%------------------------------------------------------------------------------
% File : Vampire---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 THM
% 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 12:48:20 PM UTC 2026
% Result : Theorem 2.83s 1.29s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 10 unt; 2 def)
% Number of atoms : 145 ( 4 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 160 ( 69 ~; 62 |; 17 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 44 !; 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] :
( ~ topological_space(X0)
| open_subset(subset_complement(the_carrier(X0),X1),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] :
( closed_subset(topstr_closure(X0,X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f36]) ).
fof(f67,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ),
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(f73,plain,
! [X0] :
( open_subset(subset_complement(the_carrier(sK4),X0),sK4)
| ~ top_str(sK4)
| ~ closed_subset(X0,sK4)
| ~ element(X0,powerset(the_carrier(sK4))) ),
inference(resolution,[],[f52,f69]) ).
fof(f74,plain,
! [X0] :
( open_subset(subset_complement(the_carrier(sK4),X0),sK4)
| ~ closed_subset(X0,sK4)
| ~ element(X0,powerset(the_carrier(sK4))) ),
inference(forward_subsumption_resolution,[],[f73,f68]) ).
fof(f81,plain,
! [X0] :
( interior(sK4,X0) = subset_complement(the_carrier(sK4),topstr_closure(sK4,subset_complement(the_carrier(sK4),X0)))
| ~ element(X0,powerset(the_carrier(sK4))) ),
inference(resolution,[],[f67,f68]) ).
fof(f96,plain,
! [X0] :
( open_subset(interior(sK4,X0),sK4)
| ~ closed_subset(topstr_closure(sK4,subset_complement(the_carrier(sK4),X0)),sK4)
| ~ element(topstr_closure(sK4,subset_complement(the_carrier(sK4),X0)),powerset(the_carrier(sK4)))
| ~ element(X0,powerset(the_carrier(sK4))) ),
inference(superposition,[],[f74,f81]) ).
fof(f146,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)))
| ~ element(sK5,powerset(the_carrier(sK4))) ),
inference(resolution,[],[f96,f71]) ).
fof(f149,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,[],[f146,f70]) ).
fof(f151,definition,
( spl6_7
<=> element(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),powerset(the_carrier(sK4))) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
fof(f153,plain,
( ~ element(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),powerset(the_carrier(sK4)))
| spl6_7 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f155,definition,
( spl6_8
<=> closed_subset(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),sK4) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
fof(f157,plain,
( ~ closed_subset(topstr_closure(sK4,subset_complement(the_carrier(sK4),sK5)),sK4)
| spl6_8 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,plain,
( ~ spl6_7
| ~ spl6_8 ),
inference(avatar_split_clause,[],[f149,f155,f151]) ).
fof(f159,plain,
( ~ top_str(sK4)
| ~ element(subset_complement(the_carrier(sK4),sK5),powerset(the_carrier(sK4)))
| spl6_7 ),
inference(resolution,[],[f153,f58]) ).
fof(f161,plain,
( ~ element(subset_complement(the_carrier(sK4),sK5),powerset(the_carrier(sK4)))
| spl6_7 ),
inference(forward_subsumption_resolution,[],[f159,f68]) ).
fof(f169,plain,
( ~ element(sK5,powerset(the_carrier(sK4)))
| spl6_7 ),
inference(resolution,[],[f161,f57]) ).
fof(f171,plain,
( $false
| spl6_7 ),
inference(forward_subsumption_resolution,[],[f169,f70]) ).
fof(f172,plain,
spl6_7,
inference(avatar_contradiction_clause,[],[f171]) ).
fof(f181,plain,
( ~ topological_space(sK4)
| ~ top_str(sK4)
| ~ element(subset_complement(the_carrier(sK4),sK5),powerset(the_carrier(sK4)))
| spl6_8 ),
inference(resolution,[],[f157,f59]) ).
fof(f182,plain,
( ~ top_str(sK4)
| ~ element(subset_complement(the_carrier(sK4),sK5),powerset(the_carrier(sK4)))
| spl6_8 ),
inference(forward_subsumption_resolution,[],[f181,f69]) ).
fof(f188,plain,
( ~ element(subset_complement(the_carrier(sK4),sK5),powerset(the_carrier(sK4)))
| spl6_8 ),
inference(forward_subsumption_resolution,[],[f182,f68]) ).
fof(f194,plain,
( ~ element(sK5,powerset(the_carrier(sK4)))
| spl6_8 ),
inference(resolution,[],[f188,f57]) ).
fof(f196,plain,
( $false
| spl6_8 ),
inference(forward_subsumption_resolution,[],[f194,f70]) ).
fof(f197,plain,
spl6_8,
inference(avatar_contradiction_clause,[],[f196]) ).
cnf(s6,plain,
( ~ spl6_7
| ~ spl6_8 ),
inference(sat_conversion,[],[f158]) ).
cnf(s7,plain,
spl6_7,
inference(sat_conversion,[],[f172]) ).
cnf(s9,plain,
spl6_8,
inference(sat_conversion,[],[f197]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s6,s9,s7]) ).
fof(f198,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:42:34 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.83/1.29 % (3665516)Detected formulas, will run a generic FOF schedule.
% 2.83/1.29 % (3665522)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2461789918:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.83/1.29 % (3665525)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3737496519:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.83/1.29 % (3665521)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=3974645751:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.83/1.29 % (3665523)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=763258731:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.83/1.29 % (3665524)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=689021070:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.83/1.29 % (3665527)dis-21_1_sil=8000:lcm=predicate:random_seed=1552880020:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.83/1.29 % (3665526)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4002599011:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.83/1.29 % (3665525)Refutation not found, incomplete strategy
% 2.83/1.29 % (3665525)------------------------------
% 2.83/1.29 % (3665525)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.29 % (3665524)Refutation not found, incomplete strategy
% 2.83/1.29 % (3665524)------------------------------
% 2.83/1.29 % (3665524)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.29 % (3665524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.29 % (3665525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.29 % (3665525)CaDiCaL version: 2.1.3
% 2.83/1.29 % (3665524)CaDiCaL version: 2.1.3
% 2.83/1.29 % (3665525)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.29 % (3665525)Time elapsed: 0.001 s
% 2.83/1.29 % (3665525)Peak memory usage: 87 MB
% 2.83/1.29 % (3665524)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.29 % (3665524)Time elapsed: 0.001 s
% 2.83/1.29 % (3665524)Peak memory usage: 88 MB
% 2.83/1.29 % (3665527)Refutation not found, incomplete strategy
% 2.83/1.29 % (3665527)------------------------------
% 2.83/1.29 % (3665527)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.29 % (3665527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.29 % (3665527)CaDiCaL version: 2.1.3
% 2.83/1.29 % (3665527)Termination reason: Refutation not found, incomplete strategy
% 2.83/1.29 % (3665527)Time elapsed: 0.002 s
% 2.83/1.29 % (3665527)Peak memory usage: 88 MB
% 2.83/1.29 % (3665527)Instructions burned: 1 (million)
% 2.83/1.29 % (3665526)First to succeed.
% 2.83/1.29 % (3665526)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3665516"
% 2.83/1.29 % (3665527)------------------------------
% 2.83/1.29 % (3665527)------------------------------
% 2.83/1.29 % (3665524)------------------------------
% 2.83/1.29 % (3665524)------------------------------
% 2.83/1.29 % (3665525)------------------------------
% 2.83/1.29 % (3665525)------------------------------
% 2.83/1.29 % (3665526)Refutation found. Thanks to Tanya!
% 2.83/1.29 % SZS status Theorem for theBenchmark
% 2.83/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.49 % (3665526)------------------------------
% 3.63/1.49 % (3665526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.49 % (3665526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.49 % (3665526)CaDiCaL version: 2.1.3
% 3.63/1.49 % (3665526)Termination reason: Refutation
% 3.63/1.49 % (3665526)Time elapsed: 0.008 s
% 3.63/1.49 % (3665526)Peak memory usage: 89 MB
% 3.63/1.49 % (3665526)Instructions burned: 8 (million)
% 3.63/1.49 % (3665526)------------------------------
% 3.63/1.49 % (3665526)------------------------------
% 3.63/1.49 % (3665516)Success in time 0.431 s
% 3.63/1.49 % Vampire exiting
%------------------------------------------------------------------------------