%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM469+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 12:24:26 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 12 unt; 2 def)
% Number of atoms : 135 ( 42 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 119 ( 40 ~; 40 |; 33 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 16 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f33,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240) ).
fof(f34,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xl,X0) )
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240_04) ).
fof(f35,axiom,
( xl != sz00
=> ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1298) ).
fof(f36,conjecture,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X0) )
| doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f37,negated_conjecture,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xm,xn) = sdtasdt0(xl,X0) )
| doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xl,X0) )
& doDivides0(xl,xm)
& ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xl,X1) )
& doDivides0(xl,xn) ),
inference(rectify,[],[f34]) ).
fof(f42,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f43,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f42]) ).
fof(f50,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f56,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f92,plain,
( ( aNaturalNumber0(sdtsldt0(xm,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) )
| sz00 = xl ),
inference(ennf_transformation,[],[f35]) ).
fof(f93,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(xl,X0) != sdtpldt0(xm,xn) )
& ~ doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(ennf_transformation,[],[f37]) ).
fof(f104,plain,
( aNaturalNumber0(sK2)
& xm = sdtasdt0(xl,sK2)
& doDivides0(xl,xm)
& aNaturalNumber0(sK3)
& xn = sdtasdt0(xl,sK3)
& doDivides0(xl,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f40]) ).
fof(f108,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f113,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f50]) ).
fof(f118,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f159,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f33]) ).
fof(f162,plain,
xn = sdtasdt0(xl,sK3),
inference(cnf_transformation,[],[f104]) ).
fof(f163,plain,
aNaturalNumber0(sK3),
inference(cnf_transformation,[],[f104]) ).
fof(f164,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f104]) ).
fof(f167,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| sz00 = xl ),
inference(cnf_transformation,[],[f92]) ).
fof(f169,plain,
( aNaturalNumber0(sdtsldt0(xn,xl))
| sz00 = xl ),
inference(cnf_transformation,[],[f92]) ).
fof(f171,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| sz00 = xl ),
inference(cnf_transformation,[],[f92]) ).
fof(f172,plain,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f93]) ).
fof(f173,plain,
! [X0] :
( sdtasdt0(xl,X0) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f194,definition,
( spl4_3
<=> sz00 = xl ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f195,plain,
( sz00 != xl
| spl4_3 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f196,plain,
( sz00 = xl
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f198,definition,
( spl4_4
<=> aNaturalNumber0(sdtsldt0(xn,xl)) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f200,plain,
( aNaturalNumber0(sdtsldt0(xn,xl))
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f201,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f169,f198,f194]) ).
fof(f230,plain,
xm = sdtpldt0(xm,sz00),
inference(resolution,[],[f113,f159]) ).
fof(f266,plain,
sz00 = sdtasdt0(sz00,sK3),
inference(resolution,[],[f118,f163]) ).
fof(f361,plain,
( xn = sdtasdt0(sz00,sK3)
| ~ spl4_3 ),
inference(superposition,[],[f162,f196]) ).
fof(f375,plain,
( sz00 = xn
| ~ spl4_3 ),
inference(forward_demodulation,[],[f361,f266]) ).
fof(f378,plain,
( ~ doDivides0(xl,sdtpldt0(xm,sz00))
| ~ spl4_3 ),
inference(superposition,[],[f172,f375]) ).
fof(f393,plain,
( ~ doDivides0(xl,xm)
| ~ spl4_3 ),
inference(forward_demodulation,[],[f378,f230]) ).
fof(f399,plain,
( $false
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f393,f164]) ).
fof(f400,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[],[f399]) ).
fof(f406,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f171,f195]) ).
fof(f521,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f167,f195]) ).
fof(f549,plain,
( sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| spl4_3 ),
inference(superposition,[],[f173,f521]) ).
fof(f552,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| spl4_3 ),
inference(trivial_inequality_removal,[],[f549]) ).
fof(f557,plain,
( ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| spl4_3 ),
inference(resolution,[],[f552,f108]) ).
fof(f558,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f557,f406]) ).
fof(f559,plain,
( $false
| spl4_3
| ~ spl4_4 ),
inference(forward_subsumption_resolution,[],[f558,f200]) ).
fof(f560,plain,
( spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f559]) ).
cnf(s90,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f201]) ).
cnf(s251,plain,
~ spl4_3,
inference(sat_conversion,[],[f400]) ).
cnf(s346,plain,
( spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f560]) ).
cnf(s347,plain,
~ spl4_4,
inference(rat,[],[s346,s251]) ).
cnf(s350,plain,
$false,
inference(rat,[],[s90,s347,s251]) ).
fof(f561,plain,
$false,
inference(avatar_sat_refutation,[],[s350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM469+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n006.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 20:03:55 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.48 % (3281761)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (3281769)dis+10_1_sil=32000:sp=arity:random_seed=481934616:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (3281767)% WARNING: option uhcvi not known.
% 0.16/0.48 % (3281766)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1582561896_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % (3281767)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1703879729:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (3281768)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2760387492:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (3281770)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1341527944:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (3281771)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1483780245:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % (3281772)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3138697745:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % (3281768) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3281761-3281768"...
% 0.16/0.48 % (3281768)...printing done.
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % (3281768)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (3281768)------------------------------
% 0.16/0.48 % (3281768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (3281768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (3281768)CaDiCaL version: 2.1.3
% 0.16/0.48 % (3281768)Termination reason: Refutation
% 0.16/0.48 % (3281768)Time elapsed: 0.013 s
% 0.16/0.48 % (3281768)Peak memory usage: 12 MB
% 0.16/0.48 % (3281768)Instructions burned: 18 (million)
% 0.16/0.48 % (3281761)Success in time 0.051 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------