%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM010-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:11:33 PM UTC 2026
% Result : Unsatisfiable 3.88s 1.43s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 9 unt; 2 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 137 ( 65 ~; 70 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f72,axiom,
little_set(infinity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity1) ).
fof(f73,axiom,
member(empty_set,infinity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity2) ).
fof(f74,axiom,
! [X0] :
( member(successor(X0),infinity)
| ~ member(X0,infinity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity3) ).
fof(f187,axiom,
! [X0,X1] :
( ~ member(empty_set,X1)
| ~ little_set(X1)
| ~ member(X0,natural_numbers)
| member(f43(X0,X1),X1)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers1) ).
fof(f188,axiom,
! [X0,X1] :
( ~ member(successor(f43(X0,X1)),X1)
| ~ little_set(X1)
| ~ member(empty_set,X1)
| ~ member(X0,natural_numbers)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers2) ).
fof(f189,axiom,
! [X0] :
( little_set(f44(X0))
| ~ little_set(X0)
| member(X0,natural_numbers) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers3) ).
fof(f190,axiom,
! [X0] :
( member(empty_set,f44(X0))
| ~ little_set(X0)
| member(X0,natural_numbers) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers4) ).
fof(f191,axiom,
! [X0,X1] :
( member(successor(X1),f44(X0))
| ~ little_set(X0)
| ~ member(X1,f44(X0))
| member(X0,natural_numbers) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers5) ).
fof(f192,axiom,
! [X0] :
( ~ member(X0,f44(X0))
| member(X0,natural_numbers) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers6) ).
fof(f247,axiom,
member(f74,natural_numbers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_natural_number) ).
fof(f248,negated_conjecture,
~ member(successor(f74),natural_numbers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_it_has_a_successor) ).
fof(f283,plain,
! [X0] :
( ~ little_set(successor(X0))
| ~ member(X0,f44(successor(X0)))
| member(successor(X0),natural_numbers)
| member(successor(X0),natural_numbers) ),
inference(resolution,[],[f191,f192]) ).
fof(f284,plain,
! [X0] :
( ~ little_set(successor(X0))
| ~ member(X0,f44(successor(X0)))
| member(successor(X0),natural_numbers) ),
inference(duplicate_literal_removal,[],[f283]) ).
fof(f292,plain,
! [X0] :
( ~ little_set(infinity)
| ~ member(empty_set,infinity)
| ~ member(X0,natural_numbers)
| member(X0,infinity)
| ~ member(f43(X0,infinity),infinity) ),
inference(resolution,[],[f188,f74]) ).
fof(f293,plain,
! [X0,X1] :
( ~ little_set(f44(X0))
| ~ member(empty_set,f44(X0))
| ~ member(X1,natural_numbers)
| member(X1,f44(X0))
| ~ little_set(X0)
| ~ member(f43(X1,f44(X0)),f44(X0))
| member(X0,natural_numbers) ),
inference(resolution,[],[f188,f191]) ).
fof(f294,plain,
! [X0,X1] :
( ~ little_set(f44(X0))
| ~ member(empty_set,f44(X0))
| ~ member(X1,natural_numbers)
| member(X1,f44(X0))
| ~ little_set(X0)
| member(X0,natural_numbers) ),
inference(forward_subsumption_resolution,[],[f293,f187]) ).
fof(f295,plain,
! [X0] :
( ~ little_set(infinity)
| ~ member(empty_set,infinity)
| ~ member(X0,natural_numbers)
| member(X0,infinity) ),
inference(forward_subsumption_resolution,[],[f292,f187]) ).
fof(f296,plain,
! [X0,X1] :
( ~ member(empty_set,f44(X0))
| ~ member(X1,natural_numbers)
| member(X1,f44(X0))
| ~ little_set(X0)
| member(X0,natural_numbers) ),
inference(forward_subsumption_resolution,[],[f294,f189]) ).
fof(f297,plain,
! [X0] :
( ~ member(empty_set,infinity)
| ~ member(X0,natural_numbers)
| member(X0,infinity) ),
inference(forward_subsumption_resolution,[],[f295,f72]) ).
fof(f298,plain,
! [X0,X1] :
( member(X1,f44(X0))
| ~ member(X1,natural_numbers)
| ~ little_set(X0)
| member(X0,natural_numbers) ),
inference(forward_subsumption_resolution,[],[f296,f190]) ).
fof(f299,plain,
! [X0] :
( member(X0,infinity)
| ~ member(X0,natural_numbers) ),
inference(forward_subsumption_resolution,[],[f297,f73]) ).
fof(f562,plain,
! [X0,X1] :
( member(successor(X0),natural_numbers)
| ~ member(X0,f44(successor(X0)))
| ~ member(successor(X0),X1) ),
inference(resolution,[],[f284,f1]) ).
fof(f1256,plain,
! [X0] :
( ~ member(f74,f44(successor(f74)))
| ~ member(successor(f74),X0) ),
inference(resolution,[],[f562,f248]) ).
fof(f1259,definition,
( spl0_47
<=> ! [X0] : ~ member(successor(f74),X0) ),
introduced(definition,[new_symbols(definition,[spl0_47])],[avatar_definition]) ).
fof(f1260,plain,
( ! [X0] : ~ member(successor(f74),X0)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f1262,definition,
( spl0_48
<=> member(f74,f44(successor(f74))) ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
fof(f1264,plain,
( ~ member(f74,f44(successor(f74)))
| spl0_48 ),
inference(avatar_component_clause,[],[f1262]) ).
fof(f1265,plain,
( spl0_47
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f1256,f1262,f1259]) ).
fof(f1266,plain,
( ~ member(f74,natural_numbers)
| ~ little_set(successor(f74))
| member(successor(f74),natural_numbers)
| spl0_48 ),
inference(resolution,[],[f1264,f298]) ).
fof(f1267,plain,
( ~ little_set(successor(f74))
| member(successor(f74),natural_numbers)
| spl0_48 ),
inference(forward_subsumption_resolution,[],[f1266,f247]) ).
fof(f1268,plain,
( ~ little_set(successor(f74))
| spl0_48 ),
inference(forward_subsumption_resolution,[],[f1267,f248]) ).
fof(f1272,plain,
( ! [X0] : ~ member(successor(f74),X0)
| spl0_48 ),
inference(resolution,[],[f1268,f1]) ).
fof(f1273,plain,
( spl0_47
| spl0_48 ),
inference(avatar_split_clause,[],[f1272,f1262,f1259]) ).
fof(f1294,plain,
( ~ member(f74,infinity)
| ~ spl0_47 ),
inference(resolution,[],[f1260,f74]) ).
fof(f1309,plain,
( ~ member(f74,natural_numbers)
| ~ spl0_47 ),
inference(resolution,[],[f1294,f299]) ).
fof(f1310,plain,
( $false
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1309,f247]) ).
fof(f1311,plain,
~ spl0_47,
inference(avatar_contradiction_clause,[],[f1310]) ).
cnf(s32,plain,
( spl0_47
| ~ spl0_48 ),
inference(sat_conversion,[],[f1265]) ).
cnf(s33,plain,
( spl0_47
| spl0_48 ),
inference(sat_conversion,[],[f1273]) ).
cnf(s35,plain,
~ spl0_47,
inference(sat_conversion,[],[f1311]) ).
cnf(s36,plain,
spl0_48,
inference(rat,[],[s33,s35]) ).
cnf(s37,plain,
$false,
inference(rat,[],[s32,s36,s35]) ).
fof(f1312,plain,
$false,
inference(avatar_sat_refutation,[],[s37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM010-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n014.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 18:39:16 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.88/1.43 % (1095316)Input is clausal, will run a generic CNF schedule.
% 3.88/1.43 % (1095323)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=324953686:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.88/1.43 % (1095324)lrs+10_1_sil=8000:sp=occurrence:random_seed=1644379627:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.88/1.43 % (1095326)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4125190312:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.88/1.43 % (1095327)dis-21_1_sil=8000:lcm=predicate:random_seed=2226795246:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.88/1.43 % (1095321)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=485688022:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.88/1.43 % (1095325)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=902648845:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.88/1.43 % (1095322)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1259172272:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.88/1.43 % (1095325)Refutation not found, incomplete strategy
% 3.88/1.43 % (1095325)------------------------------
% 3.88/1.43 % (1095325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.43 % (1095324)Refutation not found, incomplete strategy
% 3.88/1.43 % (1095324)------------------------------
% 3.88/1.43 % (1095324)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.43 % (1095325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.43 % (1095324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.43 % (1095325)CaDiCaL version: 2.1.3
% 3.88/1.43 % (1095324)CaDiCaL version: 2.1.3
% 3.88/1.43 % (1095324)Termination reason: Refutation not found, incomplete strategy
% 3.88/1.43 % (1095324)Time elapsed: 0.001 s
% 3.88/1.43 % (1095325)Termination reason: Refutation not found, incomplete strategy
% 3.88/1.43 % (1095325)Time elapsed: 0.001 s
% 3.88/1.43 % (1095324)Peak memory usage: 87 MB
% 3.88/1.43 % (1095325)Peak memory usage: 87 MB
% 3.88/1.43 % (1095325)Instructions burned: 1 (million)
% 3.88/1.43 % (1095326)First to succeed.
% 3.88/1.43 % (1095326)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1095316"
% 3.88/1.43 % (1095327)Instruction limit reached!
% 3.88/1.43 % (1095327)------------------------------
% 3.88/1.43 % (1095327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.43 % (1095327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.43 % (1095327)CaDiCaL version: 2.1.3
% 3.88/1.43 % (1095327)Termination reason: Instruction limit
% 3.88/1.43 % (1095327)Termination phase: Saturation
% 3.88/1.43 % (1095327)Time elapsed: 0.068 s
% 3.88/1.43 % (1095327)Peak memory usage: 89 MB
% 3.88/1.43 % (1095327)Instructions burned: 118 (million)
% 3.88/1.43 % (1095325)------------------------------
% 3.88/1.43 % (1095325)------------------------------
% 3.88/1.43 % (1095324)------------------------------
% 3.88/1.43 % (1095324)------------------------------
% 3.88/1.43 % (1095335)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2082482588:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.88/1.43 % (1095335)Refutation not found, incomplete strategy
% 3.88/1.43 % (1095335)------------------------------
% 3.88/1.43 % (1095335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.43 % (1095335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.43 % (1095335)CaDiCaL version: 2.1.3
% 3.88/1.43 % (1095335)Termination reason: Refutation not found, incomplete strategy
% 3.88/1.43 % (1095335)Time elapsed: 0.001 s
% 3.88/1.43 % (1095335)Peak memory usage: 87 MB
% 3.88/1.43 % (1095335)Instructions burned: 1 (million)
% 3.88/1.43 % (1095326)Refutation found. Thanks to Tanya!
% 3.88/1.43 % SZS status Unsatisfiable for theBenchmark
% 3.88/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.88/1.43 % (1095326)------------------------------
% 3.88/1.43 % (1095326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.43 % (1095326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.43 % (1095326)CaDiCaL version: 2.1.3
% 3.88/1.43 % (1095326)Termination reason: Refutation
% 3.88/1.43 % (1095326)Time elapsed: 0.044 s
% 3.88/1.43 % (1095326)Peak memory usage: 90 MB
% 3.88/1.43 % (1095326)Instructions burned: 57 (million)
% 3.88/1.43 % (1095326)------------------------------
% 3.88/1.43 % (1095326)------------------------------
% 3.88/1.43 % (1095316)Success in time 0.478 s
% 3.88/1.43 % Vampire exiting
%------------------------------------------------------------------------------