%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU323+2 : 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 : n005.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 12:48:21 PM UTC 2026
% Result : Theorem 5.88s 1.82s
% Output : Refutation 5.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 14 unt; 2 def)
% Number of atoms : 112 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 47 ~; 38 |; 15 &)
% ( 4 <=>; 11 =>; 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 : 44 ( 0 sgn 40 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f65,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(f148,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(f161,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(f216,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(f426,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
fof(f483,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(f484,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)],[f483]) ).
fof(f653,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,[],[f65]) ).
fof(f719,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f148]) ).
fof(f728,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f161]) ).
fof(f729,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f728]) ).
fof(f768,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,[],[f216]) ).
fof(f769,plain,
! [X0,X1] :
( closed_subset(topstr_closure(X0,X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f768]) ).
fof(f1017,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f426]) ).
fof(f1079,plain,
? [X0] :
( ? [X1] :
( ~ open_subset(interior(X0,X1),X0)
& element(X1,powerset(the_carrier(X0))) )
& topological_space(X0)
& top_str(X0) ),
inference(ennf_transformation,[],[f484]) ).
fof(f1080,plain,
? [X0] :
( ? [X1] :
( ~ open_subset(interior(X0,X1),X0)
& element(X1,powerset(the_carrier(X0))) )
& topological_space(X0)
& top_str(X0) ),
inference(flattening,[],[f1079]) ).
fof(f1675,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subset(X1,X0)
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0) ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f1017]) ).
fof(f1709,plain,
( ~ open_subset(interior(sK385,sK386),sK385)
& element(sK386,powerset(the_carrier(sK385)))
& topological_space(sK385)
& top_str(sK385) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK385,sK386]),skolemize(X0,sK385),skolemize(X1,sK386)],[f1080]) ).
fof(f1924,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,[],[f653]) ).
fof(f2155,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f719]) ).
fof(f2162,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f729]) ).
fof(f2248,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,[],[f769]) ).
fof(f2948,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1675]) ).
fof(f3046,plain,
top_str(sK385),
inference(cnf_transformation,[],[f1709]) ).
fof(f3047,plain,
topological_space(sK385),
inference(cnf_transformation,[],[f1709]) ).
fof(f3048,plain,
element(sK386,powerset(the_carrier(sK385))),
inference(cnf_transformation,[],[f1709]) ).
fof(f3049,plain,
~ open_subset(interior(sK385,sK386),sK385),
inference(cnf_transformation,[],[f1709]) ).
fof(f3472,plain,
interior(sK385,sK386) = subset_complement(the_carrier(sK385),topstr_closure(sK385,subset_complement(the_carrier(sK385),sK386))),
inference(unit_resulting_resolution,[],[f1924,f3046,f3048]) ).
fof(f3484,plain,
( open_subset(interior(sK385,sK386),sK385)
| ~ closed_subset(topstr_closure(sK385,subset_complement(the_carrier(sK385),sK386)),sK385)
| ~ element(topstr_closure(sK385,subset_complement(the_carrier(sK385),sK386)),powerset(the_carrier(sK385)))
| ~ top_str(sK385) ),
inference(superposition,[],[f2948,f3472]) ).
fof(f3485,plain,
( ~ closed_subset(topstr_closure(sK385,subset_complement(the_carrier(sK385),sK386)),sK385)
| ~ element(topstr_closure(sK385,subset_complement(the_carrier(sK385),sK386)),powerset(the_carrier(sK385)))
| ~ top_str(sK385) ),
inference(forward_subsumption_resolution,[],[f3484,f3049]) ).
fof(f3488,plain,
( ~ closed_subset(topstr_closure(sK385,subset_complement(the_carrier(sK385),sK386)),sK385)
| ~ element(topstr_closure(sK385,subset_complement(the_carrier(sK385),sK386)),powerset(the_carrier(sK385))) ),
inference(forward_subsumption_resolution,[],[f3485,f3046]) ).
fof(f3490,definition,
( spl395_55
<=> element(topstr_closure(sK385,subset_complement(the_carrier(sK385),sK386)),powerset(the_carrier(sK385))) ),
introduced(definition,[new_symbols(definition,[spl395_55])],[avatar_definition]) ).
fof(f3504,definition,
( spl395_58
<=> closed_subset(topstr_closure(sK385,subset_complement(the_carrier(sK385),sK386)),sK385) ),
introduced(definition,[new_symbols(definition,[spl395_58])],[avatar_definition]) ).
fof(f3507,plain,
( ~ spl395_55
| ~ spl395_58 ),
inference(avatar_split_clause,[],[f3488,f3504,f3490]) ).
fof(f3625,plain,
element(subset_complement(the_carrier(sK385),sK386),powerset(the_carrier(sK385))),
inference(unit_resulting_resolution,[],[f2155,f3048]) ).
fof(f4112,plain,
element(topstr_closure(sK385,subset_complement(the_carrier(sK385),sK386)),powerset(the_carrier(sK385))),
inference(unit_resulting_resolution,[],[f2162,f3046,f3625]) ).
fof(f4113,plain,
closed_subset(topstr_closure(sK385,subset_complement(the_carrier(sK385),sK386)),sK385),
inference(unit_resulting_resolution,[],[f2248,f3047,f3046,f3625]) ).
fof(f4124,plain,
spl395_55,
inference(avatar_split_clause,[],[f4112,f3490]) ).
fof(f4125,plain,
spl395_58,
inference(avatar_split_clause,[],[f4113,f3504]) ).
cnf(s48,plain,
( ~ spl395_55
| ~ spl395_58 ),
inference(sat_conversion,[],[f3507]) ).
cnf(s72,plain,
spl395_55,
inference(sat_conversion,[],[f4124]) ).
cnf(s73,plain,
spl395_58,
inference(sat_conversion,[],[f4125]) ).
cnf(s79,plain,
$false,
inference(rat,[],[s48,s73,s72]) ).
fof(f4126,plain,
$false,
inference(avatar_sat_refutation,[],[s79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU323+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n005.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 04:42:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 4.64/1.63 % (435640)Detected formulas, will run a generic FOF schedule.
% 4.64/1.63 % (435647)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=2711274687:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.64/1.63 % (435645)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=2812145622:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.64/1.63 % (435650)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=106298983:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.64/1.63 % (435648)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2137398188:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.64/1.63 % (435649)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3201245441:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.64/1.63 % (435646)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=2016758484:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.64/1.63 % (435651)dis-21_1_sil=8000:lcm=predicate:random_seed=1549897701: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)
% 4.64/1.63 % (435648)Instruction limit reached!
% 4.64/1.63 % (435648)------------------------------
% 4.64/1.63 % (435648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.63 % (435648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.63 % (435648)CaDiCaL version: 2.1.3
% 4.64/1.63 % (435648)Termination reason: Instruction limit
% 4.64/1.63 % (435648)Termination phase: Saturation
% 4.64/1.63 % (435648)Time elapsed: 0.060 s
% 4.64/1.63 % (435648)Peak memory usage: 91 MB
% 4.64/1.63 % (435648)Instructions burned: 110 (million)
% 4.64/1.63 % (435651)Instruction limit reached!
% 4.64/1.63 % (435651)------------------------------
% 4.64/1.63 % (435651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.63 % (435651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.63 % (435651)CaDiCaL version: 2.1.3
% 4.64/1.63 % (435651)Termination reason: Instruction limit
% 4.64/1.63 % (435651)Termination phase: Saturation
% 4.64/1.63 % (435651)Time elapsed: 0.065 s
% 4.64/1.63 % (435651)Peak memory usage: 90 MB
% 4.64/1.63 % (435651)Instructions burned: 130 (million)
% 4.64/1.63 % (435649)Instruction limit reached!
% 4.64/1.63 % (435649)------------------------------
% 4.64/1.63 % (435649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.63 % (435649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.63 % (435649)CaDiCaL version: 2.1.3
% 4.64/1.63 % (435649)Termination reason: Instruction limit
% 4.64/1.63 % (435649)Termination phase: Saturation
% 4.64/1.63 % (435649)Time elapsed: 0.077 s
% 4.64/1.63 % (435649)Peak memory usage: 90 MB
% 4.64/1.63 % (435649)Instructions burned: 120 (million)
% 4.64/1.63 % (435650)Instruction limit reached!
% 4.64/1.63 % (435650)------------------------------
% 4.64/1.63 % (435650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.63 % (435650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.63 % (435650)CaDiCaL version: 2.1.3
% 4.64/1.63 % (435650)Termination reason: Instruction limit
% 4.64/1.63 % (435650)Termination phase: Saturation
% 4.64/1.63 % (435650)Time elapsed: 0.092 s
% 4.64/1.63 % (435650)Peak memory usage: 91 MB
% 4.64/1.63 % (435650)Instructions burned: 140 (million)
% 4.64/1.63 % (435660)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1790020246:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.64/1.63 % (435659)lrs+10_1_sil=8000:sp=occurrence:random_seed=905913752:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.64/1.63 % (435661)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3745735140:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.64/1.63 % (435662)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=458252226:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.64/1.63 % (435660)Instruction limit reached!
% 4.64/1.63 % (435660)------------------------------
% 4.64/1.63 % (435660)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.88/1.82 % (435660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.88/1.82 % (435660)CaDiCaL version: 2.1.3
% 5.88/1.82 % (435660)Termination reason: Instruction limit
% 5.88/1.82 % (435660)Termination phase: Saturation
% 5.88/1.82 % (435660)Time elapsed: 0.090 s
% 5.88/1.82 % (435660)Peak memory usage: 90 MB
% 5.88/1.82 % (435660)Instructions burned: 157 (million)
% 5.88/1.82 % (435662)First to succeed.
% 5.88/1.82 % (435662)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-435640"
% 5.88/1.82 % (435659)Instruction limit reached!
% 5.88/1.82 % (435659)------------------------------
% 5.88/1.82 % (435659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.88/1.82 % (435659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.88/1.82 % (435659)CaDiCaL version: 2.1.3
% 5.88/1.82 % (435659)Termination reason: Instruction limit
% 5.88/1.82 % (435659)Termination phase: Saturation
% 5.88/1.82 % (435659)Time elapsed: 0.186 s
% 5.88/1.82 % (435659)Peak memory usage: 94 MB
% 5.88/1.82 % (435659)Instructions burned: 285 (million)
% 5.88/1.82 % (435667)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3695478456:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.88/1.82 % (435661)Instruction limit reached!
% 5.88/1.82 % (435661)------------------------------
% 5.88/1.82 % (435661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.88/1.82 % (435661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.88/1.82 % (435661)CaDiCaL version: 2.1.3
% 5.88/1.82 % (435661)Termination reason: Instruction limit
% 5.88/1.82 % (435661)Termination phase: Saturation
% 5.88/1.82 % (435661)Time elapsed: 0.224 s
% 5.88/1.82 % (435661)Peak memory usage: 95 MB
% 5.88/1.82 % (435661)Instructions burned: 326 (million)
% 5.88/1.82 % (435662)Refutation found. Thanks to Tanya!
% 5.88/1.82 % SZS status Theorem for theBenchmark
% 5.88/1.82 % SZS output start Proof for theBenchmark
% See solution above
% 5.88/1.82 % (435662)------------------------------
% 5.88/1.82 % (435662)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.88/1.82 % (435662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.88/1.82 % (435662)CaDiCaL version: 2.1.3
% 5.88/1.82 % (435662)Termination reason: Refutation
% 5.88/1.82 % (435662)Time elapsed: 0.060 s
% 5.88/1.82 % (435662)Peak memory usage: 92 MB
% 5.88/1.82 % (435662)Instructions burned: 99 (million)
% 5.88/1.82 % (435662)------------------------------
% 5.88/1.82 % (435662)------------------------------
% 5.88/1.82 % (435640)Success in time 0.759 s
% 5.88/1.82 % Vampire exiting
%------------------------------------------------------------------------------