%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU320+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 : n017.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 12:52:51 PM UTC 2026
% Result : Theorem 0.15s 0.52s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 9 unt; 3 def)
% Number of atoms : 139 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 146 ( 59 ~; 59 |; 12 &)
% ( 7 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 26 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,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(f10,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(f12,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(f13,conjecture,
! [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(f14,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f22,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,[],[f12]) ).
fof(f23,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,[],[f14]) ).
fof(f27,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,[],[f22]) ).
fof(f28,plain,
? [X0] :
( ? [X1] :
( ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0) )
& ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| open_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(nnf_transformation,[],[f23]) ).
fof(f29,plain,
? [X0] :
( ? [X1] :
( ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0) )
& ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| open_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
( ( ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ open_subset(sK3,sK2) )
& ( closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| open_subset(sK3,sK2) )
& element(sK3,powerset(the_carrier(sK2)))
& top_str(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,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,[],[f27]) ).
fof(f37,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,[],[f27]) ).
fof(f38,plain,
top_str(sK2),
inference(cnf_transformation,[],[f30]) ).
fof(f39,plain,
element(sK3,powerset(the_carrier(sK2))),
inference(cnf_transformation,[],[f30]) ).
fof(f40,plain,
( closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| open_subset(sK3,sK2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f41,plain,
( ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ open_subset(sK3,sK2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f44,definition,
( spl4_1
<=> open_subset(sK3,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f46,plain,
( open_subset(sK3,sK2)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f48,definition,
( spl4_2
<=> closed_subset(subset_complement(the_carrier(sK2),sK3),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f49,plain,
( ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| spl4_2 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f40,f48,f44]) ).
fof(f52,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f41,f48,f44]) ).
fof(f56,plain,
sK3 = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK3)),
inference(resolution,[],[f34,f39]) ).
fof(f58,plain,
( open_subset(sK3,sK2)
| ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2)))
| ~ top_str(sK2) ),
inference(superposition,[],[f36,f56]) ).
fof(f66,plain,
( open_subset(sK3,sK2)
| ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[],[f58,f38]) ).
fof(f68,definition,
( spl4_3
<=> element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2))) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f70,plain,
( ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2)))
| spl4_3 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( ~ spl4_3
| ~ spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f66,f44,f48,f68]) ).
fof(f73,plain,
( ~ open_subset(sK3,sK2)
| closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2)))
| ~ top_str(sK2) ),
inference(superposition,[],[f37,f56]) ).
fof(f75,plain,
( closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2)))
| ~ top_str(sK2)
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f73,f46]) ).
fof(f76,plain,
( ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2)))
| ~ top_str(sK2)
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f75,f49]) ).
fof(f77,plain,
( ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2)))
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f76,f38]) ).
fof(f78,plain,
( ~ spl4_3
| ~ spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f77,f48,f44,f68]) ).
fof(f79,plain,
( ~ element(sK3,powerset(the_carrier(sK2)))
| spl4_3 ),
inference(resolution,[],[f70,f31]) ).
fof(f81,plain,
( $false
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f79,f39]) ).
fof(f82,plain,
spl4_3,
inference(avatar_contradiction_clause,[],[f81]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f51]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f71]) ).
cnf(s5,plain,
( ~ spl4_1
| spl4_2
| ~ spl4_3 ),
inference(sat_conversion,[],[f78]) ).
cnf(s6,plain,
spl4_3,
inference(sat_conversion,[],[f82]) ).
cnf(s7,plain,
( ~ spl4_1
| spl4_2 ),
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
( spl4_1
| ~ spl4_2 ),
inference(rat,[],[s4,s6]) ).
cnf(s9,plain,
spl4_1,
inference(rat,[],[s1,s8]) ).
cnf(s10,plain,
spl4_2,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s2,s10,s9]) ).
fof(f83,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU320+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.43 % Computer : n017.cluster.edu
% 0.10/0.43 % Model : x86_64 x86_64
% 0.10/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.43 % Memory : 8046.5625MB
% 0.10/0.43 % OS : Linux 6.8.0-71-generic
% 0.10/0.43 % CPULimit : 300
% 0.10/0.43 % WCLimit : 300
% 0.10/0.43 % DateTime : Mon Sep 28 04:36:05 UTC 2026
% 0.10/0.43 % CPUTime :
% 0.10/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.46 Running first-order model finding
% 0.15/0.46 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
% 0.15/0.52 % (3206916)Will run a generic schedule for satisfiability detection.
% 0.15/0.52 % (3206921)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1462028828_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.52 % TRYING [1]
% 0.15/0.52 % TRYING [2]
% 0.15/0.52 % TRYING [3]
% 0.15/0.52 % TRYING [4]
% 0.15/0.52 % TRYING [5]
% 0.15/0.52 % (3206922)% WARNING: option uhcvi not known.
% 0.15/0.52 % TRYING [6]
% 0.15/0.52 % (3206922)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4161685546:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.52 % (3206923)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3148120401:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.52 % (3206924)dis+10_1_sil=32000:sp=arity:random_seed=3800587671:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.52 % (3206927)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1330794678:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.52 % (3206925)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3279822521:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.52 % (3206926)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2616668397:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.52 % TRYING [7]
% 0.15/0.52 % (3206924) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3206916-3206924"...
% 0.15/0.52 % (3206926) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3206916-3206926"...
% 0.15/0.52 % (3206925) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3206916-3206925"...
% 0.15/0.52 % (3206922) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3206916-3206922"...
% 0.15/0.52 % (3206924)...printing done.
% 0.15/0.52 % (3206925)...printing done.
% 0.15/0.52 % (3206927) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3206916-3206927"...
% 0.15/0.52 % (3206926)...printing done.
% 0.15/0.52 % (3206922)...printing done.
% 0.15/0.52 % (3206924)Refutation found. Thanks to Tanya!
% 0.15/0.52 % SZS status Theorem for theBenchmark
% 0.15/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.52 % (3206924)------------------------------
% 0.15/0.52 % (3206924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.52 % (3206924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.52 % (3206924)CaDiCaL version: 2.1.3
% 0.15/0.52 % (3206924)Termination reason: Refutation
% 0.15/0.52 % (3206924)Time elapsed: 0.003 s
% 0.15/0.52 % (3206924)Peak memory usage: 12 MB
% 0.15/0.52 % (3206924)Instructions burned: 2 (million)
% 0.15/0.52 % (3206916)Success in time 0.045 s
% 0.15/0.52 % Vampire exiting
%------------------------------------------------------------------------------