%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG052+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 4.38s 1.52s
% Output : Refutation 5.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 86 ( 32 unt; 1 def)
% Number of atoms : 250 ( 103 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 284 ( 120 ~; 119 |; 31 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 51 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> iLess0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
fof(f30,axiom,
! [X0] :
( aVector0(X0)
=> aNaturalNumber0(aDimensionOf0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).
fof(f32,axiom,
! [X0] :
( aVector0(X0)
=> ( aDimensionOf0(X0) != sz00
=> ! [X1] :
( X1 = sziznziztdt0(X0)
<=> ( aVector0(X1)
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& ! [X2] :
( aNaturalNumber0(X2)
=> sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInit) ).
fof(f33,axiom,
! [X0,X1] :
( ( aVector0(X0)
& aVector0(X1) )
=> ( ( aDimensionOf0(X0) = aDimensionOf0(X1)
& aDimensionOf0(X1) != sz00 )
=> aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEqInit) ).
fof(f38,axiom,
( aVector0(xs)
& aVector0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).
fof(f39,axiom,
! [X0,X1] :
( ( aVector0(X0)
& aVector0(X1) )
=> ( aDimensionOf0(X0) = aDimensionOf0(X1)
=> ( iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
=> sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1652) ).
fof(f40,axiom,
aDimensionOf0(xs) = aDimensionOf0(xt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).
fof(f41,axiom,
aDimensionOf0(xs) != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).
fof(f42,axiom,
( aVector0(xp)
& xp = sziznziztdt0(xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).
fof(f43,axiom,
( aVector0(xq)
& xq = sziznziztdt0(xt) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).
fof(f46,axiom,
( aScalar0(xC)
& xC = sdtasasdt0(xp,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1783) ).
fof(f47,axiom,
( aScalar0(xD)
& xD = sdtasasdt0(xq,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1800) ).
fof(f48,axiom,
( aScalar0(xE)
& xE = sdtasasdt0(xp,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
fof(f56,conjecture,
sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f58,plain,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(flattening,[],[f57]) ).
fof(f64,plain,
! [X0,X1] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f65,plain,
! [X0,X1] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(flattening,[],[f64]) ).
fof(f73,plain,
! [X0,X1] :
( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sz00 = aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f74,plain,
! [X0,X1] :
( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sz00 = aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( X1 = sziznziztdt0(X0)
<=> ( aVector0(X1)
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& ! [X2] :
( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
| ~ aNaturalNumber0(X2) ) ) )
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( X1 = sziznziztdt0(X0)
<=> ( aVector0(X1)
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& ! [X2] :
( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
| ~ aNaturalNumber0(X2) ) ) )
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(flattening,[],[f75]) ).
fof(f79,plain,
! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f82,plain,
! [X0] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ( X1 = sziznziztdt0(X0)
| ~ aVector0(X1)
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ? [X2] :
( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( ( aVector0(X1)
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& ! [X2] :
( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
| ~ aNaturalNumber0(X2) ) )
| sziznziztdt0(X0) != X1 ) )
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(nnf_transformation,[],[f76]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( ( X1 = sziznziztdt0(X0)
| ~ aVector0(X1)
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ? [X2] :
( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( ( aVector0(X1)
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& ! [X2] :
( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
| ~ aNaturalNumber0(X2) ) )
| sziznziztdt0(X0) != X1 ) )
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(flattening,[],[f113]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( ( X1 = sziznziztdt0(X0)
| ~ aVector0(X1)
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ? [X2] :
( sdtlbdtrb0(X1,X2) != sdtlbdtrb0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( ( aVector0(X1)
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& ! [X3] :
( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
| ~ aNaturalNumber0(X3) ) )
| sziznziztdt0(X0) != X1 ) )
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(rectify,[],[f114]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ( X1 = sziznziztdt0(X0)
| ~ aVector0(X1)
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ( sdtlbdtrb0(X1,sK0(X0,X1)) != sdtlbdtrb0(X0,sK0(X0,X1))
& aNaturalNumber0(sK0(X0,X1)) ) )
& ( ( aVector0(X1)
& szszuzczcdt0(aDimensionOf0(X1)) = aDimensionOf0(X0)
& ! [X3] :
( sdtlbdtrb0(X1,X3) = sdtlbdtrb0(X0,X3)
| ~ aNaturalNumber0(X3) ) )
| sziznziztdt0(X0) != X1 ) )
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f115]) ).
fof(f118,plain,
aVector0(xt),
inference(cnf_transformation,[],[f38]) ).
fof(f119,plain,
aVector0(xs),
inference(cnf_transformation,[],[f38]) ).
fof(f120,plain,
! [X0,X1] :
( sdtlseqdt0(sdtasdt0(sdtasasdt0(X0,X1),sdtasasdt0(X0,X1)),sdtasdt0(sdtasasdt0(X0,X0),sdtasasdt0(X1,X1)))
| ~ iLess0(aDimensionOf0(X0),aDimensionOf0(xs))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f121,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[],[f40]) ).
fof(f122,plain,
sz00 != aDimensionOf0(xs),
inference(cnf_transformation,[],[f41]) ).
fof(f123,plain,
xp = sziznziztdt0(xs),
inference(cnf_transformation,[],[f42]) ).
fof(f124,plain,
aVector0(xp),
inference(cnf_transformation,[],[f42]) ).
fof(f125,plain,
xq = sziznziztdt0(xt),
inference(cnf_transformation,[],[f43]) ).
fof(f126,plain,
aVector0(xq),
inference(cnf_transformation,[],[f43]) ).
fof(f131,plain,
xC = sdtasasdt0(xp,xp),
inference(cnf_transformation,[],[f46]) ).
fof(f133,plain,
xD = sdtasasdt0(xq,xq),
inference(cnf_transformation,[],[f47]) ).
fof(f135,plain,
xE = sdtasasdt0(xp,xq),
inference(cnf_transformation,[],[f48]) ).
fof(f151,plain,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(xC,xD)),
inference(cnf_transformation,[],[f58]) ).
fof(f156,plain,
! [X0,X1] :
( aDimensionOf0(sziznziztdt0(X0)) = aDimensionOf0(sziznziztdt0(X1))
| aDimensionOf0(X0) != aDimensionOf0(X1)
| sz00 = aDimensionOf0(X1)
| ~ aVector0(X0)
| ~ aVector0(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f158,plain,
! [X0,X1] :
( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
| sziznziztdt0(X0) != X1
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f163,plain,
! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f165,plain,
! [X0] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f200,plain,
! [X0] :
( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0)))
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(equality_resolution,[],[f158]) ).
fof(f214,plain,
aVector0(sziznziztdt0(xt)),
inference(forward_demodulation,[],[f126,f125]) ).
fof(f215,plain,
aVector0(sziznziztdt0(xs)),
inference(forward_demodulation,[],[f124,f123]) ).
fof(f353,definition,
( spl2_9
<=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f354,plain,
( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f355,plain,
( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))
| spl2_9 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f386,plain,
( ! [X0] :
( aDimensionOf0(sziznziztdt0(X0)) != aDimensionOf0(sziznziztdt0(xs))
| aDimensionOf0(X0) != aDimensionOf0(xt)
| sz00 = aDimensionOf0(xt)
| ~ aVector0(X0)
| ~ aVector0(xt) )
| spl2_9 ),
inference(superposition,[],[f355,f156]) ).
fof(f390,plain,
( ! [X0] :
( aDimensionOf0(sziznziztdt0(X0)) != aDimensionOf0(sziznziztdt0(xs))
| aDimensionOf0(X0) != aDimensionOf0(xt)
| sz00 = aDimensionOf0(xt)
| ~ aVector0(X0) )
| spl2_9 ),
inference(forward_subsumption_resolution,[],[f386,f118]) ).
fof(f392,plain,
( ! [X0] :
( aDimensionOf0(X0) != aDimensionOf0(xs)
| aDimensionOf0(sziznziztdt0(X0)) != aDimensionOf0(sziznziztdt0(xs))
| sz00 = aDimensionOf0(xt)
| ~ aVector0(X0) )
| spl2_9 ),
inference(forward_demodulation,[],[f390,f121]) ).
fof(f393,plain,
( ! [X0] :
( sz00 = aDimensionOf0(xs)
| aDimensionOf0(X0) != aDimensionOf0(xs)
| aDimensionOf0(sziznziztdt0(X0)) != aDimensionOf0(sziznziztdt0(xs))
| ~ aVector0(X0) )
| spl2_9 ),
inference(forward_demodulation,[],[f392,f121]) ).
fof(f394,plain,
( ! [X0] :
( aDimensionOf0(sziznziztdt0(X0)) != aDimensionOf0(sziznziztdt0(xs))
| aDimensionOf0(X0) != aDimensionOf0(xs)
| ~ aVector0(X0) )
| spl2_9 ),
inference(forward_subsumption_resolution,[],[f393,f122]) ).
fof(f425,plain,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasasdt0(xp,xp),xD)),
inference(superposition,[],[f151,f131]) ).
fof(f426,plain,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(xq,xq))),
inference(forward_demodulation,[],[f425,f133]) ).
fof(f427,plain,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasasdt0(xp,xp),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),
inference(forward_demodulation,[],[f426,f125]) ).
fof(f428,plain,
~ sdtlseqdt0(sdtasdt0(xE,xE),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),
inference(forward_demodulation,[],[f427,f123]) ).
fof(f429,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasasdt0(xp,xq)),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),
inference(forward_demodulation,[],[f428,f135]) ).
fof(f430,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(xp,sziznziztdt0(xt)),sdtasasdt0(xp,sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),
inference(forward_demodulation,[],[f429,f125]) ).
fof(f431,plain,
~ sdtlseqdt0(sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt)),sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xt))),sdtasdt0(sdtasasdt0(sziznziztdt0(xs),sziznziztdt0(xs)),sdtasasdt0(sziznziztdt0(xt),sziznziztdt0(xt)))),
inference(forward_demodulation,[],[f430,f123]) ).
fof(f687,plain,
( aDimensionOf0(xs) != aDimensionOf0(xs)
| ~ aVector0(xs)
| spl2_9 ),
inference(equality_resolution,[],[f394]) ).
fof(f688,plain,
( ~ aVector0(xs)
| spl2_9 ),
inference(trivial_inequality_removal,[],[f687]) ).
fof(f691,plain,
( $false
| spl2_9 ),
inference(forward_subsumption_resolution,[],[f688,f119]) ).
fof(f692,plain,
spl2_9,
inference(avatar_contradiction_clause,[],[f691]) ).
fof(f747,plain,
( aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))
| sz00 = aDimensionOf0(xt)
| ~ aVector0(xt)
| ~ spl2_9 ),
inference(superposition,[],[f200,f354]) ).
fof(f756,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ aVector0(sziznziztdt0(xt))
| ~ spl2_9 ),
inference(superposition,[],[f163,f354]) ).
fof(f760,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f756,f214]) ).
fof(f769,plain,
( aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))
| sz00 = aDimensionOf0(xt)
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f747,f118]) ).
fof(f785,plain,
( aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))
| sz00 = aDimensionOf0(xt)
| ~ spl2_9 ),
inference(forward_demodulation,[],[f769,f121]) ).
fof(f789,plain,
( sz00 = aDimensionOf0(xs)
| aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl2_9 ),
inference(forward_demodulation,[],[f785,f121]) ).
fof(f792,plain,
( aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f789,f122]) ).
fof(f808,plain,
( ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))
| ~ aVector0(sziznziztdt0(xs))
| ~ aVector0(sziznziztdt0(xt)) ),
inference(resolution,[],[f431,f120]) ).
fof(f820,plain,
( ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| ~ aVector0(sziznziztdt0(xs))
| ~ aVector0(sziznziztdt0(xt))
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f808,f354]) ).
fof(f821,plain,
( ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| ~ aVector0(sziznziztdt0(xt))
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f820,f215]) ).
fof(f822,plain,
( ~ iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f821,f214]) ).
fof(f890,plain,
( iLess0(aDimensionOf0(sziznziztdt0(xs)),aDimensionOf0(xs))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl2_9 ),
inference(superposition,[],[f165,f792]) ).
fof(f891,plain,
( ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f890,f822]) ).
fof(f897,plain,
( $false
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f891,f760]) ).
fof(f898,plain,
~ spl2_9,
inference(avatar_contradiction_clause,[],[f897]) ).
cnf(s17,plain,
spl2_9,
inference(sat_conversion,[],[f692]) ).
cnf(s36,plain,
~ spl2_9,
inference(sat_conversion,[],[f898]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s17,s36]) ).
fof(f900,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG052+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n017.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 22:58:05 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 4.38/1.52 % (3055851)Detected formulas, will run a generic FOF schedule.
% 4.38/1.52 % (3055860)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1156953977:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.38/1.52 % (3055860)Instruction limit reached!
% 4.38/1.52 % (3055860)------------------------------
% 4.38/1.52 % (3055860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.52 % (3055860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.52 % (3055860)CaDiCaL version: 2.1.3
% 4.38/1.52 % (3055860)Termination reason: Instruction limit
% 4.38/1.52 % (3055860)Termination phase: Saturation
% 4.38/1.52 % (3055860)Time elapsed: 0.032 s
% 4.38/1.52 % (3055860)Peak memory usage: 88 MB
% 4.38/1.52 % (3055860)Instructions burned: 120 (million)
% 4.38/1.52 % (3055856)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=3912842943:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.38/1.52 % (3055858)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=2371247594:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.38/1.52 % (3055859)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2241314300:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.38/1.52 % (3055857)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=3151147783:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.38/1.52 % (3055861)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3698494862:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.38/1.52 % (3055862)dis-21_1_sil=8000:lcm=predicate:random_seed=1095153819: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)
% 4.38/1.52 % (3055859)Instruction limit reached!
% 4.38/1.52 % (3055859)------------------------------
% 4.38/1.52 % (3055859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.52 % (3055859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.52 % (3055859)CaDiCaL version: 2.1.3
% 4.38/1.52 % (3055859)Termination reason: Instruction limit
% 4.38/1.52 % (3055859)Termination phase: Saturation
% 4.38/1.52 % (3055859)Time elapsed: 0.048 s
% 4.38/1.52 % (3055859)Peak memory usage: 88 MB
% 4.38/1.52 % (3055859)Instructions burned: 111 (million)
% 4.38/1.52 % (3055862)Instruction limit reached!
% 4.38/1.52 % (3055862)------------------------------
% 4.38/1.52 % (3055862)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.52 % (3055862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.52 % (3055862)CaDiCaL version: 2.1.3
% 4.38/1.52 % (3055862)Termination reason: Instruction limit
% 4.38/1.52 % (3055862)Termination phase: Saturation
% 4.38/1.52 % (3055862)Time elapsed: 0.057 s
% 4.38/1.52 % (3055862)Peak memory usage: 89 MB
% 4.38/1.52 % (3055862)Instructions burned: 129 (million)
% 4.38/1.52 % (3055861)Instruction limit reached!
% 4.38/1.52 % (3055861)------------------------------
% 4.38/1.52 % (3055861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.52 % (3055861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.52 % (3055861)CaDiCaL version: 2.1.3
% 4.38/1.52 % (3055861)Termination reason: Instruction limit
% 4.38/1.52 % (3055861)Termination phase: Saturation
% 4.38/1.52 % (3055861)Time elapsed: 0.086 s
% 4.38/1.52 % (3055861)Peak memory usage: 90 MB
% 4.38/1.52 % (3055861)Instructions burned: 140 (million)
% 4.38/1.52 % (3055864)lrs+10_1_sil=8000:sp=occurrence:random_seed=1715952289:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.38/1.52 % (3055864)Instruction limit reached!
% 4.38/1.52 % (3055864)------------------------------
% 4.38/1.52 % (3055864)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.52 % (3055864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.52 % (3055864)CaDiCaL version: 2.1.3
% 4.38/1.52 % (3055864)Termination reason: Instruction limit
% 4.38/1.52 % (3055864)Termination phase: Saturation
% 4.38/1.52 % (3055864)Time elapsed: 0.096 s
% 4.38/1.52 % (3055864)Peak memory usage: 93 MB
% 4.38/1.52 % (3055864)Instructions burned: 288 (million)
% 4.38/1.52 % (3055871)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3749597254:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.38/1.52 % (3055872)lrs+1011_1_sil=32000:sp=occurrence:random_seed=185829572:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.38/1.52 % (3055873)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=4142724936:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.38/1.52 % (3055871)Instruction limit reached!
% 4.38/1.52 % (3055871)------------------------------
% 4.38/1.52 % (3055871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.52 % (3055871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.52 % (3055871)CaDiCaL version: 2.1.3
% 4.38/1.52 % (3055871)Termination reason: Instruction limit
% 4.38/1.52 % (3055871)Termination phase: Saturation
% 4.38/1.52 % (3055871)Time elapsed: 0.075 s
% 4.38/1.52 % (3055871)Peak memory usage: 90 MB
% 4.38/1.52 % (3055871)Instructions burned: 159 (million)
% 4.38/1.52 % (3055877)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2440644230:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.38/1.52 % (3055877)First to succeed.
% 4.38/1.52 % (3055877)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3055851"
% 4.38/1.52 % (3055873)Instruction limit reached!
% 4.38/1.52 % (3055873)------------------------------
% 4.38/1.52 % (3055873)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.52 % (3055873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.52 % (3055873)CaDiCaL version: 2.1.3
% 4.38/1.52 % (3055873)Termination reason: Instruction limit
% 4.38/1.52 % (3055873)Termination phase: Saturation
% 4.38/1.52 % (3055873)Time elapsed: 0.145 s
% 4.38/1.52 % (3055873)Peak memory usage: 96 MB
% 4.38/1.52 % (3055873)Instructions burned: 249 (million)
% 4.38/1.52 % (3055872)Instruction limit reached!
% 4.38/1.52 % (3055872)------------------------------
% 4.38/1.52 % (3055872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.38/1.52 % (3055872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.38/1.52 % (3055872)CaDiCaL version: 2.1.3
% 4.38/1.52 % (3055872)Termination reason: Instruction limit
% 4.38/1.52 % (3055872)Termination phase: Saturation
% 4.38/1.52 % (3055872)Time elapsed: 0.195 s
% 4.38/1.52 % (3055872)Peak memory usage: 93 MB
% 4.38/1.52 % (3055872)Instructions burned: 327 (million)
% 4.38/1.52 % (3055879)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2977820308:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.38/1.52 % (3055877)Refutation found. Thanks to Tanya!
% 4.38/1.52 % SZS status Theorem for theBenchmark
% 4.38/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 5.22/1.61 % (3055877)------------------------------
% 5.22/1.61 % (3055877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.22/1.61 % (3055877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.61 % (3055877)CaDiCaL version: 2.1.3
% 5.22/1.61 % (3055877)Termination reason: Refutation
% 5.22/1.61 % (3055877)Time elapsed: 0.011 s
% 5.22/1.61 % (3055877)Peak memory usage: 89 MB
% 5.22/1.61 % (3055877)Instructions burned: 31 (million)
% 5.22/1.61 % (3055877)------------------------------
% 5.22/1.61 % (3055877)------------------------------
% 5.22/1.61 % (3055851)Success in time 0.666 s
% 5.22/1.61 % Vampire exiting
%------------------------------------------------------------------------------