%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM519+3 : 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 : 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 12:15:34 PM UTC 2026
% Result : ContradictoryAxioms 2.62s 1.26s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 10 unt; 2 def)
% Number of atoms : 68 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 61 ( 20 ~; 16 |; 24 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 2 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f51,axiom,
( ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xr,X0) )
& doDivides0(xr,xn) )
| ( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xr,X0) )
& doDivides0(xr,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2449) ).
fof(f52,axiom,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xr,X0) )
| doDivides0(xr,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(f53,axiom,
~ ( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xr,X0) )
| doDivides0(xr,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2698) ).
fof(f61,plain,
( ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xr,X0) )
& doDivides0(xr,xn) )
| ( ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xr,X1) )
& doDivides0(xr,xm) ) ),
inference(rectify,[],[f51]) ).
fof(f74,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xn != sdtasdt0(xr,X0) )
& ~ doDivides0(xr,xn) ),
inference(ennf_transformation,[],[f52]) ).
fof(f75,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| xm != sdtasdt0(xr,X0) )
& ~ doDivides0(xr,xm) ),
inference(ennf_transformation,[],[f53]) ).
fof(f142,definition,
( ( ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xr,X1) )
& doDivides0(xr,xm) )
| ~ sP2 ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f143,plain,
( ( ? [X0] :
( aNaturalNumber0(X0)
& xn = sdtasdt0(xr,X0) )
& doDivides0(xr,xn) )
| sP2 ),
inference(definition_folding,[],[f61,f142]) ).
fof(f157,plain,
( ( ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xr,X1) )
& doDivides0(xr,xm) )
| ~ sP2 ),
inference(nnf_transformation,[],[f142]) ).
fof(f158,plain,
( ( ? [X0] :
( aNaturalNumber0(X0)
& xm = sdtasdt0(xr,X0) )
& doDivides0(xr,xm) )
| ~ sP2 ),
inference(rectify,[],[f157]) ).
fof(f159,plain,
( ( aNaturalNumber0(sK14)
& xm = sdtasdt0(xr,sK14)
& doDivides0(xr,xm) )
| ~ sP2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f158]) ).
fof(f160,plain,
( ( aNaturalNumber0(sK15)
& xn = sdtasdt0(xr,sK15)
& doDivides0(xr,xn) )
| sP2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X0,sK15)],[f143]) ).
fof(f238,plain,
( doDivides0(xr,xm)
| ~ sP2 ),
inference(cnf_transformation,[],[f159]) ).
fof(f241,plain,
( doDivides0(xr,xn)
| sP2 ),
inference(cnf_transformation,[],[f160]) ).
fof(f244,plain,
~ doDivides0(xr,xn),
inference(cnf_transformation,[],[f74]) ).
fof(f246,plain,
~ doDivides0(xr,xm),
inference(cnf_transformation,[],[f75]) ).
fof(f380,plain,
sP2,
inference(forward_subsumption_resolution,[],[f241,f244]) ).
fof(f382,definition,
( spl48_1
<=> sP2 ),
introduced(definition,[new_symbols(definition,[spl48_1])],[avatar_definition]) ).
fof(f384,plain,
( sP2
| ~ spl48_1 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f421,plain,
spl48_1,
inference(avatar_split_clause,[],[f380,f382]) ).
fof(f920,plain,
~ sP2,
inference(resolution,[],[f246,f238]) ).
fof(f923,plain,
( $false
| ~ spl48_1 ),
inference(forward_subsumption_resolution,[],[f920,f384]) ).
fof(f924,plain,
~ spl48_1,
inference(avatar_contradiction_clause,[],[f923]) ).
cnf(s3,plain,
spl48_1,
inference(sat_conversion,[],[f421]) ).
cnf(s25,plain,
~ spl48_1,
inference(sat_conversion,[],[f924]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s3,s25]) ).
fof(f925,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM519+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:19:41 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 2.62/1.26 % (894699)Detected formulas, will run a generic FOF schedule.
% 2.62/1.26 % (894707)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2115550736:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.62/1.26 % (894707)First to succeed.
% 2.62/1.26 % (894707)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-894699"
% 2.62/1.26 % (894706)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=1726290421:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.62/1.26 % (894710)dis-21_1_sil=8000:lcm=predicate:random_seed=1514901391: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)
% 2.62/1.26 % (894704)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=362866064:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.62/1.26 % (894705)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=1046908435:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.62/1.26 % (894708)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=175749660:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.62/1.26 % (894709)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=912281365:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.62/1.26 % (894708)Also succeeded, but the first one will report.
% 2.62/1.26 % (894710)Also succeeded, but the first one will report.
% 2.62/1.26 % (894709)Also succeeded, but the first one will report.
% 2.62/1.26 % (894707)Refutation found. Thanks to Tanya!
% 2.62/1.26 % SZS status ContradictoryAxioms for theBenchmark
% 2.62/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.26 % (894707)------------------------------
% 2.62/1.26 % (894707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.26 % (894707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.26 % (894707)CaDiCaL version: 2.1.3
% 2.62/1.26 % (894707)Termination reason: Refutation
% 2.62/1.26 % (894707)Time elapsed: 0.009 s
% 2.62/1.26 % (894707)Peak memory usage: 90 MB
% 2.62/1.26 % (894707)Instructions burned: 23 (million)
% 2.62/1.26 % (894707)------------------------------
% 2.62/1.26 % (894707)------------------------------
% 2.62/1.26 % (894699)Success in time 0.303 s
% 2.62/1.26 % Vampire exiting
%------------------------------------------------------------------------------