%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:52:52 PM UTC 2026
% Result : Theorem 0.16s 0.47s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 11 unt; 3 def)
% Number of atoms : 155 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 170 ( 74 ~; 66 |; 17 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 40 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> open_subset(subset_complement(the_carrier(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tops_1) ).
fof(f6,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f7,axiom,
! [X0,X1] :
( ( top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f9,axiom,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> closed_subset(topstr_closure(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
fof(f20,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
fof(f21,conjecture,
! [X0] :
( ( topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> open_subset(interior(X0,X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
fof(f22,negated_conjecture,
~ ! [X0] :
( ( topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> open_subset(interior(X0,X1),X0) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f27,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f27]) ).
fof(f32,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f7]) ).
fof(f34,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( closed_subset(topstr_closure(X0,X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f9]) ).
fof(f36,plain,
! [X0,X1] :
( closed_subset(topstr_closure(X0,X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f35]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1)))
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f45,plain,
? [X0] :
( ? [X1] :
( ~ open_subset(interior(X0,X1),X0)
& element(X1,powerset(the_carrier(X0))) )
& topological_space(X0)
& top_str(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f46,plain,
? [X0] :
( ? [X1] :
( ~ open_subset(interior(X0,X1),X0)
& element(X1,powerset(the_carrier(X0))) )
& topological_space(X0)
& top_str(X0) ),
inference(flattening,[],[f45]) ).
fof(f51,plain,
( ~ open_subset(interior(sK4,sK5),sK4)
& element(sK5,powerset(the_carrier(sK4)))
& topological_space(sK4)
& top_str(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f46]) ).
fof(f52,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f28]) ).
fof(f57,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f32]) ).
fof(f58,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f34]) ).
fof(f59,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ top_str(X0)
| closed_subset(topstr_closure(X0,X1),X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f67,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f68,plain,
top_str(sK4),
inference(cnf_transformation,[],[f51]) ).
fof(f69,plain,
topological_space(sK4),
inference(cnf_transformation,[],[f51]) ).
fof(f70,plain,
element(sK5,powerset(the_carrier(sK4))),
inference(cnf_transformation,[],[f51]) ).
fof(f71,plain,
~ open_subset(interior(sK4,sK5),sK4),
inference(cnf_transformation,[],[f51]) ).
fof(f102,definition,
( spl6_1
<=> element(subset_complement(the_carrier(sK4),sK5),powerset(the_carrier(sK4))) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f103,plain,
( element(subset_complement(the_carrier(sK4),sK5),powerset(the_carrier(sK4)))
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f104,plain,
( ~ element(subset_complement(the_carrier(sK4),sK5),powerset(the_carrier(sK4)))
| spl6_1 ),
inference(avatar_component_clause,[],[f102]) ).
fof(f114,plain,
( ~ element(sK5,powerset(the_carrier(sK4)))
| spl6_1 ),
inference(resolution,[],[f104,f57]) ).
fof(f116,plain,
( $false
| spl6_1 ),
inference(forward_subsumption_resolution,[],[f114,f70]) ).
fof(f117,plain,
spl6_1,
inference(avatar_contradiction_clause,[],[f116]) ).
fof(f143,plain,
( interior(sK4,sK5) = subset_complement(the_carrier(sK4),topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)))
| ~ top_str(sK4) ),
inference(resolution,[],[f67,f70]) ).
fof(f148,plain,
interior(sK4,sK5) = subset_complement(the_carrier(sK4),topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5))),
inference(forward_subsumption_resolution,[],[f143,f68]) ).
fof(f150,plain,
( open_subset(interior(sK4,sK5),sK4)
| ~ topological_space(sK4)
| ~ top_str(sK4)
| ~ closed_subset(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),sK4)
| ~ element(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),powerset(the_carrier(sK4))) ),
inference(superposition,[],[f52,f148]) ).
fof(f153,definition,
( spl6_6
<=> element(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),powerset(the_carrier(sK4))) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
fof(f155,plain,
( ~ element(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),powerset(the_carrier(sK4)))
| spl6_6 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f161,plain,
( ~ topological_space(sK4)
| ~ top_str(sK4)
| ~ closed_subset(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),sK4)
| ~ element(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),powerset(the_carrier(sK4))) ),
inference(forward_subsumption_resolution,[],[f150,f71]) ).
fof(f163,plain,
( ~ top_str(sK4)
| ~ closed_subset(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),sK4)
| ~ element(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),powerset(the_carrier(sK4))) ),
inference(forward_subsumption_resolution,[],[f161,f69]) ).
fof(f165,plain,
( ~ closed_subset(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),sK4)
| ~ element(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),powerset(the_carrier(sK4))) ),
inference(forward_subsumption_resolution,[],[f163,f68]) ).
fof(f176,definition,
( spl6_10
<=> closed_subset(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),sK4) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
fof(f179,plain,
( ~ spl6_6
| ~ spl6_10 ),
inference(avatar_split_clause,[],[f165,f176,f153]) ).
fof(f186,plain,
( ~ topological_space(sK4)
| ~ top_str(sK4)
| closed_subset(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),sK4)
| ~ spl6_1 ),
inference(resolution,[],[f103,f59]) ).
fof(f188,plain,
( ~ top_str(sK4)
| closed_subset(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),sK4)
| ~ spl6_1 ),
inference(forward_subsumption_resolution,[],[f186,f69]) ).
fof(f190,plain,
( closed_subset(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),sK4)
| ~ spl6_1 ),
inference(forward_subsumption_resolution,[],[f188,f68]) ).
fof(f192,plain,
( spl6_10
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f190,f102,f176]) ).
fof(f196,plain,
( ~ top_str(sK4)
| ~ element(subset_complement(the_carrier(sK4),sK5),powerset(the_carrier(sK4)))
| spl6_6 ),
inference(resolution,[],[f155,f58]) ).
fof(f198,plain,
( ~ element(subset_complement(the_carrier(sK4),sK5),powerset(the_carrier(sK4)))
| spl6_6 ),
inference(forward_subsumption_resolution,[],[f196,f68]) ).
fof(f199,plain,
( $false
| ~ spl6_1
| spl6_6 ),
inference(forward_subsumption_resolution,[],[f198,f103]) ).
fof(f200,plain,
( ~ spl6_1
| spl6_6 ),
inference(avatar_contradiction_clause,[],[f199]) ).
cnf(s2,plain,
spl6_1,
inference(sat_conversion,[],[f117]) ).
cnf(s7,plain,
( ~ spl6_6
| ~ spl6_10 ),
inference(sat_conversion,[],[f179]) ).
cnf(s9,plain,
( ~ spl6_1
| spl6_10 ),
inference(sat_conversion,[],[f192]) ).
cnf(s10,plain,
( ~ spl6_1
| spl6_6 ),
inference(sat_conversion,[],[f200]) ).
cnf(s11,plain,
spl6_6,
inference(rat,[],[s10,s2]) ).
cnf(s12,plain,
spl6_10,
inference(rat,[],[s9,s2]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s7,s12,s11]) ).
fof(f201,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU323+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n019.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 : Mon Sep 28 04:42:18 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.16/0.47 % (3665102)Will run a generic schedule for satisfiability detection.
% 0.16/0.47 % (3665109)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4179561498:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.47 % (3665108)% WARNING: option uhcvi not known.
% 0.16/0.47 % (3665110)dis+10_1_sil=32000:sp=arity:random_seed=1347421921:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.47 % (3665107)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1181831036_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.47 % (3665108)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=686109998:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.47 % (3665112)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3112848964:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.47 % (3665111)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1011220152:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.47 % (3665113)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2161604803:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.47 % TRYING [1]
% 0.16/0.47 % TRYING [2]
% 0.16/0.47 % TRYING [3]
% 0.16/0.47 % (3665110) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3665102-3665110"...
% 0.16/0.47 % (3665111) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3665102-3665111"...
% 0.16/0.47 % (3665110)...printing done.
% 0.16/0.47 % (3665108) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3665102-3665108"...
% 0.16/0.47 % (3665110)Refutation found. Thanks to Tanya!
% 0.16/0.47 % SZS status Theorem for theBenchmark
% 0.16/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.47 % (3665110)------------------------------
% 0.16/0.47 % (3665110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.47 % (3665110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.47 % (3665110)CaDiCaL version: 2.1.3
% 0.16/0.47 % (3665110)Termination reason: Refutation
% 0.16/0.47 % (3665110)Time elapsed: 0.006 s
% 0.16/0.47 % (3665110)Peak memory usage: 12 MB
% 0.16/0.47 % (3665110)Instructions burned: 6 (million)
% 0.16/0.47 % (3665102)Success in time 0.042 s
% 0.16/0.47 % Vampire exiting
%------------------------------------------------------------------------------