%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n013.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 4.52s 1.68s
% Output : Refutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 10 ( 5 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 15 ( 8 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 5 ( 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f73,axiom,
member(empty_set,infinity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity2) ).
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(f192,axiom,
! [X0] :
( ~ member(X0,f44(X0))
| member(X0,natural_numbers) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',natural_numbers6) ).
fof(f247,negated_conjecture,
~ member(empty_set,natural_numbers),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_zero_is_a_natural) ).
fof(f303,plain,
( ~ little_set(empty_set)
| member(empty_set,natural_numbers)
| member(empty_set,natural_numbers) ),
inference(resolution,[],[f190,f192]) ).
fof(f304,plain,
( ~ little_set(empty_set)
| member(empty_set,natural_numbers) ),
inference(duplicate_literal_removal,[],[f303]) ).
fof(f305,plain,
~ little_set(empty_set),
inference(forward_subsumption_resolution,[],[f304,f247]) ).
fof(f306,plain,
! [X0] : ~ member(empty_set,X0),
inference(resolution,[],[f305,f1]) ).
fof(f307,plain,
$false,
inference(resolution,[],[f306,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n013.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 18:38:51 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 4.52/1.68 % (481776)Input is clausal, will run a generic CNF schedule.
% 4.52/1.68 % (481846)lrs+10_1_sil=8000:sp=occurrence:random_seed=1547532854:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.52/1.68 % (481846)Refutation not found, incomplete strategy
% 4.52/1.68 % (481846)------------------------------
% 4.52/1.68 % (481846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.52/1.68 % (481846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.52/1.68 % (481846)CaDiCaL version: 2.1.3
% 4.52/1.68 % (481846)Termination reason: Refutation not found, incomplete strategy
% 4.52/1.68 % (481846)Time elapsed: 0.001 s
% 4.52/1.68 % (481846)Peak memory usage: 86 MB
% 4.52/1.68 % (481841)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=4256237484:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.52/1.68 % (481844)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=585125157:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.52/1.68 % (481843)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=586298436:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.52/1.68 % (481848)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2810400279:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.52/1.68 % (481847)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2449436984:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.52/1.68 % (481849)dis-21_1_sil=8000:lcm=predicate:random_seed=2999484156: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)
% 4.52/1.68 % (481848)First to succeed.
% 4.52/1.68 % (481847)Refutation not found, incomplete strategy
% 4.52/1.68 % (481847)------------------------------
% 4.52/1.68 % (481847)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.52/1.68 % (481847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.52/1.68 % (481847)CaDiCaL version: 2.1.3
% 4.52/1.68 % (481847)Termination reason: Refutation not found, incomplete strategy
% 4.52/1.68 % (481847)Time elapsed: 0.002 s
% 4.52/1.68 % (481847)Peak memory usage: 86 MB
% 4.52/1.68 % (481847)Instructions burned: 1 (million)
% 4.52/1.68 % (481848)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-481776"
% 4.52/1.68 % (481849)Instruction limit reached!
% 4.52/1.68 % (481849)------------------------------
% 4.52/1.68 % (481849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.52/1.68 % (481849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.52/1.68 % (481849)CaDiCaL version: 2.1.3
% 4.52/1.68 % (481849)Termination reason: Instruction limit
% 4.52/1.68 % (481849)Termination phase: Saturation
% 4.52/1.68 % (481849)Time elapsed: 0.112 s
% 4.52/1.68 % (481849)Peak memory usage: 89 MB
% 4.52/1.68 % (481849)Instructions burned: 117 (million)
% 4.52/1.68 % (481846)------------------------------
% 4.52/1.68 % (481846)------------------------------
% 4.52/1.68 % (481848)Refutation found. Thanks to Tanya!
% 4.52/1.68 % SZS status Unsatisfiable for theBenchmark
% 4.52/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 4.52/1.68 % (481848)------------------------------
% 4.52/1.68 % (481848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.52/1.68 % (481848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.52/1.68 % (481848)CaDiCaL version: 2.1.3
% 4.52/1.68 % (481848)Termination reason: Refutation
% 4.52/1.68 % (481848)Time elapsed: 0.007 s
% 4.52/1.68 % (481848)Peak memory usage: 89 MB
% 4.52/1.68 % (481848)Instructions burned: 9 (million)
% 4.52/1.68 % (481848)------------------------------
% 4.52/1.68 % (481848)------------------------------
% 4.52/1.68 % (481776)Success in time 0.568 s
% 4.52/1.68 % Vampire exiting
%------------------------------------------------------------------------------