%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM183-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:11:53 PM UTC 2026
% Result : Unsatisfiable 3.49s 1.24s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 24 ( 14 unt; 1 def)
% Number of atoms : 38 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 19 ~; 13 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f155,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',limit_ordinals) ).
fof(f176,negated_conjecture,
member(x,ordinal_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordinals_are_kind_1_or_limit_1) ).
fof(f177,negated_conjecture,
~ member(x,kind_1_ordinals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordinals_are_kind_1_or_limit_2) ).
fof(f178,negated_conjecture,
~ member(x,limit_ordinals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordinals_are_kind_1_or_limit_3) ).
fof(f201,plain,
~ member(x,intersection(complement(kind_1_ordinals),ordinal_numbers)),
inference(superposition,[],[f178,f155]) ).
fof(f250,definition,
( spl0_6
<=> member(x,universal_class) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f251,plain,
( ~ member(x,universal_class)
| spl0_6 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f257,plain,
( ! [X0] :
( ~ member(x,X0)
| ~ subclass(X0,universal_class) )
| spl0_6 ),
inference(resolution,[],[f251,f1]) ).
fof(f258,plain,
( ! [X0] : ~ member(x,X0)
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f257,f4]) ).
fof(f270,plain,
( $false
| spl0_6 ),
inference(resolution,[],[f258,f176]) ).
fof(f273,plain,
spl0_6,
inference(avatar_contradiction_clause,[],[f270]) ).
fof(f274,plain,
( ~ member(x,ordinal_numbers)
| ~ member(x,complement(kind_1_ordinals)) ),
inference(resolution,[],[f23,f201]) ).
fof(f279,plain,
~ member(x,complement(kind_1_ordinals)),
inference(forward_subsumption_resolution,[],[f274,f176]) ).
fof(f280,plain,
( ~ member(x,universal_class)
| member(x,kind_1_ordinals) ),
inference(resolution,[],[f279,f25]) ).
fof(f282,plain,
~ member(x,universal_class),
inference(forward_subsumption_resolution,[],[f280,f177]) ).
fof(f283,plain,
~ spl0_6,
inference(avatar_split_clause,[],[f282,f250]) ).
cnf(s5,plain,
spl0_6,
inference(sat_conversion,[],[f273]) ).
cnf(s6,plain,
~ spl0_6,
inference(sat_conversion,[],[f283]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s5,s6]) ).
fof(f284,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM183-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n013.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 19:05:51 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.49/1.24 % (495400)Input is clausal, will run a generic CNF schedule.
% 3.49/1.24 % (495411)dis-21_1_sil=8000:lcm=predicate:random_seed=2208612331: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)
% 3.49/1.24 % (495411)Instruction limit reached!
% 3.49/1.24 % (495411)------------------------------
% 3.49/1.24 % (495411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.24 % (495411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.24 % (495411)CaDiCaL version: 2.1.3
% 3.49/1.24 % (495411)Termination reason: Instruction limit
% 3.49/1.24 % (495411)Termination phase: Saturation
% 3.49/1.24 % (495411)Time elapsed: 0.034 s
% 3.49/1.24 % (495411)Peak memory usage: 89 MB
% 3.49/1.24 % (495411)Instructions burned: 120 (million)
% 3.49/1.24 % (495407)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3288017969:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.49/1.24 % (495409)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2633107701:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.49/1.24 % (495408)lrs+10_1_sil=8000:sp=occurrence:random_seed=1391025121:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.49/1.24 % (495405)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=1241631798:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.49/1.24 % (495410)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3467028703:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.49/1.24 % (495406)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=468438691:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.49/1.24 % (495409)First to succeed.
% 3.49/1.24 % (495409)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-495400"
% 3.49/1.24 % (495408)Also succeeded, but the first one will report.
% 3.49/1.24 % (495410)Also succeeded, but the first one will report.
% 3.49/1.24 % (495419)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=1024354158:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.49/1.24 % (495419)Refutation not found, incomplete strategy
% 3.49/1.24 % (495419)------------------------------
% 3.49/1.24 % (495419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.24 % (495419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.24 % (495419)CaDiCaL version: 2.1.3
% 3.49/1.24 % (495419)Termination reason: Refutation not found, incomplete strategy
% 3.49/1.24 % (495419)Time elapsed: 0.002 s
% 3.49/1.24 % (495419)Peak memory usage: 88 MB
% 3.49/1.24 % (495419)Instructions burned: 4 (million)
% 3.49/1.24 % (495409)Refutation found. Thanks to Tanya!
% 3.49/1.24 % SZS status Unsatisfiable for theBenchmark
% 3.49/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/1.24 % (495409)------------------------------
% 3.49/1.24 % (495409)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.49/1.24 % (495409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.49/1.24 % (495409)CaDiCaL version: 2.1.3
% 3.49/1.24 % (495409)Termination reason: Refutation
% 3.49/1.24 % (495409)Time elapsed: 0.006 s
% 3.49/1.24 % (495409)Peak memory usage: 89 MB
% 3.49/1.24 % (495409)Instructions burned: 5 (million)
% 3.49/1.24 % (495409)------------------------------
% 3.49/1.24 % (495409)------------------------------
% 3.49/1.24 % (495400)Success in time 0.441 s
% 3.49/1.24 % Vampire exiting
%------------------------------------------------------------------------------