%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n008.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 12:35:51 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 13 unt; 2 def)
% Number of atoms : 130 ( 51 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 134 ( 47 ~; 38 |; 32 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(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(f99,plain,
! [X0,X1] :
( szszuzczcdt0(X0) != szszuzczcdt0(X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f132,plain,
! [X0] :
( aNaturalNumber0(aDimensionOf0(X0))
| ~ aVector0(X0) ),
inference(cnf_transformation,[],[f81]) ).
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(f183,definition,
( spl2_6
<=> aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f184,plain,
( aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f185,plain,
( ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt)))
| spl2_6 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f192,definition,
( spl2_8
<=> aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs))) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f194,plain,
( ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| spl2_8 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f221,plain,
( ~ aVector0(sziznziztdt0(xt))
| spl2_6 ),
inference(resolution,[],[f132,f185]) ).
fof(f225,plain,
( $false
| spl2_6 ),
inference(forward_subsumption_resolution,[],[f221,f148]) ).
fof(f226,plain,
spl2_6,
inference(avatar_contradiction_clause,[],[f225]) ).
fof(f1060,plain,
! [X0] :
( szszuzczcdt0(X0) != aDimensionOf0(xt)
| aDimensionOf0(sziznziztdt0(xt)) = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xt))) ),
inference(superposition,[],[f99,f147]) ).
fof(f1070,plain,
( ! [X0] :
( szszuzczcdt0(X0) != aDimensionOf0(xt)
| aDimensionOf0(sziznziztdt0(xt)) = X0
| ~ aNaturalNumber0(X0) )
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f1060,f184]) ).
fof(f1138,plain,
( aDimensionOf0(xs) != aDimensionOf0(xt)
| aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl2_6 ),
inference(superposition,[],[f1070,f144]) ).
fof(f1146,plain,
( aDimensionOf0(sziznziztdt0(xs)) = aDimensionOf0(sziznziztdt0(xt))
| ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f1138,f142]) ).
fof(f1147,plain,
( ~ aNaturalNumber0(aDimensionOf0(sziznziztdt0(xs)))
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f1146,f149]) ).
fof(f1148,plain,
( ~ spl2_8
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f1147,f183,f192]) ).
fof(f1149,plain,
( ~ aVector0(sziznziztdt0(xs))
| spl2_8 ),
inference(resolution,[],[f194,f132]) ).
fof(f1150,plain,
( $false
| spl2_8 ),
inference(forward_subsumption_resolution,[],[f1149,f145]) ).
fof(f1151,plain,
spl2_8,
inference(avatar_contradiction_clause,[],[f1150]) ).
cnf(s108,plain,
spl2_6,
inference(sat_conversion,[],[f226]) ).
cnf(s518,plain,
( ~ spl2_6
| ~ spl2_8 ),
inference(sat_conversion,[],[f1148]) ).
cnf(s521,plain,
spl2_8,
inference(sat_conversion,[],[f1151]) ).
cnf(s522,plain,
~ spl2_6,
inference(rat,[],[s518,s521]) ).
cnf(s523,plain,
$false,
inference(rat,[],[s108,s522]) ).
fof(f1152,plain,
$false,
inference(avatar_sat_refutation,[],[s523]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG047+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n008.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 23:03:09 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 % (1714287)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (1714294)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=6713279:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (1714293)% WARNING: option uhcvi not known.
% 0.17/0.47 % (1714292)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=841283800_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (1714295)dis+10_1_sil=32000:sp=arity:random_seed=2215088632:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (1714296)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=764451134:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (1714293)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2380272275:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (1714298)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2101104292:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % (1714297)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2521900482:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (1714294) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1714287-1714294"...
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % (1714294)...printing done.
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % (1714294)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Theorem for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.47 % (1714294)------------------------------
% 0.17/0.47 % (1714294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.47 % (1714294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.47 % (1714294)CaDiCaL version: 2.1.3
% 0.17/0.47 % (1714294)Termination reason: Refutation
% 0.17/0.47 % (1714294)Time elapsed: 0.012 s
% 0.17/0.47 % (1714294)Peak memory usage: 13 MB
% 0.17/0.47 % (1714294)Instructions burned: 29 (million)
% 0.17/0.47 % (1714287)Success in time 0.046 s
% 0.17/0.47 % Vampire exiting
%------------------------------------------------------------------------------