%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU320+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:48:19 PM UTC 2026
% Result : Theorem 2.85s 1.27s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 9 unt; 4 def)
% Number of atoms : 164 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 174 ( 72 ~; 73 |; 12 &)
% ( 8 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
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] :
( closed_subset(X1,X0)
| ~ open_subset(subset_complement(the_carrier(X0),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(f45,plain,
( ~ open_subset(sK3,sK2)
| spl4_1 ),
inference(avatar_component_clause,[],[f44]) ).
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(f50,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(f54,plain,
! [X0,X1] :
( open_subset(X0,X1)
| ~ closed_subset(subset_complement(the_carrier(X1),X0),X1)
| ~ element(subset_complement(the_carrier(X1),X0),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(superposition,[],[f36,f34]) ).
fof(f55,plain,
! [X0,X1] :
( open_subset(X0,X1)
| ~ closed_subset(subset_complement(the_carrier(X1),X0),X1)
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(forward_subsumption_resolution,[],[f54,f31]) ).
fof(f56,plain,
( ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ top_str(sK2)
| ~ element(sK3,powerset(the_carrier(sK2)))
| spl4_1 ),
inference(resolution,[],[f55,f45]) ).
fof(f57,plain,
( ~ top_str(sK2)
| ~ element(sK3,powerset(the_carrier(sK2)))
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f56,f50]) ).
fof(f58,plain,
( ~ element(sK3,powerset(the_carrier(sK2)))
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f57,f38]) ).
fof(f59,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f58,f39]) ).
fof(f60,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f59]) ).
fof(f61,plain,
( ~ open_subset(subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK3)),sK2)
| ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2)))
| ~ top_str(sK2)
| spl4_2 ),
inference(resolution,[],[f49,f37]) ).
fof(f62,plain,
( ~ open_subset(subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK3)),sK2)
| ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2)))
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f61,f38]) ).
fof(f64,definition,
( spl4_3
<=> element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2))) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f66,plain,
( ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2)))
| spl4_3 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl4_4
<=> open_subset(subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK3)),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f70,plain,
( ~ open_subset(subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK3)),sK2)
| spl4_4 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( ~ spl4_3
| ~ spl4_4
| spl4_2 ),
inference(avatar_split_clause,[],[f62,f48,f68,f64]) ).
fof(f72,plain,
( ~ element(sK3,powerset(the_carrier(sK2)))
| spl4_3 ),
inference(resolution,[],[f66,f31]) ).
fof(f74,plain,
( $false
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f72,f39]) ).
fof(f75,plain,
spl4_3,
inference(avatar_contradiction_clause,[],[f74]) ).
fof(f78,plain,
( ~ open_subset(sK3,sK2)
| ~ element(sK3,powerset(the_carrier(sK2)))
| spl4_4 ),
inference(superposition,[],[f70,f34]) ).
fof(f79,plain,
( ~ element(sK3,powerset(the_carrier(sK2)))
| ~ spl4_1
| spl4_4 ),
inference(forward_subsumption_resolution,[],[f78,f46]) ).
fof(f81,plain,
( $false
| ~ spl4_1
| spl4_4 ),
inference(forward_subsumption_resolution,[],[f79,f39]) ).
fof(f82,plain,
( ~ spl4_1
| spl4_4 ),
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(s3,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
( spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f71]) ).
cnf(s5,plain,
spl4_3,
inference(sat_conversion,[],[f75]) ).
cnf(s6,plain,
( ~ spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f82]) ).
cnf(s8,plain,
( spl4_2
| ~ spl4_4 ),
inference(rat,[],[s4,s5]) ).
cnf(s9,plain,
spl4_1,
inference(rat,[],[s1,s3]) ).
cnf(s10,plain,
spl4_4,
inference(rat,[],[s6,s9]) ).
cnf(s11,plain,
~ spl4_2,
inference(rat,[],[s2,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s8,s10,s11]) ).
fof(f92,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU320+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 04:40:22 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.85/1.27 % (806701)Detected formulas, will run a generic FOF schedule.
% 2.85/1.27 % (806706)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=2552851653:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.85/1.27 % (806709)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3654636078:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.85/1.27 % (806712)dis-21_1_sil=8000:lcm=predicate:random_seed=2948186464: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)
% 2.85/1.27 % (806710)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4036916008:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.85/1.27 % (806707)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=2315220555:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.85/1.27 % (806708)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=3864420589:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.85/1.27 % (806711)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3856002843:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.85/1.27 % (806709)Refutation not found, incomplete strategy
% 2.85/1.27 % (806709)------------------------------
% 2.85/1.27 % (806709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.27 % (806709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.27 % (806709)CaDiCaL version: 2.1.3
% 2.85/1.27 % (806710)Refutation not found, incomplete strategy
% 2.85/1.27 % (806710)------------------------------
% 2.85/1.27 % (806710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.27 % (806709)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.27 % (806709)Time elapsed: 0.001 s
% 2.85/1.27 % (806709)Peak memory usage: 87 MB
% 2.85/1.27 % (806710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.27 % (806710)CaDiCaL version: 2.1.3
% 2.85/1.27 % (806710)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.27 % (806710)Time elapsed: 0.001 s
% 2.85/1.27 % (806710)Peak memory usage: 88 MB
% 2.85/1.27 % (806712)Refutation not found, incomplete strategy
% 2.85/1.27 % (806712)------------------------------
% 2.85/1.27 % (806712)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.27 % (806712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.27 % (806712)CaDiCaL version: 2.1.3
% 2.85/1.27 % (806712)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.27 % (806712)Time elapsed: 0.001 s
% 2.85/1.27 % (806712)Peak memory usage: 88 MB
% 2.85/1.27 % (806711)First to succeed.
% 2.85/1.27 % (806711)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-806701"
% 2.85/1.27 % (806712)------------------------------
% 2.85/1.27 % (806712)------------------------------
% 2.85/1.27 % (806709)------------------------------
% 2.85/1.27 % (806709)------------------------------
% 2.85/1.27 % (806710)------------------------------
% 2.85/1.27 % (806710)------------------------------
% 2.85/1.27 % (806711)Refutation found. Thanks to Tanya!
% 2.85/1.27 % SZS status Theorem for theBenchmark
% 2.85/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.46 % (806711)------------------------------
% 3.50/1.46 % (806711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.46 % (806711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.46 % (806711)CaDiCaL version: 2.1.3
% 3.50/1.46 % (806711)Termination reason: Refutation
% 3.50/1.46 % (806711)Time elapsed: 0.004 s
% 3.50/1.46 % (806711)Peak memory usage: 89 MB
% 3.50/1.46 % (806711)Instructions burned: 3 (million)
% 3.50/1.46 % (806711)------------------------------
% 3.50/1.46 % (806711)------------------------------
% 3.50/1.46 % (806701)Success in time 0.411 s
% 3.50/1.46 % Vampire exiting
%------------------------------------------------------------------------------