%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU341+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 : n009.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 12:48:25 PM UTC 2026
% Result : Theorem 1.09s 1.63s
% Output : Refutation 5.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 14 unt; 2 def)
% Number of atoms : 230 ( 12 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 294 ( 125 ~; 105 |; 40 &)
% ( 5 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 82 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_connsp_2) ).
fof(f33,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( element(X1,powerset(X0))
& ~ empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f39,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f40,axiom,
! [X0] :
( ( topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ( ( open_subset(X3,X1)
=> interior(X1,X3) = X3 )
& ( interior(X0,X2) = X2
=> open_subset(X2,X0) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tops_1) ).
fof(f41,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( open_subset(X1,X0)
& in(X2,X1) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_connsp_2) ).
fof(f42,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( open_subset(X1,X0)
& in(X2,X1) )
=> point_neighbourhood(X1,X0,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f43,axiom,
! [X0,X1,X2] :
~ ( in(X0,X1)
& element(X1,powerset(X2))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f78,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( point_neighbourhood(X2,X0,X1)
<=> in(X1,interior(X0,X2)) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f77]) ).
fof(f85,plain,
! [X0] :
( ? [X1] :
( element(X1,powerset(X0))
& ~ empty(X1) )
| empty(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f90,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f91,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( interior(X1,X3) = X3
| ~ open_subset(X3,X1) )
& ( open_subset(X2,X0)
| interior(X0,X2) != X2 ) )
| ~ element(X3,powerset(the_carrier(X1))) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ top_str(X1) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( interior(X1,X3) = X3
| ~ open_subset(X3,X1) )
& ( open_subset(X2,X0)
| interior(X0,X2) != X2 ) )
| ~ element(X3,powerset(the_carrier(X1))) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ top_str(X1) )
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,X0,X2)
& open_subset(X1,X0)
& in(X2,X1)
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f95,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ point_neighbourhood(X1,X0,X2)
& open_subset(X1,X0)
& in(X2,X1)
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(ennf_transformation,[],[f43]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( point_neighbourhood(X2,X0,X1)
| ~ in(X1,interior(X0,X2)) )
& ( in(X1,interior(X0,X2))
| ~ point_neighbourhood(X2,X0,X1) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f78]) ).
fof(f105,plain,
! [X0] :
( ( element(sK4(X0),powerset(X0))
& ~ empty(sK4(X0)) )
| empty(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f85]) ).
fof(f107,plain,
( ~ point_neighbourhood(sK7,sK6,sK8)
& open_subset(sK7,sK6)
& in(sK8,sK7)
& element(sK8,the_carrier(sK6))
& element(sK7,powerset(the_carrier(sK6)))
& ~ empty_carrier(sK6)
& topological_space(sK6)
& top_str(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8)],[f95]) ).
fof(f134,plain,
! [X2,X0,X1] :
( ~ topological_space(X0)
| ~ in(X1,interior(X0,X2))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| point_neighbourhood(X2,X0,X1)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f154,plain,
! [X0] :
( element(sK4(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f161,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( interior(X1,X3) = X3
| ~ open_subset(X3,X1)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ top_str(X1)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f164,plain,
top_str(sK6),
inference(cnf_transformation,[],[f107]) ).
fof(f165,plain,
topological_space(sK6),
inference(cnf_transformation,[],[f107]) ).
fof(f166,plain,
~ empty_carrier(sK6),
inference(cnf_transformation,[],[f107]) ).
fof(f167,plain,
element(sK7,powerset(the_carrier(sK6))),
inference(cnf_transformation,[],[f107]) ).
fof(f169,plain,
in(sK8,sK7),
inference(cnf_transformation,[],[f107]) ).
fof(f170,plain,
open_subset(sK7,sK6),
inference(cnf_transformation,[],[f107]) ).
fof(f171,plain,
~ point_neighbourhood(sK7,sK6,sK8),
inference(cnf_transformation,[],[f107]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(cnf_transformation,[],[f96]) ).
fof(f184,definition,
( spl9_3
<=> ! [X2,X0] :
( ~ element(X2,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f185,plain,
( ! [X2,X0] :
( ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f187,definition,
( spl9_4
<=> ! [X1,X3] :
( interior(X1,X3) = X3
| ~ top_str(X1)
| ~ element(X3,powerset(the_carrier(X1)))
| ~ open_subset(X3,X1) ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f188,plain,
( ! [X3,X1] :
( ~ open_subset(X3,X1)
| ~ top_str(X1)
| ~ element(X3,powerset(the_carrier(X1)))
| interior(X1,X3) = X3 )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f189,plain,
( spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f163,f187,f184]) ).
fof(f198,plain,
! [X0] :
( ~ element(sK7,powerset(X0))
| ~ empty(X0) ),
inference(resolution,[],[f172,f169]) ).
fof(f199,plain,
~ empty(the_carrier(sK6)),
inference(resolution,[],[f198,f167]) ).
fof(f202,plain,
( ! [X0] :
( ~ top_str(sK6)
| ~ element(X0,powerset(the_carrier(sK6))) )
| ~ spl9_3 ),
inference(resolution,[],[f185,f165]) ).
fof(f203,plain,
( ! [X0] : ~ element(X0,powerset(the_carrier(sK6)))
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f202,f164]) ).
fof(f210,plain,
( empty(the_carrier(sK6))
| ~ spl9_3 ),
inference(resolution,[],[f203,f154]) ).
fof(f216,plain,
( $false
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f210,f199]) ).
fof(f217,plain,
~ spl9_3,
inference(avatar_contradiction_clause,[],[f216]) ).
fof(f219,plain,
( ~ top_str(sK6)
| ~ element(sK7,powerset(the_carrier(sK6)))
| sK7 = interior(sK6,sK7)
| ~ spl9_4 ),
inference(resolution,[],[f188,f170]) ).
fof(f220,plain,
( ~ element(sK7,powerset(the_carrier(sK6)))
| sK7 = interior(sK6,sK7)
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f219,f164]) ).
fof(f221,plain,
( sK7 = interior(sK6,sK7)
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f220,f167]) ).
fof(f238,plain,
! [X0,X1] :
( ~ in(X0,interior(sK6,X1))
| ~ element(X1,powerset(the_carrier(sK6)))
| ~ element(X0,the_carrier(sK6))
| empty_carrier(sK6)
| point_neighbourhood(X1,sK6,X0)
| ~ top_str(sK6) ),
inference(resolution,[],[f134,f165]) ).
fof(f239,plain,
! [X0,X1] :
( ~ in(X0,interior(sK6,X1))
| ~ element(X1,powerset(the_carrier(sK6)))
| ~ element(X0,the_carrier(sK6))
| point_neighbourhood(X1,sK6,X0)
| ~ top_str(sK6) ),
inference(forward_subsumption_resolution,[],[f238,f166]) ).
fof(f240,plain,
! [X0,X1] :
( ~ in(X0,interior(sK6,X1))
| ~ element(X1,powerset(the_carrier(sK6)))
| ~ element(X0,the_carrier(sK6))
| point_neighbourhood(X1,sK6,X0) ),
inference(forward_subsumption_resolution,[],[f239,f164]) ).
fof(f267,plain,
( ! [X0] :
( ~ in(X0,sK7)
| ~ element(sK7,powerset(the_carrier(sK6)))
| ~ element(X0,the_carrier(sK6))
| point_neighbourhood(sK7,sK6,X0) )
| ~ spl9_4 ),
inference(superposition,[],[f240,f221]) ).
fof(f268,plain,
( ! [X0] :
( ~ in(X0,sK7)
| ~ element(sK7,powerset(the_carrier(sK6)))
| point_neighbourhood(sK7,sK6,X0) )
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f267,f161]) ).
fof(f269,plain,
( ! [X0] :
( point_neighbourhood(sK7,sK6,X0)
| ~ in(X0,sK7) )
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f268,f167]) ).
fof(f293,plain,
( ~ in(sK8,sK7)
| ~ spl9_4 ),
inference(resolution,[],[f269,f171]) ).
fof(f296,plain,
( $false
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f293,f169]) ).
fof(f297,plain,
~ spl9_4,
inference(avatar_contradiction_clause,[],[f296]) ).
cnf(s2,plain,
( spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f189]) ).
cnf(s6,plain,
~ spl9_3,
inference(sat_conversion,[],[f217]) ).
cnf(s8,plain,
~ spl9_4,
inference(sat_conversion,[],[f297]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s8,s6]) ).
fof(f298,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU341+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 % Computer : n009.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 28 04:48:15 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 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
% 1.09/1.63 % (2666044)Detected formulas, will run a generic FOF schedule.
% 1.09/1.63 % (2666059)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=3674567187:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.09/1.63 % (2666064)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=730468840:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.09/1.63 % (2666064)First to succeed.
% 1.09/1.63 % (2666064)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2666044"
% 1.09/1.63 % (2666065)dis-21_1_sil=8000:lcm=predicate:random_seed=3140889776: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)
% 1.09/1.63 % (2666060)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=669164356:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.09/1.63 % (2666063)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1046291402:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.09/1.63 % (2666062)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=976180459:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.09/1.63 % (2666061)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=4066156128:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.09/1.63 % (2666062)Refutation not found, incomplete strategy
% 1.09/1.63 % (2666062)------------------------------
% 1.09/1.63 % (2666062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.09/1.63 % (2666062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/1.63 % (2666062)CaDiCaL version: 2.1.3
% 1.09/1.63 % (2666062)Termination reason: Refutation not found, incomplete strategy
% 1.09/1.63 % (2666062)Time elapsed: 0.004 s
% 1.09/1.63 % (2666062)Peak memory usage: 88 MB
% 1.09/1.63 % (2666062)Instructions burned: 2 (million)
% 1.09/1.63 % (2666063)Also succeeded, but the first one will report.
% 1.09/1.63 % (2666065)Instruction limit reached!
% 1.09/1.63 % (2666065)------------------------------
% 1.09/1.63 % (2666065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.09/1.63 % (2666065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/1.63 % (2666065)CaDiCaL version: 2.1.3
% 1.09/1.63 % (2666065)Termination reason: Instruction limit
% 1.09/1.63 % (2666065)Termination phase: Saturation
% 1.09/1.63 % (2666065)Time elapsed: 0.115 s
% 1.09/1.63 % (2666065)Peak memory usage: 88 MB
% 1.09/1.63 % (2666065)Instructions burned: 130 (million)
% 1.09/1.63 % (2666079)lrs+10_1_sil=8000:sp=occurrence:random_seed=2402513206:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 1.09/1.63 % (2666079)Also succeeded, but the first one will report.
% 1.09/1.63 % (2666064)Refutation found. Thanks to Tanya!
% 1.09/1.63 % SZS status Theorem for theBenchmark
% 1.09/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 5.04/1.85 % (2666064)------------------------------
% 5.04/1.85 % (2666064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.85 % (2666064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.85 % (2666064)CaDiCaL version: 2.1.3
% 5.04/1.85 % (2666064)Termination reason: Refutation
% 5.04/1.85 % (2666064)Time elapsed: 0.014 s
% 5.04/1.85 % (2666064)Peak memory usage: 89 MB
% 5.04/1.85 % (2666064)Instructions burned: 9 (million)
% 5.04/1.85 % (2666064)------------------------------
% 5.04/1.85 % (2666064)------------------------------
% 5.04/1.85 % (2666044)Success in time 0.603 s
% 5.04/1.85 % Vampire exiting
%------------------------------------------------------------------------------