%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 12:17:48 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 8 unt; 1 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 13 ~; 13 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 5 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',a2) ).
fof(f73,axiom,
member(empty_set,infinity),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',infinity2) ).
fof(f190,axiom,
! [X0] :
( ~ little_set(X0)
| member(X0,natural_numbers)
| member(empty_set,f44(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM003-0.ax',natural_numbers4) ).
fof(f192,axiom,
! [X0] :
( ~ member(X0,f44(X0))
| member(X0,natural_numbers) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM003-0.ax',natural_numbers6) ).
fof(f247,negated_conjecture,
~ member(empty_set,natural_numbers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_zero_is_a_natural) ).
fof(f1012,definition,
( spl0_13
<=> little_set(empty_set) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f1013,plain,
( little_set(empty_set)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f1014,plain,
( ~ little_set(empty_set)
| spl0_13 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f1021,plain,
( ! [X0] : ~ member(empty_set,X0)
| spl0_13 ),
inference(resolution,[],[f1014,f1]) ).
fof(f1027,plain,
( $false
| spl0_13 ),
inference(resolution,[],[f1021,f73]) ).
fof(f1037,plain,
spl0_13,
inference(avatar_contradiction_clause,[],[f1027]) ).
fof(f1043,plain,
( member(empty_set,natural_numbers)
| member(empty_set,f44(empty_set))
| ~ spl0_13 ),
inference(resolution,[],[f1013,f190]) ).
fof(f1056,plain,
( member(empty_set,f44(empty_set))
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1043,f247]) ).
fof(f1071,plain,
( member(empty_set,natural_numbers)
| ~ spl0_13 ),
inference(resolution,[],[f1056,f192]) ).
fof(f1073,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1071,f247]) ).
fof(f1074,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f1073]) ).
cnf(s10,plain,
spl0_13,
inference(sat_conversion,[],[f1037]) ).
cnf(s11,plain,
~ spl0_13,
inference(sat_conversion,[],[f1074]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s10,s11]) ).
fof(f1075,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n007.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 18:37:25 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
% 0.20/0.49 % (1705078)Will run a generic schedule for satisfiability detection.
% 0.20/0.49 % (1705087)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1632001900:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.49 % (1705084)% WARNING: option uhcvi not known.
% 0.20/0.49 % (1705085)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4020526817:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.49 % (1705083)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1533232140_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.49 % (1705084)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3567201506:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.49 % (1705086)dis+10_1_sil=32000:sp=arity:random_seed=764108723:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.49 % (1705088)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1963769187:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.49 % (1705089)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2069253184:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.49 % (1705087) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1705078-1705087"...
% 0.20/0.49 % (1705087)...printing done.
% 0.20/0.49 % (1705087)Refutation found. Thanks to Tanya!
% 0.20/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (1705087)------------------------------
% 0.20/0.49 % (1705087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.49 % (1705087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.49 % (1705087)CaDiCaL version: 2.1.3
% 0.20/0.49 % (1705087)Termination reason: Refutation
% 0.20/0.49 % (1705087)Time elapsed: 0.017 s
% 0.20/0.49 % (1705087)Peak memory usage: 13 MB
% 0.20/0.49 % (1705087)Instructions burned: 54 (million)
% 0.20/0.49 % (1705078)Success in time 0.05 s
% 0.20/0.49 % Vampire exiting
%------------------------------------------------------------------------------