%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU324+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 : n008.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 0.13s 0.45s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 76 ( 13 unt; 4 def)
% Number of atoms : 224 ( 40 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 245 ( 97 ~; 95 |; 24 &)
% ( 6 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 55 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f4,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(f16,axiom,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> open_subset(interior(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_tops_1) ).
fof(f17,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f22,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).
fof(f24,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( closed_subset(X1,X0)
=> topstr_closure(X0,X1) = X1 )
& ( ( topological_space(X0)
& topstr_closure(X0,X1) = X1 )
=> closed_subset(X1,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_pre_topc) ).
fof(f25,conjecture,
! [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(f26,negated_conjecture,
~ ! [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) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f31,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,[],[f1]) ).
fof(f34,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f43,plain,
! [X0,X1] :
( open_subset(interior(X0,X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f16]) ).
fof(f44,plain,
! [X0,X1] :
( open_subset(interior(X0,X1),X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f17]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ( ( topstr_closure(X0,X1) = X1
| ~ closed_subset(X1,X0) )
& ( closed_subset(X1,X0)
| ~ topological_space(X0)
| topstr_closure(X0,X1) != X1 ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( ( topstr_closure(X0,X1) = X1
| ~ closed_subset(X1,X0) )
& ( closed_subset(X1,X0)
| ~ topological_space(X0)
| topstr_closure(X0,X1) != X1 ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(flattening,[],[f54]) ).
fof(f56,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,[],[f26]) ).
fof(f57,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,[],[f56]) ).
fof(f58,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,[],[f31]) ).
fof(f60,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f67,plain,
! [X0,X1] :
( open_subset(interior(X0,X1),X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f44]) ).
fof(f68,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f45]) ).
fof(f78,plain,
! [X0,X1] :
( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ open_subset(X1,X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f80,plain,
! [X0,X1] :
( ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| topstr_closure(X0,X1) = X1 ),
inference(cnf_transformation,[],[f55]) ).
fof(f82,plain,
( ~ open_subset(sK7,sK5)
| open_subset(sK8,sK6) ),
inference(cnf_transformation,[],[f57]) ).
fof(f83,plain,
( ~ open_subset(sK7,sK5)
| sK8 != interior(sK6,sK8) ),
inference(cnf_transformation,[],[f57]) ).
fof(f84,plain,
( sK7 = interior(sK5,sK7)
| open_subset(sK8,sK6) ),
inference(cnf_transformation,[],[f57]) ).
fof(f85,plain,
( sK7 = interior(sK5,sK7)
| sK8 != interior(sK6,sK8) ),
inference(cnf_transformation,[],[f57]) ).
fof(f86,plain,
element(sK8,powerset(the_carrier(sK6))),
inference(cnf_transformation,[],[f57]) ).
fof(f87,plain,
element(sK7,powerset(the_carrier(sK5))),
inference(cnf_transformation,[],[f57]) ).
fof(f88,plain,
top_str(sK6),
inference(cnf_transformation,[],[f57]) ).
fof(f89,plain,
top_str(sK5),
inference(cnf_transformation,[],[f57]) ).
fof(f90,plain,
topological_space(sK5),
inference(cnf_transformation,[],[f57]) ).
fof(f92,definition,
( spl9_1
<=> open_subset(sK8,sK6) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f94,plain,
( open_subset(sK8,sK6)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f96,definition,
( spl9_2
<=> open_subset(sK7,sK5) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f98,plain,
( ~ open_subset(sK7,sK5)
| spl9_2 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f99,plain,
( spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f82,f96,f92]) ).
fof(f101,definition,
( spl9_3
<=> sK8 = interior(sK6,sK8) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
fof(f103,plain,
( sK8 != interior(sK6,sK8)
| spl9_3 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( ~ spl9_3
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f83,f96,f101]) ).
fof(f106,definition,
( spl9_4
<=> sK7 = interior(sK5,sK7) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
fof(f108,plain,
( sK7 = interior(sK5,sK7)
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f109,plain,
( spl9_1
| spl9_4 ),
inference(avatar_split_clause,[],[f84,f106,f92]) ).
fof(f110,plain,
( ~ spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f85,f106,f101]) ).
fof(f122,plain,
sK8 = subset_complement(the_carrier(sK6),subset_complement(the_carrier(sK6),sK8)),
inference(resolution,[],[f68,f86]) ).
fof(f136,plain,
( open_subset(sK7,sK5)
| ~ top_str(sK5)
| ~ topological_space(sK5)
| ~ element(sK7,powerset(the_carrier(sK5)))
| ~ spl9_4 ),
inference(superposition,[],[f67,f108]) ).
fof(f137,plain,
( ~ top_str(sK5)
| ~ topological_space(sK5)
| ~ element(sK7,powerset(the_carrier(sK5)))
| spl9_2
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f136,f98]) ).
fof(f138,plain,
( ~ topological_space(sK5)
| ~ element(sK7,powerset(the_carrier(sK5)))
| spl9_2
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f137,f89]) ).
fof(f139,plain,
( ~ element(sK7,powerset(the_carrier(sK5)))
| spl9_2
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f138,f90]) ).
fof(f140,plain,
( $false
| spl9_2
| ~ spl9_4 ),
inference(forward_subsumption_resolution,[],[f139,f87]) ).
fof(f141,plain,
( spl9_2
| ~ spl9_4 ),
inference(avatar_contradiction_clause,[],[f140]) ).
fof(f228,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ open_subset(X0,X1)
| ~ element(subset_complement(the_carrier(X1),X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| subset_complement(the_carrier(X1),X0) = topstr_closure(X1,subset_complement(the_carrier(X1),X0)) ),
inference(resolution,[],[f78,f80]) ).
fof(f234,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ open_subset(X0,X1)
| ~ element(subset_complement(the_carrier(X1),X0),powerset(the_carrier(X1)))
| subset_complement(the_carrier(X1),X0) = topstr_closure(X1,subset_complement(the_carrier(X1),X0)) ),
inference(duplicate_literal_removal,[],[f228]) ).
fof(f239,plain,
! [X0,X1] :
( ~ open_subset(X0,X1)
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1)))
| subset_complement(the_carrier(X1),X0) = topstr_closure(X1,subset_complement(the_carrier(X1),X0)) ),
inference(forward_subsumption_resolution,[],[f234,f60]) ).
fof(f285,plain,
! [X0] :
( ~ element(X0,powerset(the_carrier(sK6)))
| interior(sK6,X0) = subset_complement(the_carrier(sK6),topstr_closure(sK6,subset_complement(the_carrier(sK6),X0))) ),
inference(resolution,[],[f58,f88]) ).
fof(f296,plain,
interior(sK6,sK8) = subset_complement(the_carrier(sK6),topstr_closure(sK6,subset_complement(the_carrier(sK6),sK8))),
inference(resolution,[],[f285,f86]) ).
fof(f438,plain,
( ~ top_str(sK6)
| ~ element(sK8,powerset(the_carrier(sK6)))
| subset_complement(the_carrier(sK6),sK8) = topstr_closure(sK6,subset_complement(the_carrier(sK6),sK8))
| ~ spl9_1 ),
inference(resolution,[],[f239,f94]) ).
fof(f450,plain,
( ~ element(sK8,powerset(the_carrier(sK6)))
| subset_complement(the_carrier(sK6),sK8) = topstr_closure(sK6,subset_complement(the_carrier(sK6),sK8))
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f438,f88]) ).
fof(f457,plain,
( subset_complement(the_carrier(sK6),sK8) = topstr_closure(sK6,subset_complement(the_carrier(sK6),sK8))
| ~ spl9_1 ),
inference(forward_subsumption_resolution,[],[f450,f86]) ).
fof(f505,plain,
( interior(sK6,sK8) = subset_complement(the_carrier(sK6),subset_complement(the_carrier(sK6),sK8))
| ~ spl9_1 ),
inference(superposition,[],[f296,f457]) ).
fof(f515,plain,
( sK8 = interior(sK6,sK8)
| ~ spl9_1 ),
inference(forward_demodulation,[],[f505,f122]) ).
fof(f519,plain,
( $false
| ~ spl9_1
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f515,f103]) ).
fof(f520,plain,
( ~ spl9_1
| spl9_3 ),
inference(avatar_contradiction_clause,[],[f519]) ).
cnf(s1,plain,
( spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f99]) ).
cnf(s2,plain,
( ~ spl9_2
| ~ spl9_3 ),
inference(sat_conversion,[],[f104]) ).
cnf(s3,plain,
( spl9_1
| spl9_4 ),
inference(sat_conversion,[],[f109]) ).
cnf(s4,plain,
( ~ spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f110]) ).
cnf(s5,plain,
( spl9_2
| ~ spl9_4 ),
inference(sat_conversion,[],[f141]) ).
cnf(s28,plain,
( ~ spl9_1
| spl9_3 ),
inference(sat_conversion,[],[f520]) ).
cnf(s37,plain,
spl9_1,
inference(rat,[],[s5,s1,s3]) ).
cnf(s38,plain,
spl9_3,
inference(rat,[],[s28,s37]) ).
cnf(s39,plain,
spl9_4,
inference(rat,[],[s4,s38]) ).
cnf(s40,plain,
~ spl9_2,
inference(rat,[],[s2,s38]) ).
cnf(s41,plain,
$false,
inference(rat,[],[s5,s39,s40]) ).
fof(f526,plain,
$false,
inference(avatar_sat_refutation,[],[s41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU324+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.37 % Computer : n008.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 04:43:24 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 Running first-order model finding
% 0.13/0.40 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
% 0.13/0.45 % (1881976)Will run a generic schedule for satisfiability detection.
% 0.13/0.45 % (1881985)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2120721467:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.45 % (1881982)% WARNING: option uhcvi not known.
% 0.13/0.45 % (1881985) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1881976-1881985"...
% 0.13/0.45 % (1881981)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=414045572_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.45 % (1881983)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=104465860:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.45 % (1881987)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=273825847:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.45 % (1881984)dis+10_1_sil=32000:sp=arity:random_seed=1729796473:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.45 % (1881986)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2383250976:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.45 % (1881982)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1407606271:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.45 % (1881985)...printing done.
% 0.13/0.45 % (1881985)Refutation found. Thanks to Tanya!
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.45 % (1881985)------------------------------
% 0.13/0.45 % (1881985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.45 % (1881985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.45 % (1881985)CaDiCaL version: 2.1.3
% 0.13/0.45 % (1881985)Termination reason: Refutation
% 0.13/0.45 % (1881985)Time elapsed: 0.008 s
% 0.13/0.45 % (1881985)Peak memory usage: 12 MB
% 0.13/0.45 % (1881985)Instructions burned: 17 (million)
% 0.13/0.45 % (1881976)Success in time 0.034 s
% 0.13/0.45 % Vampire exiting
%------------------------------------------------------------------------------