%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG047+2 : 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 : n003.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 12:35:16 PM UTC 2026
% Result : Theorem 2.41s 1.19s
% Output : Refutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 115 ( 18 unt; 7 def)
% Number of atoms : 362 ( 137 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 401 ( 154 ~; 162 |; 56 &)
% ( 10 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 60 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNat) ).
fof(f3,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( aNaturalNumber0(szszuzczcdt0(X0))
& szszuzczcdt0(X0) != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNat) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( szszuzczcdt0(X0) = szszuzczcdt0(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEqu) ).
fof(f30,axiom,
! [X0] :
( aVector0(X0)
=> aNaturalNumber0(aDimensionOf0(X0)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mDefInit) ).
fof(f34,axiom,
( aDimensionOf0(xs) = aDimensionOf0(xt)
& aDimensionOf0(xt) != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1329_01) ).
fof(f35,conjecture,
( ( aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) ) )
=> ( ( aVector0(sziznziztdt0(xt))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xt),X0) = sdtlbdtrb0(xt,X0) ) )
=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f36,negated_conjecture,
~ ( ( aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) ) )
=> ( ( aVector0(sziznziztdt0(xt))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xt),X0) = sdtlbdtrb0(xt,X0) ) )
=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f42,plain,
~ ( ( aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X0] :
( aNaturalNumber0(X0)
=> sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0) ) )
=> ( ( aVector0(sziznziztdt0(xt))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& ! [X1] :
( aNaturalNumber0(X1)
=> sdtlbdtrb0(sziznziztdt0(xt),X1) = sdtlbdtrb0(xt,X1) ) )
=> aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt)) ) ),
inference(rectify,[],[f36]) ).
fof(f44,plain,
! [X0] :
( ( aNaturalNumber0(szszuzczcdt0(X0))
& szszuzczcdt0(X0) != sz00 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f47,plain,
! [X0,X1] :
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0,X1] :
( X0 = X1
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f47]) ).
fof(f81,plain,
! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f84,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(f85,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,[],[f84]) ).
fof(f86,plain,
( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))
& aVector0(sziznziztdt0(xt))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& ! [X1] :
( sdtlbdtrb0(sziznziztdt0(xt),X1) = sdtlbdtrb0(xt,X1)
| ~ aNaturalNumber0(X1) )
& aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X0] :
( sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f87,plain,
( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))
& aVector0(sziznziztdt0(xt))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& ! [X1] :
( sdtlbdtrb0(sziznziztdt0(xt),X1) = sdtlbdtrb0(xt,X1)
| ~ aNaturalNumber0(X1) )
& aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X0] :
( sdtlbdtrb0(sziznziztdt0(xs),X0) = sdtlbdtrb0(xs,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(flattening,[],[f86]) ).
fof(f89,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,[],[f85]) ).
fof(f90,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,[],[f89]) ).
fof(f91,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,[],[f90]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( X1 = sziznziztdt0(X0)
| ~ aVector0(X1)
| aDimensionOf0(X0) != szszuzczcdt0(aDimensionOf0(X1))
| ( sdtlbdtrb0(X1,sK1(X0,X1)) != sdtlbdtrb0(X0,sK1(X0,X1))
& aNaturalNumber0(sK1(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,[sK1]),skolemize(X2,sK1(X0,X1))],[f91]) ).
fof(f93,plain,
( aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt))
& aVector0(sziznziztdt0(xt))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) = aDimensionOf0(xt)
& ! [X0] :
( sdtlbdtrb0(sziznziztdt0(xt),X0) = sdtlbdtrb0(xt,X0)
| ~ aNaturalNumber0(X0) )
& aVector0(sziznziztdt0(xs))
& szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))) = aDimensionOf0(xs)
& ! [X1] :
( sdtlbdtrb0(sziznziztdt0(xs),X1) = sdtlbdtrb0(xs,X1)
| ~ aNaturalNumber0(X1) ) ),
inference(rectify,[],[f87]) ).
fof(f94,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f96,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| aNaturalNumber0(szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f132,plain,
! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f135,plain,
! [X0,X1] :
( aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
| sziznziztdt0(X0) != X1
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f136,plain,
! [X0,X1] :
( aVector0(X1)
| sziznziztdt0(X0) != X1
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f142,plain,
aDimensionOf0(xs) = aDimensionOf0(xt),
inference(cnf_transformation,[],[f34]) ).
fof(f144,plain,
aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xs))),
inference(cnf_transformation,[],[f93]) ).
fof(f145,plain,
aVector0(sziznziztdt0(xs)),
inference(cnf_transformation,[],[f93]) ).
fof(f147,plain,
aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))),
inference(cnf_transformation,[],[f93]) ).
fof(f148,plain,
aVector0(sziznziztdt0(xt)),
inference(cnf_transformation,[],[f93]) ).
fof(f149,plain,
aDimensionOf0(sziznziztdt0(xs)) != aDimensionOf0(sziznziztdt0(xt)),
inference(cnf_transformation,[],[f93]) ).
fof(f150,plain,
! [X0] :
( aVector0(sziznziztdt0(X0))
| sz00 = aDimensionOf0(X0)
| ~ aVector0(X0) ),
inference(equality_resolution,[],[f136]) ).
fof(f151,plain,
! [X0] :
( ~ aVector0(X0)
| sz00 = aDimensionOf0(X0)
| aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(X0))) ),
inference(equality_resolution,[],[f135]) ).
fof(f172,plain,
! [X0] :
( ~ aVector0(X0)
| aNaturalNumber0(szszuzczcdt0(aDimensionOf0(X0))) ),
inference(resolution,[],[f132,f96]) ).
fof(f248,plain,
! [X0] :
( szszuzczcdt0(X0) != szszuzczcdt0(sz00)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(resolution,[],[f99,f94]) ).
fof(f250,plain,
! [X0,X1] :
( ~ aVector0(X0)
| aDimensionOf0(X0) = X1
| ~ aNaturalNumber0(X1)
| szszuzczcdt0(X1) != szszuzczcdt0(aDimensionOf0(X0)) ),
inference(resolution,[],[f99,f132]) ).
fof(f314,plain,
( sz00 = aDimensionOf0(sziznziztdt0(xs))
| aDimensionOf0(sziznziztdt0(xs)) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(xs)))) ),
inference(resolution,[],[f151,f145]) ).
fof(f315,plain,
( sz00 = aDimensionOf0(sziznziztdt0(xt))
| aDimensionOf0(sziznziztdt0(xt)) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(xt)))) ),
inference(resolution,[],[f151,f148]) ).
fof(f320,definition,
( spl2_5
<=> aDimensionOf0(sziznziztdt0(xt)) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(xt)))) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f322,plain,
( aDimensionOf0(sziznziztdt0(xt)) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))))
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f324,definition,
( spl2_6
<=> sz00 = aDimensionOf0(sziznziztdt0(xt)) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f325,plain,
( sz00 != aDimensionOf0(sziznziztdt0(xt))
| spl2_6 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f326,plain,
( sz00 = aDimensionOf0(sziznziztdt0(xt))
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f327,plain,
( spl2_5
| spl2_6 ),
inference(avatar_split_clause,[],[f315,f324,f320]) ).
fof(f329,definition,
( spl2_7
<=> aDimensionOf0(sziznziztdt0(xs)) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(xs)))) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f331,plain,
( aDimensionOf0(sziznziztdt0(xs)) = szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(xs))))
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f333,definition,
( spl2_8
<=> sz00 = aDimensionOf0(sziznziztdt0(xs)) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f334,plain,
( sz00 != aDimensionOf0(sziznziztdt0(xs))
| spl2_8 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f335,plain,
( sz00 = aDimensionOf0(sziznziztdt0(xs))
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f336,plain,
( spl2_7
| spl2_8 ),
inference(avatar_split_clause,[],[f314,f333,f329]) ).
fof(f358,plain,
( aDimensionOf0(xt) = szszuzczcdt0(sz00)
| ~ spl2_6 ),
inference(superposition,[],[f147,f326]) ).
fof(f377,plain,
( sz00 != aDimensionOf0(sziznziztdt0(xt))
| ~ spl2_8 ),
inference(superposition,[],[f149,f335]) ).
fof(f378,plain,
( aDimensionOf0(xs) = szszuzczcdt0(sz00)
| ~ spl2_8 ),
inference(superposition,[],[f144,f335]) ).
fof(f382,plain,
( aDimensionOf0(xt) = szszuzczcdt0(sz00)
| ~ spl2_8 ),
inference(forward_demodulation,[],[f378,f142]) ).
fof(f385,plain,
( ~ spl2_6
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f377,f333,f324]) ).
fof(f512,definition,
( spl2_11
<=> aVector0(sziznziztdt0(sziznziztdt0(xt))) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f514,plain,
( ~ aVector0(sziznziztdt0(sziznziztdt0(xt)))
| spl2_11 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f528,plain,
( sz00 = aDimensionOf0(sziznziztdt0(xt))
| ~ aVector0(sziznziztdt0(xt))
| spl2_11 ),
inference(resolution,[],[f514,f150]) ).
fof(f533,definition,
( spl2_15
<=> aNaturalNumber0(aDimensionOf0(sziznziztdt0(sziznziztdt0(xt)))) ),
introduced(definition,[new_symbols(definition,[spl2_15])],[avatar_definition]) ).
fof(f534,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))))
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f535,plain,
( ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(sziznziztdt0(xt))))
| spl2_15 ),
inference(avatar_component_clause,[],[f533]) ).
fof(f537,plain,
( sz00 = aDimensionOf0(sziznziztdt0(xt))
| spl2_11 ),
inference(forward_subsumption_resolution,[],[f528,f148]) ).
fof(f538,plain,
( spl2_6
| spl2_11 ),
inference(avatar_split_clause,[],[f537,f512,f324]) ).
fof(f561,definition,
( spl2_16
<=> aVector0(sziznziztdt0(sziznziztdt0(xs))) ),
introduced(definition,[new_symbols(definition,[spl2_16])],[avatar_definition]) ).
fof(f562,plain,
( aVector0(sziznziztdt0(sziznziztdt0(xs)))
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f563,plain,
( ~ aVector0(sziznziztdt0(sziznziztdt0(xs)))
| spl2_16 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f577,plain,
( sz00 = aDimensionOf0(sziznziztdt0(xs))
| ~ aVector0(sziznziztdt0(xs))
| spl2_16 ),
inference(resolution,[],[f563,f150]) ).
fof(f587,plain,
( sz00 = aDimensionOf0(sziznziztdt0(xs))
| spl2_16 ),
inference(forward_subsumption_resolution,[],[f577,f145]) ).
fof(f588,plain,
( spl2_8
| spl2_16 ),
inference(avatar_split_clause,[],[f587,f561,f333]) ).
fof(f636,plain,
( ~ aVector0(sziznziztdt0(sziznziztdt0(xt)))
| spl2_15 ),
inference(resolution,[],[f535,f132]) ).
fof(f650,plain,
( aNaturalNumber0(szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(xt)))))
| ~ spl2_15 ),
inference(resolution,[],[f534,f96]) ).
fof(f653,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ spl2_5
| ~ spl2_15 ),
inference(forward_demodulation,[],[f650,f322]) ).
fof(f853,plain,
( ! [X0] :
( szszuzczcdt0(X0) != aDimensionOf0(xt)
| sz00 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl2_8 ),
inference(forward_demodulation,[],[f248,f382]) ).
fof(f869,plain,
( aDimensionOf0(xt) != aDimensionOf0(xt)
| sz00 = aDimensionOf0(sziznziztdt0(xt))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ spl2_8 ),
inference(superposition,[],[f853,f147]) ).
fof(f874,plain,
( sz00 = aDimensionOf0(sziznziztdt0(xt))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ spl2_8 ),
inference(trivial_inequality_removal,[],[f869]) ).
fof(f876,plain,
( ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| spl2_6
| ~ spl2_8 ),
inference(forward_subsumption_resolution,[],[f874,f325]) ).
fof(f877,plain,
( $false
| ~ spl2_5
| spl2_6
| ~ spl2_8
| ~ spl2_15 ),
inference(forward_subsumption_resolution,[],[f876,f653]) ).
fof(f878,plain,
( ~ spl2_5
| spl2_6
| ~ spl2_8
| ~ spl2_15 ),
inference(avatar_contradiction_clause,[],[f877]) ).
fof(f880,plain,
( ~ spl2_11
| spl2_15 ),
inference(avatar_split_clause,[],[f636,f533,f512]) ).
fof(f900,plain,
( aNaturalNumber0(szszuzczcdt0(aDimensionOf0(sziznziztdt0(sziznziztdt0(xs)))))
| ~ spl2_16 ),
inference(resolution,[],[f562,f172]) ).
fof(f903,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl2_7
| ~ spl2_16 ),
inference(forward_demodulation,[],[f900,f331]) ).
fof(f926,plain,
( aDimensionOf0(xs) != szszuzczcdt0(sz00)
| sz00 = aDimensionOf0(sziznziztdt0(xs))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(superposition,[],[f248,f144]) ).
fof(f939,plain,
( aDimensionOf0(xs) != szszuzczcdt0(sz00)
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| spl2_8 ),
inference(forward_subsumption_resolution,[],[f926,f334]) ).
fof(f945,plain,
( aDimensionOf0(xs) != szszuzczcdt0(sz00)
| ~ spl2_7
| spl2_8
| ~ spl2_16 ),
inference(forward_subsumption_resolution,[],[f939,f903]) ).
fof(f946,plain,
( aDimensionOf0(xt) != szszuzczcdt0(sz00)
| ~ spl2_7
| spl2_8
| ~ spl2_16 ),
inference(forward_demodulation,[],[f945,f142]) ).
fof(f1039,plain,
( $false
| ~ spl2_6
| ~ spl2_7
| spl2_8
| ~ spl2_16 ),
inference(forward_subsumption_resolution,[],[f946,f358]) ).
fof(f1040,plain,
( ~ spl2_6
| ~ spl2_7
| spl2_8
| ~ spl2_16 ),
inference(avatar_contradiction_clause,[],[f1039]) ).
fof(f1099,plain,
! [X0] :
( aDimensionOf0(sziznziztdt0(xt)) = X0
| ~ aNaturalNumber0(X0)
| szszuzczcdt0(X0) != szszuzczcdt0(aDimensionOf0(sziznziztdt0(xt))) ),
inference(resolution,[],[f250,f148]) ).
fof(f1103,plain,
! [X0] :
( szszuzczcdt0(X0) != aDimensionOf0(xt)
| aDimensionOf0(sziznziztdt0(xt)) = X0
| ~ aNaturalNumber0(X0) ),
inference(forward_demodulation,[],[f1099,f147]) ).
fof(f2196,plain,
( aDimensionOf0(xs) != aDimensionOf0(xt)
| aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(superposition,[],[f1103,f144]) ).
fof(f2201,plain,
( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
inference(forward_subsumption_resolution,[],[f2196,f142]) ).
fof(f2202,plain,
~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))),
inference(forward_subsumption_resolution,[],[f2201,f149]) ).
fof(f2203,plain,
( $false
| ~ spl2_7
| ~ spl2_16 ),
inference(forward_subsumption_resolution,[],[f2202,f903]) ).
fof(f2204,plain,
( ~ spl2_7
| ~ spl2_16 ),
inference(avatar_contradiction_clause,[],[f2203]) ).
cnf(s4,plain,
( spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f327]) ).
cnf(s5,plain,
( spl2_7
| spl2_8 ),
inference(sat_conversion,[],[f336]) ).
cnf(s9,plain,
( ~ spl2_6
| ~ spl2_8 ),
inference(sat_conversion,[],[f385]) ).
cnf(s14,plain,
( spl2_6
| spl2_11 ),
inference(sat_conversion,[],[f538]) ).
cnf(s20,plain,
( spl2_8
| spl2_16 ),
inference(sat_conversion,[],[f588]) ).
cnf(s33,plain,
( ~ spl2_5
| spl2_6
| ~ spl2_8
| ~ spl2_15 ),
inference(sat_conversion,[],[f878]) ).
cnf(s34,plain,
( ~ spl2_11
| spl2_15 ),
inference(sat_conversion,[],[f880]) ).
cnf(s43,plain,
( ~ spl2_6
| ~ spl2_7
| spl2_8
| ~ spl2_16 ),
inference(sat_conversion,[],[f1040]) ).
cnf(s85,plain,
( ~ spl2_7
| ~ spl2_16 ),
inference(sat_conversion,[],[f2204]) ).
cnf(s88,plain,
~ spl2_6,
inference(rat,[],[s43,s5,s20,s9]) ).
cnf(s90,plain,
spl2_11,
inference(rat,[],[s14,s88]) ).
cnf(s92,plain,
spl2_5,
inference(rat,[],[s4,s88]) ).
cnf(s94,plain,
spl2_15,
inference(rat,[],[s34,s90]) ).
cnf(s97,plain,
~ spl2_8,
inference(rat,[],[s33,s88,s92,s94]) ).
cnf(s98,plain,
spl2_16,
inference(rat,[],[s20,s97]) ).
cnf(s100,plain,
spl2_7,
inference(rat,[],[s5,s97]) ).
cnf(s101,plain,
$false,
inference(rat,[],[s85,s98,s100]) ).
fof(f2205,plain,
$false,
inference(avatar_sat_refutation,[],[s101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG047+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n003.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 23:04:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 2.41/1.19 % (1029704)Detected formulas, will run a generic FOF schedule.
% 2.41/1.19 % (1029714)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2342851961:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.41/1.19 % (1029711)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=2200543151:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.41/1.19 % (1029715)dis-21_1_sil=8000:lcm=predicate:random_seed=4136350927: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)
% 2.41/1.19 % (1029710)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=1927853749:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.41/1.19 % (1029709)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=2811666088:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.41/1.19 % (1029712)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2567111074:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.41/1.19 % (1029714)First to succeed.
% 2.41/1.19 % (1029714)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1029704"
% 2.41/1.19 % (1029712)Also succeeded, but the first one will report.
% 2.41/1.19 % (1029713)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2733467068:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.41/1.19 % (1029713)Also succeeded, but the first one will report.
% 2.41/1.19 % (1029715)Instruction limit reached!
% 2.41/1.19 % (1029715)------------------------------
% 2.41/1.19 % (1029715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.41/1.19 % (1029715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.41/1.19 % (1029715)CaDiCaL version: 2.1.3
% 2.41/1.19 % (1029715)Termination reason: Instruction limit
% 2.41/1.19 % (1029715)Termination phase: Saturation
% 2.41/1.19 % (1029715)Time elapsed: 0.072 s
% 2.41/1.19 % (1029715)Peak memory usage: 89 MB
% 2.41/1.19 % (1029715)Instructions burned: 131 (million)
% 2.41/1.19 % (1029714)Refutation found. Thanks to Tanya!
% 2.41/1.19 % SZS status Theorem for theBenchmark
% 2.41/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.95/1.39 % (1029714)------------------------------
% 2.95/1.39 % (1029714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.95/1.39 % (1029714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.95/1.39 % (1029714)CaDiCaL version: 2.1.3
% 2.95/1.39 % (1029714)Termination reason: Refutation
% 2.95/1.39 % (1029714)Time elapsed: 0.031 s
% 2.95/1.39 % (1029714)Peak memory usage: 91 MB
% 2.95/1.39 % (1029714)Instructions burned: 87 (million)
% 2.95/1.39 % (1029714)------------------------------
% 2.95/1.39 % (1029714)------------------------------
% 2.95/1.39 % (1029704)Success in time 0.341 s
% 2.95/1.39 % Vampire exiting
%------------------------------------------------------------------------------