ~ aNaturalNumber0(X1) )
& sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(ennf_transformation,[],[f50]) ).
fof(f118,plain,
! [X0] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f121,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f148,plain,
! [X0,X1] :
( sdtlseqdt0(sz0z00,sdtpldt0(X0,X1))
| ~ sdtlseqdt0(sz0z00,X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f151,plain,
! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f152,plain,
! [X0,X1] :
( aScalar0(sdtlbdtrb0(X0,X1))
| ~ aVector0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f159,plain,
! [X0,X1] :
( aDimensionOf0(X0) != aDimensionOf0(X1)
| aScalar0(sdtasasdt0(X0,X1))
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f161,plain,
! [X0,X1] :
( aDimensionOf0(X0) != aDimensionOf0(X1)
| sdtasasdt0(X0,X1) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X1)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X1,aDimensionOf0(X1))))
| sz00 = aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f162,plain,
aVector0(xs),
inference(cnf_transformation,[],[f37]) ).
fof(f163,plain,
! [X0] :
( ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| sdtlseqdt0(sz0z00,sdtasasdt0(X0,X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f164,plain,
sz00 != aDimensionOf0(xs),
inference(cnf_transformation,[],[f39]) ).
fof(f171,plain,
sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(cnf_transformation,[],[f106]) ).
fof(f173,plain,
aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))),
inference(cnf_transformation,[],[f106]) ).
fof(f174,plain,
aVector0(sziznziztdt0(xs)),
inference(cnf_transformation,[],[f106]) ).
fof(f178,plain,
~ sdtlseqdt0(sz0z00,sdtasasdt0(xs,xs)),
inference(cnf_transformation,[],[f51]) ).
fof(f182,definition,
sF2 = sdtasasdt0(xs,xs),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f183,plain,
sdtasasdt0(xs,xs) = sF2,
inference(reorient_equations,[],[f182]) ).
fof(f184,plain,
~ sdtlseqdt0(sz0z00,sF2),
inference(definition_folding,[],[f178,f183]) ).
fof(f201,plain,
! [X0] :
( aScalar0(sdtasasdt0(X0,X0))
| ~ aVector0(X0)
| ~ aVector0(X0) ),
inference(equality_resolution,[],[f159]) ).
fof(f202,plain,
! [X0] :
( aScalar0(sdtasasdt0(X0,X0))
| ~ aVector0(X0) ),
inference(duplicate_literal_removal,[],[f201]) ).
fof(f209,plain,
! [X0] :
( sdtasasdt0(X0,X0) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X0)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X0,aDimensionOf0(X0))))
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0)
| ~ aVector0(X0) ),
inference(equality_resolution,[],[f161]) ).
fof(f210,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| sdtasasdt0(X0,X0) = sdtpldt0(sdtasasdt0(sziznziztdt0(X0),sziznziztdt0(X0)),sdtasdt0(sdtlbdtrb0(X0,aDimensionOf0(X0)),sdtlbdtrb0(X0,aDimensionOf0(X0)))) ),
inference(duplicate_literal_removal,[],[f209]) ).
fof(f211,plain,
( sz00 = aDimensionOf0(xs)
| sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(resolution,[],[f210,f162]) ).
fof(f223,plain,
sdtasasdt0(xs,xs) = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(forward_subsumption_resolution,[],[f211,f164]) ).
fof(f224,plain,
sF2 = sdtpldt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))),
inference(forward_demodulation,[],[f223,f183]) ).
fof(f242,plain,
( sdtlseqdt0(sz0z00,sF2)
| ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(superposition,[],[f148,f224]) ).
fof(f243,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ sdtlseqdt0(sz0z00,sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(forward_subsumption_resolution,[],[f242,f184]) ).
fof(f244,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
inference(forward_subsumption_resolution,[],[f243,f171]) ).
fof(f246,definition,
( spl3_8
<=> aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs)))) ),
introduced(definition,[new_symbols(definition,[spl3_8])],[avatar_definition]) ).
fof(f248,plain,
( ~ aScalar0(sdtasdt0(sdtlbdtrb0(xs,aDimensionOf0(xs)),sdtlbdtrb0(xs,aDimensionOf0(xs))))
| spl3_8 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f250,definition,
( spl3_9
<=> aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f252,plain,
( ~ aScalar0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| spl3_9 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f254,definition,
( spl3_10
<=> sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs))) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f256,plain,
( ~ sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| spl3_10 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f257,plain,
( ~ spl3_8
| ~ spl3_9
| ~ spl3_10 ),
inference(avatar_split_clause,[],[f244,f254,f250,f246]) ).
fof(f258,plain,
( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| spl3_8 ),
inference(resolution,[],[f248,f121]) ).
fof(f259,plain,
( ~ aScalar0(sdtlbdtrb0(xs,aDimensionOf0(xs)))
| spl3_8 ),
inference(duplicate_literal_removal,[],[f258]) ).
fof(f260,plain,
( ~ aVector0(xs)
| ~ aNaturalNumber0(aDimensionOf0(xs))
| spl3_8 ),
inference(resolution,[],[f259,f152]) ).
fof(f261,plain,
( ~ aNaturalNumber0(aDimensionOf0(xs))
| spl3_8 ),
inference(forward_subsumption_resolution,[],[f260,f162]) ).
fof(f262,plain,
( ~ aVector0(xs)
| spl3_8 ),
inference(resolution,[],[f261,f151]) ).
fof(f263,plain,
( $false
| spl3_8 ),
inference(forward_subsumption_resolution,[],[f262,f162]) ).
fof(f264,plain,
spl3_8,
inference(avatar_contradiction_clause,[],[f263]) ).
fof(f265,plain,
( ~ aVector0(sziznziztdt0(xs))
| spl3_9 ),
inference(resolution,[],[f252,f202]) ).
fof(f266,plain,
( $false
| spl3_9 ),
inference(forward_subsumption_resolution,[],[f265,f174]) ).
fof(f267,plain,
spl3_9,
inference(avatar_contradiction_clause,[],[f266]) ).
fof(f327,plain,
( iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(superposition,[],[f118,f173]) ).
fof(f334,definition,
( spl3_11
<=> aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
fof(f336,plain,
( ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| spl3_11 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f348,definition,
( spl3_14
<=> iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs)) ),
introduced(definition,[new_symbols(definition,[spl3_14])],[avatar_definition]) ).
fof(f350,plain,
( iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| ~ spl3_14 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f351,plain,
( ~ spl3_11
| spl3_14 ),
inference(avatar_split_clause,[],[f327,f348,f334]) ).
fof(f352,plain,
( ~ aVector0(sziznziztdt0(xs))
| spl3_11 ),
inference(resolution,[],[f336,f151]) ).
fof(f353,plain,
( $false
| spl3_11 ),
inference(forward_subsumption_resolution,[],[f352,f174]) ).
fof(f354,plain,
spl3_11,
inference(avatar_contradiction_clause,[],[f353]) ).
fof(f415,plain,
( sdtlseqdt0(sz0z00,sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xs))
| ~ spl3_14 ),
inference(resolution,[],[f350,f163]) ).
fof(f416,plain,
( ~ aVector0(sziznziztdt0(xs))
| spl3_10
| ~ spl3_14 ),
inference(forward_subsumption_resolution,[],[f415,f256]) ).
fof(f417,plain,
( $false
| spl3_10
| ~ spl3_14 ),
inference(forward_subsumption_resolution,[],[f416,f174]) ).
fof(f418,plain,
( spl3_10
| ~ spl3_14 ),
inference(avatar_contradiction_clause,[],[f417]) ).
cnf(s6,plain,
( ~ spl3_8
| ~ spl3_9
| ~ spl3_10 ),
inference(sat_conversion,[],[f257]) ).
cnf(s7,plain,
spl3_8,
inference(sat_conversion,[],[f264]) ).
cnf(s8,plain,
spl3_9,
inference(sat_conversion,[],[f267]) ).
cnf(s13,plain,
( ~ spl3_11
| spl3_14 ),
inference(sat_conversion,[],[f351]) ).
cnf(s14,plain,
spl3_11,
inference(sat_conversion,[],[f354]) ).
cnf(s19,plain,
( spl3_10
| ~ spl3_14 ),
inference(sat_conversion,[],[f418]) ).
cnf(s20,plain,
spl3_14,
inference(rat,[],[s13,s14]) ).
cnf(s21,plain,
spl3_10,
inference(rat,[],[s19,s20]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s6,s21,s8,s7]) ).
fof(f419,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG049+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 23:02:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 5.85/1.67 % (3989567)Detected formulas, will run a generic FOF schedule.
% 5.85/1.67 % (3989577)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=885215283:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.85/1.67 % (3989576)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2469865094:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.85/1.67 % (3989573)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=131424616:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.85/1.67 % (3989578)dis-21_1_sil=8000:lcm=predicate:random_seed=1469809220: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)
% 5.85/1.67 % (3989575)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=639385264:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.85/1.67 % (3989572)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=1524582038:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.85/1.67 % (3989574)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=4105197642:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.85/1.67 % (3989577)Instruction limit reached!
% 5.85/1.67 % (3989577)------------------------------
% 5.85/1.67 % (3989577)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.67 % (3989577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.67 % (3989577)CaDiCaL version: 2.1.3
% 5.85/1.67 % (3989577)Termination reason: Instruction limit
% 5.85/1.67 % (3989577)Termination phase: Saturation
% 5.85/1.67 % (3989577)Time elapsed: 0.047 s
% 5.85/1.67 % (3989577)Peak memory usage: 90 MB
% 5.85/1.67 % (3989577)Instructions burned: 139 (million)
% 5.85/1.67 % (3989576)Instruction limit reached!
% 5.85/1.67 % (3989576)------------------------------
% 5.85/1.67 % (3989576)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.67 % (3989576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.67 % (3989576)CaDiCaL version: 2.1.3
% 5.85/1.67 % (3989576)Termination reason: Instruction limit
% 5.85/1.67 % (3989576)Termination phase: Saturation
% 5.85/1.67 % (3989576)Time elapsed: 0.050 s
% 5.85/1.67 % (3989576)Peak memory usage: 88 MB
% 5.85/1.67 % (3989576)Instructions burned: 119 (million)
% 5.85/1.67 % (3989578)Instruction limit reached!
% 5.85/1.67 % (3989578)------------------------------
% 5.85/1.67 % (3989578)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.67 % (3989578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.67 % (3989578)CaDiCaL version: 2.1.3
% 5.85/1.67 % (3989578)Termination reason: Instruction limit
% 5.85/1.67 % (3989578)Termination phase: Saturation
% 5.85/1.67 % (3989578)Time elapsed: 0.057 s
% 5.85/1.67 % (3989578)Peak memory usage: 89 MB
% 5.85/1.67 % (3989578)Instructions burned: 130 (million)
% 5.85/1.67 % (3989575)Instruction limit reached!
% 5.85/1.67 % (3989575)------------------------------
% 5.85/1.67 % (3989575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.67 % (3989575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.67 % (3989575)CaDiCaL version: 2.1.3
% 5.85/1.67 % (3989575)Termination reason: Instruction limit
% 5.85/1.67 % (3989575)Termination phase: Saturation
% 5.85/1.67 % (3989575)Time elapsed: 0.059 s
% 5.85/1.67 % (3989575)Peak memory usage: 89 MB
% 5.85/1.67 % (3989575)Instructions burned: 111 (million)
% 5.85/1.67 % (3989586)lrs+10_1_sil=8000:sp=occurrence:random_seed=3651202322:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.85/1.67 % (3989587)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2831638252:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 5.85/1.67 % (3989587)Refutation not found, incomplete strategy
% 5.85/1.67 % (3989587)------------------------------
% 5.85/1.67 % (3989587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.67 % (3989587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.67 % (3989587)CaDiCaL version: 2.1.3
% 5.85/1.67 % (3989587)Termination reason: Refutation not found, incomplete strategy
% 5.85/1.67 % (3989587)Time elapsed: 0.005 s
% 5.85/1.67 % (3989587)Peak memory usage: 88 MB
% 5.85/1.67 % (3989587)Instructions burned: 5 (million)
% 5.85/1.67 % (3989588)lrs+1011_1_sil=32000:sp=occurrence:random_seed=717411030:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 5.85/1.67 % (3989589)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=642951812:s2a=on:i=248:s2at=1.23:gtg=position_2998 on theBenchmark for (2998ds/248Mi)
% 5.85/1.67 % (3989586)Instruction limit reached!
% 5.85/1.67 % (3989586)------------------------------
% 5.85/1.67 % (3989586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.67 % (3989586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.67 % (3989586)CaDiCaL version: 2.1.3
% 5.85/1.67 % (3989586)Termination reason: Instruction limit
% 5.85/1.67 % (3989586)Termination phase: Saturation
% 5.85/1.67 % (3989586)Time elapsed: 0.095 s
% 5.85/1.67 % (3989586)Peak memory usage: 92 MB
% 5.85/1.67 % (3989586)Instructions burned: 285 (million)
% 5.85/1.67 % (3989594)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1534723096:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 5.85/1.67 % (3989589)Instruction limit reached!
% 5.85/1.67 % (3989589)------------------------------
% 5.85/1.67 % (3989589)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.67 % (3989589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.67 % (3989589)CaDiCaL version: 2.1.3
% 5.85/1.67 % (3989589)Termination reason: Instruction limit
% 5.85/1.67 % (3989589)Termination phase: Saturation
% 5.85/1.67 % (3989589)Time elapsed: 0.121 s
% 5.85/1.67 % (3989589)Peak memory usage: 93 MB
% 5.85/1.67 % (3989589)Instructions burned: 250 (million)
% 5.85/1.67 % (3989594)Instruction limit reached!
% 5.85/1.67 % (3989594)------------------------------
% 5.85/1.67 % (3989594)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.67 % (3989594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.67 % (3989594)CaDiCaL version: 2.1.3
% 5.85/1.67 % (3989594)Termination reason: Instruction limit
% 5.85/1.67 % (3989594)Termination phase: Saturation
% 5.85/1.67 % (3989594)Time elapsed: 0.082 s
% 5.85/1.67 % (3989594)Peak memory usage: 89 MB
% 5.85/1.67 % (3989594)Instructions burned: 294 (million)
% 5.85/1.67 % (3989588)Instruction limit reached!
% 5.85/1.67 % (3989588)------------------------------
% 5.85/1.67 % (3989588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.67 % (3989588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.67 % (3989588)CaDiCaL version: 2.1.3
% 5.85/1.67 % (3989588)Termination reason: Instruction limit
% 5.85/1.67 % (3989588)Termination phase: Saturation
% 5.85/1.67 % (3989588)Time elapsed: 0.202 s
% 5.85/1.67 % (3989588)Peak memory usage: 93 MB
% 5.85/1.67 % (3989588)Instructions burned: 325 (million)
% 5.85/1.67 % (3989587)------------------------------
% 5.85/1.67 % (3989587)------------------------------
% 5.85/1.67 % (3989596)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2842731330:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 5.85/1.67 % (3989597)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4290428988:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.85/1.67 % (3989597)Instruction limit reached!
% 5.85/1.67 % (3989597)------------------------------
% 5.85/1.67 % (3989597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.67 % (3989597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.67 % (3989597)CaDiCaL version: 2.1.3
% 5.85/1.67 % (3989597)Termination reason: Instruction limit
% 5.85/1.67 % (3989597)Termination phase: Saturation
% 5.85/1.67 % (3989597)Time elapsed: 0.043 s
% 5.85/1.67 % (3989597)Peak memory usage: 90 MB
% 5.85/1.67 % (3989597)Instructions burned: 115 (million)
% 5.85/1.67 % (3989598)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2157767761:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.85/1.67 % (3989599)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=961982876:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 5.85/1.67 % (3989598)Instruction limit reached!
% 5.85/1.67 % (3989598)------------------------------
% 5.85/1.67 % (3989598)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.67 % (3989598)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.67 % (3989598)CaDiCaL version: 2.1.3
% 5.85/1.67 % (3989598)Termination reason: Instruction limit
% 5.85/1.67 % (3989598)Termination phase: Saturation
% 5.85/1.67 % (3989598)Time elapsed: 0.063 s
% 5.85/1.67 % (3989598)Peak memory usage: 89 MB
% 5.85/1.67 % (3989598)Instructions burned: 127 (million)
% 5.85/1.67 % (3989599)Instruction limit reached!
% 5.85/1.67 % (3989599)------------------------------
% 5.85/1.67 % (3989599)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.85/1.67 % (3989599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.85/1.67 % (3989599)CaDiCaL version: 2.1.3
% 5.85/1.67 % (3989599)Termination reason: Instruction limit
% 5.85/1.67 % (3989599)Termination phase: Saturation
% 5.85/1.67 % (3989599)Time elapsed: 0.066 s
% 5.85/1.67 % (3989599)Peak memory usage: 89 MB
% 5.85/1.67 % (3989599)Instructions burned: 114 (million)
% 5.85/1.67 % (3989572)First to succeed.
% 5.85/1.67 % (3989602)lrs+10_1_sil=8000:sp=occurrence:random_seed=1913675340:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2993 on theBenchmark for (2993ds/907Mi)
% 5.85/1.67 % (3989573)Also succeeded, but the first one will report.
% 5.85/1.67 % (3989572)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3989567"
% 5.85/1.67 % (3989605)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=734915290:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 5.85/1.67 % (3989574)Also succeeded, but the first one will report.
% 5.85/1.67 % (3989606)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2825518650:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 5.85/1.67 % (3989572)Refutation found. Thanks to Tanya!
% 5.85/1.67 % SZS status Theorem for theBenchmark
% 5.85/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 7.91/1.86 % (3989572)------------------------------
% 7.91/1.86 % (3989572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.91/1.86 % (3989572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.91/1.86 % (3989572)CaDiCaL version: 2.1.3
% 7.91/1.86 % (3989572)Termination reason: Refutation
% 7.91/1.86 % (3989572)Time elapsed: 0.651 s
% 7.91/1.86 % (3989572)Peak memory usage: 129 MB
% 7.91/1.86 % (3989572)Instructions burned: 971 (million)
% 7.91/1.86 % (3989572)------------------------------
% 7.91/1.86 % (3989572)------------------------------
% 7.91/1.86 % (3989567)Success in time 1.066 s
% 7.91/1.86 % Vampire exiting
%------------------------------------------------------------------------------