%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM455+6 : 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 : n026.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 12:24:23 PM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 12 unt; 2 def)
% Number of atoms : 94 ( 34 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 87 ( 23 ~; 22 |; 40 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 3 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f47,axiom,
( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xp,X0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ? [X0] :
( aInteger0(X0)
& sdtasdt0(xp,X0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2232) ).
fof(f48,axiom,
( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2258) ).
fof(f49,axiom,
( sdtpldt0(sz10,xp) != smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2286) ).
fof(f50,conjecture,
? [X0] :
( ( ( aInteger0(X0)
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) )
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ~ ( ( X0 = sz10
| X0 = smndt0(sz10) )
& aElementOf0(X0,cS2200) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f51,negated_conjecture,
~ ? [X0] :
( ( ( aInteger0(X0)
& ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(X0,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) )
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ~ ( ( X0 = sz10
| X0 = smndt0(sz10) )
& aElementOf0(X0,cS2200) ) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
fof(f62,plain,
( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xp,X0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(rectify,[],[f47]) ).
fof(f125,plain,
! [X0] :
( ( ( ~ aInteger0(X0)
| ( ! [X1] :
( ~ aInteger0(X1)
| sdtasdt0(xp,X1) != sdtpldt0(X0,smndt0(sz10)) )
& ~ aDivisorOf0(xp,sdtpldt0(X0,smndt0(sz10)))
& ~ sdteqdtlpzmzozddtrp0(X0,sz10,xp) ) )
& ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
| ( ( X0 = sz10
| X0 = smndt0(sz10) )
& aElementOf0(X0,cS2200) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f213,plain,
( aInteger0(sK37)
& sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) = sdtasdt0(xp,sK37)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& aInteger0(sK38)
& sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) = sdtasdt0(xp,sK38)
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37,sK38]),skolemize(X0,sK37),skolemize(X1,sK38)],[f62]) ).
fof(f430,plain,
aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[],[f213]) ).
fof(f435,plain,
aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cnf_transformation,[],[f213]) ).
fof(f440,plain,
sz10 != sdtpldt0(sz10,smndt0(xp)),
inference(cnf_transformation,[],[f48]) ).
fof(f441,plain,
sz10 != sdtpldt0(sz10,xp),
inference(cnf_transformation,[],[f48]) ).
fof(f442,plain,
( smndt0(sz10) != sdtpldt0(sz10,xp)
| smndt0(sz10) != sdtpldt0(sz10,smndt0(xp)) ),
inference(cnf_transformation,[],[f49]) ).
fof(f444,plain,
! [X0] :
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sz10 = X0
| smndt0(sz10) = X0 ),
inference(cnf_transformation,[],[f125]) ).
fof(f552,definition,
( spl39_7
<=> smndt0(sz10) = sdtpldt0(sz10,smndt0(xp)) ),
introduced(definition,[new_symbols(definition,[spl39_7])],[avatar_definition]) ).
fof(f556,definition,
( spl39_8
<=> smndt0(sz10) = sdtpldt0(sz10,xp) ),
introduced(definition,[new_symbols(definition,[spl39_8])],[avatar_definition]) ).
fof(f558,plain,
( smndt0(sz10) != sdtpldt0(sz10,xp)
| spl39_8 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f559,plain,
( ~ spl39_7
| ~ spl39_8 ),
inference(avatar_split_clause,[],[f442,f556,f552]) ).
fof(f897,plain,
( sz10 = sdtpldt0(sz10,smndt0(xp))
| smndt0(sz10) = sdtpldt0(sz10,smndt0(xp)) ),
inference(resolution,[],[f430,f444]) ).
fof(f899,plain,
smndt0(sz10) = sdtpldt0(sz10,smndt0(xp)),
inference(forward_subsumption_resolution,[],[f897,f440]) ).
fof(f904,plain,
spl39_7,
inference(avatar_split_clause,[],[f899,f552]) ).
fof(f910,plain,
( sz10 = sdtpldt0(sz10,xp)
| smndt0(sz10) = sdtpldt0(sz10,xp) ),
inference(resolution,[],[f435,f444]) ).
fof(f912,plain,
smndt0(sz10) = sdtpldt0(sz10,xp),
inference(forward_subsumption_resolution,[],[f910,f441]) ).
fof(f915,plain,
( $false
| spl39_8 ),
inference(forward_subsumption_resolution,[],[f912,f558]) ).
fof(f916,plain,
spl39_8,
inference(avatar_contradiction_clause,[],[f915]) ).
cnf(s256,plain,
( ~ spl39_7
| ~ spl39_8 ),
inference(sat_conversion,[],[f559]) ).
cnf(s503,plain,
spl39_7,
inference(sat_conversion,[],[f904]) ).
cnf(s511,plain,
spl39_8,
inference(sat_conversion,[],[f916]) ).
cnf(s512,plain,
$false,
inference(rat,[],[s256,s511,s503]) ).
fof(f917,plain,
$false,
inference(avatar_sat_refutation,[],[s512]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM455+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:01:56 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 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
% 0.12/0.46 % (3173809)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (3173816)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2555100324:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.46 % (3173815)% WARNING: option uhcvi not known.
% 0.12/0.46 % (3173814)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=529944127_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.46 % (3173815)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2778928702:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.46 % (3173817)dis+10_1_sil=32000:sp=arity:random_seed=2948088404:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.46 % (3173819)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=296151289:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.46 % (3173818)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3248901488:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.46 % (3173820)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2271644928:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.46 % (3173816) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3173809-3173816"...
% 0.12/0.46 % (3173816)...printing done.
% 0.12/0.46 % (3173816)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Theorem for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (3173816)------------------------------
% 0.12/0.46 % (3173816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (3173816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (3173816)CaDiCaL version: 2.1.3
% 0.12/0.46 % (3173816)Termination reason: Refutation
% 0.12/0.46 % (3173816)Time elapsed: 0.009 s
% 0.12/0.46 % (3173816)Peak memory usage: 13 MB
% 0.12/0.46 % (3173816)Instructions burned: 23 (million)
% 0.12/0.46 % (3173809)Success in time 0.042 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------